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 |
k_0 | permeability at reference pressure p_0 (usually picked up at initial reservoir pressure p_0 = p_i ) |
n_k = \frac{\ln (k/k_0)}{\ln(\phi/\phi_0)} | power degree of permeability-porosity correlation |
The correlation (1) assumes constant formation compressibility which in most practical applications holds true in a wide range of pressure variations all the way down to porosity cut-off and all the way up to the fracture point.
The substantial reduction of formation pressure leads to shrinking a lot of 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.