Computed Relative Permeability Drainage and Imbibition

Abstract A brief review of the historical developments of both drainage and imbibition relative permeability reveals shortcomings in previously permeability reveals shortcomings in previously applied mathematical models. Recent investigations indicate justifiable bases for relating the Leverett "J" function directly to the relative permeabilities of both phases. Development of this procedure yields a phases. Development of this procedure yields a relationship describing the "J" function in terms of rock matrix properties, i.e.: k, krw, phi, Sw, the absolute permeability, the wetting phase relative permeability, the porosity, and wetting phase saturation, respectively. (Equations) are the expressions for the drainage cycle, while (Equations) are the expressions for the imbibition cycle. The saturation exponent relates the relative permeabilities to pertinent matrix parameters. The result is considered an improvement parameters. The result is considered an improvement over previous models that assumed krw and krnw to be exclusive functions of the mobile wetting phase saturation. A method is also presented for phase saturation. A method is also presented for computing a pseudo irreducible water saturation, Swp, below which krw is assumed negligible. The application of this value to relative permeability calculations has been very successful. Recent imbibition relative permeability studies have yielded a model that predicts imbibition parameters from drainage values. The model is an extension of the Naar-Henderson treatment.