Estimation of the Porosity and Permeability Fields of a Three-Phase Layered Reservoir Using the Spline Surfaces

The problem of determining the porosity and permeability fields of the development history under conditions of three-phase fluid flow in a layered reservoir opened by production and injection wells is considered. This problem is an inverse coefficient problem for a system of partial differential equations describing the fluid flow in a porous medium. The porosity and permeability fields of each layer are approximated by a spline surface. Measurements of the liquid flow rate in the production wells and the bottom hole pressure in the injection wells are used as initial information to determine permeability. The solution of model problems with various variants of errors in the initial data is presented.