Summary Extrapolation of history matched single-phase flow solutions is a common practice to forecast production from tight-oil reservoirs. Nonetheless, this approach (a) omits multiphase flow effects that exist below bubblepoint conditions and (b) has not included the quantification of the uncertainty of the estimated ultimate recovery (EUR). This work combines a new two-phase (oil and gas) flow solution within a Bayesian framework to address the uncertainty in the EUR. We illustrate the application of the procedure to tight-oil wells of west Texas. First, we combine the oil and the gas flow equations into a single dimensionless two-phase flow equation. The solution is a dimensionless flow rate model that can be easily scaled using two parameters: hydrocarbon pore volume and characteristic time. Second, this study generates the probabilistic production forecasts using a Bayesian approach in which the parameters of the model are treated as random variables. We construct parallel Markov chains of the parameters using an adaptative Metropolis-Hastings (M-H) Markov chain Monte Carlo (MCMC) for this purpose. Third, we evaluate the robustness of our inferences using posterior predictive checks (PPCs). Finally, we quantify the uncertainty in the EUR percentiles using the bootstrap method. The results of this research are as follows. First, this work shows that EUR estimates based on single-phase flow solutions will consistently underestimate the ultimate oil recovery factors in solution-gas drives where the reservoir pressure is less than the bubblepoint. The degree of underestimation will depend on the reservoir and flowing conditions as well as the fluid properties. Second, the application of parallel Markov chains using an adaptative M-H MCMC scheme that addresses the correlation between the model’s parameters solves the issues of mixing and autocorrelation of Markov chains and, thus, it speeds up speeding up the convergence of the Markov chains. Third, we generate replicated data from our posterior distributions to assess the robustness of our inferences (PPCs). Finally, we use hindcasting to calibrate and strengthen our inferences. To our knowledge, all these approaches are novel in EUR forecasting. Using a Bayesian framework with a low-dimensional (two-parameter) physics-based model provides a fast and reliable technique to quantify the uncertainty in production forecasts. In addition, the use of parallel chains with an adaptative M-H MCMC accelerates the rate of convergence and increases the robustness of the method.

中文翻译：

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使用基于物理的两相流模型解决致密油藏产量预测不确定性的贝叶斯框架

总结 历史匹配单相流解的外推是预测致密油油藏产量的一种常见做法。尽管如此，这种方法 (a) 忽略了存在于泡点条件以下的多相流效应，并且 (b) 没有包括对估计最终采收率 (EUR) 的不确定性的量化。这项工作在贝叶斯框架内结合了一种新的两相（石油和天然气）流动解决方案，以解决欧元的不确定性。我们说明了该程序在德克萨斯州西部致密油井中的应用。首先，我们将油气流动方程组合成一个单一的无量纲两相流动方程。该解决方案是一个无量纲流速模型，可以使用两个参数轻松缩放：烃孔体积和特征时间。第二，本研究使用贝叶斯方法生成概率产量预测，其中模型的参数被视为随机变量。为此，我们使用自适应 Metropolis-Hastings (MH) 马尔可夫链蒙特卡洛 (MCMC) 构建参数的并行马尔可夫链。第三，我们使用后验预测检查 (PPC) 来评估我们的推理的稳健性。最后，我们使用 bootstrap 方法量化欧元百分位数的不确定性。本研究的结果如下。首先，这项工作表明，基于单相流解决方案的 EUR 估计将始终低估在油藏压力小于泡点的溶液-气驱中的最终采油率。低估的程度将取决于储层和流动条件以及流体特性。其次，使用解决模型参数之间相关性的自适应 MH MCMC 方案的并行马尔可夫链的应用解决了马尔可夫链的混合和自相关问题，从而加快了马尔可夫链的收敛速度。第三，我们从我们的后验分布生成复制数据，以评估我们的推理（PPC）的稳健性。最后，我们使用后报来校准和加强我们的推论。据我们所知，所有这些方法在欧元预测中都是新颖的。使用贝叶斯框架和基于物理的低维（双参数）模型提供了一种快速可靠的技术来量化生产预测中的不确定性。