Development of a Modified Capillary Pressure J-Function

Abstract

Abstract Capillary pressure curves are represented by the equation Pc=a/ (Sw- Swi)b. It is shown that for the Leverett J-function to produce a single correlation, the tortuosity. the irreducible water saturation and the saturation exponent b must be the same for the different formations. A modified capillary pressure function J* is introduced that incorporates the tortuosity and irreducible water saturation in its definition. The modified function is correlated with the normalized saturation SD so that all curves will have their vertical asymptotes at a single point SD=0 The modified function represents a significant improvement over the original one since it is now sufficient to have the value of the saturation exponent b be the same for two samples to get the same correlation. This was verified by analyzing data from the literature and comparing the two correlations. A modified linear regression by means of weighted least squares method is used to fit the experimental capillary pressure data. Data sets from different sources were analyzed. It was found that a good single correlation can be obtained for samples from the same formation but the correlations were different for different formations. Introduction The capillary phenomena occurs in porous media when two or more immiscible fluids are present in the pore space. Due to the interfacial energy of the interface between the two phases. a difference in the pressure across the interface results and causes a curvature of the interface. The capillary forces causes retention of fluids in the pore space against the gravity forces. Immiscible fluids segregate due to gravity if placed in large containers such as tanks and pipes of large diameters. In porous rocks, however, the dense fluid (water) can be found at higher elevations above the oil-water contact. P. 547