Page 363 - Reservoir Formation Damage
P. 363

Inorganic Scaling and Geochemical  Formation Damage  343

                      TS
                 log        = log                                       (13-32)
                    10  SPkaollm,             \oK eq
              A  plot  of  K t  versus  Ks    according  to  Eq.  13-32  yields  the
                          SPcMoritt     Pkaotii,
              kaolinite-chlorite  stability  chart  (Schneider,  1997) using  the  SOLMINEQ.88
              program  (Kharaka  et  al.,  1988).  Schneider  (1997)  points  out  that  the
              determination  of the  aqueous  species  activities  is particularly  complicated
              in  highly concentrated oilfield  brines  because  of the  complexing  of  cations
              with  inorganic  and  organic  anions,  and  can  be  better  accomplished  by
              means  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  repre-
              sented  by

                 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:
                   = -log ]0[                                           (13-34)

              and

                                                                        (13-35)

              The  electrode  potential  (Eh) and  electron  activity  (pe)  are  related  by
              (Schneider, 1997)

                 „,  2.30259RT
                hh =           pe                                       (13-36)


              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 10 4  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
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