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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).
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