Adjoint based state estimation of compressible flow in porous media

Abstract

Abstract In this paper, we study the state estimation of compressible single phase flow in compressible porous media. The initial pressure distribution is estimated according to discrete adjoint approach based on the collected well pressure data. The first-order Tykhonov regularization method is used to obtain reasonable estimation. By analyzing the optimality condition of estimation problem, the discrete adjoint state equation and discrete adjoint gradient are derived based on the numerical scheme of the continuous equations. A quasi-Newton numerical optimization method related to adjoint gradient is proposed to solve the estimation problem. The estimation results with different regularization coefficients are compared and analyzed by numerical experiments. The deviation between the estimated pressure obtained without regularization and the real pressure is large. Estimation result with smaller deviation and higher smoothness can be obtained through appropriate regularization coefficient. When the observation error is large, the observed values generated by the estimated pressure fit well with the real pressure.