Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms

Abstract

A theoretically improved model incorporating the relevant mechanisms of gas retention and transport in gas-bearing shale formations is presented for determination of intrinsic gas permeability and diffusivity. This is accomplished by considering the various flow regimes according to a unified Hagen-Poiseuille-type equation, fully compressible treatment of gas and shale properties, and numerical solution of the non-linear pressure equation. The present model can accommodate a wide range of fundamental flow mechanisms, such as continuum, slip, transition, and free molecular flow, depending on the prevailing flow conditions characterized by the Knudsen number. The model indicates that rigorous determination of shale-gas permeability and diffusivity requires the characterization of various important parameters included in the present phenomenological modeling approach, many of which are not considered in previous studies. It is demonstrated that the improved model matches a set of experimental data better than a previous attempt. It is concluded that the improved model provides a more accurate means of analysis and interpretation of the pressure-pulse decay tests than the previous models which inherently consider a Darcian flow and neglect the variation of parameters with pressure. 123 926 F. Civan et al. D a Apparent transport coefficient (or hydraulic diffusivity) (m 2 /s) D o Characteristic transport coefficient (or hydraulic diffusivity) (m 2 /s) E u Upstream boundary flux error (Pa.s/m) E d Downstream boundary flux error (Pa.s/m) E uD Dimensionless upstream boundary flux error E dD Dimensionless downstream boundary flux error f (K n) Flow condition function (dimensionless) g Gravitational acceleration vector (m 2 /s) K Apparent permeability tensor of gas (m 2 ) K a Parameter (m 3 gas/m 3 solid) Kn Knudsen number (dimensionless) K ∞ Intrinsic permeability (m 2 ) L a Hydraulic length scale (m) M g Molecular weight of gas (kg/kmol) n Unit vector (dimensionless) p Absolute gas pressure (Pa) p d Downstream gas pressure (Pa) p D Dimensionless pressure p dD Dimensionless value of the measured values of p d Pe Peclet number (dimensionless) p L Langmuir gas pressure (Pa) p u Upstream gas pressure (Pa) p uD Dimensionless value of the measured values of p u q Mass of gas adsorbed per solid volume (kg/m 3 ) q a Standard volume of gas adsorbed per solid mass (std m 3 /kg) q L Langmuir gas volume (std m 3 /kg) R h Hydraulic radius of flow tube (m) R g Universal gas constant (8314 J/kmol/K) std. Denotes standard conditions (273.15 • K and 101 325 Pa) t D Dimensionless time T Absolute temperature, K u Volumetric flux vector (m 3 /m 2 -s) U a apparent convective flux vector (m/s) U o Characteristic convective flux (m/s) V b Bulk volume of core plug (m 3 ) V d Downstream reservoir volume (m 3 ) V D Dimensionless convective flux vector (dimensionless) V p Effective pore volume (m 3 ) V std Molar volume of gas at standard temperature (273.15 • K) and pressure (101,325 Pa) (std m 3 /kmol) V u Upstream reservoir volume (m 3 ) x Carte...

Numerical Simulation of Natural Gas Flow in Anisotropic Shale Reservoirs

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Investigation of shale gas microflow with the Lattice Boltzmann method

“…Due to these inherent characteristics of gas shale such as, (1) widely dispersed organic matter and (2) nano-scale pore system ), shale gas transport mechanisms do not fully follow Darcy's law. We cannot simply use Darcy's law to calculate matrix permeability of gas shale because of these special phenomena and problems (Civan 2010;Civan et al 2011).…”

Influence of gas transport mechanisms on the productivity of multi-stage fractured horizontal wells in shale gas reservoirs

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