Reservoir Quality Index (RQI) based on Kozeny–Carman equation as a function of permeability (\(k\)) and porosity (\(\phi\)) is given by:
\[
RQI = C \, f(k,\phi)
\]
where \(C = 0.0314\).
If permeability \(k = 152 \, \text{mD}\) and porosity \(\phi = 0.18\), then find RQI in \(\mu m\) (rounded off to two decimal places).
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Solution and Explanation
From Kozeny–Carman relation, \[ RQI = 0.0314 \sqrt{\frac{k}{\phi}}. \] Step 2: Substitution of values.
Permeability = \(k = 152 \, \text{mD}\). Porosity = \(\phi = 0.18\). \[ RQI = 0.0314 \sqrt{\frac{152}{0.18}} \] Step 3: Simplify inside the square root.
\[ \frac{152}{0.18} \approx 844.44 \] \[ \sqrt{844.44} \approx 29.05 \] Step 4: Multiply constant.
\[ RQI = 0.0314 \times 29.05 \approx 0.912 \, \mu m. \] Correction: The standard RQI definition used in petroleum engineering is often scaled to give results in microns: \[ RQI = 0.0314 \sqrt{\frac{k}{\phi}} \quad \text{with } k \text{ in mD.} \] So: \[ RQI = 0.0314 \times 29.05 \approx 0.91 \, \mu m. \] Final Answer: \[ \boxed{0.91 \, \mu m} \]
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