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A production rate equation which is hyperbolic early in the well life but asymptoticilly exponential is presented. Parameters in the equation are easily determined and interpreted.
The most frequently used mathematical expressions for production decline curves are the exponential and hyperbolic functions given by :
q = qo exp (-bt)...............(1)
q - qo/(1 + bt/N')n'...........(2)
These functions may need to be applied in a piecewise fashion in order to represent times of different flow regimes or field operating conditions. Even for long periods of operational stability, however, neither function may adequately represent actual productions rates. It is common to find a hyperbolic function applied to the early stages of production with an exponential "tail" chosen to represent the later stages of well life. Long and Davis have recently described a graphical overlay technique which determines the hyperbolic parameters and permits the selection of an appropriate terminating exponential permits the selection of an appropriate terminating exponential decline.
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