Fluids and minerals in petroleum-bearing formations may undergo various interactive chemical reactions in response to the alteration of the in-situ conditions by various operations, including drilling, workover, and improved recovery. Geochemical models provide scientific guidance for controlling adverse reactions that may result from rock-fluid interactions. Excellent treaties of the geochemical reaction modeling are available from several sources, including Melchior and Bassett (1990), Ortoleva (1994), and Bethke (1996). This subject is extremely complex, therefore, only the fundamentals of the overall subject are outlined here. The readers are encouraged to resort to literature for details and to use ready-made software available from various sources.

Petroleum-bearing formations can be generally viewed as being geochemical systems in which fluids consisting of oil, gas, water, and immobile solid phases formed from an assemblage of minerals interact through various chemical reactions. Lichtner (1985) classified such reactions into four categories:

(1) aqueous ion complexing,

(2) oxidation and reduction,

(3) mineral precipitation and dissolution, and

(4) ion exchange and adsorption reactions.

As stated by Kharaka et al. (1988) and Amaefule et al. (1988), such reactions occur in response to changing temperature, pressure, and fluid composition by various factors, including the addition of incompatible fluids during drilling, workover and improved recovery processes and liberation of light gases, such as CH4, CO2, H2S, and NH3, during pressure-drawdown. Changes in temperature and pressure often cause the variation of the pH of the reservoir aqueous phase, which in turn induces adverse processes such as the precipitation of iron and silica gels (Kharaka et al., 1988; Rege and Fogler, 1989; Labrid and Bazin, 1993). Geochemical reactions can also be classified as homogeneous and heterogeneous depending on whether the reaction occurs inside a phase or with another phase, respectively. Geochemical reactions can also be classified as reversible and irreversible.

As explained by Lichtner (1985), the rates of reversible reactions are independent of the surface area. Reversible reactions can attain local equilibrium over a sufficiently long period of time, at which time, the reaction rates terms vanish in the transport equations. However, Lichtner (1985) adds that irreversible reactions require kinetic or rate expressions, in terms of the pertinent driving forces, that is chemical affinity, and/or the surface available for reactions. Detailed geochemical description is a very cumbersome task and often unnecessary and unjustified in view of the lack of the basic thermodynamic and kinetic data required for description.

Rather, geochemical models are constructed to emphasize the chemical reactions of the important aqueous species and minerals, which are essential for adequate description of the rock-water interactions, and neglect all other reactions. This is done to compromise between the quality of description and the effort necessary to gather basic thermodynamic and kinetic data and to carry out the numerical computations. Among the various alternatives, the kinetic and equilibrium models are extensively utilized. The kinetic models describe the rate of change of the amount of mineral and aqueous species in porous media in terms of the relevant driving forces and factors, such as deviation from equilibrium concentration and mineral-aqueous solution contact surface.

The proportionality constant is called the rate constant. The equations formed in this way are called the rate laws or kinetic equations. The equilibrium models assume geochemical equilibrium between the pore water and the minerals of porous formation. Since equilibrium can be reached over a sufficiently long time, equilibrium models represent the closed systems at steady-state conditions. Mathematically, the equilibrium models can be derived from kinetic models in the limit of infinitely large rate constants. Hence, rapid reactions reach equilibrium faster. Therefore, the equilibrium models represent the limiting conditions and yield conservative predictions (Schneider, 1997). Equilibrium models are particularly advantageous for determining the mineral stability and graphical representations of the mineral and aqueous species interactions (Bj0rkum and Gjelsvik, 1988; Stumm and Morgan, 1996; Schneider, 1997).

Because of the highly intensive numerical computations involved, the geochemical models of the rock-water interactions are usually implemented by computer-coded software. The geochemical computer software is constantly evolving and becoming more robust and accurate as a result of the advancement in computer technology, availability of accurate thermodynamic data, and development of efficient numerical solution methods. The engineers responsible for developing operational strategies and procedures for scale control in petroleum reservoirs should rely on such software. However, efficient use of the ready-made software requires some familiarity with the fundamental concepts, theories, and methods involved in the treatment and formulation of geochemical reactions. This information is usually provided with the user's guide and/or by relevant publications. In the following, a brief review of the description and graphical representation of aqueous and mineral species reactions and various approaches to geochemical modeling are presented.

