A kinetic study of the reduction of chromium(VI) to chromium(III) by thiourea

Journal of Petroleum Science and Engineering 19 Ž1998. 253–263

A kinetic study of the reduction of chromium žVI / to chromium žIII / by thiourea Thomas A. Maxcy a , G. Paul Willhite b, Don W. Green

b,)

, Kristin Bowman-James

c

a 7119 Cornelia Lane, Dallas, TX 75214, USA Department of Chemical and Petroleum Engineering, The UniÕersity of Kansas, Lawrence, KS 66045, USA c Department of Chemistry and Medicinal Chemistry, The UniÕersity of Kansas, Lawrence, KS 66045, USA

b

Received 11 December 1996; accepted 7 July 1997

Abstract The reduction of chromiumŽVI. to chromiumŽIII. by thiourea is a key aspect of the chromiumŽVI. –thiourea–polyacrylamide gel polymer system used in oil recovery processes. A study was undertaken to develop a kinetic model for the reduction reaction. Reaction mixtures were prepared and chromiumŽVI. concentrations were determined from the mixtures’s visible absorbance. The reaction rate was found to depend on the concentrations of chromiumŽVI., thiourea, and polyacrylamide and on solution pH. A kinetic model for the reactions was developed using the experimental data and previously proposed reaction mechanisms. The model accurately predicts the reaction rate in solutions that do not contain polyacrylamide and predicts a rate that is approximately correct for solutions containing polyacrylamide. q 1998 Elsevier Science B.V. Keywords: permeability modification; secondary recovery; enhanced recovery; waterflooding; gelled polymers; gels

1. Introduction Gel polymer systems are used to reduce the permeability of oil-bearing rocks in a selective manner to improve sweep efficiency of oil recovery processes such as waterflooding ŽSchoeling et al., 1989.. ChromiumŽIII. will crosslink hydrolyzed polyacrylamide to form suitable gels for this purpose. To control the rate of the gel formation, chromium can be introduced as chromiumŽVI., which is then reduced to chromiumŽIII. using thiourea, usually in the pH 4.0 to 5.0 range. Gel times on the order of days )

Corresponding author. Tel.: q1-913-8643001. Fax: q1-9138644967.

to weeks can be achieved, which is desirable to allow proper placement of the gel system in the formation. The process is described in several papers ŽHuang, 1983; McCool, 1988; Todd, 1990; Marty et al., 1991.. Another option is to use chromiumŽIII. ligands like acetate, lactate, or malonate. Chromium ŽVI. –thiourea–polyacrylamide gels form as the result of two chemical reactions. First, chromiumŽVI. is reduced to chromiumŽIII. by thiourea. Second, the produced chromiumŽIII. reacts with carboxylate groups on the partially hydrolyzed polyacrylamide to form a crosslinked polymer gel. The rate of the reduction reaction determines the amount of chromiumŽIII. available for the crosslinking reaction and consequently influences the time

0920-4105r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 9 2 0 - 4 1 0 5 Ž 9 7 . 0 0 0 2 6 - 0

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T.A. Maxcy et al.r Journal of Petroleum Science and Engineering 19 (1998) 253–263

