Graphical Description of the Rock-Fluid Chemical Equilibria
Properly designed charts provide convenient means of describing the equilibrium chemical reactions of the rock-fluid systems. Frequently, the pe - pH, activity-activity, and saturation index charts are facilitated for convenient description of equilibrium chemical systems. The con-struction of these charts are based on the description of chemical systems at thermodynamic equilibrium. In this section, the theoretical bases, characteristics, and utilization of these charts are described according to Schneider (1997).
Saturation Index or Mineral Stability Charts
Mineral stability charts are convenient means of representing the various equilibrium reactions of the solid minerals and aqueous solutions in geological porous media in terms of the saturation index concept. Mineral stability charts can be more meaningfully developed by considering the incongruent equilibrium reactions of various solid phases including the igneous and metamorphic reactions (Schneider, 1997). Incongruent reactions represent the direct relationships of the various solid minerals involved in aqueous solution systems. The expressions of the incongruent reactions are derived from a combination of the relevant mineral dissolution/precipitation reactions in a manner to conserve certain key elements of the solid minerals so that the aqueous ionic species of these elements do not explicitly appear in the final equation.
For example, the incongruent reactions of the alumino silicate minerals, including clay minerals, feldspars, and chlorites, are usually expressed to conserve the aluminum element (Fletcher, 1993; Schneider, 1997). Aluminum is a natural choice as the conserved element because this element is mostly immobile and the activities of the aqueous aluminum species are relatively low (Hayes and Boles, 1992; Schneider, 1997). Consequently, the incongruent mineral reaction equations do not involve the potential dissolved aluminum species such as Al+3, Al(OH)2 +, Al(OH)4~, Al(OH) +2, and Al(OH)3° (Schneider, 1997). Thus, the aluminum element conserving incongruent reaction to form the chlorite mineral from the kaolinite mineral reads as (Schneider, 1997, p. 119):
The reactions for electrolyte dissolution in water can be represented by (Schneider, 1997):
Substituting unity for the activity of the solid phase, the expression of the reaction quotient leads to the actual ion activity product, given by:
At saturation, Eq. 13-27 yields the saturation ion activity product constant given by:
and is used to determine the state of saturation of an aqueous solution by a mineral as follows:
The composition of the various species in aqueous solutions undergoing dissolution/precipitation processes depends on various factors including pressure, temperature, and pH.
affect of pH on the composition of the typical carbonate species, namely H2CO3°, HCO3- and CO3-2
The Activity-Activity charts depict the regions of precipitation of various solid mineral phases. The equations of the lines separating these regions are obtained by rearranging the logarithmic expression of the equilibrium constant in a linear form to relate the saturation products of the various mineral phases. For example, the equilibrium constant for Eq. 13-25 is given by (Schneider, 1997):
in which the activities of the water and the solid kaolinite and chlorite phases were taken unity. A logarithm of Eq. 13-31 yields the linear equation for the kaolinite-chlorite phase boundary as:
The determination of the aqueous species activities is particularly complicated in highly concentrated oilfield brines because of the complexing of cations with inorganic and organic anions, and can be better accomplished by means of a simulator such as the SOLMINEQ.88 program by Kharaka et al. (1988).
pe- pH Charts
The pe - pH charts are constructed to describe the redox state of reservoirs (Stumm and Morgan, 1996; Schneider, 1997). Considering the electrons, e~, and protons, H+, involved, chemical equilibrium reactions, such as oxidation-reduction (redox) and acid-base reactions, are represented by
The electron activity (pe) and potentiometric acidity (pH) can be conveniently expressed by the following equations, respectively:
The electrode potential (Eh) and electron activity (pe) are related by (Schneider, 1997)
in which T denotes the absolute temperature in K, R = 8.31441J - K-1. mol-l is the universal gas constant and F = 9.64846 x 104 Coloumbl mol is the Faraday constant. The electrode potential can be measured directly. Eqs. 13-34 through 36 form the convenient mathematical bases for constructing the pe- pH or Eh-pH charts. However, the pe - pH charts are preferred over the Eh-pH charts because, while the sign of pH does not change and the slopes of the stability boundaries are independent of temperature, the sign of the Eh potential depends on the direction of the reaction and the slopes of the stability boundaries are temperature dependent (Schneider, 1997). For example, consider (Schneider, 1997):
Assigning unity for the activities of the water and solid mineral phases, the equilibrium constant expression reads as (Schneider, 1997):
Hence, a logarithm of Eq. 13-38 yields the equation for the hematitemagnetite boundary as:
which can be used to construct a pe - pH chart (Schneider, 1997).
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