Theoretical Comparison of Two Setups for Capillary Pressure Measurement by Centrifuge

Abstract

Summary Capillary pressure is routinely measured using a centrifuge setup where capillary forces retain a heavy, wetting phase (e.g. water) and keep a light, non-wetting phase from entering. By increasing the rotational speed of the centrifuge, the density difference of the phases forces the heavy fluid out, while the light fluid can enter. In this work, we consider and compare the behaviour of two centrifuge setups: In the first setup the core face closest to the rotation axis is open to non-wetting phase, while the core face farthest from the rotation axis is open to wetting phase; labelled Two-Ends-Open, TEO. At increased rotation, this setup generates strictly co-current flow of both phases from the inner towards the outer radius. In the second setup, only the outer radius surface is open and is exposed to the light non-wetting phase; labelled One-End-Open, OEO. All other core faces are closed. At increased rotational speed the wetting phase is forced out the open face and non-wetting phase must flow in opposite direction through the same phase. This setup induces strictly counter-current flow. The two systems are formulated mathematically and solved by implicit pressure and explicit saturation (IMPES) numerical discretization. The standard co-current setup is validated by comparison with commercial software. Experimental data from the literature are used to parameterize the models. It is mathematically, and with examples, demonstrated that the same equilibrium is obtained in both systems with the same rotational speed. This equilibrium, as represented by saturation and capillary pressure distributions, is only dependent on the rotational speed, capillary pressure curve, fluid densities and system geometry, not the relative permeabilities or fluid viscosities. The difference in flow regimes and transient data can be used to obtain better estimates of the relative permeabilities, which previously would need independent measurements using time consuming core flooding tests. It is observed that the counter-current setup has longer corresponding equilibration time scales than the co-current setup under otherwise identical conditions. For saturation function measurement it is still quick relative to comparable techniques. By performing these tests in parallel, a significant difference in flow regimes and thus different dependence on saturation intervals makes it possible to better match relative permeabilities in addition to the capillary pressure. Greater intervals of the functions can be determined with greater accuracy. Measurement of flow regime dependent relative permeabilities can be captured by an expansion of the model.