Predicting the Viscosity of Hydrocarbon Liquid Phases From Their Composition

8/19/2019 Predicting the Viscosity of Hydrocarbon Liquid Phases From Their Composition

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. .

Predicting the Viscosity of Hydrocarbon

Liquid Phases From Their Composition

A, H. Houpeurt, SPE-AIME,ELF-RE

M. B. Thelliez, U. of Paris VI

Introduction

Routine laboratory measurements of viscosities at high

pressure and high temperatureare always expensive and

often inaccurate. When values are needed for many

pressure-temperature combinations, it is obviously de-

sirable to be able to calculate them instead of measuring

them.

A few years ago, the ELF-ERAP group decided to

elaborate on a method for determining, with appropriate

accuracy, the viscosity of hydrocarbon liquid phases.

A procedure for predicting the viscosities of hy-

drocarbon liquid phases from their composition is pro-

posed. It is similar to that used by Standing and Katzs

for determining the density of reservoir oils.

This work is based on 1,092 viscosity measurements

made on 23 mixtures for 479 pressure-temperature

combinations between 30 and 130“C and between 50

and 500 atm.

These measurements were made with a specially de-

signed capillary tube viscosimeter, The analysis of 289

measurements made on n-C4, n-C5, and n-Ca in the

same range of pressures and temperatures showed a

standard deviation of less than 0,0075.

Three conclusions were reached.

1. The kinematic viscosity, v (p,T), of a C4+at pres-

sure

p

and temperature

T

may be calculated from its

composition and the kinematic viscosities, Vf, of its

components atp and T using the equation

fogv

p,T = xxi iog

Vi p, T)

2. The absolute viscosity of different values of C4+at

any pressure and temperature, P p, T , may be calcu-

lated from their “standard” viscosities, W* (at 1 atm

and 2(F’C),using functions ofp and

T

that appear to be

independent of the nature of the Cq+.

3, ‘Theabsolute viscosity, Ph p, T , of a liquid phase

composed of a C4+ and light components (methane,

ethane, propane, carbon dioxide, and nitrogen) depends

only on the viscosity of that C4+at p and T, and on the

amount of each light component in the mixture,

A tentative correlation relating the standard viscosity

of a C4+to its average molecularmass is also presented.

Fig. I allcws the determination of ~c~+ p, T from

P*c~+and also contains the correlation ~*(R).

Fig. 2 is a new presentationof the results of Standing

and Katz, It is used to determine the densities of a C4+

that are needed for calculating its kinematic viscosities.

Fig. 3 presents the netw~rks for correcting the vis-

cosity of a C4+ when it is mixed with known amounts

of propane, ethane, methane, carbon dioxide, and

nitrogen.

The procedure was experimentallychecked using two

mixtures for 16 pressure-temperaturecombinations. An

average relative error of 0.0345 was obsemed, with a

maximum deviation of 0.08, but only a limited number

of k,eavycomponents were investigated.

Review of Ulterature

Refs. 1 through 4 present methods for determining the

viscosity of oils. All are based on compilations of avail-

able data and are very empirical.

When many pressure-temperature combinations are involved in predicting viscosities, it is

‘

desirable to be able to calculate them rather than to have to measure them. Here, a

procedure similar to that used to determine the density of reservoir oils is proposed for

.

predicting the viscosities of hydrocarbon liquid phuses from their composition.

.

FEBRUARY, 1976

223


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Basic Ideas

.

We tried to find more fundamental relations governing

the viscosities of the mixtures through a systematic (al-

though obviously limited) investigation of mixtures of

paraffins and of oils. We thougnt that the viscosity of

a liquid phase could be determinedby a method similar

to that used by Standing and Katzs for calculating its

density.

In short, a “standard density” was calculated for

the C4+. This figure was corrected successively for

the propane content of the Cs+, for the ethane content

of the C2+, and for the methane content of the Cl+.

The figure thus obtained was corrected for pressure and

temperature.

It was necessaryto ( 1)elaborateon a method for cal-

culating a standard viscosity of a C4+;(2) study the ef-

fect of the presenceof light paraffins (propane, ethane,

and methane}, carbon dioxide, and nitrogen; and (3)

correct the figures for pressure and temperature.

The experimental work showed that the correction for

pressure and temperature must be applied to the stand-

ard viscosity of the C4+and that this corrected figure

had to be revised for the amount of light paraffins and

other compounds present.

