Laboratory Estimation and Modeling of Apparent Permeability for Ultra-Tight Anthracite and Shale Matrix: A Multi-Mechanistic Flow Approach

Restricted (Penn State Only)
Wang, Yi
Graduate Program:
Energy and Mineral Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
May 30, 2017
Committee Members:
  • Shimin Liu, Dissertation Advisor
  • Shimin Liu, Committee Chair
  • Derek Elsworth, Committee Member
  • Zuleima T. Karpyn, Committee Member
  • Ming Xiao, Outside Member
  • Permeability Evolution
  • Analytical Modeling
  • Geomechanical Deformation
  • Unconventional Gas Flow
  • Laboratory Measurement
Gas production from unconventional reservoirs such as gas shale and coalbed methane (CBM) has become a major source of clean energy in the United States. Reservoir apparent permeability is a critical and controlling parameter for the predictions of shale gas and coalbed methane (CBM) productions. Shale matrix and tight anthracite are characterized by ultra-tight pore structure and low permeability at micro- and nano-scale with gas molecules stored by adsorption. Gas transport in shale and anthracite matrices no longer always falls into the continuum flow regime described by Darcy’s law, rather a considerable portion of transport is sporadic and irregular due to the mean free path of gas is comparable to the prevailing pore scale. Therefore, gas transport in both anthracite and shale will be a complicated nonlinear multi-mechanistic process. A multi-mechanistic flow process is always happening during shale gas and CBM production, including Darcy viscous flow, slip flow, transition flow and Knudsen diffusion and their proportional contributions to apparent permeability are constantly changing with continuous reservoir depletion. The complexity of the gas storage and flow mechanisms in ultra-fine pore structure is diverse and makes it more difficult to predict the matrix permeability and gas deliverability. In this study, a multi-mechanistic apparent-permeability model for unconventional reservoir rocks (shale and anthracite) was derived under different stress boundary conditions (constant-stress and uniaxial-strain). The proposed model incorporates the pressure-dependent weighting coefficients to separate the contributions of Knudsen diffusion and Darcy flow on matrix permeability. A combination of both permeability components was coupled with pressure-dependent weighting coefficients. A stress–strain relationships for a linear elastic gas-desorbing porous medium under hydrostatic stress condition was derived from thermal-elastic equations and can be incorporated into the Darcian flow component, serving for the permeability data under hydrostatic stress. The modeled results well agree with anthracite and shale sample permeability measured data. In this study, laboratory measurements of gas apparent permeability were conducted on coal and shale samples for both helium and CO2 injection/depletion under different stress conditions. At low pressure under constant stress condition, CO2 permeability enhancement due to sorption-induced matrix shrinkage effect is significant, which can be either clearly observed from the pulse-decay pressure response curves or the data reduced by Cui et al.’s method. CO2 apparent permeability can be higher than He at pressure higher than 1000 psi, which may be resulted from limited shale adsorption capacity. Helium permeability is more sensitive to the variation of Terzaghi effective stress than CO2 and it is independent of pore pressure. The true effective stress coefficient can be found two values at low pressure region (<500 psi) and high pressure region (>500 psi). The negative value indicates Knudsen diffusion and slip flow effect have more impact on apparent permeability than Terzaghi stress at low pressure. Additionally, laboratory measurements of gas sorption, Knudsen diffusion coefficient and coal deformation were conducted to break down the key effects that influence gas permeability evolution. Adsorption isotherms of crushed anthracite coal samples was measured using Gibbs adsorption principle at different gas pressures. The adsorption isotherm result showed that the adsorption capacity at low pressure changes with a higher rate and thus brings a significant sorption-induced rock matrix swelling/shrinkage effect. And the isotherm data are important inputs for the Darcy permeability models. The latter was coupled in the apparent-permeability model as the Darcy flow component which involves the sorption-induced strain component. Diffusion coefficients of the pulverized samples were estimated by using the particle method and was used to calculate the effective Knudsen permeability. The Knudsen diffusion flow component in the proposed apparent-permeability model was constructed by transforming Knudsen mass flux into permeability term and used to match the effective Knudsen permeability based on diffusion data. Increasing trends for all results were performed during pressure drop down in the result plots. And the modeling result showed very good agreements with them, giving a solid proof of the availability of Knudsen diffusion component as part of the proposed model. The results of a series of experimental measurements of coal deformation with gas injection and depletion revealed that the coal sorption induced deformation exhibits anisotropy, with larger deformation in direction perpendicular to bedding than those parallel to the bedding planes. The deformation of coal is reversible for helium and methane with injection/depletion, but not for CO2. Based on the modeling results, it was found that application of isotropic deformation in permeability model can overestimate the permeability loss compared to anisotropic deformation. This demonstrates that the anisotropic coal deformation should be considered to predict the permeability behavior of CBM as well as CO2 sequestration/ECBM projects.