Relative Permeability Studies

Relative wetting phase permeabilities calculated from capillarypressure-saturation data are compared with measured relative permeability data.The equation relating relative permeability to capillary pressure-saturationdata is derived by assuming that a porous medium is analogous to a bundle ofcapillary tubes. The equation includes a term to correct for the differencebetween fluid path length and length of core. Relative oil permeability data inthe water-oil-gas system are presented, and it is shown that if the water isconsidered part of the rock matrix, the relative oil permeability curve istypical of a wetting phase relative permeability curve. Apparatus for measuringtwo and three-phase relative permeabilities are described. Introduction The difficulty in measuring relative permeability of cores has made itdesirable to have a correlation between relative permeability and some moreeasily measured property of porous media. Such an easily measured property isthe capillary pressure-saturation relation. In the past there has been a tendency to separate the capillary pressureconcept from the very complex pore geometry and to consider that the capillarypressure-saturation curve gives only some characteristic distribution ofinterfacial curvature between two fluids. Recently, however, it has beenrealized that if capillary pressure data are to yield information concerningpore size distribution and fluid flow in porous media, the pore must be assumedto have a simple shape such as a cylinder or a sphere. Childs and George showed that relative water permeability could becalculated from the capillary pressure-water saturation curve by assuming thatthe pores are cylinders in which the fluid flowing obeys Poiseuille's Law, andthat the capillary pressure curve indicated the size and number of pores.Purcell derived an equation relating the permeability of a porous medium to thecapillary pressure curve by assuming the porous medium to be analogous to abundle of capillary tubes. Gates and Lietz calculated relative permeability byan equation derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability asa function of water saturation by assuming that the core sample can berepresented by a bundle of capillary tubes in which the fluid path length isnot the same as the bulk length, and in which the fluid path length varies withsaturation. T.P. 3078