Dolomite Emulsified Acid

Reaction of Emulsified Acids With DolomiteM.A. Sayed, SPE, H.A. Nasr-El-Din, SPE, and H. Nasrabadi, SPE, Texas A&M University

Summary

Emulsified acids have been used in the oil field for many years.They are retarded systems that can be used effectively in stimula-tion of carbonate reservoirs. Emulsified acids have been used pri-marily in acid fracturing and matrix acidizing. The delayed natureof emulsified acids is useful in generating longer etched fracturesor deeper wormholes. To predict the penetration depth of thewormholes or the length obtained from an acid-fracturing treat-ment, diffusion-coefficient values need to be estimated.

This paper discusses the reaction kinetics of dolomite diskswith emulsified acids formulated using a cationic emulsifier. Theemulsified acid systems were prepared using 15 wt% HCl and 0.7acid volume fraction. The emulsifier concentration was variedfrom 0.5 to 2.0 vol%. Emulsified-acid reaction rates and, hence,acid diffusivity were measured using a rotating disk apparatus at230F. Disk-rotational speed was varied from 100 to 1,500 rev/min. Samples of the reacted acid were collected and analyzedusing the inductively coupled plasma (ICP) mass spectrometry tomeasure calcium and magnesium concentrations.

The dolomite core samples reacted slowly with emulsifiedacid. Emulsions with low emulsifier concentrations (0.5 vol%)had average droplet sizes of 8.118 lm and achieved a diffusioncoefficient of 1.413108 m2/s. While emulsions prepared withhigher emulsifier concentration (2.0 vol%) had a smaller dropletsize (2.82 lm), they achieved a diffusion coefficient of8.3671010 cm2/s. Reaction of dolomite with emulsified acid at230F was found to be mass-transfer limited. Compared with cal-cite, the dissolution rate of dolomite in emulsified acids was lowerby one order of magnitude, and the diffusion coefficient of acidwas lower by two orders of magnitude.

Introduction

Acid-stimulation treatments in carbonate reservoirs involve injec-tion of an acid to dissolve the rock in order to increase the produc-tivity (or injectivity) of oil, gas, or water wells. A number ofmodels can be used to predict the distance to which the acid pene-trates and the amount of rock that will be dissolved and removedby acids (Nierode et al. 1972; Roberts and Guin 1975; Gdanskiand Lee 1989; Ben-Naceur and Economides 1989; Lo and Dean1989).

Of the two dominant carbonates present in oilfield reservoirs,calcite and dolomite, calcite dissolution has received considerablework (Nierode and Williams 1971; Lund et al. 1975; Busenbergand Plummer 1986; Chou et al. 1989; Fredd and Fogler 1997,1998; Alkattan et al. 1998; Taylor et al. 2003, 2004a, 2006; Nasr-El-Din et al. 2008; Rabie et al. 2011, 2012), while there havebeen fewer studies devoted to dolomite (Lund et al. 1973; Busen-berg and Plummer 1982; Herman and White 1985; Chou et al.1989; Wollast 1990; Anderson 1991; Orton and Unwin 1993). Inthe case of acid dissolving minerals [e.g., hydrochloric acid (HCl)with limestone and dolomite], the solid/liquid reaction processinvolves three steps: diffusion of liquid phase to the rock, reactionat rock surface, and diffusion of reaction products into the bulksolution (Lund et al. 1973). The slowest step will control the reac-tion. Mason and Berry (1967) indicated that the rate of dissolutionof dolomite in HCl at 25C is slow compared with that of marble,

while at 100C, both of them showed rapid dissolution rates. Theysuggested that the dissolution of dolomite at low temperatures issurface-reaction limited, while at high temperatures is diffusionlimited.

Lund et al. (1973) used a rotating-disk reactor to determinewhether the dissolution of dolomite in regular HCl is reaction lim-ited, diffusion limited, or in between. They conducted a series ofexperiments using dolomite at temperatures of 25 to 100C, withan acid concentration ranging from 0.01 to 9.0 g mol/L, and diskrotational speeds from 50 to 500 rev/min. They found that thereaction was surface-reaction limited at 25 and 50C, while at100C the reaction was almost diffusion limited.

Busenberg and Plummer (1982) investigated the dissolutionkinetics of dolomite rocks over a range of pH (0 to 10), CO2 pres-sure (0 to 1 atm), and temperature (1.5 to 65C). Herman andWhite (1985) studied the effect of lithology and fluid-flow veloc-ity on the kinetics of dolomite dissolution. They tested differentstoichiometric dolomite specimens using a rotating disk. Ander-son (1991) measured the reactivity of San Andres dolomite withregular HCl. Different dolomite samples and a rotating-disk appa-ratus were used to study rock/acid dissolution rates. The disk-rota-tional speed was 120 rev/min, test time was 5 minutes, andtemperatures were 80 and 120F. Anderson (1991) concluded thatdifferent dolomites may have dramatically different surfacekinetics. Li et al. (1993) used the rotating disk to measure thereaction of dolomite rocks with emulsified acid at 116F. Theymeasured a flux that was 10 times smaller than that obtained usingregular acid. Gautelier et al. (1999) measured the dissolution ratesof dolomite at 25, 50, and 80C, for disk-rotational speeds rangingfrom 210 to 1,000 rev/min, and at pHbulk between 0.39 and 4.44using a rotating-disk mixed-flow reactor. The overall dissolutionprocess was found to be surface-reaction limited at pHsurf < 1, butthe effect of diffusional transport becomes increasingly significantwith increasing pH.

Taylor et al. (2004b) measured acid-reaction rates of a deepdolomitic gas reservoir in Saudi Arabia using a rotating-disk ap-paratus. Measurements were made from room temperature to85C and at disk-rotational speeds ranging from 100 to 1,000 rev/min for acid concentrations of 0.05 to 5N of regular HCl (0.2 to17 wt%). Measurements showed that dissolution rates changed asthe reservoir rock varied from 3 to 100 wt% dolomite. At graindensities near 2.83 g/cm3 (expected for pure dolomite), rock-dis-solution rates were higher than that observed with pure-dolomiticmarble. Reaction rates depended on the rock mineralogy and thepresence of trace amounts of clays.

