A mathematical model of non-stationary multiphase filtration in compressible porous media

It is well known that the solid skeleton of many petroleum reservoirs is compressible. Changes in reservoir pressure during exploitation may therefore cause deformation of the porous medium, leading to variations in porosity and permeability. These changes can significantly influence fluid flow, pressure distribution, and ultimately the efficiency of hydrocarbon recovery. In this paper, a mathematical model is developed for two-phase filtration through a compressible porous medium. The unique feature of this study is the numerical implementation of a two-phase flow model, using the large-particle method, that incorporates pressure-dependent porosity along with pressure-dependent oil and water densities. Subsequently, a quantitative assessment was conducted on the combined effects of rock and fluid compressibility on pressure, saturation, and production characteristics. Based on the obtained numerical results, the influence of medium compressibility on the multiphase filtration process was analyzed. Calculations indicate that as the compressibility of the medium increases, the deformational response of the porous medium’s skeleton to changes in reservoir pressure intensifies. Consequently, the reduction in porosity becomes more pronounced, and correspondingly, absolute permeability also declines more rapidly. A decrease in the medium’s permeability creates additional resistance to the movement of liquid phases, reducing the filtration rates of both oil and water. This decrease in filtration rate, in turn, slows down the pressure redistribution process within the reservoir; that is, the pressure drop over time proceeds more gradually. Concurrently, due to the restricted mobility of the oil phase, the oil flow towards the well diminishes, leading to a decrease in the oil production rate. Therefore, an increase in medium compressibility impedes the filtration process through a more drastic reduction in porosity and permeability, thereby negatively impacting oil recovery performance.

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