Research ArticleAn Improved CO2-Crude Oil Minimum MiscibilityPressure Correlation

Hao Zhang12 Dali Hou1 and Kai Li1

1School of Energy Chengdu University of Technology Chengdu Sichuan 610059 China2State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Chengdu University of TechnologyChengdu Sichuan 610059 China

Correspondence should be addressed to Dali Hou houdali08163com

Received 25 August 2015 Accepted 11 October 2015

Academic Editor Tomokazu Yoshimura

Copyright copy 2015 Hao Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Minimum miscibility pressure (MMP) which plays an important role in miscible flooding is a key parameter in determiningwhether crude oil and gas are completelymiscible On the basis of 210 groups of CO

2-crude oil systemminimummiscibility pressure

data an improvedCO2-crude oil systemminimummiscibility pressure correlationwas built bymodified conjugate gradientmethod

and global optimizing method The new correlation is a uniform empirical correlation to calculate the MMP for both thin oil andheavy oil and is expressed as a function of reservoir temperature C

7+molecular weight of crude oil and mole fractions of volatile

components (CH4and N

2) and intermediate components (CO

2 H2S and C

2simC6) of crude oil Compared to the eleven most

popular and relatively high-accuracy CO2-oil system MMP correlations in the previous literature by other nine groups of CO

2-oil

MMP experimental data which have not been used to develop the new correlation it is found that the new empirical correlationprovides the best reproduction of the nine groups of CO

2-oil MMP experimental data with a percentage average absolute relative

error (AARE) of 8 and a percentage maximum absolute relative error (MARE) of 21 respectively

1 Introduction

CO2injection is one of themost effectivemethods to enhance

oil recovery [1] Generally the oil recovery of miscible flood-ing is higher than nonmiscible flooding The minimum mis-cibility pressure (MMP) at which the crude oil and CO

2

become miscible is a key factor because in general the CO2

is not miscible at first contact with reservoir oils but mayachieve dynamic miscibility through multiple contact [2] Atpresent prediction of the MMP commonly contains threemethods experiment [3] empirical correlation [4] and equa-tion of state [5 6] The slim tube test is one of the most com-monly used test methods [3] in addition there are rising-bubble apparatus (RBA) method [7] steam density method[8] multiple contact method [9] and interfacial tensionvanishmethod [10]The experimentalmethod is the standardmethod but it needs to consume large amounts of time andmoney Equation of state is precise and fast but themiscibilityfunction is difficult to give a clear judgment standard because

a characterization procedure of the plus-fraction must beused and such a characterization can have a huge influenceon the calculated valueThus empirical correlation is usuallyused for predicting the MMP Most the MMP empiricalcorrelations are proposed based on the experimental data ofCO2-oil system while these MMP empirical correlations of

CO2-oil system have certain constraintsThis study has two objectives The first objective is to uti-

lize the modified conjugate gradient and global optimizationalgorithm for establishing a four-parameter and improvedMMP predictionmodel of CO

2-oil system which has a wider

range of application taking advantage of 210 groups of CO2-

oil MMP experimental data tested by slim tube experimentin the literature The second objective is to compare thismodel with the other elevenmost popular and relatively high-accuracy CO

2-oil MMP correlations presented in the previ-

ous literature by using other nine groups of CO2-oil MMP

experimental data which have not been used to develop thenew correlation

Hindawi Publishing CorporationJournal of ChemistryVolume 2015 Article ID 175940 10 pageshttpdxdoiorg1011552015175940

2 Journal of Chemistry

1 2

3

4

5

6

7

8

9

10

(6) Back-pressure valve

(10) Automatic pump(9) Nitrogen(8) Gasometer(7) Separator

(5) Constant temperature air bath(4) Slim tube(3) Valve(2) Reservoir oil(1) Pure CO2

Figure 1 Schematic diagram of the slim tube experimental apparatus

Table 1 Compositional analysis results of three oil samples with C7+

molecular weight in mole percentage

Component Oil sample 1 Oil sample 2 Oil sample 3CO2

2076 0889 038N2

0887 1962 056C1

31744 1496 1321C2

8217 8545 255C3

786 5563 366IC4

1756 0434 142NC4

3222 1072 378IC5

1954 0067 168NC5

1531 0165 274FC6

4366 0 826C7+

36387 66343 6179Total 10000 10000 10000119872C7+ 18369 24536 22917

2 Experimental Section

The slim tube test has become a standard method to measuretheMMP in the petroleum industry In this study theCO

2-oil

MMPs of three crude oil samples (ie oil 1 oil 2 and oil 3) aremeasured by using the slim tube test method Table 1 showsthe compositional analysis results of these three oil samplesIt can be seen from the compositional analysis results that allthese three oil samples used in this study have a large amountof volatile components (N

2and CH

4) and C

7+fraction The

molecular weights of C7+

fraction for oil 1 oil 2 and oil 3 aremeasured to be 18369 gmol 24536 gmol and 22917 gmolrespectively

The slim tube apparatus used in this study is a stainlesssteel fine tube (length of 20m inner diameter of 44mm anda total pore volume of 9275 cm3) filled with the 80sim100 meshquartz sand Schematic diagram of the slim tube experimen-tal apparatus is shown in Figure 1 The slim tube tests areperformed on the recombined reservoir fluid with CO

2at the

given reservoir temperature Once the slim tube is saturatedwith the crude oil sample the CO

2is introduced to displace

the oil at an injection rate of 0125 cm3minCO2displacement experiments are carried out at several

pressures with the temperature being maintained constant atthe reservoir temperature For each test pressure the porevolume of CO

2injected produced oil volume and produced

gas volume are recorded Figure 2 plots the oil recoveryfactors measured at 120 pore volume of CO

2injected as a

function of operating pressure for oil sample 1 The acknowl-edged criterion for determining slim tube test to achievemiscibility is the oil recovery greater than 90 when 120pore volume of CO

2or other gases is injected and with the

displacement pressure increased the displacement efficiencyis no longer increasing [11 12] The CO

2-oil MMP at 130∘C

for oil sample 1 is determined to be 2065MPa by pinpointingthe breakpoint of the oil recovery curve (see Figure 2) Byapplying the same methodology as for other temperaturepoints (110∘C 90∘C and 70∘C) for oil sample 1 the CO

2flood-

ing minimum miscibility pressure is 2035MPa 1995MPaand 1938MPa respectively As for oil sample 2 and oilsample 3 at 748∘C and 897∘C formation the CO

2flooding

minimum miscibility pressure is 2680MPa and 2265MParespectively A conservative error of 3 can be applied due toits complexity Figures 2 and 3 indicate that crude oil recov-ery increases with injecting pressure and CO

2-crude oil

minimummiscible increases with temperature

Journal of Chemistry 3

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Oil

reco

very

()

Pressure (MPa)

MMP = 2065MPa

Figure 2 Variation of the oil recoverymeasured at 120 pore volumeof CO

2injected at various injection pressure for oil sample 1

y = minus00002x2 + 00667x + 15802

R2 = 09962

21

205

20

195

19

185

18

Min

imum

misc

ibili

ty p

ress

ure (

MPa

)

40 60 80 100 120 140

Temperature (∘C)

Figure 3 Variation of oil sample miscibility pressure with temper-ature

3 Building of MMP Predicting Model

31 Existing Methods Over the years several empirical cor-relations have been developed for determining the MMPof CO

2-oil system The most popular and relatively high-

accuracy correlations applied for prediction of CO2-oil MMP

are those developed by Cronquist [4] Lee [13] Yelling-Metcalfe [14] Orr-Jensen [15] Glaso [16] Alston [17] Emera-Sarma [18] Yuan [19] Shokir [20] Chen [21] and Ju [22]Table 2 shows the expression of the above correlations and itsapplication restrictions

32Main Factors Influencing theMMP Reviewing publishedMMP slim tube test data and previously presented empiricalmodels indicates the existence of the following [21 22]

(1) The MMP of CO2-oil system is determined by the

reservoir temperature the components in the injectedgas and the components and properties of oil

(2) On the constant condition of the components in theinjected gas and the components and properties ofoil the MMP increases with increasing the reservoirtemperature

(3) On the constant condition of the components in theinjected gas and the reservoir temperature the higherthe content of C

2simC6and the lower the molecular

weight in the crude oil the smaller MMP On thecontrary themore the heavy components in the crudeoil are the less favorable it will be for miscibility

(4) On the constant condition of the reservoir temper-ature and the components and properties of oil theMMP decreases with increasing the content of inter-mediate components (CO

2 H2S and C

2simC6) and

increases with increasing the content of volatile com-ponents (CH

4and N

2) in the injected gas

The paper is focused on building an improved MMPmodel of pure CO

2-oil system so the influence of injection

gas components onMMP has been taken into account Basedon the shortages of the above empirical formula in Table 2and the sensitive factors proposed in Section 32 influencingthe MMP we selected the four sensitive factors includingreservoir temperature relative molecular weight of C

7+ the

volatile components (CH4andN

2) and intermediate compo-

nents (CO2 H2S and C

2simC6) of crude oil to develop an

improved MMP prediction correlation with four parametersby using the modified conjugate gradient and global opti-mization algorithm regression theory

33 Mathematical Model The determined MMP of CO2-

crude oil system is the result of multiple factors interactionTherefore we should take full account of the sensitive factorsin Section 32 and then maximize and utilize the experimen-tal data However when the independent variable and depen-dent variable uncertainty or error is larger prediction resultsby the traditional least squares linear regression method arevery lowThus the optimization and regression algorithm cansolve the problemwell In this paper we use themodified con-jugate gradient and global optimization algorithm to establisha prediction model for the MMP of CO

2-oil system

And the predictionmodel based onEmera-Sarmamodelalso consists of four affecting factors (reservoir temperatureC7+

molecular weight of crude oil mole fractions of volatilecomponents (CH

4and N

2) and mole fractions of interme-

diate components (CO2 H2S and C

2simC6) in the crude oil)

and four parameters the following improved correlation wasdeveloped

119875

119898minpure

= 119886 [ln (18119879 + 32)]

119887[ln (119872C

7+

)]

119888

(1 +

119909VOL119909

1015840

MED)

119889

(1)

On the basis of Emera-Sarma model reservoir tempera-ture 119872C

7+

in crude oil mole content of volatile component(CH4and N

2) and mole content ratio of intermediate com-

ponents (CO2 H2S and C

2simC6) in crude oil were modified

The term ln(18 times 119879 + 32) is used to suppress temperatureeffect on the hydrocarbon gas-oil MMP when the reservoirtemperature is relatively high The reason why 119872C

7+

insteadof119872C

5+

is used in the correlation is partially because119872C7+

is aroutinemeasurement item in a typical compositional analysis

4 Journal of Chemistry

Table2Correlatio

nsforC

O2-oilMMP

Author

Publish

edem

piric

alcorrelation

Remarks

Cron

quist

[4]

(a)119875

119898m

inpure=011027(18119879+32)

0744206+00011038119872

C 5+00015279119909VO

L

(i)Th

etestedoilgravityranged

from

237to

448∘API

(ii)Th

etested119879ranged

from

2167to

1208∘C

(iii)Th

etestedexperim

entalM

MPranged

from

74to

345MPa

Lee[13]

(b)119875

119898m

inpure=73924times10

2772minus[1519(492+18119879)]

(i)Ba

sedon

equatin

gMMPwith

CO2vapo

rpressurew

hen

119879ltCO2criticaltem

peraturew

hileusingthe

correspo

ndingcorrela

tionwhen119879⩾CO2critical

temperature

(ii)IfM

MPlt119875

119887119875119887istakenas

MMP

Yelling

-Metcalfe

[14]

(c)119875

119898m

inpure=126472+001553(18119879+32)+124192times10

minus4(18119879+32)

2minus

7169427

(18119879+32)

Limitatio

ns358leTlt889∘C

(i)IfMMPlt119875

119887119875119887istakenas

MMP

Orr-Je

nsen

[15]

(d)119875

119898m

inpure=0101386exp[1091minus

2105

255372+05556(18119879+32)

]

(i)Ba

sedon

extrapolated

vapo

rpressure(EV

P)metho

d(ii)U

sedto

estim

atethe

MMPforlow

temperature

reservoirs(119879

lt49

∘C)

Glaso

[16]

When119909

1015840 MED

lt18mol

(e1)119875

119898m

inpure=558657minus23477times10

minus2119872

C 7++11725times10

minus11119872

373

C 7+

exp7868119872

C 7+

minus1058

(18119879+32)

When119909

1015840 MED

gt18

(e2)

119875

119898m

inpure=2033minus23477times10

minus2119872

C 7++11725times10

minus11119872

373

C 7+

exp7868119872

C 7+

minus1058

(18119879+32)minus0836times119909

1015840 MED

Con

sidersthe

effecto

fintermediates(C 2

ndashC6)o

nlywhen

119909

1015840 MED

(C2ndashC6)lt

18mol

Alston

[17]

When119875

119887ge0345MPa

(f1)119875

119898m

inpure=60536times10

minus6(18119879+32)

106(119872

C 5+)

178

(

119909

VOL

119909

MED

)

0136

When119875

119887lt0345MPa

(f2)119875

119898m

inpure=60536times10

minus6(18119879+32)

106(119872

C 5+)

178

IfMMPlt119875

119887119875119887istakenas

MMP

Emera-Sarm

a[18]

When119875

119887ge0345MPa

(g1)119875

119898m

inpure=50093times10

minus5(18119879+32)

1164(119872

C 5+)

12785

(

119909

VOL

119909

MED

)

01073

When119875

119887lt0345MPa

(g2)

119875

119898m

inpure=50093times10

minus5(18119879+32)

1164(119872

C 5+)

12785

Limitatio

ns408ltTlt1122∘C

828

lt119875

119898m

inpurelt

302MPa1662lt119872

C 5+lt2675

gmol

Yuan

[19]

(h)119875

119898m

inpure=119886

1+119886

2119872

C 7+minus119886

3119909

1015840 MED

+(119886

4+119886

5119872

C 7++119886

6

119909

1015840 MED

119872

C 7+

2)(18119879+32)

+(119886

7+119886

8119872

C 7+minus119886

9119872

C 7+

2minus119886

10119909

1015840 MED)(18119879+32)

2

119886

1=minus989121198862=45588times10

minus21198863=minus31012times10

minus11198864=14748times10

minus2

119886

5=80441times10

minus41198866=56303times1011198867=minus84516times10

minus41198868=88825times10

minus6

119886

9=minus27684times10

minus811988610=minus63830times10

minus6

Limitatio

ns217

ltTlt148∘C

119875

119898m

inpurelt70

MPa

139lt119872

C 7+lt319g

mol

Journal of Chemistry 5

Table2Con

tinued

Author

Publish

edem

piric

alcorrelation

Remarks

Shok

ir[20]

(i1)119875

119898m

inpure=minus0068616119885

3+031733119885

2+49804119885+13432

(i2)119885=

4

sum 119894=1

119885

119894

(i3)119885

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

119886

1=minus291821198862=minus31227times10

minus11198863=minus49485times10

minus21198864=25430

119887

1=75340times10

minus21198872=minus79169times10

minus31198873=42165times10

minus21198874=minus39750times10

minus1

119888

1=minus55996times10

minus41198882=13644times10

minus31198883=minus27853times10

minus31198884=19860times10

minus3

119889

1=23660times10

minus61198892=minus13721times10

minus51198893=35551times10

minus51198894=minus31604times10

minus6

Limitatio

ns322ltTlt1122∘C

69lt119875

119898m

inpurelt

3028M

Pa185

lt119872

C 5+lt268g

mol

Chen

[21]

(j)119875

119898m

inpure=39673times10

minus2119879

08293(119872

C 7+)

05382

(119909

C 1+N2)

01018

(119909

C 2minusC 6)

minus02316

Limitatio

ns322ltTlt118

3∘C

69lt119875

119898m

inpurelt

2817

MPa185

lt119872

C 7+lt249g

mol

Ju[22]

(k1)119875

119898m

inim

pure=minus004562119878

3+033399119878

2+49811119878+13569

(k2)

119878=

8

sum 119894=1

119878

119894

(k3)

119878

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

Thed

etailedparametersrefer

to[18]

Limitatio

ns119875119898m

inpurelt40

MPa

6 Journal of Chemistry

Table 3 Regression parameters

Parameters Value119886 83397 times 10minus5

119887 39774119888 33179119889 17461 times 10minus1

report while119872C5+

normally need to be calculated from119872C7+

In addition it is found in this study that the use of 119872C

7+

rather than119872C

5+

even leads to a slightly better performanceof (1) in terms of the correlation coefficient 1198772 Meanwhile119872C7+

is replaced by ln(119872C7+

) to reduce the influence of119872C7+

on the MMP of CO2-oil system when 119872C

7+

is largerAnd 119909VOL119909

1015840

MED is replaced by (1 + 119909VOL1199091015840

MED) to avoidthe fact that 119909VOL119909

1015840

MED approaches to zero because of toofewer volatile components in heavy oil which result in greatdifferences between the parameters