The reaction of dolomite with regular HCl was studied beforeat temperatures up to 100C. Also, reaction of emulsified acidwith calcite was studied. To the best of our knowledge, only Liet al. (1993) measured the reaction rate of dolomite and emulsi-fied acid. In the present work, the reaction between emulsifiedacid and dolomite rock was studied by use of a rotating-disk appa-ratus at a temperature of 230F and disk-rotational speeds up to1,500 rev/min. A cationic emulsifier was used to prepare emulsi-fied acids, which can be used in stimulating deep wells drilled incarbonate reservoirs. All emulsified-acid systems were formulatedat 0.7 acid volume fraction.

Experimental Studies

Materials. The emulsified acids were prepared using diesel, anemulsifier, a corrosion inhibitor, and an acid solution (HCl andwater). In all the emulsion preparations, the same source of dieselwas used. The diesel density, viscosity, and surface tension weremeasured at 77F. A sample of the diesel was analyzed using a

Copyright VC 2013 Society of Petroleum Engineers

This paper was accepted for presentation at the SPE International Symposium andExhibition on Formation Damage Control held in Lafayette, Louisiana, 1517 February 2012,and revised for publication. Original manuscript received for review 15 June 2012. Revisedpaper received for review 24 January 2013. Paper peer approved 25 January 2013 as SPEpaper 151815.

164 May 2013 Journal of Canadian Petroleum Technology

gas chromatograph in order to determine the composition of thediesel. Table 1 provides the specifications and results of the gaschromatograph analysis of the diesel used to prepare emulsifiedacids. Deionized water, obtained from a water purification system,which has a resistivity of 18.2 MX cm at room temperature, wasused to prepare acid solutions. HCl (ACS grade) was titratedusing 1-N sodium hydroxide solution, and the HCl concentrationwas found to be 36.8 wt%. A corrosion inhibitor was added to theacid solution, while the emulsifier was added to the diesel.

Disk Preparation. Dolomite cores, from a local company, wereobtained as 6-in. long cores with a 1.5-in. diameter. Rock compo-sition was determined by X-ray fluorescence (XRF). Elementalanalysis showed that the dolomite contained more than 94 wt%calcium, magnesium, carbon, and oxygen. Tables 2 and 3 givethe XRF results of the two dolomite core samples, and the cal-cium/magnesium ratio, respectively. In Table 3, the calcium/mag-nesium molar ratio is nearly 1.20. The calcium/magnesium molarratio is larger than unity, which indicates the dolomite cores maycontain calcite. Disks with a diameter of 1.5 in. and a thickness of0.75 in. were cut and tested using the rotating-disk apparatus. Theporosity of all core plugs was measured and was found to be inthe range of 4.2 to 6.9 vol%. The porosity was then used to calcu-late the initial surface area of the disk.

Acid Preparation. Preparation of the emulsified acid wasaccomplished in a systematic method to warrant the reproducibil-ity of the results. The ACS-grade HCl (36.8 wt%) was diluted to15 wt% by adding distilled water. Then, a corrosion inhibitor wasadded to the acid such that the final corrosion-inhibitor concentra-

tion was 0.3 vol%. The emulsifier (at varying concentrations) wasadded to the diesel and was mixed using a magnetic stirrer. Then,HCl solution was added slowly to the diesel solution using a sepa-ratory funnel and mixing was performed at a high constant speed.The final volume of the emulsion was 500 mL, at an acid/dieselvolume ratio of 70:30. The electrical conductivity of the finalemulsion was measured in a conductivity meter (Marion L, ModelEP-10) to confirm the quality of the final emulsion. If the electri-cal conductivity is nearly zero, then we have a good emulsifiedacid; otherwise, the mixing time was increased to 60 minutes atthe maximum possible speed.

Equipment. Reaction-rate experiments were performed using arotating-disk apparatus (Fig. 1). All acid-wetted surfaces weremanufactured by Hastelloy. The rotating-disk apparatus consistsof an acid reservoir, reaction vessel, gas-booster system, heaters,associated pressure regulators, valves, temperature and pressuresensors, and displays. The reactor and reservoir vessels wereheated up to the desired temperature. After stabilizing the temper-ature in both vessels, the emulsified acid was transferred from thereservoir to the reactor, and the reactor pressure was adjusted to1,100 psi, in order to keep the CO2 in solution. Then, the diskrotation was started, and during the experiment, small samples(approximately 3 cm3) were collected periodically from the reac-tion vessel through the sampling valve. The samples, containedemulsions, were left to separate, and after separation, a small sam-ple of the aqueous phase was drawn by use of a syringe anddiluted in order to measure the calcium and magnesium concen-trations using the ICP mass spectrometry (optical emission spec-trometer, Optima 7000 DV).

Some of the reaction-rate experiments were repeated severaltimes to assess the reproducibility of the collected data. For emul-sified acid formulated using 1.0 vol% emulsifier at 230F, twoexperiments were performed for disk-rotational speeds of 300 and1,000 rev/min. The maximum relative error was calculated as theratio of the absolute difference between the original and repeatedvalues to the original value. The maximum relative error did notexceed 3.1%, and this indicates good reproducibility of the datacollected using the rotating-disk apparatus.

A high-pressure/high-temperature rheometer was used tomeasure the viscosity of live emulsified acids under different con-ditions. The wetted material was HastelloyVR C-276, an acid-resistant alloy. The rheometer can perform measurements at varioustemperatures up to 500F over shear rates of 0.00004 to 1870 s1.A B5 bob was used in this work, which required a sample volumeof 52 cm3. The test was applied by varying the shear rate from 1.0to 1000 s1.

