Silica transport during steam injection into oil sands

Silica transport during steam injection into oil sands

Chemical Geology, 54 (1986) 69--80 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands 69 SILICA TRANSPORT DURING STEAM INJECT...

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Chemical Geology, 54 (1986) 69--80 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

69

SILICA TRANSPORT DURING STEAM INJECTION INTO OIL SANDS 1. Dissolution and Precipitation Kinetics of Quartz: New Results and Review of Existing Data G. B I R D , J. B O O N a n d T. S T O N E Oil Sands Research Department, Alberta Research Council, Edmonton, Alta. T6H 5X2 (Canada)

(Received May 18, 1984; accepted for publication June 27, 1985)

Abstract Bird, G., Boon, J. and Stone, T., 1986. Silica transport during steam injection into oil sands, 1. Dissolution and precipitation kinetics of quartz: New results and review of existing data. Chem. Geol., 54: 69--80. New results are reported for the dissolution--precipitation kinetics of quartz in water. Sixteen dissolution and seven precipitation experiments were carried out at temperatures between 121 ° and 255°C and the corresponding water vapor pressure. The results can be described by a zero-order dissolution-first-order precipitation reaction. The literature on quartz dissolution and precipitation kinetics is critically reviewed and is in good agreement with our data. The activation energy for quartz precipitation lies between 51 and 55 kJ tool -~. The activation energy obtained from our precipitation experiments was somewhat smaller than the literature value but the difference is not statistically significant. Most of the data on both dissolution and precipitation, particularly below 200°C, can also be described by a parabolic rate law which leads to an activation energy of the magnitude as that from the zero-order--first-order rate laws. The zero-order--first-order rate law can be used to predict silica mass transport during steam injection. A silica conservation equation in differential form has been developed, coupled to a thermal multicomponent reservoir model and used successfully to describe large-scale laboratory experiments.

1. I n t r o d u c t i o n T h e in s i t u e x p l o i t a t i o n o f m a n y d e e p l y b u r i e d h e a v y o i l a n d t a r s a n d s d e p o s i t s involves the injection of large volumes of hot water or steam into quartz-rich sedimentary formations at pressures up to 12 MPa and temperatures up to 325°C. T h e s o l u b i l i t y o f s i l i c a m i n e r a l s in w a t e r is d e t e r m i n e d p r i m a r i l y b y t e m p e r a t u r e a n d pH, with ionic strength and pressure being of secondary importance under these condi0009-2541/86/$03.50

tions. Hot injection fluids react rapidly with quartz and substantial mass transport of silica must occur. Gravel pack disintegration and well collapse have been recorded (Reed, 1979). The injected fluids probably become saturated with respect to quartz and other salts at a short distance from the injection well. As this water continues to move outw a r d i n t o t h e f o r m a t i o n it c o o l s a n d s i l i c a c a n p r e c i p i t a t e , e i t h e r as a m o r p h o u s silica o r as q u a r t z . I t c a n a l s o r e a c t w i t h o t h e r dissolved mineral components to produce

© 1986 Elsevier Science Publishers B.V.

70 new mineral phases. The rate of silica precipitation or reaction will determine where in the f o r m a t i o n precipitation occurs and how it affects reservoir properties. McCorriston et al. (1981) have shown that, such reaction can lead to significm~t irreversible changes in permeability. We u n d e r t o o k our study to obtain data t h a t can be used to predict the e x t e n t o f quartz dissolution and precipitation around injection and p r o d u c t i o n well bores and to derive and refine the rate equations needed in silica mass transport. In this paper we are reporting twenty-seven new experimental measurements on appropriate oil sand and quartz sand systems and reviewing the existing literature data on quartz dissolution and precipitation. In the second paper in this series we will use this information to estimate the a m o u n t o f silica transport during in situ exploitation o f heavy oil resources.