The objective optimization function contains four param-eters (119898 = (119898

1 119898

2 119898

3 119898

4)) The CO

2-oil MMP database

used in this study includes a total of 210 MMPmeasurementsfrom the literature among which the temperature has a rangeof 2167∘Csim19197∘C and C

7+molecular weights range from

130 gmol to 4027 gmol [2 20ndash37] In addition it shouldbe noted that 176 out of the 210 measurements are obtainedfrom overseas data in the literature while the remaining34 measurements are obtained from domestic data in theliterature The CO

2-oil MMP database is used to determine

the tuned coefficients (119898 = (119898

1 119898

2 119898

3 119898

4)) in (1) by

regression fitting using the modified conjugate gradient andglobal optimization algorithmThe regression fitting has beenconducted by using the Matlab programming The tunedcoefficients are given in Table 3 and (1) generates a fit with119877

2= 09488 (Figure 4)

Step 1 Given the constant 1205901isin (0 12) 120590

1lt 120590

2lt 1 120576 gt 0

pick the initial point1198980isin 119877

4 1198890= minus119892

0 and place 119896 = 0

Step 2 If 119892119896 lt 120576 algorithm stops and 119898

119896in 119891(119898) is to

be obtained otherwise algorithm turns to Step 3 119892119896 the

conjugate gradient of119891(119898) at119898119896 represents 119892

119896= 120573

119896times119891(119898

119896)

in which 119892

119896 is the norm of 119892

119896and 120573

119896is the parameter

Generally two expression forms include 120573FR119896

= 119892

119896

2119892

119896minus1

2

and 120573

PR119896

= 119892

119879

119896(119892

119896minus 119892

119896minus1)119892

119896minus1

2 [22] In this paper 120573119896=

max0 120573FR119896

+ min0 119892119879119896119892

119896minus1119892

119879

119896minus1119889

119896minus1 in which 119892

119879

119896is the

transposed conjugate gradient

Step 3 Step length 120572119896is determined by 1D linear search

Step 4 Place119898119896+1

= 119898

119896+ 120572

119896119889

119896 in which 119889

119896is the conjugate

gradient search direction and is determined as follows

119889

119896=

minus119892

119896119896 = 0

minus120579

119896119892

119896+ 120573

119896119889

119896minus1119896 ge 1

(2)

05

101520253035404550

0 10 20 30 40 50

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

R2 = 09488

Figure 4 Resulted CO2-oil MMP from the new correlation versus

the experimental measurements

in which 120579

119896= 1 + (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896 It can be inferred that

119889

119896= minus119892

119896minus (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896119892

119896+ 120573

119896119889

119896minus1 where 119892119879

119896is to be

multiplied at both sides to obtain the following expression

119892

119879

119896119889

119896= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

minus

119892

119879

119896119889

119896minus1

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2120573

119896

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

+ 120573

119896119892

119879

119896119889

119896minus1

= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

lt 0

(3)

It is obvious that 119892119879119896119889

119896is always less than 0 and 119892

119879

119896is

greater than 0 which results in downward search directionMoreover if 120573

119896= 0 minus119892

119879

119896119892

119896minus1119892

119879

119896minus1119889

119896minus1ge 0 120573

119896= 120573

FR119896

the modified conjugate gradient method is FR conjugategradientmethod [38] Otherwise combining correlation ((c)see Table 2) we can draw that

120573

119896= 120573

FR119896

+

119892

119879

119896119892

119896minus1

119892

119879

119896minus1119889

119896minus1

=

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2minus

119892

119879

119896119892

119896minus1

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2

=

119892

119879

119896(119892

119896minus 119892

119896minus1)

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2= 120573

PR119896

(4)

It is called FR conjugate gradient method It is indicatedthat the FR conjugate gradient method takes in excellentglobal convergence of FR algorithm and excellent numericalresult of PR algorithm

Step 5 119889119896is determined and place 119896 = 119896 + 1 Process turns

to Step 2

Finally the modified MMP correlation of CO2-crude oil

is as follows

119891 (119898) = 119875

119898minpure = 83397

times 10

minus5[ln (18119879 + 32)]

39774[ln (119872C

7+

)]

33179

sdot (1 +

119909VOL119909

1015840

MED)

017461

(5)

Journal of Chemistry 7

Table 4 The nine oil samples components properties and MMP data for the new correlation validation

T (∘C) 119872C7+ 119872C5+ 119909MED 119909

1015840

MED 119909VOL Experimental data (MMP) (MPa) Reference6000 149690 136470 39370 46160 24680 11138 [39]8000 149690 136470 39370 46160 24680 14152 [39]13722 149690 136470 39370 46160 24680 18379 [39]10000 151740 138530 26760 37950 13530 14634 [40]8000 170080 160590 2630 7100 12150 16062 [41]13000 183690 165262 23131 30982 32631 20650 Current work7480 245690 229085 16501 16733 16922 26800 Current work8970 229170 211213 11790 24470 13770 22630 Current work5300 205740 182800 12933 25333 18706 13090 [42]

Compared with the other 11 correlations in Table 2the correlation has broader application (pressure range0sim70MPa temperature range 2167sim19197∘C and relativemolecular weight of C

7+ 130sim4027 gmol)

4 Calculation Results and Analysis

Generally the absolute error (6) the absolute relative error(7) and the average absolute relative error (8) are used to exp-ress the deviation between the calculatedMMP by the empir-ical correlation and optimize the most appropriate empiricalcorrelation for predicting the MMP of CO

2-oil system

AE = Cal minus Exp (6)

ARE () =119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (7)

AARE () = 1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (8)

A new correlation validation is performed with moreMMP data (Table 4) These MMP data have not been usedto develop the new correlationThe comparative results of thecalculatedMMPby the correlation proposed in this study andthe other eleven most popular and relatively high-accuracycorrelations presented in the previous literatures are shownin Figure 5 and Table 5 The average absolute relative errors(AARE) for the correlation proposed in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 8 16 37 20 32 19 20 13 27 21 14and 29 respectively The maximum absolute relative errors(MARE) for the proposed correlation in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 21 31 73 46 78 50 39 25 58 52 28and 57 respectivelyThese results indicate that the proposedcorrelation in this study is significantly more precise thanthe other correlations The results of the calculated MMP by

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

Cronquistrsquos correlationLeersquos correlationYelling-Metcalfersquos correlationOrr-Jensenrsquos correlationGlasorsquos correlationAlstonrsquos correlation

Emera-Sarmarsquos correlationYuanrsquos correlationShokirrsquos correlationChenrsquos correlationJursquos correlationThis study

Figure 5 The resulted nine-oil-sample MMP from the new corre-lation proposed in this study versus the calculated nine-oil-sampleMMP from Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlation Orr-Jensenrsquos correlation Glasorsquos correlationAlstonrsquos correlation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlation

the correlation proposed in this study the measured MMPby slim tube test and the absolute error (AE) are shownin Figures 5 and 6 From Table 5 it is clearly seen that theabsolute errors (AE) of the calculatedMMPby themodel pro-posed in this study of many oil samples are less than 15MPawhich are very close to the experimental data

5 Conclusions

(1) Four sensitive factors are determined for affecting theMMP of CO

2-oil system which includes the reservoir tem-

perature C7+

molecular weight of oil mole fractions ofvolatile components (CH

4and N

2) and mole fractions of

intermediate components (CO2 H2S and C

2simC6) of oil

Based on the above sensitive factors a four-parameter andimproved MMP prediction model of CO

2-oil system is

8 Journal of Chemistry

Table 5 Comparison of predictedMMPs for nine oil samples by the correlation proposed in this study and other eleven literature correlations

Exp (MMP)(MPa)

Correlation proposed in this study Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10594 4881 14062 26251 13055 17214 12135 894714152 12619 10833 13693 3241 18143 28201 15154 708018379 17548 4522 24043 30816 28968 57614 24077 3100414634 14243 2673 15050 2844 24340 66325 18139 2395416062 15387 4203 14645 8820 20143 25408 15154 565420650 19990 3196 25722 24561 35810 73416 22870 1075226800 22551 15853 22616 15613 16716 37627 14381 4633822630 17864 21060 16765 25919 26007 14921 16594 2667313090 12399 5278 12419 5129 11525 11959 11014 15860AARE 8055 15910 36965 19585MAARE 21060 30816 73416 46338Exp (MMP)(MPa)

Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquos correlation Emera-Sarmarsquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10002 10196 16679 49746 6756 39342 9362 1594514152 14306 1087 19472 37593 8611 39155 12214 1369518379 32845 78712 18464 0462 14032 23650 13738 2525114634 19691 34556 13128 10290 10462 28512 12071 1751316062 14306 10934 14973 6779 15941 0751 13032 1886320650 29963 45097 22617 9525 20944 1423 18150 1210526800 13087 51170 22328 16687 24636 8074 27222 157522630 16777 25863 26327 16337 15512 31454 23042 182013090 8734 33279 16029 22452 11524 11963 12102 7550AARE 32321 18874 20481 12702MAARE 78712 49746 39342 25251Exp (MMP)(MPa)

Yuanrsquos correlation Shokirrsquos correlation Chenrsquos correlation Jursquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 12775 14699 12549 12669 11002 1218 7091 3633214152 18512 30809 15783 11522 13967 1309 9539 3259818379 13735 25266 27908 51845 21849 18878 19767 755414634 8304 43255 15366 5004 15543 6210 11280 2292116062 14568 9302 15191 5420 19961 24274 13697 1472720650 17164 16879 26111 26445 24313 17739 21215 273426800 20033 25250 20132 24881 19328 27879 11409 5742822630 18113 19960 15509 31468 17374 23226 11615 4867413090 20738 58425 10647 18664 11973 8531 7577 42116AARE 27094 20880 14363 29454MAARE 58425 51845 27879 57428

established by using the modified conjugate gradient and theglobal optimization algorithm

(2) The nine groups of CO2-oil MMP experimental data

which have not been used to develop the new correlationwere calculated by the empirical correlation proposed in thisstudy and other eleven most popular and relatively high-accuracy empirical correlation presented in the literature to

validate the new correlation It can be seen from the com-parative results that the accuracy of the empirical correlationproposed in this study is significantly more precise thanthe other eleven most popular and relatively high-accuracyempirical correlations presented in the literatureThe range ofthe absolute error is less than 15MPa which corresponds tothe requirement of engineering design of CO

2displacement

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

2 Journal of Chemistry

1 2

3

4

5

6

7

8

9

10

(6) Back-pressure valve

(10) Automatic pump(9) Nitrogen(8) Gasometer(7) Separator

(5) Constant temperature air bath(4) Slim tube(3) Valve(2) Reservoir oil(1) Pure CO2

Figure 1 Schematic diagram of the slim tube experimental apparatus

Table 1 Compositional analysis results of three oil samples with C7+

molecular weight in mole percentage

Component Oil sample 1 Oil sample 2 Oil sample 3CO2

2076 0889 038N2

0887 1962 056C1

31744 1496 1321C2

8217 8545 255C3

786 5563 366IC4

1756 0434 142NC4

3222 1072 378IC5

1954 0067 168NC5

1531 0165 274FC6

4366 0 826C7+

36387 66343 6179Total 10000 10000 10000119872C7+ 18369 24536 22917

2 Experimental Section

The slim tube test has become a standard method to measuretheMMP in the petroleum industry In this study theCO

2-oil

MMPs of three crude oil samples (ie oil 1 oil 2 and oil 3) aremeasured by using the slim tube test method Table 1 showsthe compositional analysis results of these three oil samplesIt can be seen from the compositional analysis results that allthese three oil samples used in this study have a large amountof volatile components (N

2and CH

4) and C

7+fraction The

molecular weights of C7+

fraction for oil 1 oil 2 and oil 3 aremeasured to be 18369 gmol 24536 gmol and 22917 gmolrespectively

The slim tube apparatus used in this study is a stainlesssteel fine tube (length of 20m inner diameter of 44mm anda total pore volume of 9275 cm3) filled with the 80sim100 meshquartz sand Schematic diagram of the slim tube experimen-tal apparatus is shown in Figure 1 The slim tube tests areperformed on the recombined reservoir fluid with CO

2at the

given reservoir temperature Once the slim tube is saturatedwith the crude oil sample the CO

2is introduced to displace

the oil at an injection rate of 0125 cm3minCO2displacement experiments are carried out at several

pressures with the temperature being maintained constant atthe reservoir temperature For each test pressure the porevolume of CO

2injected produced oil volume and produced

gas volume are recorded Figure 2 plots the oil recoveryfactors measured at 120 pore volume of CO

2injected as a

function of operating pressure for oil sample 1 The acknowl-edged criterion for determining slim tube test to achievemiscibility is the oil recovery greater than 90 when 120pore volume of CO

2or other gases is injected and with the

displacement pressure increased the displacement efficiencyis no longer increasing [11 12] The CO

2-oil MMP at 130∘C

for oil sample 1 is determined to be 2065MPa by pinpointingthe breakpoint of the oil recovery curve (see Figure 2) Byapplying the same methodology as for other temperaturepoints (110∘C 90∘C and 70∘C) for oil sample 1 the CO

2flood-

ing minimum miscibility pressure is 2035MPa 1995MPaand 1938MPa respectively As for oil sample 2 and oilsample 3 at 748∘C and 897∘C formation the CO

2flooding

minimum miscibility pressure is 2680MPa and 2265MParespectively A conservative error of 3 can be applied due toits complexity Figures 2 and 3 indicate that crude oil recov-ery increases with injecting pressure and CO

2-crude oil

minimummiscible increases with temperature

Journal of Chemistry 3

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Oil

reco

very

()

Pressure (MPa)

MMP = 2065MPa

Figure 2 Variation of the oil recoverymeasured at 120 pore volumeof CO

2injected at various injection pressure for oil sample 1

y = minus00002x2 + 00667x + 15802

R2 = 09962

21

205

20

195

19

185

18

Min

imum

misc

ibili

ty p

ress

ure (

MPa

)

40 60 80 100 120 140

Temperature (∘C)

Figure 3 Variation of oil sample miscibility pressure with temper-ature

3 Building of MMP Predicting Model

31 Existing Methods Over the years several empirical cor-relations have been developed for determining the MMPof CO

2-oil system The most popular and relatively high-

accuracy correlations applied for prediction of CO2-oil MMP

are those developed by Cronquist [4] Lee [13] Yelling-Metcalfe [14] Orr-Jensen [15] Glaso [16] Alston [17] Emera-Sarma [18] Yuan [19] Shokir [20] Chen [21] and Ju [22]Table 2 shows the expression of the above correlations and itsapplication restrictions

32Main Factors Influencing theMMP Reviewing publishedMMP slim tube test data and previously presented empiricalmodels indicates the existence of the following [21 22]

(1) The MMP of CO2-oil system is determined by the

reservoir temperature the components in the injectedgas and the components and properties of oil

(2) On the constant condition of the components in theinjected gas and the components and properties ofoil the MMP increases with increasing the reservoirtemperature

(3) On the constant condition of the components in theinjected gas and the reservoir temperature the higherthe content of C

2simC6and the lower the molecular

weight in the crude oil the smaller MMP On thecontrary themore the heavy components in the crudeoil are the less favorable it will be for miscibility

(4) On the constant condition of the reservoir temper-ature and the components and properties of oil theMMP decreases with increasing the content of inter-mediate components (CO

2 H2S and C

2simC6) and

increases with increasing the content of volatile com-ponents (CH

4and N

2) in the injected gas

The paper is focused on building an improved MMPmodel of pure CO

2-oil system so the influence of injection

gas components onMMP has been taken into account Basedon the shortages of the above empirical formula in Table 2and the sensitive factors proposed in Section 32 influencingthe MMP we selected the four sensitive factors includingreservoir temperature relative molecular weight of C

7+ the

volatile components (CH4andN

2) and intermediate compo-

nents (CO2 H2S and C

2simC6) of crude oil to develop an

improved MMP prediction correlation with four parametersby using the modified conjugate gradient and global opti-mization algorithm regression theory

33 Mathematical Model The determined MMP of CO2-

crude oil system is the result of multiple factors interactionTherefore we should take full account of the sensitive factorsin Section 32 and then maximize and utilize the experimen-tal data However when the independent variable and depen-dent variable uncertainty or error is larger prediction resultsby the traditional least squares linear regression method arevery lowThus the optimization and regression algorithm cansolve the problemwell In this paper we use themodified con-jugate gradient and global optimization algorithm to establisha prediction model for the MMP of CO

