(207e) Modelling Capillary Pressure Curves by Means of a Distribution Function

Capillary pressure curves have been determined for long time in both, filtration technology and oil reservoir evaluation, with different aims but with quite similar modelling tools. It has been always accepted that the existence of a capillary pressure curve is the result of the pore size distribution prevailing in the porous medium, otherwise, all pores in the bulk (cake or reservoir) would drain or fill at the same pressure. However the modelling of the capillary pressure curve has been done mainly following the work of Corey and Brooks, based in the thoroughly demonstrated fact that a double logarithmic plot of capillary pressure against pore saturation leads to a straight line, except for the neighbourhood of saturation equal to one, where a concavities is present even if most times it has been not detected due to the measurement resolution. It leaded to the use of a very simple model based on the power function which has been extensively used by oil related researchers to calculate relative permeabilities using the Burdine approach. This paper incorporates the quite simple concept that if the capillary pressure curve represents a pore size distribution, a distribution function should be used to fit it. Hence, different distribution functions were analysed: the normal and log-normal functions fail to fit the well-known behaviour of straight line in double log plot; the power function fit this criterion but only the Rosin-Rammler-Bennet-Sperling function (RRSB)was able not only to reflect the linear behaviour in such a plot but also the concavity near saturation equal to one. Although the mathematical handling of the RRSB function is more difficult, the available computer programs allow to handle it without losses.