The Dynamic Context Server features an interactive Bakken Oil model showing the Red Queen effect. The model uses historical oil well count and cumulative production to estimate average well output over time and then project that a number of months into the future.
The North Dakota Mineral Resources Department releases monthly data which we use to fit against. The start of the model is set to when the oil production statistics began and continues to the recent month 378:
DC at the peak oil climate and sustainability blog recommended a projected growth of 150 new wells a month.
This leads to a maximum asymptotic value of 1.4 million barrels a day.
The Red Queen dilemma describes the effect of requiring ever increasing rates of increase to make up for quickly declining wells. Depending on the ultimate reserve potential of the Bakken formation, the production may never reach close to 1.4 million barrels per day before the number of new wells starts to decline.
Note: The early data from NoDak is contaminated with production from conventional non-fracked wells. In terms of a fit for recent data this does not make much of a difference, but as DC notes, it will not give you insight into when the fracking actually commenced and what the fracking baseline was, which may actually be about 25x lower in pre-boom times than that shown. In other words, the true Bakken output would have started much closer to zero in 1980 and the actual boom-era starting point is around 2002 or month 275 according to DC's analysis.