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 is formation compressibility, k_0 is permeability at reference pressure p_0 (usually picked up at initial reservoir pressure p_0 = p_i ), n_k is power degree of permeability-porosity correlation:
| (2) | k = k_0 \left( \frac{\phi}{\phi_0} \right)^{n_k} |
The above correlation 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.