Calculating capillary pressure curve from single-speedcentrifuge experiments

Abstract

We present a method for the calculation of the capillary pressurecurve in porous media using centrifuge single-speed experimentaldata. The mathematical model is based on the hydrostaticequilibrium equation for capillary pressure and the inverseproblem for finding the saturation distribution along the samplefrom the displaced fluid volume when all the flow has ceased.The capillary effects are interpreted as constraint forces whichkeep the oil trapped in the pores of the sample. We usethe Lagrangian formulation to find the equilibrium configurationof the oil in the sample. The great advantage of thisformulation is that the explicit inclusion of forces is notnecessary. Mathematical properties of the capillary pressure curveand centrifuge data are used as constraints of the kineticenergy minimization procedure. The discretized problem is solvedusing a nonlinear programming procedure using only thesingle-speed experimental data. Numerical results are comparedwith calculations in the frequently used multi-speed centrifugetests.