Time interval of pressure transition when pressure variation \Delta p is evolving logarithmically in time:
| (1) | \Delta p = p_{wf}(0) - p_{wf}(t) = p_{wf}(0) - p_i - \frac{q_t}{4 \pi \sigma} \, \bigg[ - 2S + \gamma - \ln \bigg( \frac{4 \chi t}{r_w^2} \bigg) \bigg] |
and hence the logarithmic pressure derivative stays constant:
| (2) | \Delta p ' = t \frac{d}{dt} \Delta p = \frac{q_t}{4 \pi \sigma} = \rm const |
This flow regime to pressure diffusion in vertical well, homogeneous reservoir and no boundary.