Numerical solution of an inverse filtration problem

Abstract

A numerical method is suggested for solving the multidimensional inverse problem of finding the flow rates of wells from given bottomhole pressures in the multidimensional flow model of a weakly compressible liquid in a poroelastic medium. Spatial approximation is based on the finite element method, which allows one to employ unstructured grids with refinements near the location of wells. Time discretization is performed with the use of implicit difference approximation. The numerical results for two- and three-dimensional test problems are presented.