Generalized Extreme Value Statistics, Physical Scaling and Forecasts of Oil Production from All Vertical Wells in the Permian Basin

Abstract

We analyze nearly half a million vertical wells completed since the 1930s in the most prolific petroleum province in the U.S., the Permian Basin. We apply a physics-guided, data-driven forecasting approach to estimate the remaining hydrocarbons in these historical wells and the probabilities of well survival. First, we cluster the production data set into 192 spatiotemporal well cohorts based on 4 reservoir ages, 6 sub-plays, and 8 completion date intervals. Second, for each cohort, we apply the Generalized Extreme Value (GEV) statistics to each year of oil production from every well in this cohort, obtaining historical well prototypes. Third, we derive a novel physical scaling that extends these well prototypes for several more decades. Fourth, we calculate the probabilities of well survival and observe that a vertical well in the Permian can operate for 10–100 years, depending on the sub-play and reservoir to which this well belongs. Fifth, we estimate the total field production of all existing vertical wells in the Permian by replacing historical production from each well with its prototype. We then time-shift and sum up these prototypes together, obtaining 34 billion barrels of oil as estimated ultimate recovery (EUR). Our most notable finding is that the rate of finding big reservoirs in the Permian has been declining drastically and irreversibly since the 1970s. Today, operators need to drill wells that are twice as deep as the 1930s’ wells, yet they produce 4–12 times less.