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Grigor’ev, Vasiliĭ Vasil’evich

Identification of homogeneous-heterogeneous pore-scale reaction rates in porous media. (Russian. English summary) Zbl 1537.76176

Mat. Zamet. SVFU 30, No. 2, 101-122 (2023).
Summary: This paper presents a model of homogeneous-heterogeneous reaction in the pore scale based on Stokes equations, convection-diffusion-reaction equations with the Robin boundary condition at the inclusion boundaries. The homogeneous reaction is described as cubic autocatalysis on the whole pore space, and the kinetics of the heterogeneous reaction is described by the Langmuir isotherm. Numerical solution of the problem is carried out by the finite element method on piecewise linear elements. The Crank-Nicholson scheme is used for discretization in time. The nonlinear problem is solved using Newton’s iteration method. The mass transfer is simulated with a calculated velocity field. In addition, a sensitivity analysis of the model to the parameters has been carried out to study their influence on the reactive transport through the porous medium. A numerical solution for the inverse problem, namely, identification of key parameters characterizing the reactive transport based on two breakthrough curves of two different solutions is presented. Noisy measurements with different noise amplitudes including mixed amplitudes were considered. For approximate solution of the multidimensional inverse problem the metaheuristic Artificial Bee Colony Algorithm was applied and showed good efficiency at rather low computational cost.

MSC:

76V05 Reaction effects in flows
76R99 Diffusion and convection
76S05 Flows in porous media; filtration; seepage
76M21 Inverse problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics

Keywords:

cubic autocatalysis; convection-diffusion-reaction equation; Stokes equations; spatial finite element method; temporal Crank-Nicholson discretization

Software:

FEniCS
Cite Review PDF
Full Text: DOI

References:

