Shale gas reservoirs are fine-grained, organic-rich rocks with a well-developed pore network structure within the organic matter (kerogen). Organic pores in shale reservoirs exhibit small radii in the range of 0.5 to 100 nanometers, which indicate that non-Darcy flow mechanisms are present in these rocks in addition to viscous flow. Gas adsorption/desorption and gas diffusion from solid kerogen are some other important flow mechanisms in shales. Therefore, consideration of these phenomena is crucial for quantification of permeability of shales. A numerical procedure to calculate permeability of shales that accounts for all the above factors is introduced in this work.

During shale's depletion, organic pore radius can change or remain approximately constant depending on the rates of adsorption and desorption. Previous investigations suggest that organic pore radius increases as desorption takes place, which in turn also increases the space available for free gas and reduces the amount of adsorbed gas. This phenomenon thus increases shale permeability. This paper goes further and indicates that pore diameter can increase, decrease or remain approximately constant with time depending on the on-going desorption, adsorption and diffusion from solid kerogen. The effects on pore radius and permeability of all these mechanisms, viscous flow and Knudsen diffusion are addressed in this paper with the development of a ID radial simulation model. Two independent methods, which approximately corroborate each other, are presented for calculating changes in pore radius.

Results show that considering pore radius changes due to sorption and diffusion have a significant impact on estimation of shale permeabilities. The effects on permeability vary under different reservoir conditions. The importance of solid kerogen as a gas source and its effect on gas flow is highlighted. The solid kerogen feeds organic pores affecting the rate of adsorption. Consequently the organic pore radius does not necessarily increase during production; it can decrease or even remain approximately constant. It is concluded that ignoring viscous flow, Knudsen diffusion and changes in pore radius lead to erroneous permeabilities. Gas diffusion from solid kerogen can be quite significant in shale reservoirs and should be taken into account.

The main contribution of this paper is the development of a numerical method for calculating sorption- dependent permeability of shales. The calculations include Darcy and diffusive flows, and changes in organic pore radius due to adsorption/desorption and diffusion from solid kerogen. This is the first time all the aforementioned mechanisms are analyzed in a single study.

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