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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-
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