Time interval of pressure transition when pressure variation
is evolving logarithmically in time:
| LaTeX Math Block |
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\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:
| LaTeX Math Block |
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\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).
