A modified Flux Corrected Transport method coupled with the MPFA-H formulation for the numerical simulation of two-phase flows in petroleum reservoirs using 2D unstructured meshes

IF 2.1 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computational Geosciences Pub Date : 2024-08-09 DOI:10.1007/s10596-024-10306-w
Phillipe C. G. da Silva, Gustavo L. S. S. Pacheco, Pedro V. P. Albuquerque, Márcio R. A. Souza, Fernando R. L. Contreras, Paulo R. M. Lyra, Darlan K. E. Carvalho
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Abstract

The numerical simulation of multiphase and multicomponent flows in oil reservoirs is a significant challenge, demanding robust and computationally efficient numerical formulations. Particularly, scenarios with high mobility ratios between injected and resident fluids can lead to Grid Orientation Effects (GOE), where numerical solutions strongly depend on the alignment between flow and computational grid and mobility ratio. This phenomenon relates to an anisotropic distribution in truncation error tied to the numerical approximation of the transport term. Although the oil industry commonly uses linear Two Point Flux Approximation (TPFA) for diffusive fluxes and the First Order Upwind (FOU) method for advective fluxes, both lack rotational invariance and TPFA struggles with non-k-orthogonal grids. This paper proposes a comprehensive cell-centered finite-volume formulation to simulate reservoir oil-water displacements, integrating the classical IMPES (Implicit Pressure Explicit Saturation) segregate approach with unstructured, non-k-orthogonal meshes. Diffusive flux discretization employs a Multipoint Flux Approximation with Harmonic Points (MPFA-H), capable of handling heterogeneous and strongly anisotropic media. A modified second-order Flux Corrected Transport (FCT) approach curbs artificial numerical diffusion for transport term discretization. Additionally, we incorporate a Flow-Oriented Scheme (FOS) for computing low-order and high-order approximations of the numerical fluxes to enhance multidimensional approximation and reduce GOE. The proposed strategy is validated through benchmark problems, yielding precise outcomes with reduced numerical diffusion and GOE effects, underscoring its efficiency for complex reservoir flow simulations.

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使用二维非结构网格对石油储层中的两相流动进行数值模拟的改良通量校正传输方法与 MPFA-H 公式相结合
油藏中多相和多组分流动的数值模拟是一项重大挑战,需要稳健且计算效率高的数值计算公式。特别是在注入流体和驻留流体之间流动比率较高的情况下,会产生网格方向效应(GOE),即数值解很大程度上取决于流动和计算网格之间的排列以及流动比率。这种现象与截断误差的各向异性分布有关,而截断误差与传输项的数值近似有关。虽然石油工业通常使用线性两点通量近似法(TPFA)来计算扩散通量,使用一阶上风法(FOU)来计算平流通量,但这两种方法都缺乏旋转不变性,而且 TPFA 在非正交网格中也很难发挥作用。本文提出了一种全面的以单元为中心的有限体积公式来模拟储层油水位移,将经典的 IMPES(隐含压力显式饱和)分离方法与非结构化、非 K 正交网格相结合。扩散通量离散化采用了带谐波点的多点通量逼近法(MPFA-H),能够处理异质和强各向异性介质。改进的二阶通量校正传输(FCT)方法抑制了传输项离散的人为数值扩散。此外,我们还采用了以流动为导向的方案(FOS)来计算数值通量的低阶和高阶近似值,以加强多维近似并减少 GOE。我们通过基准问题对所提出的策略进行了验证,结果非常精确,数值扩散和 GOE 的影响也有所降低,这表明该策略在复杂的储层流动模拟中非常有效。
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来源期刊
Computational Geosciences
Computational Geosciences 地学-地球科学综合
CiteScore
6.10
自引率
4.00%
发文量
63
审稿时长
6-12 weeks
期刊介绍: Computational Geosciences publishes high quality papers on mathematical modeling, simulation, numerical analysis, and other computational aspects of the geosciences. In particular the journal is focused on advanced numerical methods for the simulation of subsurface flow and transport, and associated aspects such as discretization, gridding, upscaling, optimization, data assimilation, uncertainty assessment, and high performance parallel and grid computing. Papers treating similar topics but with applications to other fields in the geosciences, such as geomechanics, geophysics, oceanography, or meteorology, will also be considered. The journal provides a platform for interaction and multidisciplinary collaboration among diverse scientific groups, from both academia and industry, which share an interest in developing mathematical models and efficient algorithms for solving them, such as mathematicians, engineers, chemists, physicists, and geoscientists.
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