required for polymer gels to form. A kinetic model of the reduction reaction is needed to more fully understand the behavior of the chromiumŽVI. – thiourea–polyacrylamide gel polymer system. The reduction of chromiumŽVI. to chromiumŽIII. has been studied by many researchers. Reviews of early work, in which a variety of reducing agents were used, are available ŽWestheimer, 1949; Beattie and Haight, 1972., as are papers on the reduction of chromiumŽVI. by thiols other than thiourea ŽCuthill and Atkins, 1937, Baldea and Niac, 1968; Edmonds et al., 1970; Muirhead et al., 1972; Muirhead and Haight, 1973; McCann and McAuley, 1975; Hojo et al., 1977; McAuley and Olatunji, 1977a,b; Connett and Wetterhahn, 1985.. Reduction of chromiumŽVI. by thiourea in strongly acidic solutions is used to standardize thiourea solutions ŽCuthill and Atkins, 1937; Singh and Verma, 1963; Rao, 1970; Gupta et al., 1974., and chromiumŽVI. solutions ŽVerma et al., 1978.. Olatunji and McAuley Ž1975. studied the rate of chromiumŽVI. reduction by thiourea in the 0.0 to 0.6 pH range and developed a reaction rate equation for this pH range. Southard Ž1983. studied the rate of chromiumŽVI. reduction by thiourea in the presence of polyacrylamide, but was unable to develop a kinetic model for the reaction. Todd Ž1990. concluded that no reliable kinetic model was available for the reduction of chromiumŽVI. to chromiumŽIII. by thiourea in the 4.0 to 5.0 pH range. The objective of this study was to develop a kinetic model for the reduction of chromiumŽVI. to chromiumŽIII. by thiourea in the 4.0 to 5.0 pH range. In this work, aqueous solutions of chromiumŽVI. and thiourea were prepared and their chromiumŽVI. concentrations were measured as the reduction reaction progressed. The experimental data along with reaction mechanisms available from previous studies of the reduction of chromiumŽVI. were used to develop a kinetic model.

2. Experimental technique 2.1. Buffering of the reacting mixture A brown precipitate forms during the reduction of chromiumŽVI. when the pH of the reaction mixture is 5.0 and above ŽSouthard, 1983.. Two reactions

involving aquated chromiumŽIII. lead to formation of precipitate. First, aquated chromiumŽIII. cations combine with each other and form precipitates that fall from solution at pH 5.0 and above ŽSpiccia and Marty, 1986.. Second, aquated chromiumŽIII. cations combine with chromiumŽVI. oxyanions and form brown precipitates in the same pH range ŽAten et al., 1953; Jezowska-Trzebiatowska et al., 1968.. As reported previously ŽMaxcy et al., 1991; Maxcy, 1991., the precipitate can be prevented by running the reduction reaction in the presence of an acetic acid– sodium acetate buffer. Acetate buffer in the reaction mixture complexes the aquated chromiumŽIII. produced by the reduction reaction to trisŽacetato.chromiumŽIII. and prevents formation of the brown precipitate. The acetic acid–sodium acetate buffer was added to most of the reaction mixtures. In other cases, partially hydrolyzed polyacrylamide, which contains similar carboxylate groups, was added to the reaction mixtures. 2.2. Experimental procedures and equipment Stock solutions of chromiumŽVI. –sodium chloride, thiourea, acetic acid–sodium acetate, and polyacrylamide were prepared. An appropriate amount, 100 to 200 g, of the chromiumŽVI. –sodium chloride stock solution and an appropriate amount, 0 to 300 g, of the polyacrylamide stock solution were added to a Wheaton Lab 45 Pyrex bottle. Appropriate amounts, 50 to 200 g, of the thiourea stock solution, the acetic acid–sodium acetate stock solution, and deionized water were added to a second Wheaton bottle. Both bottles were shaken, placed in a 258C constant temperature water bath, and left overnight to bring the solution temperatures to 258C. On the following day, the second bottle was poured into the bottle that contained the chromiumŽVI. –sodium chloride stock solution which became the container for the reaction mixture. The reaction container was capped, shaken for 30 s, and returned to the 258C constant temperature water bath. The chromiumŽVI. concentration of each reaction mixture was spectroscopically determined four times during the course of the reaction. Visible absorbance was measured at 4 wavelengths on a Ciba Corning Diagnostics Corporation, Gilford Response II spectrophotometer. Pairs of 2 and 10 mm path-length

T.A. Maxcy et al.r Journal of Petroleum Science and Engineering 19 (1998) 253–263 Table 1 Range of variables studied Variable

Value

Units

ChromiumŽVI.

