Numerical investigation of the POD reduced-order model for fast predictions of two-phase flows in porous media
Numerical investigation of the POD reduced-order model for fast predictions of two-phase flows in porous media
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DOI：
10.1108/hff-02-2019-0129
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发表时间：
2019-11
影响因子：
4.2
通讯作者：
Jingfa Li;Tao Zhang;Shuyu Sun;Bo Yu
中科院分区：
文献类型：
--
作者：
Jingfa Li;Tao Zhang;Shuyu Sun;Bo Yu
目的本文旨在提出一种基于全局模型降阶方法——本征正交分解（POD）的高效IMPES算法，以实现多孔介质中两相流的快速求解和预测。设计/方法/途径该算法的关键点是建立精确的两相多孔流POD降阶模型（ROM）。为此，分别采用投影原始控制方程（方法一）和投影原始控制方程离散形式（方法二）两种投影方法来构造POD-ROM，并详细比较和分析它们的区别。结果发现，方法一建立的POD-ROM不适用于多相多孔流，因为它未能引入位于网格单元边缘的流体饱和度和渗透率，这会导致结果不符合物理结果。研究结果通过使用方法二，基于POD-ROM开发了一种有效的IMPES算法，可以大大加快两相多孔流的模拟速度。通过三个数值算例验证了该算法的计算效率和数值精度，仿真结果表明，与没有任何加速技术的标准IMPES算法相比，该算法在不明显牺牲数值精度的情况下，显示出令人满意的计算加速比（一到两个数量级）。此外，还研究了POD模数的确定、润湿相压力和饱和度的相对误差以及POD模数对算法整体性能的影响。原创性/价值1．应用两种投影方法建立了两相多孔流的POD-ROM，并分析了它们的区别。本研究首先阐明了POD-ROM难以应用于多相多孔流的原因。 2.提出了一种基于POD-ROM的高效IMPES算法来加速两相多孔流的模拟。 3.在不同条件下，所提出的算法都具有令人满意的计算速度（一到两个数量级）和预测精度。
PurposeThis paper aims to present an efficient IMPES algorithm based on a global model order reduction method, proper orthogonal decomposition (POD), to achieve the fast solution and prediction of two-phase flows in porous media.Design/methodology/approachThe key point of the proposed algorithm is to establish an accurate POD reduced-order model (ROM) for two-phase porous flows. To this end, two projection methods including projecting the original governing equations (Method I) and projecting the discrete form of original governing equations (Method II) are respectively applied to construct the POD-ROM, and their distinctions are compared and analyzed in detail. It is found the POD-ROM established by Method I is inapplicable to multiphase porous flows due to its failed introduction of fluid saturation and permeability that locate on the edge of grid cell, which would lead to unphysical results.FindingsBy using Method II, an efficient IMPES algorithm that can substantially speed up the simulation of two-phase porous flows is developed based on the POD-ROM. The computational efficiency and numerical accuracy of the proposed algorithm are validated through three numerical examples, and simulation results illustrate that the proposed algorithm displays satisfactory computational speed-up (one to two orders of magnitude) without sacrificing numerical accuracy obviously when comparing to the standard IMPES algorithm that without any acceleration technique. In addition, the determination of POD modes number, the relative errors of wetting phase pressure and saturation, and the influence of POD modes number on the overall performances of the proposed algorithm, are investigated.Originality/value1. Two projection methods are applied to establish the POD-ROM for two-phase porous flows and their distinctions are analyzed. The reason why POD-ROM is difficult to be applied to multiphase porous flows is clarified firstly in this study. 2. A highly efficient IMPES algorithm based on the POD-ROM is proposed to accelerate the simulation of two-phase porous flows. 3. Satisfactory computational speed-up (one to two orders of magnitude) and prediction accuracy of the proposed algorithm are observed under different conditions.