changes.mady.by.user Arthur Aslanyan (Nafta College)
Saved on Mar 23, 2019
Saved on Mar 24, 2019
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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 = r_w} = \frac{q_t}{2 \pi \sigma}
p_{wf}(t)= p(t, r_w) - S \cdot \left[ r \frac{\partial p(t,r)}{\partial r} \right]_{r=r_w} = p(t, r_w) - \frac{q_t}{2 \pi \sigma} S
It is important to note that equations
p(t,r) = p_i - \frac{{\rm w \,} q_t }{V_e \, \phi \, c_t} \, t + \frac{{\rm w \,} q_t }{4\pi \sigma} \left[ 2 \ln \frac{r}{r_e} - \frac{r^2}{r_e^2} + 1 \right] , \quad r_{wf} < r \leq r_e, \quad {\rm w }= 1 - \frac{r_w^2}{r_e^2}
p_e(t) = p_i - \frac{{\rm w \,} q_t}{V_e \phi c_t}t
p_{wf}(t) = p_e(t) - \frac{q_t}{2 \pi \sigma} \, \left[ {\rm w\, } \ln \frac{r_e}{r_w} + 0.5 + S \right]
