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AN EMPIRICALLY DERIVED KINETIC MODEL FOR ALBITIZATION OF
DETRITAL PLAGIOCLASE
RENEE J. PEREZ*
†
and JAMES R. BOLES
University of California, Santa Barbara, Geological Sciences Department Room 1006,
Webb Hall, Santa Barbara, California, 93106-9630
ABSTRACT. We propose an empirically derived model that estimates the extent of
reaction for albitization of plagioclase as a function of time, grain surface area, and
temperature from 0 to 200°C. We use a kinetic formulation independent of pressure,
and consistent with the Rate Law, which quantifies the dependence of the reaction rate
on the initial concentration of the reacting material, and the Arrhenius equation. The
formulation is described by the function:
d[An]
dt
⫽ S
m
k[An
o
]
2
(1 ⫺ ⍀
)
where d[An]/dt is the rate change of the anorthite mole fraction with time, S
m
the
mineral surface area (cm
2
), k the rate constant 1/cm
2
s, [An
o
] is a constant representing
the initial anorthite mole fraction, and ⍀
a constant weighed average saturation index.
We derive the apparent activation energy (E
a
) and frequency factor (A), both present in
the rate constant k, by fitting them to the extent of albitization measured in 11 samples
from the San Joaquin Basin. Subsequently, we test the model against two independent
albitization trends, one from the Texas Gulf Coast basin and one from the Denver
Basin of Colorado. Our results indicate that albitization in all three basins can be fit by
an E
a
of 68 ⴞ 4 kJ/mole and A of (6.5 ⴞ 0.5) ⴛ 10
3
1/cm
2
Ma. The rate dependence on
temperature is consistent with experimental values for albite crystal growth and with
empirically derived precipitation rates of other diagenetic silicates such as illite and
quartz. The parameters and fit suggest that albitization can be modeled as a surface
controlled reaction, primarily dependent on temperature.
introduction
Kinetics of Diagenetic Reactions
The aim of this paper is to present an empirical kinetic model for albitization of
detrital plagioclase. The model is derived directly from geologic data and is applicable
to at least three different sedimentary basins. Albitization, and most diagenetic
reactions in general, are modeled empirically because (1) the extrapolation of
laboratory measurements to geologic conditions generally requires very accurate and
precise data that are so far not attainable, (2) small errors in the temperatures and
heating rates during experimentation can become a major error in activation energies
and orders of magnitude error in frequency factors (Burnham and others, 1987), and
(3) changes in reaction mechanisms complicate the validation of kinetic parameters
for wide temperature ranges (Comer, 1992). An alternative approach to estimate rate
changes over large time scales (that is millions of years), is to model them using field
observations and time-temperature burial data.
There are several examples of empirically derived reaction kinetics in geologic
systems. Some, for instance, are the kinetics of petroleum generation (Lopatin, 1971;
Waples, 1980), aromatization and isomerization of hydrocarbons (Mackenzie and
Mackenzie, 1983; Gallagher and Evans, 1991), and vitrinite reflectance (Burnham and
Sweeney, 1989). Similarly, empirically derived kinetics for illitization of smectite and
*Current affiliation: University of Calgary, Applied Geochemistry Group, Department of Geological
Sciences, Calgary, Alberta T2N 1N4 Canada
†
Corresponding author: Renee J. Perez, rene@earth.geo.ucalgary.ca
[American Journal of Science, Vol. 305, April, 2005,P.312–343]
312
epitaxial quartz overgrowth receive special and continual attention due to their
abundance in oil reservoirs (Walderhaug, 1994, 1996; Elliot and Mattissof, 1996). Our
literature review reveals, however, that albitization of feldspar, although present in all
rock settings, lacks a kinetic formulation useful for its prediction.
Albitization, A Brief Review
Albitization of plagioclase has been recognized since the turn of the twentieth
century (for example, Bailey and Grabham, 1909). Perhaps the best reviews can still be
found in Coombs (1954) and Deer and others (1963). In general, albitization refers to
the transformation of any An-Or-Ab solid solution into albite. The solid solution is
originally crystallized at high temperatures as igneous or metamorphic minerals,
whereas the albite precipitates at low temperatures. Albitization results in low albite
(Morad and others, 1990; Slaby, 1992), due to the high to low albite transition
temperature of 575 50°C (Smith, 1972; Moody and others, 1985). The newly formed
albite is porous (Boles, 1982), which, as most replacement reactions, implies a
dissolution/precipitation reaction mechanism such that the ion transport to the
reaction interface and removal away from the interface are not diffusion-transfer
limited (Putnis, 2002).
In sedimentary basins, albitization refers to a pseudomorphic replacement pro-
cess that may imply a coupled dissolution of detrital plagioclase and precipitation of
low albite at equal rates. The shape of the plagioclase parent crystal and internal
structural details are preserved in the daughter albite crystal. A priori, coupled
dissolution-precipitation reactions can not be considered to be controlled by the
dissolution step (Luttge and Metz, 1991, 1993), however, isotopic analysis and kinetic
experiments suggest that the major mechanism in feldspar replacement is dissolution
followed by precipitation, and the rate-controlling step is grain surface dissolution
(O’Neil and Taylor, 1967; Moody and others, 1985). Solid diffusion usually fails to
explain albitization, mainly due to the presence of the peristerite or miscibility gap,
which is evident in albitized grains by the presence of sharp reaction fronts separated
by zones of constant composition (Fox, ms, 1989). Furthermore, isotopic analysis
(O’Neil and Taylor, 1967; Stallard and Boles, 1989) and recent
18
O, H, D, and
Na/(NaK) mapping (Labotka and others, 2002) demonstrate that, during feldspar
replacement, the oxygen isotope distribution re-equilibrates in the product, which
indicates the breaking of Si-O and Al-O bonds, and the oxygen redistribution is
facilitated by cation exchange (O’Neil and Taylor, 1967; Labotka and others, 2002).
The preservation of internal details and oxygen re-equilibration strongly suggest that
the replacement mechanism involves fine-scale solution and re-deposition in a structur-
ally organized fluid film at the interface between the exchanged minerals (O’Neil,
1977; Putnis, 2002).
Albitization is probably one of the most common alumino-silicate reactions in the
shallow crust of the Earth. It has been reported in deuterically altered granite and
granodiorite (for example, Bailey and Grabham, 1909; Hess, 1950; Deer and others,
1963; Fox, ms, 1989), alkali-carbonatite complexes (Bodart, 1980), spilitized lava
(Eskola and others, 1935; Rosenbauer and others, 1988), volcanic tuff (Coombs, 1954;
Boles and Coombs, 1977), and sedimentary basins (Tester and Atwater, 1934; Middle-
ton, 1972; Merino, 1975a; Land and Milliken, 1981; Boles, 1982; Gold, 1987; Boles and
Ramseyer, 1988; Morad and others, 1990). Albitization is usually described with Al
3
conservative reactions that reproduce the characteristic volume conservation observed
in thin sections. For example:
NaAlSi
3
O
8
䡠 CaAl
2
Si
2
O
8
H
4
SiO
4
Na
2NaAlSi
3
O
8
Al
3
Ca
2
4OH
(1)
313R. J. Perez and J. R. Boles 313
2SiO
2
⫹ 0.5H
2
O ⫹ H
⫹ Na
⫹ CaAl
2
Si
2
O
8
⫽ NaAlSi
3
O
8
⫹ 0.5Al
2
Si
2
O
5
OH
4
⫹ Ca
2
(2)
Merino (1975b) proposed equation (1), and Boles (1982) proposed equation (2).
Reaction 2 assumes that silica is provided by quartz, instead of being supplied by pore
fluid in the form of Si(OH)
4
—for example Si(OH)
4
may be supplied from clay
diagenetic reactions (Boles and Franks, 1979).
