Reaction-diffusion processes and ``dead zone'' in a porous catalyst granule

V. V. Andreev

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Tome 186 (2020), pp. 3-12.

Résumé

In this paper, we discuss reaction-diffusion processes in porous catalyst granules of spherical, cylindrical, and lamellar forms for various types of chemical reactions. We obtain approximate solutions of the quasi-homogeneous model for general catalytic reactions. Also, we analyze necessary conditions for the appearance of a “dead zone” in the central domain of a porous catalyst granule in the case of a general catalytic reaction.

Détail

Keywords: heterogeneous catalysis, “dead zone”.
Mots-clés : reaction-diffusion process, porous catalyst granule

Bibliographie

[2] Andreev V. V., “Analiz nestatsionarnykh rezhimov v poristykh granulakh katalizatora s gaussovym raspredeleniem aktivnykh tsentrov po glubine”, Vestn. Chuvash. un-ta., 2003, no. 2, 8–15

[3] Andreev V. V., “«Mertvaya zona» v poristoi granule katalizatora dlya nestatsionarnoi parallelnoi reaktsii”, Zh. fiz. khim., 80:4 (2006), 628–633

[4] Andreev V. V., “Formirovanie «mertvoi zony» v poristykh strukturakh v khode protsessov, protekayuschikh v statsionarnom i nestatsionarnom rezhimakh”, Obz. zh. khim., 3:3 (2013), 262–293

[5] Andreev V. V., “Issledovanie effektivnosti korochkovykh poristykh granul katalizatorov”, Tr. X Vseross. konf. «Neobratimye protsessy v prirode i tekhnike», MGTU im. N. E. Baumana, M., 2019, 129–132

[6] Andreev V. V., Alekseev B. V., Koltsov N. I., “«Mertvaya zona» v plastinchatom zerne katalizatora dlya slozhnykh reaktsii so stepennoi kinetikoi”, Izv. vuzov. Khimiya khim. tekhn., 35:11–12 (1992), 52–55

[7] Andreev V. V., Vozyakov V. I. Koltsov N. I., “Obtekanie potokom reaktsionnoi smesi poristykh granul katalizatora s khimicheskoi reaktsiei na vnutrennei poverkhnosti”, Khim. fiz., 13:11 (1994), 55–64

[8] Andreev V. V., Gritsai V. I., “Modelirovanie neaktivnykh zon v poristykh granulakh katalizatora i v biosensore”, Mat. model., 17:2 (2005), 57–64 | Zbl

[9] Andreev V. V., Gritsai V. I., “«Mertvaya zona» v poristykh granulakh katalizatora v nestatsionarnom rezhime pri treugolnoi reaktsii”, Izv. vuzov. Khimiya khim. tekhn., 50:7 (2007), 50–54

[10] Andreev V. V., Gritsai V. I., Prilutskii Yu. I., “Issledovanie fiziko-khimicheskikh parametrov neaktivnykh zon poristoi granuly katalizatora”, Dokl. NAN Ukrainy., 6 (2007), 61–69

[11] Andreev V. V., Koltsov N. I., “«Mertvaya zona» v poristykh zernakh katalizatora dlya reaktsii s proizvolnoi kinetikoi”, Dokl. RAN., 332:5 (1993), 581–584 | MR

[12] Andreev V. V., Koltsov N. I., Vozyakov V. I., “Usloviya vozniknoveniya «mertvoi zony» v zernakh katalizatora dlya reaktsii s proizvolnoi kinetikoi”, Izv. vuzov. Khimiya khim. tekhn., 36:11 (1993), 61–66

[13] Gritsai V. I., Andreev V. V., “Rol diffuzii v formirovanii neaktivnykh zon v poristykh reaktsionno-diffuzionnykh sredakh”, Mat. model., 18:12 (2006), 88–94

[14] Koltsov N. I., Andreev V. V., “Ob osobennostyakh protekaniya prostykh i slozhnykh reaktsii v poristykh zernakh katalizatora”, Kinetika i kataliz., 36:1 (1995), 77–81

[15] Andreev V. V., “Conditions required to maximise the productivity of porous catalyst granules with a controlled activity profile”, Mendeleev Commun., 2 (1998), 77–79 | DOI

[16] Andreev V. V., “A mathematical treatment of the use of ultrasound in homogeneous and heterogeneous catalysis”, Ultrason. Sonochem., 6:1–2 (1999), 21–24 | DOI

[17] Andreev V. V., “A mathematical treatment of the use of ultrasound in a catalytic reactor with controlled activity profile”, Proc. 15th Int. Symp. “Nonlinear Acoustics at the Turn of the Millenium” (Göttingen, Germany, 1–4 September 1999), Am. Inst. Phys., Melville–New York, 2000, 469–472

[18] Andreev V. V., Koltsov N. I., “Optimal catalyst distribution on a non-isothermal porous granule for a mono-irreversible reaction with arbitrary kinetics”, Acta Chim. Sloven., 42:1 (1995), 43–46 | MR

[19] Andreev V. V., Koltsov N. I., Ivanova A. F., Konstantinova N. V., “On the possibility of increasing the effectiveness of a porous catalyst granule for a simple reaction in a non-stationary regime”, Mendeleev Commun., 4 (1995), 152–153 | DOI

[20] Ellery A. J., Simpson M. J., “An analytical method to solve a general class of nonlinear reactive transport models”, Chem. Eng. J., 169:1–3 (2011), 313–318 | DOI

[21] Hernandez Aguirre A., Morales Cabrera M. A., Morales Zarate E., Rivera V. M., Puebla H., Hernandez Martinez E., “Non-isothermal effectiveness factor for catalytic particles with non-Fickian diffusion”, Int. J. Chem. Reactor Eng., 15:5 (2017)

[22] Król G., Szukiewicz M., “Conditions of dead zone forming in porous catalyst pellets”, Chem. Process Eng., 39:1 (2018), 129–138

[23] Król G., Szukiewicz M., Chutkowski M., “Formation of dead zone in catalytic particles in catalysis and biocatalysis — new alternative method of determination”, Can. J. Chem. Eng., 2019

[24] Satterfield C. N., Sherwood T. K., The Role of Diffusion in Catalysts, Addison-Wesley, London, 1963

[25] Simpson M. J., Ellery A. J., “An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell”, Appl. Math. Model., 36:7 (2012), 3329–3334 | DOI | MR | Zbl

[26] Szukiewicz M. K., “Efficient numerical method for solution of boundary value problems with additional conditions”, Brazil. J. Chem. Eng., 34:3 (2017), 873–883 | DOI

[27] York R. L., Bratlie K. M., Hile L. R., Jang L. K., “Dead zones in porous catalysts: Concentration profiles and efficiency factors”, Catal. Today., 160 (2011), 204–212 | DOI