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time change in theproduction forecast period, the identified hyperbolic equationfrom the production history is no longer applicable.In this paper, a generalized hyperbolic equation is derived toovercome the above limitations.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