Importance
The question of which reaction best represents albitization, however, remains a
subject of great debate but the implications are clear: overall consumption of Na
,
Si
4
,H
, and release of Ca
2
and Al
3
. In other words, albitization reflects mass
transfer (Merino, 1975b; Boles, 1982; Aagaard and others, 1990; Morad and others,
1990) and causes chemical changes in basinal pore fluids (Fisher and Boles, 1990;
Davisson and Criss, 1996). Furthermore, albitization influences the porosity and
permeability of fluid reservoirs, especially when CO
2
supply is constant. Kaolinite and
calcite precipitation (as products of reactions 1 and 2) are commonly reported in the
San Joaquin Basin as a consequence of the albitization of plagioclase (Merino, 1975b;
Boles, 1984; Hayes and Boles, 1992; Wilson and others, 2000). Clearly, albitization is
one of the most important and common reactions in all rock settings, and yet little is
known about its transformation rate and predictability.
The Thermodynamic Problem
In spite of the reaction’s universality, the temperature range of the so called
“albitization zone” is not the same everywhere. Among some possible causes are the
grain reactivity, degree of fracturing, initial composition, structural states (Ramseyer
and others, 1992), and grain provenance (Boles and Ramseyer, 1988). Our literature
review reveals, however, that the appearance of the albitization zone may be associated
with differences in sediment ages and burial-thermal histories of the basins (Gold,
1987; Pittman, 1988; Ramseyer and others, 1992). This premise leads us to postulate
that time, temperature, and heating rates may strongly influence the replacement zone
as well, and that albitization is kinetically controlled by a critical activation energy.
One unanswered question is—Why are fluid compositions, at depths and tempera-
tures less than the albitization zone, commonly in the albite dickite stability field?
(Merino, 1975b; Boles, 1982; Morad and others, 1990; Helgeson and others, 1993).
Pore fluid compositions demonstrate that this is the case in several sedimentary basins
(fig. 1). The equilibrium boundaries in figure 1 are based on reaction 2 assuming that
the silica is provided by quartz. The estimated error on the equilibrium boundary,
using errors assigned to the Gibbs free energy values at 25° C given by Robie and
Waldbaum (1968), and using standard error estimate formulas is 1.0 pH unit (Boles,
1982). If silica is assumed to be provided by pore fluids, for example supplied by clay
reactions (Boles and Franks, 1979) in the form of H
4
SiO
4
in equilibration with quartz
at the appropriate temperatures, the equilibrium boundaries would be 0.2 to 0.3 pH
units higher at fixed calcium and sodium activity ratio (log([a
Ca
2
]/[a
Na
])) than those
shown in the plot (Boles, 1982). If the aqueous silica concentrations were higher than
required for equilibration with quartz, the albite-dickite stability field would expand
even more, and pore fluid data would plot even further in the albite-dickite stability
field. Additionally, reservoir fluids from the San Joaquin Basin are saturated with
respect to albite, allowing low albite precipitation in open pore spaces at temperatures
as low as 43°C, yet albitization (as a replacement) doesn’t start until the temperatures
are higher than 83°C (Boles and Ramseyer, 1988).
It is clear that fluid chemistry plays an important role in albitization (Baccar and
others, 1993), but time and temperature may be the main controlling factors. In other
314 R. J. Perez and J. R. Boles—An empirically derived
words, the albitization zone is thermodynamically constrained by the pore fluid
chemistry in basins. The reaction onset, however, is kinetically controlled and pro-
ceeds at an appreciable rate after a critical activation energy is reached, presumably at
temperatures higher than 70°C.
relevant kinetic experimentation and modeling
There is a long tradition of dissolution and precipitation experiments and
modeling involving feldspars; Helgeson and others (1984), Hellmann (1994), and
Blum and Stillings (1995) give excellent reviews. Most experiments on albite precipita-
tion have been performed at green schist and lower amphibolite P-T-X conditions
(250-500°C and up to 1 kbar), generally in 0.1 M NaCl and 0.05 M Na
2
SiO
3
solutions
(Matthews, 1980; Moody and others, 1985). Alkali metal halides, such as NaCl and
CaCl, have a dramatic effect on reaction kinetics (Winkler and Luttge, 1999), and it
may be reasonable to consider that this is the case of subsurface environments.
However, these temperature conditions are not observed in sedimentary basins and
these experiments do not truly reproduce the nature of a pseudomorphic replacement
(Merino and others, 1993).
Previous modeling of plagioclase albitization includes Baccar and others (1993)
and Wilson and others (2000). The former study focused on the minimum time of
albitization from 60 to 150° C in a closed system. It allowed a critical saturation before
nucleation and growth, and assumed an initial fluid volume, fluid composition, and
grain size distribution. The rate constants were derived using specific dissolution and
precipitation kinetic constants and thermodynamic equilibrium constants. Baccar and
others (1993) concluded that the albitization rate decreases with the extent of the
reaction (which increases with temperature) and that plagioclase is not stable at high
Pco
2
conditions. These results give insight into dissolution-precipitation processes,
Fig. 1. Equilibrium boundary of albitization according to reaction 2 (see text), after Boles (1982). The
error in the equilibrium constant calculated from free energy values given by Robie and Waldbaum (1968) is
1 pH unit. We assume quartz provides silica. The plot shows that reservoir fluids are in the albite stability
field and yet albitization was not observed.
315kinetic model for albitization of detrital plagioclase
such as the effect of Pco
2
, but not into replacement mechanisms. The preservation of
plagioclase internal details such as twin planes and cleavages, requires, among still
many unknown parameters, at least: a) plagioclase to dissolve and albite to grow at
equal and slow volumetric rates (Merino and others, 1993), b) a stress-controlled
coupled dissolution/precipitation mechanism (Merino and Dewers, 1998), c) a struc-
turally self-organized fluid film at the mineral interface (O’Neil and Taylor, 1967;
Reyhani and others, 1999), and d) differences between parent and daughter crystal
solubility (Putnis, 2002).
The latter study, (Wilson and others, 2000), considered albitization as a process
independent of fluid composition. The model used an activation energy of 65 kJ/mol
based on plagioclase dissolution experiments at low temperatures (Blum and Stillings,
1995) and fit the reaction order and the frequency factor to a single compositional
data (Boles and Ramseyer, 1988). This empirical approach was useful to simulate the
chemical evolution of the pore fluids in the San Joaquin Basin. It also proved to be
successful by yielding results consistent with geologic observations. The model, how-
ever, lacked a chemical affinity term, validation in other settings, and was also
independent of a surface area variable. After reviewing these two studies, we concluded
that an albitization kinetic model could be better formulated by including a surface
area variable, a saturation index term, and by testing it widely against data from several
basins.
hypothesis
We postulate that the albitization rate is a function of time, temperature, fluid
composition, and surface area. Our rate equation follows a kinetic formulation
consistent with the Rate Law and the Arrhenius equation (Lasaga, 1984). Rate laws
quantify the dependence of reaction rates on the concentration of the starting
material. They take the general form:
dC
dt
⫽ kC
n
(3)
where dC/dt is proportional to the change in concentration of C raised to the power of
n. The Arrhenius equation quantifies changes in the rate constant k with temperature
and has the form:
k ⫽ Ae
E
a
/Rt
(4)
where A is the frequency factor, E
a
the activation energy, R the universal gas constant,
and T temperature. In our work, the kinetic parameters (E
a
and A) present within the
reaction rate k are fitted using solely molar compositional trends with depth, which are
implicit functions of time and temperature. In reality, plagioclase composition, pore
fluid pH, and temperature are the main controlling factors of the rate constant.
However, different plagioclase compositions occur together in samples with identical
pore fluid and temperature history, strongly suggesting that the chemical composition
of the plagioclase has a stronger effect on the rate constant than pore fluid (Ramseyer
and others, 1992). Furthermore, based on the following observations:
(1) pore water from marine basins have a limited initial variation in pH values and
chemical composition (Fisher and Boles, 1990); and
(2) oil field brines are almost always in equilibrium or saturated with respect to
albite and unsaturated with respect to anorthite (Helgeson and others, 1993),
We assumed that (1) albitization is a dissolution reaction, which should have an E
a
between 40 and 80 kJ/mol (Lasaga, 1984), and (2) during albitization the sum of the
anorthite, orthoclase, and albite mole fraction is one at all times.
