parallel reaction kinetics of smectite to illite conversion

Clay Minerals (1996) 31, 365-376

P A R A L L E L R E A C T I O N KINETICS OF S M E C T I T E TO ILLITE C O N V E R S I O N

H. W E I , E. R O A L D S E T AND M. B J O R O Y *

Department of Geology and Mineral Resources Engineering, The Norwegian Institute of Technology (NTH), 7034 Trondheim, Norway, and * Geolab Nor A/S, 7002 Trondheim, Norway

(Received 24 May 1994; revised 11 January 1996)

ABSTRACT: A parallel reaction model is developed for describing the conversion of smectite to illite. Each reaction represents a group of similar smectite layers that require the same activation energy and have the same iUitization rate. The model considers that the rate-determining reactant is smectite itself which follows first-order Arrhenius kinetics. By modelling the data from hydrothermal illitization experiments and from a Gulf Coast well, the activation energies are found to be distributed in the range of 11-24 kcal/mol with a maximum reaction at 18 kcal/mol, which involves 65% of reactive smectite. A frequency factor in the order of 10-3-10-4/s, obtained from the data fitting, appears to be adequate for modelling natural diagenesis in sedimentary basins. The distribution pattern of activation energies is considered to be controlled by the degree of heterogeneity of the initial smectite and the degree of electrostatic interactions between smectite layers and the newly formed illite layers during reaction.

The main diagenetic process in claystones is the formation of illite from smectite via a mixed-layer illite-smectite (I-S) intermediate (Perry & Hower, 1970; Hower et al., 1976; Boles & Franks, 1979; McCubbin & Patton, 1981; Smart & Clayton, 1985; Pearson & Small, 1988; Hillier & Clayton, 1989). With increasing burial depth and temperature, the percentage of expandable (smectite) layer in the I-S clay decreases and the pattern of interlayering changes from random to ordered. This alteration has also been observed in the contact metamorphic environment (Pytte, 1982). The reaction has been verified by hydrothermal experiments (Eberl & Hower, 1976). It is considered that the extent of this transformation is a function of reaction temperature and time, and therefore can be used as a maturity indicator for a thermal history study of sedimentary basins (Srodofi, 1979; McCubbin & Patton, 1981; Pearson & Small, 1988; Pytte & Reynolds, 1989; Pearce et al., 1991).

Although this alteration has been used in a variety of mineralogical and geochemical fields, the basic reaction mechanism remains unclear and has been the subject of much work since the 1970s. The proposed mechanisms include solid-state smectite illitization with replacement of tetrahedral Si 4§ by A13§ and fixing of K § in interlayer sites (Eberl &

Hower, 1976; Hower et al., 1976); dissolution of smectite and crystallization of illite (Boles & Franks, 1979) with significant weight loss in l-S; illite formation induced by the change from high- charge to low-charge smectite (Bouchet et al., 1988), a reaction that requires Si 4§ instead of releasing it.

Early kinetic modelling of the smectite to illite conversion was attempted experimentally by hydrothermal alteration of glass (Eberl & Hower, 1976). An activation energy of 19.6 -I- 3.5 kcal/mol has been derived for conversion of synthetic beidellite with the composition A12Si3.66A10.34Olo(OH)2K0.34 to mixed-layer illite-smectite, and a reaction of A13§ + K § + smectite ~ I-S + SiO2 has been proposed. Models involving first- to sixth-order reactions with activation energy ranging from 22.5 to 33 kcal/mol and frequency factors of 1.0 to 5.2 x 107 s -1 were developed somewhat later (McCubbin & Patton, 1981; Pytte, 1982). These models treated the illitization of smectite as a single reaction.

Smectites are composed of individual layers which are not identical in chemical composition (Newman & Brown, 1987), layer charge (Lagaly, 1982) and other structural characteristics. These properties determine the reactivity of fundamental smectite layers. Smectites as weathering products

�9 1996 The Mineralogical Society

366 H. Wei et al.

generally have heterogeneous layer-charge distributions (Lagaly, 1982). Electrostatic attraction between interlayer cations and layer charge has been considered to control the binding energy between the incoming K ion and the silicate sheet (Sawhney, 1969), and hence the alteration kinetics (Howard & Roy, 1985). Obviously, the heterogeneity of natural smectite indicates that its conversion to illite, at layer or particle level, may have more than one reaction rate. Each smectite layer or each group of similar layers may differ in illitization rate from others. This paper presents a kinetic model which is composed of parallel reactions for the illitization of smectite.

K I N E T I C M O D E L

In the kinetic model discussed here, the alteration of one smectite layer is assumed to be a single reaction with one rate constant. When these layers are put together, the alteration rates could be the same for all layers if they behave similarly during the thermal alteration. In this case, the apparent overall alteration rate can be described by a single reaction model. However, the natural heterogeneity in layer charge (Lagaly, 1982) and in the associated properties of smectite (Sawhney, 1969; Howard & Roy, 1985; Bouchet et al., 1988) is very well known. The activation energies required for destruction of these heterogeneous layers and formations of illite layers are likely to be different. Apparently more than one reaction rate is required to describe the illitization of heterogeneous smectite.

