Abstract
Nearly all the decline curve equations used today are based on the Arps hyperbolic equation1 , given as:
Using this equation, the production rate ‘Q’ at anytime ‘t’ can be calculated from the hyperbolic exponent ‘b’, the initial production rate ‘Q0’ and its corresponding decline rate ‘D0’ at time zero.
Although Equation (1) is easy to use, the variation of the decline rate with time (except b = 0) limits the applicability of the equation. For a hyperbolic decline curve (b>0), if a different production rate ‘Qi’ on the curve is used an initial rate, a different corresponding decline rate ‘Di’ needs to be identified for the equation to represent the same decline curve. Moreover, if there is a rate or reference time change in the production forecast period, the identified hyperbolic equation from the production history is no longer applicable.
In this paper, a generalized hyperbolic equation is derived to overcome the above limitations. Once a set of ‘Q0’, ‘D0’ and ‘b’ is identified from the production history, the equation can be used to predict the future rate regardless of the initial rate or time change.