Laboratory Measurement.sof Absolute

Viscositks

An adequate viscosimeter was needed to measure the

viscosities in the large range of pressures, temperatures,

and viscosities that had been chosen, ‘l%isapparatus is

described in the Appendix.

Determining the Viscosity of a C4

Eyring’s theory, if applied to the viscosity of the

liquids, leads to the approximate expression

h NA

AFW

()

=~exp ~ .

. . . . . . . . . . . . . .

(1)

If the activation energies were actually additive in a

mixture, the following would result from Eq. 1:

logpv=xx,logp~l~~. . . . . . . . . . . . . . . ...0.(2)

Eq, 2 is equivalent to

logvfi=zx*logv*Mf. . . . . . . . . . . . . . . . . ...(3)

Fig.1 —viscosityof heavyliquidphaeasG+.

224 JOURNALOF PETROLEUMTECHNOLOGY


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Since the activation energies are not really additives, it

seemed possible to simplify Eq. 2 to

logp=xx/log ~,

..00..0 ..,,0.0,0,...0(4)

or to simplify Eq, 3 to

logv=zx~logv~,

. . . . . . .

..,,.,,..:..,6(5)

Since these equations were only approximate, it was

necessary to test them exp&imentally.

Eqs. 4 and 5 were tested with two different mixtures

of C,+ for 50 pressure-temperature combinations; the

compositions of the mixtures are given in the first and

last lines of Table 1. The comparison was favorable to

Eq. 5; the average experimental and calculated ‘:alues

were 0,01 and 0.024, respectively, using Eq. 5, and

0.029 and 0.041 using [email protected].

It was concluded that [email protected] couId lead to a conve-

nient calculation of the viscosity of a mixture of liquid

CA+

. “

Practica Use of Eq. 5

[email protected] may be used only if the kinematic viscosities of

the componentsare known in the range of pressures and

temperatures of interest.

As a preliminary part of the research, we collected

data for density and viscosity and selected the best val-

ues. This study showed the need for completing the

network of the viscosities for n-C4, n-C5, n-C6, and

n-C7, which was performed using the appwatus de-

scribed in the Appendix.

These data were published in a handbookGgiving

densities, absolute viscosities, and kinematic viscosities

between 50 and 500 atm and between 3(Yand 130 ‘C

for the first 10paraffins, carbon dioxide, and nitrogen,

When an oil field is discovered, measurements of its

viscosities and densities in the range of interest can be

included with the basic measurements. Consequently, it

was concluded that the published monographs and such

specific measurements allowed calculation of the vis-

cosity of any C4+at any pressure and temperature using

Eq. 5.

Structure and Use of Fig. 1

It seemed worthwhile to investigate the possibility of

avoiding the numerousmeasurementsof the viscosity of

the C,+ covering the range of pressure and temperature

that had been chosen, “

It is well known that C,+ with the same molecular

mass may behave very differently. It is obvious that the

degree of uncertaintyof the calculated values of the vis-

cosity of a C4-I.will reflect that of the viscosity of the

c, +

I twas decided to study first the kind of relations that

could exist between the viscosities of a given C4+ at

different pressuresand temperatures. A standard viscos-.

ity was defined as ~e true viscosity at 1atm and 20 “C,

written as

P (PJn = P* f(P) gw)

. . . . . . . . . . . . . . . . . . . . ( 6 )

In Eq. 6, K* is specific for the given CA+,but~ (p) and

g~) me, resp=tiveiy, functions of the pressure and the

temperature that are valid for any C4+.

Eq. 6 allows calculation of P* if Y (p,n is known.

It was determined that different values of P led to

FEBRUARY, 1976

the same value of A*, and that the value of P* fitted

with the true value of the viscosity in the standard

conditions.

Moreover, when many values of P* were compared

with the average molecular mass of the corresponding

C4+,it was concluded that a pr~tical correlation could

be established bptweenP* and M.

This comelati~n does not include the pure compo-

nents that were not included in Eq. 6, Moreover, if

many different C,+ had been used, it is likely that the

correlation would have been more compiex and that the

possibility of drawing different curves grouping dif-

ferent kinds of C,+ would have been noticed.

The correlation only offers a way to calculate an ap-

proximate value of the viscosity of a CA+when the only

data available on the C,+ are its molecular mass and

specific gravity. Obviously, it is much better to know

the true value of its standard viscosity and to use Fig. 1

after calculating the standard viscosity of the C4+using

Eq. 5.

