Abstract

This study presents a pore-scale model of a complex homogeneous-heterogeneous reaction. It is based on the Stokes equations, convection-diffusion-reaction equations, and Robin boundary conditions. The fluid is considered non-Newtonian, and the Carreau model of viscosity is employed. A heterogeneous reaction is defined by the Langmuir isotherm, whereas a homogeneous reaction is described by cubic autocatalysis over the entire pore space. The finite element method is used for space discretization, namely, Taylor–Hood elements (\(P_{2}\) – \(P_{1}\)) for hydrodynamic processes and Lagrange polynomials of the first degree (\(P_{1}\)) for reactive transport. The Crank–Nicholson scheme is used for time discretization. Newton’s iterative method is implemented to solve a non-linear problem for reactive mass transport and Picard iterations for non-Newtonian fluid flow. The fluid flow influences the species transport, but there is no backward influence of the species concentration on the fluid flow. The influence of the power law parameter of the Carreau model for viscosity on the reacting processes is verified. The dimensionless form of equations was used throughout the entire numerical analysis in this paper. The numerical results show that the fluid flow parameters slightly affect the breakthrough curves, specifically for the catalyst.

中文翻译：

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均质-非均质孔隙尺度反应输运的非牛顿流动：计算分析

摘要

这项研究提出了复杂的均相-非均相反应的孔隙尺度模型。它基于斯托克斯方程、对流扩散反应方程和 Robin 边界条件。该流体被认为是非牛顿流体，并且采用卡罗粘度模型。非均相反应由朗缪尔等温线定义，而均相反应由整个孔隙空间的立方自催化描述。空间离散采用有限元方法，即流体动力过程的泰勒-胡德元（\(P_{2}\) – \(P_{1}\)）和一次拉格朗日多项式（\(P_{ 1}\) ) 用于反应性运输。克兰克-尼科尔森方案用于时间离散化。牛顿迭代法用于解决反应质量传递的非线性问题，而皮卡德迭代则用于非牛顿流体流动。流体流动影响物质传输，但物质浓度对流体流动没有向后影响。验证了Carreau粘度模型的幂律参数对反应过程的影响。本文的整个数值分析均采用无量纲形式的方程。数值结果表明，流体流动参数对突破曲线略有影响，特别是对于催化剂。