changes.mady.by.user Arthur Aslanyan (Nafta College)
Saved on Apr 30, 2019
Saved on May 23, 2023
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V_e = \pi r_e^2 h, \quad dV = 2\pi r \, h dr
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:
p(t,r) = p_e(t) + \frac{q_t}{2 \pi \sigma} \, \ln \frac{r}{r_e} = p_i + \frac{q_t}{2 \pi \sigma} \, \ln \frac{r}{r_e}
and substituting the above to
p_r = \frac{2}{r_e^2} \int \bigg[ p_i + \frac{q_t}{2\pi \sigma} \ln \frac{r}{r_e} \bigg] \, r \, dr = p_e(t)i - \frac{q_t}{4\pi \sigma}