The different way$of using Fig. 1 follow.

Use of Fig, 1 ‘ “

The correlation w*(R) is presented in the upper left-

hand comer of Fig, 1.

The value ofW*is corrected first for the pressure and

then for the temperature using the two networks irl the

central part’of the figure.

An additional and often useful correlation betweenM

and

p ,

a standard density at 20 ‘C and 1 atm, is given

in the lower right-hand comer of Fig. 1. It is extracted

from Fig, 2.

Use of Fig. 2 and Eq. 5

Two different methods are presented for determining

the absolute viscosity of a CQ+at any pressure and

[email protected] – Densityof liquidphases.

225


4/9

.,

temperature, They offer two different ways for checking

theresults given by Fig. 1 i%I.S,

Iogu = Zxiloglq ,

can be used to calculate the kinematic viscosity of a C4+

from the viscosities of its components, and we can de-

duce the absolute viscosity if we know the density.

@. S can be used both for the standard viscosities

and for the viscosities at any pressure and temperature.

The kinematic viscosities of Cf, Cs. and G at any

pressure and temperature are easily obtained from

previouslypublishedmaterial. The kinematicviscosityof

C,+ could be calculated from the absolute viscosity

if the density were known. The absolute viscosity is

known either through direct measurement, or through

Fig. 1 if the molecular weight of the C,+ is known. The

density of C,+ will be determined through Fig. 2, along

with the density of C4+, which is required to complete

the calculation.

Fig, 2 is a presentationof the results of Standing and

Katz5concerning the densities of the C4+ at any pres-

sure and temperature. The purpose of Fig, 2 is to save

time when applyingthe methodof Standing and Katz to

Eq. 5.

Examples

Caicuiate the viscosity of oil 1, whose composition is

given in Table 2, at 300 atm and 100‘C.

use

of h rt

From the composition, we first calculate

~c,+ = ~

X f ,s

253,7,

Through the comelationP* (B)* ~lg. 1 gives

L*~4+= 12.0

Cp,

Entering thisvaiue into the pressure-correctionnetwork

(going horizontally to the l-atm line, then vertically to

the 300-atm line), we get 19.3 cp.

Entering the temperature-correction network (going

horizontally to the 20 ‘C line, then verticallyto the 100

“C line), we get

PC4+

= 3.65

CF.

Use of Fig. 2 and Eq. 5

Table 3 contains the dataa needed for solving the prob-

lem. P* and V*are the actual values of P and v for the

bodies that are actuaily liquids at 300 atm and 100 ‘C.

.

. .

TI

226

Fig. 3 – Viscosity of

liquid

phasascontainingdisaolvadgases.

JOURNALFPETROLEUMECHNOLOGY


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TABLE 1- ~EITlON OF MVE$T’KJATEDmRES AND GENEnALDATAON W WASUFW%NTS

Bodbs (peroentMOW

Number of Numb. ’ of ?om~rature Pressure

Point*

CO* N* C,

Measuro-

Fy

l?:inm~

Ca C~ t% G Ca n+, CB H, H, H, P,?.

memta

—— .— —. .

——

5.0

11.5

46.7

53.3

73.8

%

65.7

9.6 35.2

1,354,0

17.6

20.1

82.4

79.9

10.s

89.6

20.5

10.8

21.5

34.6

30.1 1s.0

20.0 30.1

25.0 15.0 20.0

30.0 10.0 25.1

15.0520.0 30.0

4.3

05.7

10.4

69.6

95.0

5.6 23,9 19.9

4.9 5,0 24,7 10,0 15,1

4.0 3.5 3.8

For Cq, they were extrapolated from the values in the

liquid state.

Calculating P*cq+ instead of deducing it_from the

molecular weight through the correlation F*(M) of Fig.

1: Eq. 5, written for the standard viscosities, is

log V*C,+= x .q Iog V**.

For CT+,the correlationM*(R) of Fig. 1 gives

/L*c,+= 32.5 CF.

For C,+, the correlation p*(~) from Fig, 2 gives

/l*c,+ = 0.s47

gdcc,

and for C4+,

P*c,+ = 0.833

gin/cc.

so,

V*C7+

= 38.3 cSt.

Eq. 5 gives

V*C4+

= 14077‘cSt,

from which we calculate *cq+ = 12.3 cp, a value

that is different by only 0.02 from that given by Fig, 1

when applied directly to C4+.The result of the calcula-

tion is then the same as above,

Calculation

of PG.: Eq, 5, written for ,tie required

pressure and temperature, is

log VC4+ = x -q

log vi.