0.001–0.003 50.0–150.0 0.010, 0.020, 0.040 760, 1520, 3040 0.000100–0.000010 4.0–5.0 0.0, 0.042, 0.070 0, 3000, 5000 0–0.075 0–5300 0.275–0.338 1.60–1.93 0.60 new Pyrex 25

molrkg ppm molrkg ppm molrkg pH molrkg ppm molrkg ppm molrkg wt% cm2 rg

Thiourea wHq x Polyacrylamide Buffer NaCl Surface area Bottles Temperature

8C

quartz cuvets were used with the path-length for a given measurement, chosen so that the absorbance of the sample was between 0.18 and 0.90 absorbance units. ChromiumŽVI. concentration was determined from the four visible absorbance measurements, with an average error of approximately 1%, using an analytical technique that has been previously described ŽMaxcy et al., 1991; Maxcy, 1991.. Reaction mixture pH was determined ten times during the course of each reaction using a Corning, flat surface combination electrode and a Fisher Scientific, Accumet Model 910 pH meter. Initial solu-

255

tion pH was controlled by the amount of acetic acid and sodium acetate added to each reaction mixture. Additional experimental details are reported by Maxcy Ž1991.. 2.3. Surface effects The reaction rate was found to depend on two variables previously thought to be unimportant. First, the reaction rate was a function of the ratio of the surface area of the reaction container to the mass of the reaction mixture. Second, the reaction rate was a function of the chemical state of the reaction container’s surface. No previous discussion of the effect of the surface of the reaction container on the rate of chromiumŽVI. reduction was found in the literature. These issues were addressed and the effects minimized by maximizing the reaction mass-to-surface area ratios in the reactor vessels and by use of new glassware only ŽMaxcy, 1991.. While the surface effect on the reaction rate was controlled to make it negligible in this study, it is recognized that when the reacting solution is flowing through porous media the effect could be very important. 2.4. Range of experimental conditions The nominal range of experimental conditions is shown in Table 1. Experiments were conducted in a

Fig. 1. Replicate chromiumŽVI. versus time data.

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T.A. Maxcy et al.r Journal of Petroleum Science and Engineering 19 (1998) 253–263

Fig. 2. Modeling results, comparison of model to experimental data, thiourea and buffer concentrations varied.

saline solution at an ionic strength of 0.350 molrkg. Sodium chloride was used to adjust ionic strength.

3. Experimental results To demonstrate reproducibility of the experimental data, two experiments were performed at each of twelve sets of concentration conditions. Data for three pairs, which are typical for the twelve pairs, are shown in Fig. 1. As shown, the data are reproducible. The solid lines on the figures are results

from model calculations which will be described later. Other typical data are shown in Figs. 2 and 3 for varied conditions. Again, the solid lines are model results to be discussed in a following section. In Fig. 2, six runs are shown for which two parameters were changed, the thiourea and buffer concentrations. At a given thiourea concentration, increasing the buffer concentration by 50% resulted in a small increase in reaction rate. As seen, increasing the thiourea concentration by factors of two and four significantly increased the reaction rate.

Fig. 3. Modeling results, comparison of model to experimental data, pH and buffer concentrations varied.

T.A. Maxcy et al.r Journal of Petroleum Science and Engineering 19 (1998) 253–263

The data in Fig. 3 show primarily the effect of buffer concentration and the marked effect of pH. Hydrogen ion concentration data for three of the twelve pairs of replicated experiments are shown in Fig. 4. An algebraic correlating equation developed by Southard Ž1983. and modified by Todd Ž1990., Eq. Ž1., was fit to each set of hydrogen ion concentration data,

w Hq x t s

1.0

Ž A q Bt C .

.

Ž 1.

The standard deviation of the data about the correlating equation is 0.012 in pH units, or 2.7% in concentration units. This is consistent with the level of error reported by Silva during determination of sodium concentration with a sodium selective electrode ŽSilva, 1990.. Results of the twelve pairs of experiments demonstrate that reproducible kinetic data can be generated using the techniques developed as a part of this study. In agreement with previous studies, the reaction rate increases with the concentrations of chromiumŽVI. and thiourea, and decreases as solution pH increases. Contrary to initial expectations, the acetate buffer increases the rate of the reduction reaction. Polyacrylamide also increases the reaction

257

rate as the addition of 500, 1000, and 1500 ppm of the polymer led to equal increases in reaction rate.

