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.

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