T. R. Zakirov, O. S. Zhuchkova, M. G. Khramchenkov
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引用次数: 0
摘要
摘要 本文提出了描述三维多孔介质中动态吸附过程的数学模型。该模型的新颖之处在于能够研究多孔介质中不相溶多相流的传质过程。描述流体流动和活性成分对流扩散的控制方程基于晶格玻尔兹曼方程。两种流体之间以及流体与固相之间的界面现象,包括界面张力和润湿效应,采用最现代的颜色梯度法进行描述。活性成分和吸附剂颗粒之间的传质动力学采用 Langmuir 吸附方程进行描述。该数值算法已在两个基准上得到验证,包括活性成分和被置换流体的不可溶性,以及活性成分在多孔介质中的吸附和传输过程中的质量守恒问题。该数学模型适用于天然多孔介质的 X 射线计算机断层扫描图像所显示的多孔介质。
Mathematical Model for Dynamic Adsorption with Immiscible Multiphase Flows in Three-dimensional Porous Media
Abstract
In this paper, we present the mathematical model describing the dynamic adsorption processes in three-dimensional porous media. The novelty of this model lies in the ability to study the mass transfer processes with immiscible multiphase flows in porous media. The governing equations describing fluid flow and convective-diffusion of the active component are based on the lattice Boltzmann equations. The phenomena on the interface between two fluids and between fluids and solid phase, including interfacial tension and wetting effects, are described using the most modern version of the color-gradient method. The kinetic of the mass transfer between active component and adsorbent particles is described using the Langmuir adsorption equation. The numerical algorithm has been validated on two benchmarks including the immiscibility of the active component and the displaced fluid, as well as the problem of mass conservation of the active component during its adsorption and transport in porous media. The mathematical model has been adapted for porous media presented by X-ray computed tomography images of natural porous media.
期刊介绍:
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.