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Models for deep bed filtration in the injection of seawater 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 on solving a functional equation derived from the model equations. Well-posedness of the numerical procedure is discussed. Numerical results are shown.

There are two goals of this study. The first is to provide an introduction to the wave curve method for finding the analytic solution of a porous medium injection problem. Similar to fractional and chromatographic flow theory, the wave curve method is based on the method of characteristics, but it is applicable to an expanded range of physical processes in porous medium flow. The second goal is to solve injection problems for immiscible threephase flow, as described by Corey's model, in which a mixture of gas and water is injected into a porous medium containing oil and irreducible water. In particular we determine, for any 123 100 A. V. Azevedo et al.choice of the phase viscosities, the proportion of the injected fluids that maximizes recovery around breakthrough time. Numerical simulations are performed to compare our solutions for Corey's model with those of other models. For the injection problems we consider, solutions for Corey's model are very similar to those for Stone's model, despite the presence of an elliptic region in the latter; and they are very different from those for the Juanes-Patzek model, which preserves strict hyperbolicity. A nice feature of our analytical method is that it facilitates explaining both differences and similarities among the solutions for the three models considered.