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Adaptive POD-Galerkin Technique for Reservoir Simulation and Optimization
Mathematical Geosciences ( IF 2.6 ) Pub Date : 2021-06-22 , DOI: 10.1007/s11004-021-09958-6
Dmitry Voloskov , Dimitri Pissarenko

This paper introduces a novel method using an adaptive functional basis for reduced order models based on proper orthogonal decomposition (POD). The method is intended to be applied, in particular, to hydrocarbon reservoir simulations, where a range of varying boundary conditions must be explored. The proposed method allows updating the POD functional basis constructed for a specific problem setting to match varying boundary conditions, such as modified well locations and geometry, without the necessity to recalculate each time the entire set of basis functions. This adaptive technique leads to a significant reduction in the number of snapshots required to calculate the new basis, and hence reduces the computational cost of the simulations. The proposed method was applied to a two-dimensional immiscible displacement model; the simulations were performed using a high-resolution model, a classical POD reduced model, and a reduced model whose POD basis was adapted to varying well locations and geometry. Numerical simulations show that the proposed approach leads to a reduction of the required number of model snapshots by a few orders of magnitude compared to the classical POD scheme, without noticeable loss of accuracy of calculated fluid production rates. The adaptive POD scheme can therefore provide a significant gain in computational efficiency for problems where multiple or iterative simulations with varying boundary conditions are required, such as optimization of well design or production optimization.



中文翻译:

油藏模拟与优化的自适应POD-Galerkin技术

本文介绍了一种新方法,该方法使用基于适当正交分解 (POD) 的降阶模型的自适应函数基础。该方法旨在特别应用于油气藏模拟,其中必须探索一系列不同的边界条件。所提出的方法允许更新为特定问题设置构建的 POD 函数基础以匹配不同的边界条件,例如修改后的井位和几何形状,而无需每次都重新计算整个基础函数集。这种自适应技术显着减少了计算新基所需的快照数量,从而降低了模拟的计算成本。将该方法应用于二维不混相位移模型;模拟是使用高分辨率模型、经典 POD 简化模型以及 POD 基础适应不同井位和几何形状的简化模型进行的。数值模拟表明,与经典的 POD 方案相比,所提出的方法导致所需的模型快照数量减少了几个数量级,而计算出的流体产量的准确性没有明显损失。因此,对于需要具有不同边界条件的多次或迭代模拟的问题,例如井设计优化或生产优化,自适应 POD 方案可以显着提高计算效率。数值模拟表明,与经典的 POD 方案相比,所提出的方法导致所需的模型快照数量减少了几个数量级,而计算出的流体产量的准确性没有明显损失。因此,对于需要具有不同边界条件的多次或迭代模拟的问题,例如井设计优化或生产优化,自适应 POD 方案可以显着提高计算效率。数值模拟表明,与经典的 POD 方案相比,所提出的方法导致所需的模型快照数量减少了几个数量级,而计算出的流体产量的准确性没有明显损失。因此,对于需要具有不同边界条件的多次或迭代模拟的问题,例如井设计优化或生产优化,自适应 POD 方案可以显着提高计算效率。

更新日期:2021-06-22
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