changes.mady.by.user Arthur Aslanyan (Nafta College)
Saved on Mar 23, 2019
...
r_{wf} < r \leq r_e
\frac{\partial p}{\partial t}= \chi \left[ \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right]
\left[ \frac{\partial p}{\partial r} \right]_{r=r_e} = 0
\left[ r\frac{\partial p(t,r )}{\partial r} \right]_{r \rightarrow r_w} = \frac{q_t}{2 \pi \sigma}
p_{wf}(t)= p(t, r_w ) - S \cdot r_w \, \frac{\partial p(t,r)}{\partial r} \Bigg|_{r=r_w}
p(r) = p_i - \frac{q_t}{V_e \, \phi \, c_t} \, t + \frac{q_t}{4\pi \sigma} \bigg[ 2 \ln \frac{r}{r_e} - \frac{r^2}{r_e^2} \bigg] , \quad r_{wf} < r \leq r_e
p_{wf}(t) = p_
e(t) - \frac{q_t}{2 \pi \sigma} \, \bigg[ S + \ln \frac{r_e}{r_w} \bigg]
p_e(t) = p_i - \frac{q_t}{V_e \phi c_t}t