Its use requires the knowledgeof PC,+.

From Fig. 1, through the correlationP*(M), we get

~*~V= 32.S

Cp.

The pressure correction gives 53.5 cp, and the tempera-

ture correction leads to

&c,+= 7.4 Cp.

From Fig, 2, through the correlation p* Af , we get

p*c7+= 0.847 gdcc.

FE BRUARY,976

79.6

69,2

78.5

65.5

64.9

49.9

2::

34.95

88.5

44.6

40.9

68.7

3oto130 looto500

23 to 131

100 to 500

71,6 to 132 170 to 516

19to 130.2 103to 516

17,9 to 131,4 51

to

516

31.0

to

129.6 60 to 516

18.7 to 133.5 50 t o 516

19,2 to 132,2 50 to516

15,3 to 129,9 51 to 516

30.6 to 129.2 51 to 516

30.3 to 132.7 51 to516

30.5to 130.2 103to S 6

31.0 to 130.5 103 to 516

30.5 to 133.7 130 to 515

32.7 to 128.3 150to 515

32.7to 126.2 144to 515

33.4 to 123.6 102to 515

33.6 to 126.3 154to 515

33,0 to91.2 102 to 515

34.5 to 127.7 102to 515

.34,5to 130.5 217to 515

35.0 to 130.1 206to 515

35to 130 103 to 515

This becomes 0,865 after pressure correction. After the

temperature correction,

Pc,. = 0.810 gin/cc.

From this figure, we deduce

VC7+ 90.1 Cp,

and from Eq. 5,

Vc,+= 44.7 Cp.

Through the correlation p*(M), Fig, 2 gives

@cd+==0.833 grnicc.

Applying the pressure correction, we get 0.851; after

the temperature correction,

pq+ =

0.797

gmlcc,

The final value of ~cq+is

/.Lc4+ 3.56 Cp.

This value agrees well with the value deduced directly

from Fig. 1 and calculated above (3.65 cp), with the

discrepancy being less than 0.03.

Determining the Viscosity of a Lk@d Phase

Containing Light Paraffks, Carbon

Dioxide, and Nitrogen

Table 1 shows the composition of the different mixtures

investigated to evaluate the effect of light paraffins,

carbon dioxide, and nitrogen on the viscosity of a

liquid-phase.C4+, and to elabort’te on Fig. 3. It also

gives the number of pressure-temp..raturecombinations

for which the viscosity was measwed, the effective

number of measurementsmade (two or i??ree,as a rule,

for each combination), and the range of prmures and

temperaturescovered in each case.

Table 4 gives the molecular weight and the true den-

sity of the three oils (Hl, Hz, and H~) at 20 ‘C and

1 atm that were used as natural heavy components in

the experiment.

227


6/9

YAWE 2- COWO$lTlON Of OIL 1

Body _n-C4

n-cfi

n.CB

c,+

M,

56.12 ‘ K5 WY7

300. 0

x( 0.10

0.05

0.05

0.60

‘1’ABl. 3- vtSOOSITIESOF wC* n=CMAND tie

(FROM REF. 6)

~

n-C4 n-C6

n.cc

/&*

P

1,650 X 10-6 2,345 X 104 3,125 X 10d

“* &

2,650 x 104

3,750 x 10+

4,740 x 10-6

vSt

2,315 x 10-’

2,660 x 10-’

“3,460x 10-6

The effect of methane was examined for 110 combi-

nations of pressure, temperature, molar fraction, and

CT+.The effect of ethane was investigated in 48 combi-

nations, and that of propane was studied in 71 combina-

tions. The effect of mixtures of methane and ethane was

observed for 39 combinations of pressures, tempera-

tures, and compositions, and the effect of ternary mix-

tures of methane, ethane, and propane was studied for

57 combinations. Finally, the effects of nitrogen content

and carbondioxide were studied for 37 and 35 combina-

tions of the variables, respectively.

From these 839 viscosity measurements, we con-

cluded that the viscosity of a CA+,when mixed with

light components, depends on the components’ molar

fraction only. Figs, 4 through 8 show the experimental

correlation between the viscosity of such mixtures and

the viscosity of the Cq+, respectively, when the light

component is methane, ethane, propane, carbon di-

oxide, or nitrogen, They show that neither the pressure

nor the temperatureacts alone as a significant factor.

