Abstract

The centrifuge method is commonly used to determine the capillary pressure of a core. The data obtained from such an experiment is the average saturation of the core at different centrifugal speeds. It is necessary to back out the capillary pressure saturation relation based on our understanding of the equilibrium distribution of two fluids in porous media. The governing set of equations and two approximate solution methods were presented by Hassler and Brunner in 1945, and accepted by the industry in general. In most of the papers given in the literature on this method the basic assumptions stated by Hassler and Brunner were accepted, and the improvements were limited to the solution procedure. Surprisingly, the pressure drop, ΔP2, across the interface at the exit end appeared to have escaped the attention of both Hassler and Brunner, and the other authors. They might have consider it to be zero, so that it can be dropped out of the governing set of equations. It was only recently that experimental evidence was presented to show that this may not be so.

The objective of this study is to include a non-zero ΔP2 into the formulation of the problem, and to examine its implication on some of the data reduction procedures given in the literature. The condition under which de-saturation of water at the exit end might occur has also been examined.

Introduction

The measurement of capillary pressure saturation relation of a core by the centrifuge was proposed by Hassler and Brunnerl. They formulated the governing set of equations for the equilibrium distribution of two fluids under constant centrifugal acceleration and presented two approximation methods to calculate capillary pressure saturation relation from measured data. Since then there were a large number of attempts to improve on, these approximate solutions. Only four of this works1–4 will be discussed in this study. Interested readers are referred to Ruth and Chen's5 review article on centrifuge capillary pressure experiment. The underlying theory as derived by Hassler and Brunner were accepted by all these authors.

In the original formulation1, the authors were not clear in treating the condition at the exit end. More specifically, the pressure drop, ΔP2, across the interface at the exit end was not mentioned. Even in the discussions on the problem with exit end boundary condition6–10, it was not quite clear if the authors were considering the capillary pressure inside the core at the exit end or the pressure drop across the interface there. We have shown in a previous paper11 that ΔP2 may not be zero, and that its magnitude would affect the calculation of displacement pressure from centrifuge capillary pressure data.

In the present study we will re-formulate the centrifuge capillary pressure experiment in light of a possibly non-zero ΔP2. This set of equations differs from Hassler and Brunner's1 in the radial dependence of capillary pressure. As it is a key equation in the system data reduction procedures based on the original formulation may be in error.

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