TABLE 1PROPERTIES AND COMPOSITION OF THE DIESEL

USED TO PREPARE EMULSIFIED ACIDS

Density at 77F 0.82 g/cm3

Viscosity at 77F 2.9 cp

Surface tension at 77F 27.7 dyne/cm

Component Concentration (wt%)

Cyclobutane, ethenyl- 5.01

Decane 7.32

Undecane 6.37

Dodecane 8.18

Tridecane 9.29

Decane, 2,3,5-trimethyl- 8.58

Pentadecane 10.17

Hexadecane 10.16

Heptadecane 8.76

Octadecane 7.60

Nonadecane 6.20

Eicosane 4.98

Heneicosane 4.57

Docosane 2.15

Octacosane 0.67

TABLE 2ELEMENTAL ANALYSIS OF TWO DOLOMITE

CORES USING THE XRF TECHNIQUE

Concentration (wt%)

Element Sample # 1 Sample # 2

O 51.3 48.5

Ca 22.7 21.8

C 12.6 11.6

Mg 11.6 10.3

Si 0.533 3.29

Na 0.458 2.32

Al 0.235 0.837

Fe 0.204 0.489

K 0.16 0.273

Cl 0.0779 0.252

S 0.0475 0.18

Mn 0.0196 0.0155

Sn 0.0112 0.0112

Total 100.03 99.9963

TABLE 3CALCIUM/MAGNESIUM MOLAR RATIO IN

DOLOMITE ROCKS USED IN THE STUDY*

Sample # Element Moles Molar Ratio of Ca/Mg

1 Ca 0.567 1.174

Mg 0.483

2 Ca 0.545 1.270

Mg 0.429

* Calcium/magnesium molar ratio in pure dolomite should be 1.0.

May 2013 Journal of Canadian Petroleum Technology 165

Droplet-Size Measurements. The droplet-size distribution wasmeasured using a Zeiss Axiophot microscope. Images were ana-lyzed using ImageJ software (Abramoff et al. 2004). This micro-scope can measure particles as small as 0.03 lm. A fluorescencemicroscope uses the phenomena of fluorescence and phosphores-cence instead of, or in addition to, reflection and absorption. Asample is illuminated with a light of a particular wavelength,which causes fluorescence in the sample. The light emitted by fluo-rescence, which is at a different and longer wavelength than that ofthe illumination, is then detected through a microscope objective.

Results and Discussion

Droplet-Size Distribution of Emulsified Acids. The averagedroplet size of the emulsified acid system has been measuredbefore (Guidry et al. 1989; Al-Anazi et al. 1998; Al-Mutairi et al.2009). Table 4 lists the measured average droplet size of theemulsified acid systems used in these studies.

The acid volume fraction was 0.7, and the emulsifier concentra-tion was varied from 0.5 to 2.0 vol% (5 to 20 gallon/thousand gal-lons). A small sample of each emulsified acid system wasexamined using the Zeiss Axiophot microscope in order to measurethe droplet-size distribution of acid droplets. The photomicrographsof the emulsified acids prepared using emulsifier concentrations of0.5, 1.0, and 2.0 vol% are shown in Figs. 2a through 2c, respec-tively. As the emulsifier concentration was increased from 0.5 to2.0 vol%, the droplet size of the emulsified acid decreased. Thephotomicrographs were analyzed using ImageJ software (Abramoffet al. 2004), and the droplet size of emulsified acid was measured.The droplet-size distributions of the three emulsified acid systemsare shown in Figs. 3a through 3c. The droplet-size distribution ofemulsified acid systems formulated at 2.0 vol% emulsifier showsthe classical bell-curve shape of a normal distribution. For emulsi-fied acids prepared using 0.5 and 1.0 vol% emulsifier, the droplet-size distribution of emulsified acid is not symmetric, and the distri-

bution is negatively skewed. The average, median, standard devia-tion, and errors with 95% confidence limits of these distributionsare presented in Table 5. The photomicrographs and droplet-sizemeasurements showed that as the emulsifier concentrationincreased from 0.5 to 2.0 vol%, the average droplet size decreasedfrom 8.1 to 2.8 lm, which indicates that emulsifier concentrationhas a great effect on the average droplet size and droplet-size distri-bution of the produced emulsions. These results are in agreementwith what was noted by Al-Mutairi et al. (2009).

Viscosity of Emulsified Acids

Because the emulsified acid is a non-Newtonian shear-thinningfluid (Al-Mutairi et al. 2009), the rheological parameters are im-portant in determining and studying the acid diffusivity. Theapparent viscosity of the emulsified acid was measured at shearrates up to 1000 s1. Fig. 4 shows the effect of increasing theshear rate on the apparent viscosity of the emulsified acid systemat 230F. These data can be represented by a straight line on thelog-log plot, indicating a non-Newtonian shear-thinning behav-iour that can be fitted using a power-law model. The power-lawmodel is given by Eq. 1:

la K _cn1; 1

where K is the power-law consistency factor, g/cm s(n2); n is thepower-law index; la is the fluid apparent viscosity, poise; and _c isthe shear rate, s1.

Table 6 gives the values of K and n for the 15 wt% HCl emul-sified acid samples prepared using 0.5, 1.0, and 2.0 vol% emulsi-fier and measured at 230F.

The apparent viscosity of emulsified acid prepared using 1.0vol% emulsifier after the reaction of emulsified acid with dolo-mite was studied. At the end of the rotating-disk experiment per-formed at disk-rotational speed of 1,000 rev/min, a sample of theremaining emulsified acid in the reactor was drawn and cooled to75F. The apparent viscosity of the drawn sample was measuredas a function of the shear rate. Then, the measured apparent vis-cosity was compared with the apparent viscosity of emulsifiedacid before the reaction. Fig. 5 shows the comparison of the appa-rent viscosity of emulsified acid measured at a temperature of75F before and after the reaction with dolomite. There is a goodagreement between the apparent viscosity of emulsified acid afterand before the reaction with dolomite, which means that there isno significant change in the emulsified-acid apparent viscosity,indicating the stability of the emulsified acid.

