Modelling facility for 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)	$\begin{array}{l}\displaystyle A_e h_e \int_{p_i}^p \phi_e(p) \, c_t(p) \, dp = Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)\end{array}$

where

$\begin{array}{l}p_i = p(0)\end{array}$	initial formation pressure
$\begin{array}{l}\phi_e(p)\end{array}$	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 $\begin{array}{l}p(t)\end{array}$
$\begin{array}{l}A_e\end{array}$	drainage area
$\begin{array}{l}h_e\end{array}$	effective formation thickness averaged over drainage area
$\begin{array}{l}Q^{\uparrow}_t(t)\end{array}$	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 $\begin{array}{l}t\end{array}$

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

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

Page tree

See Also

Page tree

MatBal Pressure @model

See Also