2-oil system

And the predictionmodel based onEmera-Sarmamodelalso consists of four affecting factors (reservoir temperatureC7+

molecular weight of crude oil mole fractions of volatilecomponents (CH

4and N

2) and mole fractions of interme-

diate components (CO2 H2S and C

2simC6) in the crude oil)

and four parameters the following improved correlation wasdeveloped

119875

119898minpure

= 119886 [ln (18119879 + 32)]

119887[ln (119872C

7+

)]

119888

(1 +

119909VOL119909

1015840

MED)

119889

(1)

On the basis of Emera-Sarma model reservoir tempera-ture 119872C

7+

in crude oil mole content of volatile component(CH4and N

2) and mole content ratio of intermediate com-

ponents (CO2 H2S and C

2simC6) in crude oil were modified

The term ln(18 times 119879 + 32) is used to suppress temperatureeffect on the hydrocarbon gas-oil MMP when the reservoirtemperature is relatively high The reason why 119872C

7+

insteadof119872C

5+

is used in the correlation is partially because119872C7+

is aroutinemeasurement item in a typical compositional analysis

4 Journal of Chemistry

Table2Correlatio

nsforC

O2-oilMMP

Author

Publish

edem

piric

alcorrelation

Remarks

Cron

quist

[4]

(a)119875

119898m

inpure=011027(18119879+32)

0744206+00011038119872

C 5+00015279119909VO

L

(i)Th

etestedoilgravityranged

from

237to

448∘API

(ii)Th

etested119879ranged

from

2167to

1208∘C

(iii)Th

etestedexperim

entalM

MPranged

from

74to

345MPa

Lee[13]

(b)119875

119898m

inpure=73924times10

2772minus[1519(492+18119879)]

(i)Ba

sedon

equatin

gMMPwith

CO2vapo

rpressurew

hen

119879ltCO2criticaltem

peraturew

hileusingthe

correspo

ndingcorrela

tionwhen119879⩾CO2critical

temperature

(ii)IfM

MPlt119875

119887119875119887istakenas

MMP

Yelling

-Metcalfe

[14]

(c)119875

119898m

inpure=126472+001553(18119879+32)+124192times10

minus4(18119879+32)

2minus

7169427

(18119879+32)

Limitatio

ns358leTlt889∘C

(i)IfMMPlt119875

119887119875119887istakenas

MMP

Orr-Je

nsen

[15]

(d)119875

119898m

inpure=0101386exp[1091minus

2105

255372+05556(18119879+32)

]

(i)Ba

sedon

extrapolated

vapo

rpressure(EV

P)metho

d(ii)U

sedto

estim

atethe

MMPforlow

temperature

reservoirs(119879

lt49

∘C)

Glaso

[16]

When119909

1015840 MED

lt18mol

(e1)119875

119898m

inpure=558657minus23477times10

minus2119872

C 7++11725times10

minus11119872

373

C 7+

exp7868119872

C 7+

minus1058

(18119879+32)

When119909

1015840 MED

gt18

(e2)

119875

119898m

inpure=2033minus23477times10

minus2119872

C 7++11725times10

minus11119872

373

C 7+

exp7868119872

C 7+

minus1058

(18119879+32)minus0836times119909

1015840 MED

Con

sidersthe

effecto

fintermediates(C 2

ndashC6)o

nlywhen

119909

1015840 MED

(C2ndashC6)lt

18mol

Alston

[17]

When119875

119887ge0345MPa

(f1)119875

119898m

inpure=60536times10

minus6(18119879+32)

106(119872

C 5+)

178

(

119909

VOL

119909

MED

)

0136

When119875

119887lt0345MPa

(f2)119875

119898m

inpure=60536times10

minus6(18119879+32)

106(119872

C 5+)

178

IfMMPlt119875

119887119875119887istakenas

MMP

Emera-Sarm

a[18]

When119875

119887ge0345MPa

(g1)119875

119898m

inpure=50093times10

minus5(18119879+32)

1164(119872

C 5+)

12785

(

119909

VOL

119909

MED

)

01073

When119875

119887lt0345MPa

(g2)

119875

119898m

inpure=50093times10

minus5(18119879+32)

1164(119872

C 5+)

12785

Limitatio

ns408ltTlt1122∘C

828

lt119875

119898m

inpurelt

302MPa1662lt119872

C 5+lt2675

gmol

Yuan

[19]

(h)119875

119898m

inpure=119886

1+119886

2119872

C 7+minus119886

3119909

1015840 MED

+(119886

4+119886

5119872

C 7++119886

6

119909

1015840 MED

119872

C 7+

2)(18119879+32)

+(119886

7+119886

8119872

C 7+minus119886

9119872

C 7+

2minus119886

10119909

1015840 MED)(18119879+32)

2

119886

1=minus989121198862=45588times10

minus21198863=minus31012times10

minus11198864=14748times10

minus2

119886

5=80441times10

minus41198866=56303times1011198867=minus84516times10

minus41198868=88825times10

minus6

119886

9=minus27684times10

minus811988610=minus63830times10

minus6

Limitatio

ns217

ltTlt148∘C

119875

119898m

inpurelt70

MPa

139lt119872

C 7+lt319g

mol

Journal of Chemistry 5

Table2Con

tinued

Author

Publish

edem

piric

alcorrelation

Remarks

Shok

ir[20]

(i1)119875

119898m

inpure=minus0068616119885

3+031733119885

2+49804119885+13432

(i2)119885=

4

sum 119894=1

119885

119894

(i3)119885

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

119886

1=minus291821198862=minus31227times10

minus11198863=minus49485times10

minus21198864=25430

119887

1=75340times10

minus21198872=minus79169times10

minus31198873=42165times10

minus21198874=minus39750times10

minus1

119888

1=minus55996times10

minus41198882=13644times10

minus31198883=minus27853times10

minus31198884=19860times10

minus3

119889

1=23660times10

minus61198892=minus13721times10

minus51198893=35551times10

minus51198894=minus31604times10

minus6

Limitatio

ns322ltTlt1122∘C

69lt119875

119898m

inpurelt

3028M

Pa185

lt119872

C 5+lt268g

mol

Chen

[21]

(j)119875

119898m

inpure=39673times10

minus2119879

08293(119872

C 7+)

05382

(119909

C 1+N2)

01018

(119909

C 2minusC 6)

minus02316

Limitatio

ns322ltTlt118

3∘C

69lt119875

119898m

inpurelt

2817

MPa185

lt119872

C 7+lt249g

mol

Ju[22]

(k1)119875

119898m

inim

pure=minus004562119878

3+033399119878

2+49811119878+13569

(k2)

119878=

8

sum 119894=1

119878

119894

(k3)

119878

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

Thed

etailedparametersrefer

to[18]

Limitatio

ns119875119898m

inpurelt40

MPa

6 Journal of Chemistry

Table 3 Regression parameters

Parameters Value119886 83397 times 10minus5

119887 39774119888 33179119889 17461 times 10minus1

report while119872C5+

normally need to be calculated from119872C7+

In addition it is found in this study that the use of 119872C

7+

rather than119872C

5+

even leads to a slightly better performanceof (1) in terms of the correlation coefficient 1198772 Meanwhile119872C7+

is replaced by ln(119872C7+

) to reduce the influence of119872C7+

on the MMP of CO2-oil system when 119872C

7+

is largerAnd 119909VOL119909

1015840

MED is replaced by (1 + 119909VOL1199091015840

MED) to avoidthe fact that 119909VOL119909

1015840

MED approaches to zero because of toofewer volatile components in heavy oil which result in greatdifferences between the parameters

The objective optimization function contains four param-eters (119898 = (119898

1 119898

2 119898

3 119898

4)) The CO

2-oil MMP database

used in this study includes a total of 210 MMPmeasurementsfrom the literature among which the temperature has a rangeof 2167∘Csim19197∘C and C

7+molecular weights range from

130 gmol to 4027 gmol [2 20ndash37] In addition it shouldbe noted that 176 out of the 210 measurements are obtainedfrom overseas data in the literature while the remaining34 measurements are obtained from domestic data in theliterature The CO

2-oil MMP database is used to determine

the tuned coefficients (119898 = (119898

1 119898

2 119898

3 119898

4)) in (1) by

regression fitting using the modified conjugate gradient andglobal optimization algorithmThe regression fitting has beenconducted by using the Matlab programming The tunedcoefficients are given in Table 3 and (1) generates a fit with119877

2= 09488 (Figure 4)

Step 1 Given the constant 1205901isin (0 12) 120590

1lt 120590

2lt 1 120576 gt 0

pick the initial point1198980isin 119877

4 1198890= minus119892

0 and place 119896 = 0

Step 2 If 119892119896 lt 120576 algorithm stops and 119898

119896in 119891(119898) is to

be obtained otherwise algorithm turns to Step 3 119892119896 the

conjugate gradient of119891(119898) at119898119896 represents 119892

119896= 120573

119896times119891(119898

119896)

in which 119892

119896 is the norm of 119892

119896and 120573

119896is the parameter

Generally two expression forms include 120573FR119896

= 119892

119896

2119892

119896minus1

2

and 120573

PR119896

= 119892

119879

119896(119892

119896minus 119892

119896minus1)119892

119896minus1

2 [22] In this paper 120573119896=

max0 120573FR119896

+ min0 119892119879119896119892

119896minus1119892

119879

119896minus1119889

119896minus1 in which 119892

119879

119896is the

transposed conjugate gradient

Step 3 Step length 120572119896is determined by 1D linear search

Step 4 Place119898119896+1

= 119898

119896+ 120572

119896119889

119896 in which 119889

119896is the conjugate

gradient search direction and is determined as follows

119889

119896=

minus119892

119896119896 = 0

minus120579

119896119892

119896+ 120573

119896119889

119896minus1119896 ge 1

(2)

05

101520253035404550

0 10 20 30 40 50

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

R2 = 09488

Figure 4 Resulted CO2-oil MMP from the new correlation versus

the experimental measurements

in which 120579

119896= 1 + (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896 It can be inferred that

119889

119896= minus119892

119896minus (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896119892

119896+ 120573

119896119889

119896minus1 where 119892119879

119896is to be

multiplied at both sides to obtain the following expression

119892

119879

119896119889

119896= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

minus

119892

119879

119896119889

119896minus1

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2120573

119896

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

+ 120573

119896119892

119879

119896119889

119896minus1

= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

lt 0

(3)

It is obvious that 119892119879119896119889

119896is always less than 0 and 119892

119879

119896is

greater than 0 which results in downward search directionMoreover if 120573

119896= 0 minus119892

119879

119896119892

119896minus1119892

119879

119896minus1119889

119896minus1ge 0 120573

119896= 120573

FR119896

the modified conjugate gradient method is FR conjugategradientmethod [38] Otherwise combining correlation ((c)see Table 2) we can draw that

120573

119896= 120573

FR119896

+

119892

119879

119896119892

119896minus1

119892

119879

119896minus1119889

119896minus1

=

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2minus

119892

119879

119896119892

119896minus1

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2

=

119892

119879

119896(119892

119896minus 119892

119896minus1)

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2= 120573

PR119896

(4)

It is called FR conjugate gradient method It is indicatedthat the FR conjugate gradient method takes in excellentglobal convergence of FR algorithm and excellent numericalresult of PR algorithm

Step 5 119889119896is determined and place 119896 = 119896 + 1 Process turns

to Step 2

Finally the modified MMP correlation of CO2-crude oil

is as follows

119891 (119898) = 119875

119898minpure = 83397

times 10

minus5[ln (18119879 + 32)]

39774[ln (119872C

7+

)]

33179

sdot (1 +

119909VOL119909

1015840

MED)

017461

(5)

Journal of Chemistry 7

Table 4 The nine oil samples components properties and MMP data for the new correlation validation

T (∘C) 119872C7+ 119872C5+ 119909MED 119909

1015840

MED 119909VOL Experimental data (MMP) (MPa) Reference6000 149690 136470 39370 46160 24680 11138 [39]8000 149690 136470 39370 46160 24680 14152 [39]13722 149690 136470 39370 46160 24680 18379 [39]10000 151740 138530 26760 37950 13530 14634 [40]8000 170080 160590 2630 7100 12150 16062 [41]13000 183690 165262 23131 30982 32631 20650 Current work7480 245690 229085 16501 16733 16922 26800 Current work8970 229170 211213 11790 24470 13770 22630 Current work5300 205740 182800 12933 25333 18706 13090 [42]

Compared with the other 11 correlations in Table 2the correlation has broader application (pressure range0sim70MPa temperature range 2167sim19197∘C and relativemolecular weight of C

7+ 130sim4027 gmol)

4 Calculation Results and Analysis

Generally the absolute error (6) the absolute relative error(7) and the average absolute relative error (8) are used to exp-ress the deviation between the calculatedMMP by the empir-ical correlation and optimize the most appropriate empiricalcorrelation for predicting the MMP of CO

2-oil system

AE = Cal minus Exp (6)

ARE () =119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (7)

AARE () = 1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (8)

A new correlation validation is performed with moreMMP data (Table 4) These MMP data have not been usedto develop the new correlationThe comparative results of thecalculatedMMPby the correlation proposed in this study andthe other eleven most popular and relatively high-accuracycorrelations presented in the previous literatures are shownin Figure 5 and Table 5 The average absolute relative errors(AARE) for the correlation proposed in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 8 16 37 20 32 19 20 13 27 21 14and 29 respectively The maximum absolute relative errors(MARE) for the proposed correlation in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 21 31 73 46 78 50 39 25 58 52 28and 57 respectivelyThese results indicate that the proposedcorrelation in this study is significantly more precise thanthe other correlations The results of the calculated MMP by

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

Cronquistrsquos correlationLeersquos correlationYelling-Metcalfersquos correlationOrr-Jensenrsquos correlationGlasorsquos correlationAlstonrsquos correlation

Emera-Sarmarsquos correlationYuanrsquos correlationShokirrsquos correlationChenrsquos correlationJursquos correlationThis study

Figure 5 The resulted nine-oil-sample MMP from the new corre-lation proposed in this study versus the calculated nine-oil-sampleMMP from Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlation Orr-Jensenrsquos correlation Glasorsquos correlationAlstonrsquos correlation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlation

the correlation proposed in this study the measured MMPby slim tube test and the absolute error (AE) are shownin Figures 5 and 6 From Table 5 it is clearly seen that theabsolute errors (AE) of the calculatedMMPby themodel pro-posed in this study of many oil samples are less than 15MPawhich are very close to the experimental data

5 Conclusions

(1) Four sensitive factors are determined for affecting theMMP of CO

2-oil system which includes the reservoir tem-

perature C7+

molecular weight of oil mole fractions ofvolatile components (CH

4and N

2) and mole fractions of

intermediate components (CO2 H2S and C

2simC6) of oil

Based on the above sensitive factors a four-parameter andimproved MMP prediction model of CO

2-oil system is

8 Journal of Chemistry

Table 5 Comparison of predictedMMPs for nine oil samples by the correlation proposed in this study and other eleven literature correlations

Exp (MMP)(MPa)

Correlation proposed in this study Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10594 4881 14062 26251 13055 17214 12135 894714152 12619 10833 13693 3241 18143 28201 15154 708018379 17548 4522 24043 30816 28968 57614 24077 3100414634 14243 2673 15050 2844 24340 66325 18139 2395416062 15387 4203 14645 8820 20143 25408 15154 565420650 19990 3196 25722 24561 35810 73416 22870 1075226800 22551 15853 22616 15613 16716 37627 14381 4633822630 17864 21060 16765 25919 26007 14921 16594 2667313090 12399 5278 12419 5129 11525 11959 11014 15860AARE 8055 15910 36965 19585MAARE 21060 30816 73416 46338Exp (MMP)(MPa)

Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquos correlation Emera-Sarmarsquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10002 10196 16679 49746 6756 39342 9362 1594514152 14306 1087 19472 37593 8611 39155 12214 1369518379 32845 78712 18464 0462 14032 23650 13738 2525114634 19691 34556 13128 10290 10462 28512 12071 1751316062 14306 10934 14973 6779 15941 0751 13032 1886320650 29963 45097 22617 9525 20944 1423 18150 1210526800 13087 51170 22328 16687 24636 8074 27222 157522630 16777 25863 26327 16337 15512 31454 23042 182013090 8734 33279 16029 22452 11524 11963 12102 7550AARE 32321 18874 20481 12702MAARE 78712 49746 39342 25251Exp (MMP)(MPa)

Yuanrsquos correlation Shokirrsquos correlation Chenrsquos correlation Jursquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 12775 14699 12549 12669 11002 1218 7091 3633214152 18512 30809 15783 11522 13967 1309 9539 3259818379 13735 25266 27908 51845 21849 18878 19767 755414634 8304 43255 15366 5004 15543 6210 11280 2292116062 14568 9302 15191 5420 19961 24274 13697 1472720650 17164 16879 26111 26445 24313 17739 21215 273426800 20033 25250 20132 24881 19328 27879 11409 5742822630 18113 19960 15509 31468 17374 23226 11615 4867413090 20738 58425 10647 18664 11973 8531 7577 42116AARE 27094 20880 14363 29454MAARE 58425 51845 27879 57428

established by using the modified conjugate gradient and theglobal optimization algorithm

