Traditionally, viscous flow based on Darcy's law has been considered as the primary transport mechanism in petroleum reservoirs. In the micropores of tight sands and nanopores of shale, fluid transport is more complicated than Darcy flow. In unconventional gas reservoirs, in addition to viscous flow, diffusion can play a significant role in gas transport especially in ultra-low permeability reservoirs.
An easy-to-use dual mechanism approach that accounts for the contribution of both Darcy flow and diffusion to apparent permeability in tight sandstone and shale formations is developed in this paper. The study elaborates on how the traditional Darcy permeability is modified to account for the effect of diffusion. This is achieved through an additional term that accounts for diffusion contribution as a function of gas viscosity, compressibility, and diffusion coefficient. The proposed model is then applied to experimental data of tight gas and shale gas reservoirs.
For the case of tight gas reservoirs, Mesaverde sandstone data from the United States Basins are analyzed. For the shale gas case, Duvernay formation in the Western Canada Sedimentary Basin is studied. Laboratory measured permeability supplemented with petrographical SEM images and MICP data is investigated. The application of the proposed methodology is demonstrated for estimating the percentage of diffusion contribution to total gas transport in the rock matrix.
The transition from viscous flow to diffusion is identified with the use of Knudsen number. Viscous flow is usually observed in larger pores and higher pressures where continuous flow is driven by a pressure gradient. In micropores, and especially nanopores of shale formations, diffusion driven by a concentration gradient becomes the major transport mechanism.
The results indicate that in extremely tight reservoirs with nanodarcy permeability, diffusion is the dominant transport mechanism for gas delivery from matrix nanopores to natural fractures. This is important and should not be ignored in engineering applications. Practical guidelines and recommendations are provided for the proper use of the proposed methodology.