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

$\begin{array}{l}\displaystyle J(t) = \frac{4 \pi \sigma}{ \ln \frac{1.781 \cdot A_e^2}{ 4 \pi \chi t} }\end{array}$

where

$\begin{array}{l}Q_{WAQ}(t)\end{array}$	water influx from aquifer at time moment $\begin{array}{l}t\end{array}$
$\begin{array}{l}J(t)\end{array}$	aquifer productivity index at time moment $\begin{array}{l}t\end{array}$
$\begin{array}{l}p_i\end{array}$	initial formation pressure
$\begin{array}{l}p(t)\end{array}$	field-average formation pressure at time moment $\begin{array}{l}t\end{array}$
$\begin{array}{l}\sigma\end{array}$	aquifer transmissibility
$\begin{array}{l}\chi\end{array}$	aquifer diffusivity

This model is based on assumption of:

Reference

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