A Triple-Mechanism Fractal Model with Hydraulic Dispersion for Gas Permeation in Tight Reservoirs

Abstract

Abstract This paper presents a triple-mechanism-fractal model including the hydraulic dispersion effect to more accurately describe the gas flow in tight gas reservoirs than the frequently used Darcy law. By comparison to Darcy's law, this paper demonstrates that the improved formulation presented in this paper is more adequate. A Darcy-like equation using an apparent permeability is derived by considering the gas transport by three mechanisms, which may occur in tight pore space under different Knudsen number criteria. This equation incorporates the Knudsen, slip, and viscous flow mechanisms into the description of gas flow, each prevailing under different conditions. The characteristics of porous media are represented by fractal equations. The equation of continuity includes the effect of hydraulic dispersion, which has been omitted in the usual reservoir analysis. These equations are solved analytically for one-dimensional, horizontal, and steady flow in laboratory core tests and radial flow in the near-well bore region. The present analysis indicates that Darcy's law fails to describe the flow of gas in tight formations under the Knudsen and slip flow conditions, because Darcy's law was designed to represent the viscous flow by analogy to liquid flow. Hence, the flow of gases through porous medium should be treated differently than liquids. In addition, the walls of tight pores in porous media interfere with the mean-free motion of gas molecules and cause a strong deviation from Darcy's law. Further, the porous media macroscopic mass conservation equation should include a term for transport by hydraulic dispersion due to mixing and compressibility effects. Therefore, the conventional well test interpretation methods require a correction when the flow occurs under the Knudsen and slip flow conditions. This confirms the significance of the model presented in this paper. The triple-mechanism with hydraulic dispersion model presented in this paper can be used for accurate and convenient means of describing gas flow in tight-geological porous media undergoing various flow regimes.