Numerical Solution of the Inverse Problem of Non-stationary Filtration of Bingham Non-Newtonian Fluid to a Horizontal Well

Abstract

Unsteady filtration of a Bingham non-Newtonian fluid to a horizontal well is considered. The experimental results show that when such liquids flow in porous media at low pressure gradients, deviations from the linear Darcy law appear. A feature of the movement of Bingham non-Newtonian fluids in a porous medium is the fact that filtration becomes noticeable only after the pressure gradient reaches a certain critical value—the limiting pressure gradient. The formulation of the inverse coefficient problem for determining filtration parameters during the flow of Bingham non-Newtonian fluid to a horizontal well is given. Pressure change curves measured at the well are used as initial information. To numerically solve the inverse coefficient problem, a computational algorithm based on regularization methods is proposed.