Correlation between formation compressibility $\begin{array}{l}k_a(p)\end{array}$ at a given pressure $\begin{array}{l}p\end{array}$ and initial formation compressibility $\begin{array}{l}k_{ai}\end{array}$ at initial formation pressure $\begin{array}{l}p_i\end{array}$

Corrrelation

Name/Author

Scope

(1)	$\begin{array}{l}\displaystyle k_a(p) = k_{ai} \cdot \exp [ - c_k \cdot (p_i - p) ]\end{array}$

Yilmaz and Nur

Narrow pressure range below $\begin{array}{l}p_i: \quad p\leq p_i\end{array}$

(2)	$\begin{array}{l}\displaystyle k_{a}(p) = k_{ai} \cdot \frac{1-2(1+\gamma)c_{rm} \xi(p)}{1-2(1+\gamma)c_{rm} \xi(p_i)}\end{array}$

(3)	$\begin{array}{l}\displaystyle \xi(p) = p_{\rm min} + 1.75 \cdot \phi^{0.51} \cdot (p_{\rm\end{array}$

Dobrynin

Sandstone

Wide pressure range: p_min = 1 MPa < p < p_max = 200 MPa

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Permeability-pressure correlations

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