Reservoir Formation Damage Episode 2 Part 5 potx

Ion Exchange and Adsorption Reactions Ion exchange and adsorption are surface chemical or surface plexation processes leading to the exchange of chemical species betweenthe aqueous solut

where 7Va is the total number of aqueous species involved; Nf and N*

denote the total number of aqueous and mineral reactions, respectively;

W/ and W rs 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 bymeans 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 plexation processes leading to the exchange of chemical species betweenthe aqueous solution and mineral surfaces present in geological porousformations (Jennings and Kirkner, 1984; Lichtner, 1985; Kharaka et al.,1988) Kharaka et al (1988) explain the difference between ion exchangeand adsorption as following: "The ion exchange model treats the exchange

com-of cations or anions on a constant charge surface" and "the adsorptionmodel simulates the exchange process on a surface where the surfacecharge is developed due to the ionization of surface sites at the solution-surface interface." Therefore, adsorption is a more general concept andion exchange is a special case of adsorption (Lichtner, 1985; Sahai andSverjensky, 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, asdescribed in Figure 13-2 (Sahai and Sverjensky, 1998) according toWestall (1986) As indicated in Figure 13-2, this model considers themineral surface, referred to as the O-plane, for adsorption of hydroxideions 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 andSverjensky, 1998)

Clays present in geological porous formations have many active ionexchange sites, a, occupied by various cations and cation exchange takesplace 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 ity (CEC) of rocks can be expressed as the total number of moles of

capac-exchange sites a per unit mass of rock, Qf x, or per unit volume of rock,

wa, which are related by (Lichtner, 1985):

% (13-15)

Lichtner (1985) points out that "precipitation/dissolution reactions canalter the exchange capacity of the porous medium by creating or destroy-

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 forModeling 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 inmost reported studies In Eq 13-15, <j) and p^ denote the porosity andthe 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 Sf , and the concentration of the i th species attached to the exchangesites a by C™, expressed in moles per unit bulk volume Lichtner (1985)then describes the chemical reactions at mineral surfaces by

(13-16)

and the conservation of the ion exchange sites by

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 adsorptionreactions in soils typically require a time of seconds to days to attainequilibrium Therefore, Jennings and Kirkner (1984) describe thesereactions by rate equations for full kinetic modeling Applying theirapproach 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

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 therate of the reactions of the /"'cation of the aqueous solution other thanadsorption, the transport equation for the /""cation present in aqueoussolution is given by (Lichtner, 1985):

o=l j=l

M

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 theaqueous solution, expressed in moles per unit volume of the aqueous phase

The balance of the /""cation adsorbed on the a' h site of the mineralsurface is given by (Litchner, 1985):

where Cf is the concentration of the i th species attached to the exchangesites a expressed in moles per unit bulk volume Because

(13-24)

Geochemical Modeling

As stated by Plummer (1992)*: "Geochemical modeling attempts tointerpret and (or) predict chemical reactions of minerals, gases, andorganic matter with aqueous solutions in real or hypothetical water-rocksystems." Figure 13-3 by Bassett and Melchior (1990) outlines the basicconstituents and options of most geochemical models

Plummer (1992)* classified the various geochemical modeling effortsinto four groups:

1 Aqueous speciation models for geochemical applications,

2 Inverse geochemical modeling techniques for interpreting observedhydrochemical data,

3 Forward geochemical modeling techniques for simulating the cal evolution of water-rock systems, and

chemi-4 Reaction-transport modeling for the coupling of geochemical tion modeling with equations describing the physics of fluid flowand solute transport processes

reac-Brief descriptions of these models are presented in the following, ing to Plummer (1992)

accord-* 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 orderfrom: A A Balkema, Old Post Road, Brookfield, Vermont 05036 (telephone: 802-276-3162; telefax: 802-276-3837; e-mail: info@ashgate.com)

SECONDARY COMPUTATIONS

• Saturation Index

• Computed Cation/Anlon Balance

• Geotherraometers

• Percentage Species Distribution

• Computed Gas Partial Pressures

OPTIONS AND EVOLUTIONARY CHANGES

- 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 ofAqueous Systems—An Overview," Chapter 1, pp 1-14, in Chemical Modeling

of Aqueous Systems II, Melchior, D C & Basset, R L (eds.), ACS sium Series 416, ACS, Washington, 1990, Figure 2, page 6; ©1990 AmericanChemical Society)

Sympo-Aqueous Speciation Models

Aqueous Speciation models describe the thermodynamic properties ofaqueous 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 ion formation, and

complex-3 Equations that define individual ion-activity coefficients

Two types of aqueous specification models are popular: (a) association models and (b) specific interaction models The ion associationand the specific interaction models facilitate, respectively, the extensionsand a complex expansion of the Debye-Hiickel theory to estimate theindividual ion activity coefficients of aqueous species (Plummer, 1992).The specific interaction models are preferred for highly concentratedsolutions of mixed-electrolytes (Plummer, 1992) As pointed out byPlummer (1992), aqueous geochemical models can be used for forwardand inverse geochemical modeling

ion-Geochemical Modeling—Inverse and Forward

Plummer (1992)* summarizes that "Two approaches to geochemicalmodeling have evolved—"inverse modeling," which uses water and rockcompositions to identify and quantify geochemical reactions, and "forwardmodeling," which uses hypothesized geochemical reactions to predictwater and rock compositions." However, the application of these models

is rather difficult because the basic data necessary for these models areoften incomplete and/or uncertain (Plummer, 1992)

