# 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.

## Related

### Relative permeability - Corey exponents

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