In a classic paper, J. J. Arps[1] took many observations from other investigators and concluded that the decline in the oil production rate, , over time from actual oil reservoirs could be described by the equations:
where the decline rate, , is a time dependent function:
Where:
Decline curve analysis is essentially a curve fitting, or trend-line, analysis procedure where the form of the trend-line is developed from Arps[1] observations (Equation 4.68 and Equation 4.69). In this procedure, once the form of the trend-lines is established, we can use the parameters, , ,and to best match the data. We can develop these trend-lines or rate-time relationships if we integrate Equation 4.68 with respect to time. The resulting relationships have three forms depending on the value of the b-parameter.
[1] Arps, J. J.: “Analysis of Decline Curves,” SPE-945228-G, Trans. of the AIME (1945)