Plummer (1992)* describes the most essential information necessaryfor 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 inground-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 orderfrom: A A Balkema, Old Post Road, Brookfield, Vermont 05036 (telephone: 802-276-3162; telefax: 802-276-3837; e-mail: info@ashgate.com)

6 The temporal variation of these properties,

7 The fundamental knowledge on the kinetics and mechanisms ofimportant 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 combinesinformation on mineral saturation indices with mass-balance modeling toidentify and quantify mineral reactions in the system." The mass-balancemodeling 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 bestsuited for steady-state regional aquifers, where effects of hydrodynamicdispersion 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 dissolutionand 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 orderfrom: A A Balkema, Old Post Road, Brookfield, Vermont 05036 (telephone: 802-276-3162; telefax: 802-276-3837; e-mail: info@ashgate.com)

7 Calculation of mineral solubilities with and without accompanyingirreversible reaction,

8 Calculation of boiling, cooling, wall-rock alteration, ground-watermixing 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 beused "in developing reaction models that can account for the observedcompositional-mineralogical relations in the deposit, if there are noaqueous or solid data for the system."

Reaction-Transport Geochemical Modeling

The reaction-transport models describe the geochemical reactions underthe influence of fluid flow and convective and dispersive transport ofvarious species in geological porous media These models couple thegeochemical reaction and the fluids and species transport submodels toaccomplish 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 reservoirexploitation and scale formation studies

Graphical Description of the Rock-Fluid Chemical Equilibria

Properly designed charts provide convenient means of describing theequilibrium 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 dynamic equilibrium In this section, the theoretical bases, characteristics, andutilization of these charts are described according to Schneider (1997)

thermo-Saturation Index or Mineral Stability Charts

Mineral stability charts are convenient means of representing thevarious 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 orderfrom: A A Balkema, Old Post Road, Brookfield, Vermont 05036 (telephone: 802-276-3162; telefax: 802-276-3837; e-mail: info@ashgate.com)

Mineral stability charts can be more meaningfully developed by sidering the incongruent equilibrium reactions of various solid phasesincluding the igneous and metamorphic reactions (Schneider, 1997).Incongruent reactions represent the direct relationships of the varioussolid minerals involved in aqueous solution systems The expressions ofthe incongruent reactions are derived from a combination of the relevantmineral dissolution/precipitation reactions in a manner to conserve certainkey elements of the solid minerals so that the aqueous ionic species ofthese elements do not explicitly appear in the final equation For example,the incongruent reactions of the alumino silicate minerals, including clayminerals, feldspars, and chlorites, are usually expressed to conserve thealuminum element (Fletcher, 1993; Schneider, 1997) Aluminum is anatural choice as the conserved element because this element is mostlyimmobile and the activities of the aqueous aluminum species are relativelylow (Hayes and Boles, 1992; Schneider, 1997) Consequently, the incon-gruent mineral reaction equations do not involve the potential dissolvedaluminum species such as Af3, Al(OH) 2+, Al(OH)4~, Al(OH) +2 , and Al(OH) 3°

con-(Schneider, 1997) Thus, the aluminum element conserving incongruentreaction to form the chlorite mineral from the kaolinite mineral reads as(Schneider, 1997, p 119):

L4Al2Si2O5(OH)4 + 2A5Mg+2 + 2.25Fe+2

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

Figure 13-4 Effect of pH on distribution of carbonate species (after Schneider,

©1997; reprinted by permission of G W Schneider)

affect of pH on the composition of the typical carbonate species, namely H2CO3, HCO3 and CO '2

Similarly Figure 13-5 indicates the affect of pH on the composition of typical aqueous aluminum species, namely At* 3, Al(OH)2+, Al(OH)4~, and +2

Al(OH)+, generated by Schneider (1997) using the SOLMINEQ.88 software.

Activity-Activity Charts

The Activity-Activity charts depict the regions of precipitation ofvarious solid mineral phases The equations of the lines separating theseregions are obtained by rearranging the logarithmic expression of theequilibrium constant in a linear form to relate the saturation products ofthe various mineral phases For example, the equilibrium constant for

Eq 13-25 is given by (Schneider, 1997):

0.1

in which the activities of the water and the solid kaolinite and chloritephases were taken unity A logarithm of Eq 13-31 yields the linearequation for the kaolinite-chlorite phase boundary as:

> AI(OH)4 - • M(OH)2 + •AJ(OH) (+2) • Al (+3)

Figure 13-5 Effect of pH on distribution of aluminum species (after Schneider,

©1997; reprinted by permission of G W Schneider)

in highly concentrated oilfield brines because of the complexing of cationswith inorganic and organic anions, and can be better accomplished bymeans 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 sented by

repre-aA + bB + ne~ + mH+ <-> cC + dZ) + (13-33)

The electron activity (pe) and potentiometric acidity (pH) can be

con-veniently expressed by the following equations, respectively:

in which T denotes the absolute temperature in K, /? = 8.31441

J - K~ ] - 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