332 Reservoir Formation Damage where 7V a is the total number of aqueous species involved; Nf and N* denote the total number of aqueous and mineral reactions, respectively; W/ and W r s represent the rates of the r th aqueous and mineral reactions, respectively; v£. and v^. denote the stochiometric coefficients of the species a in the aqueous and mineral reactions, respectively, and q a represents the rate of species a addition per bulk formation volume by means of direct injection of fluids through wells completed in the reservoir. Ion Exchange and Adsorption Reactions Ion exchange and adsorption are surface chemical or surface com- plexation processes leading to the exchange of chemical species between the aqueous solution and mineral surfaces present in geological porous formations (Jennings and Kirkner, 1984; Lichtner, 1985; Kharaka et al., 1988). Kharaka et al. (1988) explain the difference between ion exchange and adsorption as following: "The ion exchange model treats the exchange of cations or anions on a constant charge surface" and "the adsorption model simulates the exchange process on a surface where the surface charge is developed due to the ionization of surface sites at the solution- surface interface." Therefore, adsorption is a more general concept and ion exchange is a special case of adsorption (Lichtner, 1985; Sahai and Sverjensky, 1998). Among the various surface complexation models, Sahai and Sverjensky (1998) facilitate the triple-layer model (Yates et al., 1974) for describing the electrical charge near mineral surfaces, as described in Figure 13-2 (Sahai and Sverjensky, 1998) according to Westall (1986). As indicated in Figure 13-2, this model considers the mineral surface, referred to as the O-plane, for adsorption of hydroxide ions and protons and at a short distance near the mineral surface, referred to as the p-plane, for adsorption of electrolyte ions and the surface charge is generated by adsorption of the electrolyte ions and protons (Sahai and Sverjensky, 1998). Clays present in geological porous formations have many active ion exchange sites, a, occupied by various cations and cation exchange takes place for replacement of the cations in the order of the replacing tendency of Ca +2 > Mg +2 > K + > Na + (Li et al., 1997). The cation exchange capac- ity (CEC) of rocks can be expressed as the total number of moles of exchange sites a per unit mass of rock, Qf x , or per unit volume of rock, w a , which are related by (Lichtner, 1985): % (13-15) Lichtner (1985) points out that "precipitation/dissolution reactions can alter the exchange capacity of the porous medium by creating or destroy- Inorganic Scaling and Geochemical Formation Damage 333 compact layer of adsorbed ions bulk solution DISTANCED (meters) 0-plane (mineral surface) p*-plane (electrolyte adsorption) Figure 13-2. Triple-layer description of the potential vs. distance from the mineral surface (Reprinted from Journal of Computers and Geosciences, Vol. 24, Sahai, N., & Sverjensky, D. A., "GEOSURF: A Computer Program for Modeling Adsorption on Mineral Surfaces from Aqueous Solution," pp. 853- 873, ©1998, with permission from Elsevier Science). ing exchange sites," but this effect has not been taken into account in most reported studies. In Eq. 13-15, <j) and p^ denote the porosity and the grain density of the rock, respectively. Represent the exchange sites by a, the total number of different exchange sites by N a , an exchange site of type ot with unit charge by E a , the i' h cation species with valence Zi by S f , and the concentration of the i th species attached to the exchange sites a by C™, expressed in moles per unit bulk volume. Lichtner (1985) then describes the chemical reactions at mineral surfaces by (13-16) 334 Reservoir Formation Damage and the conservation of the ion exchange sites by «„ = (13-17) jt=i where N is the total number