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p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS |
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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| V = \pi r_e^2 h, \quad dV = 2\pi r \, h, dr |
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| p_r = \frac{1}{V} \int p(r) dV = \frac{2}{r_e^2} \int p(r) \, r \, dr = \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_e}{r_w} -1 \bigg] |
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See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Well & Reservoir Management / Formation pressure (Pe)
Subsurface E&P Disciplines / Production Technology
[Reservoir pressure] [Initial formation pressure, Pi] [Drilled formation pressure, Pd] [Startup formation pressure, P0] [ Multiphase formation pressure ]