For the homogeneous smectite to be described by a single reaction, it is necessary to keep smectite layers identical not only at the beginning of, but also throughout, the thermal transformation. This condition is unlikely to be reached since the "electrostatic inducing interactions" (Bassett, 1958; Sawhney, 1969) will occur between smectite layers and the newly formed illite layers. While some illite layers are formed, the properties of the neighbouring smectite layers are likely to be altered through inducing interaction. This alteration may result in higher or lower activation energy being required to convert to illite. The initial homogeneity is then destroyed.

The electrostatic-inducing interaction also occurs in heterogeneous smectite after illite layers begin to appear. This inducing effect exists during the whole process of thermal alteration. Bouchet et al. (1988)

and Howard & Roy (1985) have related surface charge density to illitization.

M e c h a n i c a l m o d e l

At the beginning of illitization, owing to the heterogeneity of smectite, those layers which require low activation energy (easiest to be transformed to illite) begin to convert first. For homogeneous smectite, the layer illitization takes place randomly at the beginning. While some illite layers have been formed, the smectite layers can be roughly divided into three types based on the inducing polarization effect of the nearest-neigh- bour layers: SSS, SSI(=ISS), and ISI (the under- lined S indicates the smectite layer under consideration). Obviously, these three types of layers differ in terms of illitization rate. Bethke & Altaner (1986) have proposed the same types of smectite layers and assigned each type of layer a probability of reacting (junction probability, Bethke et al., 1986).

lllite formation results in layer collapse due to the replacement of Ca/Mg by K. Sawhney (1969) has proposed that the collapse in one layer will reduce the effective negative charge on the silicate sheet of the adjacent layer, and thus prevents the entry of the cation into this adjacent layer. The cation will instead enter the next layer. This means the polarization effect induced between the smectite and illite layers will probably make the illitization more difficult for the neighbouring smectite layers. These neighbouring layers will require higher activation energy (higher temperature) to convert to illite. Apparently, the proposed three types of smectite layers have the reaction priority of SSS > SSI > ISI, with the ISI type having the lowest reactivity. Bethke & Altaner (1986) assigned a reaction priority of SSI > SSS > ISI to allow the formation of R2 (SIISIISII) ordering. By this priority, it does not seem possible to produce RI (SISISISI) ordering before R2. However the R1, R2 and R3 (SIIISIII) sequences can be achieved with the priority of SSS > SSI > ISI (Fig. 1, see details below). As mentioned before, charge heterogeneity has influence on the reactivities of various types of smectites. The relative reactivities of these three smectite types are considered to be determined by the chemical composition and physical properties of starting smectite. A quantitative model describing the distribution pattern of the reaction rates (activation energies and frequency factors) will be

Kinetics o f I-S conversion 367

discussed in the following section (see Numerical model).

Figure 1 schematically illustrates possible cases of layer-by-layer illitization process by assuming the reaction priority of SSS > SSI > ISI. With increasing temperature, the SSS type smectite will be illitized first. There are two basic types of illitization sequence for SSS smectite. The illitization of every second layer will go directly to ideal R1 ordering with 50% illite (Fig. la), while the illitization of every third smectite layer (Fig. lb) will form a random I-S which will produce ideal R2 (66% illite) ordering when the SSI type is illitized. At higher temperatures, the IS._I type smectite layers that require high activation energies to initiate the conversion start illitization. This will result in the long-range ordering sequences. The ideal RI will go to ideal R3 with 75% illite (Fig. la); and the ideal R2 will go to ideal R5 (Fig. lb). If illitization of SSS smectite takes place randomly or at a higher range (e.g. every fourth and (or) fifth layer), the random I-S can be further illitized (SSS illitization) until it contains only every second and third illite layers (Fig. lc). This is the most likely case which occurs in natural diagenesis where the charge heterogeneity causes the newly formed illite layers to be irregularly distributed. Illitization of SSI smectite in this random I-S will produce R1 ordering with extra illite layers randomly located in the SISISI sequence as shown in Fig. lc. Further illitization (ISI type) will direct to R3 ordering with extra illite. Figure lc shows the case with more every second illite layer than every third, which forms R1 ordering. Consequently, a random I-S with more every third itlite layer than every second will produce R2 ordering with extra illite. Extra illite percentage compared with the ideal ordering is commonly observed in diagenetic clays (e.g. R1 at >65%, R2 at 75-85%, and R3 at >90% illite, Reynolds & Hower, 1970; Perry & Hower, 1970; Bethke et al., 1986). Finally, at an advanced stage, all the reactive smectite will be converted to illite.