of chemically reacting species. ^ ; (^a) z and Sf(E a ] represent the cations attached to the active exchange sites. Sears and Langmuir (1982) report that ion exchange and adsorption reactions in soils typically require a time of seconds to days to attain equilibrium. Therefore, Jennings and Kirkner (1984) describe these reactions by rate equations for full kinetic modeling. Applying their approach to Eq. 13-16 according to Chang and Civan (1997) yields the following kinetic expression for the rates of consumption of Sj (E a ) and production of Sf(E a ] , respectively: J iy ' as , „_ T dt (13-18) where (|) is the porosity and kj and k' r j denote the rate coefficients for the forward and reverse reactions, respectively. If /" is the reaction rate for the exchange of the i th cation present in aqueous solution with the j th cation attached to the a th site on the mineral surface, and I r is the rate of the reactions of the /"'cation of the aqueous solution other than adsorption, the transport equation for the /""cation present in aqueous solution is given by (Lichtner, 1985): o=l j=l M r=l (13-19) where e a denotes the volume fraction of the aqueous phase in the bulk of porous formation and c i denotes the concentration of the /"" cation in the aqueous solution, expressed in moles per unit volume of the aqueous phase. The balance of the /""cation adsorbed on the a' h site of the mineral surface is given by (Litchner, 1985): a? (13-20) Inorganic Scaling and Geochemical Formation Damage 335 where Cf is the concentration of the i th species attached to the exchange sites a expressed in moles per unit bulk volume. Because (13-21) (13-22) then, (13-23) Thus, Lichtner (1985) combined Eqs. 13-19 and 20 into the following convenient form by summing Eq. 13-20 over all the exchange sites a, adding the resultant equation to Eq. 13-19, and eliminating the exchange reaction rates by means of Eq. 13-23: (13-24) Geochemical Modeling As stated by Plummer (1992)*: "Geochemical modeling attempts to interpret and (or) predict chemical reactions of minerals, gases, and organic matter with aqueous solutions in real or hypothetical water-rock systems." Figure 13-3 by Bassett and Melchior (1990) outlines the basic constituents and options of most geochemical models. Plummer (1992)* classified the various geochemical modeling efforts into four groups: 1. Aqueous speciation models for geochemical applications, 2. Inverse geochemical modeling techniques for interpreting observed hydrochemical data, 3. Forward geochemical modeling techniques for simulating the chemi- cal evolution of water-rock systems, and 4. Reaction-transport modeling for the coupling of geochemical reac- tion modeling with equations describing the physics of fluid flow and solute transport processes. Brief descriptions of these models are presented in the following, accord- ing to Plummer (1992). * Reprinted from "Water-Rock Interaction," Proceedings of the 7th international symposium, WRI-7, Park City, Utah, 13-18 July 1992 Kharaka, Y. K. & A. S. Maest (eds.), 90 5410 075 3, 1992, 25 cm, 1730 pp., 2 vols., EUR 209.00/US$246.00 GBP147. Please order from: A. A. Balkema, Old Post Road, Brookfield, Vermont 05036 (telephone: 802-276- 3162; telefax: 802-276-3837; e-mail: info@ashgate.com). 336 Reservoir Formation Damage THERMODYNAMIC DATABASE INPUT CHEMICAL DATA MATRIX INVERSION OR ITERATIVE SOLUTIOt ALGORITHM SECONDARY COMPUTATIONS • Saturation Index • Computed Cation/Anlon Balance • Geotherraometers • Percentage Species Distribution • Computed Gas Partial Pressures ( V V P CO,' P CH. ' etC -> 1 AQUEOUS MODEL AND ANCILLARY CALCULATIONS • Solvent Parameters (a^. p, D, ^) • Solute Fitting Parameters (b, B, etc.) Conversion to molal units Log K Interpolation Cation/Anion Balance Redox (Eh, pe) Activity Coefficient (7 ) Alkalinity vs. Total C * OPTIONS AND EVOLUTIONARY CHANGES - Mixing of Waters - Titration of Solids and Gases - Outgassing - Samples at Multiple Temperatures - Organic Ligands - Adsorption Models - Reaction Path Simulation - Adherence to Phase Boundaries - Isotope Mass Balance - Pressure Correction for Log K - Pseudo-Kinetic Expressions - Pitzer Ion-Interaction Expression - Mixed Redox Couples Figure 13-3. Common elements of aqueous chemical models (Reprinted with permission from 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, Melchior, D. C. & Basset, R. L. (eds.), ACS Sympo- sium Series 416, ACS, Washington, 1990, Figure 2, page 6; ©1990 American Chemical Society). Inorganic Scaling and Geochemical Formation Damage 337 Aqueous Speciation Models Aqueous Speciation models describe the thermodynamic properties of aqueous solutions and they are an integral part of the geochemical models. Plummer (1992)* summarizes the constituents of these models as: 1. Mass balance equations for each element, 2. Mass action equations and their equilibrium constants, for complex- ion formation, and 3. Equations that define individual ion-activity coefficients. Two types of aqueous specification models are popular: (a) ion- association models and (b) specific interaction models. The ion association and the specific interaction models facilitate, respectively, the extensions and a complex expansion of the Debye-Hiickel theory to estimate the individual ion activity coefficients of aqueous species (Plummer, 1992). The specific interaction models are preferred for highly concentrated solutions of mixed-electrolytes (Plummer, 1992). As pointed out by Plummer (1992), aqueous geochemical models can be used for forward and inverse geochemical modeling. Geochemical Modeling—Inverse and Forward Plummer (1992)* summarizes that "Two approaches to geochemical modeling have evolved—"inverse modeling," which uses water and rock compositions to identify and quantify geochemical reactions, and "forward modeling," which uses hypothesized geochemical reactions to predict water and rock compositions." However, the application of these models is rather difficult because the basic data necessary for these models are often incomplete and/or uncertain (Plummer, 1992). Plummer (1992)* describes the most essential information necessary for geochemical modeling and its applications as following: 1. The mineralogy, and its spatial variation in the system, 2. The surface area of reactants in contact with aqueous fluids in ground-water systems, 3. The chemical and isotopic composition of reactants and products in the system, 4. The hydrology of the system, 5. The extent to which the system is open or closed, * Reprinted from "Water-Rock Interaction," Proceedings of the 7th international symposium, WRI-7, Park City, Utah, 13-18 July 1992 Kharaka, Y. K. & A. S. Maest (eds.), 90 5410 075 3, 1992, 25 cm, 1730 pp., 2 vols., EUR 209.00/US$246.00 GBP147. Please order from: A. A. Balkema, Old Post Road, Brookfield, Vermont 05036 (telephone: 802-276- 3162; telefax: 802-276-3837; e-mail: info@ashgate.com). 338 Reservoir Formation Damage 6. The temporal variation of these properties, 7. The fundamental knowledge on the kinetics and mechanisms of important water-rock reactions, 8. The kinetics of sorption processes, and 9. The degradation pathways of organic matter. Inverse Geochemical Modeling Plummer (1992)* explains that "Inverse geochemical modeling combines information on mineral saturation indices with mass-balance modeling to identify and quantify mineral reactions in the system." The mass-balance modeling requires (Plummer, 1992): 1. Element mass balance equations, 2. Electron conservation equations, 3. Isotope mass balance equations, when applicable, 4. Aqueous compositional and isotopic data, and 5. Mineral stochiometry data for all reactants and products. Plummer (1992)* warns that "The inverse-modeling approach is best suited for steady-state regional