Reactions in Porous Media

The various chemical reactions occurring in the pore space can be classified into the groups of homogeneous and heterogeneous reactions (Lichtner, 1992). The reactions occurring within the aqueous fluid phase are called the homogeneous or aqueous reactions. The reactions of the aqueous phase species with the solid minerals of porous formation, occurring at the pore surface, are called the heterogeneous or mineral reactions. A convenient treatment of the geochemical reactions can be achieved by grouping the various reacting solute species into the primary and secondary sets of species (Kandiner and Brinkley, 1950; Lichtner, 1992). The primary set of species is formed by selecting a minimum, critical number of reacting aqueous species, Sα, necessary for adequate description of the homogeneous and heterogeneous reactions. Thus, all other species form the set of the secondary species. The secondary species are derived from the primary species by means of the equations of the relevant chemical reactions.

Aqueous Phase Reactions

(a) ion pairing/exchange reactions,

(b) complexing reactions, and

(c) redox reactions.

The aqueous phase reactions are generally rapid relative to the mineral reactions (Liu et al., 1997). The rapid rates of aqueous phase reactions require kinetic descriptions with significantly large rate constants. Thus, for all practical purposes, these reactions can be assumed instantaneous and a transport controlled, local chemical equilibrium assumption is usually considered reasonable (Walsh et al., 1982, Lichtner, 1992; Liu et al., 1997; Liu and Ortaleva, 1996, 1996). Consider an aqueous phase undergoing a total of Nfr chemical aqueous reactions, r = 1,2,...,Nf denotes the index for the various aqueous reactions. Nr represents the total number of aqueous species involved in the rth aqueous or homogeneous reaction. Sa:а. = l,2,...,Nr denotes the various aqueous species involved in the r̩th aqueous reaction. Then, the aqueous reactions can be typically represented by (Walsh et al., 1982; Liu et al., 1996):

where νrfα denotes the stochiometric coefficient of species a involved in the rth aqueous reaction. Note v/a is negative for the reactants and positive for the products. Applying the mass action law of Prigogine and DeFay (1954), the chemical equilibria between the products and reactants of the rth reaction can be expressed as (Walsh et al., 1982; Liu et al., 1996):

Kfr denotes the thermodynamic equilibrium constant for the rth aqueous reaction given as the ratio of the rate constants kfrf and kfrb of the forward and backward reactions represented by Eq. 13-3:

αa is the chemical activity of the aqueous species a, which can be expressed in terms of the molal concentration, Cα, of species α as:

in which үa is the activity coefficient determined by the Debye-Huckel theory (Helgeson et al., 1970).

Mineral Reactions

The reactions of the aqueous phase species with the solid mineral matter of the porous matrix are referred to as the mineral reactions. Most mineral reactions are typically hydrolysis reactions. The interactions of minerals and aqueous species are generally slow relative to the aqueous phase reactions (Lichtner, 1992). Their reaction kinetics are controlled by the external mineral surface area contacting the aqueous phase. The mineral surface area is determined by the sizes of the grains of the porous formation. The rates of mineral reactions are gradual and, therefore, require kinetic descriptions with finite reaction rate constants. Consider a porous formation containing a total of Ns different mineral species and undergoing a total of Nsr different chemical reactions between its minerals species and the aqueous phase species. s = 1,2,...,Ns denotes the index for the participating mineral species of the porous formation. Nr denotes the total number of aqueous species involved in the rth heterogeneous reaction. Msr denotes the sth mineral species undergoing the rth heterogeneous reaction. Sa:a = l,2,...,Nr denotes the various aqueous species involved in the rth mineral reaction. Then, the reactions between porous formation minerals and aqueous species can be typically represented by (Lichtner, 1992, Liu et al., 1996):

where νsra denotes the stochiometric coefficients associated with the aqueous phase species per one participating mineral species. Note that vs m is negative for the reactants and positive for the products. Applying the mass action law (Prigogine and DeFay, 1954), and assuming that the activity of the solid minerals is equal to one, the chemical equilibria between the minerals of the porous formation and the aqueous species of the rth reaction can be expressed in terms of the equilibrium saturation solubility product as (Walsh et al., 1982):