The layer-by-layer reaction model can describe the smectite to illite alteration sequence: development of random interlayering and transition to ordered interstratification (short-range first and then long-range). However, it is not possible to go directly from R1 to R2 and from R2 to R3 by the layer transformation mechanism. The R2 ordering, as a further step from the R1, has been shown to have occurred in nature by Nadeau et al. (1984a,b) using transmission electron microscopy. To explain

such observations, other mechanisms for the illitization, such as dissolution/precipitation (Boles & Franks, 1979) and the fundamental particle concept (Nadeau et al., 1984a,b,c) have to be applied. Regarding these mechanisms, the charge heterogeneity and smectite configuration (SSS, SSI, ISI) and perhaps also the boundary condition, have to be considered. In the case of the dissolution/ precipitation mechanism, the rates of smectite dissolution and illite precipitation are not the same for all the fundamental particles under consideration. It may be that a smectite layer, having a given reactivity, dissolves at one location, while an illite layer precipitates somewhere else from the dissolved material at another rate. The reactivity of smectite is affected by various factors and is not constant during the reaction. By splitting the reactivity into several groups, each with a given reaction rate, it is possible to simulate the whole process properly.

N u m e r i c a l m o d e l

As discussed above, the smectite layers can be roughly divided into three types, in terms of neighbouring layers. The kinetics of illitization of smectite can be described by assigning to each type of layer a reaction rate (three reactions in total; Bethke & Altaner, 1986). However, there may exist considerable differences among the smectite layers of the same type, depending on their chemical composition and the associated properties. This means the illitization kinetics may not be successfully modelled by only three parallel reactions. Instead, we consider multi-parallel reactions. In this model, the reaction rates are distributed in a certain range, and the pattern of rate distribution is determined by the properties of the starting smectite.

Illitization of smectite has been considered to be kinetically (time and temperature) controlled. Eberl & Hower (1976) successfully interpreted their hydrothermal experiments as a first-order reaction with respect to smectite content. McCubbin & Patton (1981) also fitted a first-order kinetic equation for natural I-S samples with known geothermal histories. However, it is arguable that first-order reaction predicts a greater illitization rate in illitic I-S and a more complete reaction than is observed in nature (Pytte, 1982; Bethke & Altaner, 1986). Pytte (1982) has developed high-order reaction models to approach the observed data.

368 H. Wei et al.

S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S

S S S

S S S S S S IIIIII

? s s s s s s IIIIII

S S S S S S IIIIII

S S S S S S IIIIII

S S S S S S IIIIII

S S S S S S IIIIII

Ideal R1

ISl

S S S S S S IIIIII IIIIII IIIIII

S S S S S S IIIIII IIIIII IIIIII

S S S S S S IIIIII IIIIII IIIIII i

Ideal R3

S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S

S S S SSI ISI

S S S S S S | S S S S S S ! S S S S S S /

�9 ~ IIIIII , IIIIII ~ IIIIII -

S S S S S S - - ~ IIIIII ~ IIIIII �9 S S S S S S S S S S S S ~ , IIIIII .

- - ~ IIIIII ~ IIIIII IIIIII S S S S S S ! ~ IIIIII IIIIII

! S S S S S S " S S S S S S S S S S S S : I IIIIII IIIIII IIIIII ;

. : S S S S S S ~ IIIIII IIIIII i " S S S S S S S S S S S S ~ IIIIII I

IIIIII IIIIII IIIIII I S S S S S S - - ~ IIIIII IIIIII I

Random I-S Ideal R2 Ideal R5

S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S

s ~ s s_ss s_sl I_Sl

S S S S S S ~ s s s s s s / S S S S S S I s s s s s s :

i S S S S S S ~ IIIIII IIIIII IIIIII

S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S - - -e IIIIII IIIIII

~ IIIIII IIIIII IIIIII IIIIII -

�9 S S S S S S S S S S S S S S S S S S : ~ IIIIII - 4

S S S S S S - - -e IIIIII IIIIII IIIIII S S S S S S S S S S S S S S S S S S S S S S S S

�9 ~ IIIIII IIIIII IIIIII IIIIII -

�9 S S S S S S F S S S S S S S S S S S S ----> IIIIII - S S S S S S ~ IIIIII IIIIII IIIIII

i

Random I-S Random I-S R1 R3

54 % illite 77 % illite

FIG. 1. A scheme illustrating the conversion of smectite layers to illite layers and progressive ordering of I-S clay. The smectite layers adjacent to illite layers are considered different from others in reactivity, because of the polarization effect induced by neighbouring illite layers. The reaction priority of smectites with different configuration is assumed to be SSS > SSI > ISI. (a) Every second layer is illitized, which will lead to ideal RI and R3. (b) Every third layer is iHitized,which will lead to ideal R2 and R5. (c) Random illitization, which can be further illitized (SSS type) to produce random I-S composed primarily of every second and third illite layer.

This will produce R1 and R3 with extra illite layers randomly located in the ordering sequences.

'Smectite'

kl X,,

k= X~

R e a

C k~

t x,o i V e

k. X.o

Unreactive a

Kinetics of I-S conversion

' l l l i te'

xl

x,

x,

x.

Initial b

FIG. 2. A parallel reaction model for 'smectite' to 'illite' conversion�9 Each reaction represents a group of similar smectite layers that have same illitization rate.

