Approach to Solving the Inverse Problem of Filtration Based on Descriptive Regularization

This paper presents the results of a study of inverse problem for the nonlinear parabolic equation for the fluid filtration in the fractured media. An approach to solve the inverse problem by using the descriptive regularization method is proposed. A mathematical model for the 3-D flow of a fluid through a pressure sensitive naturally fractured formation, with pseudosteady state matrix-fracture flow is developed. This model includes the effects of wellbore storage and fluid flow in the wellbore. A computational algorithm based on the proposed approach to estimate the dependence of the fractures permeability on pressure from the results of hydrodynamic studies of horizontal well is developed.