Skip to main content
SpringerLink
Log in

Experimental and numerical investigation of dynamic heat transfer parameters in packed bed

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

Dynamic experiments in a nonadiabatic packed bed were carried out to evaluate the response to disturbances in wall temperature and inlet airflow rate and temperature. A two-dimensional, pseudo-homogeneous, axially dispersed plug-flow model was numerically solved and used to interpret the results. The model parameters were fitted in distinct stages: effective radial thermal conductivity (K r) and wall heat transfer coefficient (h w) were estimated from steady-state data and the characteristic packed bed time constant (τ) from transient data. A new correlation for the K r in packed beds of cylindrical particles was proposed. It was experimentally proved that temperature measurements using radially inserted thermocouples and a ring-shaped sensor were not distorted by heat conduction across the thermocouple or by the thermal inertia effect of the temperature sensors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

Bi :

Biot number (dimensionless)

Bi s :

Solid-wall Biot number (dimensionless)

Cp f :

Fluid heat capacity (J/kg °C)

Cp s :

Solid heat capacity (J/kg °C)

d p :

Sphere-equivalent particle diameter (m)

d t :

Tube diameter (m)

G :

Superficial mass flow rate (kg/m2 s)

h w :

Wall heat transfer coefficient (W/m2 °C)

\( h_{w}^{o} \) :

Wall heat transfer coefficient with a stagnant fluid (W/m2 °C)

J o :

Zeroth-order Bessel function, first kind

J 1 :

First-order Bessel function, first kind

K a :

Effective axial thermal conductivity (W/m °C)

K r :

Effective radial thermal conductivity (W/m °C)

\( K_{r}^{o} \) :

Effective radial thermal conductivity of the bed with a stagnant fluid (W/m °C)

k f :

Fluid conductivity (W/m °C)

k p :

Pellet conductivity (W/m °C)

k s :

Solid conductivity (W/m °C)

L :

Fixed bed length (m)

N S :

Interphase heat transfer group (dimensionless)

Pe a :

Axial Peclet number (dimensionless)

Pe af :

Axial fluid Peclet number (dimensionless)

Pe r :

Radial Peclet number (dimensionless)

Pr :

Prandtl number (dimensionless)

R :

Tube radius (m)

r :

Radial position (m)

r * :

Radial position (dimensionless)

Re :

Reynolds number (G d p /μ)

t :

Time (s)

T :

Temperature (°C)

T o :

Inlet air temperature (°C)

T w :

Wall temperature (°C)

T ini :

Fixed bed initial temperature (°C)

\( T_{ij}^{calc} \) :

Calculated temperature (°C)

\( T_{ij}^{\exp } \) :

Experimental temperature (°C)

T*:

Temperature (dimensionless)

u c :

Superficial velocity in the core of the bed (m/s)

\( \bar{u}_{o} \) :

Average superficial velocity (m/s)

z :

Axial position (m)

z * :

Axial position (dimensionless)

α:

Significance level (dimensionless)

ε b :

Bed porosity (dimensionless)

ε p :

Particle porosity (dimensionless)

μ :

Fluid viscosity (kg/m s)

θ :

Time (s)

ρ s :

Solid density (kg/m3)

τ :

Packed bed time constant (s)

τ T :

Temperature sensor time constant (s)

Φ:

Objective function (°C2)

References

  1. Kotanjac ZS, Van Sint Annaland M, Kuipers JAM (2009) A packed bed membrane reactor for the oxidative dehydrogenation of propane on a Ga2O3/MoO3 based catalyst. Chem Eng Sci 65(1):114–119

    Google Scholar 

  2. Rady MA (2009) Experimental and numerical investigations on the performance of dehumidifying desiccant beds composed of silica-gel and thermal energy storage particles. Heat Mass Transf 45:545–561

    Article  Google Scholar 

  3. Gnesdilov NN, Dobrego KV, Kozlov IM (2007) Parametric study of recuperative VOC oxidation reactor with porous media. Int J Heat Mass Transf 50:2787–2794

    Article  MATH  Google Scholar 

  4. DeWasch AP, Froment GF (1972) Heat transfer in packed beds. Chem Eng Sci 27:567–576

    Article  Google Scholar 

  5. Gunn DJ, Khalid M (1975) Thermal dispersion and wall heat transfer in packed beds. Chem Eng Sci 30:261–267

    Article  Google Scholar 

  6. Dixon AG, Paterson WR, Cresswell DL (1978) Heat transfer in packed beds of low tube/particle diameter ratio. ACS Symp Ser 65:238–253