However, the high-order reactions have no fundamental physical-chemical significance concerning the reaction mechanisms (Pytte & Reynolds, 1989). It is hard to accept that two or more smectite layers are required to collide (contact) with each other in order to be converted to an illite layer (second or higher order reaction). With a parallel reaction model, the first-order reaction kinetics can provide reasonable reaction rates for the illitization of smectite in a diagenetic environment.

To model the reactions of such a system, we p r o p o s e that the c o n v e r s i o n o f s m e c t i t e (expandable) to illite (non-expandable) is accom- plished by first-order, independent parallel reactions (Fig. 2). Each reaction represents a group of similar smectite layers that have the same illitization rate during the reaction. The rate for a parallel reaction can be expressed as:

dXi/dt = k i ( X i o - X i ) i = 1, n (1)

where Xio is the initial fraction of smectite for reaction i, Xi is the fraction of illite formed from reaction i, t is the time, n is the total number of parallel reactions and kl is the rate constant of reaction i, which follows the Arrhenius law.

ki = Aiexp(-Ei/RT) (2)

where A i is the frequency factor for reaction i, Ei is the activation energy for reaction i, R is the universal gas constant and T is the temperature.

The overall illitization rate (dX/dt) is then the sum of rates of parallel reactions:

369

dX d----/- = ~.= at (3)

At any time, the illite percentage in mixed-layer illite-smectite can be calculated by

illite b "~ )"]~in__l X i

smectite + illite -- a + b + Y~in=l Xio (4)

where the constants a and b denote the unreacfive fraction of smectite and the initial fraction of illite (fractions of illite layers before conversion takes place), respectively.

Reactions that require low activation energies take place at an early diagenetic stage�9 For instance, the proposed illite formation during high-charge to low-charge smectite conversion (Bouchet et al., 1988) is considered to be the first step of alteration under low-temperature conditions. Those reactions with high activation energies start at a relatively high temperature�9 The alterations that form ordered I-S may require high activation energies since the smectite layers for these reactions differ from others owing to the inducing effect from the neighbouring layers. Only when the special smectite layers (the SSI type in most cases, as illustrated in Fig. 1) located in the mixed-layer I-S are illitized can the interlayering structure become ordered. Obviously, the distribution pattern of Xio as a function of reaction rate determines the I-S diagenetic characteristics.

The number of parallel reactions represents the degree of heterogeneity of initial smectite and the degree of the inducing effect. If the starting smecti te was homogeneous (all layers were identical) and no inducing interaction occurred when illite layers appeared, the number of parallel reactions should be one. In this case, the present model is reduced to a single reaction as suggested by Eberl & Hower (1976). In practice, it is unlikely that the smectite involved in the alteration is composed of a series of identical layers and that no inducing polarization occurs in the mixed-layer I-S clay. Junction probability diagrams (Bethke et al., 1986) and Monte Carlo modelling of the three types of smectite layers (Bethke & Altaner, 1986) is the n = 3 equivalent of the present multi-parallel reaction model. The present model will be tested on hydrothermal experiment data and on natural I-S samples to evaluate the n value.

370 H. Wei et al.

As mentioned, layer heterogeneity and layer configuration have to be considered as rate- determining factors in smectite illitization, regard- less of the mechanism. The present numerical model describing the heterogeneity of reaction rate applies to either solid state layer-by-layer conversion mechanism or dissolution/precipitation mechanism.

M O D E L T E S T

Evaluation of the kinetic constants for the model is a kind of inverse modelling, to which curve fitting or the optimization procedure can be applied. The input data for the inverse modelling are the heating history (temperature and time) and the associated product composition. Equation (1) can be integrated to give Xi as a function of time and temperature, using presumed kinetic constants (Ei, Ai, Xio, a, b). The computed illite percentage, using equation (4), is then compared with the observed composition. The method searches for the kinetic constants to minimize the discordance between the observations and calculations. We used optimization algorithms for searching the kinetic constants for the data from hydrothermal experiments (Eberl & Hower, 1976) and the Gulf Coast well 6 (Hower et al., 1976; Aronson & Hower, 1976).

To reduce the number of independent variables when running a numerical search, the frequency factor of the Arrhenius equation was considered to be the same for all parallel reactions (A i = A , i = 1,

n). This is a general assumption for parallel reaction kinetics of kerogen maturation (Burnham et al., 1988; Ungerer, 1990) and shows a good fit under both laboratory and geological conditions. Thus the resulting kinetic model for parallel reactions will be a distribution of initial smectite fractions (Xio) as a function of activation energies (Ei). The constants, a and b, can usually be estimated from experimental data or from I-S diagenetic data.

The average activation energy for smectite to illite alteration was reported to range from 16 to 33 kcal/mol (Eberl & Hower, 1976; McCubbin & Patton, 1981; Pytte, 1982). To find the activation energy distribution for our parallel reaction model, we set the activation energy in the range from 10 to 40 kcal/mol for numerical search. The step size is set at 1 kcal/mol (discrete model), which means the layers that require activation energies of x 5 : 0 . 5 kcal/mol are grouped as equal layers that require x kcal/mol to convert to illite. The results show that

the step of 5 : 0 . 5 kcal/mol is accurate enough to simulate the smectite to illite alteration. Decreasing the activation energy step to 5 : 0 . 0 5 kcal/mol shows no better fit, whereas a step size of -I- 1.0 kcal/mol results in an improper fit of data. Another approach to describe the parallel reaction is to set the activation energy as a continuous distribution function, such as a Gaussian distribution. Although this method has fewer free parameters to fit, the discrete model is preferred since the Gaussian model cannot give satisfactory results when the heterogeneity of smectite requires an asymmetric distribution of activation energy.

