Effect of the Spreading Coefficient on Two-Phase Relative Permeability

Abstract

Abstract Understanding the dynamics of multiphase flow is essential for optimizing enhanced oil recovery processes. One of the properties that describes the behavior of the fluids in the reservoir is the relative permeability. Despite the development of empirical functional forms and the gathering of a growing body of experimental data, the subject lacks a fundamental basis based on the analysis of the configuration of the fluids at the microscopic scale. In this direction, we have addressed a systematic study of the effect of the spreading coefficient on two-phase relative permeabilities for systems of known wettability. We have developed a method to evaluate the spreading coefficient for solid/liquid/liquid and solid/liquid/gas systems. Samples used for evaluation of the effect of the spreading coefficient on relative permeability were chosen within a wide range of wettability conditions which include water wet, mixed and oil wet samples. Relative permeability was measured using the dynamic method at reservoir conditions. It is found that oil recovery and relative permeability are higher for spreading than for non-spreading conditions. This information is relevant for gas drainage displacements. We comment on the fluid distribution for positive and negative spreading energy and the effect on residual oil saturation. Introduction The distribution of fluids and the wetting phase saturation or its irreducible value after the displacement with a non-wetting phase, are important quantities to be known for the proper design and optimization of injection processes and oil recovery1. Kalaydjian et al. 2 have shown that several parameters may affect the efficiency of two-phase flow processes, and therefore, the final oil recovery. Among those parameters, wettability and the spreading energy are very relevant. These two parameters reflect the macroscopic outcome of the different interfacial phenomena occurring at the solid-liquid and liquid-liquid interfaces. Wettability refers to an indication of the affinity of a fluid to be in contact with the solid surface, trying to occupy the maximum area. In an oil reservoir, wettability gives an indication of the affinity of the rock surface for the oleic or the aqueous phase. This quantity is fundamental in the determination of the distribution of the fluid phases in the porous structure. The understanding of the process by which the crude oil adheres to a rock surface helps in the design and selection of the more appropiate oil recovery strategies. The spreading coefficient has been defined by Rowlinson and Widom3 as an interfacial tension balance:Equation (1) where ?ij is the interfacial tension of each pair of the various phases associated to the system (w=water, o=oil and g=gas). When the phases involved are the rock surface and two different liquids (denoted here by L1 and L2) Eq. 1 givesEquation (2) Spreading coefficients may have positive or negative values according to the nature of the rock surface and the liquids present in the system. A positive spreading coefficient indicates that a thin fluid film becomes a continuous phase through the substrate. In the case of a water/oil/gas system, the oil phase is able to spread on the water in the presence of gas. This process favors the hydraulic continuity of the oil, and therefore leads to a very low residual oil saturation2. Kalaydjian4 showed that the spreading coefficient not only affects the residual oil saturation but also the drainage capillary pressure curve. Furthemore, since the flow mechanisms at the microscopic level (meniscus displacement) are affected by the spreading coefficient, we should expect that flow related quantities, such as relative permeability, be modified and to notice the effects on the oil production. This motivates the evaluation of the effects of the spreading coefficient on relative permeabilities, the study undergone in this work.