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| V_e = \pi r_e^2 h, \quad dV = 2\pi r \, h dr |
LaTeX Math Block |
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| p_r = \frac{1}{V_e} \int p(r) dV = \frac{2}{r_e^2} \int p(r) \, r \, dr |
For the Pseudo-Steady State Radial Flow in finite reservoir the reservoir pressure is going to be: LaTeX Math Block |
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| p(r) = p_i + \frac{q_t}{4 \pi \sigma} \, \left[ 2 \ln \frac{r}{r_e} - \frac{r^2}{r_e^2} \right] |
and substituting the above to LaTeX Math Block Reference |
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| and integrating: LaTeX Math Block |
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| p_r(t) = \frac{2}{r_e^2} \int \bigg[ p_e(t) + \frac{q_t}{4\pi \sigma} \left[ 2 \ln \frac{r}{r_e} - \frac{r^2}{r_e^2} \right] \bigg] \, r \, dr = p_i - 0.75 \cdot \frac{q_t}{2\pi \sigma} |
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Petroleum Industry / Upstream / Production / Subsurface Production / Well & Reservoir Management / Formation pressure (Pe)
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