A New Mathematical Model for the Prediction of Internal Recirculation in Impinging Streams Reactors

Document Type: Research Article


1 Chemical Engineering Department, Amirkabir University of Technology, Tehran, I.R. IRAN

2 Petroleum Refining Technology Development Division, Research Institute of Petroleum Industry (RIPI), Tehran, I.R. IRAN


A mathematical model for the prediction of internal recirculation of complex impinging stream reactors has been presented. The model constitutes a repetition of a series of ideal plug flow reactors and CSTR reactors with recirculation. The simplicity of the repeating motif allows for the derivation of an algebraic relation of the whole system using the Laplace transform. An impinging streams reactor system with one axial and two tangential inlet fluid streams was constructed and considered as a case study. The model predicts satisfactorily the complex and flow rate dependent experimental residence time distribution functions obtained employing a pulse tracer method for different total flow rates of the incoming feed. The variation of the controlling parameters with changing the total inlet flow rate is discussed. The presented model can predict complex internal recirculation streams within the impinging streams reactor system.


Main Subjects

[1] Elperin T., Heat and Mass Transfer in Opposing Currents, J. Eng. Phys., 6: 62-68 (1961).

[2] Wu Y., Xiao Y., Zhou Y., Micromixing in the Submerged Circulative Impinging Stream Reactor, Chin. J. Chem. Eng., 11(4): 420-425 (2003).

[3] Akhbarifar S., Shirvani M., Zahedi S., Zahiri M. R., Shamsaii Y., Improving Cyclone Efficiency by Recycle and Jet Impingement Streams, Iran. J. Chem. Chem. Eng. (IJCCE), 30(2): 119-124 (2011).

[4] Mahajan A. J., Kirwan D. J., Micromixing Effects in a Two Impinging-Jets Precipitator, AlChe J., 42(7): 1801-1814 (1996).

[6] Bar T., Tamir A., An Impinging–Streams Reactor with Two Pairs of Tangential Air Feeds, Can. J. Chem. Eng., 68: 541-552 (1990).

[7] Tamir A., Elperin I., Luzzatto K., Drying in a Nnew Two Impinging Stream Reactor, Chem. Eng. Sci., 39(1): 139-146 (1984).

[8] Ramirez-Verduco L. F., Murrieta-Guevara F., Torres-Garcia E., Gomez-Quintana F., Gonzalez-Pena V., Desulfurization of diesel by Oxidation/Extraction Scheme: Influence of the Extraction Solvent, J. Pet. Sci. Eng., 24: 289-294 (2004).

[9] Unger D.R., Muzzio F.J., Brodkey R.S., Experimental and Numerical Characterization of Viscous Flow and Mixing in an Impinging Jet Contactor, Can. J. Chem. Eng.,76(3):, 546-555 (1998).

[10] Wu Y., Properties and Application of Impinging Streams, Chem. Ind. Eng. Prog., 20(11): 8-13 (2001).

[11] Higman C., van der Burgt M.J., “Gasification”, Gulf Professional Publishing, (2003).

[12] Perry K.H., Green D.W., “Chemical Engineering Handbook”, Mcgraw-Hill, New York (1984).

[13] Ji L., Wu B., Chen K., Zhu J., Experimental Study and Modeling of Residence Time Distribution
in Impinging Stream Reactor with GDB Model
, J. Ind. Eng. Chem., 16: 646-650 (2010).

[14] Royaee S J., Sohrabi M., Jafarikojour M., Kinetic Modeling for Phenol Degradation Using Photo-Impinging Streams Reactor, Res. Chem. Intermed., 41(9): 6409-6431 (2014).

[15] Wibel W., Wenka A., Brandner J. J., Dittmeyer R., Measuring and Modeling the Residence Time Distribution of Gas Flows in Multichannel Microreactors, Chem. Eng. J., 215-216: 449-460

[16] Rajamanickam A., Balu K., Design and Development of Mathematical Model for Static Mixer, Iran. J. Chem. Chem. Eng. (IJCCE), 35(1): 109-116 (2016).

[17] Wang X., Tian B., Wang C., Wu J., Mathematical Modelling of Residence Time Distribution
in Tubular Loop Reactors
, Can. J. Chem. Eng., 9999: 1-8 (2016).

[19] Jafarikojour M., Mohammadi M., Sohrabi M., Royaee S.J., Evaluation and Modeling of a Newly Designed Impinging Stream Photoreactor Equipped with a TiO2 Coated Fiberglass Cloth, Roy. Soc. Chem. Adv., 5: 9019-9027 (2015).

