Natural gas from tight shale formations will provide the United States with a major source of energy over the next several decades. Estimates of gas production from these formations have mainly relied on formulas designed for wells with a different geometry. We consider the simplest model of gas production consistent with the basic physics and geometry of the extraction process. In principle, solutions of the model depend upon many parameters, but in practice and within a given gas field, all but two can be fixed at typical values, leading to a nonlinear diffusion problem we solve exactly with a scaling curve. The scaling curve production rate declines as 1 over the square root of time early on, and it later declines exponentially. This simple model provides a surprisingly accurate description of gas extraction from 8,294 wells in the United States' oldest shale play, the Barnett Shale. There is good agreement with the scaling theory for 2,057 horizontal wells in which production started to decline exponentially in less than 10 y. The remaining 6,237 horizontal wells in our analysis are too young for us to predict when exponential decline will set in, but the model can nevertheless be used to establish lower and upper bounds on well lifetime. Finally, we obtain upper and lower bounds on the gas that will be produced by the wells in our sample, individually and in total. The estimated ultimate recovery from our sample of 8,294 wells is between 10 and 20 trillion standard cubic feet.hydrofracturing | shale gas | scaling laws | energy resources | fracking T he fast progress of hydraulic fracturing technology (SI Text, Figs. S1 and S2) has led to the extraction of natural gas and oil from tens of thousands of wells drilled into mudrock (commonly called shale) formations. The wells are mainly in the United States, although there is significant potential on all continents (1). The "fracking" technology has generated considerable concern about environmental consequences (2, 3) and about whether hydrocarbon extraction from mudrocks will ultimately be profitable (4). The cumulative gas obtained from the hydrofractured horizontal wells and the profits to be made depend upon production rate. Because large-scale use of hydraulic fracturing in mudrocks is relatively new, data on the behavior of hydrofractured wells on the scale of 10 y or more are only now becoming available.There is more than a century of experience describing how petroleum and gas production declines over time for vertical wells. The vocabulary used to discuss this problem comes from a seminal paper by Arps (5), who discussed exponential, hyperbolic, harmonic, and geometric declines. Initially, these types of decline emerged as simple functions providing good fits to empirical data. Thirty-six years later, Fetkovich (6) showed how they arise from physical reasoning when liquid or gas flows radially inward from a large region to a vertical perforated tubing, where it is collected. For specialists in this area, the simplicity and familiarity of hyperbolic de...

The Permian Basin is being transformed by the "shale revolution" from a major conventional play to the world's largest unconventional play, but water management is critical in this semiarid region. Here we explore evolving issues associated with produced water (PW) management and hydraulic fracturing water demands based on detailed well-by-well analyses. Our results show that although conventional wells produce ∼13 times more water than oil (PW to oil ratio, PWOR = 13), this produced water has been mostly injected back into pressure-depleted oil-producing reservoirs for enhanced oil recovery. Unconventional horizontal wells use large volumes of water for hydraulic fracturing that increased by a factor of ∼10-16 per well and ∼7-10 if normalized by lateral well length (2008-2015). Although unconventional wells have a much lower PWOR of 3 versus 13 from conventional wells, this PW cannot be reinjected into the shale reservoirs but is disposed into nonproducing geologic intervals that could result in overpressuring and induced seismicity. The potential for PW reuse from unconventional wells is high because PW volumes can support hydraulic fracturing water demand based on 2014 data. Reuse of PW with minimal treatment (clean brine) can partially mitigate PW injection concerns while reducing water demand for hydraulic fracturing.

A B S T R A C TAssessing the production potential of shale gas can be assisted by constructing a simple, physics-based model for the productivity of individual wells. We adopt the simplest plausible physical model: one-dimensional pressure diffusion from a cuboid region with the effective area of hydrofractures as base and the length of horizontal well as height. We formulate a nonlinear initial boundary value problem for transient flow of real gas that may sorb on the rock and solve it numerically. In principle, solutions of this problem depend on several parameters, but in practice within a given gas field, all but two can be fixed at typical values, providing a nearly universal curve for which only the appropriate scales of time in production and cumulative production need to be determined for each well. The scaling curve has the property that production rate declines as one over the square root of time until the well starts to be pressure depleted, and later it declines exponentially. We show that this simple model provides a surprisingly accurate description of gas extraction from 8305 horizontal wells in the United States' oldest shale play, the Barnett Shale. Good agreement exists with the scaling theory for 2133 horizontal wells in which production started to decline exponentially in less than 10 yr. We provide upper and lower bounds on the time in production and original gas in place.

Production of oil from shale and tight reservoirs accounted for almost 50% of 2016 total U.S. production and is projected to continue growing. The objective of our analysis was to quantify the water outlook for future shale oil development using the Eagle Ford Shale as a case study. We developed a water outlook model that projects water use for hydraulic fracturing (HF) and flowback and produced water (FP) volumes based on expected energy prices; historical oil, natural gas, and water-production decline data per well; projected well spacing; and well economics. The number of wells projected to be drilled in the Eagle Ford through 2045 is almost linearly related to oil price, ranging from 20 000 wells at $30/barrel (bbl) oil to 97 000 wells at $100/bbl oil. Projected FP water volumes range from 20% to 40% of HF across the play. Our base reference oil price of $50/bbl would result in 40 000 additional wells and related HF of 265 × 10 gal and FP of 85 × 10 gal. The presented water outlooks for HF and FP water volumes can be used to assess future water sourcing and wastewater disposal or reuse, and to inform policy discussions.