A New Approach to Estimating Reserves in a Shale
I recently had the opportunity to attend the SPE Annual Technical Conference and Exhibition (ATCE) in Florence, Italy (yes it was very nice). One of the highlights for me was a paper presented by Dr. Lee of Texas A&M University titled A Better Way To Forecast Production From Unconventional Gas Wells. The paper is SPE 134231 authored by Peter P. Valko and W. John Lee, both from Texas A&M University.
In this paper, and another paper authored by John Lee and Rod Sidle, Texas A&M (SPE 130102) a method for forecasting reserves using decline curves is presented. This method, termed “Stretched Exponential Decline” uses a different set of equations than most of us are used to using for forecasting these types of reserves.
Historically we have used equations developed by Arps in 1945 which describe three variations of the decline equations for exponential, hyperbolic and harmonic declines; the difference being the value of “b” the “decline exponent.” The general form of the equation is
q= qi/(1+bDit) (1/b)
Exponential decline (straight line on a semi-log graph) occurs when b=0. Hyperbolic decline occurs when b is between 0 and 1 and demonstrates a curved plot on a semi-log graph, like we have seen in shale gas wells during early time production; and harmonic decline occurs in the unique case when b=1.
In practical experience, hyperbolic declines are often used to forecast tight reservoirs, such as shales, since the shape of the early-time production data can be matched using these equations; however, it is not uncommon for “matched” b factors to be well in excess of 1, which is outside of the parameters described by Arps. The problem is when the b factor is 1 or greater the Arps equation will approach infinity; which is obviously not possible. In real life most evaluators deal with this problem by placing an arbitrary minimum limit on the production decline and forcing the forecast to an exponential decline late in the well’s life. This arbitrary minimum limit solves the problem of infinite reserves, but it is arbitrary and different evaluators may use different limits.
Lee et al’s Stretched Exponential Decline takes a different approach. This approach is totally empirical and can be thought of as a sum of a series of individual exponential declines with differing decline rates. In other words, it’s like a given shale well is producing from multiple smaller volumes with each behaving exponentially (heterogeneity). The mathematics are a little more complicated, and definitely outside the scope of this blog, but supposedly Valko has developed software to handle the difficult parts (I have yet to see or use the software).
The advantages of the Stretched Exponential Decline approach are many; including a bounded EUR (Estimated Ultimate Recovery) and a graphical straight line of recovery potential (rp) versus cumulative production. Experience with the Arps hyperbolic equation is that as more data become available over time for a given well the “matched” b factor is usually reduced from earlier matches suggesting early-time estimates of recoveries may be reduced over time (depending on how the “tail” was handled by the evaluator, as discussed earlier).
Using decline curves to determine reserves is a very common and important methodology available to the evaluator. This is even more important in the shale-type resource plays where other traditional methods of determining reserves are limited by data availability and our understanding of the production mechanism, and is compounded by the need to determine expected reserves early in the life of a play for business decisions such as leasing and drilling. I don’t know if the Stretched Exponential Decline method will catch on and become the norm, I guess it will depend on the ease of use and whether the economic software providers support it, but I applaud the effort to understand the production mechanism and attempt to create a usable model for the evaluator.
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