These experimental results justify the procedure for

calculating the viscosity of a liquid phase and the design

10

0.+

0.8

OJ*

0.6

0.5

0,4

z

SOJ

a.

0.2

0.1s

‘ i A/r I “’-”

~fllmllll

‘,l

0.2

0,3 0.4 0.S

M 0>

F .4 — Viscosity,p, of methane-oilmixturesas a function

? the “oil”viscosity,&Ii,andof the percentageofmethane.

TABLE 4- PROPERTIESOF 01Lf3

H,,H*,md Ha

oil $

He

F&

CJ%,motpercent

7

CtH1@mot percent

k;

:; 4.7

CA%%,mol percent

17.2

12.3

6.4

CM,* mol peroent

12.2 10?2

7.6

~+, mol parcent 64.4

70.7

78.5

~c7+, gm

143

190

235

M, gm

118 156

203

Density,gin/cc

at 20 “C,1 atm

0.726 0.774

0.812

Note: It Isaatlnutad that~ laknown with an

ccumcy of fived gltein the third

place,

I

of Fig. 3. This procedureis as follows.

The viscosity of the CA+at the required pressure and

temperature is first determined using Fig. 1 (Fig, 2 and

Eq. ”5 offer i-malternative method for checkjng the re-

sults). The figure thus obtained is then corrected suc-

cessively for the propane content of the C3+,,the ethane

content of the C2+and the methane content of the Cl+

using the three networks of Fig. 3.

The correction for the carbon dioxide is made using

the network located in the upper left-handcorner of Fig.

3; this network is quite similar to the three others. The

correction for the nitrogen is made through the correla-

tion presented in the lower right-hand corner of Fig. 3;

the viscosity, P, of the mixture is proportional to the

viscosity of the mixture without nitrogen, ~h, by a fac-

tor depending on the nitrogen content only, as proved .

by Fig. 8.

Fi~. 8 shows that the experimental relation between

P and/& is linear for a given content of nitrogen in the

mixture and that the slope of the strahzht line is not

dependent on this percentage.

,

9%

Smv.

1197,

h (C?)

‘%

5 — VkcOSltY,w of ethane-oilmixturesas a functionof

t e “oil” viscosity,&/Isand of the percentageof ethane.

228

JOURNALOF PETROLEUMTECHNOLOGY


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Examples

1. Table igivesth ecompositionof a complex mix-

ture containing methane, ethane, propane, butane, pen-

tane, hexane, and a C7+, We calculate the viscosity of

this mixture at 300

atm and 100 ‘C, The steps of the

calculation are as follows.

Calculating ~c,+ (by ~C4+ = Z xtMi),

m,

= 245.

From the correlation in Fig. 1,

p*(R) : /L*c,+= 10 1 Cp.

After pressure correction, this figure becomes 16.2 cp.

After temperature correction,

pQ+ = 3.30 Cp.

Using Fig, 3, for a content of 0.071 of propane,

wc& +

= 2.94

CP.

For a content of 0.096 of ethanc,

PQ?+

= 2,51 Cp.

For a content of 0.375 of methane,

PC,.

= l.llcp.

2. Calculate the viscosity (at 300 atm and 100“C) of

Oil 3, whose composition is given in Table 6. From the

COZ network, entering down with 1.11 cp, and then

going up to the 0.03 line and to the left toward the

scale, we get

Pcoz+

= 0.98 CP.

H=EE w

H=I=kP

0,}

0,1

0,1

p~.”.w)

[email protected] — Viscosity,P, of pro ane-dl mixtureses a function

of the’’oii” viecoaity,wh,an$of the peroentageof propane.

M

I I r

Q7 -

0,4

1

0 4

03

Q2

Q2

0.3 0.40> Q4Q70B 1.0

.5 20

ao 4.05,06s2zoao 10

Fig. 7 “—Viscosity,IA,of carbondioxide-oiimixturesae a

functionof the ‘“oil”viscosity, /i, andof the percentage

of carbondioxide,

1,(

0,1

04

O,J

0.4

0.s

0.4

%

; 0.3

0.2

O.1.s

0.

Oa 0.3

p~ c?

0, o.* 0.7 0.1O.*1.0

F@. 8 – Viscosity,p, of nitrogen-oilmixturesasa function

of the “oii” viscosity,w*,and of the percentageof nitrogen.

