Novel Shale Permeability Model Coupling Sorption-Induced Differential Deformation and Multiple Flow Regimes

Abstract

Under certain stress conditions, tight shale is characterized by the features of gas storage rocks, such as low permeability, low porosity, multiscale pore network, and elastic deformation. Flow-regime-based permeability models can reflect the behavior of non-Darcy gas transport but cannot characterize the elastic performance of tight shale. In this study, we introduce a novel permeability model that couples the sorption-induced differential deformation and multiple flow regimes in shale. The model not only determines flow-regime-based permeability for low pore pressures and micro−nano flow paths but also reflects the differential-swelling-index-based poroelasticity for high pore pressures and macro flow paths. The parameter sensitivity of the proposed model is analyzed. The results show that, with the increase in pore pressure at a constant confining pressure, the model is more sensitive to initial permeability than to initial porosity. The compressibility coefficient, which quantifies shale deformability, significantly affects the permeability evolution predicted by the model. The sorption-capacity-controlled differential deformation does not affect the overall permeability evolution but affects the upper and lower limits of permeability distribution in the intermediate process.

A Review of Swelling Effect on Shale Permeability: Assessments and Perspectives

“…According to eqs and , shale porosity and permeability are defined as a function of pore and bulk swelling strains. The popular viewpoint now is that bulk and pore swelling strains are either the same ,,− or have different magnitudes. − ,− Our analysis in section indicates that bulk and pore swelling strains should have different magnitudes rather than being the same. When bulk and pore swelling strains are assumed to have different magnitudes, a constant ratio, namely the strain splitting factor, has been widely used to define the relation between these two strains.…”

“…On the one hand, the gas adsorption layer on nanopore wall reduces the effective radius of nanopores − and thus influences shale permeability. On the other hand, gas adsorption on rock grains causes matrix swelling, compresses the nanopore radius, and thus changes the shale permeability. ,,− In addition to the above-mentioned three factors, shale permeability could also be influenced by other factors. For instance, Cai et al proposed an easy-to-implement model and disclosed that shale permeability could be influenced by heterogeneous pore size distribution.…”

Novel Shale Permeability Model Considering the Internal Dependencies of Effective Stress, Gas Sorption, and Flow-Regime Effects

“…The gas adsorption-induced porosity change is the result of competing strains from fracture aperture contraction and matrix expansion . The compatibility between the adsorption-induced strains of shale bulk, matrix, and fracture can be defined by introducing a distribution factor, thus leading to more accurate poroelasticity-based permeability calculations with coupled adsorption effects . The differential swelling index (DSI) f in eq is defined as the ratio of the fracture strain increment to the total strain increment of the bulk material and is expressed as follows f = normalΔ ε normalf normals normalΔ ε normalb normals = 1 φ 0 ( 1 − false( 1 − φ 0 false) ε L m p L m false( p + p normalL normalb false) false( p 0 + p normalL normalb false) ε L b p L b false( p + p normalL normalm false) false( p 0 + p normalL normalm false) ) where p Lb is the Langmuir pressure constant of the bulk shale (MPa) and ε b s , ε m s , and ε f s are the sorption/desorption-induced shale bulk, matrix, and fracture strains, respectively.…”

“…54 The compatibility between the adsorptioninduced strains of shale bulk, matrix, and fracture can be defined by introducing a distribution factor, thus leading to more accurate poroelasticity-based permeability calculations with coupled adsorption effects. 55 The differential swelling index (DSI) f in eq 12 is defined as the ratio of the fracture strain increment to the total strain increment of the bulk material and is expressed as follows 29 In a porous medium, the loss in porosity is equal to the loss of the cross-sectional area of the hydraulic diameter. Therefore, the effective porosity (φ) can be expressed as By substituting eq 12 in eq 14, the effective hydraulic diameter under the effective stress and adsorption effect coupling can be expressed as…”