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 pressure log-derivative stays constant:
(2) | \Delta p ' = \frac{d \, \Delta p}{d \, \ln t} = \frac{q_t}{4 \pi \sigma} = \rm const |
This flow regime is native to pressure diffusion in vertical well, homogeneous reservoir and no boundary (see Fig. 1).
Fig. 1. PTA Diagnostic Plot with IARF regime developed after 100 hrs | Fig. 2. PTA Diagnostic Plot with IARF regime developed between 100 hrs and 1,000 hrs |
Snce IARf is normally