316 R. J. Perez and J. R. Boles—An empirically derived
The Saturation Index Hypothesis
The dissolution rate of a given plagioclase composition depends on the rate
constant k, and the saturation index . In our model the rate constant k is the fitted
parameter and we will deal with it in more detail later. The saturation index ,ata
fixed temperature and water composition, is commonly defined as:
⫽
IAP
K
eq
(5)
where IAP is the ionic activity product of the solution, and K
eq
the equilibrium
constant. From the log
10
positive numbers represent supersaturation and negative
undersaturation (for example Bethke, 1996). Based on field observations that suggest
that anorthite dissolution is the albitization rate-limiting step we assume that reaction 2
is adequate to represent albitization throughout geological time in sedimentary basins.
Again, reaction 2 may be written as:
2quartz ⫹ 0.5water ⫹ H
⫹ Na
⫹ anorthite ⫽ albite ⫹ 0.5dickite ⫹ Ca
2
(6)
in which the IAP is defined by:
IAP ⫽
a
Ca
䡠 a
dickite
1/2
䡠 a
albite
a
anorthite
䡠 a
Na
䡠 a
H
䡠 a
H
2
O
1/2
䡠 a
quartz
2
(7)
where the a’s are the activities of both, the solids and aqueous species. In this work, the
solid phases were considered pure with unit activity, except anorthite. The anorthite
content of plagioclase being albitized is 0.35 mole fraction, and its activity is 0.45
(Saxena and Ribbe, 1972). The equilibrium constant K
eq
is calculated from the Gibbs
free energy of the reaction. The free energy change at any T and P and solution
composition Q, in its simplest form, is given by:
r
G
T,P
⫽
r
H
°
298
⫹
冕
298
T
r
Cpdt ⫺ T
冉
r
S
°
298
冕
298
T
r
Cp
T
dt
冊
⫹
冕
1
P
r
Vdp ⫹ RTlnQ (8)
where
r
G
T,P
is the Gibbs free energy
r
H
°
298
enthalpy,
r
S
°
298
entropy,
r
Cp heat
capacity, and
r
V the molar volume change for the reaction, all in calories/mole (table
1). The subscript 298 refers to the reference temperature 298.15 Kelvin. At equilib-
rium, Q becomes K
eq
, and the free energy change of the reaction is zero so that:
lnK
eq
⫽
冋
r
H
°
298
冕
298
T
r
Cpdt ⫺ T
冉
r
S
°
298
⫹
冕
298
T
r
Cp
T
dt
冊
⫹
冕
1
P
r
Vdp
册
RT ⫹ ln0.45 (9)
As shown above, the equilibrium constant for any reaction is ultimately a function of P,
T, fluid composition, and solids composition. To calculate K
eq
for reaction 2 we used
thermodynamic data from two different, but consistent, sources. Free energies of
formation, enthalpies of formation, and third law entropies for all solid phases were
obtained from Robie and Waldbaum (1968). We used the database reported by Robie
and Waldbaum (1968) instead of the more recent and standard database SUPCRT92
(Johnson and others, 1992) for the following reasons:
317kinetic model for albitization of detrital plagioclase
Table 1
Formation water compositions associated with partial or complete albitization. Data compiled from several sources
Concentrations in mg/liter
*Reported as Si
TGCB Gulf Coast Basin
SJB San Joaquin Basin
NI No Information
References 1) Boles (1982); 2) Fisher and Boles (1990).
Temperature in degrees Celsius
Depth in meters
318 R. J. Perez and J. R. Boles—An empirically derived
a) Consistency with previous studies. Boles (1982) determined the albitization
stability field and errors in the free energy of formation and equilibrium constant
of reaction 2 using the Robie and Waldbaum (1968) database.
b) Contrary to Robie and Waldbaum’s database, SUPCRT92 lacks standard enthalpy
and Gibbs free energy data for Dickite, which is part of the products in the
reaction under study.
d) Robie and Waldbaum’s database contains thermodynamic data for Dmisteinber-
gite, an hexagonal anorthite polymorph used, as we will explain later, as a proxy
to evaluate the influence of the atomic arrangement and crystalline structure on
the transformation kinetics.
On the other hand, the standard Gibbs free energy, enthalpy and entropy of
formation of anorthite, low albite, and quartz present in Robie and Waldbaum (1968)
differ by less than 1.4 percent from those present in SUPCRT92, so, in spite of the
other differences, we felt comfortable using heat capacity data from SUPCRT92 as
summarized by Anderson and Crear (1993).
In order to keep our model simple and ease the calculation of the equilibrium
constant we made several simplifications. First, justified by the narrow range of
temperatures being considered here, we assumed that the heat capacity for ions was
constant. We also assumed that our model is pressure independent, and the net solid
volume change is close to zero (Boles, 1982) thereby assuming P 1 bar in equation
(9) and neglecting the pressure correction term. Consequently, lnK
eq
is left as a
function of temperature and can be represented by the following polynomial equa-
tion:
log
10
K
eq
⫽ p
1
T
3
⫹ p
2
T
2
⫹ p
3
T ⫹ p
4
(10)
where p
1
1.7513 10
7
, p
2
2.7925 10
4
, p
3
0.1685, and p
4
37.993 (fig.
2). The error in the equilibrium constant at 298.15 K, calculated from standard error
estimation formulas is 0.98. It is likely that this error may expand at higher
temperatures. The thermodynamic values used are summarized in table 2. As we will
discuss further in the text, we plan to qualitatively examine the effect of the anorthite
crystalline structure on albitization, in other words, on reaction 2. Thus, figure 2 also
illustrates the log
10
K
eq
for reaction 2 assuming that an hexagonal anorthite (an
anorthite polymorph) detrital grain is being albitized, in which case we use different
standard free energy and entropy values (table 2). Heat capacity data for hexagonal
anorthite are, to our knowledge, not available, so we retained the same heat capacity
equations. The equilibrium constant for reaction 2 assuming hexagonal anorthite can
also be fitted to equation (10) with different coefficients: p
1
1.4412 10
7
, p
2
2.2995 10
4
, p
3
0.13938, and p
4
30.421. The error in log
10
K
eq
is larger than
0.98, but no further calculations were performed.
Speciation and ion activities were, on the other hand, calculated with
SOLMINEQ.88 (Kharaka and Barnes, 1973; Perkins and others, 1990). We used
reservoir fluid compositions from the San Joaquin and Gulf Coast Basins, at depth
intervals where albitization is present and thermodynamically active (see our table 1;
data from Boles, 1982; Fisher and Boles, 1990). Based on the water chemistry data we
assumed that the oil field waters are in equilibrium with quartz, so that the activity of
the solid quartz activity is one. This assumption is justified by the presence of
authigenic quartz in intervals above the albitization zone, also by fluid chemistry data
(Wilson and others, 2000). The SOLMINEQ.88 code is only partially consistent with
the origins of the thermodynamic database presented in table 2. However, the
analyzed Na
and Ca
2
concentrations in the reservoir waters differ by less than 10
percent from those concentrations calculated by the code, clearly indicating that the
319kinetic model for albitization of detrital plagioclase
complexation of these ions in minerals is negligible. Consequently, any thermody-
namic calculation of Na
and Ca
2
activities would be consistent with the thermody-
namic database used in our paper. The resulting activities, ionic activity products, and
equilibrium constants for a variety of fluid compositions and temperatures used in our
model are shown in table 3.
The former table shows the variation of the saturation index from San Joaquin
and Gulf Coast Basin fluids that are currently at temperatures between 100 and 130° C,
and where albitization is actively occurring (Boles, 1982). However, considering the
waters’ ages are considerably different, in general several millions of years of differ-
ence, and that they have gone through different time-temperature paths, it could be
considered that the variation of is relatively small. Thus, given 1) the narrow range of
Fig. 2. Plot showing the equilibrium constant for reaction 2 assuming pure anorthite and its hexagonal
polymorph (see text). The log
10
K is calculated with equation (9) as a function of temperature. Thermody-
namic data is from Robie and Waldbaum (1968) and Johnson and others (1992). The error in log
10
K
(anorthite) at 298.15 K and 1 bar, calculated from standard error estimation formulas and from thermochemi-
cal errors in the former database is 0.98. It is likely that this error may expand at higher temperatures.
