A method to numerically solve the two-parameter non-linear hyperbolic decline curve equation utilized in petroleum engineering is presented. The method only requires the initial production rate and cumulative production at two points in the decline trend to calculate the decline curve exponent 'n' and the initial decline rate Di. The proposed method eliminates the need for a trial and error estimation of 'n' or the need for type-curve or graphical analysis to determine the value of 'n'. This paper demonstrates that the decline curve exponent 'n' lies between negative infinity and positive infinity and includes the exponential (n=0) and harmonic (n=1) decline cases. The results of the application of the method to both published and field data, and a comparison of the results is presented.
As an adjunct to this work and for comparison, a two-dimensional, non-linear least squares regression analysis was used to calculate the two parameters, 'n' and Di. The regression analysis was based on a GAUSS-NEWTON type iterative technique which is capable of generating its own initial values. The results of using this regression analysis approach to the determination of 'n' and are in excellent agreement with the new numerical solution.