A Unified Model for Gas Transfer in Nanopores of Shale-Gas Reservoirs: Coupling Pore Diffusion and Surface Diffusion

Abstract

Summary A model for gas transfer in nanopores is the basis for accurate numerical simulation, which has important implications for economic development of shale-gas reservoirs (SGRs). The gas-transfer mechanism in SGRs is significantly different from that of conventional gas reservoirs, which is mainly caused by the nanoscale phenomena and organic matter as a medium of gas sourcing and storage. The gas-transfer mechanism includes bulk-gas transfer and adsorption-gas surface diffusion in nanopores of SGRs, where the bulk-gas-transfer mechanism includes continuous flow, slip flow, and Knudsen diffusion. First, a model for bulk-gas transfer in nanopores was established, which was dependent on slip flow and Knudsen diffusion. The total gas flux in the bulk phase is not a simple sum of slip-flow flux and Knudsen-diffusion flux but a weighted sum on the basis of corresponding contributions. The weighted factors are primarily controlled by the mutual interaction between slip flow and Knudsen diffusion, which is determined by probabilities between gas molecules colliding with each other and colliding with nanopore surface in this newly proposed model. Second, a model for adsorbed-gas surface diffusion in nanopores was established, which was modeled after the Hwang and Kammermeyer (1966) model and considered the effect of gas coverage under a high-pressure condition. Finally, with the combination of these two models, a unified model for gas transport in nanopores of SGRs was established, and this model was validated through molecular simulation and experimental data. Results show that: Slip flow makes a great contribution to gas transfer under the condition of meso/macropores (pore radius greater than 2 nm) and high pressure. Knudsen diffusion makes an important contribution to gas transfer under the condition of macropores (pore radius greater than 50 nm) and less than 1 MPa in pressure, whereas it can be ignored in other cases. A surface-diffusion coefficient is comparable with a pore-diffusion coefficient, and gas transfer is always dominated by surface diffusion over all the ranges of pressure in micropores (pore radius ≤ 2 nm). Surface-diffusion contribution decreases with an increase in pore size, isosteric sorption heat, pressure, and temperature in SGRs.