4. Kinetic model The initial approach to development of a kinetic model was to write rate equations based on studies reported in the literature. The resulting model was then tested against the experimental data of this work and modified, as required, to be consistent with the data. 4.1. DeÕelopment of reaction rate equations from mechanistic arguments Oxidation of the sulfur atom in a molecule of thiourea by chromiumŽVI. is a two-step reaction ŽRao, 1970; Gupta et al., 1974.. In the first step, Eq. Ž2., the sulfur atom in thiourea is oxidized from y2 to y1, converting thiourea to a disulfide and chromiumŽVI. to chromiumŽIII. ŽSingh and Verma, 1963; Olatunji and McAuley, 1975; Verma et al., 1978., 6 Ž H 2 N . 2CS q 2HCrO4y q 8Hqq 4H 2 O ™ 3 Ž H 2 N . Ž HN . CSSC Ž NH . Ž NH 2 . 3q

q2Cr Ž H 2 O . 6 .

Fig. 4. Comparison of correlated, predicted and experimental hydrogen ion activities.

Ž 2.

T.A. Maxcy et al.r Journal of Petroleum Science and Engineering 19 (1998) 253–263

258

In the second step ŽEq. Ž3.., the sulfur atoms in the disulfide are oxidized from y1 to q6, converting the disulfide to sulfate and chromiumŽVI. to chromiumŽIII. ŽCuthill and Atkins, 1937; Gupta et al., 1974., 3 Ž H 2 N . Ž HN . CSSC Ž NH . Ž NH 2 . q 14HCrO4y q44H q 58H 2 O ™ 6 Ž H 2 N . CO 3q

Ž 3.

Insight into the mechanism of Eq. Ž2. is provided in the Appendix A. As indicated previously, an acetic acid–sodium acetate buffer was added to the reaction mixtures to prevent formation of a brown precipitate. The acetate buffer increases the rate of the reduction reaction in two ways. First, it prevents the solution pH from increasing as the reaction proceeds, leading to higher reaction rates than in unbuffered solutions. Second, the acetate buffer catalyzes formation of the chromiumŽVI. –thiourea complex ŽConnett and Wetterhahn, 1985., possibly by forming an intermediate chromium–acetate–thiourea complex as shown in Eq. Ž4. which is similar to structures discussed by Haim Ž1972., k2

HCrO4y q Hqq L q CH 3 COOH m ky2

w intermediatex

yCH 3COOH k3

m

ky3 qCH 3COOH

LCrO 3 q H 2 O,

žž ž ž ž

= 1.0 q

q

q14Cr Ž H 2 O . 6 q 6SO42y .

constant. The derivation is included in Appendix A and is given by Eq. Ž5. ŽMaxcy, 1991., d Cr Ž VI . y Ž due reaction of Eq. Ž 2. . dt k1 k5 2 2 s HCrO4y w L x w Hq x ky1 q k 4

Ž 4.

where LCrO 3 is a thiourea thioester. Reaction rate equations are often derived from proposed reaction mechanisms based on the assumption that one or more of the reactions reaches a pseudo steady-state in which the concentrations of the intermediates are constant ŽLevenspiel, 1972.. A reaction rate expression for the reaction of Eq. Ž2. was derived assuming that the concentrations of the chrom ium Ž V I . – thiourea thioester and the chromiumŽVI. –thiourea–acetic acid complexes are

= 1.0 q 1.0 q

/

k 3 k 2 w CH 3 COOHx k 1 Ž ky2 q k 3 . k4 k 5 w L xw Hq x

q

/

k 6 w Hq x k5

ky3 ky2 w CH 3 COOHx

Ž ky2 q k 3 . Ž ky1 q k 4 .

// q

k 5 w L xw Hq x ky1 q k 4

q 2

q

k 6 w L xw H x ky1 q k 4

/

Ž 5.

