Significance: Ten years ago, US natural gas cost 50% more than that from Russia. Now, it is threefold less. US gas prices plummeted because of the shale gas revolution. However, a key question remains: At what rate will the new hydrofractured horizontal wells in shales continue to produce gas? We analyze the simplest model of gas production consistent with basic physics of the extraction process. Its exact solution produces a nearly universal scaling law for gas wells in each shale play, where production first declines as 1 over the square root of time and then exponentially. The result is a surprisingly accurate description of gas extraction from thousands of wells in the United States’ oldest shale play, the Barnett Shale.

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.

Assessing 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. NOMENCLATURE Symbols and dimensions of key quantities Symbol SI dimensions Field dimensions c –compressibility Pa − 1 μ cip d –half-distance between hydrofractures m ft D –production decline coefficient k –permeability m 2 darcy K –partitioning coefficient m –gas pseudopressure Pa s − 1 psi 2 / cp m –cumulative produced mass kg ton M –Original gas in place kg ton M –molecular weight kmol lbmol H –formation thickness m ft p –pressure Pa psi q –volumetric flow rate m 3 s − 1 bbl/d Q –volumetric cumulative production m 3 bbl R —universal gas constant J/kmol-K psi-ft3/lb-mol RF –recovery factor S –saturation t –time in production s month, y T –temperature K °F, °C v ^ –specific volume m 3 / kg ft 3 / lbm y –molar composition Z –compressibility factor α –hydraulic diffusivity m 2 s − 1 ft 2 / y κ –dimensionless constant for gas production in square root phase K –dimensional constant for gas production in square root phase kg / s ton / month μ –gas viscosity Pa s cp ρ –density kg m − 3 lbm / ft 3 τ –time to interference s y ϕ –porosity Subscripts and Superscripts Symbol Meaning a adsorbed f (hydro)fracture g gas i initial L Langmuir S T stock tank conditions w water w c connate water ∼ dimensionless ∧ specific 0 reference or standard conditions