Flow simulation in multiscale porous structure and estimation of apparent gas permeability of shale

Shale is a fine-grained sedimentary rock. Flow simulation in shale is challenging due to its multiscale porous structure (consisting of nano- to micropores and fractures) and multi-physics gas flow mechanism (including continuum flow, slip flow, transition flow, Knudsen diffusion and surface diffusion) in these pores. Previous studies have improved our understanding of the flow processes in shale; however, they fail to capture the multiple flow mechanisms in the complex porous structure. In this thesis, gas flow in the multiscale porous structure of shale matrix was investigated. A multiple-relaxation-time lattice Boltzmann method (LBM) was presented to simulate the non-continuum gas flow in microchannels. Simulation results show that the proposed LBM successfully mimics the behaviour of rarefied gas with Knudsen number up to 10. This success provides a physical explanation to the semi-analytical B-K equation. B-K equation was then applied to a bundle of tortuous capillaries representing the porous structure of shale matrix. With the aids of fractal dimensions for pores and tortuosity, an analytical equation was developed to estimate the apparent gas permeability of shale. The simulated apparent gas permeability was validated against over 100 laboratory data varying from100 nano-Darcy to10 mili-Darcy. The deficiency of the capillary model, however, is that the interconnection of capillaries is not considered. In view of this, a pore network was constructed to represent the porous structure of shale matrix, with the employment of a self-similarity based stochastic method. The simulation results show that the apparent gas permeability increases by a factor of 3.2, with 36% contribution arising from surface diffusion. Sensitivity analyses indicate that the apparent gas permeability is influenced by the pore size, shape of voids, gas type, surface diffusivity, adsorption parameters and reservoir conditions. It is concluded that the network modelling method can successfully capture the multiple flow mechanisms in the multiscale porous structure of shale matrix. In order to compare the results with laboratory measurements, it is required to upscale the simulation results from the matrix subset to the core scale. This is computationally exhaustive in consideration of the broad span of scales. This improvement, therefore, is left for the future study