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

CompressedNitrogen Gas

HeatingJacket

SamplingTube

HeatingJacket

To Drainage

SampleCollector

Vent Lines

AcidReservoir

Reactor

Fig. 1A schematic of the rotating-disk apparatus.

TABLE 4AVERAGE DROPLET SIZE FOR EMULSIFIED ACID

SYSTEMS PUBLISHED BY OTHER AUTHORS

Authors Average Droplet Size

Guidry et al. 1989 0.2 mm

Al-Anazi et al. 1998 77 lmAl-Mutairi et al. 2009 6 to 12.4 lm


Reaction Rate of Emulsified Acid With Dolomite

Determination of Emulsified-Acid/Dolomite Reaction Rate.Samples were withdrawn from the reactor every minute for a totaltime of 10 minutes. The concentrations of calcium and magne-sium ions in each sample were measured using the ICP mass spec-trometry Because the XRF analysis indicated that the coresamples contain calcite, the dissolution rate will be obtained usingthe data measured for magnesium ions. The dissolution rate isthen obtained by dividing the slope of the best-fit straight line bythe initial surface area of the disk with use of Eq. 2:

RDh 1

A0

dMgdt

; 2

where RDh is the initial dissolution rate, and A0 is the initial sur-face area of the disk, which equals

A0 Ac

1 / ; 3

where Ac is the disk cross-sectional area and / is the initial poros-ity of the disk (as a volume fraction).

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

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

(b) 1.0 vol% Emulsifier(a) 0.5 vol% Emulsifier

(c) 2.0 vol% Emulsifier

Fig. 2Droplet-size distributions of emulsified acid systems (40X objective: 0.0960 micrometres per pixel).

00 1

Fre

quen

cy,%

Acid-Droplet Size, m2 3 4 5 6 7 8 9 10

11 12 13 14 15

51015202530354045

(a) 0.5 vol% emulsifier concentration

(b) 1.0 vol% emulsifier concentration

(c) 2.0 vol% emulsifier concentration

00 1

Fre

quen

cy,%

Acid-Droplet Size, m2 3 4 5 6 7 8 9 10 11 12 13 14 15

5101520253035

00 1

Fre

quen

cy,%

Acid-Droplet Size, m2 3 4 5 6 7 8 9 10 11 12 13 14 15

10

20

30

40

50

60

Fig. 3Droplet-size distributions of emulsified acids preparedat three emulsifier concentrations.

TABLE 5STATISTICAL ANALYSIS OF THE DROPLET-SIZE

DISTRIBUTIONS FOR EMULSIFIED ACID SYSTEMS USED IN

THE PRESENT STUDY

Emulsifier

Concentration

(vol%)

Average

Droplet

Size (lm)

Median

Droplet

Size (lm)

Standard

Deviation

(lm)

0.5 8.160.28 7.9 1.3

1.0 6.960.36 6.5 2.0

2.0 2.860.17 2.7 0.9


Figs. 6 and 7 show the change of the calcium and magnesiumconcentrations as a function of the reaction time, respectively,when dolomite reacted with 15 wt% HCl emulsified acid preparedusing 1.0 vol% emulsifier. The calcium and magnesium concen-trations increased as the disk-rotationalal speed was increased. Asthe disk-rotational speed was increased, the transport of the aciddroplets to the surface of the disk was enhanced, leading to fasteroverall reaction rate. Fig. 8 shows a plot of the amount of magne-sium liberated as a function of time for 15 wt% HCl emulsified

acid system at 230F and 750-rev/min disk-rotational speed fordifferent emulsifier concentrations. Fig. 8 indicates that the dis-solution of dolomite decreased as the emulsifier concentrationincreased. Table 7 gives the reaction rate as a function of thedisk-rotational speed for different emulsifier concentrations.

The emulsified acid-reaction-rate experiments were repeatedat disk-rotational speeds of 300 and 1,000 rev/min to determinethe reproducibility of the measured data. Two additional experi-ments were performed at each disk-rotational speed to assess therepeatability and data reproducibility. Fig. 9 shows the amount ofmagnesium liberated as a function of reaction time for emulsifiedacids formulated at 1.0 vol% emulsifier and for disk-rotationalalspeeds 300 and 1,000 rev/min. Table 8 shows the reaction rateobtained as a function of the disk-rotational speed for the originaland repeated tests. As shown in Table 8 and Fig. 9, the maximumrelative difference was less than 3.1% and the data measuredshow good reproducibility of the results.

The plot of the reaction rate vs. the disk-rotational speed to thepower [1/(1n)], where n is the power-law index (Table 6), is usedto study the effect of the disk-rotational speed on the dissolutionrate and to determine the boundary between the mass-transfer-lim-ited regime and the surface-reaction-limited regime. Fig. 10 shows

11 10

Shear Rate, s1

App

aren

t Vis

cosi

ty, c

p

100 1000

10

Y = 58.77x0.249

R2 = 0.9759

Y = 1734.1x0.62

0.5 vol% Emulsifier

1.0 vol% Emulsifier

2.0 vol% Emulsifier

R2 = 0.9887

Y = 544.39x0.528

R2 = 0.9573100

1000

10000

230F, = 0.7,15 wt% HCl

Fig. 4Effect of shear rate on the apparent viscosity of emulsified acids at 230F.

