PNG 301
Introduction to Petroleum and Natural Gas Engineering 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:

1 q o q o t =D
Equation 4.68

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

D= D i 1+b D i t
Equation 4.69


  • 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 0b1 , 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)