aquifers, where effects of hydrodynamic dispersion can often be ignored." Forward Geochemical Modeling The objective of the forward geochemical modeling is to predict mineral solubilities, mass transfers, reaction paths, pH and pe by using available solid-aqueous data in aqueous specification models (Plummer, 1992). Some of the important features of the advanced forward geo- chemical models are cited by Plummer (1992) as: 1. Access to a large thermodynamic data base, 2. Generalized reaction-path capability, 3. Provision for incorporation of reaction kinetics in both dissolution and precipitation, 4. A variety of activity coefficient models, 5. Treatment of solid solutions, 6. Calculation of pH and pe, * Reprinted from "Water-Rock Interaction," Proceedings of the 7th international symposium, WRI-7, Park City, Utah, 13-18 July 1992 Kharaka, Y. K. & A. S. Maest (eds.), 90 5410 075 3, 1992, 25 cm, 1730 pp., 2 vols., EUR 209.00/USS246.00 GBP147. Please order from: A. A. Balkema, Old Post Road, Brookfield, Vermont 05036 (telephone: 802-276- 3162; telefax: 802-276-3837; e-mail: info@ashgate.com). Inorganic Scaling and Geochemical Formation Damage 339 7. Calculation of mineral solubilities with and without accompanying irreversible reaction, 8. Calculation of boiling, cooling, wall-rock alteration, ground-water mixing with hot waters and evaporation, and 9. Equilibrium or partial equilibrium states in gas-solid-aqueous systems. Plummer (1992)* states that forward geochemical modeling can be used "in developing reaction models that can account for the observed compositional-mineralogical relations in the deposit, if there are no aqueous or solid data for the system." Reaction-Transport Geochemical Modeling The reaction-transport models describe the geochemical reactions under the influence of fluid flow and convective and dispersive transport of various species in geological porous media. These models couple the geochemical reaction and the fluids and species transport submodels to accomplish temporal and spatial prediction of the evolution of geo- chemical reactions in compositionally-complex geological systems (Plummer, 1992). These models are more applicable in most petroleum reservoir exploitation and scale formation studies. 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 thermo- dynamic 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. * Reprinted from "Water-Rock Interaction," Proceedings of the 7th international symposium, WRI-7, Park City, Utah, 13-18 July 1992 Kharaka, Y. K. & A. S. Maest (eds.), 90 5410 075 3, 1992, 25 cm, 1730 pp., 2 vols., EUR 209.00/US$246.00 GBP147. Please order from: A. A. Balkema, Old Post Road, Brookfield, Vermont 05036 (telephone: 802-276- 3162; telefax: 802-276-3837; e-mail: info@ashgate.com). 340 Reservoir Formation Damage Mineral stability charts can be more meaningfully developed by con- sidering 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 incon- gruent mineral reaction equations do not involve the potential dissolved aluminum species such as Af 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): L4Al 2 Si 2 O 5 (OH) 4 + 2A5Mg +2 + 2.25Fe +2 Kaolinite +5.8//0 <-» +0.1/f 4 S*0 4 °+8.8// + Chlorite (13-25) The reactions for electrolyte dissolution in water can be represented by (Schneider, 1997): AB <->m^ w +ne w (13-26) Substituting unity for the activity of the solid phase, the expression of the reaction quotient leads to the actual ion activity product, given by: (actual) (actual) (13-27) At saturation, Eq. 13-27 yields the saturation ion activity product constant given by: p =[< +n ] -la" I V)L} I B ( Inorganic Scaling and Geochemical Formation Damage 341 (13-28) Thus, a saturation index can be defined as: 'K^} SI -log 10 (13-29) and is used to determine the state of saturation of an aqueous solution by a mineral as follows: SI < 0 , undersaturated = 0 , saturated > 0 , supersaturated (13-30) The composition of the various species in aqueous solutions undergoing dissolution/precipitation processes depends on various factors including pressure, temperature, and pH. For example, Figure 13-4, generated by Schneider (1997) using SOLMINEQ.88 (Kharaka et al., 1988) depicts the 100 pH Control for Carbonate Species 25 and 100 degrees Centigrade COS (-2) HCO3 - H2CO3 Figure 13-4. Effect of pH on distribution of carbonate species (after Schneider, ©1997; reprinted by permission of G. W. Schneider). [...]