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.

Keywords: energy resources; fracking; hydrofracturing; scaling laws; shale gas.

Fig. 1.

Horizontal well with 10–20 hydrofracture “stages” spaced uniformly along its entire length. The common fracture height is H, and the tip-to-tip length of each fracture is 2L. The distance between the hydrofractures is 2d. Gas flows into each fracture plane from both sides, and the permeability of a hydrofracture is assumed to be infinite in comparison to the effective permeability of the rock matrix and natural fractures feeding gas into it.

Fig. 2.

Cumulative production and production rate from scaling theory. (A) Dimensionless RF vs. dimensionless time computed from the scaling solution (black) compared with five typical wells (burnt orange). The fracture pressure p_f is 500 psi, and the initial reservoir pressure p_i is 3,500 psi. (B) Dimensionless well production rate vs. dimensionless time (black) under the same conditions compared with the same five typical wells (burnt orange). Production rates of individual wells are noisy, although cumulative production matches the scaling function well. Because the production rate becomes linear on a semilog plot, production decline is exponential for .

Fig. 3.

Comparison of 8,294 wells with scaling function. (A) Time history of 2,057 wells in the Barnett Shale, scaled so as to fit our scaling function (initial reservoir pressure of 3,500 psi and well flowing pressure of 500 psi), for which the dimensionless time starts below 0.25 and reaches 0.64 or more. The burnt orange curves give the scaled production of each well, and the black curve is the scaling function. Overall agreement is satisfactory. (B) Time history of 6,237 wells in the Barnett Shale for which the scaled maximum time comes out as (burnt orange). These wells are too young to trust our estimate of the interference time τ; therefore, we simply compare them with a square root function (black line). Time is scaled by the maximum time reached for each well, and production m is scaled by .

Fig. 4.

Values of interference time τ and gas in place ℳ for the 2,057 wells in Fig. 3A. Error bars indicate two standard uncertainties. Maximum interference times here are around 10 y due to the fact that wells more than 10 y old are still rare; interference times of, say, 30 y will only be reliably detected when wells are 19 y old or more.

Fig. 5.

Upper and lower bounds on cumulative production from 8,294 wells in our sample. Vertical wells are excluded from the analysis, whereas twofold more wells will ultimately be drilled; thus, the upper bound is not an upper bound on the whole field.