where wLx is the concentration of thiourea. No studies of the reduction of metal ions by disulfides were found when the collective indices of Chemical Abstracts from 1940 to 1990 were searched. Thus, it was necessary to develop an empirical expression for the rate of reaction for Eq. Ž3.. Several rate expressions were investigated by fitting the kinetic model to the experimental data. The best agreement between the predictions of the kinetic model and the experimental data was obtained when Eq. Ž6. was used to predict the rate for the reaction given by the following equation d Cr Ž VI . y Ž due reaction of Eq. Ž 3. . dt s k 7 Cr Ž VI . Ž L–LX . , Ž 6. X where L–L is the disulfide molecule. 4.2. Calculations of secondary reagent concentration The kinetic model of the reduction reaction is made up of two parts: reaction rate equations and secondary or stoichiometric relationships. Three moles of thiourea are removed from the reaction mixture when one mole of chromiumŽVI. is reduced by the reaction of Eq. Ž2., leading to the secondary equation for thiourea that follows, where DC3 is the amount of chromiumŽVI. reduced, w Thioureax s w Thioureax initial y 3DC3. Ž 7. The following secondary equations were developed

T.A. Maxcy et al.r Journal of Petroleum Science and Engineering 19 (1998) 253–263

for disulfide and acetate buffer, where DC4 is the amount of chromiumŽVI. reduced by the reaction in Eq. Ž2.,

w Disulfidex s w Disulfidex initial q Ž 3r2. DC3 y Ž 3r14 . DC4 w Bufferx s w Bufferx initial y 3 Ž DC3 q DC4. .

Ž 8. Ž 9.

The polyacrylamide used in this work was 3% hydrolyzed, meaning that 3% of the amide functional groups had been converted to carboxylate groups. When polyacrylamide was present in the reaction mixture, the initial buffer concentration in Eq. Ž9. was defined as the sum of the initial acetic acid, sodium acetate, and 3% of the polymer repeat unit concentrations. A secondary equation for reaction mixture pH can be generated by correlating experimental pH data with Eq. Ž1.. As an alternative to correlation of experimental data, reaction mixture pH can be estimated from the stoichiometry of the reduction reactions and the equilibrium concentrations of acetic acid–sodium acetate, protonated–deprotonated hydrolyzed polyacrylamide, and chromate–bichromate–dichromate. Using this technique, the number of protons removed from the reaction mixture by the reduction reactions is calculated using Eq. Ž10., where the constants result from Eq. Ž3., Protons removeds Ž 8r2 . DC3 q Ž 44r14. DC4.

Ž 10 . As protons are removed from the reaction mixture by the reduction reaction, solution pH increases and acetic acid is converted to sodium acetate, bichromate is converted to chromate and the carboxylate sites on the polymer are deprotonated. The number of protons contributed to the reaction mixture by the above reactions is calculated using Eq. Ž11., Protons contributeds CrO42y y CrO42y

initial

q w CH 3 COOHx initial y w CH 3 COOHx q 0.03 w Protonated Polymerx initial y 0.03 w Protonated Polymerx .

Ž 11 .

Equations, equilibrium constants, and activity coefficients needed to calculate the concentrations of the species in Eq. Ž11. are available in the literature ŽDavis, 1938, 1962; Tong and King, 1953; Kotrly

259

and Sucha, 1985.. The expression for the protons removed from the reaction mixture ŽEq. Ž10.. and the expression for the protons contributed to the reaction mixture ŽEq. Ž11.. can be combined into the following expression for the reaction mixture’s hydrogen ion concentration,

w Hq x s w Hq x initial y Ž 8r2. DC2 y Ž 44r14. DC3 y CrO42y q

CrO42y

initial

y w CH 3 COOHx

q w CH 3 COOHx initial y 0.03 w Protonated Polymerx q 0.03 w Protonated Polymerx initial .

Ž 12 .

Eq. Ž12. is an implicit expression in that the concentrations of the species on the right-hand side of the equation are functions of the hydrogen ion concentration. Hydrogen ion concentration, as a function of the progress of the reduction reaction, is calculated by iteration during numerical integration of the reaction rate equations. 4.3. Determination of reaction rate constants A fast and flexible technique for the determination of reaction rate constants was developed by Ball and Groenweghe Ž1966.. Using this technique, rate constants are determined by minimizing the sum of squared error as given by the following equation, N

