Relative permeability

Input(s)

$q_{o}$: Oil Flow Rate $\left(\mathrm{cm}^{3} / \mathrm{s}\right)$

$q_{w}$: Water Flow Rate $\left(\mathrm{cm}^{3} / \mathrm{s}\right)$

$q_{T}$: Total Flow Rate $\left(\mathrm{cm}^{3} / \mathrm{s}\right)$

$k_{o}$: Effective Permeability to Oil (mD)

$k_{w}$: Effective Permeability to Water (mD)

$k$: Absolute Permeability (mD)

$\mu_{o}$: Viscosity of Oil Phase $(\mathrm{cP})$

$\mu_{w}$: Viscosity of Water Phase $(\mathrm{cP})$

$P$: Pressure value that read from Pressure Gauge (Atm)

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

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

Output(s)

$k_{r o}$: Relative Permeability to Oil (mD)

$k_{r w}$: Relative Permeability to Water (mD)

Formula(s)

$$ \begin{gathered} \mathrm{k}_{\mathrm{ro}}=\frac{\mathrm{k}_{\mathrm{o}}}{\mathrm{k}} \\ \mathrm{k}_{\mathrm{rw}}=\frac{\mathrm{k}_{\mathrm{w}}}{\mathrm{k}} \\ \mathrm{k}_{\mathrm{ro}}=-\frac{1}{0.001127} \cdot \frac{\mathrm{q}_{\mathrm{o}} \mu_{\mathrm{o}} \mathrm{L}}{\mathrm{k} \cdot \mathrm{A} \cdot \Delta P} \\ \mathrm{k}_{\mathrm{rw}}=-\frac{1}{0.001127} \cdot \frac{\mathrm{q}_{\mathrm{w}} \mu_{\mathrm{w}} \mathrm{L}}{\mathrm{k} \cdot \mathrm{A} \cdot \Delta P} \end{gathered} $$

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: 4-2.