(2) The nine groups of CO2-oil MMP experimental data

which have not been used to develop the new correlationwere calculated by the empirical correlation proposed in thisstudy and other eleven most popular and relatively high-accuracy empirical correlation presented in the literature to

validate the new correlation It can be seen from the com-parative results that the accuracy of the empirical correlationproposed in this study is significantly more precise thanthe other eleven most popular and relatively high-accuracyempirical correlations presented in the literatureThe range ofthe absolute error is less than 15MPa which corresponds tothe requirement of engineering design of CO

2displacement

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal ofPhotoenergy

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Carbohydrate Chemistry

International Journal of

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Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

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Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

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Medicinal ChemistryInternational Journal of

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Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Analytical ChemistryInternational Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Journal of Chemistry 3

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Oil

reco

very

()

Pressure (MPa)

MMP = 2065MPa

Figure 2 Variation of the oil recoverymeasured at 120 pore volumeof CO

2injected at various injection pressure for oil sample 1

y = minus00002x2 + 00667x + 15802

R2 = 09962

21

205

20

195

19

185

18

Min

imum

misc

ibili

ty p

ress

ure (

MPa

)

40 60 80 100 120 140

Temperature (∘C)

Figure 3 Variation of oil sample miscibility pressure with temper-ature

3 Building of MMP Predicting Model

31 Existing Methods Over the years several empirical cor-relations have been developed for determining the MMPof CO

2-oil system The most popular and relatively high-

accuracy correlations applied for prediction of CO2-oil MMP

are those developed by Cronquist [4] Lee [13] Yelling-Metcalfe [14] Orr-Jensen [15] Glaso [16] Alston [17] Emera-Sarma [18] Yuan [19] Shokir [20] Chen [21] and Ju [22]Table 2 shows the expression of the above correlations and itsapplication restrictions

32Main Factors Influencing theMMP Reviewing publishedMMP slim tube test data and previously presented empiricalmodels indicates the existence of the following [21 22]

(1) The MMP of CO2-oil system is determined by the

reservoir temperature the components in the injectedgas and the components and properties of oil

(2) On the constant condition of the components in theinjected gas and the components and properties ofoil the MMP increases with increasing the reservoirtemperature

(3) On the constant condition of the components in theinjected gas and the reservoir temperature the higherthe content of C

2simC6and the lower the molecular

weight in the crude oil the smaller MMP On thecontrary themore the heavy components in the crudeoil are the less favorable it will be for miscibility

(4) On the constant condition of the reservoir temper-ature and the components and properties of oil theMMP decreases with increasing the content of inter-mediate components (CO

2 H2S and C

2simC6) and

increases with increasing the content of volatile com-ponents (CH

4and N

2) in the injected gas

The paper is focused on building an improved MMPmodel of pure CO

2-oil system so the influence of injection

gas components onMMP has been taken into account Basedon the shortages of the above empirical formula in Table 2and the sensitive factors proposed in Section 32 influencingthe MMP we selected the four sensitive factors includingreservoir temperature relative molecular weight of C

7+ the

volatile components (CH4andN

2) and intermediate compo-

nents (CO2 H2S and C

2simC6) of crude oil to develop an

improved MMP prediction correlation with four parametersby using the modified conjugate gradient and global opti-mization algorithm regression theory

33 Mathematical Model The determined MMP of CO2-

crude oil system is the result of multiple factors interactionTherefore we should take full account of the sensitive factorsin Section 32 and then maximize and utilize the experimen-tal data However when the independent variable and depen-dent variable uncertainty or error is larger prediction resultsby the traditional least squares linear regression method arevery lowThus the optimization and regression algorithm cansolve the problemwell In this paper we use themodified con-jugate gradient and global optimization algorithm to establisha prediction model for the MMP of CO

2-oil system

And the predictionmodel based onEmera-Sarmamodelalso consists of four affecting factors (reservoir temperatureC7+

molecular weight of crude oil mole fractions of volatilecomponents (CH

4and N

2) and mole fractions of interme-

diate components (CO2 H2S and C

2simC6) in the crude oil)

and four parameters the following improved correlation wasdeveloped

119875

119898minpure

= 119886 [ln (18119879 + 32)]

119887[ln (119872C

7+

)]

119888

(1 +

119909VOL119909

1015840

MED)

119889

(1)

On the basis of Emera-Sarma model reservoir tempera-ture 119872C

7+

in crude oil mole content of volatile component(CH4and N

2) and mole content ratio of intermediate com-

ponents (CO2 H2S and C

2simC6) in crude oil were modified

The term ln(18 times 119879 + 32) is used to suppress temperatureeffect on the hydrocarbon gas-oil MMP when the reservoirtemperature is relatively high The reason why 119872C

7+

insteadof119872C

5+

is used in the correlation is partially because119872C7+

is aroutinemeasurement item in a typical compositional analysis

4 Journal of Chemistry

Table2Correlatio

nsforC

O2-oilMMP

Author

Publish

edem

piric

alcorrelation

Remarks

Cron

quist

[4]

(a)119875

119898m

inpure=011027(18119879+32)

0744206+00011038119872

C 5+00015279119909VO

L

(i)Th

etestedoilgravityranged

from

237to

448∘API

(ii)Th

etested119879ranged

from

2167to

1208∘C

(iii)Th

etestedexperim

entalM

MPranged

from

74to

345MPa

Lee[13]

(b)119875

119898m

inpure=73924times10

2772minus[1519(492+18119879)]

(i)Ba

sedon

equatin

gMMPwith

CO2vapo

rpressurew

hen

119879ltCO2criticaltem

peraturew

hileusingthe

correspo

ndingcorrela

tionwhen119879⩾CO2critical

temperature

(ii)IfM

MPlt119875

119887119875119887istakenas

MMP

Yelling

-Metcalfe

[14]

(c)119875

119898m

inpure=126472+001553(18119879+32)+124192times10

minus4(18119879+32)

2minus

7169427

(18119879+32)

Limitatio

ns358leTlt889∘C

(i)IfMMPlt119875

119887119875119887istakenas

MMP

Orr-Je

nsen

[15]

(d)119875

119898m

inpure=0101386exp[1091minus

2105

255372+05556(18119879+32)

]

(i)Ba

sedon

extrapolated

vapo

rpressure(EV

P)metho

d(ii)U

sedto

estim

atethe

MMPforlow

temperature

reservoirs(119879

lt49

∘C)

Glaso

[16]

When119909

1015840 MED

lt18mol

(e1)119875

119898m

inpure=558657minus23477times10

minus2119872

C 7++11725times10

minus11119872

373

C 7+

exp7868119872

C 7+

minus1058

(18119879+32)

When119909

1015840 MED

gt18

(e2)

119875

119898m

inpure=2033minus23477times10

minus2119872

C 7++11725times10

minus11119872

373

C 7+

exp7868119872

C 7+

minus1058

(18119879+32)minus0836times119909

1015840 MED

Con

sidersthe

effecto

fintermediates(C 2

ndashC6)o

nlywhen

119909

1015840 MED

(C2ndashC6)lt

18mol

Alston

[17]

When119875

119887ge0345MPa

(f1)119875

119898m

inpure=60536times10

minus6(18119879+32)

106(119872

C 5+)

178

(

119909

VOL

119909

MED

)

0136

When119875

119887lt0345MPa

(f2)119875

119898m

inpure=60536times10

minus6(18119879+32)

106(119872

C 5+)

178

IfMMPlt119875

119887119875119887istakenas

MMP

Emera-Sarm

a[18]

When119875

119887ge0345MPa

(g1)119875

119898m

inpure=50093times10

minus5(18119879+32)

1164(119872

C 5+)

12785

(

119909

VOL

119909

MED

)

01073

When119875

119887lt0345MPa

(g2)

119875

119898m

inpure=50093times10

minus5(18119879+32)

1164(119872

C 5+)

12785

Limitatio

ns408ltTlt1122∘C

828

lt119875

119898m

inpurelt

302MPa1662lt119872

C 5+lt2675

gmol

Yuan

[19]

(h)119875

119898m

inpure=119886

1+119886

2119872

C 7+minus119886

3119909

1015840 MED

+(119886

4+119886

5119872

C 7++119886

6

119909

1015840 MED

119872

C 7+

2)(18119879+32)

+(119886

7+119886

8119872

C 7+minus119886

9119872

C 7+

2minus119886

10119909

1015840 MED)(18119879+32)

2

119886

1=minus989121198862=45588times10

minus21198863=minus31012times10

minus11198864=14748times10

minus2

119886

5=80441times10

minus41198866=56303times1011198867=minus84516times10

minus41198868=88825times10

minus6

119886

9=minus27684times10

minus811988610=minus63830times10

minus6

Limitatio

ns217

ltTlt148∘C

119875

119898m

inpurelt70

MPa

139lt119872

C 7+lt319g

mol

Journal of Chemistry 5

Table2Con

tinued

Author

Publish

edem

piric

alcorrelation

Remarks

Shok

ir[20]

(i1)119875

119898m

inpure=minus0068616119885

3+031733119885

2+49804119885+13432

(i2)119885=

4

sum 119894=1

119885

119894

(i3)119885

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

119886

1=minus291821198862=minus31227times10

minus11198863=minus49485times10

minus21198864=25430

119887

1=75340times10

minus21198872=minus79169times10

minus31198873=42165times10

minus21198874=minus39750times10

minus1

119888

1=minus55996times10

minus41198882=13644times10

minus31198883=minus27853times10

minus31198884=19860times10

minus3

119889

1=23660times10

minus61198892=minus13721times10

minus51198893=35551times10

minus51198894=minus31604times10

minus6

Limitatio

ns322ltTlt1122∘C

69lt119875

119898m

inpurelt

3028M

Pa185

lt119872

C 5+lt268g

mol

Chen

[21]

(j)119875

119898m

inpure=39673times10

minus2119879

08293(119872

C 7+)

05382

(119909

C 1+N2)

01018

(119909

C 2minusC 6)

minus02316

Limitatio

ns322ltTlt118

3∘C

69lt119875

119898m

inpurelt

2817

MPa185

lt119872

C 7+lt249g

mol

Ju[22]

(k1)119875

119898m

inim

pure=minus004562119878

3+033399119878

2+49811119878+13569

(k2)

119878=

8

sum 119894=1

119878

119894

(k3)

119878

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

Thed

etailedparametersrefer

to[18]

Limitatio

ns119875119898m

inpurelt40

MPa

6 Journal of Chemistry

Table 3 Regression parameters

Parameters Value119886 83397 times 10minus5

119887 39774119888 33179119889 17461 times 10minus1

report while119872C5+

normally need to be calculated from119872C7+

In addition it is found in this study that the use of 119872C

7+

rather than119872C

5+

even leads to a slightly better performanceof (1) in terms of the correlation coefficient 1198772 Meanwhile119872C7+

is replaced by ln(119872C7+

) to reduce the influence of119872C7+

on the MMP of CO2-oil system when 119872C

7+

is largerAnd 119909VOL119909

1015840

MED is replaced by (1 + 119909VOL1199091015840

MED) to avoidthe fact that 119909VOL119909

1015840

MED approaches to zero because of toofewer volatile components in heavy oil which result in greatdifferences between the parameters

The objective optimization function contains four param-eters (119898 = (119898

1 119898

2 119898

3 119898

4)) The CO

2-oil MMP database

used in this study includes a total of 210 MMPmeasurementsfrom the literature among which the temperature has a rangeof 2167∘Csim19197∘C and C

7+molecular weights range from

130 gmol to 4027 gmol [2 20ndash37] In addition it shouldbe noted that 176 out of the 210 measurements are obtainedfrom overseas data in the literature while the remaining34 measurements are obtained from domestic data in theliterature The CO

2-oil MMP database is used to determine

the tuned coefficients (119898 = (119898

1 119898

2 119898

3 119898

4)) in (1) by

regression fitting using the modified conjugate gradient andglobal optimization algorithmThe regression fitting has beenconducted by using the Matlab programming The tunedcoefficients are given in Table 3 and (1) generates a fit with119877

2= 09488 (Figure 4)

Step 1 Given the constant 1205901isin (0 12) 120590

1lt 120590

2lt 1 120576 gt 0

pick the initial point1198980isin 119877

4 1198890= minus119892

0 and place 119896 = 0

Step 2 If 119892119896 lt 120576 algorithm stops and 119898

119896in 119891(119898) is to

be obtained otherwise algorithm turns to Step 3 119892119896 the

conjugate gradient of119891(119898) at119898119896 represents 119892

119896= 120573

119896times119891(119898

119896)

in which 119892

119896 is the norm of 119892

119896and 120573

119896is the parameter

Generally two expression forms include 120573FR119896

= 119892

119896

2119892

119896minus1

2

and 120573

PR119896

= 119892

119879

119896(119892

119896minus 119892

119896minus1)119892

119896minus1

2 [22] In this paper 120573119896=

max0 120573FR119896

+ min0 119892119879119896119892

119896minus1119892

119879

119896minus1119889

119896minus1 in which 119892

119879

119896is the

transposed conjugate gradient

Step 3 Step length 120572119896is determined by 1D linear search

Step 4 Place119898119896+1

= 119898

119896+ 120572

119896119889

119896 in which 119889

119896is the conjugate

gradient search direction and is determined as follows

119889

119896=

minus119892

119896119896 = 0

minus120579

119896119892

119896+ 120573

119896119889

119896minus1119896 ge 1

(2)

05

101520253035404550

0 10 20 30 40 50

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

R2 = 09488

Figure 4 Resulted CO2-oil MMP from the new correlation versus

the experimental measurements

in which 120579

119896= 1 + (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896 It can be inferred that

119889

119896= minus119892

119896minus (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896119892

119896+ 120573

119896119889

119896minus1 where 119892119879

119896is to be

multiplied at both sides to obtain the following expression

119892

119879

119896119889

119896= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

minus

119892

119879

119896119889

119896minus1

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2120573

119896

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

+ 120573

119896119892

119879

119896119889

119896minus1

= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

lt 0

(3)

It is obvious that 119892119879119896119889

119896is always less than 0 and 119892

119879

119896is

greater than 0 which results in downward search directionMoreover if 120573

119896= 0 minus119892

119879

119896119892

119896minus1119892

119879

119896minus1119889

119896minus1ge 0 120573

119896= 120573

FR119896

the modified conjugate gradient method is FR conjugategradientmethod [38] Otherwise combining correlation ((c)see Table 2) we can draw that

120573

119896= 120573

FR119896

+

119892

119879

119896119892

119896minus1

119892

119879

119896minus1119889

119896minus1

=

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2minus

119892

119879

119896119892

119896minus1

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2

=

119892

119879

119896(119892

119896minus 119892

119896minus1)

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2= 120573

PR119896

(4)

It is called FR conjugate gradient method It is indicatedthat the FR conjugate gradient method takes in excellentglobal convergence of FR algorithm and excellent numericalresult of PR algorithm

Step 5 119889119896is determined and place 119896 = 119896 + 1 Process turns

to Step 2

Finally the modified MMP correlation of CO2-crude oil

is as follows

119891 (119898) = 119875

119898minpure = 83397

times 10

minus5[ln (18119879 + 32)]

39774[ln (119872C

7+

)]

33179

sdot (1 +

119909VOL119909

1015840

MED)

017461

(5)

Journal of Chemistry 7

Table 4 The nine oil samples components properties and MMP data for the new correlation validation

T (∘C) 119872C7+ 119872C5+ 119909MED 119909

1015840

MED 119909VOL Experimental data (MMP) (MPa) Reference6000 149690 136470 39370 46160 24680 11138 [39]8000 149690 136470 39370 46160 24680 14152 [39]13722 149690 136470 39370 46160 24680 18379 [39]10000 151740 138530 26760 37950 13530 14634 [40]8000 170080 160590 2630 7100 12150 16062 [41]13000 183690 165262 23131 30982 32631 20650 Current work7480 245690 229085 16501 16733 16922 26800 Current work8970 229170 211213 11790 24470 13770 22630 Current work5300 205740 182800 12933 25333 18706 13090 [42]

Compared with the other 11 correlations in Table 2the correlation has broader application (pressure range0sim70MPa temperature range 2167sim19197∘C and relativemolecular weight of C

7+ 130sim4027 gmol)

4 Calculation Results and Analysis

Generally the absolute error (6) the absolute relative error(7) and the average absolute relative error (8) are used to exp-ress the deviation between the calculatedMMP by the empir-ical correlation and optimize the most appropriate empiricalcorrelation for predicting the MMP of CO