[20] Jafarikojour M., Sohrabi M., Royaee S.J., Rezaei M., A New Model for Residence Time Distribution of Impinging Stream Reactors Using Descending-Sized Stirred Tank in Series, Chem. Eng. Research. Des., 109: 86-96 (2016).

[21] Royaee S.J., Sohrabi M., Jabari barjesteh P., Performance Evaluation of Continuous Flow Photo-Impinging Streams Cyclone Reactor for Phenol Degradation, Chem. Eng. Res. Des., 90: 1923-1929 (2012).

[22] Rajaie E., Sohrabi M., Application of the Monte Carlo Technique in Simulation of Flow and Modeling the Residence Time Distribution
in a Continuous Two Impinging Liquid–Liquid Streams Contactor, Chem. Eng. J., 143: 249–256 (2008).

[23] Ghasemi N., Sohrabi M., Khosravi M., Mujumdar A., Goodarzi M., CFD Simulation of Solid–Liquid Flow in a Two Impinging Streams Cyclone Reactor: Prediction of Mean Residence Time and Holdup of Solid Particles, Chem. Eng. Process., 49: 1277–1283 (2010).

[24] Sohrabi M., Jamshidi A. M., Application of the Continuous Two Impinging Stream Reactors
in Chemical Absorption, Stud. Surf. Sci. Cat., 122: 423–426 (1999).

[25] Sohrabi M., Ahmadi Marvast M., Application of a Continuous Two Impinging Stream Reactor
in Solid−Liquid Enzyme Reactions, Ind. Eng. Chem. Res., 39: 1903-1910 (2000).

[26] Sohrabi M., Zareikar B., Modeling of the Residence Time Distribution and Application of the Continuous Two Impinging Stream Reactor in Liquid-Liquid Reactions, Chem. Eng. Tech., 28: 61-66 (2005).

[27] Sohrabi M., Kaghazchi T., Yazdani F., Modelling and Application of the Continuous Impinging Stream Reactors in Liquid-Liquid Heterogeneous Reactions, Chem. Eng. Tech., 58: 363-370 (1993).

[28] Jafarikojour M., Sohrabi M., Royaee S. J., Rezaee M., Residence Time Distribution Analysis and Kinetic Study of Toluene Photo-Degradation Using a Continuous Immobilized Photoreactor, Roy. Soc. Chem. Adv., 4: 53097-53104 (2014).

[29] Sohrabi M., Jamshidi A. M., Studies on the Behaviour and Application of the Continuous Two Impinging Stream Reactors in Gas–Liquid Reactions, J. Chem. Tech. Biotech., 69: 415-420 (1997).

[30] Royaee S.J., Sohrabi M., Application of Photo-Impinging Streams Reactor in Degradation of Phenol in Aqueous Phase, Desalination, 253: 57–61 (2010).

[31] Fatourehchi N., Sohrabi M., Dabir B., Royaee S. J., Haji-Malayeri A., Application of a Novel Type Impinging Stream Reactor in Solid-Liquid Enzyme Reactions and Modeling of Residence Time Distribution Using GDB Model, Enz. Mic.Tech., 55: 14-20 (2014).

[32] Madadi S., Sohrabi M., Royaee S. J., Performance Evaluation of a Novel Multi-Stage Axial-Radial Impinging Flow Photo-Reactor for Degradation of p-Nitrophenol, J. Tai. Institute Chem. Eng., 55: 101-111 (2015). 

[33] Madadi S., Sohrabi M., Royaee S.J., Photodegradation of 4-Nitrophenol Using an Impinging Streams Photoreactor Coupled with a Membrane, Chem. Eng. Process. Proc. Intens., 99: 1-9 (2016). 

[34] Guo Q., Liang Q., Ni J., Xu S., Yu G., Yu Z., Markov Chain Model of Residence Time Distribution in a New Type Entrained-Flow Gasifier, Chem. Eng. Process. Proc. Intens., 47: 2061–2065 (2008).

[35] Wang Y., Brannock, M., Leslie G., Diagnosis of Membrane Bioreactor Performance Through Residence Time Distribution Measurements—A Preliminary Study, Desalination, 236: 120–126 (2009).

[36] Fogler H.S., “Elements of Chemical Reaction Engineering. Massachusetts”, Pearson Education INC. (2005).

Volume 39, Issue 2 - Serial Number 100
March and April 2020
Pages 251-261