Small variations of formation pressure p lead to exponential changes in permeability:
| (1) | k=k_0 \, e^{n_k \cdot c_r (p-p_0)} |
where
c_r | formation compressibility |
n_k = \frac{\ln (k/k_0)}{\ln(\phi/\phi_0)} | power degree of permeability-porosity correlation |
k_0 | formation permeability at reference pressure p_0 |
\phi_0 | formation porosity at reference pressure p_0 |
p_0 | reference pressure, usually picked up at initial formation pressure p_0 = p_i |
The substantial reduction of formation pressure leads to shrinking of numerous pore throats and massive reduction in permeability deviating from exponential.
The substantial increase of formation pressure leads to microfracturing and massive increase in permeability deviating from exponential.