Relative Permeability to Liquid in Liquid-Gas Systems

Abstract

Abstract As a preliminary, consideration is given to the conventional definition ofrelative permeability and to the conditions governing the simultaneous flow ofoil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drivereservoir, the oil and gas can reasonably be supposed to be in capillaryequilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function ofsaturation. The relative permeability to liquid in that case is dependent uponthe distribution of fluids which itself is shown to be related to the capillarypressure, and, in turn, to the saturation. As a consequence, relativepermeability to liquid can be expressed in terms of the volume and surface areaof a network of liquid channels bounded by the rock and the gas phase. Whilethe volume of this network can be evaluated accurately, the surface areacannot. However, for any such volume, maximum and minimum values of thecorresponding surface area can be calculated from capillary pressure data. Itis then possible to establish for any saturation the limits within which thevalue of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of anexperimental method for measuring relative permeability to liquid whichutilizes a stationary gas phase is demonstrated. In this method capillarybarriers are cemented to the ends of the core sample to permit the maintenanceof capillary equilibrium between the two phases. At the same time, thisprocedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results ofother laboratory methods. The results obtained by theoretical calculations, and experimentally, arediscussed. In view of the overall precision that can presently be obtained inreservoir calculations, the agreement between the calculated and measuredrelative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure ofcalculating limiting relative permeability to liquid curves from capillarypressure data is indicated for general engineering purposes. It is shown thatthe above procedure can easily be extended to the cases where connate water ispresent. Its use for reservoir studies is particularly recommended inconjunction with the method for measuring relative permeability to gas whichsimultaneously yields the capillary pressure data necessary for thecalculations. T.P. 3021