2. T h e o r y



]

(dC/dt)forward = k ÷ ( A / M )

(1)

( d C / d t )backwar d = --k_C( A / M )

(2}

where C = silica c o n c e n t r a t i o n {mass fraction); t = time; k÷, k = f or w a r d and backward rate constant, respectively; A = surface area o f t h e sample; and M = mass of water. Assuming unit activity of water and unit activity coefficient o f dissolved silica and using d C / d t = 0 at equilibrium, eqs. 1 and 2 can be rearranged to give: (3)

where Keq = t h e r m o d y n a m i c equilibrium constant; and Ceq = equilibrium concentration in solution. Crerar and Anderson (1971)

"f

,

,

ln[(1 ~ C/C~q), (1 -- C v6,,,~ii :--k_(A/M)t

~4 }

where Co = silica concentration at ~ = 0. If C~ = 0, eq. 4 reduces to: In[1

C/Ceq ] =

k_{A/MJ[

{5}

It is convenient to express all results relative to a reference system of constant surface area and mass of water. We chose the same reference system as Rimstidt (1979) and Rimstidt and Barnes (1980): surface area 1 m 2, mass o f water 1 kg. Therefore, in this paper k with dimension T-~ has the unit s~. In addition to eq. 5, kinetic equations of several different types were fitted to our data [see discussion in Lasaga ( 1 9 8 1 ) ] , and in this paper we will discuss the results obtained with an equation of the form: C = k ( A / M l t ~'2

It has been generally assumed that the dissolution rate o f quartz is controlled by a zero-order surface reaction (eq. 1) and t hat its precipitation rate is first order (eq. 2) (van Lier, 1960; Rimstidt, 1979; Rimstidt and Barnes, 1980):

k ÷ / k = Keq -- Ceq

derived a regression equation that ~:M~resseCeq as a funct i on of t e m p e r a t u r e Combining eqs. 2 and 3 and mi, egrating gives:

~6

The t e m p e r a t u r e dependence of the rate constant can be described by the Arrhenius equation: I~ = k'_ e x p ( E A / R T )

~7}

where k' is a constant; EA, the activation energy for precipitation; R, the gas c o n s t a n t ; and T, the t em perat ure in kelvins. EA can be calculated from the slope of a in k vs. 1 T plot, assuming t hat the dissolution or precipitation mechanism does not change over the t e m p e r a t u r e range. 3. Experimental Natural quartz sands were used in all experiments. The dissolution experiments were carried out on oil sand from the McMurray formation, Alberta, Canada, from which the bi t um en had been previously removed by Soxhlet ext ract i on with toluene. Small am ount s o f carbonaceous material that was not soluble in toluene were removed by dry

71 sieving th r o u g h a 32 mesh sieve, gravity separation in t e t r a b r o m o e t h a n e and hand picking. The cleaned sand consisted mainly of quartz, with very small am ount s o f kaolinite, illite and rutile, and contained 97 wt.% SiO2. BET(*) surface areas were measured on a Quantasorb®instrument. The results for eight 1-g sand samples ranged from 0.22 to 0.32 m 2 g-1 with a mean o f 0.26 -+ 0.03 m 2 g-1. F o r the precipitation experiments it was necessary to use a coarser-grained sand fraction to prevent fines transport and t he 120-170 mesh fraction of an industrial quartz sand was selected. This sand was cleaned by ultrasonic vibration of small batches in tap water to loosen adhering fines. The water and suspended fines were decanted and the process was repeated until the water became clear. The sand was t hen washed twice with deionized water and dried. The cleaned sand contained 99 wt.% SiO2. BET Quantasorb ® surface areas of two duplicate samples were 0.0468 and 0.0473 m 2 g-l, equal within experimental error. Dissolution experiments were c o n d u c t e d in deionized water and in 0.01 M borax solutions th at had been brought to pH's 6.5 and 7.5 by the addition of HC1. All precipitation experiments were carried out in deionized water. The dissolution experiments were carried o u t in 300-ml stainless-steel autoclaves that were equipped with a sampling t ube and valve. A 7-pm sintered stainless-steel filter prevented fines f r om entering the tube. A weighed a m o u n t o f cleaned oil sand was put in the autoclave and ~ 200 ml of solution were added. The autoclave was t hen sealed and placed in a forced convection oven at the desired temperature. Several autoclaves were placed in the oven simultaneously for each temperature. At regular intervals, one autoclave was taken f r o m the oven and placed in an electric heating mantle at the same t e m p e r a t u r e as the oven and sampled. The first 5 ml were discarded, and the next 5 ml were collected in sufficient cold de*Brunauer, Emmett and Teller adsorption isotherm.

