Gas production in the Barnett Shale obeys a simple scaling theory
Gas production in the Barnett Shale obeys a simple scaling theory
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DOI：
10.1073/pnas.1313380110
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发表时间：
2013-12-03
影响因子：
11.1
通讯作者：
Marder, Michael
中科院分区：
文献类型：
--
作者：
Patzek, Tad W.;Male, Frank;Marder, Michael
来自致密页岩地层的天然气将在未来几十年为美国提供主要能源。对这些地层的天然气产量的估计主要依赖于为不同几何形状的井设计的公式。我们考虑与提取过程的基本物理和几何结构一致的最简单的天然气生产模型。原则上，模型的解取决于许多参数，但在实践中和在给定气田内，除两个参数外，所有参数都可以固定为典型值，从而导致我们用比例曲线精确求解非线性扩散问题。缩放曲线生产率在早期以 1 随时间的平方根下降，随后呈指数下降。这个简单的模型对美国最古老的页岩区 Barnett 页岩的 8,294 口井的天然气开采进行了令人惊讶的准确描述。这与 2,057 口水平井的结垢理论非常吻合，这些井的产量在不到 10 年的时间内开始呈指数下降。我们分析中剩余的 6,237 口水平井还太年轻，无法预测何时会出现指数下降，但该模型仍然可以用来确定井寿命的下限和上限。最后，我们获得了样本中各个井生产的气体的上限和下限，无论是单独的还是总体的。我们的 8,294 口井样本的估计最终采收率在 10 到 20 万亿标准立方英尺之间。
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.