Page 123 - Formation Damage during Improved Oil Recovery Fundamentals and Applications
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Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 105
Figure 3.13 Solution zones for the three cases: (A) X i , 2X m , (B) X i . 2X m , and
(C) X i 5 2X m (X: dimensionless spatial coordinate, T: dimensionless time, X i : spatial
coordinate of damaged radius (outside of which, no particles are detached), X m :
spatial coordinate of the maximum detachment radius (inside of which, all attached
particles are detached)).
where X 0 denotes the starting point on the X-axis. The solution space in
Fig. 3.13 is split into multiple zones. The solution for the suspended and
strained concentrations is presented below for each zone.
Along the characteristic lines, Eq. (3.68) reduces to the ODE:
dC ΛC
52 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : (3.76)
dT 2 X 0 2 T