320 R. J. Perez and J. R. Boles—An empirically derived
compositions of albitized detrital plagioclase grains, 2) the relatively small variations
for waters of considerably different ages (millions of years) and different T-t paths, and
3) the occurrence of different plagioclase compositions in samples with identical pore
fluid and temperature history, we hypothesize that a weighted average integration of a
saturation index as a function of temperature, may be useful to simplify the variations
of water chemistry of the studied basins.
All our assumptions may seem, a priori, very simplistic and far from realistic but they are
constrained by field data and petrographic observations, and they are not unreasonable. First,
normally all replacement reactions are considered isovolumetric (Merino and others,
1993; Nahon and Merino, 1997; Merino and Dewers, 1998). Second, it might be
justified that during the pseudomorphic replacement, the coupled dissolution-
precipitation of plagioclase and albite, establishes locally a small-scale steady state or at
least a “quasi” steady state composition of the pore fluid, leading to a local saturation
that could be assumed to be about constant over long time intervals. This idea would
be particularly justified if the Al
3
and Ca
2
leave the local system at a constant rate
and fluid transport would not be too fast, as in the case in deep crustal settings away
from fractures and faults, where permeabilities could be in the range of tenths of
milidarcies and the average flow velocity is, at times, less than 1 cm/Ma (Garven, 1995).
Table 2
Thermodynamic values used to calculate the equilibrium constant for reaction 2
*Delta of the reaction assuming anorthite
**Delta of the reaction assuming hexagonal anorthite
G° Standard Gibbs Free Energy of Formation (Calories/mole)
S° Standard Entropy “Third Law” of phase (Calories/K mole)
H° Standard Enthalpy of Formation (Calories/mole)
a Calories/mole
b Calories/mole K
2
c Calories/mole K
5
The sum considers the stoichiometry of the reaction
Heat capacity of pure phases and thermodynamic data for aqueous ions from SUPCRT92 and
summarized by Anderson and Crear (1993)
321kinetic model for albitization of detrital plagioclase
Table 3
Input data for saturation index calculation. Speciation performed with SOLMINEQ.88
IAP Ionic activity product Keq Equilibrium constant
322 R. J. Perez and J. R. Boles—An empirically derived
general kinetic models and equations
Lasaga (1984, 1995, and 1998) explains all theoretical and fundamental ap-
proaches to describe dissolution and precipitation rates of minerals. The general
kinetic formulation for mineral/fluids interactions is equation (11):
Rate ⫽ S
m
Ae
E
a
/RT
a
OH
n
䡠 g I
写
i
a
i
n
i
f
r
G (11)
where the Rate is a function of the reactive surface area S
m
(cm
2
), the frequency factor
A (1/s), the apparent overall activation energy E
a
(kJ/mol) the temperature T (K), the
universal gas constant R (J/K mol), the OH
activity raised to the power of na
OH
n
(dimensionless), the ionic strength of the solution g(I )(I has units of molality times
the ionic charge squared ), the activity products a
i
n
of the rate-determining specie i
(dimensionless) raised to the power of n, and a general function of the free energy of
the reaction f(
r
G) that can take many forms, where
r
G has units of J/mol. Another
widely used empirical kinetic model, written as an adaptation of equation (11) by
Aagaard and Helgeson (1982) is:
Rate ⫽ S
m
k
m
a
i
m
1 ⫺ (12)
where S
m
is the interfacial area (cm
2
) between the mineral and the aqueous solution,
k
m
is the rate constant (1/s), a
i
n
is the activity of the rate-determining aqueous species i
in solution. On the other hand, the kinetics of pseudomorphic replacement have been
formulated with two simultaneous reactions that occur at equal volumetric rates,
driven by a force of crystallization generated by supersaturation (Maliva and Seiver,
1988; Dewers and Ortoleva, 1990; Merino and others, 1993; Nahon and Merino, 1997).
In this case, the sum of the rates equals zero as in equation (13)
R
a
⫹ R
b
⫽ 0 (13)
where R
i
is the linear dissolution rate of mineral i in cm/s represented by equation
(14):
R
i
⫽ k
i
1 ⫺ (14)
where k
i
(cm/s) and
i
have the usual meanings. Equations (11) through (14) depend
on the aqueous ionic species present during the reaction and are founded on a
well-developed physical-chemical theoretical basis, and only laboratory-based measure-
ments, with good control of fluid composition (in either closed or open systems) can
be most easily used for a rigorous interpretation of kinetic rate laws and reaction
mechanisms. However, the prediction and modeling of the fluid saturation path in
sedimentary basins is far from attainable. The variation and evolution of chemical and
ionic species through geologic time is even more difficult to predict or model with
precision. Furthermore, invalid extrapolations of experimental kinetic parameters to
geological settings and our poor understanding of reaction mechanisms (and of many
other variables) limit the applicability of rigorous and experimental approaches to
field examples.
Based on the reasons explained previously, most empirical models of diagenetic
reactions take a different and simple approach; they reduce and ignore a vast amount
of variables, specifically fluid compositions by avoiding or leaving constant the satura-
tion index or chemical affinity parameter in the rate expression. The models lack a
physical-chemical basis (Oelkers and others, 2000), however, they can successfully
predict dissolution and precipitation over long time scales, which is the ultimate goal
of these studies.
323kinetic model for albitization of detrital plagioclase
The smectite to illite conversion during shale diagenesis provides one example of
empirically derived kinetics. Several models for this particular reaction have been
proposed and evaluated (Elliot and Matisoff, 1996). The most recent model (Huang
and others, 1993) computes the rate with:
dS
dt
⫽ k K
S
2
(15)
where dS/dt is the change of the smectite fraction with respect to time t, k is the rate
constant, [K
] is a fixed and constant potassium concentration (in ppm), and S is the
dimensionless fraction of smectite in the illite/smectite raised to the power of 2.
Another example is quartz overgrowth precipitation. Commonly, models for
quartz precipitation couple diffusion, kinetic, and thermodynamic aspects of the
reaction (Oelkers, 1996; Oelkers and others, 2000). In contrast, a simpler mathematic/
kinetic model based on time-temperature and surface area (Walderhaug, 1994 and
1996) continues to be successfully tested in basins around the world (for example
Awwiller and Summa, 1997; Lander and Walderhaug, 1999; Perez and others, 1999a,
1999b). The quartz precipitation model uses a logarithmic rate function dependent on
temperature (eq 16):
Rate ⫽ a10
b 䡠Tt
(16)
where a (moles/cm
2
) and b (1/°C) are pre-exponential and exponential constants and
T(t) is temperature expressed as a function of time. The precipitated quartz volume Vq
(cm
3
) is calculated as a sum of integrals within sequences of time steps i (eq 17):
Vq ⫽
M
a
冘
i1
n
冉
A
i
冕
t
i
t
i1
10
b 䡠Tt
dt
冊
(17)
where M is quartz molar volume (g/mole), is quartz density (g/cm
3
), A
i
is surface
area (cm
2
), and t is time (sec). As we explained previously, these empirical models
depend mainly on the variations of the heating rate through geologic time, obtained
through basin modeling (Siever, 1983), and lack an affinity term.
albitization kinetic model
Based on previous formulations in the San Joaquin Basin (Wilson and others,
2000), we modeled albitization with a kinetic/mathematical formulation expressed in
equation (18) by:
d An
dt
⫽ S
m
kAn
o
2
1 ⫺
(18)
where d[An]/dt is the change of the anorthite mole fraction with respect to time t, k is
the rate constant in 1/cm
2
s, [An
o
]
2
is the initial anorthite mole fraction squared, and
the weighted average saturation index. In equation (18) S
m
is the area of the
mineral-solution interface (Lasaga, 1984) and is expressed in equation (19) in the
following form:
S
m
⫽
A
m
V
m
䡠 v (19)
where, A
m
is the mineral surface area (cm
2
), V
m
is the mineral volume assuming
spherically-shaped grains (cm
3
), and v is the unit volume of the sandstone, which
324 R. J. Perez and J. R. Boles—An empirically derived
includes porosity and is equal to 1 cm
3
. Simplifying, the surface area interface results in
equation (20):
S
m
⫽
6
d
v (20)
where d is the grain diameter (cm). In all analyzed samples the grain size ranges from
0.012 0.001 to 0.086 0.018 cm, varying from one sample to another, however,
average grain diameter is 0.031 0.002 cm (table 4). These values are obtained by
measuring the mean grain diameter in 40 grains per thin section, using a standard
polarized light petrographic microscope.
