Computation of Wag Process and Experimental Verification of Fractional Flow Hysterisis in Porous Media

Abstract

Abstract We present a methodology for computation of the water alternated gas (WAG) injection process for oil recovery. In this methodology we use the method of characteristics to construct the analytical solution of the displacement, and we design a computer program to perform the intermediary steps required for the effective calculation of the solutions. We also analyze the effect of the hysterisis phenomenon on the fluid displacement in porous media, due to the sequential imbibition and drainage process. In our analysis we use published analytical hysteretical models and experimental results acquired in our laboratory apparatus. The comparison between experimental and analytical results are presented. Introduction Water-Alternate-Gas is an effective process to enhance oil recovery. The process is modeled by a system of hyperbolic partial differential equations; the conservation of water-hydrocarbon phase and the conservation of the gas component. As it is known, there are discontinuities in the solution of this kind of problems. Also the sequence of water and gas injection means that the boundary condition is a step function. Therefore, there are several jumps in the water saturation profile. Simulation of this process using usual numerical methods, such as finite difference and finite elements, is impractical, since the numerical dispersion near the jumps will propagate and interact themselves, destroying the character of the solution. In this paper we describe a semi-analytical method to solve the WAG model. We use the characteristic method to construct simple waves and the coherence principle to obtain compatible connections of simple waves that solve the Riemann problem, with arbitrary left and right states, for the model. The effective calculations of the front trajectories, water saturations and gas concentrations are done by means of a computer code that perform the intermediary computations. On the other hand, the water-alternated-gas injection causes a sequence of imbibition and drainage process in the porous media. This process is the cause of the appearance of the hysterisis in the relative permeabilities curves, and in consequence, the hysterisis in the fractional flow curves. In this paper we also analyze the hysterisis effect on fluid displacement in porous media. We restricted our study to two-phase water and oil flow. Our hysterisis analysis is performed using experimental results, analytical formulation and calculation, and the comparison between experimental and analytical results.