Multi-Fidelity Bayesian Approach for History Matching in Reservoir Simulation

R. Santoso, Xupeng He, M. AlSinan, Ruben Figueroa Hernandez, H. Kwak, H. Hoteit
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引用次数: 5

Abstract

History matching is a critical step within the reservoir management process to synchronize the simulation model with the production data. The history-matched model can be used for planning optimum field development and performing optimization and uncertainty quantifications. We present a novel history matching workflow based on a Bayesian framework that accommodates subsurface uncertainties. Our workflow involves three different model resolutions within the Bayesian framework: 1) a coarse low-fidelity model to update the prior range, 2) a fine low-fidelity model to represent the high-fidelity model, and 3) a high-fidelity model to re-construct the real response. The low-fidelity model is constructed by a multivariate polynomial function, while the high-fidelity model is based on the reservoir simulation model. We firstly develop a coarse low-fidelity model using a two-level Design of Experiment (DoE), which aims to provide a better prior. We secondly use Latin Hypercube Sampling (LHS) to construct the fine low-fidelity model to be deployed in the Bayesian runs, where we use the Metropolis-Hastings algorithm. Finally, the posterior is fed into the high-fidelity model to evaluate the matching quality. This work demonstrates the importance of including uncertainties in history matching. Bayesian provides a robust framework to allow uncertainty quantification within the reservoir history matching. Under uniform prior, the convergence of the Bayesian is very sensitive to the parameter ranges. When the solution is far from the mean of the parameter ranges, the Bayesian introduces bios and deviates from the observed data. Our results show that updating the prior from the coarse low-fidelity model accelerates the Bayesian convergence and improves the matching convergence. Bayesian requires a huge number of runs to produce an accurate posterior. Running the high-fidelity model multiple times is expensive. Our workflow tackles this problem by deploying a fine low-fidelity model to represent the high-fidelity model in the main runs. This fine low-fidelity model is fast to run, while it honors the physics and accuracy of the high-fidelity model. We also use ANOVA sensitivity analysis to measure the importance of each parameter. The ranking gives awareness to the significant ones that may contribute to the matching accuracy. We demonstrate our workflow for a geothermal reservoir with static and operational uncertainties. Our workflow produces accurate matching of thermal recovery factor and produced-enthalpy rate with physically-consistent posteriors. We present a novel workflow to account for uncertainty in reservoir history matching involving multi-resolution interaction. The proposed method is generic and can be readily applied within existing history-matching workflows in reservoir simulation.
油藏模拟历史匹配的多保真贝叶斯方法
历史匹配是油藏管理过程中使模拟模型与生产数据同步的关键步骤。历史匹配模型可用于规划油田的最佳开发,并进行优化和不确定性量化。我们提出了一种新的基于贝叶斯框架的历史匹配工作流,以适应地下不确定性。我们的工作流程涉及贝叶斯框架内三种不同的模型分辨率:1)用于更新先验范围的粗低保真模型,2)用于表示高保真模型的精细低保真模型,以及3)用于重建真实响应的高保真模型。低保真度模型采用多元多项式函数构建,高保真度模型基于油藏模拟模型。我们首先利用两级实验设计(DoE)建立了一个粗糙的低保真度模型,旨在提供更好的先验。其次,我们使用拉丁超立方体采样(LHS)来构建用于贝叶斯运行的精细低保真模型,其中我们使用Metropolis-Hastings算法。最后,将后验值输入到高保真度模型中,对匹配质量进行评价。这项工作证明了在历史匹配中考虑不确定性的重要性。贝叶斯提供了一个强大的框架,允许在油藏历史匹配中的不确定性量化。在均匀先验条件下,贝叶斯算法的收敛性对参数范围非常敏感。当解远离参数范围的平均值时,贝叶斯引入bios并偏离观测数据。结果表明,从粗糙的低保真度模型中更新先验加速了贝叶斯收敛,提高了匹配收敛性。贝叶斯需要大量的运行来产生准确的后验。多次运行高保真模型是昂贵的。我们的工作流通过部署一个好的低保真模型来表示主运行中的高保真模型来解决这个问题。这个良好的低保真模型运行速度很快,同时它尊重高保真模型的物理和准确性。我们还使用方差分析灵敏度分析来衡量每个参数的重要性。排名让人们意识到那些可能有助于匹配准确性的重要因素。我们演示了具有静态和操作不确定性的地热储层的工作流程。我们的工作流程可以精确匹配热采收率和产焓率与物理一致的后验值。我们提出了一种新的工作流程来解释涉及多分辨率相互作用的油藏历史匹配中的不确定性。该方法具有通用性,可以很容易地应用于油藏模拟中现有的历史匹配工作流程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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