For a mineral s undergoing a dissolution/precipitation reaction r, the reaction driving force is given by (Liu et al., 1996):

ΔGrs > 0 for mineral dissolution and ΔGri < 0 for mineral precipitation. Κrs denotes the dissolution rate constant of the rth reaction of the sth mineral. Approximating the shape of the mineral grains by a sphere, and assuming that the mineral reactions are kinetic reactions, Liu et al. (1996) express the rate of dissolution or precipitation of the sth mineral by the rth reaction by:

as being proportional to the number of the Sth mineral grains per formation bulk volume, ns, the surface area of the sth mineral grain, 4ԉR2s, and the reaction driving force, ΔGrj. The grain mass density of the sth mineral, Ps, is inserted to express the mass rate of dissolution or precipitation of the ith mineral grain. Rs represents the radius of the Sth mineral grain. Thus, Liu et al. (1996) express the rate of change of the sth grain radius by dissolution and/or precipitation by various reactions as:

The mass conservation equation for species a undergoing transport through porous media by various mechanisms is given by Eq. 7-34 derived in this article. The rate of generation of the Oith aqueous species per bulk formation volume, required for Eq. 7-34, is given by Liu et al. (1996) as:

where Na is the total number of aqueous species involved; Nrf and Nrs denote the total number of aqueous and mineral reactions, respectively; Wrf and Wrs represent the rates of the rth aqueous and mineral reactions, respectively; Ѵfar. and Ѵsar. denote the stochiometric coefficients of the species a in the aqueous and mineral reactions, respectively, and qa represents the rate of species a addition per bulk formation volume by means of direct injection of fluids through wells completed in the reservoir.


Aja, S. U., Rosenberg, P. E., & Kittrick, J. A., "Illite Equilibria in Solutions: I. Phase Relationships in the System K2O-Al2O3-SiO2-H2O between 25 and 250°C," Geochimica et Cosmochimica Acta, Vol. 55, 1991a, pp. 1353-1364.

Aja, S. U., Rosenberg, P. E., & Kittrick, J. A., "Illite Equilibria in Solutions: II. Phase Relationships in the System K2O-MgO-Al2O3-SiO2-H2O," Geochimica et Cosmochimica Acta, Vol. 55, 1991b, pp. 1365-1374.

Amaefule, J. O., Kersey, D. G., Norman, D. L., & Shannon, P. M., "Advances in Formation Damage Assessment and Control Strategies," CIM Paper No. 88-39-65, Proceedings of the 39th Annual Technical Meeting of Petroleum Society of CIM and Canadian Gas Processors Association, June 12-16, 1988, Calgary, Alberta, 16 p.

Basset, R. L., & Melchior, D. C., "Chemical Modeling of Aqueous Systems—An Overview," Chapter 1, pp. 1-14, in Chemical Modeling of Aqueous Systems II, Melchoir, D. C. & Basset, R. L. (Eds.), ACS Symposium Series 416, ACS, Washington, 1990.

Bertero, L., Chierici, G. L., Gottardi, G., Mesini, E., & Mormino, G., "Chemical Equilibrium Models: Their Use in Simulating the Injection of Incompatible Waters," SPE Reservoir Engineering Journal, February 1988, pp. 288-294.

Bethke, C. M., Geochemical Reaction Modeling, Concepts and Application, Oxford University Press, New York, 1996, 397 p.

Bj0rkum, P. A., & Gjelsvik, N., "An Isochemical Model for Formation of Authigenic Kaolinite, K-feldspar, and Illite in Sediments," Journal of Sedimentary Petrology, Vol. 58, No. 3, 1988, pp. 506-511.

Carnahan, C. L., "Coupling of Precipitation-Dissolution Reactions to Mass Diffusion via Porosity Changes," Chemical Modeling of Aqueous Systems II, Chapter 18, pp. 234-242, D.C. Melchior & R. L. Basset (Eds.), ACS Symposium Series 416, American Chemical Society, Washington, DC, 1990.