SSE s Ý 1

M

Ý ŽCc m , n Ž X1 ,

2

X 2 , X 3 , . . . . y Ce m , n . ,

1

Ž 13 . where: SSE s sum of squared error, Ce m, n s experimentally determined chromiumŽVI. concentration values, Cc m, n s chromiumŽVI. concentration values calculated from the kinetic model, M s number of experiments from which data are available, m s designation of a given experiment, N s number of kinetic data points taken during experiment m, n s designation of a given data point in experiment m, and X 1 , etc.s reaction rate constants. Calculated chromiumŽVI. concentration values corresponding to each of the available experimental chromiumŽVI. concentration values are generated from the kinetic model by numerically integrating the reaction rate equations using the least complex of

260

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the fourth-order Runge–Kutta algorithms ŽCarnahan et al., 1969.. More sophisticated Runge–Kutta integration methods, such as the fourth-order method proposed by Gill Ž1951., were tried and were found to yield results identical to those generated using the simpler method. Concentrations of the reagents other than chromiumŽVI. were calculated during the numerical integration of the reaction rate equations using stoichiometric relationships and Eq. Ž1.. The sum of squared error in Eq. Ž12. was minimized using the IMSL ŽInternational Mathematical and Statistical Libraries, 1987., subroutine ZXSSQ. This computer algorithm is an implementation of Levenberg Ž1944. –Marquardt Ž1963. nonlinear regression. 4.4. Further deÕelopment of the reaction rate equations When the kinetic model was fit to the experimental data, some of the terms in Eq. Ž5. did not contribute to the fit of the model to the data. For example, at the pH levels in this study, 4.0 to 5.0, k 6 wHqx rk 5 and k 6 wLxwHqx 2rŽ ky1 q k 4 ., were found to have insignificantly small values. Terms that did not contribute to the fit of the kinetic model to the experimental data were eliminated from the model. Reactions involving chromiumŽVI. were written with bichromate as the reactive species because it is the predominate species at the chromiumŽVI. concentrations and pH values used in this work ŽTong

and King, 1953; Linge and Jones, 1968.. The kinetic model was fitted to the experimental data using the assumptions that bichromate was the only reactive species and that the three chromiumŽVI. species were equally reactive. The fit of the kinetic model to the experimental data was significantly better when it was assumed that the three chromiumŽVI. species were equally reactive. Eqs. Ž4. and Ž5. are written with acetic acid as the catalytic species. The kinetic model was tested against the experimental data using different assumptions. First, it was assumed that acetic acid was the catalytic species and that sodium acetate was not catalytic. A second assumption was that sodium acetate was the catalytic species and acetic acid was not catalytic. Finally, the model was tested assuming that both species were equally catalytically active. The fit of the kinetic model to the experimental data was significantly better when it was assumed that acetic acid and sodium acetate were equally catalytically active. Partially hydrolyzed polyacrylamide was found to increase the rate of the reduction reaction. The polymer was assumed to catalyze formation of the thiochromate intermediate, as does the acetate buffer. A correction term for the increase in reaction rate due to the polymer, k poly , was added to the reaction rate equation. The increase in reaction rate due to the polymer was found to be independent of the polymer concentration over the range of polymer concentrations used here, 3000–5000 ppm.

Fig. 5. Comparison of correlated, predicted and experimental hydrogen ion activities with polymer present.

T.A. Maxcy et al.r Journal of Petroleum Science and Engineering 19 (1998) 253–263

261

Fig. 6. Model results using predicted solution pH.

With the above input, Eq. Ž5. becomes, y

d Cr Ž VI . dt s

ž

q

Ž due reaction of Eq. Ž 2. .

k1 k5 ky1 q k 4

2

HCrO4y w L x w Hq x

k 3 k 2 w Buffer x k 1 Ž ky2 q k 3 .

=

ž

1.0 q

q k poly

k 5 w L xw Hq x ky1 q k 4

// /

2

ž

1.0

Ž 14 .

