Preprint A394/2005
A fast inverse solver for the filtration function for flow in porous media

J.R. Rodriguez | Alvarez, A.C. | Bedrikovetsky, P.G. | Hime, G. | Marchesin, D.

**Keywords: **
Inverse problem | Formation damage | Deep bed filtration | Iterative functional equation | System of convection-reaction equations

Models for deep bed filtration in the injection of sea water with
solid inclusions depend on an empirical filtration function that
represents the rate of particle retention. This function must be
calculated indirectly from experimental measurements of other
quantities. The practical petroleum engineering purpose is to
predict injectivity loss in the porous rock around wells. In this
work, we determine the filtration function from the
effluent particle concentration history measured in laboratory
tests knowing the inlet particle concentration.
The recovery procedure is based in solving a functional equation
derived from the model equations. Well-posedness of the numerical procedure
is discussed. Numerical results are shown.