The rate constant k follows the Arrhenius equation (21):
k ⫽ A exp
冋
E
a
RTt
册
(21)
where A and E
a
are apparent pre-exponential and exponential parameters in 1/cm
2
s
and kJ/mole respectively, R the universal gas constant (J/K mole), and T(t)is
temperature in K expressed as a function of time t.
The initial anorthite molar fraction value [An
o
] is obtained through field measure-
ments. It is determined on detrital plagioclase grains with an ARL microprobe
analyzer, model SMX-SM equipped with three wavelength-dispersive spectrometers
and a Tracor Northern TN2000 energy dispersive system, by simultaneously analyzing
for sodium, potassium, and calcium, aluminum, and silicon. Each grain is analyzed on
the rim and in the core, and 50 grains are usually analyzed per thin section from
different depth intervals and temperatures (Boles, 1982; Boles and Ramseyer, 1988;
Pitmman, 1988).
Based on the reasons explained above we used a mean saturation index term
(
) obtained with a weighted average integration. The method to obtain
is as
follows: a) first we calculate several numerical values of (defined in equation 5) using
waters compositions from different reservoirs of different ages, depths and burial
temperatures where albitization is active (table 3); b) observing a slight temperature
dependence of these values, we fit them to a function of temperature–which is
implicitly a function of time; c) we weight averaged the function with equation (22), so
that:
⫽
冕
T
TdT
冕
dT
(22)
The integration along the (T ) function (solution to equation 22), neglecting the
extreme values and within the temperature of interest, results in a constant log
10
2.632. This positive number suggests that pore fluid compositions are in the albite
dickite stability field, which is consistent with field observations. In short, to start the
albitization, pore fluids must be supersaturated with respect to albite, that is, in the
albite stability field according to reaction 2.
It is well known that, in laboratory experiments, dissolution and precipitation
reactions are usually not independent of fluid composition, and such assumption
would only be valid if the reaction occurs far from equilibrium. Thus, a constant
may
be somewhat problematic. However, based on (1) the small range of water composi-
325kinetic model for albitization of detrital plagioclase
Table 4
Summary of data sets used as input in our model. Data include unpublished well
names, and samples’ temperature, age, and grain size.
*Gulf Coast Basin data from Boles (1982), the San Joaquin Basin data from Boles and Ramseyer (1988) and the Denver Basin data from Pittman (1988)
**Present day depth
***Present day temperature
Ab stands for ablite, Or for orthoclase and An for anorthite
s.d. stands for standard deviation of spot analysis per sample [100 spots for Boles (1982) and Boles and Ramseyer (1988) and 20–27 spots for Pitmann (1988)]
N.I. No information
The grain size units are in millimeters
326 R. J. Perez and J. R. Boles—An empirically derived
tions present in the San Jaoquin and Gulf Coast Basin where albitization is active
(Boles, 1982), (2) a narrow albitization temperature window, (3) the relatively small
range of albitized plagioclase compositions (fig. 2), we propose that the heating rate
may be the most important parameter for the actual kinetics of the replacement.
Particularly because experiments suggest that this is the case when the reaction
products grow on the reactant (Luttge and others, 1998), as in the case of replacement
reactions.
In addition, at depths greater than 3 to 4 km, where albitization occurs, the rock
permeabilities are on the order of the tenths of milidarcies and the rate of fluid
transport is very small; and it is reasonable to assume that some minerals can establish
locally a steady state or at least a “quasi” steady state composition of the pore fluid,
leading to a local saturation that could be assumed to be about constant over long time
intervals.
Numerical Solution
The solution of equation (18) is reached by the integration of equation (23):
冕
dAn ⫽
冕
t
0
t
m
Ae
E
a
/R 䡠Tt
6
d
v An
o
2
1 ⫺
dt (23)
An analytical integration of the right hand side of equation (23) from time t
0
to t
m
is
not trivial due to the time dependence of the temperature, and some proposed
rational approximations (for example Burnham and others, 1987) introduce errors at
high temperatures (Comer, 1992). Alternatively, a numerical solution can be reached
if T(t) is divided in increments, and a mean value
T
i
is calculated within the (i) (i
1) time steps. In the general case, the mean temperature
T
i
may be calculated
through a weighted average integration expressed in equation (24) as:
T
i
⫽
冕
t
i
t
i1
Ttdt
冕
t
i
t
i1
dt
(24)
If the increments are small and considered linear, T(t) takes the form of equation (25)
Tt ⫽
冘
i1
n
m
i
t ⫹ d
i
(25)
where the slope m is the temperature change rate (in °C/s), t is time, and d is the initial
temperature (in °C), and
T
i
is reduced to an average between two time steps, that is
(T
i
T
i1
)/2. If a time-temperature curve, represented by the function TT(t), is
divided in small linear increments from (T
i
,t
i
)to(T
i1
,t
i1
), the slope m
i
between
each interval would be:
m
i
⫽
T
i1
⫺ T
i
t
i1
⫺ t
i
(26)
and the initial temperature d
i
is:
d
i
⫽ T
i
⫺
冉
T
i1
⫺ T
i
t
i1
⫺ t
i
冊
t
i1
(27)
327kinetic model for albitization of detrital plagioclase
Our model uses variable times steps, between 0.3 and 0.7 million years, depending
upon the sample age and temperature history. The model results are independent of
the time step length, although intervals of 0.5 million years are preferred because they
give best results. The substitution of T(t)by
T
i
results in equation (28):
冕
d An ⫽
冕
t
i
t
i1
Ae
E
a
/R 䡠
T
6
d
v An
o
2
1 ⫺
dt (28)
Although equations (23) and (28) may seem similar, the substitution simplifies the
integration, because
T is now a constant. Finally, the integration is numerically
expressed with equation (29):
An
i1
⫽
冘
i0
n
冉
An
o
i
⫺ Ae
E
a
/R
T
i
6
d
vAn
o
i
2
1 ⫺
t
i1
⫺ t
i
冊
(29)
where i is the time step.* During albitization of detrital plagioclase in the studied
basins, the anorthite mole fraction decreases from An
35
to An
0
, and the albite mole
fraction increases simultaneously from Ab
65
to Ab
99
(table 4). By definition the sum of
the mole fractions is unity, that is:
An ⫹ Ab ⫹ Or ⫽ 1 (30)
where An, Ab, and Or are the anorthite, albite, and orthoclase mole fractions.
Therefore, the simultaneous gain of the albite component, as a result of albitization, is
computed with equation (31)
Ab
i1
⫽ 1 ⫺
冘
i1
n
冉
An
o
i
⫺ Ae
E
a
/R
T
i
6
d
v An
o
i
2
1 ⫺
t
i1
⫺ t
i
冊
⫺ Or
o
(31)
where [Ab] is the final albite mole fraction per time step i,[Or
o
] is the initial orthoclase
mole fraction that could be set constant to 0.05 0.01, or simply ignored.
The only unknown parameters in equation 29 are E
a
and A. When only two
parameters are being optimized, both least squares fit and direct search techniques are
efficient methods (Gallagher and Evans, 1991). We approached the problem with a
direct grid search, using an iteration method, which breaks the time-temperature
domain into a series of discrete blocks, where equations 23 through 31 are calculated.
We began our search of A by fixing E
a
from 60 to 70 kJ/mol following Walther and
Wood (1984) and Lasaga (1984). We decided to search with small E
a
and wide A
increments. Our decision was based on the limited E
a
range (60 E
a
80 kJ/mol)
reported for a great number of dissolution reactions of alumino silicates (Lasaga,
1984) and specifically for feldspar hydrolysis reactions at neutral pH within the
temperature of interest (Hellman, 1994; Blum and Stillings, 1995).
