Gas sorption and non-Darcy flow in shale reservoirs

Abstract

Abstract Gas sorption and non-Darcy flow are two important issues for shale gas reservoirs. The sorption consists of dissolution and adsorption. Dissolved gas and adsorbed gas are different. The former is dissolved in the shale matrix, while the latter is concentrated near the solid walls of pores. In this paper, the Langmuir equation is used to describe adsorption and Henry’s law is used to describe dissolution. The K coefficient in Henry’s law of 0.052 mmol/(MPa g TOC) is obtained by matching experimental data. The amount of dissolved gas increases linearly when pressure increases. Using only the Langmuir equation without considering dissolution can lead to a significant underestimation of the amount of sorbed gas in shales. For non-Darcy gas flow, the apparent permeability model for free gas is established by combining slip flow and Knudsen flow. For adsorbed gas, the surface diffusion effect is also considered in this model. The surface diffusion coefficient is suggested to be of the same scale as the gas self-diffusion coefficient, and the corresponding effective permeability is derived. When $$\frac{1}{p}$$ 1 p increases, $$\frac{{k_{\text{app}} }}{{k_{\text{D}} }}$$ k app k D increases, but the relationship is not linear as the Klinkenberg effect suggests. The effect of adsorption on the gas flow is significant in nanopores ( $$r \le 2\;{\text{nm}}$$ r ≤ 2 nm ). Adsorption increases apparent permeability in shales at low pressures and decreases it at high pressures.

Keywords

• Apparent gas permeability
• Shale
• Adsorbed gas
• Dissolved gas
• Surface diffusion