    Article  Google Scholar 

  7. Thoméo JC, Freire JT (2000) Heat transfer in fixed bed: a model non-linearity approach. Chem Eng Sci 55:2329–2338

    Article  Google Scholar 

  8. Bauer M, Adler R (2003) Novel method for investigation and evaluation of heat transfer in fixed bed tubular reactors with gas flow. Heat Mass Transf 39:421–427

    Google Scholar 

  9. Wen D, Ding Y (2006) Heat transfer of gas flow through a packed bed. Chem Eng Sci 61:3532–3542

    Article  Google Scholar 

  10. Polesek-Karczewska S (2003) Effective thermal conductivity of packed beds of spheres in transient heat transfer. Heat Mass Transf 39:375–380

    Google Scholar 

  11. Dixon AG, Cresswell DL (1986) Effective heat transfer parameters for transient packed-bed models. AIChE J 32(5):809–819

    Article  Google Scholar 

  12. Vortmeyer D, Schaefer RJ (1974) Equivalence of one- and two-phase models for heat transfer processes in packed beds: one dimensional theory. Chem Eng Sci 29:485–491

    Article  Google Scholar 

  13. Danckwerts PV (1953) Continuous flow systems. Distribution of residence times. Chem Eng Sci 2:1–13

    Article  Google Scholar 

  14. Wehner JF, Wilhelm RH (1956) Boundary conditions of flow reactor. Chem Eng Sci 6:89–93

    Article  Google Scholar 

  15. Pearson JRA (1959) A note on the “Danckwerts” boundary conditions for continuous flow reactors. Chem Eng Sci 10:281–284

    Article  Google Scholar 

  16. Bischoff KB (1961) A note on boundary conditions for flow reactors. Chem Eng Sci 16:131–133

    Article  Google Scholar 

  17. Van Cauwenberghe AR (1966) Further note on Danckwerts’ boundary conditions for flow reactors. Chem Eng Sci 21:203–205

    Article  Google Scholar 

  18. Michelsen ML (1994) The axial dispersion model and orthogonal collocation. Chem Eng Sci 49(21):3675–3676

    Article  Google Scholar 

  19. Clement K, Jorgensen SB (1983) Experimental investigation of axial and radial thermal dispersion in a packed bed. Chem Eng Sci 38(6):835–842

    Article  Google Scholar 

  20. Giudici R (1990) Modelagem de reator de oxidação de etileno: estudo de parâmetros térmicos e estratégia de diluição de catalisador. DSc thesis, Universidade de São Paulo, São Paulo, Brazil

  21. Jorge LMM (1992) Transferência de calor em reator catalítico de leito fixo. MSc dissertation, Universidade de São Paulo, São Paulo, Brazil

  22. Giudici R, Nascimento CAO (1994) Analysis of a ring-shaped sensor for use in packed-bed heat transfer studies. Can J Chem Eng 72:43–49

    Article  Google Scholar 

  23. Jorge LMM (1998) Estudo experimental e modelagem matemática de reator catalítico de leito fixo: transferência de calor em sistemas sem e com reação de reforma a vapor de metano. DSc thesis, Universidade de São Paulo, São Paulo, Brazil

  24. Jorge LMM, Oliveira GP, Jorge RMM, Giudici R (2003) Time constants determination and analysis for a ring-shaped temperature sensor in fixed bed. Acta Sientiarum Technol 25(1):9–15

    Google Scholar 

  25. Finlayson BA (1980) Nonlinear analysis in chemical engineering. McGraw-Hill, NewYork

    Google Scholar 

  26. Kahaner D, Moler C, Nash S (1989) Numerical methods and software. Prentice-Hall, New Jersey

    MATH  Google Scholar 

  27. Ogunnaike BA, Ray WH (1994) Process dynamics modeling and control. Oxford University Press, New York

    Google Scholar 

  28. Marquardt DW (1963) An algorithm for least squares estimation of non linear parameters. J Soc Ind Appl Math 11(2):431–441

    Article  MATH  MathSciNet  Google Scholar 

  29. Dixon AG, Cresswell DL (1979) Theoretical prediction of effective heat transfer parameters in packed beds. AIChE J 25(4):663–676

