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Bayesian calibration of hydrocarbon reservoir models using an approximate reservoir simulator in the prior specification

机译:使用先前规范中的近似储层模拟器对烃储层模型进行贝叶斯校准

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We consider prediction and uncertainty analysis for the 'history matching' problem in petroleum reservoir evaluation. Unknown reservoir properties are represented on a fine three dimensional lattice. A 'reservoir simulator' takes the reservoir properties as input and gives production properties as output. The history matching problem is to infer the reservoir properties from the observed production history. To run the reservoir simulator on the lattice size of interest is computer intensive, and this severely limits the number of runs possible. We formulate the problem in a Bayesian setting and, following suggestions in the statistical literature, consider the reservoir simulator as an unknown function. To obtain a realistic prior distribution for this function, we propose to combine a coarse lattice (faster) version of the simulator with parameters correcting for bias introduced by the coarser lattice. We simulate from the resulting posterior by Markov chain Monte Carlo (MCMC). We construct an artificial reference reservoir, generate corresponding flow observations, and use our procedure to evaluate the reservoir properties in the resulting posterior distribution. Convergence and mixing are acceptable. The case study demonstrates how the observed production history provides information about both the reservoir properties and the bias correcting parameters included in the prior specification.
机译:我们考虑对储层评价中的“历史匹配”问题进行预测和不确定性分析。未知的储层特性以精细的三维晶格表示。 “油藏模拟器”将油藏属性作为输入,并将生产属性作为输出。历史匹配问题是从观察到的生产历史中推断储层性质。在感兴趣的晶格尺寸上运行储层模拟器是计算机密集型的,这严重限制了可能的运行次数。我们在贝叶斯环境中制定问题,并根据统计文献的建议,将油藏模拟器视为未知函数。为了获得该功能的实际先验分布,我们建议将模拟器的粗晶格(较快)版本与参数校正相结合,以校正由较粗晶格引入的偏差。我们通过马尔可夫链蒙特卡罗(MCMC)从所得后验进行模拟。我们构建了一个人工参考储层,生成了相应的水流观测值,并使用我们的程序评估了后验分布中的储层性质。收敛和混合是可接受的。案例研究表明观察到的生产历史如何提供有关储层特性和先前规范中包含的偏差校正参数的信息。

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