Chang, F. F., and Civan, F., "Modeling of Formation Damage due to Physical and Chemical Interactions between Fluids and Reservoir Rocks," SPE 22856 paper, Proceedings of the 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, October 6-9, 1991, Dallas, Texas.

Chang, F. F., & Civan, F., "Predictability of Formation Damage by Modeling Chemical and Mechanical Processes," SPE 23793 paper, Proceedings of the SPE International Symposium on Formation Damage Control, February 26-27, 1992, Lafayette, Louisiana, pp. 293-312.

Chang, F. F., & Civan, F., "Practical Model for Chemically Induced Formation Damage," Journal of Petroleum Science and Engineering, Vol. 17, No. 1/2, February 1997, pp. 123-137.

Curtis, C. D., Ireland, B. J., Whiteman, J. A., Mulvaney, R., & Whittle, C. K., "Authigenic Chlorites: Problems with Chemical Analysis and Structural Formula Calculation," Clay Minerals, Vol. 19, 1984, pp. 471-481.

Curtis, C. D., Hughes, C. R., Whiteman, J. A., & Whittle, C. K., "Compositional Variation Within Some Sedimentary Chlorites and Some Comments on their Origin," Mineralogical Magazine, Vol. 49, 1985, pp. 375-386.

Demir, L, "Formation Water Chemistry and Modeling of Fluid-Rock Interaction for Improved Oil Recovery in Aux Vases and Cypress Formations," Department of Natural Resources, Illinois State Geological Survey, Illinois Petroleum Series 148, 1995, 60 p.

Dewers, T, Civan, E, and Atkinson, G., "Formation Damage and Carbonate Scale During Sub-Salt Petroleum Production," research proposal funded by the Interdisciplinary Research Incentive Program at the University of Oklahoma, 2000, 20 p. unpublished.

Drever, J. I., The Geochemistry of Natural Waters, Second Edition, Prentice Hall, New York City, 1988.

Dullien, F. A. L., Porous Media Fluid Transport and Pore Structure, 2nd ed., Academic Press, Inc., San Diego, 1992, 574 p.

ESTSC/COSMIC, "Geochemical Modeling of Aqueous Systems, EQ3NR," Software Technology Transfer, Energy Science and Technology Software Center (ESTSC), Oak Ridge, TN, and NASA Computer Software Technology Transfer Center (COSMIC), the University of Georgia, Athens, GA, Vol. 1, No. 1, Winter 1993, p. 17.

Fletcher, P., Chemical Thermodynamics for Earth Scientists, Longman Group UK Ltd., London, 1993.

Glover, M. C., & Guin, J. A., "Dissolution of a Homogeneous Porous Medium by Surface Reaction," AIChE Journal, Vol. 19, No. 6, November 1973, pp. 1190-1195.

Haggerty, D. J., & Seyler, B., "Investigation of Formation Damage from Mud Cleanout Acids and Injection Waters in Aux Vases Sandstone Reservoirs," Department of Natural Resources, Illinois State Geological Survey, Illinois Petroleum Series 152, 1997, 40 p.

Hayes, M. J., & Boles, J. R., "Volumetric Relations Between Dissolved Plagioclase and Kaolinite in Sandstones: Implications for Aluminum Mass Transfer in San Joaquin Basin, California," Origin, Diagenesis, and Petrophysics of Clay Minerals in Sandstones, SEPM Special Publication No. 47, 1992, pp. 111-123.

Helgeson, H. C., Brown, T. H., Nigrini, A., & Jones, T. A., "Calculation of Mass Transfer in Geochemical Processes Involving Aqueous Solutions," Geochimica Cosmochimica Acta, Vol. 34, 1970, pp. 569-592.

Holstad, A., "Mathematical Modeling of Diagenetic Processes in Sedimentary Basins," Mathematical Modelling of Flow Through Porous Media, Bourgeat, A. P., Carasso, C., Luckhaus, S., & Mikelic, A., (Eds.), World Scientific Publ. Co. Pte. Ltd., 1995, pp. 418-428.

Israelachvili, J., Intermolecular and Surface Forces, 2nd ed., Academic Press, San Diego, 1992, 450 p.

