Analysis of Effective Porosity and Effective Permeability in Shale-Gas Reservoirs With Consideration of Gas Adsorption and Stress Effects
Authors: Pang Y.. , Soliman M. Y. , Deng H.. , Emadi Hossein 
Published: July 2017

Summary
Nanoscale porosity and permeability play important roles in the characterization of shale-gas reservoirs and predicting shale-gas-production behavior. The gas adsorption and stress effects are two crucial parameters that should be considered in shale rocks. Although stress-dependent porosity and permeability models have been introduced and applied to calculate effective porosity and permeability, the adsorption effect specified as pore volume (PV) occupied by adsorbate is not properly accounted. Generally, gas adsorption results in significant reduction of nanoscale porosity and permeability in shale-gas reservoirs because the PV is occupied by layers of adsorbed-gas molecules.
In this paper, correlations of effective porosity and permeability with the consideration of combining effects of gas adsorption and stress are developed for shale. For the adsorption effect, methane-adsorption capacity of shale rocks is measured on five shale-core samples in the laboratory by use of the gravimetric method. Methane-adsorption capacity is evaluated through performing regression analysis on Gibbs adsorption data from experimental measurements by use of the modified Dubinin-Astakhov (D-A) equation (Sakurovs et al. 2007) under the supercritical condition, from which the density of adsorbate is found. In addition, the Gibbs adsorption data are converted to absolute adsorption data to determine the volume of adsorbate. Furthermore, the stress-dependent porosity and permeability are calculated by use of McKee correlations (McKee et al. 1988) with the experimentally measured constant pore compressibility by use of the nonadsorptive-gas-expansion method.
The developed correlations illustrating the changes in porosity and permeability with pore pressure in shale are similar to those produced by the Shi and Durucan model (2005), which represents the decline of porosity and permeability with the increase of pore pressure in the coalbed. The tendency of porosity and permeability change is the inverse of the common stress-dependent regulation that porosity and permeability increase with the increase of pore pressure. Here, the gas-adsorption effect has a larger influence on PV than stress effect does, which is because more gas is attempting to adsorb on the surface of the matrix as pore pressure increases. Furthermore, the developed correlations are added into a numerical-simulation model at field scale, which successfully matches production data from a horizontal well with multistage hydraulic fractures in the Barnett Shale reservoir. The simulation results note that without considering the effect of PV occupied by adsorbed gas, characterization of reservoir properties and prediction of gas production by history matching cannot be performed reliably.
The purpose of this study is to introduce a model to calculate the volume of the adsorbed phase through the adsorption isotherm and propose correlations of effective porosity and permeability in shale rocks, including the consideration of the effects of both gas adsorption and stress. In addition, practical application of the developed correlations to reservoir-simulation work might achieve an appropriate evaluation of effective porosity and permeability and provide an accurate estimation of gas production in shale-gas reservoirs.