ionized water to dilute the e x p e c t e d SiO: concent rat i on to less than 100 ppm. The solution was adjusted to pH 2 with HNO3 and was submitted for silica analysis. Samples were withdrawn periodically from an individual autoclave which resulted in a decrease in the mass of H20 remaining. In most cases, sampling moved to a n o t h e r autoclave from the same experimental series after withdrawal o f 3--4 samples. In this m anner we were able to e x t e n d our runs to longer duration w i t h o u t having to account for large changes in the surface area to mass ratio. Several experiments were c o n d u c t e d to measure the effect of changing the ratio of surface area of the sand to the mass of H20 in the system. These experiments were run in the same autoclaves as t he dissolution experiments described above. The ratio of sand to water was varied and sampling was carried o u t at a fixed time. k calculated from these experiments should be equal to k calculated f r o m the experiments with time as a variable. The precipitation experiments were conduct ed in a flow-through system in which a positive displacement p u m p or a highpressure c h r o m a t o g r a p h y p u m p was used to forced water through two autoclaves placed in t andem with pressure maintained by a back-pressure regulator set at 1--2 MPa above the saturated water vapor pressure at run temperature. The autoclaves were filled with the cleaned industrial quartz sand, sealed and flooded with deionized water. The temperature in the oven was raised to a selected value in the range 250--275°C and kept at this level until t he solution was saturated with silica. The t e m p e r a t u r e was t h e n lowered to the desired value while injecting water to maintain t he pressure. When the t e m p e r a t u r e stabilized, samples were t aken at regular intervals by injecting water and withdrawing an equivalent a m o u n t of solution through the back-pressure regulator. The first 5 ml of sample were discarded and one or more samples ranging in size from 5 to 10 ml were collected. In this experimental design, the

72

first autoclave served as a buffer between the pump and the precipitation vessel. Cal.culations based on the assumption of plug flow showed that the deionized water injected during sampling never reached the b o t t o m of the precipitation vessel and no dilution correction is required. In precipitation run No. 2, the "saturation" and "precipitation" vessels were put in separate ovens. At the start of the experiment, the solution in both vessels was saturated at 250°C, after which the temperature of the precipitation vessel was lowered to 155~C. Samples were taken from both vessels using the method described above. All samples from the dissolution experiments were analyzed by atomic absorption spectrometry (AAS) (Devine and Suhr, 1977). In the precipitation experiments all samples were analyzed by both AAS and inductively coupled plasma spectrometry (ICP). Comparison of the analytical results showed that the ICP data are somewhat more precise than the AAS data and that 2.5% is a reasonable estimate of the relative standard deviation.

A comparative study of the analytical results will be published elsewhere. The numerical results have been treated in a number of ways. For the dissolution experiments in which several sampies were withdrawn from a single autoclave, we used eq. 5 in a modified form. The relationship between silica concentrations in sequential samples is given by: l n [ ( C e q - - C i ) / ( Ceq - - C i _ t )] =

--(A t / M i ) k f l

i 8}

where Ci = SiO: concentration in sample !, taken at time ti; A t = ti -- ti--1;Mi is the mass of water present during the period At; and Ceq is calculated from Crerar and Anderson (1971). A least-squares fit of eq. 8 to the data gives a straight line with slope k_A. Eq. 8 however: cannot be used to calculate the error on the slope as subsequent values of t h e logarithmic terms are not independent: The concentration that appears in the numerator of one term appears in the denominator of the next.

TABLE I D i s s o l u t i o n k i n e t i c r u n results Dissolution run No.

Temperature (°C)

Run duration (hr.)

N u m b e r of samples taken

AIM ( m 2 kg ~)

k ( t 0 -: s ~)

3 deionizedH:O 4 deionized H:O 5 deionizedH20 6 deionized H20 7 deionized H:O 8 deionized H20 9 deionized H:O 10 d e i o n i z e d H : O 11 d e i o n i z e d H : O 12 d e i o n i z e d H~O 13 d e i o n i z e d H : O 14 d e i o n i z e d H : O 15 pH 6.5 16 pH 6.5 1 7 pH 7.5 18 p H 7.5

150 170 205 252 250 200 200 250 250 250 255 255 200 250 200 250

668 120 1,027 288 48 500 646 338 513 48 24 48 507 432 454 336

6 6 9 7 7 11 10 7 14 13 6 11 11 10 10 11

17.3 17.3 17.3 17.3 5.2 5.2 5.2 5.2 5.2 5.2 5.2 5.2 5.2 5.2 5.2 5.2

0.411 0.647 1.63 4.40 18.3 2.68 1.51 7.29 10.8 23.4 12:7 16.8 2.62 8.25 2.91 5.17

2a

C o m p l e t e t a b l e s of t h e a c t u a l e x p e r i m e n t a l d a t a are given in Bird a n d B o o n ( 1 9 8 5 ) .

