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A Production Characterization of the Eagle Ford Shale, Texas - A Bayesian Analysis Approach

机译：杰斯福特页岩，德克萨斯州 - 贝叶斯分析方法的生产表征

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We begin this research by asking "can we better estimate reserves in unconventional reservoirs using Bayes' theorem?" To attempt to answer this question, we obtained data for 68 wells in the Greater Core of the Eagle Ford Shale, Texas. As process, we eliminated the wells that did not have enough data, that did not show a production decline and/or wells that had too much data noise (this left us with 8 wells for analysis). We next performed decline curve analysis (DCA) using the Modified Hyperbolic (MH) and Power-Law Exponential (PLE) models (the two most common DCA models), consisting in user-guided analysis software. Then, the Bayesian paradigm was implemented to calibrate the same two models on the same set of wells.The primary focus of the research was the implementation of the Bayesian paradigm on the 8 well data set. We first performed a "best fit" parameter estimation using least squares optimization, which provided an optimized set of parameters for the two decline curve models. This was followed by using the Markov Chain Monte Carlo (MCMC) integration of the Bayesian posterior function for each model, which provided a full probabilistic description of its parameters. This allowed for the simulation of a number of likely realizations of the decline curves, from which first order statistics were computed to provide a confidence metric on the calibration of each model as applied to the production data of each well.Results showed variation on the calibration of the MH and PLE models. The forward models (MH and PLE) either over- or underestimate the reserves compared with the Bayesian calibrations, proving that the Bayesian paradigm was able to capture a more accurate trend of the data and thus able to determine more accurate estimates of reserves. In industry, the same decline curve models are used for unconventional wells as for conventional wells, even though we know that the same models may not apply. Based on the proposed results, we believe that Bayesian inference yields more accurate estimates of reserves for unconventional reservoirs than deterministic DCA methods. Moreover, it provides a measure of confidence on the prediction of production as as function of varying data and varying decline curve models.
机译：我们通过询问“我们可以使用贝叶斯定理更好地估计无常规水库中的储备来开始这项研究？”为了回答这个问题，我们在德克萨斯州鹰福特页岩的大核心中获得了68个井的数据。作为过程，我们消除了没有足够数据的井，没有显示出具有太多数据噪声的生产下降和/或井（这使我们留下了8个井进行分析）。我们接下来使用修改的双曲线（MH）和Power-Law指数（PLE）模型（两个最常见的DCA模型）进行了衰减曲线分析（DCA），包括在用户引导的分析软件中。然后，实施贝叶斯范式以在同一组井上校准相同的两种模型。研究的主要焦点是在8井数据集上实施贝叶斯范式。我们首先使用最小二乘优化执行“最佳拟合”参数估计，这为两个拒绝曲线模型提供了优化的参数集。接下来，使用Markov链蒙特卡罗（MCMC）集成了每个模型的贝叶斯后函数，这提供了对其参数的完整概率描述。这允许模拟许多可能的下降曲线的实现，从中计算第一阶统计数据来提供应用于每个井的生产数据的每个模型的校准的置信度。结果显示校准的变化MH和PLE模型。与贝叶斯校准相比，前向模型（MH和PLE）过度或低估了储备，证明贝叶斯范式能够捕获更准确的数据趋势，从而能够确定更准确的储备估计。在工业中，相同的下降曲线模型用于非传统的井作为传统井，即使我们知道相同的型号可能不适用。基于拟议的结果，我们认为贝叶斯推理对非传统水库的储备更准确地估计，而不是确定性DCA方法。此外，它为对生产预测的令人信心提供了衡量标准的令人信心，如不同数据的功能和变化的下降曲线模型。

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