Capillary Pressure Term Research Articles

A Numerical Solution of the Linear Displacement Equation with Capillary Pressure

Introduction The displacement equations of Buckley and Leverett have been successfully applied to the prediction of oil recovery in frontal drives for a number of years. Commonly, the capillary pressure term is omitted from Leverett's fractional flaw formula. The resulting saturation-vs-distance curves became multi-valued, however. Buckley and Leverett, recognizing that the neglect of capillarity was most likely the cause, proposed that this part of the solution be ignored. An ingenious method of propagating a discontinuity in place of the multi-valued portion of the curve was devised by Cardwell using "non-capillary displacement theory". However, it would seem that a complete description of the displacement process would require the inclusion of capillary forces. Three publications on displacement theory have appeared in which capillary pressure was included. Terwilliger, et al, calculated saturation profiles which matched those which they observed when gas displaced water vertically downward. Based on their study, Jones-Parra and Calhoun proposed a method of computing saturation distributions sufficiently removed in time from the initial conditions so that all saturations in the flood front region were assumed to move with the same velocity. This latter assumption corresponds to the tangent construction on the flowing fraction-vs-saturation curve proposed by Welge.

Displacement Experiments in a Consolidated Porous System

Published in Petroleum Transactions, AIME, Volume 201, 1954, pages 57–66. Abstract A series of four displacement experiments has been run in a large alundum core. Flow potential distribution in each liquid phase was measured continuously through oil-wet and water-wet capillary barriers, using a null-point pressure balance, and saturated distribution was determined from electrical resistivity measurements. A method has been devised for calculating the effective (and relative) permeability to each phase at any time and at any point in the flow system for the transient displacement process. Relative permeability points have been calculated and average curves drawn for oil displacing water and water displacing oil. The values of dynamic capillary pressure have also been determined. Data have been substituted into the generalized Buckley-Leverett fractional flow equation and a comparison between actual and theoretical breakthrough recoveries is shown. Introduction Displacement experiments have been performed in the laboratory for many years in an effort to determine the effect of a number of parameters on multiphase flow in porous materials. In the literature of petroleum technology, Wyckoff and Botset were among the first to develop the relative permeability concept and to show experimentally that oil, gas, and water can flow simultaneously through a porous medium in a precise way governed by certain fluid properties, by the relative saturation of each fluid, and by characteristics of the medium itself. Somewhat later, Leverett and Hassler, Brunner, and Deahl developed some theoretical concepts of capillary behavior in porous materials. The work of Buckley and Leverett presented a theoretical analysis of immiscible liquid displacement based on the equation of continuity and the Darcy equation for viscous flow of each fluid. Subsequent investigators attempting to verify the Buckley-Leverett equation have, in general, deliberately neglected the capillary pressure term or have performed experiments in such a manner that it could be neglected.