0.41 0.76 0.94 1.5 10 1.1 1.8 4.2 3.1 4.8 6.0 3.0 1.2 2.0 1.2 1.5

73 This means that a positive deviation from the " t r u e value" for one data point automatically results in a negative deviation from the " t r u e value" for the next data point and the calculated error in slope is too large. Since the deviations compensate for each other, the slope is still correct. We also fitted eq. 5 to the dissolution data w i t h o u t making any correction for sample withdrawal using a weighted least-squares linear regression procedure. In general it was found that the first few data points fell off the least-squares regression lines and a considerably better fit could be obtained using an equation of the form: --ln[(1 -- C/Ceq)] = k_(A/M) + B

(9)

where B is a constant. Putting t = 0: C0 = Ceq [1 -- exp(--B)]

(9a)

It was f o u n d that the k_-values from eqs. 8 and 9 are equal within the error estimate from eq. 9, and it seems reasonable to assume that the experimental errors in k-values f o u n d using eq. 8 are of the same magnitude as those estimated from eq. 9. The k -values reported in Table I were calculated using eq. 8 and the associated errors were calculated with eq. 9. For the dissolution experiments in which A / M was varied at constant time --ln(1 -C/Ceq ) w a s plotted as a function of A / M and the data were subjected to least-squares linear regression analysis. The precipitation data were analyzed with the aid of eq. 4 using the weighted leastsquares linear regression technique to calculate k_ and associated error. Activation energies were obtained from eq. 7 for both the dissolution and precipitation experiments by a weighted least-squares linear regression of log k o n 1 0 0 0 / T . E A and k' were calculated from the slope and y-intercept, respectively. 4. Results and discussion Sixteen dissolution experiments with time as the independent variable, seven precipita-

tion experiments and four dissolution experiments with A / M as the independent variable were carried out. The experimental conditions and complete data tables for these runs are given in Bird and Boon (1985). Table I summarises the results of our dissolution experiments and lists k_-values and associated errors as calculated from eqs. 8 and 9, respectively. Fig. 1 shows the results for dissolution experiment 4 as a typical example. In Fig. 1A, B and C, eqs. 9, 8 and 6 were used, respectively. The positive intercept with the vertical axis in Fig. 1A has been observed by other authors (van Lier et al., 1960; Bergman, 1963; Henderson et al., 1970; Rimstidt and Barnes, 1980) who assumed that it was caused by rapid dissolution of a disturbed surface layer of high solubility. Moore and Rose (1975) t h o u g h t that it resulted from the dissolution of very fine particles adhering to the quartz surface. In either case, "Co" (eq. 9a) should be a measure of the a m o u n t of quartz dissolved during the initial rapid dissolution stage. To test this hypothesis, we re-used the sand remaining from dissolution experiments 6, 8, 10 and 12 in dissolution experiments 7, 9, 11 and 13, respectively (see Table I). As part of the disturbed surface layer should have been removed in the initial experiments, "Co" should be smaller in the second experiment. For the three pairs, 6--7, 8--9 and 10-11 "Co" was lower in the second experiment, which agrees with the hypothesis outlined above. However, the reverse occurred in the pair 12--13 where "Co" was higher in the second experiment. In our dissolution runs, we noted that the length of time over which the dissolution results could be modeled with a parabolic rate law (eq. 6) changed with temperature. At 150°C, the parabolic region can last to several hundred hours, at 200°C this was reduced to 10 hr. or less, and a t 250°C, to 6 hr. or less. In the experiments of van Lier et al. (1960), the concentration of silica in solution followed a parabolic, linear or logarithmic time dependence depending on the ionic strength of the solution (see Dibble,

1980, pp. 53 and 54, figs. 2A and 2B). Similar observations have been made on the dissolution kinetics of other silicate systems and a number of models, none of which have been 10

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= "

=,~]

J

tA)

09 /t

/"

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: !