James, R. O., & Parks, G. A., "Characterization of Aqueous Colloids by their Electrical Double-Layer and Intrinsic Surface Chemical Properties," in Surface and Colloid Science, Vol. 12, Matijevic, E. (ed.), Plenum Press, New York, pp. 119-216.

Jennings, A. A., & Kirkner, D. J., "Instantaneous Equilibrium Approximation Analysis," J. of Hydraulic Eng., Vol. 110, No. 12, 1984, pp. 1700-1717.

Kaiser, W. R., "Predicting Reservoir Quality and Diagenetic History in the Frio Formation (Oligocene) of Texas," Clastic Diagenesis: AAPG Memoir 37, McDonald, D. A. & Surdam, R. C. (Eds.), American Association of Petroleum Geologists, 1984, pp. 195-215.

Kandiner, H. J., & Brinkley, S. R., "Calculation of Complex Equilibrium Relations," Ind. Eng. Chem., Vol. 42, 1950, pp. 850-855.

Kharaka, Y. K., & Barnes, I., "SOLMINEQ: Solution-mineral-equilibrium Computations: U.S. Geological Survey Computer Contributions," NTIS No. PB215-899, 1973, 81 p.

Kharaka, Y. K., Gunter, W. D., Aggarwal, P. K., Perkins, E. H., & DeBraal, J. D., "SOLMINEQ.88: A Computer Program for Geochemical Modeling of Water-Rock Interactions," U.S. Geological Survey Water-Resources Investigations Report 88-4227, Menlo Park, CA, 1988, 429 p.

Labrid, J., & Bazin, B., "Flow Modeling of Alkaline Dissolution by a Thermodynamic or by a Kinetic Approach," SPE Reservoir Engineering, May 1993, pp. 151-159.

Li, Y-H., Crane, S. D., Scott, E. M., Braden, J. C., & McLelland, W. G., "Waterflood Geochemical Modeling and a Prudhoe Bay Zone 4 Case Study," SPE Journal, Vol. 2, March 1997, pp. 58-69.

Li, Y-H., Fambrough, J. D., & Montgomery, C. T., "Mathematical Modeling of Secondary Precipitation from Sandstone Acidizing," SPE Journal, December 1998, pp. 393-401.

Lichtner, P. C., "Continuum Model for Simultaneous Chemical Reactions and Mass Transport in Hydrothermal Systems," Geochimica et Cosmochimica Acta, Vol. 49, 1985, pp. 779-800.

Lichtner, P. C., "The Quasi-Stationary State Approximation to Coupled Mass Transport and Fluid-Rock Interaction in a Porous Medium," Geochimica et Cosmochimica Acta, Vol. 52, 1988, pp. 143-165.

Lichtner, P. C., "Time-Space Continuum Description of Fluid/Rock Interaction in Permeable Media," Water Resources Research, Vol. 28, No. 12, December 1992, pp. 3135-3155.

Liu, X., Ormond, A., Bartko, K., Li, Y, & Ortoleva, P., "A Geochemical Reaction-Transport Simulator for Matrix Acidizing Analysis and Design," J. of Petroleum Science and Engineering, Vol. 17, No. 1/2, February 1997, pp. 181-196.

Liu, X., & Ortoleva, P., "A Coupled Reaction and Transport Model for Assessing the Injection, Migration, and Fate of Waste Fluids," SPE 36640 paper, Proceedings of the 1996 SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 6-9, 1996, pp. 661-673.

Liu, X., & Ortoleva, P., "A General-Purpose, Geochemical Reservoir Simulator," SPE 36700 paper, Proceedings of the 1996 SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 6- 9, 1996, pp. 211-222.

Melchior, D. C., & Bassett, R. L. (Eds.), "Chemical Modeling of Aqueous Systems II," ACS Symposium Series 416, American Chemical Society, Washington, DC, 1990, 556 p.

Nordstrom, D. K., & Munoz, J. L., Geochemical Thermodynamics, 2nd ed., Blackwell Scientific Publications, Boston, 1994.

Ortoleva, P., Geochemical Self-Organization, Oxford University Press, New York, 1994.

