References
[1] Aris R., The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Clarendon Press, Oxford, 1975, 1-444.
[2] Temkin M.I., 1981. Gas diffusion in porous catalysts. Kinet. Cat.; 22, 1365-75.
[3] Diaz, J.I., Hernandez, J., 1984. On the existence of a free boundary for a class of reaction-diffusion systems, SIAM J. Math. Anal. 15, 670–685.
[4] Bandle, C., Stakgold, I., 1984. The formation of the dead core in parabolic reaction-diffusion problems, Trans. of The American Mathematical Society, 286, 275-293.
[5] Bobisud, L.E., 1987. Singular perturbations and dead core behavior, Journ. of Math. Analysis and Appl., 124, 139-156.
[6] Bobisud, L.E., Royalty, W.D., 1989. Approach to a Dead Core for Some Reaction-Diffusion Equations, Journ. of Math. Analysis and Appl., 142, 542-557.
[7] Fedotov, V. Kh., Alekseev, B.V., Koltsov, N.I., 1985. “Dead zone” in porous catalyst grains for reactions with slightly nonmonotonic kinetics, React. Kinet. Catal. Lett., 29, 71-77.
[8] Garcia-Ochoa, F., Romero, A., 1988. The dead zone in a catalyst particle for fractional-order reactions, AIChE J., 34, 1916-1918.
[9] Andreev, V.V., 2013. Formation of a “Dead Zone” in Porous Structures During Processes That Proceeding under SteadyState and Unsteady State Conditions, Rev. J. Chem., 3, 239-269.
[10] Lee, J.K., Ko, J.B., Kim, D.H., 2004. Methanol steam reforming over Cu/ ZnO/Al2O3 catalyst: kinetics and effectiveness factor, Applied Catalysis A: General., 278, 25–35.
[11] Jiracek, F., Horak, J., Pasek, J., 1969. The Effects of Internal Mass Transfer on the hydrogenation of benzene over Nickel-Alumina catalyst, AIChE J., 15, 400-404.
[12] Levec, J., Herskowitz, M., Smith, J. M., 1976. An active catalyst for the oxidation of acetic acid solutions, AIChE J., 22, 919- 920.
[13] Look, K., Smith, J.M., 1978. Effectiveness Factors for Oxidation Kinetics, Ind. Eng. Chem. Proc. Des. Dev., 17, 368-371.
[14] Szukiewicz M., Chmiel-Szukiewicz E., Kaczmarski K., Szałek A., 2019. Dead zone for hydrogenation of propylene reaction carried out on commercial catalyst pellets., Open Chemistry, 17, 295–301.
[15] Araujo, M.L.G.C., Giordano, R.C., Hokka, C.O., 1998. Comparison Between Experimental and Theoretical Values of Effectiveness Factor in Cephalosporin C Production Process with Immobilized Cells Appl. Biochem. Biotechnol.,70, 493-504.
[16] Cruz, A.J.G., Almeida, R.M.R.G., Araujo, M.L.G.C., Giordano, R.C., Hokka, C.O., 2001. The dead core model applied to beads with immobilized cells in a fed-batch cephalosporin C production bioprocess, Chem. Eng. Sci., 56, 419-425.
[17] Cascaval, D., Turnea, M., Galaction, A.-I., Blaga, A.C., 2012. 6-Aminopenicillanic acid production in stationary basket bioreactor with packed bed of immobilized penicillin amidase— Penicillin G mass transfer and consumption rate under internal diffusion limitation, Biochem. Eng. J., 69, 113-122.
[18] Konti, A., Mamma, D., Hatzinikolaou, D.G., Kekos, D., 2016. 3-Chloro- 1,2-propanediol biodegradation by Ca-alginate immobilized Pseudomonas putida DSM 437 cells applying different processes: mass transfer effects, Bioproc. Biosys. Eng., 39, 1597-1609.
[19] Zaiat M., J. Rodrigues A. D., Foresti E., 2000. External and internal mass transfer effects in an anaerobic fixed-bed reactor for wastewater treatment Proc. Biochem., 35, 943-949.
[20] Pereira, F.M., Oliveira, S.C., 2016. Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis–Menten kinetics and assessment of numerical methods, Bioproc. Biosys. Eng., 39, 1717.
[21] Zhang, Q., Pastor-Pérez, L., Jin, W., Gu, S., Reina, T. R., 2019. Understanding the promoter effect of Cu and Cs over highly effective β- Mo2C catalysts for the reverse water-gas shift reaction, Applied Catalysis B: Environmental., 244, 889-898.
[22] Quindimil, A., De-La-Torre, U., Pereda-Ayo, B., González-Marcos, J.A., González-Velasco, J.R., 2018. Ni catalysts with La as promoter supported over Y- and BETA- zeolites for CO2 methanation, Applied Catalysis B: Environmental, , 238, 393-403.
[23] Mukherjee, S., Devaguptapu, S.V., Sviripa, A., Lund, C.R.F., Wu, G., 2018. Low-temperature ammonia decomposition catalysts for hydrogen generation, Applied Catalysis B: Environmental, 226, 162-181.
[24] Pang, J., Sun, J., Zheng, M., Li, H., Zhang, T., 2019. Transition metal carbide catalysts for biomass conversion: A review, Applied Catalysis B: Environmental., 254, 510-522.
[25] Szukiewicz M., 2017. Efficient numerical method for solution of boundary value problems with additional conditions Braz. J. Chem. Eng., 34, 873-883.
[26] York R.L., Bratlie K.M., Hile L.R., Jang L.K., 2011. Dead zones in porous catalysts: Concentration profiles and efficiency factors. Catal. Today, 160, 204–212.
[27] Fletcher, A., 1971. A modified Marquardt subroutine for nonlinear least squares, Harwell Report, AERE R.6799.
[28] M. Szukiewicz, 2015. Exact analytical solution of a non-linear reaction-diffusion problem, Book of Abstracts, MaCKiE–2015, ISBN 9789082401004, Ghent, Belgium, 24-27.
[29] Kaczmarski, K., Mazzoti, M., Storti, G., Morbidelli, M., 1997. Modeling fixed-bed adsorption columns through orthogonal collocations on moving finite elements, Computers Chem. Engng. 21, 641-660.
[30] Antos, D., Kaczmarski, K., Wojciech, P., Seidel-Morgenstern, A., 2003. Concentration dependence of lumped mass transfer coefficients – Linear versus non-linear chromatography and isocratic versus gradient operation, J. Chromatogr. A. 1006, 61-76.
[31] Kaczmarski, K., 2011. On the optimization of the solid core radius of superficially porous particles for finite adsorption rate, J. Chromatogr. A. 1218, 951-958.