0.8 07 ~-~

0.6

~

o5

~

o.4

~

Ti

"

~e~ lour~ i

~4r, F ItS) ~2( ! \ 5o0

0.3 0.2

~,-

0,1 0

~ I 10

l 20

~1 30

i 40

i 50

I 60

i ..1 .. i ?0 80 90

i i 100 110 120

~

~-

Time (hours) I

3.0

ioQ)

Tpme "z

2,0

nour~

iT a~

l

I

Fig. 2. Plots for p r e c i p i t a t i o n e x p e r i m e n t s . A. A first-order rate plot for run No. 3 (Table I1) at 177°C (eq. 4). B. The silica c o n c e n t r a t i o n for run No. 3 (Table lI) p l o t t e d against t 1/~ (eq. 6/.

1<0

0

02

0.4

06

08

10

12

j 14

&ti/Mi

200

d

(C)

100

05

2

4

6 Time

8

10

12

1/2 (hours)

Fig, 1. Plots for d i s s o l u t i o n e x p e r i m e n t s . A. Plot o f - - l n ( 1 - - C[Ceq) vs. time for run No. 4, Table I (eq. 9). B. Plot o f --ln[(Ceq - - C i ) / ( C e q --Ci--~)] vs. z, ti]M 1 for run No. 4, Table I (eq. 8), See t e x t for discussion. C. Silica c o n c e n t r a t i o n vs; t "~ for run No. 4, Table I (eq. 6). See t e x t for discussion,

completely successful, have been put forward to rationalize these observations (e.g., Wollast, 1967; Luce et al., 1972; Lagache, 1976; Petrovic et al., 1976; Fung et al., 1980; Dibble and Tiller, 1981; Aagard and Helgeson, 1982). In this context, it is important to note that a parabolic kinetic model cannot track the dissolution or precipitation process as it approaches equilibrium, and in this sense, the duration o f the "'parabolic kinetics" is in itself a function of the rate o f approach to equilibrium and a parabolic rate law by itself can never provide a complete description o f the process. The complete data for our precipitation experiments are given in Bird and Boon (1985), and the results are summarized in Table II which lists the experimental conditions and the rate constants k_ with the as-

75

sociated errors as calculated from eq. 4 using Ceq-Values calculated with the regression coefficients of Crerar and Anderson (1971). Fig. 2A shows a plot of the data for dissolution run No. 3 (Bird and Boon, 1985) using eq. 4. Fig. 2B shows the same experimental data using eq. 6. The goodness of fit using eqs. 4 and 6 is nearly identical. The only other precipitation data for quartz available in the literature are those of Rimstidt (1979). For comparison, we analyzed his raw data in exactly the same way as we analyzed ours and concluded that his precipitation data follow the same trends as ours and can be described by both eqs. 4 and 6 (see Figs. 4A and 4B in Bird and Boon, 1985). Although parabolic dissolution behavior has been discussed widely in the geochemical literature, only one other example of a parabolic precipitation rate has been reported. Holdren and Adams (1982) showed that coprecipitation of aluminosilicate minerals and quartz could account for the observed change in the silica concentration with time. It seems unlikely however, t h a t this mechanism is responsible for the results reported here where the parabolic time dependence occurred over a wide range of experimental conditions using a variety of reaction materials of varying degrees of purity. It is not possible to account for the parabolic time dependence through a reaction of a disturbed surface layer or attached fines. The dis-

solution experiments were carried out for long periods of time and any disturbed surface layer would have dissolved very early on in the experiment. In the precipitation experiments, the sand was initially reacted for several tens of hours at a higher temperature than that used for precipitation. This pre-equilibration step should have removed any disturbed surface layer before the precipitation was initiated. For the range of conditions studied, parabolic and first-order precipitation plots have very similar shapes, and at this time, we have no satisfactory theoretical explanation for this observation. In four experiments [data are given in Bird and Boon {1985)], time was fixed and the surface area to mass of water ratio (A/M) was the independent variable (eq. 5 with t fixed and A/M variable). Plotting --ln(1 C/Ceq) against AIM results in a distinct curve which can be resolved into two linear segments with different slopes (see fig. 4 in Bird and Boon, 1985). For run l a (Table III), the slope of the segment with A/M ratios between 1.3 and 15.7 m 2kg -1 corresponds to k = 3.3 • 10 -T s -1, whereas the slope of the segm e n t with AIM ratios between 17.4 and 39.2 m 2 kg -~ (Run lb), corresponds to k = 9 . 5 - 10 -8 s -~. The other three experiments {Table III) showed a similar trend; k_ is smaller at higher A/M ratios and larger at lower A/M ratios. Rimstidt (1979) reported experiments -