2-oil system

AE = Cal minus Exp (6)

ARE () =119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (7)

AARE () = 1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (8)

A new correlation validation is performed with moreMMP data (Table 4) These MMP data have not been usedto develop the new correlationThe comparative results of thecalculatedMMPby the correlation proposed in this study andthe other eleven most popular and relatively high-accuracycorrelations presented in the previous literatures are shownin Figure 5 and Table 5 The average absolute relative errors(AARE) for the correlation proposed in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 8 16 37 20 32 19 20 13 27 21 14and 29 respectively The maximum absolute relative errors(MARE) for the proposed correlation in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 21 31 73 46 78 50 39 25 58 52 28and 57 respectivelyThese results indicate that the proposedcorrelation in this study is significantly more precise thanthe other correlations The results of the calculated MMP by

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

Cronquistrsquos correlationLeersquos correlationYelling-Metcalfersquos correlationOrr-Jensenrsquos correlationGlasorsquos correlationAlstonrsquos correlation

Emera-Sarmarsquos correlationYuanrsquos correlationShokirrsquos correlationChenrsquos correlationJursquos correlationThis study

Figure 5 The resulted nine-oil-sample MMP from the new corre-lation proposed in this study versus the calculated nine-oil-sampleMMP from Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlation Orr-Jensenrsquos correlation Glasorsquos correlationAlstonrsquos correlation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlation

the correlation proposed in this study the measured MMPby slim tube test and the absolute error (AE) are shownin Figures 5 and 6 From Table 5 it is clearly seen that theabsolute errors (AE) of the calculatedMMPby themodel pro-posed in this study of many oil samples are less than 15MPawhich are very close to the experimental data

5 Conclusions

(1) Four sensitive factors are determined for affecting theMMP of CO

2-oil system which includes the reservoir tem-

perature C7+

molecular weight of oil mole fractions ofvolatile components (CH

4and N

2) and mole fractions of

intermediate components (CO2 H2S and C

2simC6) of oil

Based on the above sensitive factors a four-parameter andimproved MMP prediction model of CO

2-oil system is

8 Journal of Chemistry

Table 5 Comparison of predictedMMPs for nine oil samples by the correlation proposed in this study and other eleven literature correlations

Exp (MMP)(MPa)

Correlation proposed in this study Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10594 4881 14062 26251 13055 17214 12135 894714152 12619 10833 13693 3241 18143 28201 15154 708018379 17548 4522 24043 30816 28968 57614 24077 3100414634 14243 2673 15050 2844 24340 66325 18139 2395416062 15387 4203 14645 8820 20143 25408 15154 565420650 19990 3196 25722 24561 35810 73416 22870 1075226800 22551 15853 22616 15613 16716 37627 14381 4633822630 17864 21060 16765 25919 26007 14921 16594 2667313090 12399 5278 12419 5129 11525 11959 11014 15860AARE 8055 15910 36965 19585MAARE 21060 30816 73416 46338Exp (MMP)(MPa)

Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquos correlation Emera-Sarmarsquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10002 10196 16679 49746 6756 39342 9362 1594514152 14306 1087 19472 37593 8611 39155 12214 1369518379 32845 78712 18464 0462 14032 23650 13738 2525114634 19691 34556 13128 10290 10462 28512 12071 1751316062 14306 10934 14973 6779 15941 0751 13032 1886320650 29963 45097 22617 9525 20944 1423 18150 1210526800 13087 51170 22328 16687 24636 8074 27222 157522630 16777 25863 26327 16337 15512 31454 23042 182013090 8734 33279 16029 22452 11524 11963 12102 7550AARE 32321 18874 20481 12702MAARE 78712 49746 39342 25251Exp (MMP)(MPa)

Yuanrsquos correlation Shokirrsquos correlation Chenrsquos correlation Jursquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 12775 14699 12549 12669 11002 1218 7091 3633214152 18512 30809 15783 11522 13967 1309 9539 3259818379 13735 25266 27908 51845 21849 18878 19767 755414634 8304 43255 15366 5004 15543 6210 11280 2292116062 14568 9302 15191 5420 19961 24274 13697 1472720650 17164 16879 26111 26445 24313 17739 21215 273426800 20033 25250 20132 24881 19328 27879 11409 5742822630 18113 19960 15509 31468 17374 23226 11615 4867413090 20738 58425 10647 18664 11973 8531 7577 42116AARE 27094 20880 14363 29454MAARE 58425 51845 27879 57428

established by using the modified conjugate gradient and theglobal optimization algorithm

(2) The nine groups of CO2-oil MMP experimental data

which have not been used to develop the new correlationwere calculated by the empirical correlation proposed in thisstudy and other eleven most popular and relatively high-accuracy empirical correlation presented in the literature to

validate the new correlation It can be seen from the com-parative results that the accuracy of the empirical correlationproposed in this study is significantly more precise thanthe other eleven most popular and relatively high-accuracyempirical correlations presented in the literatureThe range ofthe absolute error is less than 15MPa which corresponds tothe requirement of engineering design of CO

2displacement

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

4 Journal of Chemistry

Table2Correlatio

nsforC

O2-oilMMP

Author

Publish

edem

piric

alcorrelation

Remarks

Cron

quist

[4]

(a)119875

119898m

inpure=011027(18119879+32)

0744206+00011038119872

C 5+00015279119909VO

L

(i)Th

etestedoilgravityranged

from

237to

448∘API

(ii)Th

etested119879ranged

from

2167to

1208∘C

(iii)Th

etestedexperim

entalM

MPranged

from

74to

345MPa

Lee[13]

(b)119875

119898m

inpure=73924times10

2772minus[1519(492+18119879)]

(i)Ba

sedon

equatin

gMMPwith

CO2vapo

rpressurew

hen

119879ltCO2criticaltem

peraturew

hileusingthe

correspo

ndingcorrela

tionwhen119879⩾CO2critical

temperature

(ii)IfM

MPlt119875

119887119875119887istakenas

MMP

Yelling

-Metcalfe

[14]

(c)119875

119898m

inpure=126472+001553(18119879+32)+124192times10

minus4(18119879+32)

2minus

7169427

(18119879+32)

Limitatio

ns358leTlt889∘C

(i)IfMMPlt119875

119887119875119887istakenas

MMP

Orr-Je

nsen

[15]

(d)119875

119898m

inpure=0101386exp[1091minus

2105

255372+05556(18119879+32)

]

(i)Ba

sedon

extrapolated

vapo

rpressure(EV

P)metho

d(ii)U

sedto

estim

atethe

MMPforlow

temperature

reservoirs(119879

lt49

∘C)

Glaso

[16]

When119909

1015840 MED

lt18mol

(e1)119875

119898m

inpure=558657minus23477times10

minus2119872

C 7++11725times10

minus11119872

373

C 7+

exp7868119872

C 7+

minus1058

(18119879+32)

When119909

1015840 MED

gt18

(e2)

119875

119898m

inpure=2033minus23477times10

minus2119872

C 7++11725times10

minus11119872

373

C 7+

exp7868119872

C 7+

minus1058

(18119879+32)minus0836times119909

1015840 MED

Con

sidersthe

effecto

fintermediates(C 2

ndashC6)o

nlywhen

119909

1015840 MED

(C2ndashC6)lt

18mol

Alston

[17]

When119875

119887ge0345MPa

(f1)119875

119898m

inpure=60536times10

minus6(18119879+32)

106(119872

C 5+)

178

(

119909

VOL

119909

MED

)

0136

When119875

119887lt0345MPa

(f2)119875

119898m

inpure=60536times10

minus6(18119879+32)

106(119872

C 5+)

178

IfMMPlt119875

119887119875119887istakenas

MMP

Emera-Sarm

a[18]

When119875

119887ge0345MPa

(g1)119875

119898m

inpure=50093times10

minus5(18119879+32)

1164(119872

C 5+)

12785

(

119909

VOL

119909

MED

)

01073

When119875

119887lt0345MPa

(g2)

119875

119898m

inpure=50093times10

minus5(18119879+32)

1164(119872

C 5+)

12785

Limitatio

ns408ltTlt1122∘C

828

lt119875

119898m

inpurelt

302MPa1662lt119872

C 5+lt2675

gmol

Yuan

[19]

(h)119875

119898m

inpure=119886

1+119886

2119872

C 7+minus119886

3119909

1015840 MED

+(119886

4+119886

5119872

C 7++119886

6

119909

1015840 MED

119872

C 7+

2)(18119879+32)

+(119886

7+119886

8119872

C 7+minus119886

9119872

C 7+

2minus119886

10119909

1015840 MED)(18119879+32)

2

119886

1=minus989121198862=45588times10

minus21198863=minus31012times10

minus11198864=14748times10

minus2

119886

5=80441times10

minus41198866=56303times1011198867=minus84516times10

minus41198868=88825times10

minus6

119886

9=minus27684times10

minus811988610=minus63830times10

minus6

Limitatio

ns217

ltTlt148∘C

119875

119898m

inpurelt70

MPa

139lt119872

C 7+lt319g

mol

Journal of Chemistry 5

Table2Con

tinued

Author

Publish

edem

piric

alcorrelation

Remarks

Shok

ir[20]

(i1)119875

119898m

inpure=minus0068616119885

3+031733119885

2+49804119885+13432

(i2)119885=

4

sum 119894=1

119885

119894

(i3)119885

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

119886

1=minus291821198862=minus31227times10

minus11198863=minus49485times10

minus21198864=25430

119887

1=75340times10

minus21198872=minus79169times10

minus31198873=42165times10

minus21198874=minus39750times10

minus1

119888

1=minus55996times10

minus41198882=13644times10

minus31198883=minus27853times10

minus31198884=19860times10

minus3

119889

1=23660times10

minus61198892=minus13721times10

minus51198893=35551times10

minus51198894=minus31604times10

minus6

Limitatio

ns322ltTlt1122∘C

69lt119875

119898m

inpurelt

3028M

Pa185

lt119872

C 5+lt268g

mol

Chen

[21]

(j)119875

119898m

inpure=39673times10

minus2119879

08293(119872

C 7+)

05382

(119909

C 1+N2)

01018

(119909

C 2minusC 6)

minus02316

Limitatio

ns322ltTlt118

3∘C

69lt119875

119898m

inpurelt

2817

MPa185

lt119872

C 7+lt249g

mol

Ju[22]

(k1)119875

119898m

inim

pure=minus004562119878

3+033399119878

2+49811119878+13569

(k2)

119878=

8

sum 119894=1

119878

119894

(k3)

119878

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

Thed

etailedparametersrefer

to[18]

Limitatio

ns119875119898m

inpurelt40

MPa

6 Journal of Chemistry

Table 3 Regression parameters

Parameters Value119886 83397 times 10minus5

119887 39774119888 33179119889 17461 times 10minus1

report while119872C5+

normally need to be calculated from119872C7+

In addition it is found in this study that the use of 119872C

7+

rather than119872C

5+

even leads to a slightly better performanceof (1) in terms of the correlation coefficient 1198772 Meanwhile119872C7+

is replaced by ln(119872C7+

) to reduce the influence of119872C7+

on the MMP of CO2-oil system when 119872C

7+

is largerAnd 119909VOL119909

1015840

MED is replaced by (1 + 119909VOL1199091015840

MED) to avoidthe fact that 119909VOL119909

1015840

MED approaches to zero because of toofewer volatile components in heavy oil which result in greatdifferences between the parameters

The objective optimization function contains four param-eters (119898 = (119898

1 119898

2 119898

3 119898

4)) The CO

2-oil MMP database

used in this study includes a total of 210 MMPmeasurementsfrom the literature among which the temperature has a rangeof 2167∘Csim19197∘C and C

7+molecular weights range from

130 gmol to 4027 gmol [2 20ndash37] In addition it shouldbe noted that 176 out of the 210 measurements are obtainedfrom overseas data in the literature while the remaining34 measurements are obtained from domestic data in theliterature The CO

2-oil MMP database is used to determine

the tuned coefficients (119898 = (119898

1 119898

2 119898

3 119898

4)) in (1) by

regression fitting using the modified conjugate gradient andglobal optimization algorithmThe regression fitting has beenconducted by using the Matlab programming The tunedcoefficients are given in Table 3 and (1) generates a fit with119877

2= 09488 (Figure 4)

Step 1 Given the constant 1205901isin (0 12) 120590

1lt 120590

2lt 1 120576 gt 0

pick the initial point1198980isin 119877

4 1198890= minus119892

0 and place 119896 = 0

Step 2 If 119892119896 lt 120576 algorithm stops and 119898

119896in 119891(119898) is to

be obtained otherwise algorithm turns to Step 3 119892119896 the

conjugate gradient of119891(119898) at119898119896 represents 119892

119896= 120573

119896times119891(119898

119896)

in which 119892

119896 is the norm of 119892

119896and 120573

119896is the parameter

Generally two expression forms include 120573FR119896

= 119892

119896

2119892

119896minus1

2

and 120573

PR119896

= 119892

119879

119896(119892

119896minus 119892

119896minus1)119892

119896minus1

2 [22] In this paper 120573119896=

max0 120573FR119896

+ min0 119892119879119896119892

119896minus1119892

119879

119896minus1119889

119896minus1 in which 119892

119879

119896is the

transposed conjugate gradient

Step 3 Step length 120572119896is determined by 1D linear search

Step 4 Place119898119896+1

= 119898

119896+ 120572

119896119889

119896 in which 119889

119896is the conjugate

gradient search direction and is determined as follows

119889

119896=

minus119892

119896119896 = 0

minus120579

119896119892

119896+ 120573

119896119889

119896minus1119896 ge 1

(2)

05

101520253035404550

0 10 20 30 40 50

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

R2 = 09488

Figure 4 Resulted CO2-oil MMP from the new correlation versus

the experimental measurements

in which 120579

119896= 1 + (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896 It can be inferred that

119889

119896= minus119892

119896minus (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896119892

119896+ 120573

119896119889

119896minus1 where 119892119879

119896is to be

multiplied at both sides to obtain the following expression

119892

119879

119896119889

119896= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

minus

119892

119879

119896119889

119896minus1

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2120573

119896

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

+ 120573

119896119892

119879

119896119889

119896minus1

= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

lt 0

(3)

It is obvious that 119892119879119896119889

119896is always less than 0 and 119892

119879

119896is

greater than 0 which results in downward search directionMoreover if 120573

119896= 0 minus119892

119879

119896119892

119896minus1119892

119879

119896minus1119889

119896minus1ge 0 120573

119896= 120573

FR119896

the modified conjugate gradient method is FR conjugategradientmethod [38] Otherwise combining correlation ((c)see Table 2) we can draw that

120573

119896= 120573

FR119896

+

119892

119879

119896119892

119896minus1

119892

119879

119896minus1119889

119896minus1

=

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2minus

119892

119879

119896119892

119896minus1

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2

=

119892

119879

119896(119892

119896minus 119892

119896minus1)

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2= 120573

PR119896

(4)

It is called FR conjugate gradient method It is indicatedthat the FR conjugate gradient method takes in excellentglobal convergence of FR algorithm and excellent numericalresult of PR algorithm

Step 5 119889119896is determined and place 119896 = 119896 + 1 Process turns

to Step 2

Finally the modified MMP correlation of CO2-crude oil

is as follows

119891 (119898) = 119875

119898minpure = 83397

times 10

minus5[ln (18119879 + 32)]

39774[ln (119872C

7+

)]

33179

sdot (1 +

119909VOL119909

1015840

MED)

017461

(5)

Journal of Chemistry 7

Table 4 The nine oil samples components properties and MMP data for the new correlation validation

T (∘C) 119872C7+ 119872C5+ 119909MED 119909

1015840

MED 119909VOL Experimental data (MMP) (MPa) Reference6000 149690 136470 39370 46160 24680 11138 [39]8000 149690 136470 39370 46160 24680 14152 [39]13722 149690 136470 39370 46160 24680 18379 [39]10000 151740 138530 26760 37950 13530 14634 [40]8000 170080 160590 2630 7100 12150 16062 [41]13000 183690 165262 23131 30982 32631 20650 Current work7480 245690 229085 16501 16733 16922 26800 Current work8970 229170 211213 11790 24470 13770 22630 Current work5300 205740 182800 12933 25333 18706 13090 [42]

Compared with the other 11 correlations in Table 2the correlation has broader application (pressure range0sim70MPa temperature range 2167sim19197∘C and relativemolecular weight of C

7+ 130sim4027 gmol)

4 Calculation Results and Analysis

Generally the absolute error (6) the absolute relative error(7) and the average absolute relative error (8) are used to exp-ress the deviation between the calculatedMMP by the empir-ical correlation and optimize the most appropriate empiricalcorrelation for predicting the MMP of CO

