Gas production in the Barnett Shale obeys a simple scaling theory

Abstract

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...

Trade-offs and Implications of Two-stage Versus One-stage Unconventional Oil and Gas Exploration and Production Investment Strategies: A Case Study of the Barnett Play

“…"First, it is an excellent example of parsimonious modeling: the development of a minimal-ingredients model that enables [it] to explain observations. Second, their theory can be used to estimate, with limited data, lower and upper bounds of cumulative production" (CuetoFelgueroso and Juanes 2013) <Figure 35> The gas production rate prediction model (Patzek, Male, and Marder 2013) This analysis uses an expanded data set which consists of 18,184 wells for which EURs are determined in the same methodology as Patzek, Male, and Marder (2013). Then, the selected wells' EURs are selected from the 18,184 wells and added to determine the total EUR of each strategy ( …”

Economic appraisal of shale gas resources, an example from the Horn River shale gas play, Canada

“…In a recent study, Patzek et al (2013) proposed a ''diffusion-type'' equation to model production decline from shale reservoirs. By introducing physical mechanisms behind natural gas recovery for shale formations to the production rate, this model represents a contribution toward reducing uncertainty (Cueto-Felguerosoa and Juanesa 2013).…”

Natural gas: The fracking fallacy

“…The research was funded by a US$1.5-million grant from the Alfred P. Sloan Foundation in New York City, and has been appearing gradually in academic journals [1][2][3][4][5] and conference presentations. That work is the "most authoritative" in this area so far, says Weijermars.…”