changes.mady.by.user Arthur Aslanyan (Nafta College)
Saved on Mar 23, 2019
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\frac{\partial p}{\partial t} = \chi \, \left( \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right)
p(t = 0, {\bf r}) = p_i
p(t, r \rightarrow \infty ) = p_i
\left[ r\frac{\partial p(t, r )}{\partial r} \right]_{r \rightarrow r_w} = \frac{q_t}{2 \pi \sigma}
p_{wf}= p(r_w ) - S \cdot r_w \, \frac{\partial p}{\partial r} \Bigg|_{r=r_w}
p(t,r) = p_i - \frac{q_t}{4 \pi \sigma} \, F \bigg( - \frac{r^2}{4 \chi t} \bigg)
p_{wf}(t) = p_i - \frac{q_t}{4 \pi \sigma} \, \bigg[2S + F \bigg( - \frac{r_w^2}{4 \chi t} \bigg) \bigg]
where