2-oil system

AE = Cal minus Exp (6)

ARE () =119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (7)

AARE () = 1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (8)

A new correlation validation is performed with moreMMP data (Table 4) These MMP data have not been usedto develop the new correlationThe comparative results of thecalculatedMMPby the correlation proposed in this study andthe other eleven most popular and relatively high-accuracycorrelations presented in the previous literatures are shownin Figure 5 and Table 5 The average absolute relative errors(AARE) for the correlation proposed in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 8 16 37 20 32 19 20 13 27 21 14and 29 respectively The maximum absolute relative errors(MARE) for the proposed correlation in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 21 31 73 46 78 50 39 25 58 52 28and 57 respectivelyThese results indicate that the proposedcorrelation in this study is significantly more precise thanthe other correlations The results of the calculated MMP by

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

Cronquistrsquos correlationLeersquos correlationYelling-Metcalfersquos correlationOrr-Jensenrsquos correlationGlasorsquos correlationAlstonrsquos correlation

Emera-Sarmarsquos correlationYuanrsquos correlationShokirrsquos correlationChenrsquos correlationJursquos correlationThis study

Figure 5 The resulted nine-oil-sample MMP from the new corre-lation proposed in this study versus the calculated nine-oil-sampleMMP from Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlation Orr-Jensenrsquos correlation Glasorsquos correlationAlstonrsquos correlation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlation

the correlation proposed in this study the measured MMPby slim tube test and the absolute error (AE) are shownin Figures 5 and 6 From Table 5 it is clearly seen that theabsolute errors (AE) of the calculatedMMPby themodel pro-posed in this study of many oil samples are less than 15MPawhich are very close to the experimental data

5 Conclusions

(1) Four sensitive factors are determined for affecting theMMP of CO

2-oil system which includes the reservoir tem-

perature C7+

molecular weight of oil mole fractions ofvolatile components (CH

4and N

2) and mole fractions of

intermediate components (CO2 H2S and C

2simC6) of oil

Based on the above sensitive factors a four-parameter andimproved MMP prediction model of CO

2-oil system is

8 Journal of Chemistry

Table 5 Comparison of predictedMMPs for nine oil samples by the correlation proposed in this study and other eleven literature correlations

Exp (MMP)(MPa)

Correlation proposed in this study Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10594 4881 14062 26251 13055 17214 12135 894714152 12619 10833 13693 3241 18143 28201 15154 708018379 17548 4522 24043 30816 28968 57614 24077 3100414634 14243 2673 15050 2844 24340 66325 18139 2395416062 15387 4203 14645 8820 20143 25408 15154 565420650 19990 3196 25722 24561 35810 73416 22870 1075226800 22551 15853 22616 15613 16716 37627 14381 4633822630 17864 21060 16765 25919 26007 14921 16594 2667313090 12399 5278 12419 5129 11525 11959 11014 15860AARE 8055 15910 36965 19585MAARE 21060 30816 73416 46338Exp (MMP)(MPa)

Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquos correlation Emera-Sarmarsquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10002 10196 16679 49746 6756 39342 9362 1594514152 14306 1087 19472 37593 8611 39155 12214 1369518379 32845 78712 18464 0462 14032 23650 13738 2525114634 19691 34556 13128 10290 10462 28512 12071 1751316062 14306 10934 14973 6779 15941 0751 13032 1886320650 29963 45097 22617 9525 20944 1423 18150 1210526800 13087 51170 22328 16687 24636 8074 27222 157522630 16777 25863 26327 16337 15512 31454 23042 182013090 8734 33279 16029 22452 11524 11963 12102 7550AARE 32321 18874 20481 12702MAARE 78712 49746 39342 25251Exp (MMP)(MPa)

Yuanrsquos correlation Shokirrsquos correlation Chenrsquos correlation Jursquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 12775 14699 12549 12669 11002 1218 7091 3633214152 18512 30809 15783 11522 13967 1309 9539 3259818379 13735 25266 27908 51845 21849 18878 19767 755414634 8304 43255 15366 5004 15543 6210 11280 2292116062 14568 9302 15191 5420 19961 24274 13697 1472720650 17164 16879 26111 26445 24313 17739 21215 273426800 20033 25250 20132 24881 19328 27879 11409 5742822630 18113 19960 15509 31468 17374 23226 11615 4867413090 20738 58425 10647 18664 11973 8531 7577 42116AARE 27094 20880 14363 29454MAARE 58425 51845 27879 57428

established by using the modified conjugate gradient and theglobal optimization algorithm

(2) The nine groups of CO2-oil MMP experimental data

which have not been used to develop the new correlationwere calculated by the empirical correlation proposed in thisstudy and other eleven most popular and relatively high-accuracy empirical correlation presented in the literature to

validate the new correlation It can be seen from the com-parative results that the accuracy of the empirical correlationproposed in this study is significantly more precise thanthe other eleven most popular and relatively high-accuracyempirical correlations presented in the literatureThe range ofthe absolute error is less than 15MPa which corresponds tothe requirement of engineering design of CO

2displacement

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Journal of Chemistry 5

Table2Con

tinued

Author

Publish

edem

piric

alcorrelation

Remarks

Shok

ir[20]

(i1)119875

119898m

inpure=minus0068616119885

3+031733119885

2+49804119885+13432

(i2)119885=

4

sum 119894=1

119885

119894

(i3)119885

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

119886

1=minus291821198862=minus31227times10

minus11198863=minus49485times10

minus21198864=25430

119887

1=75340times10

minus21198872=minus79169times10

minus31198873=42165times10

minus21198874=minus39750times10

minus1

119888

1=minus55996times10

minus41198882=13644times10

minus31198883=minus27853times10

minus31198884=19860times10

minus3

119889

1=23660times10

minus61198892=minus13721times10

minus51198893=35551times10

minus51198894=minus31604times10

minus6

Limitatio

ns322ltTlt1122∘C

69lt119875

119898m

inpurelt

3028M

Pa185

lt119872

C 5+lt268g

mol

Chen

[21]

(j)119875

119898m

inpure=39673times10

minus2119879

08293(119872

C 7+)

05382

(119909

C 1+N2)

01018

(119909

C 2minusC 6)

minus02316

Limitatio

ns322ltTlt118

3∘C

69lt119875

119898m

inpurelt

2817

MPa185

lt119872

C 7+lt249g

mol

Ju[22]

(k1)119875

119898m

inim

pure=minus004562119878

3+033399119878

2+49811119878+13569

(k2)

119878=

8

sum 119894=1

119878

119894

(k3)

119878

119894=119886

119894+119887

119894119909

119894+119888

119894119909

119894

2+119889

119894119909

119894

3

Thed

etailedparametersrefer

to[18]

Limitatio

ns119875119898m

inpurelt40

MPa

6 Journal of Chemistry

Table 3 Regression parameters

Parameters Value119886 83397 times 10minus5

119887 39774119888 33179119889 17461 times 10minus1

report while119872C5+

normally need to be calculated from119872C7+

In addition it is found in this study that the use of 119872C

7+

rather than119872C

5+

even leads to a slightly better performanceof (1) in terms of the correlation coefficient 1198772 Meanwhile119872C7+

is replaced by ln(119872C7+

) to reduce the influence of119872C7+

on the MMP of CO2-oil system when 119872C

7+

is largerAnd 119909VOL119909

1015840

MED is replaced by (1 + 119909VOL1199091015840

MED) to avoidthe fact that 119909VOL119909

1015840

MED approaches to zero because of toofewer volatile components in heavy oil which result in greatdifferences between the parameters

The objective optimization function contains four param-eters (119898 = (119898

1 119898

2 119898

3 119898

4)) The CO

2-oil MMP database

used in this study includes a total of 210 MMPmeasurementsfrom the literature among which the temperature has a rangeof 2167∘Csim19197∘C and C

7+molecular weights range from

130 gmol to 4027 gmol [2 20ndash37] In addition it shouldbe noted that 176 out of the 210 measurements are obtainedfrom overseas data in the literature while the remaining34 measurements are obtained from domestic data in theliterature The CO

2-oil MMP database is used to determine

the tuned coefficients (119898 = (119898

1 119898

2 119898

3 119898

4)) in (1) by

regression fitting using the modified conjugate gradient andglobal optimization algorithmThe regression fitting has beenconducted by using the Matlab programming The tunedcoefficients are given in Table 3 and (1) generates a fit with119877

2= 09488 (Figure 4)

Step 1 Given the constant 1205901isin (0 12) 120590

1lt 120590

2lt 1 120576 gt 0

pick the initial point1198980isin 119877

4 1198890= minus119892

0 and place 119896 = 0

Step 2 If 119892119896 lt 120576 algorithm stops and 119898

119896in 119891(119898) is to

be obtained otherwise algorithm turns to Step 3 119892119896 the

conjugate gradient of119891(119898) at119898119896 represents 119892

119896= 120573

119896times119891(119898

119896)

in which 119892

119896 is the norm of 119892

119896and 120573

119896is the parameter

Generally two expression forms include 120573FR119896

= 119892

119896

2119892

119896minus1

2

and 120573

PR119896

= 119892

119879

119896(119892

119896minus 119892

119896minus1)119892

119896minus1

2 [22] In this paper 120573119896=

max0 120573FR119896

+ min0 119892119879119896119892

119896minus1119892

119879

119896minus1119889

119896minus1 in which 119892

119879

119896is the

transposed conjugate gradient

Step 3 Step length 120572119896is determined by 1D linear search

Step 4 Place119898119896+1

= 119898

119896+ 120572

119896119889

119896 in which 119889

119896is the conjugate

gradient search direction and is determined as follows

119889

119896=

minus119892

119896119896 = 0

minus120579

119896119892

119896+ 120573

119896119889

119896minus1119896 ge 1

(2)

05

101520253035404550

0 10 20 30 40 50

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

R2 = 09488

Figure 4 Resulted CO2-oil MMP from the new correlation versus

the experimental measurements

in which 120579

119896= 1 + (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896 It can be inferred that

119889

119896= minus119892

119896minus (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896119892

119896+ 120573

119896119889

119896minus1 where 119892119879

119896is to be

multiplied at both sides to obtain the following expression

119892

119879

119896119889

119896= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

minus

119892

119879

119896119889

119896minus1

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2120573

119896

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

+ 120573

119896119892

119879

119896119889

119896minus1

= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

lt 0

(3)

It is obvious that 119892119879119896119889

119896is always less than 0 and 119892

119879

119896is

greater than 0 which results in downward search directionMoreover if 120573

119896= 0 minus119892

119879

119896119892

119896minus1119892

119879

119896minus1119889

119896minus1ge 0 120573

119896= 120573

FR119896

the modified conjugate gradient method is FR conjugategradientmethod [38] Otherwise combining correlation ((c)see Table 2) we can draw that

120573

119896= 120573

FR119896

+

119892

119879

119896119892

119896minus1

119892

119879

119896minus1119889

119896minus1

=

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2minus

119892

119879

119896119892

119896minus1

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2

=

119892

119879

119896(119892

119896minus 119892

119896minus1)

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2= 120573

PR119896

(4)

It is called FR conjugate gradient method It is indicatedthat the FR conjugate gradient method takes in excellentglobal convergence of FR algorithm and excellent numericalresult of PR algorithm

Step 5 119889119896is determined and place 119896 = 119896 + 1 Process turns

to Step 2

Finally the modified MMP correlation of CO2-crude oil

is as follows

119891 (119898) = 119875

119898minpure = 83397

times 10

minus5[ln (18119879 + 32)]

39774[ln (119872C

7+

)]

33179

sdot (1 +

119909VOL119909

1015840

MED)

017461

(5)

Journal of Chemistry 7

Table 4 The nine oil samples components properties and MMP data for the new correlation validation

T (∘C) 119872C7+ 119872C5+ 119909MED 119909

1015840

MED 119909VOL Experimental data (MMP) (MPa) Reference6000 149690 136470 39370 46160 24680 11138 [39]8000 149690 136470 39370 46160 24680 14152 [39]13722 149690 136470 39370 46160 24680 18379 [39]10000 151740 138530 26760 37950 13530 14634 [40]8000 170080 160590 2630 7100 12150 16062 [41]13000 183690 165262 23131 30982 32631 20650 Current work7480 245690 229085 16501 16733 16922 26800 Current work8970 229170 211213 11790 24470 13770 22630 Current work5300 205740 182800 12933 25333 18706 13090 [42]

Compared with the other 11 correlations in Table 2the correlation has broader application (pressure range0sim70MPa temperature range 2167sim19197∘C and relativemolecular weight of C

7+ 130sim4027 gmol)

4 Calculation Results and Analysis

Generally the absolute error (6) the absolute relative error(7) and the average absolute relative error (8) are used to exp-ress the deviation between the calculatedMMP by the empir-ical correlation and optimize the most appropriate empiricalcorrelation for predicting the MMP of CO

2-oil system

AE = Cal minus Exp (6)

ARE () =119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (7)

AARE () = 1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (8)

A new correlation validation is performed with moreMMP data (Table 4) These MMP data have not been usedto develop the new correlationThe comparative results of thecalculatedMMPby the correlation proposed in this study andthe other eleven most popular and relatively high-accuracycorrelations presented in the previous literatures are shownin Figure 5 and Table 5 The average absolute relative errors(AARE) for the correlation proposed in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 8 16 37 20 32 19 20 13 27 21 14and 29 respectively The maximum absolute relative errors(MARE) for the proposed correlation in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 21 31 73 46 78 50 39 25 58 52 28and 57 respectivelyThese results indicate that the proposedcorrelation in this study is significantly more precise thanthe other correlations The results of the calculated MMP by

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

Cronquistrsquos correlationLeersquos correlationYelling-Metcalfersquos correlationOrr-Jensenrsquos correlationGlasorsquos correlationAlstonrsquos correlation

Emera-Sarmarsquos correlationYuanrsquos correlationShokirrsquos correlationChenrsquos correlationJursquos correlationThis study

Figure 5 The resulted nine-oil-sample MMP from the new corre-lation proposed in this study versus the calculated nine-oil-sampleMMP from Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlation Orr-Jensenrsquos correlation Glasorsquos correlationAlstonrsquos correlation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlation

the correlation proposed in this study the measured MMPby slim tube test and the absolute error (AE) are shownin Figures 5 and 6 From Table 5 it is clearly seen that theabsolute errors (AE) of the calculatedMMPby themodel pro-posed in this study of many oil samples are less than 15MPawhich are very close to the experimental data

5 Conclusions

(1) Four sensitive factors are determined for affecting theMMP of CO

2-oil system which includes the reservoir tem-

perature C7+

molecular weight of oil mole fractions ofvolatile components (CH

4and N

2) and mole fractions of

intermediate components (CO2 H2S and C

2simC6) of oil

Based on the above sensitive factors a four-parameter andimproved MMP prediction model of CO

2-oil system is

8 Journal of Chemistry

Table 5 Comparison of predictedMMPs for nine oil samples by the correlation proposed in this study and other eleven literature correlations

Exp (MMP)(MPa)

Correlation proposed in this study Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10594 4881 14062 26251 13055 17214 12135 894714152 12619 10833 13693 3241 18143 28201 15154 708018379 17548 4522 24043 30816 28968 57614 24077 3100414634 14243 2673 15050 2844 24340 66325 18139 2395416062 15387 4203 14645 8820 20143 25408 15154 565420650 19990 3196 25722 24561 35810 73416 22870 1075226800 22551 15853 22616 15613 16716 37627 14381 4633822630 17864 21060 16765 25919 26007 14921 16594 2667313090 12399 5278 12419 5129 11525 11959 11014 15860AARE 8055 15910 36965 19585MAARE 21060 30816 73416 46338Exp (MMP)(MPa)

Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquos correlation Emera-Sarmarsquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10002 10196 16679 49746 6756 39342 9362 1594514152 14306 1087 19472 37593 8611 39155 12214 1369518379 32845 78712 18464 0462 14032 23650 13738 2525114634 19691 34556 13128 10290 10462 28512 12071 1751316062 14306 10934 14973 6779 15941 0751 13032 1886320650 29963 45097 22617 9525 20944 1423 18150 1210526800 13087 51170 22328 16687 24636 8074 27222 157522630 16777 25863 26327 16337 15512 31454 23042 182013090 8734 33279 16029 22452 11524 11963 12102 7550AARE 32321 18874 20481 12702MAARE 78712 49746 39342 25251Exp (MMP)(MPa)

