DETERMINATION OF RELATIVE PERMEABILITIES AND CAPILLARY PRESSURES BY AN AUTOMATIC ADJUSTMENT METHOD.

An automatic adjustment method based on optimal control theory is presented. The unsteady one dimensional biphasic flow differential equations have been rewritten so as to exhibit three linearly independent terms which are functions of relative permeabilities and capillary pressure. These three functions are determined by a least square technique following discretization of the equations by a mixed finite elements method. Running the automatic adjustment scheme on the results of the two experiments mentioned above yields directly the relative permeability curves and the capillary term function. The capillary curve is deduced from the capillary term function. Use of mixed finite elements significantly contributes to accuracy and stability in the solution of the equations. Furthermore, the method remains valid in the two limiting cases of hyperbolic (imbibition alone) and parabolic equations (Buckley-Leverett approximation).