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Synonym: Pore Compressibility = CPHI

A measure of formation porosity $\begin{array}{l}\phi\end{array}$ change due to reservoir pressure $\begin{array}{l}p\end{array}$ variation:

(1)	$\begin{array}{l}\displaystyle c_\phi = \frac{1}{\phi} \frac{\partial \phi}{\partial p}\end{array}$

There is a statistical correlation between initial formation compressibility $\begin{array}{l}c_\phi(\phi)\end{array}$ and formation porosity which can be picked by various compressibility-porosity models.

Pore compressibility stays constant for small pressure variations but in a wide range of pressure variations the dependence on ambient pressure $\begin{array}{l}c_\phi(p)\end{array}$ can not be neglected and should be tabulated from laboratory core tests or estimated from compressibility-pressure correlations.

The typical values are:

c_ϕ = 0.5 ÷ 1.5 GPa^-1

but may go higher for poorly consolidated rocks.

In many practical cases the pore compressibility can be considered as poorly dependent on reservoir pressure variation: $\begin{array}{l}c_\phi(p) = c_\phi = \rm const\end{array}$ .

In this case porosity dependence on reservoir pressure can be simulated as:

(2)	$\begin{array}{l}\displaystyle \phi(p) = \phi_i \cdot \left[ 1 + c_\phi \, (p-p_i) + 0.5 \, c^2_\phi \, (p-p_i)^2 \right]\end{array}$

But in case the reservoir pressure is changing substantially one may need to account for the effect it takes on pore compressibility (see Pore compressibility @model) and then reservoir pressure - porosity model is going to take the following form:

(3)	$\begin{array}{l}\displaystyle \phi(p) = \phi_i \cdot \exp \left[ \int_{p_i}^p c_\phi\, dp \right]\end{array}$

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