-

T A B L E II P r e c i p i t a t i o n k i n e t i c r u n results Precipi-

T e m p e r a t u r e , T (°C)

Run duration

Number of

A/M

tation run No.

saturation

precipitation

(hr.)

data points

(m~ kg-1)

2 3 4 5 6 7 8

250 265 265 265 271 271 275

155 177 177 200 155 221 123

1,042 217 113 210 266 266 512

27 11 8 15 14 13 12

140 156 124 209 116 177 156

duplicate duplicate duplicate duplicate duplicate

C o m p l e t e tables of t h e a c t u a l e x p e r i m e n t a l data are given in Bird a n d B o o n ( 1 9 8 5 ) .

k (10 9 s 1) 2a 0.99 6.5 7.6 17 13 25 2.8

0.28 1.4 3.0 5.2 1.4 16 0.62

T A B L E III

Experiments with A/M as the independent variable Experiment No.

Temperature (°C~

Time (hr.)

A/M range (m 2 kg ~)

k_

min,

max.

(10 ~s '}

la lb

205 205

21 21

1.3 t7.41

15.66 39.2

2a 2b

200 200

40.5 40,5

0.52 3.91

1.30 6.25

6.73 1.30

3a 3b

250 250

21 21

0.13 5.22

2.61 26.1

20.3 6.28

4a 4b

250 250

40.5 40.5

2.61 7.83

7.83 26.1

6.67 8.09

3.3 0.948

Each A/M range used to obtain k is defined by its m i n i m u m and m a x i m u m value. See text for explanation. C o m p l e t e tables of the actual experimental data are given in Bird and Boon ( 1 9 8 5 ) .

carried out by E. Usdowski in which AIM was varied. Five samples with A/M between 0.173 and 1.36 m 2 kg-' were reacted at 173 °, 202 ° and 223°C, presumably in static autoclaves. As in our experiments, the dissolution rate decreased with increasing A/M [see Bird and Boon (1985) for more complete discussion]. The decrease in k_ with increasing values of A/M is possibly due to the way the dissolution experiments were conducted, Samples were taken from the bulk fluid just above the sand. The pore fluid in the sand equilibrates with the bulk fluid by diffusion of dissolved silica. The diffusion path is tortuous, the cross,section for diffusion is small and concentration gradients along the path get smaller with increasing distance from the sand--bulk solution interface. With increasing A/M, diffusion from the deepest sand layers probably becomes slower than dissolution, and the bulk solution concentration increases more slowly than predicted by eq. 5. These observations suggest that pore geometry and diffusion may be important in controlling the rate of transport from the dissolving silica grains to the bulk solution. Most of our dissolution experiments were carried o u t at an A/M of 5.2 m 2 kg -' where eq. 5 applies. Experiments 2--5 (Table I) fall somewhat beyond the range where eq. 5 is

\.,

-60

\ ~'V',.

;°! i

80 ~-

".

\

Dissolution Experiments • . . . . . . *.

Van Lier et a1.(1960) Rirnstidt (t979) This w o r k

Precipitation Experiments rJ

This w o r k

[] ......

Rimstidt (1979) Rimstidt (1979)

--

This w o r k

.....

Combined Results

Combined Results i 15 1/T~ 1000 IK )

Fig. 3. Arrhenius plot of our dissolution and precipitation experiments (Tables I and II), a n d those of van Lier et al. ( 1 9 6 0 ) and R i m s t i d t (1979). Usdowski's data were not plotted for the reason discussed in the text. Regression lines are s h o w n for our dissolution and precipitation results and Rimstidt's c o m b i n e d data. Constants for these lines are listed in Table IV.

77

valid and k_ derived for these experiments may be too low. In the precipitation experiments, the pore solution was sampled directly and diffusion rates should not have affected the silica concentration in the fluid. The activation energy for precipitation and the pre-exponential constant k' were determined from an Arrhenius plot (eq. 7). Our data (from Tables I and II) are plotted in Fig. 3, together with those of van Lier et al. (1960) and Rimstidt and Barnes (1980). Usdowski's results were not included on the figure because they plot well away from the major trend in Fig. 3 and we susp%ct some inconsistency in effective surface area. Also, the k -values we calculated from Usdowski's data were four times greater than those calculated by Rimstidt and Barnes from the same data. We also corrected the k_-values of Rimstidt's (1979) points 2M and 20 as there was a mistake in his calculations. The data in Fig. 3 occur in clusters corresponding to precipitation, dissolution or investigators. Within each set, there is considerable scatter and an even greater scatter between the different sets. Activation energies, values of the preexponential constant and error estimates for each set of data were obtained by linear regression and are listed in Table IV. The experimental error in both the activation energy and the pre-exponential term k' is very large and there is no statistically significant dif-