Tests of the present model carried out on laboratory simulation samples and on natural samples reported in the literature show that more than one parallel reaction exists and that activation energies are distributed mainly in the range of 11 to 24 kcal/mol (Figs. 3, 4). Figure 3 shows the optimized kinetic constants for the conversion of synthetic beidellite AI2Si3.66A10.34OIo(OH)2Ko.34 to illite, using the experimental heating programs and product composition data of Eberl & Hower (1976). The unreactive smectite (constant a, in this case the unreactive beidellite) is set to be 10% and the initial fraction of illite (constant b) to zero, according to the experimental data. Figure 4 shows the activation energy distribution for the illitization of smectite in the <0.1 ~m shale fraction of Gulf Coast well 6, optimized from the palaeotemperature history and mineral composition of Hower et al. (1976) and Aronson & Hower (1976). For the <0.1 I.tm size fraction, the constant a is set at 20% and b at I0%, based on the reported diagenetic data.

These two sets of kinetic constants show similar activation energy distributions, both with a maximum reaction at 18 kcal/mol which involves 65% of the initial reactive smectite. This indicates that for both the artificial sample and natural smectite, most of the layers are identical. They require 18 kcal/mol activation energy to be converted to illite. When the alteration of these layers is completed, the I-S interstratification is expected to be ordered (R1 ordering at ~65% illite, Reynolds & Hower, 1970; Perry & Hower, 1970).

A wide range of the frequency factor (A) for the first-order smectite illitization has been reported. A value of 10 -3 s - ! with 18 kcal/mol of activation energy was used by Bethke & Altaner (1986). The hydrothermal experiments by Eberl & Hower (1976) showed a frequency factor of 1.4 s -1 (derived from their Arrhenius plot) with activation

Kinetics of I-S conversion 371

70

60

50

40

30

20

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Activation energy (El, kcal/mol)

FIG. 3. Activation energy distribution for the illitization of synthetic beidellite (composition II, Eberl & Hower, 1976). Frequency factor A = 0.5 s- l ; number of parallel reactions n = 8; unreactive smectite a = 10%; initial illite

b = 0 % .

energy E = 19.6 kcal/mol. McCubbin & Patton (1981), from natural I-S samples and known palaeotemperature histories, fit a frequency factor of 1.0 s -1 with E = 22.5 kcal/mol. This is approximately equal to A = 10-2 -10 -3 s -1 when

E is set at 18 kcal/mol (calculated by Arrhenius law, eqn. 2, for geological temperatures in the range of 50-150~ Obviously, the reported kinetics from laboratory simulation show a greater illitization rate than do those for natural diagenesis. Our

d

_o

t L

70-

I 6 0 . . i

50. I

40-

30

I ! L . . 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Activation energy (E~, kcal/mol)

FIG. 4. Activation energy distribution of smectite to illite conversion (Gulf Coast well 6, < 0.1 Ixm shale fraction, Hower et al., 1976; Aronson & Hower, 1976). Frequency factor A = 8.6 -4 s-r; number of parallel reactions n =

14; unreactive smectite a = 20%; initial illite b = 10%.

372 H. Wei et al.

optimized kinetic constants (Figs. 3, 4) also show a greater frequency factor for the synthetic beidellite (0.5 s -1) than that for the Gulf Coast well (8.6 • 10 -4 s-I). This may be due to the differences in properties of the starting materials and in the chemistry of the fluid phase. The artificial samples and chemical solutions used in laboratory experiments may not represent the characteristics of natural clays and their pore water.

Another difference is in the number of parallel reactions. A small proportion of smectite layers that require low activation energies (11-15 kcal/mol) exists in the <0.1 pm shale fraction from Gulf Coast well 6, but is not present in the synthetic beidellite, indicating a greater homogeneity in the artificial sample than in the natural smectite.

Figure 5 compares the application of the evaluated kinetic parameters for the parallel reactions to a model well under geological heating conditions. The model well has a surface temperature of 4~ and a heating rate of 1.5~ corresponding to a burial rate of 50 m/Ma with a geothermal gradient of 30~ The test, using kinetics from laboratory simulation of synthetic smectite shows a very low and narrow temperature range (<10~ to 60~ for the illitization to complete. This is not comparable with the I-S diagenesis in sedimentary basins and was considered to be due to the differences between artificial samples and natural clays as well as the chemical environment of the reaction system. Hydrothermal experiments by Eberl & Hower (1976) had shown that the K-saturated Wyoming bentonites formed illite much faster than did synthetic beidellite. However, the Na-saturated bentonites have very low illitization rates compared with the synthetic beidellite. The influence of the fluid phase on the reaction rate will be discussed below.

