Page 198 - Percolation Models for Transport in Porous Media With
P. 198

196           CHAPTER 11  GAS COLMATATION IN ELECTRIC ACTION

















                                    'f·"'·
                                    0'----....U..---L--l



                                     0
         Figure 72:   Plots for  the  time  dependencies  of the  permeability  1,  the electric
         resistance 2 of the medium  (a}  and  the electric field  intensity {b)  in experiments
         on electric treatment of media saturated with leaching solutions


         bubble in the temperature field,  r 9  "' 10 4  seconds.  This fact confirms the validity
         of the speculation on the movement of bubbles being quasi-uniform.  Experimental
         data (fig.72}  yield  r 9  ~ 1.5 hours {5 · 10 3  seconds).  The overestimated calculated
         value of r 9  was obtained because an overestimated value of JL  and an underesti-
         mated value  of x'  were  used  in  substituting in  the formula  {11.17}.  (When  the
         temperature grows form  20°  C to 100° C, the viscosity drops by a factor of three,
         and x'  increases by  more than 20%.)  In  the estimates,  the constant values of JL
         and x' were used, which correspond to T  = 20°  C. Taking account of the changes
         in these quantities as the temperature of the liquid grows, yields a result which is
         much closer to the experimental one, r 9  ~ 1.1  hours (4 · 10 3  seconds).
            Having  got  inside  the  capillary,  the  bubbles  begin  to grow.  The first  stage
         of the growth takes place for  T  < Tb.  For the specified  parameters of the field,
         medium, and liquid, the temperature in  the liquid inside the capillary reaches n
         after t  ~ 1.6 hours.  This result agrees adequately with  the experiment, where a
         sharp drop of the electric conductivity occurs at the time t = 1.5 hours.  An earlier
         termination  of the flow  (see  fig.  72)  is  due  to the fact  that  the grown  bubbles
         impede the fluid flow to a greater extent than they impede the current flow in the
         medium.  Up to the instant of merging, the growth of the bubbles is described by
         equations (11.36)- (11.38).
            The parameters defined in deducing these equations have the following values,
         A = 2.5 · 10- ,  Ao  = 4 · 10- 5 ,  X  = 2.54 · 10- 5  s- 1 •  The  quantities  H  and
                      4
         Z  depend  on  the  temperature  inside  the  bubble  and  vary  within  the  following
         ranges, H = (2.14 + 1.44} · 10 3 ,  Z = 1.45 + 1.18.
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