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p_r = \frac{1}{V_e} \iint_{A_e} p(x,y,z) dV |
For the steady state flow in Steady State Radial Flow in finite reservoir the relationship between Boundary-average formation pressure
and
Field-average formation pressure is going to be:
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| V_e = \pi r_e^2 h, \quad dV = 2\pi r \, h dr |
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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 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}{2 \pi \sigma} \, \ln \frac{r}{r_e} = p_{wf} + \frac{q_t}{2 \pi \sigma} \, \ln \frac{r}{r_w} , \quad r_{wf} < r \leq r_e |
and substituting the above to LaTeX Math Block Reference |
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| and integrating: 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}{4\pi \sigma} |
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