229

EBRUARY, 1976


8/9

CH4

C *H.

C3Hg

n-C4H0

n-CsHlz

n-Cti,4

c,+

TAoLE6. coMPoSll10NoF01L2

Molar

Molar Fraction

Fraction

M or~ of Cl in CI+l

0.3760

16.04

0.3750

000600

30.07 0.0960

0.0400 44;09

0.0710

0,0676

66.12

o.@300

72.16

0.0275 66.17

0.4000 297.00

NA=

Avogadro

number

p = pressure, attq

q = rate of flow of the pump, cc/see

r = radius of the capillary tube, cm

R =

constantof the perfect gases, erg

t = time, seconds

T =

temperature, “K

V= molar volume, cc

x{= molar fraction of component i

TABLE6 COMF02KiOU OF OtL 3

Oii2

0.9500

co*

0.0300

N,

0.0200

After the correction for the nitrogen content by a ratio

of 0.98 corresponding to a content of 0.02, we get

~h

= o Cp.

Check of the Method and Conclusions

Table 1 shows that two mixtures, the first containing

Nz, CI&, CZH6,and the oil H3, and the second conhin-

ing COZ,Ng,CH4, C2H13,nd C3H.S,and the same oil,

were investigated, each for 16 pressure-temperature

combinations, These experimental results were used to

check the method. The average discrepancies between

the calculated and experimental values were 0.024 and

0,045, respectively, with the maximum values being

0.076 and 0.08.

The question arose as to whether the heavy material

acts on the viscosity of the mixture through its own vis-

cosity only. If it does, we can hope that the correction

for the light components is valid for any type of heavy

material, and that only Fig. 1 would need some im-

provements if a more extensive experitpental study

showed that the pressure and temperature correction

chart for the C4+is not accurate enough in some cases

or that the correlation P*(E) would have to account

for a second parameter to cover very different heavy

materials.

If the heavy material does not act through its own

viscosity only, Fig. 3 also would lose its validity. How-

ever, we think that the intermolecular forces between

the heavy materirdsand the light ones are probably not

very dependent on the nature of the former as Iong as

only viscosity is concerned, This is because of the very

large difference in the sizes of the molecules of the light

components and that of the heavy material, which tends

to minimize the differertcesin the intermolecular forces

when the nature of this material is changed, and when

the complexity of the molecules is increased.

Nomenclature I

Au= cross-section of the branch of the U tube

connected to the top of the reception

cell, sq cm

A.= identificationfor the other branchof the U

tube, sq cm

g = gmvity$CmlSCC2.

h = Pkmck’s constant, erg/see

f = length of the capillary tube, cm

M = molecular mass, gm

R = average molecular mass, gm

230

y = location of the meniscus above its starting

point in the branch of the U tube

connected to the top of the reception

cell, cm

z

= identificationfor the meniscus in the other

branch of the U tube, cm

Ap = differencebetween the density of the

mercury and that of the fluid in the

operating conditions, gin/cc

AFp =

free energy of viscosity, erg

e = time constant =

8 PIIW r4 A pg,

Au Az/AM -i- Az, seconds

= absolute viscosity, cp

P* = standard absolute viscosity, cp

Pc,,+= absolute viscosity of a mixture, with the

lighter hydrocarbon being C., cp

PC02

= absolute viscosity of a mixture containing

some C02, cp

~h

= absolute viscosity of a mixture of

hydrocarbons with or without

hetero-elements, cp

v = Vktematicviscosity, stokes

p = density, grn/cc

Acknowhxlgments

We thank the ELF-ERAP Group for permission to pub-

lish this paper. We are deeply indebted to Gondouin,

Dlehl, and Zuravsky, who were in charge of the ex-

perimental work in the laboratories of GEOPETROLE,

and to Neoschil and Verrien (ELF-RE) for many sug-

gestions and contributions.

References

1.

2.

3.

4.

5,

6.

Beal, C.: “’llte Viscasityof Air, Water, NaturalGases, Crude OiI

and Its AssociatedGazes at OMieldTemperaturesandPressures.”

Trans., AIME (1946) 16S, 94-115.

Chew, J. N. and Connaiiy, C. A., Jr.: “A Viscosity Comelation

forGas-SaturatedCrudeOils,”’

Trans.,

AIME(1959)216,23-25.

