Gas permeability measurement (lab measurement using Klinkenberg effect)

Input(s)

$\mu$: Viscosity of Liquid Phase $(\mathrm{cP})$

$\mu_{\text {air }}$: Viscosity of Air $(\mathrm{cP})$

$\mu_{\mathrm{CO}_{2}}$: Viscosity of $\mathrm{CO}_{2}(\mathrm{cP})$

$Q_{\text {avg }}$: Average Rate in Porous Media $\left(\mathrm{cm}^{3} / \mathrm{s}\right)$

$P_{\text {avg }}$: Average Pressure in Porous Media (Atm)

L: Plug Length $(\mathrm{cm})$

A: Open-Flow Area of the Plug $\left(\mathrm{cm}^{2}\right)$

$P_{1}$: Inlet Pressure (Atm)

$P_{2}$: Outlet Pressure (Atm)

$V$: Liquid Volume that flows in time $t\left(\mathrm{~cm}^{3}\right)$

$V_{1}$: Liquid Volume that flows at Inlet Part in Time $t\left(\mathrm{~cm}^{3}\right)$

$V_{2}$: Liquid Volume that flows at Outlet Part in Time $t\left(\mathrm{~cm}^{3}\right)$

$Q_{1}$: Liquid Rate that flows at Inlet Part $\left(\mathrm{cm}^{3}\right)$

$Q_{2}$: Liquid Rate that flows at Outlet Part $\left(\mathrm{cm}^{3}\right)$

Output(s)

$k$: Liquid Permeability (D)

$k_{g}$: Gas Permeability (D)

Formula(s)

$$ \begin{gathered} \mathrm{k}=\frac{2 \mu \cdot \mathrm{Q}_{\mathrm{avg}} \cdot \mathrm{P}_{\mathrm{avg}} \cdot \mathrm{L}}{\mathrm{A} \cdot\left(\mathrm{P}_{1}^{2}-\mathrm{P}_{2}^{2}\right)} \\ \mathrm{P}_{1} \cdot \mathrm{V}_{1}=\mathrm{P}_{2} \cdot \mathrm{V}_{2}=\mathrm{P}_{\mathrm{avg}} \cdot \mathrm{V}_{\mathrm{avg}} \\ \mathrm{P}_{1} \cdot \mathrm{Q}_{1}=\mathrm{P}_{2} \cdot \mathrm{Q}_{2}=\mathrm{P}_{\mathrm{avg}} \cdot \mathrm{Q}_{\mathrm{avg}} \\ \mathrm{k}_{\mathrm{g}}=\mathrm{k}\left(1+\frac{\mathrm{b}}{\mathrm{P}_{\mathrm{avg}}}\right) \\ \mu_{\mathrm{air}}=0.000044848 \cdot \mathrm{T}+0.0165 \\ \mu_{\mathrm{CO}_{2}}=0.00005000 \cdot \mathrm{T}+0.0138 \end{gathered} $$

Reference(s)

Mihcakan, I.M., Alkan, K.H., Ugur, Z., Petroleum and Natural Gas Laboratory, Course Notes, II-Properties of Porous Media, ITU, Petroleum and Natural Gas Engineering, Istanbul, Turkey, 2001. Page: 3-4.