Simultaneous Estimation of Relative Permeabilities and Capillary Pressure

Abstract

Summary An automatic numerical method is proposed for simultaneous determination of relative permeabilities and capillary pressure from the results of a single two-phase flow experiment in a range of velocities representative of field flow conditions. The experiment is a standard imbibition or drainage displacement with an imposed difference of pressure or flow rate. The experimental data used are the outlet production, the pressure drop between the two faces, and local saturation profiles at different times along the core. Relative permeabilities and capillary pressure are estimated with a least-squares technique. Use of a high-order numerical scheme significantly reduces the numerical diffusion. The optimal control theory is used to solve the minimization problem. The corresponding FORTRAN code is generated by a symbolic program. The validity of the method first is demonstrated with simulated data, then is tested in two laboratory experiments: one imbibition and one drainage. Good agreement is obtained for both situations.