Estimation of Capilary Pressure Functions From Centrifuge Data

摘要

The capillary pressure is a fundamental property arising in the theory of multiphase flow in porous media. It is generally assumed that it can be expressed as a function of the saturation of the fluids only. One of the most commonly used methods to determine the capillary pressure experimentally is the centrifuge method. In the centrifuge, the capillary pressure will be responsible for the centripetal forces which will be directly related to the angular velocity. The measured quantities will be the average fluid saturation and the angular velocity. Solving for the capillary pressure, the resulting equation leads to a Volterra integral equation of the first kind. In this work this integral equation is solved by representing the inverse capilary pressure function with B-splines. The coefficients are determined through a linear parameter estimation problem in which constraints, as well as regularization, are incorporated. Two test cases, one synthetic and one experimental, are shown.