Summary The main objective of this work is to improve robust, repeatable interpretation of reservoir characteristics using rate transient analysis (RTA). This is to generate probabilistic credible intervals for key reservoir and completion variables. This resulting data-driven algorithm was applied to production data from both synthetic and actual case histories. Synthetic production data from a multistage, hydraulically fractured horizontal completion in a reservoir modeled after the Marcellus Shale reservoir were generated using a reservoir model. The synthetic production data were analyzed using a combination of RTA and Bayesian techniques. First, the traditional log-log plot was produced to identify the linear flow production regime. Using the linear flow production data and traditional RTA equations, Bayesian inversion was carried out using two distinct Bayesian methods. The “rjags” and “EasyABC” packages in the open-source statistical software R were used for the traditional and approximate inversion, respectively. Model priors were based on (1) information available about the Marcellus Shale from technical literature and (2) results from a hydraulic fracturing forward model. Posterior distributions and credible intervals were produced for the fracture length, matrix permeability, and skin factor. These credible intervals were then compared with true reservoir and hydraulic fracturing data. The methodology was also repeated for an actual case in the Barnett shale. The most substantial finding was that for nearly all the investigated cases—including complicated scenarios (such as including finite fracture conductivity, fracturing fluid flowback, and heterogeneity in fracture length in the reservoir/hydraulic fracturing forward model)—the combined RTA-Bayesian model provided a 95% credible interval that encompassed the true values of the reservoir/hydraulic fracture parameters. We also found that the choice of the prior distribution did not affect the posterior distribution/credible interval in a significant manner as long as it was moderately concentrated and consistent with engineering science. Also, a comparison of the approximate Bayesian computation (ABC) and the traditional Bayesian algorithms showed that the ABC algorithm reduced computational time by at least an order of magnitude with minimal loss in accuracy. In addition, the production history used, the number of iterations, and the tolerance of fitting in the ABC analysis had a minimal impact on the posterior distribution after an optimal point, which were determined to be at least 1-year production history, 10,000 iterations, and 0.001, respectively. In summary, the RTA-Bayesian production analysis method was implemented using relatively user-friendly computational platforms [R and Excel® (Microsoft Corporation, Redmond, Washington, USA)]. This methodology provided reasonable characterization of all key variables such as matrix permeability, fracture length, and skin when compared to results obtained from analytical methods. This probabilistic characterization has the potential to enable better understanding of well performance ranges expected from shale gas wells. The methodology described here can also be generalized to shale oil systems during linear flow.

中文翻译：

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使用速率瞬态分析和贝叶斯算法对非常规气井线性流动过程中的储层进行表征

总结 这项工作的主要目标是使用速率瞬态分析 (RTA) 改进对储层特征的稳健、可重复的解释。这是为了生成关键储层和完井变量的概率可信区间。这种产生的数据驱动算法被应用于来自合成和实际案例历史的生产数据。以 Marcellus 页岩油藏为模型的油藏中的多级水力压裂水平完井的合成生产数据是使用油藏模型生成的。综合生产数据使用 RTA 和贝叶斯技术的组合进行分析。首先，制作了传统的对数对数图来识别线性流量生产机制。使用线性流量生产数据和传统的 RTA 方程，使用两种不同的贝叶斯方法进行贝叶斯反演。开源统计软件 R 中的“rjags”和“EasyABC”包分别用于传统和近似反演。模型先验基于 (1) 技术文献中有关 Marcellus 页岩的可用信息和 (2) 水力压裂正向模型的结果。产生了裂缝长度、基质渗透率和表皮因子的后验分布和可信区间。然后将这些可信区间与真实的储层和水力压裂数据进行比较。对于 Barnett 页岩中的一个实际案例，也重复了该方法。最重要的发现是，对于几乎所有调查的案例——包括复杂的情景（例如包括有限裂缝导流能力、压裂液回流和储层/水力压裂正向模型中裂缝长度的非均质性）——组合的 RTA-贝叶斯模型提供了 95% 的可信区间，其中包含储层/水力压裂参数的真实值。我们还发现，先验分布的选择不会显着影响后验分布/可信区间，只要它适度集中并与工程科学一致。此外，近似贝叶斯计算 (ABC) 和传统贝叶斯算法的比较表明，ABC 算法将计算时间减少了至少一个数量级，并且精度损失最小。此外，使用的生产历史、迭代次数、ABC 分析中的拟合容差对最优点后的后验分布影响最小，最优点分别确定为至少 1 年的生产历史、10,000 次迭代和 0.001。总之，RTA-贝叶斯生产分析方法是使用相对用户友好的计算平台 [R and Excel® (Microsoft Corporation, Redmond, Washington, USA)] 实现的。与从分析方法获得的结果相比，该方法提供了所有关键变量的合理表征，例如基质渗透率、裂缝长度和表皮。这种概率表征有可能更好地理解页岩气井的预期井性能范围。此处描述的方法也可以推广到线性流动期间的页岩油系统。