Lohrenz, J., Brsy, B. G., and Clark, C. R.: “Calculating Vis-

cosities of Reservoir Fluids Fmm Their Compositions,” J. Pet.

Td.

Oct.964 1171-1176

rans., AIME, 231.

Little, J. E. and Kennedy, H. T.: “A Correlationof the Viscosity

of Hydrocarbon Systems with Pressure, Temperature, and Com-

tmsition,” Ser. Pet. EnR.J. (June 196S)157-16Z Trans., AfME,

M3.

Standing, M. B. astdKatz, D. L.: “Density of Crude Oiis Satu-

rated With NaturalGases.” Trans., AIME (1942) 146, 159-165.

CR@S-GEOPETROLE “Viscosity and Density of Light Paraf-

fins, Nitrogen and Carbon Dioxyde,” Techt@, cd.; 27 Rue

Wtoux, 75737 Paris. (Fuil-size copies of Figs. 1 through 3 are

now insertedin this book.)

APPENDIX

Fig. 9 shows a schematic of the viscosimeter. The vis-

cosimeter is composedof three vertical, cylindrical cells

and a two-cylinder mercury pump for dkplacing fluids

at a constant volume. The two cells on the right form a

JOURNALFPBTROLBUMTECHNOLOGY


9/9

seat

E

/

/

r-

two cylinders mercury pump

Fig 9 — Schematicof the viaoosimeter.

U tube whose bottom is connected to the right sid~ of

the pump; the cell on the left is divided into two rooms

by a seat that holds the capillary tube, One branch of

the U tube is conntictedto the upper room and the see-

ond branchis contteetedto the lower room. The bottom

of that cell is connected to the left side of the pump. As

mercury is displaced from the left side to the right side

of the pump, the cell receives the fluid pushed through

each branchof the U tube. ‘he reception cell and tbe U

tube are immerged in a thermostatic bath.

With the capillary tube in place, the cells are filled

with the liquid under pressure, and convenient amounts

of mercury are Iefl in the reeeption cell and in the U

tube. A bypass enables the operator to equilibrate the

levels of the interfaces in the two branches of the U

tube.

When the thermostaticbath is at the correct tempera-

ture, the pressure is adjusted to its correct value and

measurement is started. When the pump is running at a

constant rate, pushing the mercury into the U tube, the

two interfacesare not rising at first at the same velocity;

the friction in the capillary tube restricts theiflow in the

FEBRUARY,1976

?

~. 10 – Locationof the meniscusvstime in the two

branchesof the U tube for givemvaluesofEland q.

branch that is connected to the top of the reception cell.

The hydrostatic pressure that is thus created will pro-

gressively counterbalance the pressure 10S in the capil-

lary tube, and, after some time, the two meniscusrise at

the same constant velocity (Fig. 10).

Each branch of the U tube holds five electrodes for

recording the displacement of the meniscus. These data

are treated by the least-squares method to get the two

coefficients of the two straight lines corresponding to

the movementof the two meniscus, The commoii slope

of these lines gives the rate of flow through the capil-

lary tube, and the difference betwpen the two constant

terms gives the hydrostatic head pushing the fluid, It is

easy to calculate the viscosity then.

When the preselected values of the radius of the

capillary tube and the rate of flow are convenient, “

the steady flow is obtained before the meniscus touch

the lower electrode in each tube. When the preselected

values are not convenient, the two slopes are different

and the operator is, thus, instantaneous]y informed. It

is nevertheless theoretically possible to calculate the

viscosity from therecordeddata using instantaneous val-

ues of the slope and of the difference of the ordinates,

but such a procedure involves many opportunities of

miscalculation.

With the apparatus working automatically, personal

errors are eliminated and time is saved.

It was experimentally found that the standard devia-

tion was less than 0.0075.

SPT

Original manuscript raoeivadirrStXiety of Petroleum Eng[nwra office July 13,

1974. Paper acwpfed for publication Maii 16,1976. ReMaedmanuecrlpt reoelved

NOW.7, 1975. Paper (SPE S0S7)waa fkat ~reaented at the SPE-AIME 49th Annual

Fall Meeting, held In Houefon, Or%S-9, 1974. @ Oopyrtght197S ArnerioanIrrafi.

tute of Mlnlng, Metallurgical, &mdPatmleum Englneara, hrc.

This paper will be Inoluded In the 1976 Trenaaotlonsvolume.

231

Documents

Predicting the Viscosity of Hydrocarbon Liquid Phases From Their Composition