Large Scale Voxel-Based FEM Formulation for NMR Relaxation in Porous Media

IF 2.7 3区 工程技术 Q3 ENGINEERING, CHEMICAL Transport in Porous Media Pub Date : 2024-08-30 DOI:10.1007/s11242-024-02118-4
Luiz F. Bez, Ricardo Leiderman, André Souza, Rodrigo B. de V. Azeredo, André M. B. Pereira
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Abstract

Nuclear magnetic resonance (NMR) techniques are key in the study of porous reservoir rocks. They can provide valuable insight into the pore size distribution of the pore space of a given rock sample due to its dependence on the magnetic fluid/matrix interaction. The pore space is often studied at the μm scale through the use of micro-CT images, which are often composed of hundreds of millions of voxels, posing significant challenges to numerical simulations. In this paper, we present an image-based, fully explicit, and matrix-free finite element implementation for the simulation of NMR relaxation process that is capable of handling such large 3D problems in single GPUs. The chosen explicit time-integration scheme uses a lumped capacitance formulation and stabilization via hyperbolization, and it is capable of handling arbitrary time-step sizes with controllable error levels. The image-based representation of the pore space is used for a memory-efficient, matrix-free formulation of the time integration using massively parallel processes on a single GPU. In addition, we propose the substitution of a global digital roughness correction factor that depends on the porous space’s geometry for a problem-independent local correction factor, based on nodal neighborhoods. We show that the numerical scheme converges with successive refinements as expected and that our local correction coefficient is capable of estimating the correct S/V parameter of several different classical geometries. We tested our formulation against an image-based Random Walk simulation of four digital rock core samples, achieving good agreement between them. We manage to simulate a giga-voxel image-based model on a personal use GPU (less than 10GB of memory use) in 33 min with our FEM implementation.

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多孔介质中核磁共振弛豫的大规模体素有限元计算
核磁共振(NMR)技术是研究多孔储层岩石的关键。由于核磁共振技术依赖于磁性流体/基质的相互作用,因此可以深入了解特定岩石样本孔隙空间的孔径分布。通过使用显微 CT 图像,通常可以在微米尺度上研究孔隙空间,而显微 CT 图像通常由数以亿计的体素组成,这给数值模拟带来了巨大挑战。在本文中,我们介绍了一种基于图像、完全显式和无矩阵的有限元实现方法,用于模拟核磁共振弛豫过程,能够在单 GPU 中处理此类大型三维问题。所选的显式时间积分方案使用了叠加电容公式,并通过超凸化实现稳定,能够以可控误差水平处理任意时间步长的问题。孔隙空间的基于图像的表示法可用于在单个 GPU 上使用大规模并行处理对时间积分进行内存效率高的无矩阵表述。此外,我们还提出以节点邻域为基础,用与问题无关的局部校正因子代替取决于多孔空间几何形状的全局数字粗糙度校正因子。我们的结果表明,数值方案随着连续细化而收敛,符合预期,而且我们的局部校正系数能够估算出几种不同经典几何形状的正确 S/V 参数。我们用基于图像的随机漫步模拟对四种数字岩芯样本进行了测试,两者之间取得了良好的一致性。使用我们的有限元实现,我们能够在个人使用的 GPU(内存使用不到 10GB)上在 33 分钟内模拟出基于图像的千兆像素模型。
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来源期刊
Transport in Porous Media
Transport in Porous Media 工程技术-工程:化工
CiteScore
5.30
自引率
7.40%
发文量
155
审稿时长
4.2 months
期刊介绍: -Publishes original research on physical, chemical, and biological aspects of transport in porous media- Papers on porous media research may originate in various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering)- Emphasizes theory, (numerical) modelling, laboratory work, and non-routine applications- Publishes work of a fundamental nature, of interest to a wide readership, that provides novel insight into porous media processes- Expanded in 2007 from 12 to 15 issues per year. Transport in Porous Media publishes original research on physical and chemical aspects of transport phenomena in rigid and deformable porous media. These phenomena, occurring in single and multiphase flow in porous domains, can be governed by extensive quantities such as mass of a fluid phase, mass of component of a phase, momentum, or energy. Moreover, porous medium deformations can be induced by the transport phenomena, by chemical and electro-chemical activities such as swelling, or by external loading through forces and displacements. These porous media phenomena may be studied by researchers from various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering).
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