This post is by Dennis Coyne
The eventual peak and decline of light tight oil (LTO) output in the Bakken/ Three Forks play of North Dakota and Montana and the Eagle Ford play of Texas are topics of much conversation at the Peak Oil Barrel and elsewhere.
The decline rates of individual wells are very steep, especially early in the life of the well (as much as 75% in the first year for the average Eagle Ford well), though the decline rates become lower over time and eventually stabilize at around 6 to 7% per year in the Bakken.
What is not obvious is that for the entire field (or play), the decline rates are not as steep as the decline rate for individual wells. I will present a couple of simple model to illustrate this concept.
Much of the presentation is a review of ideas that I have learned from Rune Likvern and Paul Pukite (aka Webhubbletelescope), though any errors in the analysis are mine.
A key idea underlying the analysis is that of convolution. I will attempt an explanation of the concept which many people find difficult.
At Wikipedia there is a fairly mathematical presentation of the concepts which often confuses people. There are a couple of nice visuals to convey the concept as well see this page.
In the visual below a function f (in blue) is convolved with a function g (in red) to produce a third function (in black) which we could call h where h=f*g and the asterisk represents convolution, just as a + symbol is used to represent addition.
“Convolution of box signal with itself2” by Convolution_of_box_signal_with_itself.gif: Brian Amberg
derivative work: Tinos (talk) – Convolution_of_box_signal_with_itself.gif. Licensed under CC BY-SA 3.0 via Wikimedia Commons.
I think the best way to present convolution is with pictures. Chart A below shows a relationship between oil output (in barrels per month) and months from the first oil output for the average well in an unspecified LTO play.
This relationship is a simple hyperbola of the form q=a/(1+kt), where a and k are constants of 13,000 and 0.25 respectively, t is time in months, and q is oil output.
Chart A is often referred to as a well profile. The values for the constants were chosen to make the well profile fairly similar to an Eagle Ford average well profile. EUR30 is the estimated ultimate recovery from this average well over a 30 year well life.
