An Integrative Model To Simulate Gas Transport and Production Coupled With Gas Adsorption, Non-Darcy Flow, Surface Diffusion, and Stress Dependence in Organic-Shale Reservoirs

Gas adsorption, stress dependence, non-Darcy flow, and surface diffusion of the adsorbed layer are significant mechanisms in shale-gas reservoirs. However, the volume occupied by the adsorbed layer is generally overlooked by current industry standards and numerical models. In addition, stress dependence of matrix pores does not draw as much attention as hydraulic fractures, and surface diffusion has not been included in commercial simulators. Moreover, all these effects significantly affect each other, which can lead to additional complexity of gas transport and production. Therefore, development of an integrative model with consideration of these complicated mechanisms is needed. In this paper, we develop such a fully coupled model for shale-gas-reservoir simulations. We present the derivation of models reflecting the time-dependence, effects of gas adsorption/desorption upon original gas in place (OGIP) and petrophysical properties. In particular, both the Langmuir and Brunauer, Emmett, and Teller (BET) (Brunauer et al. 1938) isotherms are included by use of a unified formula. Surface diffusion of adsorbed layer is also added to this model on the basis of rigorous derivation. More features, such as non-Darcy flow and stress dependence in matrix, natural fractures, hydraulic fractures, and leakage effect between matrix and natural fractures, are incorporated. After that, we present an implicit numerical algorithm to solve the model. Numerical simulations were performed in both 1D and 3D cases and compared with two sets of experimental data and three sets of production data in Marcellus and Barnett shale-gas fields. The simulations indicated that the new simulator cannot only lead to consistent results with these data, but also gives an accurate estimation of OGIP, which traditional models failed to do. It is noted that the model parameters we used for the simulations were close to the values suggested by the literature, if available. By use of this validated simulator, we demonstrated applications with respect to real shale reservoirs, studied the effects of the model parameters upon the gas transport and production, and achieved a variety of new insights.