TABLE 6POWER-LAW PARAMETERS FOR EMULSIFIED

ACIDS AT 230F

Emulsifier

Concentration

(vol%) K (mPasn)Power-Law

Index (n)

0.5 58.77 0.751

1.0 544.39 0.472

2.0 1734.1 0.38

10

100

1000

10000

App

aren

t Vis

cosi

ty, c

p

0.1 1 10 100

Before After

1000Shear Rate, s1

75F, = 0.7, 15 wt% HCl1.0 vol% Emulsifier

Fig. 5Apparent viscosity of emulsified acid before and after the reaction with dolomite.


00 2

Time, minutes

Ca

Coc

entr

atio

n, m

g/L

4 6 8 10 12

200

400

600

800

100 rev/min

500 rev/min

1000 rev/min

300 rev/min

750 rev/min

1500 rev/min

1000

1200

= 0.7, 15 wt% HCl, 230F, 10 minutes of Contact Time

Fig. 6Calcium concentration as a function of time for reaction between emulsified acid (1 vol% emulsifier) and dolomite at 230F.

00 2 4 6 8 10 12

50

100

150

200

250

300

350

400

450

500

Time, minutes

Mg

Coc

entr

atio

n, m

g/L

100 rev/min

500 rev/min

1000 rev/min

300 rev/min

750 rev/min

1500 rev/min


Fig. 7Magnesium concentration as a function of time for reaction between emulsified acid (1 vol% emulsifier) and dolomite at230F.

00 2 4 6 8 10 12

50

100

150

200

250

Time, minutes

Mg,

mg

0.5 vol% Emulsifier

1.0 vol% Emulsifier

2.0 vol% Emulsifier


Fig. 8Amount of magnesium liberated as a function of time for reaction of emulsified acid and dolomite at 750 rev/min and 230F.


TABLE 7DISSOLUTION RATES (in g mol/cm2s) OF DOLOMITE WITH EMULSIFIED ACIDS AT VARIOUSDISK-ROTATIONAL SPEEDS

X (rev/min)Emulsifier

Concentration (vol%) 100 300 500 750 1,000 1,500

0.5 5.70107 8.06107 8.97107 1.03106 1.19106 1.53106

1.0 4.51107 6.734107 7.58107 9.57107 1.12106 1.23106

2.0 4.82107 5.23107 5.54107 5.94107 6.26107 7.29107

0

50

100

150

200

250

0 2 4 6 8 10 12Time, minutes

Mg,

mg

300 rev/min300 rev/min(2)1000 rev/min(2)

300 rev/min(1)1000 rev/min1000 rev/min(2)

= 0.7, 15 wt% HCl, 230F,10 minutes of Contact Time

Fig. 9Amount of magnesium liberated as a function of time for reaction between emulsified acid (1 vol% emulsifier) and dolomiteat 230F for disk-rotational speeds of 300 and 1,000 rev/min.

TABLE 8DISSOLUTION RATES (in g mol/cm2s) OF DOLOMITE AT DISK-ROTATIONAL SPEEDS OF 300 AND 1,000 REV/MIN

X (rev/min) 300 300 (1) 300 (2) 1,000 1,000 (1) 1,000 (2)

Dissolution Rate (g mol/cm2s) 6.734107 6.929107 6.947107 1.120106 1.124106 1.131106

0

Y = 6.474x108x + 3.035x107

0.00x10

2.00x107

4.00x107

6.00x107

8.00x107

1.00x106

1.20x106

1.40x106

1.60x106

1.80x106

5

Dis

solu

tion

Rat

e, g

mol

/cm

2 .s

10 15 20

1/(1+n), (rad/s)1/(1+n)25 30 35 40

0.5 vol%

1.0 vol%

2.0 vol%

45

R2 = 9.804x101

Y = 3.394x108x + 2.937x107

R2 = 9.930x101

Y = 7.1305x109 x + 4.3392x107

R2 = 9.8074x101 = 0.7, 15 wt% HCl, 230F, 10 minutes of Contact Time

Fig. 10Effect of disk-rotational speed on the dissolution rate of dolomite at different emulsifier concentrations.


the reaction rate as a function of the disk-rotational speed (rad/s) tothe power [1/(1n)]. It is apparent that as the emulsifier concentra-tion was increased, the reaction rate decreased. This reduction inthe reaction rate occurred because higher loads of emulsifier cre-ated emulsified acids with smaller acid-droplet sizes (Table 5),resulting in higher viscosity (Fig. 4) and therefore lower acidmobility.

For emulsified acid formulated at 0.5 vol% emulsifier, the dis-solution rate increased as the disk-rotational speed increased up to1,500 rev/min, which indicates that the reaction of emulsified acidand dolomite is mass-transfer limited. The dissolution rate in-creased in a linear fashion with an increase in the disk-rotationalspeed raised to the power [1/(1n)], where n 0.751 (Table 6).Using these data, the diffusion coefficient of emulsified acid canbe determined by use of Eq. 4 (de Rozieres et al. 1994):

R "/n K

q

13n1

r1n

3n1x1

n1D23#Cb 4

or

R Ax1

1n; 5

where Cb is the reactant concentration in the bulk solution, g mol/cm3; D is the diffusion coefficient, cm2/s; K is the power-law con-sistency factor (g/cm sn2); n is the power-law index; r is the ra-dius of the disk, cm; R is the rate of reaction (g mol/cm2 s); q isthe fluid density, g/cm3; x is the disk-rotational speed, s1; ande(n) is a function that depends on n (Table 9).

For certain initial bulk concentrations, plotting the initial rateof reaction vs. the disk-rotational speed to the power [1/(1n)]should yield a straight line with Slope A (Eq. 5), which is propor-tional to the diffusion coefficient raised to the power (2/3).

With increasing the emulsifier concentration to 1.0 vol%, thereaction rate between emulsified acid and dolomite rocks de-creased. As shown in Fig. 10, the dissolution rate of dolomiterocks increased as the disk-rotational speed increased up to 1,500

rev/min, indicating that the reaction is diffusion (or mass-transfer)limited. For emulsified acid formulated at 2.0 vol% emulsifier, thereaction rate, as a function of the disk-rotational speed to thepower [1/(1n)], increased as the disk-rotational speed increased,which indicates that the reaction is mass-transfer limited. Asshown in Fig. 10, the reaction rate of dolomite and emulsifiedacid decreased with the increase in the emulsifier concentration.Also, the reaction of dolomite and emulsified acid at a tempera-ture of 230F is mass-transfer limited.

