# Measurement of Shale Matrix Permeability and Adsorption with Canister Desorption Test

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## Abstract

Permeability estimation is a crucial part of the shale mudrock characterization because it affects the production rate, the pace of recovery and the technically recoverable hydrocarbons. Shale permeability typically falls in the low range of tens of micro-Darcy down to nano-Darcy. Accurate measurement of permeability is a challenging task because the measurement errors are more likely to occur in the low permeability range. This paper presents a common and accurate experimental method for permeability measurement of shale mudrocks known as the canister desorption test. We describe the experiment procedure and present the governing partial differential equation (PDE). The impact of linear and nonlinear adsorption isotherms and the corresponding analytical and numerical solutions are discussed. A workflow for the estimation of permeability and the gas adsorption parameter is presented. The workflow is used to measure the shale matrix permeability and the adsorption parameter for an organic-rich sample from the Marcellus formation. The measurements are in good agreement with an independent study on the Marcellus organic-rich core samples. The results show that the measurement of the adsorption parameter is as important as the permeability measurement in the organic-rich shales. In addition, given that the measurements of permeability and adsorption parameter are performed at a small scale and the gas properties are approximated by average values, it is recommended to perform multiple experiments at different pressures to constrain the uncertainty of the permeability and adsorption measurements. The limitations of the proposed workflow are discussed.

## Keywords

Canister desorption experiment Shale permeability measurement Linear and nonlinear adsorption isotherms## List of symbols

- \(a_n\)
Coefficient of the solution series

- \(c_g\)
Volumetric gas compressibility (Pa\(^{-1}\))

- \(F_D\)
Fractional gas release

*J*Bessel function

*k*Permeability function (m\(^2\))

- \(k_m\)
Mass transfer coefficient (cm /

*s*)- \(k_n\)
Eigen function solution

- \(K_\mathrm{ads}\)
Derivative of adsorbate density (adsorption coefficient)

- \(K_\mathrm{n}\)
Eigenfunction

*L*Length of core sample (cm)

*m*Gas pseudo-pressure potential (Pa/s)

- \(m_\mathrm{D}\)
Dimensionless gas pseudo-pressure potential (Pa/s)

- \(\bar{m}_\mathrm{D}\)
Average dimensionless gas pseudo-pressure potential (Pa/s)

- \(m_e\)
Ambient gas pseudo-pressure potential (Pa/s)

- \(m_i\)
Initial gas pseudo-pressure potential (Pa/s)

- \(m_\mathrm{LD}\)
Dimensionless Langmuir pseudo-pressure

*n*Initial gas moles, index of dimensionless pseudo-pressure solution

*p*Pressure (Pa)

- \(\bar{p}\)
Average core pressure (Pa)

- \(p_\mathrm{e}\)
Equilibrium pressure

- \(p_\mathrm{L}\)
Langmuir pressure (Pa)

- \(p_\mathrm{sc}\)
Standard pressure

*r*Distance in radial coordinates

- \(r_\mathrm{D}\)
Dimensionless radius

*R*Universal gas constant, 8.314 (J/mol/K)

- \(R_{a}\)
Radius of core sample (cm)

*t*Time

*T*Temperature (K)

- \(T_{app}\)
Apparent transmissibility (cm\(^2\)/s)

- \(T_{rD}\)
Transmissibility ratio

- \(T_\mathrm{sc}\)
Standard temperature

- \(V_d\)
Cumulative volume of released gas (cm\(^3\))

- \(V_\mathrm{L}\)
Langmuir volume (scm\(^3\)/g)

- \(V_\mathrm{LD}\)
Dimensionless Langmuir volume

- \(V_\mathrm{p}\)
Core sample pore volume (cm\(^3\))

- \(V_\mathrm{r}\)
Reservoir chamber volume (cm\(^3\))

- \(V_\mathrm{s}\)
Sample chamber volume (cm\(^3\))

*z*Real gas compressibility factor

- \(\Gamma \)
Total core sample storage capacity (cm\(^3\))

- \(\mu \)
Gas viscosity (Pa.s)

- \(\xi \)
Eigenvalue solution

- \(\rho \)
Gas density (mol/cm\(^3\))

- \(\rho _\mathrm{ads}\)
Molar adsorbate density (mol/cm\(^3\))

- \(\rho _\mathrm{adsD}\)
Dimensionless molar desorption

- \(\rho _\mathrm{b}\)
Bulk density (g/cm\(^3\))

- \(\tau \)
Dimensionless time

- \(\phi \)
Porosity

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