Calculating Capillary Pressure Curve from Single-Speed Centrifuge Experiments

We present a method for the calculation of capillary pressure curve in porous media using centrifuge single-speed experimental data. The mathematical model is based on the hydrostatic equilibrium equation for capillary pressure and the inverse problem for finding the saturation distribution along the sample from the displaced fluid volume when all the flow ceased.The capillary effects are interpreted as constraint forces which maintain the oil trapped into the pores of the sample. We use the Lagrangian formulation to find the equilibrium configuration of the oil in the sample. The great advantage of this formulation is that the explicit inclusion of forces is not necessary. Mathematical properties of capillary pressure curve and centrifuge data are used as constraints of the kinetic energy minimization procedure. The discretized problem is solved using a nonlinear programming procedure using only the single-speed experimental data. Numerical results are confronted with calculations in the frequently used multi-speed centrifuge tests.