The effect of the average droplet size of the emulsified acidsystems on the dissolution rate of dolomite rocks in emulsifiedacid at different disk-rotational speeds is shown in Fig. 11. As theaverage droplet size increased, the dissolution rate increased, andthis was noted for both high and low disk-rotational speeds.

Determination of Emulsified-Acid Diffusion Coefficient.Hansford and Litt (1968) introduced the values for the functione(n) (Table 9). All these values were calculated assuming a mass-transfer-limited reaction. From the rheological study, the values ofK, n, and e(n) were determined at 230F. From the definition of Ain Eq. 4, the diffusion coefficient D can be estimated for emulsifiedacid systems formulated at emulsifier concentrations of 0.5, 1.0,and 2.0 vol%. Table 10 gives the power-law-model data, values ofe(n), and the diffusion coefficient. The diffusion coefficient as afunction of the emulsifier concentration is plotted in Fig. 12. It isclear that as the emulsifier concentration increased, the diffusioncoefficient decreased significantly. The diffusion coefficient foremulsified acids formulated at 0.5 vol% emulsifier was found to be1.413108 cm2/s. For emulsified acid systems prepared usingemulsifier concentrations of 1.0 and 2.0 vol% emulsifier, the diffu-sion coefficient was found to be 6.751109 and 8.3671010 cm2/s, respectively. The diffusion coefficient decreased by 17 time,when the emulsifier concentration increased from 0.5 to 2.0 vol%.The high viscosity of emulsified acid resulted in a reduction in themobility of acid droplets and hence reduced the reaction rate.

The diffusion coefficient of emulsified acid systems has beenmeasured before (Hoefner and Fogler 1989; de Rozieres et al.

. . . . . . . . .

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

TABLE 9VALUES OF e(n) AS A FUNCTION OF n*

n 0.2 0.4 0.5 0.6 0.8 1.0 1.3

e(n) 0.695 0.662 0.655 0.647 0.633 0.620 0.618

* Hansford and Litt 1968.

0.00x10

2.00x107

4.00x107

6.00x107

8.00x107

1.00x106

1.20x106

1.40x106

1.60x106

1.80x106

0 1

300 rev/min

500 rev/min

1000 rev/min

1500 rev/min

Average Droplet Size, m2 3 4 5 6 7 8 9

Dis

solu

tion

Rat

e, g

mol

/cm

2 .s


Fig. 11Effect of the average droplet size of emulsified acid on the dissolution rate of dolomite.


1994; Al-Mutairi et al. 2009). Table 11 lists the diffusion coeffi-cients obtained in these studies. Hoefner and Fogler (1989) used arotating-disk technique and measured diffusion-coefficient valuesin the range of 108 cm2/s for a microemulsified acid system. deRozieres et al. (1994) measured the diffusion coefficients of emul-sified acids with Carrara marble using both the diaphragm diffu-sion cell and the rotating disk at a temperature of 147F. At atemperature of 147F, de Rozieres et al. (1994) predicted a diffu-sion coefficient of 4.60108 cm2/s. Al-Mutairi et al. (2009)measured the diffusion coefficient of emulsified acid at 85C(185F), and it was 2.8187108 cm2/s. Comparing the acid diffu-sion coefficient of the emulsified acid with dolomite rocks at230F (D 1.413108 cm2/s) to the values obtained by Hoefnerand Fogler (1989), de Rozieres et al. (1994), and Al-Mutairi et al.(2009), the diffusion of emulsified acid in the presence of dolo-mite rocks was lower although the reaction-rate experiments wereperformed at higher temperature.

Hoefner and Fogler (1989) tried to relate the measured diffu-sion coefficient to the particle size using the Stokes-Einstein equa-tion for the Brownian diffusion. The Brownian diffusion

coefficient of spherical particles of radius (rD) in a fluid of a vis-cosity (g) is given by

DB RgT

6pNArDg; 6

where DB is the Brownian diffusion coefficient, m2/s; Rg is the

universal gas constant, 8.31 J/(mole K); NA is Avogadros num-ber, 6.0221023 mol1; g is the viscosity of the continuous phase,Pas; and rD is the radius of the droplets of the dispersed phase, m.

The diffusion coefficients measured in this study fall in therange of 108 to 1010 cm2/s. The Brownian diffusion coefficientof spherical particles depends mainly on the radius of the aciddroplets and the viscosity of the continuous phase (de Roziereset al. 1994). Eq. 6 suggests that the diffusion coefficient is inver-sely proportional to the radius of the particle in the Brownian-motion regime. Solving Eq. 6, for emulsifier concentration of 0.5vol% and 1.413108 cm2/s, a droplet size of 0.066 lm wasobtained. The calculated droplet size by use of Eq. 6 is small com-pared with the average size of acid droplets measured in the

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

0.00x10

2.00x109

4.00x109

6.00x109

8.00x109

1.00x108

1.20x108

1.40x108

1.60x108

Diff

usio

n C

oeffi

cien

t, cm

2 /s

0 2 4 6 8 10

0 0.5 1 1.5 2 2.5

Average Droplet Size, m

Emulsifier Concentration, vol%

vs. Emulsifier Concentration

vs. Droplet Size


Fig. 12Effect of the emulsifier concentration and average droplet size on the diffusion coefficient.

