p(t = 0, {\bf r}) = p_i

\left[ a \cdot ( p(t, r ) - p_i) + b \cdot \frac{\partial p}{\partial r} \right]_{r \rightarrow \infty )} = p_i0

\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}{\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]