(1)	$\begin{array}{l}\displaystyle \frac{d Q_{WAQ}}{dt} + \frac{1}{\tau} Q_{WAQ} = J \cdot ( p_i - p(t))\end{array}$

$\begin{array}{l}\displaystyle J = \frac{2 \pi \sigma}{\ln \frac{A_{AQ}}{A_e} - \frac{3}{4} }\end{array}$

where

$\begin{array}{l}Q_{WAQ}(t)\end{array}$	water influx from aquifer at time moment $\begin{array}{l}t\end{array}$	$\begin{array}{l}\sigma\end{array}$	aquifer transmissibility
$\begin{array}{l}J = \rm const\end{array}$	aquifer productivity index	$\begin{array}{l}\displaystyle \tau = \frac{V_{WAQ} \, c_t}{J}\end{array}$	aquifer relaxation time
$\begin{array}{l}p_i\end{array}$	initial formation pressure	$\begin{array}{l}A_{AQ}\end{array}$	aquifer area
$\begin{array}{l}p(t)\end{array}$	field-average formation pressure at time moment $\begin{array}{l}t\end{array}$	$\begin{array}{l}A_e\end{array}$	pay area

This model is based on assumptions:

Derivation

Const PI expansion:

$\begin{array}{l}\displaystyle q_{WAQ} = \frac{d Q_{WAQ}}{dt} = J \cdot ( p_{AQ} - p(t))\end{array}$

Finite-volume reservoir PSS depletion:

$\begin{array}{l}\displaystyle p_{AQ} = p_i - \frac{Q_{WAQ}}{V_{WAQ} c_t}\end{array}$

Reference

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