As input, we used (1) compositional data that revealed increasing albitization with
depth and temperature (table 2), and (2) time-temperature curves obtained through
1-D burial-thermal modeling of the basins. We performed the basin modeling using
Genesis
tm
(Zhiyong, 2003).
*Note that [An
o
]
i
2
is a constant per time step.
328 R. J. Perez and J. R. Boles—An empirically derived
model fit and tests
San Joaquin Basin.—We began our search in the San Joaquin Basin. Callaway
(1971) provided an excellent review of its geologic framework. In summary, the basin
contains more than 7 km of Tertiary Miocene sediment, and underwent down warping
by compaction during its burial history. In the center of the basin, where we focused
our study, the present depths represent maximum burial. For the albitization kinetic
fit, we selected from the published compositional data (Boles and Ramseyer, 1988) a
total of 11 samples from nine different wells (table 4). The selection was based on the
availability of thin sections and well data. We constructed time-temperature histories
for each sample and determined grain sizes by averaging the diameter of 40 plagioclase
grains per sample.
We extracted input parameters from the literature for basin modeling pur-
poses, including stratigraphic information from field-scale structural cross sections
(California Oil and Gas Division, 1985), formation ages (COSUNA, 1984 and Wood
and Boles, 1991). The latter paper also provided formation thickness and subsi-
dence rates. We assumed a constant basal heat flow of 50 mW/m
2
, based on present
day thermal data (Lachenbruch and Sass, 1980) and geothermal studies in the San
Joaquin Basin (Dumitru, 1988; Wilson and others, 2000) and we used thermal
conductivity values compiled in Genesis
tm
by Zhiyong (2003). It is important to
emphasize that heat fluxes in the San Joaquin Basin were likely lower than 50
mW/m
2
during active subduction, and that thermal gradients have recovered since
then (Dumitru, 1988). Figure 3 depicts the resulting burial histories. The kinetic
modeling search (fig. 4) indicates that the albitization trend can be reasonably
simulated using an apparent activation energy of 68 4 kJ/mole and apparent
frequency factors of (6.5 0.5) 10
3
1/cm
2
Ma. The error bars in the data points
(fig. 4) represent the standard deviation, computed as the square root of the
variance, which is in turn calculated as the average squared deviation from the
Fig. 3. Several time-temperature paths of albitized samples from the San Joaquin Basin used in the
kinetic model.
329kinetic model for albitization of detrital plagioclase
mean. The errors in E
a
and A represents the range of values in E
a
and A required to
enclose the variation in the compositional data.
Tests Results
Once we calculated the set of unknown parameters in the San Joaquin Basin, we
proceeded to test them against plagioclase compositional trends from the Texas Gulf
Coast (Boles, 1982) and Denver Basin of Colorado (Pittman, 1988).
Texas Gulf Coast Basin.—Galloway and others (1994) provided a synthesis of the
geologic, structural, and depositional history of the onshore Tertiary deposits present
in the southern part of the Texas Gulf Coast Basin. The stratigraphic column in the
southern part of the Texas Gulf Coast consists of 4 to 6 km of sedimentary rocks, buried
in a simple down-warped fashion without major regional uplifts (Murray, 1960).
Present-day depths and temperatures in the basin represent, in many cases, maximum
values (Boles, 1982). We used the kinetic model and parameters derived from the San
Joaquin Basin fit to simulate the plagioclase compositional trend reported for the
Oligocene Frio Formation of south Texas (Boles, 1982). The data comprise eight
samples distributed over eight wells from six different counties. Grain sizes were
determined by measuring the mean diameter of 50 plagioclase grains in thin sections
(table 4).
We constructed 1-D burial-thermal curves for each sample using Genesis
tm
(Zhiyong, 2003). From Dodge and Posey’s (1981) set of subsurface structural cross
sections, we obtained well locations, formation tops, gamma-rays/spontaneous poten-
tial logs, bottom hole temperatures, and biostratigraphic information. We used the
biostratigraphy information from the COSUNA (1984) chart and the U.S. Department
of Interior Biostratigraphic Chart for the Gulf of Mexico (OCS) Region (2002) to
derive formation ages. For the time-temperature reconstruction, the present day heat
Fig. 4. Initial model fit to albitization in the San Joaquin Basin. Measured and calculated data are
plotted as functions of temperature. The ■ symbol with vertical lines represents data from Boles and
Ramseyer (1988) with standard deviation computed as the square root of the variance. Symbols E, 〫, ‚, and
▫ represent sequences of simulations performed for different samples. The data fit an E
a
of 68 4 kJ/mol
and an A (6.5 0.5) 10
3
1/cm
2
Ma. The E
a
and A errors represent the required deviation mean value to
enclose the standard deviation of the compositional data.
330 R. J. Perez and J. R. Boles—An empirically derived
flux (53 mW/m
2
) was set constant from the middle Oligocene to the present. The heat
flux was calculated by the code using formation temperatures and thermal conductiv-
ity values compiled by Zhiyong (2003). We calibrated our time-temperature histories
with temperature measurements taken along the depth of the wells (Dodge and Posey,
1981). Results are plotted in figure 5.
Using the previous results, we modeled albitization and computed the loss of the
anorthite component (fig. 6A). Additionally, due to the fact that the orthoclase
fraction in a detrital plagioclase remains constant and is usually less than 5 percent, an
albitized grain can be conveniently studied as a binary system. In a binary system, when
the compositional data is normalized to 100 percent, the variance of each component
is the same, and consequently, the standard deviations are equal. Thus, we modeled
the gain of the albite component using the standard deviation from the anorthite mole
fraction (fig. 6B). Ten waters analysis from fluid reservoirs that have gone through
different time-temperature trajectories, have significantly different ages (millions or
years), and where albitization is active, the waters have relatively similar saturation
index values compared to subsurface waters from the San Joaquin Basin (table 3).
Thus for modeling purposes, we used the same weight averaged log
10
2.632 value
as in the San Joaquin Basin. The albite gain or anorthite loss during albitization in
Tertiary Gulf Coast Basin can be simulated assuming reaction 2 with an apparent
activation energy of 68 4 kJ/mole and apparent frequency factors of (6.5 0.5)
10
3
1/cm
2
Ma. Again, errors of E
a
and A represent the values required to enclose the
variations in the compositional data. The error bars of the data (fig. 6B) represent the
standard deviation calculated as the square root of the variance.
Denver Basin.—We tested the kinetic model against data from the Cretaceous
Terry sandstone in the Spindel field, Denver Basin of Colorado. Pittman (1988 and
1989) presented a geologic synthesis of the basin and plagioclase albitization data. The
history of the basin is rather complex. The heat flux varied through time resulting in
Fig. 5. Time-temperature history of albitized samples from the Gulf Coast Basin, derived from
basin-burial modeling.
331kinetic model for albitization of detrital plagioclase
Fig. 6(A) Plot illustrating simulated and measured anorthite mole fractions versus temperature in the
Gulf Coast Basin. Measured and calculated data are plotted as a function of temperature. The ■ symbol
represents data extracted from Boles (1982). Vertical lines represent standard deviation of 100 spot analyses
per sample, computed as the square root of the variance. All other symbols represent sequences of
simulations calculated for fine-grained sandstones deposited between 28.6 and 32.1 Ma (see legend). Fit
corresponds to E
a
68 4 kJ/mole and A (6.5 0.5) 10
3
1/cm
2
Ma. The errors represent the range of
values in E
a
and A required to enclose the variation in the composition data.
Fig. 6(B) Calculated and measured albite mole fractions as a function of temperature in Gulf Coast
Basin. The ■ symbol represents data from Boles (1982). The vertical lines represent standard deviations
(square root of variance) of anorthite component. Vertical lines represent standard deviation of 100 spot
analyses per sample.
332 R. J. Perez and J. R. Boles—An empirically derived
changing thermal gradients and heating rates, and the sedimentary section was
uplifted 800 m during Early Paleocene and Miocene time. Burial and thermal
histories were calibrated against R
o
profiles, K/Ar data, and multiple temperature logs
(Pittman, 1988).
