Reservoir Permeability Identification under Three-Phase Filtration Using a Priori Information on Wells

A method is proposed to solve the identification problem of the permeability field of a three-dimensional reservoir under conditions of three-phase fluid filtration. The peculiarity of the method lies in the fact that the wells retain the proportionality of the values of the permeability coefficients of the layers obtained a priori from the results of geophysical studies. The approximation of the permeability field was carried out in layers using surface splines. The problem of identifying the permeability field belongs to the class of inverse coefficient problems for a system of nonlinear partial differential equations describing the process of fluid flow in a porous medium. The solution of the problem was reduced to minimizing the residual function constructed on the total liquid production rate at the wells. Minimization of the residual function was carried out by the Levenberg–Marquardt method. The black oil model was used to describe the fluid filtration process. The filtration equations were solved numerically by the method of the simultaneous solution, and the control volume method was used to approximate the equations by spatial variables. The proposed approach was used to solve a model problem. The influence of various types of errors on the results of identification was investigated.