Generalized Extreme Value Statistics, Physical Scaling, and Forecasts of Gas Production in the Barnett Shale

Abstract

We develop a new method of predicting fieldwide gas or oil production from unconventional reservoirs, using the Barnett shale as an illustration. First, we divide the qualifying 13 141 horizontal gas wells in the Barnett into six static samples in which reservoir quality and completion technologies are similar. These samples contain wells of all ages. The Barnett samples coincide with the main gas producing counties, Tarrant, Johnson, Denton, Wise, Parker, and Hood. Second, for each sample, we use a purely data-driven nonparametric approach to arrive at appropriate generalized extreme value (GEV) distributions of gas production from the sample’s dynamic well cohorts with at least 1, 2, 3, ..., up to 14 years on production. We now have up to 14 cumulative probability distribution functions (cdfs) of annual well productivity per sample. From these cdfs, we stitch together six P 50, P 10, and P 90 statistical well prototypes, one per sample or county. Our statistical well prototypes are conditioned by well attrition, hydrofracture deterioration, pressure interference, well interference, progress in technology, and so forth. So far, there has been no physical scaling. Third, we fit the parameters of our physical scaling model to the statistical well prototypes and obtain their smooth extrapolations to 30 years on production. At late times, we add radial inflow of gas external to the stimulated reservoir volumes of the mean wells. Fourth, we calculate the number of potential wells per square mile of each Barnett county and schedule future drilling programs. We then stack up the extended well prototypes to obtain the plausible forecasts of gas production in the Barnett until the year 2034. We predict that the six Barnett counties will ultimately produce 24.5 trillion standard cubic feet (Tscf) of gas from the existing wells. On energy equivalent basis, in this “do nothing” scenario, these counties will produce 4.2 billion barrels of oil equivalent, making it one of the top producers of fuel for the US. Finally, we consider a possible addition of 4.5 Tscf from the future 3570 surviving wells or 6800 new wells drilled between 2019 and 2028. On the average, only 1/2 of the current Barnett wells will survive beyond 15 years on production.

Physical Scaling Predicts Oil Production Rates and Ultimate Recovery from All Horizontal Wells in the Bakken Shale

“…Elsewhere [33], we outline a hybrid method that combines the precise GEV statistics of horizontal oil wells in the Bakken with the physics-based scaling method developed in this paper and combined with late-time inflow [45]. This hybrid approach follows from our comprehensive evaluation of the Barnett play futures [34].…”

“…Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 25 December 2019 doi:10.20944/preprints201912.0334.v1 Figure 6. (Left) The probability density function (PDF) and (Right) the cumulative distribution function (CDF) of oil rate for the Bakken wells after 12 months on production [33,34]. The field data were fit with the generalized extreme value (GEV) distribution function that matches perfectly the experimental probability distributions.…”

“…This distribution is positively skewed, meaning that the majority of Bakken wells have low oil rates and the best wells with the significantly higher oil rates in the long tail are rare. The Generalized Extreme Value (GEV) distribution is most suitable to model the empirical oil rate distribution in the Bakken and other shales [33][34][35]. Using the GEV statistics of well populations, we calculate the high (P 10 ), mean (P 50 ), and low (P 90 ), oil rate values from the cumulative distribution function (CDF).…”

“…have fewer years on production because they were drilled after the year 2010. The P 10 , P 50 , and P 90 wells were calculated with the method discussed elsewhere [33,34] and in the caption of Figure 6. The expected (P ) maximum oil rate and cumulative oil are about 500 bbl/d and 200,000 bbl of oil for both Bakken and Three Forks.…”

“…The lines show the corresponding EUR values from the physical scaling and the EIA statistical predictions. The P 10 , P 50 , and P 90 wells were obtained by applying the generalized extreme value (GEV) distribution [33,34] for each set of EURs from the scaling curve method in each sub-region as demonstrated before in Figure 6. In most cases, where there are enough wells per sample, the expected P 50 EURs from physical scaling agree with the EUR estimates by EIA.…”