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| p(t,r) = p_i + \frac{q_t}{4 \pi \sigma} {\rm Ei} \left(-\frac{r^2}{4 \chi t} \right) |
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Approximations
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| Pressure Drop |
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| \delta p = p_i - p_{wf}(t) = \frac{q_t}{4 \pi \sigma} {\rm Ei} \left(-\frac{r^2}{4 \chi t} \right) |
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| \delta p \sim \ln t + {\rm const}, \ t \gg \frac{r^2}{4\chi} |
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| Log derivative |
| LaTeX Math Block |
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| p' = t \frac{d (\delta p)}{dt} = \frac{q_t}{2\pi\sigma} \exp \left( - \frac{r^2}{4\chi t} \right) |
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| LaTeX Math Block |
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| p' \sim \rm const, \ t \gg \frac{r^2}{4\chi} |
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Fig. 1. PTA Diagnostic Plot for LSS pressure response for the 0.1 md reservoir in a close line source vicinity (0.1 m), which is about a typical wellbore size. One can easily see that with wellbore effects neglected even for a very low permeability reservoir the IARF regime is getting formed very early at 0.01 hr (36 s). |
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[ Radial Flow Pressure @model ] [ 1DR pressure diffusion of low-compressibility fluid ] [ Exponential Integral ]
