Small deviations of ambient pressure p from initial pressure formation p_0 lead to the exponential changes in porosity:
| (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 | permeability at reference pressure p_0 |
\phi_0 | porosity at reference pressure p_0 |
p_0 | reference pressure, usually picked up at initial reservoir 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.