When does the extrapolation of a shale gas well's production decline curve transition from a hyperbolic to an exponential decline flow regime? This was one of the issues examined in assessing ultimate recoveries from shale gas wells in Ryder Scott Co. LP's September-November 2011 quarterly newsletter.
Production decline curves use empirical equations developed before 1945 by J.J. Arps and others. These equations have found wide use in the industry because they are simple and fast for estimating future recovery from a well or field.
Decline curves
The decline curve equations have problems when applied to tight gas reservoirs such as shales. One problem explained in the newsletter is that Arps based the equations on boundary-dominated flow, which conventional reservoirs reach in months compared with years in shales.
Arps also in his hyperbolic equation defined the b exponent as being between 0 and 1, but as explained in the newsletter this does not mesh with actual observations where in some cases b approaches 2. Another observation noted is that b values decrease as the well transitions to boundary-dominated flow and exponential flow.
For the exponential part of the curve, evaluators often use a minimum decline in the production tail that may last for 25 years or more, the newsletter explained.
As an example of b and Dmin in five shale plays, the newsletter gave values from Jason Baihly et al. paper SPE 135555, as follows:
- Barnett: b = 1.5933, Dmin = 0.0089.
- Fayetteville: b = 0.6377, Dmin = 0.0325.
- Woodford: b = 0.8436, Dmin = 0.0227.
- Haynesville: b = 1.1852, Dmin = 0.0632.
- Eagle Ford: b = 1.694, Dmin = 0.0826.
A high Dmin will understate reserves and conversely a low Dmin will overstate them.
The newsletter explained that evaluators also often use analogs from wells in the same field to generate type curves because early-time decline is often difficult to define.
Type curves require wells with comparable completions such as similar frac length, sand concentration, lateral length, hole orientation, reservoir properties, and well spacing. These factors often vary from well to well in shale plays.
The newsletter explains two ways to find the end of transient flow. One is the time at which the upward curvature of flow rate on a log-log plot ends, as discussed by Fetkovich and others. A more complicated method involves plotting an inverse of flow rate vs. the square root of time multiplied by time. In this method, linear flow ends when the straight line curves down.
New techniques
The industry has developed new methods for decline curves that may hold promise.
One method is the stretched-exponential production decline (SEPD). The newsletter notes that the stretched exponential function was first introduced in the mid-1800s to describe capacitor discharge.
In shale gas well evaluation, the SEPD technique models fracture-dominated flow by considering the reservoir to be heterogeneous and consisting of many contributing volumes individually in exponential decline, as discussed in paper SPE 134231 by John Lee and Peter Valko.
The newsletter notes that the SEPD model modestly improves Arps' hyperbolic because it eliminates the need for Dmin.
Another method introduced by Anh N. Duong of ConocoPhillips in paper SPE 137748 uses an empirically derived decline model based on long-term linear flow for a large number of wells in tight shale gas reservoirs.
The newsletter quotes Lee, a professor at the University of Houston, as saying, "The method that looks best to me is not the SEPD model, but the method proposed by Duong."
Lee said, "We have not found a single case with decent data in which the method failed and it works in the Bakken oil shales, Barnett gas shales, and elsewhere."
The newsletter further adds Lee as explaining that although some companies have publicly stated their use of Arps with no Dmin, "I believe that Arps, with or without Dmin, is subject to abuse and is, in fact, abused regularly.
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