For the parallel reaction model derived from the Gulf Coast well 6, the test results show the illitization to start at around 40~ at 1200 m depth with ~20% of illite and to cease around 100~ at 3200 m depth with 80% of illite. These modelled temperatures and mineral compositions are geologically reasonable. At the beginning, the reaction rate is relatively slow, which is the result of reactions that require activation energies <18 kcal/mol (Fig. 4), and which correspond with the random illitization of starting smectite layers. The illitization rate increases systematically with burial depth (temperature). When the major reaction requiring 18 kcal/mol is completed, the inter-

2

3

% I[lite

20 40 60 80

I 1 I ]

\ \ Synthetic beidellite

Gul f C o a s t we l l 6

\ \

\ \

\ \

\ \

0 40 80 120 t60 Temperature ( *C)

FiG. 5. Test of the parallel reaction kinetics obtained from Gulf Coast well 6 and from the hydrothermal experiments on a model well. See text for details of the model well and Figs. 3, 4 for the kinetic constants. The kinetic constants from the Gulf Coast shale show a geologically reasonable temperature range for the

illitization of smectite.

layering becomes ordered and the illitization rate decreases again. At this stage, the slow reaction rate corresponds with the structure ordering of short- range to long-range ordered I-S. This behaviour of smectite illitization agrees very well with the I-S diagenesis observed in sedimentary basins.

The changes of reaction rate from slow to fast and then back to slow are the consequent results of the distribution of activation energies associated with parallel reaction kinetics. Actually, the distribution pattern of activation energies determines the pattern of diagenetic curves as illustrated in Fig. 6. The fast-to-slow and slow-to-fast reaction rate changes can be described by positively and negatively skewed distributions of Ei, respectively.


E

o .

r l

0

I

I

t

' I ' I '

,~platykur t ic ' E~

' nega t i ve l y skew' E I

I i I i

I ~ i t ive ly skew ' E i

"\ ' tw in -peak ' E i

\

I

\ . \ \ % \ N

'1

0 20 40 60 80 100

Extent of illitization (%)

FIG. 6. Extent of illitization with burial depth calculated on a model well, showing that the pattern of I-S diagenetic curve is determined by the distribution pattern of activation energies. See text for details of the model

well.

The platykurtic and leptokurtic distributions simulate the slow-fast-slow illitization rate sequence. In addition, the former gives a more platy (linear) diagenetic curve. The single reaction model is close to the leptokurtic distribution, but results in a deeper diagenetic curve. A more complex situation is illustrated by a 'twin-peak' distribution, which models a slow-fast-slow-fast-slow rate sequence. Data from Gulf Coast wells suggested this kind of

activation energy distribution. For instance, the relationship between expandability and temperature for 1-S from well 'E' (a typical Gulf Coast well) of Perry & Hower (1970) may be modelled by a twin- peak distribution of activation energies (see Fig. 1 of Eberl & Hower, 1976). Figure 6 demonstrates that the parallel reaction model has a good flexibility in numerical approaches to I-S diagenesis.

374 H. Wei et al.

D I S C U S S I O N

I-S diagenesis and numerical approaches

In sedimentary basins, a sharply-reduced illitization rate at high illite contents is commonly observed. Natural diagenesis appears to slow or cease at a composition of ~20% smectite in I-S, and this composition persists over a considerable temperature range (Aronson & Hower, 1976; Hower et al., 1976; Smart & Clayton, 1985; Pearson & Small, 1988). Pytte (1982) used fourth- to sixth- order reactions (first-order concerning cation contents and third- to fifth-order concerning smectite content) to approach I-S reactions, since the high reaction order causes the reaction rate to be dras t ica l ly reduced as the composi t ion approaches pure illite. However, the high reaction order with respect to smectite content can hardly be interpreted in the reaction mechanism. Pytte & Reynolds (1989) have pointed out that high-order reaction kinetics is only an empirical formulation that approximates the observed I-S reaction.

Another approach to this significant change in reaction rate at the later diagenetic stage is to consider the illitization of smectite as a chain of two-scale serial reactions (Whitney & Northrop, 1988; Vasseur & Velde, 1993). The first step corresponds with the formation of a disordered I-S phase at the expense of pure smectite; and the second step corresponds to the formation of ordered I-S structure. The rate for the first step reaction is usually greater than that of the second step. From the reconstructed palaeotemperatures and the clay compositions, Vasseur & Velde (1993) fitted rate constants for each step of the reaction and have successfully modelled several wells in different sedimentary basins.

The parallel reaction model presented in this paper can simulate various patterns of rate change by means of varying the distribution pattern of activation energies, as already illustrated in Fig. 6. Significant reduction in reaction rate at a later stage of illitization can be modelled by decreasing the fractions (Xio) at high activation energies (see the curve of positively skew Ei distribution in Fig. 6). Similarly, decreases in the fractions at low activation energies will slow down the illitization rate at an early stage of transformation (see the curve of negatively skew E~ distribution in Fig. 6). Other patterns of activation energy distribution, such as platykurtic, leptokurtic, and twin-peak

distributions (Fig. 6), give other trends of I-S transformation. Obviously, parallel reaction kinetics have the advantage of providing flexible numerical approaches to model various I-S diagenetic characteristics observed in sedimentary basins.