4.5. Modeling results The numerical procedures described above were used to determine values for the groups of reaction rate constants in Eqs. Ž6. and Ž14.. This was done by comparing calculated values of solution pH and chromiumŽVI. concentration to the experimental data. The following set of parameters was determined: k 1) k 5rŽ ky1 q k 4 . s 0.1750)10 11 kg 4rmol 4 P h, k 3 k 2rk 1Ž ky2 q k 3 . s 0.1868)10 2 kgrmol, k 5rŽ ky1 q k 4 . s 0.7184)10 7 kg 2rmol 2 , k poly s 0.6995)10 0 dimensionless, k 7 s 0.2149)10 1 kgrmolP h. The agreement between the model calculations and experimental data is shown in Figs. 1–3. Model calculations are given by the solid lines in the fig-

ures. The pH values used in the model calculations are calculated using the empirical model ŽEq. Ž1... Reaction mixture pH can be calculated by correlating experimental data with Eq. Ž1. or by using Eq. Ž12.. Results from the two approaches are compared in Fig. 4 for solutions that did not contain polyacrylamide, and in Fig. 5 for solutions that did contain polyacrylamide. As seen, Eq. Ž1., which is an empirical correlation determined from sets of experimental data, provides a more accurate estimation of solution pH than the predictive method. The fit of the kinetic model to the experimental data using Eq. Ž12. to estimate the solution pH is shown in Fig. 6. ChromiumŽVI. concentration values calculated using Eq. Ž12. to estimate solution pH are almost as accurate as those generated using correlated experimental data. 5. Conclusions Ž1. Reproducible kinetic data were obtained for the reduction of chromiumŽVI. by thiourea in the pH range of 4.0 to 5.0. Ž2. The reaction rate increases with increasing concentrations of chromiumŽVI., thiourea, hydrogen ion, and acetate buffer. Ž3. The reaction rate was affected by the containing vessel surface area in contact with the reacting solution. This effect was relatively small in the experimental system used to obtain the kinetic data.

T.A. Maxcy et al.r Journal of Petroleum Science and Engineering 19 (1998) 253–263

262

Ž4. A kinetic model was developed based on mechanisms of chromiumŽVI. reduction described in the literature and the model is in good agreement with the experimental data.

Eqs. Ž6. – Ž8. describe pathways for the decomposition of the thioester into a thiourea radical, designated as LP, or a disulfide molecule, designated as LX –LX , k4

LCrO 3 ™ Cr Ž V . q LP 6. Nomenclature

k5

LCrO 3 q Hqq L ™ Cr Ž IV . q LX –LX ,

w x denotes concentration A, B, C empirical constants Cc m, n chromiumŽVI. concentration values calculated from the kinetic model Ce m, n experimentally determined chromiumŽVI. concentration values k reaction rate constant wLx ligand concentration LØ thiourea radical disulfide species LX –LX M number of experiments from which data are available m designation of a given experiment N number of kinetic data points taken during experiment m n designation of a given data point in experiment m SSE sum of squared error t time X 1 , etc. reaction rate constants

Ž A.2 . Ž A.3 .

and k6

LCrO 3 q 2Hqq L ™ Cr Ž IV . q LX –LX .

Ž A.4 .

ChromiumŽV., produced by the reaction of Eq. Ž6., is quickly reduced to chromiumŽIV. which, along with the chromiumŽIV. produced by the reactions described by Eqs. Ž7. and Ž8., is reduced to chromiumŽIII. by the reactions of Eqs. Ž9. and Ž10., fast

Cr Ž IV . q L l Cr Ž IV . L n ,

Ž A.5 .

and fast

Cr Ž IV . L n l Cr Ž III . L ny1 q LP.

Ž A.6 .

Thiourea radicals produced by reactions in Eqs. Ž6. and Ž10. combine to form disulfide, as shown in Eq. Ž11., fast

2LP ™ LX –LX .

Ž A.7 .

Similar reaction mechanisms have been proposed for the reduction of chromiumŽVI. by other thiols ŽConnett and Wetterhahn, 1985..

Acknowledgements This work was supported by the Department of Energy, and the Tertiary Oil Recovery Project and Department of Chemistry, University of Kansas.

Appendix A. Supplementary material Insight into the mechanism of Eq. Ž2. is available in the literature as the following reaction sequence was proposed by Olatunji and McAuley Ž1975.. In Eq. Ž5., thiourea, designated as L for ligand, reacts with chromiumŽVI. to form a thioester, k1

HCrO4y q Hqq L m LCrO 3 q H 2 O. ky1

Ž A.1 .

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