Random networks in modeling heat and mass transfer in porous materials
DOI:
https://doi.org/10.17721/1812-5409.2026/1.23Keywords:
flows in porous media, random graphs, machine learning methods, mathematical modelingAbstract
A detailed literature review on mathematical models of mass and heat transfer processes in porous media based on random graphs (networks) is presented. In these models, individual pores (graph nodes) are considered to be connected with a given probability by narrow channels (graph edges) through which a liquid or gas can move. A classification of the main types of random networks used in mathematical modeling of porous media is given, as well as corresponding discrete and continuous mathematical models for single-component Newtonian liquids and mixtures of immiscible liquids. In coupled heat and mass transfer problems, double random networks are usually considered, one of which corresponds to heat-mass transfer with a liquid, and another is associated with heat transfer through a solid phase. The available algorithms for constructing random graphs, mathematical models of heat and mass transfer on networks, and the results of modeling of liquid flow, several miscible or immiscible liquids of Newtonian and non-Newtonian liquids are presented. It is shown that, in addition to the possibility of the disappearance of a network edge due to the suffusion and/or aggregation of liquid/solid phase particles, it is also possible to restore the connection between neighboring nodes due to the destruction and washout of the solid phase, as well as disaggregation/disintegration of particle conglomerates. The results of the review analysis of the literature can be used to select the best random graph (network) model, discrete or continuous mathematical model, and numerical method for calculations on a specific case of a porous medium.
Pages of the article in the issue: 170 - 175
Language of the article: English
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Copyright (c) 2026 Oleg Afanasiev, Natalya Kizilova, Sergii Poslavskyi
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