Influences o f chemical environment

Generally, the reaction of smectite to illite can be expressed as

smectite + necessary cations ~ illite + released cations

The kinetic characteristics of such a reaction are obviously determined by the chemistry of the smectite and the pore water which in turn is affected by the lithology of the surrounding sediments.

Necessary cations in the above reaction usually include K § AI 3+, Si 4+ and the released cations include Ca z§ Mg z+, Fe 3§ Na + and Si 4§ (Hower et al., 1976; Boles & Franks, 1979; Bouchet et al., 1988). In principle, an increase in the activity of the necessary cations will promote the reaction, whereas an increase in the activity of the released cations will inhibit the reaction.

Pytte (1982) derived a kinetic equation to include K § and Na § influence on smectite illitization. This raises the question of whether we need to include other cations, such as Ca 2+, Mg 2+, Fe 3+, A13+, Si *~ in the kinetic equation. There is no straightforward answer to this. Firstly, it is impossible to estimate precisely the cation activities in pore water, since they change with burial depth. Including all the cations will make the kinetic expression less general. Extrapolation from laboratory simulation to natural diagenesis, or from one basin to another will be more limited. Secondly, to what extent the reaction system is open or closed has to be considered, since cation availability is significantly different in open and closed systems (Altaner et al., 1984; Altaner, 1990). (Xher issues are the rates of dissolution of other minerals that can provide the necessary cations, diffusion of these cations into the I-S interlayers (Altaner, 1990; Pearee et al., 1991) and diffusion of the released cations out of the interlayers.

Other possible factors include the properties of surrounding rocks and the chemical composition of the initial smectite. It has been observed that the reaction does not proceed so far in sandstones as in shales with the same burial/deposition history (Boles & Franks, 1979; Hillier & Clayton, 1989). This suggests that the porosity/permeability and chemical composition of surrounding pore water and minerals determine the availability of necessary


cations for the smectite to illite alteration. It is difficult to conclude that shales favour illitization. Although shales can provide more cations than sandstones, the latter usually have higher permeability for pore water. As indicated by many authors (Eberl & Hower, 1976; Huff & Turkmenoglu, 1981; Bouchet et al., 1988; Hillier & Clayton, 1989), the reactivity of smectites depends on their chemical composition. For instance, K-smectites react more readily to iltite than Na or Ca varieties; Al-rich smectites are more reactive than Al-poor ones.

C O N C L U S I O N S

The parallel reaction model is derived conceptually from the heterogeneity of smectite and from the electrostatic-inducing interactions between smectite and illite layers in I-S. It explains the illitization of smectite at a level of fundamental layers. The model has the advantage of numerical flexibility to approach various types of I-S diagenetic behaviour which may occur in sedimentary basins. However, further work needs to be done to quantify how important and to what extent the cations will affect the illitization rate. Experimental work on this subject is in progress.

ACKNOWLEDGMENTS

This paper is a contribution to the 'Research Programme on Clays, Claystone and Shales in Petroleum Geology', a joint research programme between the University of Oslo and the University of Trondheim. We thank CONOCO Norway Inc. for financial support. Constructive reviews by J. ~rodori and R.J. Merriman and English correction from Peter B. Hall are gratefully acknowledged.

REFERENCES

ALTANER S.P. (1990) Calculation of K diffusional rates in bentonite beds. Geochim. Cosmochim. Acta, 53, 923-931.

ALTANER S.P., HOWER J., WHITNEY G. & ARONSON J.L. (1984) Model for K-bentonite formation: Evidence from zoned K-bentonites in the disturbed belt, Montana. Geology, 12, 412-415.

ARONSON J.L. & HOWER J. (1976) Mechanism of burial metamorphism of argillaceous sediment: 2. Radiogenic argon evidence. Geol. Soc. Am. Bull. 87, 738-744.

BASSETT W.A. (1958) Copper vermiculites from Northern Rhodesia. Am. Miner. 43, I 112-1133.

BETHKE C.M. & ALTANER S.P. (1986) Layer-by-layer mechanism of smectite illitization and application to a new rate law. Clays Clay Miner. 34, 136-145.

BETHKE C.M., VERGO N. & ALTANER S.P. (1986) Pathways of smectite illitization. Clays Clay Miner. 34, 125-135.

BOLES J.R. & FRANKS S.G. (1979) Clay diagenesis in Wilcox sandstones of Southwest Texas: Implications of smectite diagenesis on sandstone cementation. J. Sed. Pet. 49, 55-70.

BOUCHET A., PROUST D., MEUNIER A. & BEAUFORT D. (1988) High-charge to low-charge smectite reaction in hydrothermal alteration processes. Clay Miner. 23, 133-146.

