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

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

(2)	$\begin{array}{l}\displaystyle D(t) = D_0 ( 1 + a \cdot (n+1) \cdot t^n )\end{array}$

where

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

DCA Power Law decline is an empirical correlation for production from the infinite-reserves $\begin{array}{l}Q_{\rm max} \leq \infty\end{array}$ reservoir.

Alternative form

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

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

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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Alternative form

See Also

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DCA Power Law @model

Alternative form

See Also