Specific type of production rate $\begin{array}{l}q(t)\end{array}$ decline:

(1)	$\begin{array}{l}\displaystyle q(t)=q_0 \exp \left( -D_0 \, t \right)\end{array}$

(2)	$\begin{array}{l}\displaystyle Q(t)=\frac{q_0-q(t)}{D_0}\end{array}$

(3)	$\begin{array}{l}\displaystyle Q_{\rm max}=\frac{q_0}{D_0}\end{array}$

(4)	$\begin{array}{l}\displaystyle D(t)=D_0 = \rm const\end{array}$

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 which in this specific case stays consant: $\begin{array}{l}D(t) = D_0 = \rm const\end{array}$
$\begin{array}{l}\displaystyle Q(t)=\int_0^t q(t) \, dt\end{array}$	cumulative production by the time moment $\begin{array}{l}t\end{array}$
$\begin{array}{l}Q_{\rm max} =\int_0^{\infty} q(t) \, dt\end{array}$	Estimated Ultimate Recovery (EUR)
$\begin{array}{l}\displaystyle D(t) = - \frac{dq}{dQ}\end{array}$	Production decline rate

It can be applied to any fluid production: water, oil or gas.

Exponential Production Decline has a physical meaning of producing from the finite-volume reservoir with finite reserves $\begin{array}{l}Q_{\rm max}\end{array}$ under Pseudo Steady State (PSS) conditions, resulting in constant Production decline rate $\begin{array}{l}D(t) = D_0 = \rm const\end{array}$ .

A typical example of various fitting efforts of Exponential Production Decline are brought on Fig. 1 – Fig. 3 with exponential fitting being a clear winner.


Fig. 1. Exponential best fit to Exponential Production Decline	Fig. 2. Hyperbolic best fit to Exponential Production Decline	Fig. 3. Harmonic best fit to Exponential Production Decline

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