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

(1)	$\begin{array}{l}\displaystyle q(t) = \frac{q_0}{ \left( 1+b \cdot D_0 \cdot t \right)^{1/b} }\end{array}$

(2)	$\begin{array}{l}\displaystyle Q(t)=\frac{q_0}{D_0 \, (1-b)} \, \left[ 1- \left( \frac{q(t)}{q_0} \right)^{1-b} \right]\end{array}$

(3)	$\begin{array}{l}\displaystyle Q_{\rm max}=\frac{q_0}{D_0 \cdot (1-b)}\end{array}$

(4)	$\begin{array}{l}\displaystyle D(t) = \frac{D_0}{1+ b \cdot D_0 \cdot t}\end{array}$

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
$\begin{array}{l}0 < b < 1\end{array}$	model parameter characterizing the decline rate
$\begin{array}{l}\displaystyle Q(t)=\int_0^t q(t) \, dt\end{array}$	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.

Hyperbolic Production Decline is an empirical correlation for production from a finite-reserves $\begin{array}{l}Q_{\rm max} \leq \infty\end{array}$ reservoir.

The Production decline rate is starting at its maximum $\begin{array}{l}D_0\end{array}$ and then gradually reduces to zero.

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


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

Page tree

See Also