BURNHAM A.K., BRAUN R.L. & SAMOUN A.M. (1988) Further comparison of methods for measuring kerogen pyrolysis rates and fitting kinetic parameters. Pp. 839-845 in: Advances in Organic Geochemistry 1987 (L. Mattavelli & L. Novelli, editors). Organic Geochemistry, 13.

EBERL D.D. & HOWER J. (1976) Kinetics of illite formation. Geol. Soc. Am. Bull. 87, 1326-1330.

HILLIER S. t~ CLAYTON T. (1989) Illite-smectite diagenesis in Devonian Lacustrine mudrocks from Northern Scotland and its relationship to organic maturity indicators. Clay Miner. 24, 181-196.

HOWARD J.J. (1981) Lithium and potassium saturation of illite-smectite clays from interlaminated shales and sandstones. Clays Clay Miner. 29, 136-142.

HOWARD J.J. & RoY D.M. (1985) Development of layer charge and kinetics of experimental smectite alteration. Clays Clay Miner. 33, 81-88.

HOWER J., ESLINGER E.V., HOWER M.E. & PERRY E.A. (1976) Mechanism of burial metamorphism of argillaceous sediment: 1. Mineralogical and chemical evidence. Geol. Soc. Am. Bull. 87, 725-737.

HUFF W.D. & TURKMENOGLU A.G. (1981) Chemical characteristics and origin of Ordovician K-bentonites along the Cincinnati Arch. Clays Clay Miner. 29, 113-123.

LAGALY G. (1982) Layer charge heterogeneity in vermiculites. Clays Clay Miner. 30, 215-222.

McCUBBIN D.G. & PATRON J.W. (1981) Burial diagenesis of illite-smectite, a kinetic model. Am. Assoc. Petrol. Geol. Bull. 65, 956 (ahs.).

NADEAU P.H., WILSON M.J., MCHARDY W.J. & TAIT J.M. (1984a) Interstratified clay as fundamental particles. Science, 225, 923-925.

NADEAU P.H., WILSON M.J., MCHARDY W.J. & TAn" J.M. (1984b) Interparticle diffraction: a new concept for interstratified clays. Clay Miner. 19, 757-769.

NADEAU P.H., TAIT J.M., MCHARDY W.J. & WILSON M.J. (1984c) Interstratified XRD characteristics of physical mixtures of elementary clay particles. Clay Miner. 19, 67-76.

NEWMAN A.C.D. & BROWN G. (1987) The chemical constitution of clays. Pp. 1-128 in: Chemistry ~f

376 H. Wei et al.

Clays and Clay Minerals (A.C.D. Newman, editor). Mineralogical Society, London, Monograph No 6, Longman Scientific & Technical.

PEARCE R.B., CLAYTON T. & KEMP A.E.S. (1991) Illitization and organic maturity in Silurian sediments from the Southern Uplands of Scotland. Clay Miner. 26, 199-210.

PEARSON M.J. & SMALL J.S. (1988) Illite-smectite diagenesis and palaeotemperatures in Northern North Sea Quaternary to Mesozoic shale sequences. Clay Miner. 23, 109-132.

PERRY E.A. & HOWER J. (1970) Burial diagenesis in Gulf pelitic sediments. Clays Clay Miner. 18, 165-177.

PYYrE A.M. (1982) The kinetics of the smectite to illite reaction in contact metamorphic' shales. MA thesis, Dartmouth College, Hanover, New Hampshire, USA.

PYYrE A.M. & REYNOLDS R.C. (1989) The thermal transformation of smectite to illite. Pp. 133-140 in: Thermal History of Sedimentary Basins: Methods and Case Histories (N.D. Naeser & T.H. McCulloh, editors). Springer-Verlag, New York.

REYNOLDS R.C. & HOWER J. (1970) The nature of interlayering in mixed-layer iUite-montmorillonites. Clays Clay Miner. 18, 25-36.

SAWHNEY B.L. (1969) Regularity of interstratification as

affected by charge density in layer silicates. Soil Sci. Soc. Amer. Proc. 33, 42-46.

SMART G. & CLAYTON T. (1985) The progressive illitization of interstratified illite-smectite from carboniferous sediments of Northern England and its relationship to organic maturity indicators. Clay Miner. 20, 455-466.

SRODOr~ J. (1979) Correlation between coal and clay diagenesis in the Carboniferous of the Upper Silesian Coal Basin. Proc. 6th Int. Clay Conf., Oxford, 251-260.

UNCERER P. (1990) State of the art of research in kinetic modelling of oil formation and expulsion. Pp. 1-25 in: Advances in Organic" Geochemistry 1989 (B. Durand & F. Behar, editors). Organic Geochemistry 16.

VASSEUR G. & VELDE B. (1993) A kinetic interpretation of the smectite-to-illite transformation. Pp. 173-184 in: Basin Modelling: Advances and Applications (Dor6 et al., editors). NPF Special Publication 3, Elsevier, Amsterdam.

WHITNEY G. & NORTHROP H.R. (1988) Experimental investigation of the smectite to illite reaction: Dual reac t ion mechanisms and oxygen - i so tope systematics. Am. Miner. 73, 77-90.

Documents

parallel reaction kinetics of smectite to illite conversion