Abstract
In this paper we construct coupled gas flow models in shale-matrix and hydraulic fractures within the framework of the reiterated homogenization procedure in conjunction with the treatment of fractures as (n-1) interfaces (n = 2, 3) and adsorption isotherm of Langmuir-based monolayer model in the nanopores. At the nanoscale the Langmuir model is applied to reconstruct general monolayer adsorption isotherms of pure methane in the intra-particle porosity of the gas-wet organic matter. The nanoscopic model is upscaled to the microscale where kerogen particles and nanopores are viewed as overlaying continua forming the organic aggregates at thermodynamic equilibrium with the free gas in the water partially saturated interparticle pores. The reaction/diffusion equation for pure gas movement in the kerogen aggregates is coupled with both Fickian diffusion of dissolved gas in water and Darcy free gas flow in the interparticle pores also lying in the vicinity of the inorganic solid phase (clay, quartz, calcite) assumed impermeable. By postulating continuity of fugacity between free and dissolved gas in the interparticle pores and neglecting the bound water movement, we upscale the microscopic problem to the mesoscale, where organic and inorganic matter, and interparticle pores are homogenized. The upscaling gives rise to a new nonlinear pressure equation for gas hydrodynamics in the interparticle pores including a new storage parameter dependent on the total carbon content (TOC) and porosities. The new pressure equation in the shale matrix is coupled with single phase gas flow in the hydraulic fractures. The reduction of dimensionality method is applied to treat fractures as interfaces by averaging the flow equation across the fracture aperture. Combination of the methods give rise to a new matrix/fracture coupled problem. Numerical simulations illustrate the potential of the multiscale approach proposed for computing gas production curves and recovery factor in different gas flow regimes.
