Centrifuge Capillary Pressure Curves
Authors: Ruth Douglas , Wong Sidney 
Published: March 2010

Abstract
This paper presents a comparison of six methods jar calculating capillary pressure curves from centrifuge data: Hassler and Brunner's iterative method, Hoffman's second method, Ruth and Wong's method (LIM), a new integral method (ElM), and the two parameter estimation techniques proposed by Bentsen and co-workers. Two comparison techniques are used; reinterpretation of synthetic data, using Bentsen's first model as the standard and interpretation of experimental data. The results for the first three methods are shown to be essentially the same, with a marginal advantage shown by the LIM. The EIM is shown to give the best results in some cases, but to completely fail in others. For experimental data, it is shown that Bentsen's second model is preferred over Bentsen's first model. Variations between the models suggest the simultaneous use of more than one method ill order to ensure that data interpretation is correct.

Introduction
This paper represents a continuation and extension of previous work (Ruth and Wong(1)). The previously reported study examined the accuracy of the common methods used to calculate capillary pressure curves from centrifuge data. The classic method, due to Hassler and Brunner(2), was shown to be inadequate in many instances, while the parameter estimation techniques proposed by Bentsen and co-workers(3,4) were shown to be reliable. A new technique, referred to as the linear interpolation method (LIM), based on approximating the capillary pressure by straight line segments and evaluating the correction integral proposed by Melrose(5) was also shown to give good results.
In Reference 1, the iterative and integral methods that exist in the literature were not considered. The primary examples of these methods are the iterative technique proposed by Hassler and Brunner(2) to improve their solutions, and the second method offered by Hoffman (presented in an author's response to comments made by Luffel(6)). The present paper treats these two methods, as well as a new method that is an extension of the LIM described in Reference 1.
One of the techniques used to compare the various data analysis methods is to specify type-curves based on the Bentsen equation:
Equation (Available In Full Paper)
where Pc is the capillary pressure, S is the water saturation, Srw is the irreducible water saturation, and Sro is the residual oil saturation. The b is a curve-shape factor, while for a primary drainage curve, the a represents the threshold capillary pressure. In the current work, this equation is made dimensionless by dividing through with the threshold capillary pressure, and writing it in the form
Equation (Available In Full Paper)
where the prime denotes a dimensionless capillary pressure, and Be is a "Bentsen type-number", given by b/a. This treatment of the equation provides a convenient method of distinguishing, and studying, different types of capillary pressure curves. Obviously, Be must relate to other properties of the rock, such as pore throat size distribution. Further study of this parameter may lead to new methods of classifying the behaviour of various types of porous material.