A MATHEMATICAL FUNCTION FOR DESCRIBING CAPILLARY PRESSURE-DESATURATION DATA

Abstract

The equations of Brooks and Corey for relating effective saturation S ^e to capillary pressure p ^e describe experimental data quite well for small values of S ^e but overestimate p ^e as S ^e approaches unity. Using assumed functions for the distribution of pore volume with respect to pore radius, Brutsaert was able to describe experimental data satisfactorily provided that constants such as mean pore radius and the standard deviation of pore radius were determined from distribution functions derived from experimental data rather than from the assumed functions. White developed a mathematical model which described experimental data of S(p ^e ) satisfactorily but the technique required the determination of thirteen constants describing the relationship. In this paper, a pore-volume probability density function is introduced which permits the development of a function for describing effective saturation in terms of dimensionless capillary pressure p ^e , that is, capillary pressure scaled in terms of bubbling pressure. The capillary pressure-saturation data on the drainage cycle are described better by the new function than by the equations of Brooks and Corey. The correspondence between experiment and theory is better at small values of Se than for values approaching unity. The relationship between S ^e and p. is characterized by three constants, each of which is, in turn, a function of the pore-size distribution index. Two of these constants are related to mean pore radius and to the standard deviation of the pore-volume distribution.