Multiscale Representation for Simultaneous Estimation of Relative Permeabilities and Capillary Pressure

Abstract

ABSTRACT This paper proposes an improvement in a numerical method for the simultaneous determination of relative permeabilities and capillary pressure. It uses the results of only one laboratory flooding test performed under representative reservoir conditions. Relative permeabilities and capillary pressure axe estimated by using a least-squares technique after the one-dimensional saturation equation has been solved. The experimental data required are the outlet production, the pressure drop between the two faces and (or) local saturation profiles measured at different times in the sample. The improvement described in this paper enables relative permeabilities and capillary pressure to be determined simultaneously as piecewise linear functions, thus eliminating the need for any closed-form formula representation. This improvement consists of the use of a multiscale approach to represent the parameters, coupled with a scale-by-scale optimization. The validity of the method is first demonstrated with simulated data. With the multiscale approach, the minimization procedure converges in cases when standard parametrization fails to do so. Secondly, the method is applied to immiscible two-phase flow experiment. Very good matching is obtained.