Plummer, L. N., Geochemical Modeling of Water-Rock Interaction: Past, Present, Future," in Water-Rock Interation, Vol. 1, Kharaka, Y. K. & Maest, A. S. (Eds.), 1992, Balkema, Rotterdam, Brookfield, 858 p.

Prigogine, I., & DeFay, R., Chemical Thermodynamics, D.H. Everett (trans.), Longmans Green and Co., London, 1954, 543 p.

Rege, S. D., & Fogler, H. S., "Competition Among Flow, Dissolution and Precipitation in Porous Media," AIChE J., Vol. 35, No. 7, 1989, pp. 1177-1185.

Sahai, N., & Sverjensky, D. A., "GEOSURF: A Computer Program for Modeling Adsorption on Mineral Surfaces from Aqueous Solution," Computers and Geosciences, Vol. 24, No. 9, 1998, pp. 853-873.

Schechter, R. S., & Gidley, J. L., "The Change in Pore Size Distribution from Surface Reactions in Porous Media," AIChE Journal, Vol. 15, No. 3, May 1969, pp. 339-350.

Schneider, G. W., "A Geochemical Model of the Solution-Mineral Equilibria Within a Sandstone Reservoir," M.S. Thesis, The University of Oklahoma, 1997, 157 p.

Scott, A. R., "Organic and Inorganic Geochemistry, Oil-Source Rock Correlation, and Diagenetic History of the Permian Spraberry Formation, Jo Mill Field, Northern Midland Basin, West Texas," M.S. Thesis, Sul Ross State University, Alpine, Texas, 1988.

Sears, S. O., & Langmuir, D., "Sorption and Mineral Equilibria Controls on Moisture Chemistry in a C-Horizon Soil," Journal of Hydrology, Vol. 56, 1982, pp. 287-308.

Shaughnessy, C. M., & Kline, W. E., "EDTA Removes Formation Damage at Prudhoe Bay," SPE 11188 paper, presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, September 26-29, 1982.

Shaughnessy, C. M., & Kline, W. E., "EDTA Removes Formation Damage at Prudhoe Bay," Journal of Petroleum Technology, October 1983, pp. 1783-1792.

Steefel, C. I., & Lasaga, A. C., "Evolution of Dissolution Patterns- Permeability Change Due to Coupled Flow and Reaction," Chemical Modeling of Aqueous Systems II, Chapter 16, pp. 212-225, D.C. Melchior & R. L. Basset (Eds.), ACS Symposium Series 416, American Chemical Society, Washington, DC, 1990.

Stumm, W., & Morgan, J. J., Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters, John Wiley and Sons, New York, New York, 1996.

Todd, A. C., & Yuan, M. D., "Barium and Strontium Sulfate Solid Solution Formation in Relation to North Sea Scaling Problems," SPE 18200 paper, Proceedings of the Society of Petroleum Engineers 63rd Annual Technical Conference and Exhibition, Houston, Texas, October 2-5, 1988, pp. 193-198.

Walsh, M. P., Lake, L. W, & Schechter, R. S., "A Description of Chemical Precipitation Mechanisms and Their Role in Formation Damage During Stimulation by Hydrofluoric Acid," Journal of Petroleum Technology, September 1982, pp. 2097-2112.

Warren, E. A., & Curtis, C. D., "The Chemical Composition of Authigenic Illite Within Two Sandstone Reservoirs as Analysed by TEM," Clay Minerals, Vol. 24, 1989, pp. 137-156.

Westall, J. C., "Reactions at the Oxide-Solution Interface: Chemical and Electrostatic Models," in Geochemical Processes at Mineral Surfaces, Davis, J. A. & Hayes, K. F. (Eds.), ACS, Washington, 1986, pp. 54-78.

Yates, D. E., Levine, S., & Healy, T. W., "Site-Binding Model of the Electrical Double Layer at the Oxide/Water Interface," Journal of the Chemical Society Fraday Transactions /, Vol. 70, 1974, pp. 1807-1818.

Yeboah, Y. D., Somuah, S. K., & Saeed, M. R., "A New and Reliable Model for Predicting Oilfield Scale Formation," SPE 25166 paper, Proceedings of the SPE International Symposium on Oilfield Chemistry, New Orleans, Louisiana, March 2-5, 1993, pp. 167-176.