Theoretical comparison of two setups for capillary pressure measurement by centrifuge

Abstract

There are several approaches for the calculation of capillary pressure curves in porous media including the centrifuge method. In this work, a new installation of centrifuge test is introduced and compared with the traditional setup. In the first setup, which is a standard approach in labs, the core face closest to the rotational axis is open to the non-wetting phase, while the farthest face is open to the wetting phase where strictly co-current flow is generated in rotations; labeled Two-Ends-Open (TEO). In the second setup, which is proposed as a new approach, only the outer radius surface is open and is exposed to the light non-wetting phase; labeled One-End-Open (OEO). This setup strictly induces counter-current flow. The two systems and their corresponding boundary conditions are formulated mathematically and solved by a fully implicit numerical solver. The TEO 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, and changing the installation does not influence the measured capillary pressure. This equilibrium state is only dependent on the rotational speed, rock capillary pressure properties, and fluid densities, not the installation geometry, relative permeabilities, or fluid viscosities. However, the dynamic transition trend and saturation profiles were found to be dependent on the applied installation. It was observed that the OEO setup takes almost identical equilibration time as the TEO setup for mixed-wet states, although it needed much longer time in water-wet states. The presence of threshold capillary pressure significantly increased the time scale of the OEO setup. Also, it was found that in contradiction to the TEO setup, the dynamic saturation profile in OEO was rarely influenced by viscosity ratio. To conclude, the performed history matching analysis demonstrated that the OEO setup can be applied for the calculation of counter-current relative permeability from the production data with reasonable accuracy.

Keywords: Centrifuge capillary pressure measurement; Counter-current flow; One-End-Open (OEO); Special core analysis (SCAL).