Yuanrsquos correlation Shokirrsquos correlation Chenrsquos correlation Jursquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 12775 14699 12549 12669 11002 1218 7091 3633214152 18512 30809 15783 11522 13967 1309 9539 3259818379 13735 25266 27908 51845 21849 18878 19767 755414634 8304 43255 15366 5004 15543 6210 11280 2292116062 14568 9302 15191 5420 19961 24274 13697 1472720650 17164 16879 26111 26445 24313 17739 21215 273426800 20033 25250 20132 24881 19328 27879 11409 5742822630 18113 19960 15509 31468 17374 23226 11615 4867413090 20738 58425 10647 18664 11973 8531 7577 42116AARE 27094 20880 14363 29454MAARE 58425 51845 27879 57428

established by using the modified conjugate gradient and theglobal optimization algorithm

(2) The nine groups of CO2-oil MMP experimental data

which have not been used to develop the new correlationwere calculated by the empirical correlation proposed in thisstudy and other eleven most popular and relatively high-accuracy empirical correlation presented in the literature to

validate the new correlation It can be seen from the com-parative results that the accuracy of the empirical correlationproposed in this study is significantly more precise thanthe other eleven most popular and relatively high-accuracyempirical correlations presented in the literatureThe range ofthe absolute error is less than 15MPa which corresponds tothe requirement of engineering design of CO

2displacement

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

6 Journal of Chemistry

Table 3 Regression parameters

Parameters Value119886 83397 times 10minus5

119887 39774119888 33179119889 17461 times 10minus1

report while119872C5+

normally need to be calculated from119872C7+

In addition it is found in this study that the use of 119872C

7+

rather than119872C

5+

even leads to a slightly better performanceof (1) in terms of the correlation coefficient 1198772 Meanwhile119872C7+

is replaced by ln(119872C7+

) to reduce the influence of119872C7+

on the MMP of CO2-oil system when 119872C

7+

is largerAnd 119909VOL119909

1015840

MED is replaced by (1 + 119909VOL1199091015840

MED) to avoidthe fact that 119909VOL119909

1015840

MED approaches to zero because of toofewer volatile components in heavy oil which result in greatdifferences between the parameters

The objective optimization function contains four param-eters (119898 = (119898

1 119898

2 119898

3 119898

4)) The CO

2-oil MMP database

used in this study includes a total of 210 MMPmeasurementsfrom the literature among which the temperature has a rangeof 2167∘Csim19197∘C and C

7+molecular weights range from

130 gmol to 4027 gmol [2 20ndash37] In addition it shouldbe noted that 176 out of the 210 measurements are obtainedfrom overseas data in the literature while the remaining34 measurements are obtained from domestic data in theliterature The CO

2-oil MMP database is used to determine

the tuned coefficients (119898 = (119898

1 119898

2 119898

3 119898

4)) in (1) by

regression fitting using the modified conjugate gradient andglobal optimization algorithmThe regression fitting has beenconducted by using the Matlab programming The tunedcoefficients are given in Table 3 and (1) generates a fit with119877

2= 09488 (Figure 4)

Step 1 Given the constant 1205901isin (0 12) 120590

1lt 120590

2lt 1 120576 gt 0

pick the initial point1198980isin 119877

4 1198890= minus119892

0 and place 119896 = 0

Step 2 If 119892119896 lt 120576 algorithm stops and 119898

119896in 119891(119898) is to

be obtained otherwise algorithm turns to Step 3 119892119896 the

conjugate gradient of119891(119898) at119898119896 represents 119892

119896= 120573

119896times119891(119898

119896)

in which 119892

119896 is the norm of 119892

119896and 120573

119896is the parameter

Generally two expression forms include 120573FR119896

= 119892

119896

2119892

119896minus1

2

and 120573

PR119896

= 119892

119879

119896(119892

119896minus 119892

119896minus1)119892

119896minus1

2 [22] In this paper 120573119896=

max0 120573FR119896

+ min0 119892119879119896119892

119896minus1119892

119879

119896minus1119889

119896minus1 in which 119892

119879

119896is the

transposed conjugate gradient

Step 3 Step length 120572119896is determined by 1D linear search

Step 4 Place119898119896+1

= 119898

119896+ 120572

119896119889

119896 in which 119889

119896is the conjugate

gradient search direction and is determined as follows

119889

119896=

minus119892

119896119896 = 0

minus120579

119896119892

119896+ 120573

119896119889

119896minus1119896 ge 1

(2)

05

101520253035404550

0 10 20 30 40 50

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

R2 = 09488

Figure 4 Resulted CO2-oil MMP from the new correlation versus

the experimental measurements

in which 120579

119896= 1 + (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896 It can be inferred that

119889

119896= minus119892

119896minus (119892

119879

119896119889

119896minus1119892

119896

2)120573

119896119892

119896+ 120573

119896119889

119896minus1 where 119892119879

119896is to be

multiplied at both sides to obtain the following expression

119892

119879

119896119889

119896= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

minus

119892

119879

119896119889

119896minus1

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2120573

119896

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

+ 120573

119896119892

119879

119896119889

119896minus1

= minus

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

lt 0

(3)

It is obvious that 119892119879119896119889

119896is always less than 0 and 119892

119879

119896is

greater than 0 which results in downward search directionMoreover if 120573

119896= 0 minus119892

119879

119896119892

119896minus1119892

119879

119896minus1119889

119896minus1ge 0 120573

119896= 120573

FR119896

the modified conjugate gradient method is FR conjugategradientmethod [38] Otherwise combining correlation ((c)see Table 2) we can draw that

120573

119896= 120573

FR119896

+

119892

119879

119896119892

119896minus1

119892

119879

119896minus1119889

119896minus1

=

1003817

1003817

1003817

1003817

119892

119896

1003817

1003817

1003817

1003817

2

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2minus

119892

119879

119896119892

119896minus1

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2

=

119892

119879

119896(119892

119896minus 119892

119896minus1)

1003817

1003817

1003817

1003817

119892

119896minus1

1003817

1003817

1003817

1003817

2= 120573

PR119896

(4)

It is called FR conjugate gradient method It is indicatedthat the FR conjugate gradient method takes in excellentglobal convergence of FR algorithm and excellent numericalresult of PR algorithm

Step 5 119889119896is determined and place 119896 = 119896 + 1 Process turns

to Step 2

Finally the modified MMP correlation of CO2-crude oil

is as follows

119891 (119898) = 119875

119898minpure = 83397

times 10

minus5[ln (18119879 + 32)]

39774[ln (119872C

7+

)]

33179

sdot (1 +

119909VOL119909

1015840

MED)

017461

(5)

Journal of Chemistry 7

Table 4 The nine oil samples components properties and MMP data for the new correlation validation

T (∘C) 119872C7+ 119872C5+ 119909MED 119909

1015840

MED 119909VOL Experimental data (MMP) (MPa) Reference6000 149690 136470 39370 46160 24680 11138 [39]8000 149690 136470 39370 46160 24680 14152 [39]13722 149690 136470 39370 46160 24680 18379 [39]10000 151740 138530 26760 37950 13530 14634 [40]8000 170080 160590 2630 7100 12150 16062 [41]13000 183690 165262 23131 30982 32631 20650 Current work7480 245690 229085 16501 16733 16922 26800 Current work8970 229170 211213 11790 24470 13770 22630 Current work5300 205740 182800 12933 25333 18706 13090 [42]

Compared with the other 11 correlations in Table 2the correlation has broader application (pressure range0sim70MPa temperature range 2167sim19197∘C and relativemolecular weight of C

7+ 130sim4027 gmol)

4 Calculation Results and Analysis

Generally the absolute error (6) the absolute relative error(7) and the average absolute relative error (8) are used to exp-ress the deviation between the calculatedMMP by the empir-ical correlation and optimize the most appropriate empiricalcorrelation for predicting the MMP of CO

2-oil system

AE = Cal minus Exp (6)

ARE () =119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (7)

AARE () = 1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (8)

A new correlation validation is performed with moreMMP data (Table 4) These MMP data have not been usedto develop the new correlationThe comparative results of thecalculatedMMPby the correlation proposed in this study andthe other eleven most popular and relatively high-accuracycorrelations presented in the previous literatures are shownin Figure 5 and Table 5 The average absolute relative errors(AARE) for the correlation proposed in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 8 16 37 20 32 19 20 13 27 21 14and 29 respectively The maximum absolute relative errors(MARE) for the proposed correlation in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 21 31 73 46 78 50 39 25 58 52 28and 57 respectivelyThese results indicate that the proposedcorrelation in this study is significantly more precise thanthe other correlations The results of the calculated MMP by

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

Cronquistrsquos correlationLeersquos correlationYelling-Metcalfersquos correlationOrr-Jensenrsquos correlationGlasorsquos correlationAlstonrsquos correlation

Emera-Sarmarsquos correlationYuanrsquos correlationShokirrsquos correlationChenrsquos correlationJursquos correlationThis study

Figure 5 The resulted nine-oil-sample MMP from the new corre-lation proposed in this study versus the calculated nine-oil-sampleMMP from Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlation Orr-Jensenrsquos correlation Glasorsquos correlationAlstonrsquos correlation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlation

the correlation proposed in this study the measured MMPby slim tube test and the absolute error (AE) are shownin Figures 5 and 6 From Table 5 it is clearly seen that theabsolute errors (AE) of the calculatedMMPby themodel pro-posed in this study of many oil samples are less than 15MPawhich are very close to the experimental data

5 Conclusions

(1) Four sensitive factors are determined for affecting theMMP of CO

2-oil system which includes the reservoir tem-

perature C7+

molecular weight of oil mole fractions ofvolatile components (CH

4and N

2) and mole fractions of

intermediate components (CO2 H2S and C

2simC6) of oil

Based on the above sensitive factors a four-parameter andimproved MMP prediction model of CO

2-oil system is

8 Journal of Chemistry

Table 5 Comparison of predictedMMPs for nine oil samples by the correlation proposed in this study and other eleven literature correlations

Exp (MMP)(MPa)

Correlation proposed in this study Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10594 4881 14062 26251 13055 17214 12135 894714152 12619 10833 13693 3241 18143 28201 15154 708018379 17548 4522 24043 30816 28968 57614 24077 3100414634 14243 2673 15050 2844 24340 66325 18139 2395416062 15387 4203 14645 8820 20143 25408 15154 565420650 19990 3196 25722 24561 35810 73416 22870 1075226800 22551 15853 22616 15613 16716 37627 14381 4633822630 17864 21060 16765 25919 26007 14921 16594 2667313090 12399 5278 12419 5129 11525 11959 11014 15860AARE 8055 15910 36965 19585MAARE 21060 30816 73416 46338Exp (MMP)(MPa)

Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquos correlation Emera-Sarmarsquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10002 10196 16679 49746 6756 39342 9362 1594514152 14306 1087 19472 37593 8611 39155 12214 1369518379 32845 78712 18464 0462 14032 23650 13738 2525114634 19691 34556 13128 10290 10462 28512 12071 1751316062 14306 10934 14973 6779 15941 0751 13032 1886320650 29963 45097 22617 9525 20944 1423 18150 1210526800 13087 51170 22328 16687 24636 8074 27222 157522630 16777 25863 26327 16337 15512 31454 23042 182013090 8734 33279 16029 22452 11524 11963 12102 7550AARE 32321 18874 20481 12702MAARE 78712 49746 39342 25251Exp (MMP)(MPa)

Yuanrsquos correlation Shokirrsquos correlation Chenrsquos correlation Jursquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 12775 14699 12549 12669 11002 1218 7091 3633214152 18512 30809 15783 11522 13967 1309 9539 3259818379 13735 25266 27908 51845 21849 18878 19767 755414634 8304 43255 15366 5004 15543 6210 11280 2292116062 14568 9302 15191 5420 19961 24274 13697 1472720650 17164 16879 26111 26445 24313 17739 21215 273426800 20033 25250 20132 24881 19328 27879 11409 5742822630 18113 19960 15509 31468 17374 23226 11615 4867413090 20738 58425 10647 18664 11973 8531 7577 42116AARE 27094 20880 14363 29454MAARE 58425 51845 27879 57428

established by using the modified conjugate gradient and theglobal optimization algorithm

(2) The nine groups of CO2-oil MMP experimental data

which have not been used to develop the new correlationwere calculated by the empirical correlation proposed in thisstudy and other eleven most popular and relatively high-accuracy empirical correlation presented in the literature to

validate the new correlation It can be seen from the com-parative results that the accuracy of the empirical correlationproposed in this study is significantly more precise thanthe other eleven most popular and relatively high-accuracyempirical correlations presented in the literatureThe range ofthe absolute error is less than 15MPa which corresponds tothe requirement of engineering design of CO

2displacement

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Journal of Chemistry 7

Table 4 The nine oil samples components properties and MMP data for the new correlation validation

T (∘C) 119872C7+ 119872C5+ 119909MED 119909

1015840

MED 119909VOL Experimental data (MMP) (MPa) Reference6000 149690 136470 39370 46160 24680 11138 [39]8000 149690 136470 39370 46160 24680 14152 [39]13722 149690 136470 39370 46160 24680 18379 [39]10000 151740 138530 26760 37950 13530 14634 [40]8000 170080 160590 2630 7100 12150 16062 [41]13000 183690 165262 23131 30982 32631 20650 Current work7480 245690 229085 16501 16733 16922 26800 Current work8970 229170 211213 11790 24470 13770 22630 Current work5300 205740 182800 12933 25333 18706 13090 [42]

Compared with the other 11 correlations in Table 2the correlation has broader application (pressure range0sim70MPa temperature range 2167sim19197∘C and relativemolecular weight of C

7+ 130sim4027 gmol)

4 Calculation Results and Analysis

Generally the absolute error (6) the absolute relative error(7) and the average absolute relative error (8) are used to exp-ress the deviation between the calculatedMMP by the empir-ical correlation and optimize the most appropriate empiricalcorrelation for predicting the MMP of CO

2-oil system

AE = Cal minus Exp (6)

ARE () =119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (7)

AARE () = 1

119873

119873

sum

119894=1

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Cal minus ExpExp

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816119894

times 100 (8)

A new correlation validation is performed with moreMMP data (Table 4) These MMP data have not been usedto develop the new correlationThe comparative results of thecalculatedMMPby the correlation proposed in this study andthe other eleven most popular and relatively high-accuracycorrelations presented in the previous literatures are shownin Figure 5 and Table 5 The average absolute relative errors(AARE) for the correlation proposed in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 8 16 37 20 32 19 20 13 27 21 14and 29 respectively The maximum absolute relative errors(MARE) for the proposed correlation in this study Cron-quistrsquos correlation Leersquos correlation Yelling-Metcalfersquos corre-lation Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquoscorrelation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlationare 21 31 73 46 78 50 39 25 58 52 28and 57 respectivelyThese results indicate that the proposedcorrelation in this study is significantly more precise thanthe other correlations The results of the calculated MMP by

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Calc

ulat

ed M

MP

(MPa

)

Measured MMP (MPa)

Cronquistrsquos correlationLeersquos correlationYelling-Metcalfersquos correlationOrr-Jensenrsquos correlationGlasorsquos correlationAlstonrsquos correlation

Emera-Sarmarsquos correlationYuanrsquos correlationShokirrsquos correlationChenrsquos correlationJursquos correlationThis study

Figure 5 The resulted nine-oil-sample MMP from the new corre-lation proposed in this study versus the calculated nine-oil-sampleMMP from Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlation Orr-Jensenrsquos correlation Glasorsquos correlationAlstonrsquos correlation Emera-Sarmarsquos correlation Yuanrsquos correlationShokirrsquos correlation Chenrsquos correlation and Jursquos correlation

the correlation proposed in this study the measured MMPby slim tube test and the absolute error (AE) are shownin Figures 5 and 6 From Table 5 it is clearly seen that theabsolute errors (AE) of the calculatedMMPby themodel pro-posed in this study of many oil samples are less than 15MPawhich are very close to the experimental data

5 Conclusions

(1) Four sensitive factors are determined for affecting theMMP of CO

2-oil system which includes the reservoir tem-

perature C7+

molecular weight of oil mole fractions ofvolatile components (CH

4and N

2) and mole fractions of

intermediate components (CO2 H2S and C

2simC6) of oil

Based on the above sensitive factors a four-parameter andimproved MMP prediction model of CO

2-oil system is

8 Journal of Chemistry

Table 5 Comparison of predictedMMPs for nine oil samples by the correlation proposed in this study and other eleven literature correlations

Exp (MMP)(MPa)

Correlation proposed in this study Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10594 4881 14062 26251 13055 17214 12135 894714152 12619 10833 13693 3241 18143 28201 15154 708018379 17548 4522 24043 30816 28968 57614 24077 3100414634 14243 2673 15050 2844 24340 66325 18139 2395416062 15387 4203 14645 8820 20143 25408 15154 565420650 19990 3196 25722 24561 35810 73416 22870 1075226800 22551 15853 22616 15613 16716 37627 14381 4633822630 17864 21060 16765 25919 26007 14921 16594 2667313090 12399 5278 12419 5129 11525 11959 11014 15860AARE 8055 15910 36965 19585MAARE 21060 30816 73416 46338Exp (MMP)(MPa)

Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquos correlation Emera-Sarmarsquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10002 10196 16679 49746 6756 39342 9362 1594514152 14306 1087 19472 37593 8611 39155 12214 1369518379 32845 78712 18464 0462 14032 23650 13738 2525114634 19691 34556 13128 10290 10462 28512 12071 1751316062 14306 10934 14973 6779 15941 0751 13032 1886320650 29963 45097 22617 9525 20944 1423 18150 1210526800 13087 51170 22328 16687 24636 8074 27222 157522630 16777 25863 26327 16337 15512 31454 23042 182013090 8734 33279 16029 22452 11524 11963 12102 7550AARE 32321 18874 20481 12702MAARE 78712 49746 39342 25251Exp (MMP)(MPa)

Yuanrsquos correlation Shokirrsquos correlation Chenrsquos correlation Jursquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 12775 14699 12549 12669 11002 1218 7091 3633214152 18512 30809 15783 11522 13967 1309 9539 3259818379 13735 25266 27908 51845 21849 18878 19767 755414634 8304 43255 15366 5004 15543 6210 11280 2292116062 14568 9302 15191 5420 19961 24274 13697 1472720650 17164 16879 26111 26445 24313 17739 21215 273426800 20033 25250 20132 24881 19328 27879 11409 5742822630 18113 19960 15509 31468 17374 23226 11615 4867413090 20738 58425 10647 18664 11973 8531 7577 42116AARE 27094 20880 14363 29454MAARE 58425 51845 27879 57428

established by using the modified conjugate gradient and theglobal optimization algorithm

(2) The nine groups of CO2-oil MMP experimental data

which have not been used to develop the new correlationwere calculated by the empirical correlation proposed in thisstudy and other eleven most popular and relatively high-accuracy empirical correlation presented in the literature to

validate the new correlation It can be seen from the com-parative results that the accuracy of the empirical correlationproposed in this study is significantly more precise thanthe other eleven most popular and relatively high-accuracyempirical correlations presented in the literatureThe range ofthe absolute error is less than 15MPa which corresponds tothe requirement of engineering design of CO

2displacement

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

8 Journal of Chemistry

Table 5 Comparison of predictedMMPs for nine oil samples by the correlation proposed in this study and other eleven literature correlations

Exp (MMP)(MPa)

Correlation proposed in this study Cronquistrsquos correlation Leersquos correlation Yelling-Metcalfersquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10594 4881 14062 26251 13055 17214 12135 894714152 12619 10833 13693 3241 18143 28201 15154 708018379 17548 4522 24043 30816 28968 57614 24077 3100414634 14243 2673 15050 2844 24340 66325 18139 2395416062 15387 4203 14645 8820 20143 25408 15154 565420650 19990 3196 25722 24561 35810 73416 22870 1075226800 22551 15853 22616 15613 16716 37627 14381 4633822630 17864 21060 16765 25919 26007 14921 16594 2667313090 12399 5278 12419 5129 11525 11959 11014 15860AARE 8055 15910 36965 19585MAARE 21060 30816 73416 46338Exp (MMP)(MPa)

Orr-Jensenrsquos correlation Glasorsquos correlation Alstonrsquos correlation Emera-Sarmarsquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 10002 10196 16679 49746 6756 39342 9362 1594514152 14306 1087 19472 37593 8611 39155 12214 1369518379 32845 78712 18464 0462 14032 23650 13738 2525114634 19691 34556 13128 10290 10462 28512 12071 1751316062 14306 10934 14973 6779 15941 0751 13032 1886320650 29963 45097 22617 9525 20944 1423 18150 1210526800 13087 51170 22328 16687 24636 8074 27222 157522630 16777 25863 26327 16337 15512 31454 23042 182013090 8734 33279 16029 22452 11524 11963 12102 7550AARE 32321 18874 20481 12702MAARE 78712 49746 39342 25251Exp (MMP)(MPa)

Yuanrsquos correlation Shokirrsquos correlation Chenrsquos correlation Jursquos correlationMMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE MMP (MPa) ARE

11138 12775 14699 12549 12669 11002 1218 7091 3633214152 18512 30809 15783 11522 13967 1309 9539 3259818379 13735 25266 27908 51845 21849 18878 19767 755414634 8304 43255 15366 5004 15543 6210 11280 2292116062 14568 9302 15191 5420 19961 24274 13697 1472720650 17164 16879 26111 26445 24313 17739 21215 273426800 20033 25250 20132 24881 19328 27879 11409 5742822630 18113 19960 15509 31468 17374 23226 11615 4867413090 20738 58425 10647 18664 11973 8531 7577 42116AARE 27094 20880 14363 29454MAARE 58425 51845 27879 57428

established by using the modified conjugate gradient and theglobal optimization algorithm

(2) The nine groups of CO2-oil MMP experimental data

which have not been used to develop the new correlationwere calculated by the empirical correlation proposed in thisstudy and other eleven most popular and relatively high-accuracy empirical correlation presented in the literature to

validate the new correlation It can be seen from the com-parative results that the accuracy of the empirical correlationproposed in this study is significantly more precise thanthe other eleven most popular and relatively high-accuracyempirical correlations presented in the literatureThe range ofthe absolute error is less than 15MPa which corresponds tothe requirement of engineering design of CO

2displacement

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Journal of Chemistry 9

minus10

minus5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9

Pres

sure

(MPa

)

Sample number

Measured MMPCalculated MMP

Absolute error

Figure 6 The MMPs of the system of nine CO2-oil samples and

their errors predicted by the correlation proposed in this paper

Nomenclature

119872C5+

Molecular weight of C5+

in the crude oilgmol

119879 Reservoir temperature ∘C119872C7+

Molecular weight of C7+

in the crude oilgmol

119909VOL Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909MED Mole fraction of intermediate components(CO2 H2S and C

2simC4) in the crude oil

mol119909

1015840

MED Mole fraction of intermediate components(CO2 H2S and C

2simC6) in the crude oil

mol119875

119898minpure Minimummiscibility pressure by pureCO2injection MPa

119875

119898minimpure Minimummiscibility pressure by impureCO2injection MPa

119909

1 Reservoir temperature ∘C

119909

2 Mole fraction of volatile components

(CH4+ N2) in the crude oil mol

119909

3 Mole fraction of intermediate components

(CO2 H2S and C

2simC6) in the crude oil

mol119909

4 Molecular weight of C

5+in the crude oil

gmol119909

5 Mole fraction of volatile components (C

1)

in the injection gas mol119909

6 Mole fraction of intermediate components

(C2simC4) in the injection gas mol

119909

7 Mole fraction of volatile components (N

2)

in the injection gas mol119909

8 Mole fraction of volatile components

(H2S) in the injection gas mol

119909C1+N2

Mole fraction of volatile components(CH4+ N2) in the crude oil mol

119909C2minusC6

Mole fraction of intermediate components(C2simC6) in the crude oil mol

AE Absolute errorARE Percentage absolute relative errorAARE Percentage average absolute relative errorMARE Percentage maximum average absolute

relative error

Conflict of Interests

Here all the authors solemnly declare that there is no conflictof interests regarding the publication of this paper

Acknowledgment

This work was supported by a Grant from the NationalNatural Science Foundation of China (no 51374044)

References

[1] TW Teklu S G Ghedan RM Graves and X Yin ldquoMinimummiscibility pressure determination modified multiple mixingcell methodrdquo in Proceedings of the SPE EOR Conference at OilandGasWest Asia Paper SPE 155454-MSMuscat OmanApril2012

[2] H Z Li J S Qin and D Y Yang ldquoAn improved CO2-oil

minimum miscibility pressure correlation for live and deadcrude oilsrdquo Industrial and Engineering Chemistry Research vol51 no 8 pp 3516ndash3523 2012

[3] A M Amao S Siddiqui and H Menouar ldquoA New Look atthe minimum miscibility pressure (MMP) determination fromslimtubemeasurementsrdquo in Proceedings of the SPE Improved OilRecovery Symposium SPE-153383-MS Tulsa Okla USA April2012

[4] C Cronquist ldquoCarbon dioxide dynamic miscibility with lightreservoir oilsrdquo in Proceedings of the 4th Annual US DOESymposium Tulsa Okla USA August 1977

[5] T Ahmed ldquoMinimum miscibility pressure from EOSrdquo inProceedings of the Canadian International Conference PaperSPE 2000-001 Calgary Canada June 2000

[6] Y Wang andM Franklin ldquoCalculation of minimummiscibilitypressurerdquo in Proceedings of the SPEDOE Improved Oil RecoverySymposium Paper SPE 39683-MS Tulsa Okla USA April 1998

[7] R K Srivastava and S S Huang ldquoNew interpretation techniquefor determining minimummiscibility pressure by rising bubbleapparatus for enriched-gas drivesrdquo in Proceedings of the SPEIndia Oil andGas Conference Paper SPE 39566-MS NewOethiIndia February 1998

[8] R A Harmon and R B Grigg ldquoVapor-density measurementfor estimating minimummiscibility pressurerdquo in Proceedings ofthe SPE Annual Technical Conference and Exhibition Paper SPE15403-PA New Orleans La USA October 1986

[9] W N Razak W A Daud A H Faisal et al ldquoMulti-componentmass transfer in multiple contact miscibility test forward andbackward methodrdquo in Proceedings of the SPEEAGE ReservoirCharacterization and Simulation Conference Paper SPE 125219-MS Abu Dhabi UAE October 2009

[10] M Nobakht S Moghadam and Y A Gu ldquoDetermination ofCO2minimum miscibility pressure from measured and pre-

dicted equilibrium interfacial tensionsrdquo Industrial and Engi-neering Chemistry Research vol 47 no 22 pp 8918ndash8925 2008

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

10 Journal of Chemistry

[11] PM Jarrell C E FoxMH Stein et al Practical Aspects of CO2

Flooding vol 22 of SPEMonograph Series Society of PetroleumEngineers Richardson Tex USA 2002

[12] F L Yang G-B Zhao H Adidharma B Towler and MRadosz ldquoEffect of oxygen on minimum miscibility pressure incarbon dioxide floodingrdquo Industrial and Engineering ChemistryResearch vol 46 no 4 pp 1396ndash1401 2007

[13] J I Lee ldquoEffectiveness of carbon dioxide displacement undermiscible and immiscible conditionsrdquo Report RR-40 PetroleumRecovery Institute Calgary Canada 1979

[14] W F Yellig and R S Metcalfe ldquoDetermination and predictionof CO

2minimum miscibility pressuresrdquo Journal of Petroleum

Technology vol 32 no 1 pp 160ndash168 1980[15] F M Orr Jr and C M Jensen ldquoInterpretation of pressure-

composition phase diagrams for CO2crude-oil systemsrdquo Soci-

ety of Petroleum Engineers Journal vol 24 no 5 pp 485ndash4971984

[16] O S Glaso ldquoGeneralized minimum miscibility pressure corre-lationrdquo Society of Petroleum Engineers journal vol 25 no 6 pp927ndash934 1985

[17] R B Alston G P Kokolis and C F James ldquoCO2minimum

miscibility pressure a correlation for impure CO2streams and

live oil systemsrdquo Society of Petroleum Engineers Journal vol 25no 2 pp 268ndash274 1985

[18] M K Emera and H K Sarma ldquoUse of genetic algorithmto estimate CO

2-oil minimum miscibility pressuremdasha key

parameter in design ofCO2miscible floodrdquo Journal of Petroleum

Science and Engineering vol 46 no 1-2 pp 37ndash52 2005[19] H Yuan R T Johns A M Egwuenu and B Dindoruk

ldquoImproved MMP correlations for CO2floods using analytical

gasflooding theoryrdquo SPE Reservoir Evaluation and Engineeringvol 8 no 5 pp 418ndash425 2005

[20] E M E-M Shokir ldquoCO2-oil minimum miscibility pressure

model for impure and pure CO2streamsrdquo Journal of Petroleum

Science and Engineering vol 58 no 1-2 pp 173ndash185 2007[21] B L Chen H D Huang Y Zhang et al ldquoAn improved

predicting model for minimum miscibility pressure (MMP) ofCO2and crude oilrdquo Journal of Oil and Gas Technology vol 35

no 2 pp 126ndash130 2013[22] B S Ju J S Qin Z P Li and X Chen ldquoA prediction model for

theminimummiscibility pressure of the CO2-crude oil systemrdquo

Acta Petrolei Sinica vol 33 no 2 pp 274ndash277 2012[23] J L Shelton and L Yarborough ldquoMultiple phase behavior in

porous media during CO2or rich-gas floodingrdquo SPE 5827

Society of Petroleum Engineers 1976[24] R K Srivastava S S Huang and M Dong ldquoLaboratory

investigation of Weyburn CO2miscible floodingrdquo Journal of

Canadian Petroleum Technology vol 39 no 2 pp 41ndash51 2000[25] J-N Jaubert L Avaullee and J-F Souvay ldquoA crude oil data bank

containingmore than 5000 PVT and gas injection datardquo Journalof PetroleumScience andEngineering vol 34 no 1ndash4 pp 65ndash1072002

[26] Z L Gao T M Yang J F Zhang et al ldquoCO2miscible displace-

ment and reservoir numerical simulation in block wen 184rdquoJournal of Jianghan Petroleum Institute vol 22 no 4 pp 61ndash622000

[27] G J Yuan J AWang Z L Zhou et al ldquoThe indoor experimen-tal study for CO

2floodingrdquo InnerMongolia Petroleum Chemical

industry vol 4 no 8 pp 94ndash96 2005[28] P Zhao Study on CO

2Flooding for Enhancing Oil Recovery

in Pucheng Shayixia Reservoir China University of Petroleum2011

[29] S Yang and R Bao ldquoResearch on increasing recovery efficiencyin Shayixia oil reservoir by CO

2miscible displacement agentrdquo

Advances in Fine Petrochemicals vol 13 no 10 pp 20ndash22 2012[30] P Li Study on injection-production system in low permeability

reservoirs in Jilin [PhD thesis] Daqing Petroleum InstituteHeilongjiang China 2009

[31] Y Zhang Study on CO2-EOR and geological storage in

Caoshe reservoir in Jiangsu [PhD thesis] China University ofPetroleum Beijing China 2009

[32] Y M Hao Y M Chen and H L Yu ldquoDetermination andprediction of minimum miscibility pressure in CO

2floodingrdquo

PetroleumGeology and Recovery Efficiency vol 12 no 6 pp 64ndash66 2005

[33] Y Xiong L Sun S L Li L T Sun F L Zhang and YWu ldquoExperimental evaluation of carbon dioxide injection forenhanced oil recovery in Liaohe light oil districtrdquo Journal ofSouthwestern Petroleum Institute vol 23 no 2 pp 30ndash32 2001

[34] X L Li P Guo H C Li et al ldquoDetermination of minimummiscibility pressure between formation crude and carbon diox-ide in Fan 124 block of Daluhu oilfieldrdquo Petroleum Geology andRecovery Efficiency vol 9 no 6 pp 62ndash63 2002

[35] X Yang Study on the MMP in gas-injection oil reservoirs [PhDthesis] Southwest Petroleum Institute Chengdu China 2003

[36] K Zhang Interfacial Characteristics and Application Researchon CO

2-Formation Oil System Institute of Porous Flow and

Fluid Mechanics Chinese Academy of Sciences 2011[37] Q Zheng L S Cheng S J Huang et al ldquoPrediction of themini-

mummiscibility pressure of CO2-flooding for low permeability

reservoirrdquo Special Oil andGas Reservoirs vol 17 no 5 pp 67ndash692010

[38] C Guo H Tang and L Zhang ldquoGlobal convergence for a classof conjugate gradientmethodsrdquo Journal ofOperational Researchvol 3 no 2 pp 46ndash49 1999

[39] J Bon H K Sarma and A MTheophilos ldquoAn investigation ofminimummiscibility pressure forCO

2-rich injection gaseswith

pentanes-plus fractionrdquo in Proceedings of the SPE InternationalImproved Oil Recovery Conference in Asia Pacific SPE-97536-MS Kuala Lumpur Malaysia December 2005

[40] J Bon M K Emera and H K Sarma ldquoAn experimental studyand genetic algorithm (GA) correlation to explore the effect ofnC5on impure CO

2minimum miscibility pressure (MMP)rdquo

SPE 101036 Society of Petroleum Engineers 2006[41] H Zhou Experimental study on CO

2miscible flooding in ultra

low permeability reservoir [PhD thesis] Daqing PetroleumInstitute Heilongjiang China 2008

[42] C Peng Feasibility assessment on CO2miscible flooding for

enhancing oil recovery in Gbeibe oil reservoirs [PhD thesis]Southwest Petroleum University Chengdu China 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Analytical ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of