1 Nov, 2018

Forecasting Oil and Gas Production For Unconventional Wells

Forecasting future oil and gas production for a well is one of the most important tasks of a reservoir engineer. These production forecasts are used for estimating remaining reserves, optimizing production operations and business planning, among other tasks. Similar to conventional wells, future oil and gas production for unconventional wells is often forecasted by fitting a curve through historical production volumes then extrapolating the curve to predict future production, a technique called decline curve analysis (DCA). The classic DCA method developed by Arps for conventional wells has been adapted for use with unconventional wells. The modified Arps method retains the original method for early time data then later imposes an exponential decline a specified decline such as 5%/yr.   

With little regard for reservoir physics, reservoir engineers began predicting future well performance with simple curve fits to production data early in the twentieth century. These early empirical methods were summarized and extended in a semi-empirical, semi-rigorous method based on assumptions about the well and the reservoir it is draining by Arps in 19441. Oil production was described by a simple equation with three empirical coefficients. 


A plot of the Arps equation fit to production data is shown in Figure 1. Arps hyperbolic plots typically show a steep initial decline followed by an extended period of gentle decline. At late times, the calculated decline rate can fall to a value of 1%/yr or less.

Figure 1. Arps hyperbolic decline curve fit to data


For reserves purposes, the decreasing production rate is often described with the effective decline rate. The Arps coefficient Di is related to the effective decline rate by:

The effective decline rate for the above example is 85.0 %/yr.


Unique to each well, the three Arps coefficients, qi, Di, and b, are determined by the curve fit exercise. Both the initial production rate and initial decline rate have physical meaning but the Arps b value does not. Arps noted in his experience the b value ranged between 0 and 1 with the majority between 0 and 0.4. A b value of 0 leads to the special case of exponential decline:

And a b value of 1 gives the special case of harmonic decline:

Although Arps did not discuss b values greater than one, reservoir engineers soon discovered that such values were usually associated with transient flow data, violating Arps’ assumption that the well is in boundary dominated flow. The resulting forecasted rates and recoveries were erroneously high. However, sporadic reports of credible b values greater than one were discussed by Long and Davis2 and they proposed a modified Arps method for such cases. When the decline rate of the hyperbolic curve fell to a specified limiting rate - for example, 6%/year - an exponential decline was used to forecast future production.

With the emergence of unconventional wells, especially long horizontal laterals, in the last twenty years, Arps b values greater than one are quite common. These wells often experience linear flow for a large portion of their life. This flow regime is characterized by a b value of exactly 23.

Imposing a minimum terminal decline of 10%/yr on the above Arps curve (Fig 2) cases the forecast decline to switch to an exponential decline after 15.4 years.

Figure 2. Modified Arps curve with a 10% minimum terminal decline rate


This brief introduction to decline curve analysis introduced the classic Arps equation and the modern modified Arps method which is widely used to forecast future production from unconventional wells. Given the difficulty and poor understanding of production mechanisms in shale formations, decline curve analysis is an important approach to forecasting performance for wells producing from these reservoirs. Multiple PetroSkills classes extend this brief introduction to include wells producing gas or condensate, discuss other decline methods for unconventionals such as the Duong and stretched exponential decline models, and introduce methods to detect well interference, reservoir pressure dropping below bubble point or dew point, and diagnostic methods to determine flow regime.

If you are interested in learning more about advanced decline curve analysis and reserve estimation techniques, we recommend enrolling in the following related courses. 


Written By: Dr. John P. Seidle

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1. Arps, J. J, 1944, “Analysis of Decline Curves”, Trans. AIME (1945), vol 160, p. 228.

2. Long, D. R., and Davis, M. J., 1987, “A New Approach to the Hyperbolic Curve”, SPE 16237.

3. Lee, W. J., 2016, Chapter 6 in SPEE Monograph 4, Estimating Ultimate Recovery of Developed Wells in Unconventional Reservoirs.