Arp's mathematical model of Decline Curve Analysis is based on the following equation:

(1)	$\begin{array}{l}\displaystyle q(t)=q_{i} \cdot \left( 1+b \cdot D \cdot t \right)^{-1/b}\end{array}$

where

$\begin{array}{l}q_i = q(t=0)\end{array}$	Initial production rate of a well (or groups of wells)
$\begin{array}{l}D=-\frac{1}{q}\frac{dq}{dt}\end{array}$	decline decrement (the higher the $\begin{array}{l}D\end{array}$ the stringer is decline)
$\begin{array}{l}0 \leq b \leq 1\end{array}$	defines the type of decline (see below)

The cumulative production is then:

(2)	$\begin{array}{l}\displaystyle Q(t)=\int_0^t q(t) dt\end{array}$

Power Loss

$\begin{array}{l}D=D_{\infty} + \frac{t^{n-1}}{\tau^{n}}\end{array}$

(3)	$\begin{array}{l}\displaystyle q(t)=q_{i} \exp \left( -D_{\infty}t- \left( t/\tau \right)^{n} \right)\end{array}$

Page tree

See Also