A New Matrix/Fracture Multiscale Coupled Model for Flow in Shale-Gas Reservoirs

Abstract

Summary A new computational model for coupled gas flow in hydraulic fractures and multiporosity shale matrix is developed within the framework of multiscale modeling. The hydrodynamics in the network of hydraulic fractures are constructed by averaging the mass-conservation equation across the fracture aperture, giving rise to an averaged balance law supplemented by a source term arising from the jump in the gas flux from the shale matrix. The resultant flow equation in the fracture is coupled with a new pressure equation that governs the averaged gas movement in the shale matrix. Such a pressure equation exhibits a new storage coefficient and is rigorously derived by homogenizing the pore-scale model of gas flow in the interparticle pores, partially saturated with water, lying adjacent to the nanopores within the kerogen and impermeable inorganic matter composed of a reactive clay and an inert solid. The free gas at the interparticle pores is assumed at local thermodynamic equilibrium with the dissolved gas in the water and adsorbed gas lying in the nanopores of the kerogen aggregates and at the surface of the active clay. The constitutive laws for the partition coefficients, which appear in the pressure equation, are derived from the adsorption isotherms, which are rigorously constructed from the thermodynamics of confined gases on the basis of the density-functional-theory (DFT) approach. Numerical simulations of both canonical and real computational examples of gas primary recovery in the Barnett, Marcellus, and Eagle Ford formations illustrate the potential of the multiscale approach proposed herein in computing production in different flow regimes.