A mathematical model of fractured porous media including mass transfer process

Abstract

Enormous percentage of total original oil in place lies in the fractured reservoirs. There dual permeability plays an important role to enhance the oil production rate which is governed by the large surface area provided by fractures so that fluids can move easily from low permeability zone matrix to high permeability channeled network zone. Convective current is setup in reservoir due to density inversion. This creates a favorable condition of mass transfer by diffusion. Due to high geo thermal gradient and convective motion of fluids in geothermal reservoir, diffusion can lead to the elevation or depression of bubble point pressure. When reservoir pressure gets drops it leads to evolution of gas from matrix zone which eventually gets transferred to gas cap. This leads to depression of Bubble Point. Now, when reservoir pressure increases it leads to transportation of gas from gas cap to matrix zone. This leads to elevation of Bubble point. In this paper a quantitative analysis of diffusion process for an arbitrary inclined fracture [1] by the help of FICK'S law of diffusion and continuity equation of diffusion is done. Through this analysis we obtain a final differential equation by applying material balance on the dissolved gas in the fracture. Lastly effective diffusion coefficient of the fractured media is quantitatively analyzed. Thus, correct analysis of reservoir in terms of microscopic and macroscopic sweep efficiency is done by the inclusion of this diffusion process. Hence, a better model to simulate the fractured reservoir can be made by selecting appropriate boundary conditions for the final differential equation obtained and proposed in this paper. Also we can understand the actual solution gas drive mechanism in the fractured reservoirs correctly. Negligible works have been done on the Mass Transfer analysis in the inclined fractured reservoir theoretically or experimentally and thus here an effective mathematical model of the mass transfer in an arbitrary inclined fracture has been formulated and presented for regulators of hydrocarbon industry for high outcome from a field.