The resulting time-temperature history of the Terry sandstone corresponds to a
single horizon at 1,325 m depth (fig. 7). Not having compositional data at specifically
1,325 m depth, we chose the closest samples where data were available, corresponding
to those in the well Rademacher No. 1 at 1,283.2 and 1,286.9 m depth (see table 2, p.
752, Pittman, 1988). Albitized plagioclase in this setting was mainly reported in fine to
very fine-grained sandstone. Hence, we modeled albitization using three surface area
assumptions, calculated from three different sand grain sizes (1) fine grain, with d
0.0177 cm, (2) very fine grain with d 0.0088 cm, and (3) fine to very fine grain with
d 0.0125 cm.
Having no information regarding the oil field water chemistry or saturation
indexes, we computed the reaction using the same log
10
2.632 used in the San
Joaquin and Gulf Coast Basin. Again, results indicate that the albitization data can be
consistently predicted with an apparent activation energy of 68 4 kJ/mole and
apparent frequency factors of (6.5 0.5) 10
3
1/cm
2
Ma (fig. 8). The same fitting
scheme performed with data from the San Joaquin Basin was performed indepen-
dently using data from the Louisiana Gulf Coast and Denver Basin, and the results
showed no skew.
model evaluation
Comparison with Other Diagenetic Reactions
We compared the albitization rate constant k with the rate constants of quartz
precipitation and smectite-to-illite models derived from field data and burial-
temperature histories by different authors (fig. 9). Although smectite-to-illite and
Fig. 7. Thermal history of the Terry Sandstone, Spindle field, Denver Basin, after Pittman (1988).
Time-temperature profile corresponds to a horizon at 1,325 meters depth and was used as input for
albitization model.
333kinetic model for albitization of detrital plagioclase
quartz precipitation are all very different reactions, their reaction rates were derived
with an empirical-numerical approach, similar to ours. Additionally, smectite-to-illite
and quartz overgrowth precipitation, together with albitization, constitute the main
diagenetic reactions in sedimentary basins: they are all strongly dependent on heating
rates and surface area or grain size. In our model, the rate constant k, is calculated with
equation (32), identical to equation (4), as shown below:
k ⫽ Ae
E
a
/RT
(32)
The k is plotted in figure 9. There k ranges from 1 10
21
1/cm
2
s at 25°C to
1 10
18
1/cm
2
s at 200°C (fig. 9), assuming E
a
and A to be 68 kJ/mol and 6.5 10
3
1/cm
2
Ma and making the appropriate unit conversion to 1/cm
2
s.
Our rate constant values are higher than the quartz precipitation rate of Walder-
haug (1994) and smectite-illite transformation rates of Huang and others (1993), and
lower than Pytte and Reynolds’ (1988) and Velde and Vaseur’s (1992) smectite to illite
rates. We also compared our model to growth rates of albite (fig. 9). Aagaard and
others (1990) estimated albite growth rates from albite dissolution rates (Knauss and
Wolery, 1986) and the principle of microscopic reversibility (Lasaga, 1984). According
to Aagaard and others (1990), dissolution would not normally be the limiting factor in
the case of K-feldspar albitization. This conclusion is reached by comparing the
relatively fast K-feldspar dissolution rate (Helgeson and others, 1984) with the rela-
tively slow albite precipitation rate—omitting nucleation.
Contrary to the K-feldspar case, in our model the rates of albitization (plagioclase
dissolution) are slower than the albite growth rates of all temperatures (fig. 9), which is
Fig. 8. Plot of comparison between calculated and measured anorthite mole fractions in Denver Basin.
Measured and calculated data are plotted as a function of time. The ■ symbol represents two data points at
1,283.2 and 1,283.9 m depth (Pittman, 1988), and the error bar the standard deviation. Other symbols
represent sequences of simulations performed for very fine-grained sandstones (‚), fine-grained (
䉬
) and
very fine to fine sand ( ). Age of samples is 73.3 Ma. The data fit an E
a
68 4 kJ/mole and A(6.5
0.5) 10
3
1/cm
2
Ma. The errors in E
a
and A represents the range of values in E
a
and A required to enclose
the variation in the composition data.
334 R. J. Perez and J. R. Boles—An empirically derived
fairly consistent with field observations. In sedimentary basins, plagioclase dissolution
is the rate-limiting step of albitization based on the fact that low albite precipitates in
porous sandstones at temperatures lower than the temperature onset of albitization
(Ramseyer and others, 1992).
Sensitivity Studies and Model Limitations
We performed several sensitivity analyses to illustrate the model’s response to
variations in the input parameters. The common input to all simulations was an
arbitrarily chosen time-temperature profile, somewhat similar to the thermal history of
the Gulf Coast and San Joaquin Basins (fig. 10). From the simulation results (figs. 11
and 12), we are able to evaluate the effects of the initial composition and the surface
area on albitization. Additionally, based on the Denver and Gulf Coast Basin results, we
discuss the effect of heating rates on albitization.
Effects of initial composition.—The effect of the initial anorthite [An
0
] composition
on the rates of albitization is depicted in figure 11. From 0 to 65°C, the reaction rates
are relatively slow and all modeled initial compositions, An
30
Ab
65
,An
40
Ab
60
,An
60
Ab
30
and pure An
100
, remain constant. Between 75 and 125°C all compositions are partially
albitized. Finally, at temperatures over 125°C, the different compositional trends
converge to a single value, that is [An] 0 mole percent. It is clear that the
plagioclase’s detrital composition in terms of anorthite content affects the reaction,
but the effect is minimal at high temperatures. The wide standard deviations at low
temperature and small standard deviations at high temperature (figs. 4 and 6) of the
data (table 1), can both be partially explained by differences in the initial anorthite
fraction.
Fig. 9. Comparison of the albitization rate calculated in this paper assuming E
a
68 kJ/mole and A
6.5 10
3
1/cm
2
Ma)–with other rates of mineral reactions as a function of temperature. For illitization of
smectite (S/I) based on Pytte and Reynolds (1988), Velde and Vassseur (1992) and Huang and others
(1993); quartz precipitation based on Walderhaug’s (1994); albite growth rate based on Aagaard and others
(1990).
335kinetic model for albitization of detrital plagioclase
Another rate determining factor to examine, but well beyond the scope of this
paper, is the influence of the ordered (that is plutonic) versus disordered (that is
volcanic) atomic arrangement of the albitization kinetics. At present we know of no
Fig. 10. Time-temperature profile representing a single burial cycle, similar to profiles from the San
Joaquin and Gulf Coast Basins. This curve was used as input for several sensitivity analyses illustrated in
figures 8 and 9.
Fig. 11. Sensitivity of albitization kinetic model to plagioclase initial composition, as a function of
temperature using profile in figure 7. The initial plagioclase composition is function of An. Simulations show
that initial composition persists until 100°C, slows albitization at temperatures below 125°C, and
converges to a single composition trend over 135°C.
336 R. J. Perez and J. R. Boles—An empirically derived
thermodynamic data of ordering at constant anorthite content in plagioclase. Thus as
a proxy, we used thermodynamic data of an hexagonal polymorph named Dmisteinber-
gite. This polymorph is rare but has been reported on fractured surfaces in coal from
the Chelyabinsk coal basin, Southern Ural Mountains, Russia.
As mentioned the thermochemical data for hexagonal anorthite is taken from
Robie and Waldbaum (1968). Hence, we calculated the equilibrium constants of
reaction 2 assuming an hexagonal anorthite and graphed it in figure 2. We also
calculated
values for reaction 2 under the same assumption and using fluid
compositions from the San Joaquin Basin and Gulf Coast Basin (table 3). The resulting
values of log
10
hexagonal
suggest that if Dmisteinbergite was present in the San Joaquin
Basin, reaction 2 would proceed far enough to the right until the saturation point,
either because the pore fluids have been in contact with sufficient amounts of the
mineral or have reacted with the mineral long enough. In short, pore fluids are
saturated with respect to hexagonal anorthite, and we can only speculate that the
albitization of this polymorph would be faster, assuming the same rate constant.