    Article  Google Scholar 

  30. Edwards MF, Richardson JF (1968) Gas dispersion in packed beds. Chem Eng Sci 23:109–123

    Article  Google Scholar 

  31. Mongkhonsi T, López-Isunza HF, Kershenbaum LS (1992) The distortion of measured temperature profiles in fixed-bed reactors. Chem Eng Res Des 70:255–264

    Google Scholar 

  32. Thoméo JC, Freire JT (2000) Heat transfer in fixed bed: a model non-linearity approach. Chem Eng Sci 55:2329–2338

    Article  Google Scholar 

  33. Moreira MFP, Ferreira MC, Freire JT (2006) Evaluation of pseudohomogeneous models for heat transfer in packed beds with gas flow and gas-liquid cocurrent downflow and upflow. Chem Eng Sci 61:2056–2068

    Article  Google Scholar 

  34. Dolan KD, Yang L, Trampel CP (2007) Nonlinear regression technique to estimate kinetic parameters and confidence intervals in unsteady-state conduction-heated foods. J Food Eng 80:581–593

    Article  Google Scholar 

  35. VanBoekel MAJS (1996) Statistical aspects of kinetic modeling for food science problems. J Food Sci 61(3):477–486

    Article  Google Scholar 

  36. Johnson ML, Faunt LM (1992) Parameter estimation by least squares methods. Methods Enzymol 210:1–37

    Article  Google Scholar 

  37. Paterson WR, Carberry JJ (1983) Fixed bed catalytic reactor modelling. Chem Eng Sci 38(1):175–180

    Article  Google Scholar 

  38. Wakao N, Kaguei S (1982) Heat and mass transfer in packed beds. Gordon and Breach Science Publishers Inc., New York

    Google Scholar 

  39. Krupiczka R (1967) Analysis of thermal conductivity in granular materials. Int J Chem Eng 7:122–144

    Google Scholar 

  40. Smirnov EI, Muzykantov AV, Kuzmin VA, Kronberg AE, Zolotarskii IA (2003) Radial heat transfer in packed beds of spheres, cylinders and Rashig rings. Verification of model with a linear variation of λer in the vicinity of the wall. Chem Eng J 91:243–248

    Article  Google Scholar 

  41. Winterberg M, Tsotsas E (2000) Correlations for effective heat transport coefficients in beds packed with cylindrical particles. Chem Eng Sci 55:5937–5943

    Article  Google Scholar 

  42. Beek J (1962) Design of packed catalytic reactors. Adv Chem Eng 3:229–303

    Article  Google Scholar 

  43. Calderbank PH, Pogorski LA (1957) Heat transfer in packed beds. Trans Inst Chem Eng 35:195–207

    Google Scholar 

  44. Ziólkowski D, Legawiec B (1987) Remarks upon thermokinetic parameters of the one- and two-dimensional mathematical models of heat transfer in a tubular flow apparatus with a packed bed. Chem Eng Process 21:65–76

    Article  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge financial support from CAPES—Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Brasília, Brazil) and FAPESP—Fundação de Amparo à Pesquisa do Estado de São Paulo (São Paulo, Brazil).

Author information

Authors and Affiliations

  1. Departamento de Engenharia Química, Universidade Estadual de Maringá, Av. Colombo, 5790 Bloco D90, Maringá, PR, CEP 87020-900, Brazil

    Luiz Mario de Matos Jorge

  2. Departamento de Engenharia Química, Universidade Federal do Paraná, C.P. 19011, Curitiba, PR, CEP 81531-990, Brazil

    Regina Maria Matos Jorge

  3. Departamento de Engenharia Química, Escola Politécnica da Universidade de São Paulo, C.P. 61548, São Paulo, SP, CEP 05424-970, Brazil

    Reinaldo Giudici

Authors
  1. Luiz Mario de Matos Jorge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Regina Maria Matos Jorge
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Reinaldo Giudici
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luiz Mario de Matos Jorge.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jorge, L.M.M., Jorge, R.M.M. & Giudici, R. Experimental and numerical investigation of dynamic heat transfer parameters in packed bed. Heat Mass Transfer 46, 1355–1365 (2010). https://doi.org/10.1007/s00231-010-0659-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-010-0659-6

Keywords

Search

Navigation