Field-average formation pressure <Pe>

(1)	$\begin{array}{l}\displaystyle p_r = \sum_{k=1}^N {\rm w}_k \cdot p_{rk}, \quad {\rm w}_k = \frac{q_k}{\sum q_k}, \quad \sum {\rm w}_k = 1\end{array}$

where $\begin{array}{l}k=1..N\end{array}$ is running through wells with formation pressure tests $\begin{array}{l}p_{rk}\end{array}$ and rates $\begin{array}{l}q_k\end{array}$

For the steady state flow in finite reservoir the relationship between Boundary-average formation pressure $\begin{array}{l}p_e\end{array}$ and Field-average formation pressure $\begin{array}{l}p_r\end{array}$ is going to be:

(2)	$\begin{array}{l}\displaystyle p_r = p_i + \frac{q_t}{2 \pi \sigma} \Bigg[ \ln \frac{r_e}{r_w} -0.5 \Bigg]\end{array}$

Derivation

(3)	$\begin{array}{l}\displaystyle V = \pi r_e^2 h, \quad dV = 2\pi r \, h, dr\end{array}$

(4)	$\begin{array}{l}\displaystyle p_r = \frac{1}{V} \int p(r) dV = \frac{2}{r_e^2} \int p(r) \, r \, dr = \frac{2}{r_e^2} \int \Bigg[ p_i - \frac{q_t}{2\pi \sigma} \ln \frac{r}{r_w} \Bigg] \, r \, dr = p_i - \frac{q_t}{2\pi \sigma} \Bigg[ 2 \ln \frac{r}{r_w} -1 \Bigg]\end{array}$

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Field-average formation pressure <Pe>