Relationships between permeability, porosity and effective stress for low-permeability sedimentary rock

Abstract

As the effective stress increases, low-permeability rock undergoes fairly small porosity changes, but significant decrease in the permeability. Empirical relationships based on laboratory-measured data, typically exponential or power laws, have been proposed to describe the stress-permeability, stress-porosity, and permeability-porosity relationships. However, these approximations yield poor fitting in low effective stress ranges, or unreasonable prediction for certain effective stresses. In this study, we develop a series of theoretical models for the essential relationships among the porosity, permeability and the effective stresses for lowpermeability sedimentary rock, based on the concept of Two-Part Hooke Model (TPHM). The TPHM conceptualizes an intact rock into a soft part and a hard part, which comply with the natural-strain-based and engineering-strain-based Hooke's law, respectively. The derived relationships are validated by the experimental data from the literature. The comparisons show that the theoretical predictions agree well with the experimental results. The soft-part, comprising of only a small portion of the rock body, is responsible for the significant permeability reduction in low stress levels. The high stress-sensitivity of permeability is mainly attributed to the micro-crack (soft-part) closure in the intact rock.

Stress and Damage Induced Gas Flow Pattern and Permeability Variation of Coal from Songzao Coalfield in Southwest China

“…Zhang et al conducted the experiments to investigate relations among the flow rate, permeability and fracture aperture in fractured media [14]. Empirical relations based on laboratory results have been proposed to describe the relations among stress, permeability and porosity of sedimentary rock [15]. Cai et al explored the contribution of stress and damage on the evolution of permeability through X-ray CT images and acoustic emission profiling together with concurrent measurements of the P-wave velocity [16].…”

A Study of Nonlinear Elasticity Effects on Permeability of Stress Sensitive Shale Rocks Using an Improved Coupled Flow and Geomechanics Model: A Case Study of the Longmaxi Shale in China

“…Curve fittings with cubic equations are also provided. Equation (13) shows the cubic equations for Young's modulus as functions of stress for all cores. Table 2 shows the cubic coefficients for all five cores.…”

“…The increase of confining stress is used to represent the increase of effective stress caused by shale gas production in the reservoir. Several confining stress values in the stress loading process (13,16 and 19 MPa) are used for the numerical modeling that considers nonlinear elasticity. Young's modulus values used in this quantification study are in Table 3, corresponding to the calibrated correlations in Equation (13).…”

“…Several confining stress values in the stress loading process (13,16 and 19 MPa) are used for the numerical modeling that considers nonlinear elasticity. Young's modulus values used in this quantification study are in Table 3, corresponding to the calibrated correlations in Equation (13). Numerical simulations of both the reference linear elasticity scenarios and the nonlinear elasticity scenarios are carried out.…”

“…Based on experiments, many correlations between permeability, porosity, rock elastic properties, pore structures, anisotropy, stress, and pore pressure were established, and some of the correlations were used to validate theoretically proposed mathematical functions that depict property changes in stress sensitive shale rocks [1][2][3][4][5][6][7][8][9][10][11][12][13]. These experimental results help to establish validated correlations describing shale rock stress sensitivity, and help to improve the accuracy and reliability of theoretically proposed analytical models.…”