Development of a new fast proxy model for transport in multi-scale heterogeneous porous media based on random walk techniques

石油工程中的一个主要挑战是评价非均质性及其对油藏动态的影响。由于地质地层的建模总是在数据不足的情况下进行，而且非均质性往往发生在很大范围的长度尺度上，因此岩石性质在许多尺度上都存在显著的不确定性，并在随后的开采行为中引入了不确定性。快速代理模型可以作为耗时的有限差分计算的有效替代方案来模拟多孔介质中的传输，从而允许与不确定性评估相关的任务可靠地完成。 提出了一种基于随机游走技术的粒子跟踪算法。通过在入口处发射许多粒子，允许它们基于预定义的转移概率函数在站点之间跳跃，并跟踪与每个粒子相关联的时间计数器，对传输行为进行数值模拟。这项工作提出的主要新颖想法是，将跟踪浓度的转变，而不是单个粒子。在次网格区域执行的流动模拟的结果将被用来校准这些概率函数。以往的工作大多集中在单相系统上，而忽略了亚网格尺度上的非均质性的影响。提出的研究目标是：(1)设计一种新的建模策略，以解释多尺度非均质性；(2)开发改进的技术，以获得准确地表示不同恢复过程的传输物理的转移概率函数。 在混合溶剂注入中发现了一种立即应用于提高稠油采收率的方法。该建模技术将考虑注入流体和原地流体之间的粘度差异。通过沿流线推进饱和度(而不是浓度)，该方法将扩展到不混相流动系统，允许对多尺度非均质性进行概率处理，在二氧化碳地质储存模拟中具有潜在的应用。

A major challenge in petroleum engineering is the assessment of heterogeneity and its impacts on reservoir performance. Since modeling of geologic formations is always carried out with insufficient data and heterogeneity tends to occur over a wide range of length scales, significant uncertainty in rock properties exists at many scales and introduces uncertainty in the ensuing recovery behavior. Fast proxy models can be used as efficient alternatives to time-consuming finite difference computations to model transport in porous media, allowing tasks associated with uncertainty assessment to be reliably accomplished. A new particle-tracking algorithm based on random walk techniques is proposed. Transport behavior is modeled numerically by launching many particles at the inlet, allowing them to hop between sites based on a pre-defined transition probability function, and tracking the time counter associated with each particle. The main novel idea proposed in this work is that transitions of concentrations, instead of individual particles, will be tracked. Results from flow simulations performed at the sub-grid domain will be used to calibrate these probability functions. Previous works focus mostly on single-phase systems and ignore effects of heterogeneity occurring at sub-grid scales. The proposed research objectives are to: (1) devise a new modeling strategy that accounts for multi-scale heterogeneities; (2) develop improved techniques for obtaining the transition probability functions that accurately represent transport physics tailored to different recovery processes. An immediate application is found in the miscible solvent injection for enhanced heavy oil recovery. The modeling technique will take into account the viscosity differences between injected and in-situ fluids. The method will be extended to immiscible flow systems by advancing saturation (instead of concentration) along streamlines, allowing a probabilistic treatment of the multi-scale heterogeneity with potential applications in modeling of geologic storage of CO2.