Relative Permeabilities and Capillary Pressure Estimation through Least Square Fitting

Relative permeabilities and capillary pressure are determined from two-phase immiscible flow laboratory experiments using numerical matching. An automatic method based on optimal control theory is proposed to identify simultaneously relative permeabilities and capillary pressure. These three parameters are determined by using a least square technique after discretizing the one-dimensional saturation equation by a higher order Godunov scheme associated with Van Leer’s slope limiter. The Fortran codes for the numerical simulator and for the calculation of the gradient of the least square function are generated automatically by a Macsyma program that allows a fast and reliable programmation. Experimental data used for matching are production and pressure drop, and/or saturation profiles. New laboratory techniques (gammametry or tomodensidometry) provide saturation measurements in the core at different times and these extra data improve drastically the matching. The validity of the method is demonstrated on simulated data.