ference between the values from the various sets. However, the clustering of data points suggests that there are systematic differences between the groups and that the data from different experimental systems should not be combined. In fact, combination of all data results in an activation energy of 78 kJ mo1-1 which is much larger than that for any of the individual sets (see Table IV). An Arrhenius plot of our parabolic rate constants (see eq. 6) resulted in an activation energy for precipitation of 62 kJ mo1-1, which is equal, within the error, to that obtained from the first-order rate law. The activation energies from our dissolution experiments and Rimstidt's are equal within experimental error. The activation energies from the precipitation experiments seem to be smaller than those from dissolution, even though the large experimental error makes it difficult to draw a definite conclusion and more experiments would be needed to verify this observation. We have not been able to suggest a possible cause for such a difference but speculate that effective surface area in the experiments may differ from the measured surface area. Errors in measuring surface area may also contribute to spread within and between the data reported by different investigators. The BET m e t h o d for estimating surface area is not particularly accurate for the low surface areas used by all investigators. A systematic error

T A B L E IV C a l c u l a t e d a c t i v a t i o n e n e r g y for p r e c i p i t a t i o n (E A ) for v a r i o u s e x p e r i m e n t a l c o n d i t i o n s Experiment

Dissolution experiments Precipitation experiments Combined dissolution-precipitation Dissolution experiments Dissolution experiments withA/M = 17.4 m 2 kg -~ Precipitation experiments Combined data Dissolution

Reference

Number of data points

E A ( k J m o l 1) 2o

log k'_

Rimstidt (1979) Rimstidt (1979) Rimstidt (1979)

6 5 II

55.1 41.7 60.5

7.6 11.9 6.1

--0.42 --2.18 --0.35

8.34 1.48 0.76

this work this w o r k

16 4

51.4 43.3

14.7 23.3

-0.97 --2.03

1.36 2.27

this w o r k R i m s t i d t ( 1 9 7 9 ) , this w o r k * E. U s d o w s k i r e p o r t e d in R i m s t i d t ( 1 9 7 9 ) *

7 34 15

34.3 78.3 75.4

10.3 6.1 13.6

4.19 1.68 2.67

1.26 0.36 1.50

* U s d o w s k i ' s d a t a were n o t i n c l u d e d in t h e c o m b i n e d d a t a set for r e a s o n s d i s e u s s e d in t e x t .

2a

in estimating surface w o u l d n o t a p p e a r if o n l y one starting material were used in an individual set o f e x p e r i m e n t s b u t will a p p e a r w h e n t h e results o f d i f f e r e n t investigators are c o m p a r e d . At this time it is impossible m spec, ify a detailed r e a c t i o n m e c h a n i s m in terms o f either the q u a r t z surface or the silica species p r e s e n t in solution. The similarity b e t w e e n the dissolution b e h a v i o r o f q u a r t z and o t h e r silicates and the high a c t i v a t i o n energies o f dissolution and p r e c i p i t a t i o n suggest t h a t r e a c t i o n o f the Si--O f r a m e w o r k is p r o b a b l y the m o s t i m p o r t a n t aspect o f silica and silicate dissolution reactions. This r e a c t i o n is c o m p l e x and d e p e n d s o n a n u m b e r o f variables including surface charge, ionic strength o f the solution, t e m p e r a t u r e , pressure, etc. It almost c e r t a i n l y p r o c e e d s t h r o u g h several steps. Much m o r e detailed e x p e r i m e n t a t i o n is n e e d e d to d e v e l o p a m e c h a n i s t i c kinetic m o d e l f o r q u a r t z dissolution. H o w e v e r , the a c t i v a t i o n energies and p r e - e x p o n e n t i a l t e r m s listed in Table IV can be used to calculate a rate c o n s t a n t for any t e m p e r a t u r e and are very useful in the p r e d i c t i o n o f silica mass transport. No d a t a o n t h e dissolution and precipitat i o n behavior o f q u a r t z at high t e m p e r a t u r e , as a f u n c t i o n o f salinity or p H (at p H > 7.5) are n o w available. F u r t h e r studies in this area w o u l d e x t e n d t h e range over which mass t r a n s p o r t p r e d i c t i o n s can be made.

