Multi-scale Gas Transport in Shales with Local Kerogen Heterogeneities
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AbstractBased on micro and meso-scale investigations, a new mathematical formulation is introduced in detail to investigate multiscale gas transport phenomena in organic-rich shale core plugs. The formulation includes dual porosity continua, where shale permeability is associated with inorganic matrix having relatively large irregularly-shaped pores and fractures, whereas molecular phenomena (diffusion and nonlinear sorption) are with the kerogen pores. Kerogen is considered as a nanoporous organic material finely-dispersed within the inorganic matrix. The formulation is used to model and history-match gas permeation measurements in the laboratory using shale core plugs. The results indicate significance of molecular transport and strong transient effects due to gas/solid interactions within the kerogen. In the second part of the paper, we present a novel multi-scale perturbation approach to quantify the overall impact of local porosity fluctuations associated with a spatially nonuniform kerogen distribution on the adsorption and transport in shale gas reservoirs. Adopting weak-noise and mean-field approximation, the approach applies a stochastic upscaling technique to the mathematical formulation developed earlier for the laboratory. It allows us to investigate local kerogen heterogeneity effects in spectral (Fourier-Laplace) domain and to obtain an upscaled "macroscopic" model, which consists of the local heterogeneity effects in real time-space domain. The new upscaled formulation is compared with the previous homogeneous case numerically using finite-difference approximations to initial/boundary value problems simulating the matrix gas release. We show that macro-transport and macro-kinetics effects of kerogen heterogeneity are nontrivial and impact cumulative gas recovery. The work is important and timely for development of new-generation shale gas reservoir flow simulators and it can be used in the laboratory for organic-rich gas shale characterization.
