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摘要
In Alvarez et al (2006 Inverse Problems 22 69-88), we studied the direct and inverse problem of deep bed filtration for a model proposed by Herzig et al (1970 Indus. Eng. Chem. 65 8-35), which describes particle retention in a porous medium under injection of water with solid inclusions. However, many questions were left unanswered. Here most of these issues are solved for an alternate model of deep bed filtration also from [10]. Both models depend on the filtration function, which must be recovered from experimental data histories by solving an inverse problem. The main issues solved here are: (i) we establish the stability of the inverse problem under adequate conditions, leading to a robust numerical procedure; (ii) we present a numerical method for the direct problem that allows us to solve the inverse problem by parameter estimation in several spatial dimensions. We impose conditions on the experimental data preprocessing that allow us to recover analytic filtration functions with adequate physical behavior.
- 出版日期2013-2