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[32] Поступила в редакцию 3 марта 2023 г. После доработки 29 апреля 2023 г. Принята к публикации 29 мая 2023 г.
[33] Григорьев Василий Васильевич Лаборатория Вычислительные технологии моделирования многофизичных и многомасштабных процессов криолитозоны . Северо-Восточный федеральный университет имени М. К. Аммосова, ул. Кулаковского 42, Якутск 677000;
[34] Северо-Кавказский центр математических исследований, ул. Пушкина, 1, Ставрополь 355000 v.v.grigorev@s-vfu.ru REFERENCES
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[37] Myers R., The Basics of Chemistry, Greenwood Publ. Group (2003).
[38] Yang Q., Zhong Y., Li X.-M., et al., “Adsorption-coupled reduction of bromate by Fe(II)-Al(III) layered double hydroxide in fixed-bed column: Experimental and breakthrough curves analysis,” J. Ind. Eng. Chem., 28, 54-59 (2015).
[39] Wartha E., Birkelbach F., Bösenhofer M., et al., “Enhanced kinetic model identification for gas-solid reactions through computational fluid dynamics,” Chem. Eng. J., 430, article No. 132850 (2022).
[40] Chen L., He A., Zhao J., et al., “Pore-scale modeling of complex transport phenomena in porous media,” Progress Energy Combust. Sci., 88, article No. 100968 (2022).
[41] Sadhukhan S., Gouze P., and Dutta T., “Porosity and permeability changes in sedimentary rocks induced by injection of reactive fluid: A simulation model,” J. Hydrol., 450, 134-139 (2012).
[42] Miller K., Vanorio T., and Keehm Y., “Evolution of permeability and microstructure of tight carbonates due to numerical simulation of calcite dissolution,” J. Geophys. Res., Solid Earth, 122, No. 6, 4460-4474 (2017).
[43] Shimura T., Jiao Z., and Shikazono N., “Evaluation of nickel-yttria stabilized zirconia anode degradation during discharge operation and redox cycles operation by electrochemical calcu-lation,” J. Power Sources, 330, 149-155 (2016).
[44] Mosser L., Dubrule O., and Blunt M. J., “Reconstruction of three-dimensional porous media using generative adversarial neural networks,” Phys. Rev. E, 96, No. 4, article No. 043309 (2017).
[45] Liu Y., “Some consideration on the Langmuir isotherm equation,” Colloids Surfaces, A, Physic-ochem. Eng. Aspects, 274, No. 1-3, 34-36 (2006).
[46] Merkin J. H., “A model for isothermal homogeneous-heterogeneous reactions in boundary-layer flow,” Math. Comput. Model., 24, No. 8, 125-136 (1996). · Zbl 0884.76090
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[48] Khan M. I., Waqas M., Hayat T., and Alsaedi A., “A comparative study of casson fluid with homogeneous-heterogeneous reactions,” J. Colloid Interface Sci., 498, 85-90 (2017).
[49] Waqas M., “A mathematical and computational framework for heat transfer analysis of fer-romagnetic non-newtonian liquid subjected to heterogeneous and homogeneous reactions,” J. Magnet. Magn. Mater., 493, article No. 165646 (2020).
[50] Mozaffari M., Kordzadeh-Kermani V., Ghalandari V., et al., “Adsorption isotherm models: A comprehensive and systematic review (2010-2020),” Sci. Total Environment, 812, article No. 151334 (2022).
[51] Grigoriev V. V., Iliev O., and Vabishchevich P. N., “Computational identification of adsorption and desorption parameters for pore scale transport in periodic porous media,” J. Comput. Appl. Math., 370, article No. 112661 (2020). · Zbl 1430.76441
[52] Grigoriev V. V. and Vabishchevich P. N., “Bayesian estimation of adsorption and desorption parameters for pore scale transport,” Math., MDPI, 9, No. 16, 1-16 (2021).
[53] Grigoriev V. V. and Savvin A. V., “Numerical study of the influence of the electrokinetic effect on the growth of an oxide film at the pore scale,” AIP Conf. Proc., 2528, No 1, article No. 020047 (2022).
[54] Alnoes M. S., Blechta J., Hake J., et al., The FEniCS Project Version 1.5, Arch. Numer. Software, 3, No. 100 (2015).
[55] Liu Q., Li X., Liu H., et al., “Multi-objective metaheuristics for discrete optimization problems: A review of the state-of-the-art,” Appl. Soft Comput., 93, article No. 106382 (2020).
[56] Karimi-Mamaghan M., Mohammadi M., Meyer P., et al., “Machine learning at the service of meta-heuristics for solving combinatorial optimization problems: A state-of-the-art,” Eur. J. Oper. Res., 296, No. 2, 393-422, (2022). · Zbl 1490.90250
[57] Karaboga D. and Akay B., “A comparative study of artificial bee colony algorithm,” Appl. Math. Comput., 214, No. 1, 108-132 (2009). · Zbl 1169.65053
[58] Grigoriev V. V., Iliev O., and Vabishchevich P. N., “On parameter identification for reaction-dominated pore-scale reactive transport using modified bee colony algorithm,” Algorithms, 15, No. 1 (2022).
[59] Kralchevsky P. A., Danov K. D., and Denkov N. D., “Chemical Physics of Colloid Systems and Interfaces,” in: Handbook of Surface and Colloid Chemistry, CRC Press (1997).
[60] Reddy J. N., Introduction to the Finite Element Method, McGraw-Hill Education (2019).
[61] Samarskii A. A., The Theory of Difference Schemes, vol. 240, CRC Press (2001). · Zbl 0971.65076
[62] Mohring J., Milk R., Ngo A., et al., “Uncertainty quantification for porous media flow using multilevel Monte Carlo,” in: Int. Conf. Large-Scale Scientific Computing, pp. 145-152, Sprin-ger (2015). · Zbl 1459.76109
[63] Dokeroglu T., Sevinc E., Kucukyilmaz T., and Cosar A., “A survey on new generation meta-heuristic algorithms,” Comput. Ind. Eng., 137, article No. 106040 (2019).
[64] Song X., Zhao M., Yan Q., and Xing S., “A high-efficiency adaptive artificial bee colony algorithm using two strategies for continuous optimization,” Swarm Evolut. Comput., 50,
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