TABLE 11DIFFUSION COEFFICIENT OF EMULSIFIED ACID SYSTEMS USED IN PREVIOUS

AND CURRENT STUDIES

Authors Diffusion Coefficient (cm2/s) Notes

Hoefner and Fogler 1989 10108 Microemulsion with calcitede Rozieres et al. 1994 4.60108 147F with Carrara marbleAl-Mutairi et al. 2009 2.8187108 185F with calcitePresent Study 1.413108 to 8.3671010 230F with dolomite rocks

TABLE 10DIFFUSION COEFFICIENT AT DIFFERENT EMULSIFIER CONCENTRATIONS

AT 230F

Emulsifier

Concentration

(vol%)

Power-Law

Constant

K (mPasn)Power-law

Index (n) e(n) D (cm2/s)

0.5 58.77 0.751 0.637212 1.41373108

1 544.39 0.472 0.66188 6.75175109

2 1734.1 0.38 0.67000 8.36741010


emulsified acid system used in the current study (8.118 lm foremulsified acid prepared using 0.5 vol% emulsifier). For emulsi-fied acids prepared using 2.0 vol% emulsifier concentration, how-ever, the diffusion coefficient was 8.36741010 cm2/s and theacid-droplet size calculated by use of Eq. 6 was found to be 1.12lm. The droplet size, which was predicted by use of Eq. 6, wasfound to be 60% less than the value measured using the micro-scope. Al-Mutairi et al. (2009) mentioned that the size of macroe-mulsion is too large for Brownian motion to occur. In addition,dense emulsions exhibit droplet/droplet interactions that preventsignificant Brownian motion, and the flow in the rotating-disk sys-tem is centrifugal and induced by a forced convection. Fig. 12shows the diffusion coefficient of emulsified acid as a function ofthe measured average droplet size of emulsified acid. The aciddiffusion coefficient decreased as the average droplet size ofemulsified acid decreased. This is contrary to what was indicatedin the Stokes-Einstein equation for the Brownian diffusion ofspherical particles. As a result, the Stokes-Einstein equation forthe Brownian diffusion is not applicable for the emulsified acidsused in the present study.

Comparison of Reaction Rate and Diffusion Coefficient WithPrevious Work. Lund et al. (1973) measured the dissolution rateof dolomite in 1 N regular HCl at 100C (212F). The measureddissolution rates ranged from 5.3106 to 1.32105 g mol/cm2 s.Herman and White (1985) measured dolomite dissolution rate inregular HCl at 75F. Anderson (1991) measured the dissolutionrate of dolomite in approximately 1 to 5 N regular HCl at 120F.Dissolution rates were measured in the range of 1.8106 to3.47106 g mol/cm2 s. Taylor et al. (2004b) measured the reactionrate and diffusion coefficient of regular HCl using dolomite coresamples and for HCl concentration up to 17 wt%. The reaction ratemeasured was in the range of 2106 to 1.6105 g mol/cm2 s at185F. In the present work, the dissolution rate of dolomite in theemulsified acid systems was lower than the values measured previ-ously (using regular HCl) by at least one order of magnitude. Thevalues of the dissolution rate range from 4.828107 to1.527106 g mol/cm2 s. Although the dolomite reaction withemulsified acid was studied at a higher temperature, the dolomitedissolution rate in emulsified acid was lower than the values meas-ured previously using regular HCl. The emulsified acid systemtested in the current study achieved low reaction rates and low dif-fusion coefficient with dolomite cores, and this will lead to the cre-ation of deep wormholes and etched fracture surfaces, which willincrease the benefits from the stimulation treatment.

Anderson (1991) measured the diffusion coefficient of 1 to 5N regular HCl at 120F using dolomite core samples. The diffu-

sion coefficient was measured as 6.65105 cm2/s. Li et al.(1993) measured the diffusion coefficient for an emulsified acidsystem and dolomite at a temperature of 116F, and they found avalue near 1.65107 cm2/s. Conway et al. (1999) measured dif-fusion coefficient of regular HCl at temperatures of 110 and150F using dolomite cores. They measured diffusion coefficientsin the range of 1.7105 to 2.28105 cm2/s. Taylor et al.(2004b) measured the diffusion coefficient of regular HCl usingdolomite core samples and for HCl concentration up to 17 wt% at185F. Their diffusion coefficients ranged from 6.24105 to7.35105 cm2/s. In the present work, the diffusion coefficient ofemulsified acid systems measured using dolomite core sampleswas lower than the values measured previously using regular HClby at least three to five orders of magnitude. The values of the dif-fusion coefficient of emulsified acid were found to be in the rangeof 10108 to 101010 cm2/s.

In a previous work, Sayed et al. (2012) measured the dissolu-tion rate of calcite in emulsified acids using a rotating-disk appa-ratus. Indiana limestone core samples were used as a source forcalcite. In these experiments, the emulsified acid was preparedusing the same emulsifier, acid, and diesel. The emulsifier concen-tration varied from 0.5, 1.0, and 2.0 vol%. Fig. 13 gives a compar-ison of the dissolution rate, as a function of x1/(1n) for anemulsified acid prepared using 1.0 vol% emulsifier for both dolo-mite and calcite rocks. The dissolution rate of the dolomite wasfound to be lower than that of calcite, and the difference increasedas the rotational speed was increased.

Fig. 14 shows of the diffusion coefficients of emulsified acidswhen reacted with calcite and dolomite as a function of emulsifierconcentration. The diffusion coefficients of emulsified acids whenreacted with dolomite were found to be at least one order of mag-nitude lower than those of emulsified acids when reacted with cal-cite. At emulsifier concentration of 2.0 vol%, the diffusioncoefficients of emulsified acids when reacted with dolomite werelower by two orders of magnitude than those obtained withcalcite.

The emulsified acid system achieved a low diffusion coeffi-cient and low dissolution rates. These low values will retard acid/rock reaction and enhance the outcome of the stimulation treat-ment by creating deep wormholes (matrix acidizing) or etchedfracture surface (acid fracturing).

