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Time interval of pressure transition when pressure variation
is evolving logarithmically in time:
| LaTeX Math Block |
|---|
|
p_{wf}(t) = p_i + \frac{q_t}{4 \pi \sigma} \, \bigg[ - 2S + \gamma
- \ln \bigg( \frac{4 \chi t}{r_w^2} \bigg) \bigg]
\\
\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:
| LaTeX Math Block |
|---|
|
\Delta p ' = t \frac{d}{dt} \Delta p = \frac{q_t}{4 \pi \sigma} = \rm const |
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