Effect of surface area.—The mineral/fluid surface area interface is key in diagenetic
modeling (Oelkers, 1996). Our model is designed such that plagioclase dissolution
rate is inversely proportional to the grain diameter. A simple and direct inspection of
equation (18) shows that d[An]/dt S
n
so that [An]
i1
(6/d)v. Thus, given the same
initial composition and time-temperature path, smaller grains will albitize faster than
bigger grains. Figure 12 illustrates albitization trends plotted against temperature for
several grain diameters. Below 60°C the influence of the initial grain size on albitiza-
tion is small, but over 70°C the transformation rate increases as grain size decreases. As
a result plagioclase with different grain sizes may have different degrees of albitization
and/or albitization paths that persist over a wide temperature range. Perhaps the wide
deviations of the albitization trends may be explained by the standard deviations in
grain size distributions (table 4). However, the dissolution of minerals, and particularly
Fig. 12. Sensitivity of albitization to detrital grain size as a function of temperature. The initial
plagioclase composition is common to all simulations. Simulations indicate that grain size differences affect
the degree of albitization throughout the transformation. Effects of the grain size persist until high
temperatures are reached, but it minimizes at temperatures over 160°C.
337kinetic model for albitization of detrital plagioclase
feldspars, is certainly not uniform over all the surface. Leaching occurs at preferred
crystallographic sites, twin planes, microfractures, and dislocations.
An additional parameter not addressed in our study is the effect of permeability
on albitization. Fine-grained sandstone presumably has low initial permeability and
much of its original water could be lost through compaction/cementation by the time
of albitization (Boles and Coombs, 1977). Increasing albitization with increasing grain
size has been reported (Boles and Coombs, 1977), but these results may indirectly
reflect permeability effects rather than solely a surface area effect. Albitization requires
a local steady state composition of the pore fluid, in which Ca
2
and Al
3
leave the
local system on a constant rate and fluid transport is not rapid. Differences in
permeability and flow rates would establish different saturation states of the fluid over
short time intervals and would change from one depth to another dramatically. In
general, sandstone with contrasting permeability may have different anorthite content
through time and different degrees of albitization.
Effect of heating rates.—Heating rates can influence the dissolution, precipitation, and
even the nucleation rates of mineral reactions (Luttge and others, 1998). The effect of the
heating rate on albitization can be evaluated by comparing results from our simulations.
For instance the San Joaquin Basin consists of relatively young deposits, from 6.7 to 33 my,
but mostly less than 20 my old, and moderate to low thermal gradients between 25 and
27°C/km. At temperatures higher than 170°C, our modeling suggest that at low tempera-
ture albite has replaced almost all plagioclase, leaving the anorthite mole fraction below 5
percent. The Gulf Coast Tertiary Basin consists of sediments 30 to 35 my old and a
relatively high thermal gradient between 32 and 37°C/km. Albitization occurs there
between 90 and 130°C, and at temperatures higher than 130°C the plagioclase approaches
pure albite composition. In contrast, the Denver Basin was subject to periods of 50 my at
temperatures in the neighborhood of 90°C, and, in our model, plagioclase has not
reached pure albite composition as it does in the San Joaquin and Gulf Coast Basins. Based
on these three different sets of simulations, it is clear that albitization is primarily sensitive
to temperature rather than time.
The model dependence on temperature may also be evaluated by calculating
time-temperature end-member values for albitization. In other words, calculating
minimum temperatures at constant time (fig. 13A) and minimum times at constant
temperature (fig. 13B) required to albitize plagioclase. To perform these calculations,
we modeled albitization in fine-grain sandstone, set the initial composition to
An
35
Ab
60
Or
5
, and used our average kinetic parameters: E
a
and A equal to 68 kJ/mole
and 6.5 10
3
1/cm
2
Ma.
For the specified conditions, sedimentary rocks as old as 500 my must be subject to
temperatures over 90°C in order to be albitized (fig. 10A). The minimum temperature
decreases with time. Sandstone as old as 300 my must be subject to constant tempera-
tures over 95°C, and sandstone 200 my old at temperatures over 105°C. In contrast, at
temperatures over 170°C, albitization may occur in less than 0.6 my (fig. 13B).
It is important to emphasize that the replacement has a strong dependence on
temperature and weak dependence on time (fig. 13). Nevertheless, these results
suggest that albitization could occur slowly over long periods of time, and might occur
rapidly in rocks subject to rapid thermal events, for example, thermal alteration
associated with fluid flow along faults.
some model implications
With available compositional and petrologic data, our model may be used to put
limits on burial and thermal histories of basins. The albitization kinetics may be used as
a paleo-thermometer providing independent calibration for other thermal indicators,
such as vitrinite reflectance, TAI (Thermal Alteration Index, observed by spore
darkening), quartz precipitation overgrowth, and smectite-illite, in sedimentary basins.
338 R. J. Perez and J. R. Boles—An empirically derived
The knowledge of the degree of albitization, for a given time-temperature data set,
may be also useful for predicting the relative amounts of byproducts involved in
reaction (2). For instance, significant Ca
2
enrichment in pore fluids within the
albitized plagioclase zone has been reported (Fisher and Boles, 1990). The enrich-
ment is mainly caused by the uptake of Na
and release of Ca
2
implied in reaction
(2). The calcium release can now be quantitatively estimated in arkosic basins through
geologic time with the albitization kinetic model. In short, the model has the potential
Fig. 13(A). Minimum temperatures required to complete albitization at constant time assuming
fine-grained sandstone, which we considered to be an average value for all three basins. (B) Minimum time
required to complete albitization at constant temperature. We assume fine-grain size sandstone, E
a
68
kJ/mole and A 6.5 10
3
1/cm
2
Ma.
339kinetic model for albitization of detrital plagioclase
to lead to a better understanding of the evolution of basin fluids in geological time
scales. The kinetic model may also be used by petroleum geologists for predicting the
precipitation of kaolinite or calcite (assuming a CO
2
supply) associated with albitiza-
tion, during burial in a given oil reservoir. Any estimation may be done by simply
integrating the kinetic equation through a time-temperature burial history of a given
siliciclastic formation, and applying basic rules of stoichiometry.
conclusions
Albitization of plagioclase trends present in sedimentary basins can be reasonably
reproduced with a kinetic equation that has a rate constant with a pre-exponential
parameter A (6.5 0.5) 10
3
1/cm
2
Ma, an activation energy E
a
68 4 kJ/mole
and an weighted average saturation index log
10
2.632. The only fitted parameter
was A, the other parameters E
a
and omega were fixed or calculated from real field data
prior to the kinetic analysis. Our study demonstrates that time, surface area, initial
composition, and primarily temperature are the most important parameters control-
ling the replacement reaction. Our model was tested against data from three geologic
settings: Texas Gulf Coast Basin, Denver Basin of Colorado, and San Joaquin Basin with
different burial and thermal histories. These results evidence that the proposed
equation and its parameters can reasonably reproduce the extent of the albitization
within our knowledge of variables involved.
The kinetic parameters yield rates within the range of other diagenetic reactions
involving precipitation of silicates, specifically quartz overgrowth cementation, illite
precipitation, and with calculations of albite crystal growth rates. The initial composi-
tion of detrital plagioclase affects albitization during the initial stages. The grain size
affects albitization until the transformation is completed. Subtle differences in grain
size, initial composition, and to a less extent the degree of order of the albite
component may be enough to explain the wide standard deviations reported in the
literature that we reference. We conclude that the albitization zone depends more on
temperature and the heating rate, than time and fluid chemistry. All variables,
however, are important and must be considered.
acknowledgments
We would like to acknowledge editorial work by Emma Perez and Dr. Arthur
Sylvester, and constructive comments by Drs. Thomas L. Dunn and Bradley Hacker.
Dr. Alicia Wilson provided important input with numerical methods and some burial
histories from the San Joaquin Basin. Comments and revisions by Dr. Rolland
Hellmann and the AJS anonymous reviewer greatly improved the content and theoreti-
cal basis of our study. The U.S. Department of Energy (DOE) funded our research
under grant no. 444033-22433.
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343kinetic model for albitization of detrital plagioclase