Conclusions

The reaction of dolomite with regular HCl was studied previously,while reaction of dolomite with emulsified acids did not get thesame attention. The reaction of 15 wt% emulsified HCl with dolo-mite disks was examined using the rotating-disk apparatus at

0.00x10

2.00x106

4.00x106

6.00x106

8.00x106

1.00x105

1.20x105

0 20

Calcite Dolomite

40 60 80 100 120 140 160

Dis

solu

tion

Rat

e, g

mol

/cm

2 .s

1/(1+n), rev/min1/(1+n)


Fig. 13Comparison of dissolution rate of dolomite and calcite (Sayed et al. 2012) in the emulsified acid systems formulated using1.0 vol% emulsifier at different disk-rotational speeds.


disk-rotational speeds of 100 to 1,500 rev/min. On the basis of theresults obtained, the following conclusions can be drawn:1. At 230F, the reaction of dolomite with emulsified acid is a

mass-transfer-limited reaction.2. The dissolution rate and diffusion coefficient decreased as the

emulsifier concentration was increased.3. The reaction rate of emulsified acids with dolomite is lower by

one order of magnitude than that of calcite.4. The diffusion coefficient of emulsified acid in presence of do-

lomite is two orders of magnitude less than that obtained usingcalcite disks.

5. The dissolution rate of dolomite in emulsified acids is lower byone or two orders of magnitude than that measured previouslyusing regular HCl acids.

6. Diffusion coefficients of emulsified acid in the presence of do-lomite rock were found to be lower by three to five orders ofmagnitude than those measured previously using regular HCl.

Nomenclature

Ac cross-sectional area of the disk, cm2A0 initial surface area of the disk, cm2Cb reactant concentration in the bulk solution, g mol/cm3D diffusion coefficient, cm2/s

DB Brownian diffusion coefficient, m2/sK power-law consistency factor, g/cm s(n2)n power-law index

NA Avogadros number, 6.0221023 mol1r radius of the disk, cmR rate of reaction (g mol/cm2 s)

rD radius of the dispersed-phase droplets, mRDh initial dissolution rate, g mol/s cm2

Rg universal gas constant, 8.31 J/(mole.K)_c shear rate, s1

e(n) function that depends on ng viscosity of the continuous phase, Pas

la fluid apparent viscosity, cpq fluid density, g/cm3U acid volume fraction/ core porosity, volume fractionx disk-rotational speed, rad/s

Acknowledgements

This paper was made possible by NPRP grant 09-828-2-316 fromthe Qatar National Research Fund (a member of Qatar Founda-tion). The statements made herein are solely the responsibility of

the authors. The authors would like to acknowledge Ahmad Al-Douri and Olusegun Adenuga for assisting with the experimentalwork and Kate Brady for proofreading the paper.

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Fig. 14Comparison of diffusion coefficient of emulsified acid when reacted with dolomite and calcite (Sayed et al. 2012).


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Mohammed A. Sayed is a PhD candidate studying at the Petro-leum Engineering Department, Texas A&M University. Hisresearch interests include testing and evaluating new acid sys-tems for high-temperature applications in matrix acidizing andacid fracturing in both dolomite and calcite formations. Themain focus of work is on emulsified acid systems, traditional andnew organic acids, and chelating agents. Sayed holds BSc andMSc degrees in petroleum engineering from Cairo University. Hehas published several SPE conference papers on acidizing.Sayed can be reached at [email protected]

Hisham A. Nasr-El-Din is a professor and holder of the JohnEdgar Holt Endowed Chair at Texas A&M University in petro-leum engineering. Previously, he worked for 15 years as Princi-pal Professional and Team Leader of the Stimulation Researchand Technology Team for Saudi Aramco. Before joining SaudiAramco, Nasr-El-Din worked for 4 years as a staff researchengineer with the Petroleum Recovery Institute in Calgary. Healso worked as a research associate with the University of Sas-katchewan, the University of Ottawa, and the University ofAlberta. Nasr-El-Dins research interests include well stimula-tion, formation damage, enhanced oil recovery, conform-ance control, interfacial properties, adsorption, rheology,cementing, drilling fluids, two-phase flow, and nondamagingfluid technologies. He holds several patents and has publishedand presented more than 480 technical papers. Nasr-El-Dinhas received numerous awards within Saudi Aramco for signifi-cant contributions in stimulation and treatment-fluid technolo-gies and stimulation design, and for his work in training andmentoring. He holds BSc and MSc degrees from Cairo Univer-sity and a PhD degree from the University of Saskatchewan, allin chemical engineering. Nasr-El-Din serves on the SPE steeringcommittees on Stimulation and Oilfield Chemistry, is a ReviewChairperson for SPE Journal and is a Technical Editor for SPEProduction & Operations and SPE Drilling & Completion. Hewas invited to give keynote presentations in various SPE andNACE International conferences. Nasr-El-Din received the SPERegional Technical Discipline Award for Production and Oper-ations in 2006, was named a Distinguished SPE Member in2007, and received SPE awards for Outstanding Associate Edi-tor (SPE Journal) and Outstanding Technical Editor (SPE Pro-duction & Operations) in 2008. In addition, he received theSPE Production and Operations Award and Outstanding Asso-ciate Editor Award (SPE Journal) in 2009. Nasr-El-Din alsoreceived SPE A Peer Apart status in 2011 for reviewing morethan 100 papers.

Hadi Nasrabadi is an Assistant Professor of petroleum engi-neering at Texas A&M University. Before joining Texas A&M Uni-versity, he worked for 5 years as an assistant professor inpetroleum engineering at Texas A&M University at Qatar. Nas-rabadis research interests include numerical study of varioustransport phenomena in porous media with applications (e.g.,modelling acid fracturing). He holds a BS degree in civil engi-neering from Sharif University of Technology in Tehran, Iran,and a PhD degree in petroleum engineering from ImperialCollege, London.


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Dolomite Emulsified Acid