5. Conclusions and applications N i n e t e e n dissolution and seven precipitat i o n e x p e r i m e n t s were carried o u t at t e m p e r a tures b e t w e e n 121 ° and 250°C and corresponding w a t e r v a p o r pressure. T h e results o f the dissolution e x p e r i m e n t s are in reasonable a g r e e m e n t with t h o s e r e p o r t e d previously by van Lier et al. {1960), R i m s t i d t ( 1 9 7 9 ) and R i m s t i d t and Barnes ( 1 9 8 0 ) and can be described b y a z e r o - o r d e r d i s s o l u t i o n - - f i r s t - o r d e r p r e c i p i t a t i o n reaction. T h e activation e n e r g y f o r q u a r t z p r e c i p i t a t i o n lies b e t w e e n 51 and

55 kJ mol J. The activation e n e r g y ~mtamec!, f r o m o u r p r e c i p i t a t i o n e x p e r i m e n t s ~:~°es o m e what smaller b u t the d i f f e r e n c e is t~:A static': tically significant. Most o f t h e Jatao puJ> ticularly below 200°C, can also be-ci~scrib,.% by a parabolic rate e q u a t i o n , which teads t.o ~.~.i activation energy in the same rang~ as bhat, f o u n d above. T h e high activatio~ energy suggests t h a t d i s r u p t i o n o f the Si----~:i:~lram~ ~w o r k is t h e r a t e - d e t e r m i n i n g step. F o r the e x p e r i m e n t s in which ~he ra~io (surface area of q u a r t z ) / ( m a s s o f H20) was the i n d e p e n d e n t variable, we f o u n d that the rate c o n s t a n t s o b t a i n e d at high .~/M arv smaller t h a n those o b t a i n e d at low A/M. It was s h o w n t h a t this m a y have bee~:~ caused b y the e x p e r i m e n t a l set-up, in which diffusion f r o m p o r e solution to bulk ?~olution m a y b e c o m e t h e r a t e - d e t e r m i n i n g step at. high A/M. The z e r o - o r d e r - - f i r s t - o r d e r equa~ton can be used to p r e d i c t silica mass t r a n s p o r t during steam injection. T h a t is, in a system in which steam, w a t e r and oil are flowing, a sitiea conservation e q u a t i o n in differential f o r m m a y be w r i t t e n as:

5t

(q~pwSwrs)

V.

7s

,,~

Uv~"

+ qs + k (1

#)pRASw(%eq

~s~

I10~

where ¢ = p o r o s i t y , pw = density of water: Sw = s a t u r a t i o n o f water: ~w -- mole fraction o f silica m t h e w a t e r phase; rseq = equilibrium mole f r a c t i o n o f silica in the water phase; Kw = the p e r m e a b i l i t y o f the f o r m a t i o n t o water, ~w = viscosity o f water; ~ ::: pressure p o t e n t i a l ; qs = source and sink terms for silica; p R = density o f quartz; and A = surface area o f the quartz. It is s h o w n in S t o n e e~ al. (1985), t h a t w h e n the above silica conservation e q u a t i o n is c o u p l e d t o a t h e r m a l m u l t i c o m p o n e n t reservoir m o d e l ~see S t o n e and Malcolm, 1984), t h a t silica c o n c e n t r a t i o n s in the prod u c t i o n fluids f r o m large-scale e x p e r i m e n t s can be p r e d i c t e d successfully. These predic-

79

tions used only the experimentally determined constants discussed in this paper.

Acknowledgements This work was carried out as part of the Hydrothermal Chemistry Project in the Oil Sands Research Department of the Alberta Research Council. Financial support was provided by the Alberta Research Council/ Alberta Oil Sands Technology and Research Authority Joint Oil Sands Research Program. Our colleagues, W.D. Gunter and Peter Tremaine provided many constructive suggestions during the experimental phase of the work and on the manuscript. Brian Wiwchar, Larry ttolloway and Shawn Cake carried o u t most of the experimental work. Larry Holloway and Brian Fuhr of Oil Sands Analytical Services spent m a n y hours on the silica analyses and even more hours discussing the results. Diane Teppan and Phyllis Kozak were responsible for turning our illegible scribbles into a completed manuscript. We gratefully acknowledge all of these contributions.

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