Modelling facility for field-average formation pressure $\begin{array}{l}p(t)\end{array}$ at any time moment $\begin{array}{l}t\end{array}$ as response to production flowrates history:

(1)	$\begin{array}{l}\displaystyle V_e \int_{p_i}^p \phi_e(p) \, c_t(p) \, dp = Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)\end{array}$

where

$\begin{array}{l}p_i = p(0)\end{array}$	initial formation pressure
$\begin{array}{l}Q^{\uparrow}_t(t)\end{array}$	cumulative offtakes by the time moment $\begin{array}{l}t\end{array}$
$\begin{array}{l}Q^{\downarrow}_t(t)\end{array}$	cumulative intakes by the time moment $\begin{array}{l}t\end{array}$
$\begin{array}{l}\phi_e(p)\end{array}$	effective porosity as function of formation pressure $\begin{array}{l}p(t)\end{array}$
$\begin{array}{l}c_t(p)\end{array}$	total compressibility as function of formation pressure $\begin{array}{l}p(t)\end{array}$
$\begin{array}{l}V_e = A_e \, h_{eff}\end{array}$	drainage volume
$\begin{array}{l}A_e\end{array}$	drainage area
$\begin{array}{l}h_{eff}\end{array}$	effective formation thickness averaged over drainage area

For low compressibility rocks and fluids $\begin{array}{l}\{ \phi_e = {\rm const}, \ c_t = {\rm const} \}\end{array}$ the MatBal equation (1) can be explicitly integrated:

(2)	$\begin{array}{l}\displaystyle p(t) = p_i - \frac{Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)}{V_e\cdot \phi_e \cdot c_t}\end{array}$

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MatBal Pressure @model

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