4.5.2.1: Field and Well Performance with Arps Decline Curves

In a classic paper, J. J. Arps^[1] took many observations from other investigators and concluded that the decline in the oil production rate, $q_o$, over time from actual oil reservoirs could be described by the equations:

where the decline rate, $D$, is a time dependent function:

Where:

• $q_o$ is the oil production rate, STB/day
• $t$ is the time, days (other units of time, such as months or years, can be used with an appropriate unit conversion constant)
• $D$ is the time dependent decline rate (time dependence defined by Equation 4.63), days^-1
• $D_i$ is the initial decline rate (constant), days^-1
• $b$ is a constant (typically used as a tuning parameter to match actual field data) and is in the range of $0\le b\le 1$, dimensionless

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, $q_{oi}$, $D_i$,and $b$ 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)