A Fully-Coupled Free and Adsorptive Phase Transport Model for Shale Gas Reservoirs Including Non-Darcy Flow Effects

Abstract Accurate modeling of gas through shale-gas reservoirs characterized by nano-meter pores where the effects of various non- Darcy flow regimes and the adsorbed-layer are important is presented and demonstrated by several examples. Quantification of gas transport may be accomplished using the transport equation that is valid for all flow regimes. This equation though needs further modification when transport is through a media where the gas is adsorbed onto the pore wall. In the presence of adsorption, there is a pore pressure dependent loss of porosity and cross-sectional area to free gas transport. The apparent gas permeability correction is accomplished for various flow regimes using the Knudsen number by consideration of the reduction of the cross-sectional area to free gas transport in the presence of adsorption. We show that transport in the adsorbed layer may contribute significantly in the total gas transport in these nanopores. An effective transport model is presented to account for the impact of adsorption through two mechanisms. First, we modify the transport equation to account for the pore-pressure dependent-reduction in the volume available to free gas transport; second, we model transport through the adsorbed layer using Fick's law of diffusion. The coupled model is then compare to conventional transport models over a wide range of reservoir properties and conditions. As pore-pressure is reduced, adsorbed phase gas desorbs into free gas and apparent permeability increases. The difference in the estimated apparent permeability with and without the consideration of the adsorption volume can be a factor of two or more at initial reservoir conditions. Diffusion on the surface of organic pores can be a substantial transport mechanism in shales depending on the pore connectivity, pore pressure, and pore size distribution in the organic pores. The interpretation of production data will be compromised without considering the effects of adsorption on apparent permeability. This work implies that permeability measurements for shale gas reservoirs must be done with methane at in-situ pore pressures. Because these corrections are pore-pressure not effective pressure dependent, effective pressure is not a valid parameter to use in quantifying the pressure dependence of these transport equations.