Three-Phase Relative Permeabilities from Displacement Experiments with Full Account for Capillary Pressure

Relative permeabilities are important characteristics of multiphase flow in porous media. Displacement experiments for relative permeabilities are frequently interpreted by the JBN method neglecting capillary pressure. The experiments are therefore conducted at high flooding rates, which tend to be much higher than those experienced during reservoir exploitation. Another disadvantage is that the relative permeabilities only can be determined for the usually small saturation interval outside the shock. We present a method to interpret displacement experiments with the capillary pressure included, using in-situ measurements of saturations and phase pressures. The experiments can then be run at low flow rates, and relative permeabilities can be determined for all saturations. The method is demonstrated by using simulated input data. Finally, experimental scenarios for three-phase displacement experiments are analyzed using experimental three-phase relative permeability data. Introduction Relative permeabilities are important characteristics of multiphase flow in porous media. These quantities arise from a generalization of Darcy's law, originally defined for single phase flow. Relative permeabilities are used as input to simulation studies for predicting the performance of potential strategies for hydrocarbon reservoir exploitation. The relative permeabilities are usually determined from flow experiments performed on core samples. The most direct way to measure the relative permeabilities is by the steady-state method. Each experimental run gives only one point on the relative permeability curve (relative permeability vs. saturation). To make a reasonable determination of the whole curve, the experiment has to be repeated at different flow rate fractions. To cover the saturation plane in a three-phase system, a large number of experiments have to be performed. The method is therefore very time consuming. Relative permeabilities can also be calculated from a displacement experiment. Typically, the core is initially saturated with a single-phase fluid. This phase is then displaced by injecting the other phases into the core. For the two-phase case, Welge showed how to calculate the ratio of the relative permeabilities from a displacement experiment. Efros was the first to calculate individual relative permeabilities from displacement experiments. Later, Johnson et al. presented the calculation procedure in a more rigorous manner, and the method is often referred to as the JBN method. The analysis has also been extended to three phases. In this approach, relative permeabilities are calculated at the outlet end of the core; saturations vs. time at the outlet end is determined from the cumulative volumes produced and time derivatives of the cumulative volumes produced, and relative permeabilities vs. time are calculated from measurements of pressure drop over the core and the time derivative of the pressure drop. Although the JBN method is frequently used for relative permeability determination, it has several drawbacks. The method is based on the Buckley-Leverett theory of multiphase flow in porous media. The main assumption is the neglection of capillary pressure. In homogenous cores capillary effects are most important at the outlet end of the core and over the saturation shock front. To suppress capillary effects, the experiments are performed at a high flow rate. Usually, these rates are significantly higher than those experienced in the underground reservoirs during exploitation.