Power Law mathematical model of Decline Curve Analysis is based on the following equation:

(1)	$\begin{array}{l}\displaystyle q(t)=q_0 \cdot \exp \left[ -D(t) \cdot t \right] = q_0 \cdot \exp \left[ -D_0 \cdot t- a \cdot t^{n+1} \right]\end{array}$

where

$\begin{array}{l}q_0 = q(t=0)\end{array}$	Initial production rate of a well (or groups of wells)
$\begin{array}{l}D_0\end{array}$	initial production decline rate
$\begin{array}{l}\displaystyle D(t) =- \frac{dq}{dQ}\end{array}$	production decline rate
$\begin{array}{l}\displaystyle Q(t)=\int_0^t q(t) dt\end{array}$	cumulative production

Alternative form

The original form was developed as correction of Arps for tight gas and shales:

(2)	$\begin{array}{l}\displaystyle q(t)=q_0 \cdot \exp \left( -D_{\infty}t- \left( t/\tau \right)^{n} \right)\end{array}$

where

$\begin{array}{l}D_{\infty}\end{array}$

decline decrement at long times (the higher the $\begin{array}{l}D\end{array}$ the stronger is decline)

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