...
where
is running through wells with
formation pressure tests
and rates
For the steady state flow in finite reservoir the relationship between Boundary-average formation pressure
and Field-average formation pressure is going to be:| LaTeX Math Block |
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p_r = p_i + \frac{q_t}{2 \pi \sigma} \Bigg[ \ln \frac{r_e}{r_w} -0.5 \Bigg] |
| Expand |
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| LaTeX Math Block |
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| p_r = \frac{1}{V} \int p(r) dV = \frac{1}{\pi \, r_e^2 h} \int p(r) 2 \pi \, r \, h \, dr = \frac{2}{r_e^2} \int p(r) \, r \, dr |
| LaTeX Math Block |
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| p_r = \frac{2}{r_e^2} \int \Bigg[ p_i - \frac{q_t}{2\pi \sigma} \ln \frac{r}{r_w} \Bigg] \, r \, dr = p_i - \frac{q_t}{2\pi \sigma} \Bigg[ 2 \ln \frac{r}{r_w} -1 \Bigg] |
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