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.

We aim to replace the current industry-standard empirical forecasts of oil production from hydrofractured horizontal wells in shales with a statistically and physically robust, accurate and precise method of matching historic well performance and predicting well production for up to two more decades. Our Bakken oil forecasting method extends the previous work on predicting fieldwide gas production in the Barnett shale and merges it with our new scaling of oil production in the Bakken. We first divide the existing 14,678 horizontal oil wells in the Bakken into 12 static samples in which reservoir quality and completion technologies are similar. For each sample, we use a purely data-driven non-parametric approach to arrive at an appropriate generalized extreme value (GEV) distribution of oil production from that sample's dynamic well cohorts with at least 1, 2, 3, . . . years on production. From these well cohorts, we stitch together the P 50 , P 10 , and P 90 statistical well prototypes for each sample. These 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. Now we fit the parameters of our physical scaling model to the statistical well prototypes, and obtain a smooth extrapolation of oil production that is mechanistic, and not just a decline curve. At late times, we add radial inflow from the outside. By calculating the number of potential wells per square mile of each Bakken region (core and noncore), and scheduling future drilling programs, we stack up the extended well prototypes to obtain the plausible forecasts of oil production in the Bakken. We predict that Bakken will ultimately produce 5 billion barrels of oil from the existing wells, with the possible addition of 2 and 6 billion barrels from core and noncore areas, respectively.

A recent study by the Wall Street Journal reveals that the hydrofractured horizontal wells in shales have been producing less than the industrial forecasts with the empirical hyperbolic decline curve analysis (DCA). As an alternative to DCA, we introduce a simple, fast and accurate method of estimating ultimate recovery in oil shales. We adopt a physics-based scaling approach to analyze oil rates and ultimate recovery from 14,888 active horizontal oil wells in the Bakken shale. To predict the Estimated Ultimate Recovery (EUR), we collapse production records from individual horizontal shale oil wells onto two segments of a master curve: (1) We find that cumulative oil production from 4845 wells is still growing linearly with the square root of time; and (2) 6401 wells are already in exponential decline after approximately seven years on production. In addition, 2363 wells have discontinuous production records, because of refracturing or changes in downhole flowing pressure, and are matched with a linear combination of scaling curves superposed in time. The remaining 1279 new wells with less than 12 months on production have too few production records to allow for robust matches. These wells are scaled with the slopes of other comparable wells in the square-root-of-time flow regime. In the end, we predict that total ultimate recovery from all existing horizontal wells in Bakken will be some 4.5 billion barrels of oil. We also find that wells completed in the Middle Bakken formation, in general, produce more oil than those completed in the Upper Three Forks formation. The newly completed longer wells with larger hydrofractures have higher initial production rates, but they decline faster and have EURs similar to the cheaper old wells. There is little correlation among EUR, lateral length, and the number and size of hydrofractures. Therefore, technology may not help much in boosting production of new wells completed in the poor immature areas along the edges of the Williston Basin. Operators and policymakers may use our findings to optimize the possible futures of the Bakken shale and other plays. More importantly, the petroleum industry may adopt our physics-based method as an alternative to the overly optimistic hyperbolic DCA that yields an ‘illusory picture’ of shale oil resources.

SummaryOver the last six years, crude oil production from shales 1 and ultra-deep GOM 2 in the United States has accounted for most of the net increase of global oil production. Therefore, it is important to have a good predictive model of oil production and ultimate recovery in shale wells. Here we introduce a simple model of producing oil and solution gas from the horizontal hydrofractured wells. This model is consistent with the basic physics and geometry of the extraction process. We then apply our model thousands of wells in the Eagle Ford shale.Given well geometry, we obtain a one-dimensional nonlinear pressure diffusion equation that governs flow of mostly oil and solution gas. In principle, solutions of this equation depend on many parameters, but in practice and within a given oil shale, all but three can be fixed at typical values, leading to a nonlinear diffusion problem we linearize and solve exactly with a scaling "type" curve. After the initial 1-3 months of the generally unstable production, the scaled production rate declines as one over the square root of time early on and later it declines exponentially. The three governing parameters are the mean cumulative gas-oil ratio, GOR, the mass of saturated oil in place, M , and the characteristic time of pressure interference between each pair of consecutive hydrofractures, τ. This time depends on the effective formation permeability to oil, porosity, oil saturation, and the overall reservoir compressibility. GOR influences ultimate recovery, while the other two parameters determine where on the master curve production from a given well falls, depending on the M , and how it stretches or shrinks, depending on the τ. The distribution of τ also provides constraints on infill well locations. We implemented our automatic fitting procedure on a PC.In February 2017, there were 13,057 physical oil wells in the Eagle Ford shale. However, there were only 4,734 unallocated well records because of the peculiar reporting requirements in Texas, explained in the paper. This means that up to 71 physical wells can be reported as one unallocated lease production record in the Eagle Ford. Since we are only interested in black oil horizontal wells, we have selected 2,611 wells with at least 6 months of oil production, GOR less than 2500 scf/stb and liquid gravity less than 40 0 API. In practice, we match the production data for each well to a dimensionless 1 Strictly speaking, the calcarious and silicious mudrock reservoirs in the Bakken, Eagle Ford, Permian, etc. 2 Oil & gas production from federal leases on the continental shelf in the Gulf of Mexico, Tainter and Patzek (2011). SPE 187226-MSmaster curve with the recovery factor, RF = N p /M , as the y-axis and the dimensionless time, t/τ, as the x-axis. The match relies on adjusting the unknown parameters M and τ. Here N p is cumulative mass production of oil and t is elapsed time on production in months. 429 selected wells were still in the early time flow regime with t/τ < 1. In the remaining 2,182 wells, hydrofract...

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