Data Reduction In Centrifuge Capillary Pressure Experiments

Abstract

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 was first presented by Hassler and Brunner in 1945, and was accepted by the industry in general. With the use of ultra centrifugation in recent years, the possibility of water de-saturation at the exit end became a concern. While there was experimental evidence that de-saturatation can occur, some theoretical calculations indicated that this could only happen at much higher speed. The motivation to do the present study was to address this concern. While going over the original formulation it was noted that the radial dependence of capillary pressure was given by the authors without any discussion. According to their formulation, capillary pressure, which was the difference in pressure of two fluids, was taken to be defined even in a single fluid region. There was no reason given for taking this physically unrealistic definition. The pressure drop across the interface at the exit end was also taken to be zero, this was contrary to our expectation of interfacial behaviour in a capillary system. A re-formulation of the problem indicated that the error due to a wrong definition of capillary pressure was usually small, but that due to neglecting pressure drop at the exit end, must be evaluated by a separate experiment. This re-formulation also allowed us to derive a simple formula to estimate the centrifugal speed at which de-saturation of water at the exit end might occur. Introduction The measurement of capillary pressure saturation relation of a core by the centrifuge was proposed by Hassler and Brunner(1). 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 have been a large number of attempts to improve on these approximate solutions. Only four of these works(1–4) will be discussed in this study. Interested readers are referred to Ruth and Chen's(5) review article. The underlying theory as derived by Hassler and Brunner was accepted by all these authors. With the use of higher powered centrifuges some authors(6–10) started to be concerned with the possibility of de-saturation of water at the exit end. If this happened then the assumptions used by Hassler and Brunner might not be valid. In particular according to the original formulation the capillary pressure should be zero at the exit end, and it was interpreted(6–10) as equivalent to water saturation being 100% there. When Wunderlich(6) found that it could be less than 100 at high centrifuge speeds, he considered it as an indication that the boundary condition was being violated there.