| THEORY & FORMULAE |
Production decline is assumed to obey the general rate-versus-time expression:
where:
q = production rate
t = time
K = decline constant
n = decline exponent
K and n are the 2 unknown non-negative parameters.
The solution of this equation leads to the two-parameter non-linear Hyperbolic Decline equation: 
where:
qt = production rate at time t
qi = initial production rate
There are 2 special cases of the hyperbolic decline curve: the Exponential curve and the Harmonic curve.
If n = 0, the rate equation reduces to a one-parameter Exponential decline equation:
If n = 1, the rate equation reduces to the one-parameter Harmonic decline equation:
For a given series of production rate data over time, the constant parameters can be determined by a non-linear least-squares fitting method. The Marquardt's method is employed here. This numerical approach leads to a unique unbiased interpretation, and eliminates the trial-and-error graphical and type-curve approaches.
Once the parameters are known the equations can then be used for the prediction of future rates and cumulatives. The equations for cumulatives at time t (Qt) are as follows:
Hyperbolic Cumulatives:
Exponential Cumulatives:
Harmonic Cumulatives:
As implemented here, a user can enter between 6 to 20 consecutive observed rates at constant timesteps. To ensure an overall declining trend, each of the last 3 observed rates must not be greater than 95% of each of the first 3 rates.
Extrapolation is performed to the 30th timestep. The user chooses one of four timesteps: monthly, quarterly, half-yearly and yearly. Also volumetric units can be in barrels for oil or 1000 standard cubic feet for gas.
Each of the three curves are fitted to the data, and the associated parameters displayed. Also displayed are R-Squared factors (range 0.0 to 1.0, usually > 0.9) which measures the goodness of fit - a higher values implies a better fit.
The user may also enter a minimum economic cut-off rate which will be shown as a green like in the Graph.