... 0 .5 106400 8 35 28 3 0 24 0 2. 2 6.83 170837 ND ND 24 .6 ND 23 .3 304 22 5. 7 ND 60430 3037 753 4 12 2.18 8 12 0.16 0.6 110000 8 92 246 0 24 0 4.3 7 .23 1 759 32 ND ND 26 .2 ND 8.3 29 0 8.9 5. 4 0: K 0 Si < 0: 20 80 100 Figure 13-9 . Al cr Br so 4 - 2 C0 3 ~ 2 HCO 3 H 4 Si0 4 ° pH TDS Tartarate Malonate Succinate Glycolate Formate Acetate Propianate Butyrate Oxalate JMU # 723 4 58 650 28 47 663 9 62 2.41 780 10.3 0 .5 106400 8 35 28 3 0 24 0 2. 2 6.83 170837 ND ND 24 .6 ND 23 .3 304 22 5. 7 ND JMU # 723 1 60430 3037 753 4 12 2.18 8 12 0.16 0.6 110000 8 92 246 0 24 0 4.3 7 .23 1 759 32 ND ND 26 .2 ND 8.3 29 0 8.9 5. 4 <3.0 JMU # 623 4 57 340 28 64 693 994 2. 2 788 20 .7 0 .5 9 950 0 788 364 0 73 1.7 6.97 1 626 39 ND ND 21 .5 ND 28 .9 313 18.6 ND <3.0 JMU #1333 58 140 28 90 779 300 3 .5 828 <0.03 0.6 1 055 00 9 02 161 0 22 0 3.7 7 .56 168 822 ND ND 22 .1 ND 5. 5 1 95 ND ND ND JMU #24 33 54 950 28 54 736 964 1. 95 761 1.14 . 05 94000 793 26 5 0 29 3 2. 4 7 .21 154 826 ND ND 19.3 ND 7.7 326 22 .5 6.3 ND Mule Shoe Ranch Water 18 62 42 19 14 0.03 1.7 <0.03 0.07 1 450 5. 3 1669 16 484 3.6 8.41 55 59 ND ND ND ND ND ND ND ND <3.0 Canyon Reef Water 52 6 00 4617 980 53 8 0. 75 301 11.6 0.7 9 450 0 4. 52 689 0 134 2. 8 7.09 154 370 ND ND 15. 1 ND 8.4 36.1 ND <3.0 ND * . Al cr Br so 4 - 2 C0 3 ~ 2 HCO 3 H 4 Si0 4 ° pH TDS Tartarate Malonate Succinate Glycolate Formate Acetate Propianate Butyrate Oxalate JMU # 723 4 58 650 28 47 663 9 62 2.41 780 10.3 0 .5 106400 8 35 28 3 0 24 0 2. 2 6.83 170837 ND ND 24 .6 ND 23 .3 304 22 5. 7 ND JMU # 723 1 60430 3037 753 4 12 2.18 8 12 0.16 0.6 110000 8 92 246 0 24 0 4.3 7 .23 1 759 32 ND ND 26 .2 ND 8.3 29 0 8.9 5. 4 <3.0 JMU # 623 4 57 340 28 64 693 994 2. 2 788 20 .7 0 .5 9 950 0 788 364 0 73 1.7 6.97 1 626 39 ND ND 21 .5 ND 28 .9 313 18.6 ND <3.0 JMU #1333 58 140 28 90 779 300 3 .5 828 <0.03 0.6 1 055 00 9 02 161 0 22 0 3.7 7 .56 168 822 ND ND 22 .1 ND 5. 5 1 95 ND ND ND JMU #24 33 54 950 28 54 736 964 1. 95 761 1.14 . 05 94000 793 26 5 0 29 3 2. 4 7 .21 154 826 ND ND 19.3 ND 7.7 326 22 .5 6.3 ND Mule Shoe Ranch Water 18 62 42 19 14 0.03 1.7 <0.03 0.07 1 450 5. 3 1669 16 484 3.6 8.41 55 59 ND ND ND ND ND ND ND ND <3.0 Canyon Reef Water 52 6 00 4617 980 53 8 0. 75 301 11.6 0.7 9 450 0 4. 52 689 0 134 2. 8 7.09 154 370 ND ND 15. 1 ND 8.4 36.1 ND <3.0 ND * . Al cr Br so 4 - 2 C0 3 ~ 2 HCO 3 H 4 Si0 4 ° pH TDS Tartarate Malonate Succinate Glycolate Formate Acetate Propianate Butyrate Oxalate JMU # 723 4 58 650 28 47 663 9 62 2.41 780 10.3 0 .5 106400 8 35 28 3 0 24 0 2. 2 6.83 170837 ND ND 24 .6 ND 23 .3 304 22 5. 7 ND JMU # 723 1 60430 3037 753 4 12 2.18 8 12 0.16 0.6 110000 8 92 246 0 24 0 4.3 7 .23 1 759 32 ND ND 26 .2 ND 8.3 29 0 8.9 5. 4 <3.0 JMU # 623 4 57 340 28 64 693 994 2. 2 788 20 .7 0 .5 9 950 0 788 364 0 73 1.7 6.97 1 626 39 ND ND 21 .5 ND 28 .9 313 18.6 ND <3.0 JMU #1333 58 140 28 90 779 300 3 .5 828 <0.03 0.6 1 055 00 9 02 161 0 22 0 3.7 7 .56 168 822 ND ND 22 .1 ND 5. 5 1 95 ND ND ND JMU #24 33 54 950 28 54 736 964 1. 95 761 1.14 . 05 94000 793 26 5 0 29 3 2. 4 7 .21 154 826 ND ND 19.3 ND 7.7 326 22 .5 6.3 ND Mule Shoe Ranch Water 18 62 42 19 14 0.03 1.7 <0.03 0.07 1 450 5. 3 1669 16 484 3.6 8.41 55 59 ND ND ND ND ND ND ND ND <3.0 Canyon Reef Water 52 6 00 4617 980 53 8 0. 75 301 11.6 0.7 9 450 0 4. 52 689 0 134 2. 8 7.09 154 370 ND ND 15. 1 ND 8.4 36.1 ND <3.0 ND *