Skip to main content
SpringerLink
Log in

Comparison of Uniform and Non-uniform Pressure Approaches Used to Analyze an Adsorption Process in a Closed Type Adsorbent Bed

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

Heat and mass transfer in an annular adsorbent bed filled with silica gel particles is numerically analyzed by uniform and non-uniform pressure approaches. The study is performed for silica gel–water pair, particle radius from 0.025 to 1 mm and two bed radii of 10 and 40 mm. For uniform pressure approach, the energy equation for the bed and the mass transfer equation for the particle are solved. For non-uniform pressure approach, the continuity and Darcy equations due to the motion of water vapor in the bed are added, and four coupled partial differential equations are solved. The changes of the adsorbate concentration, pressure, and temperature in the bed throughout the adsorption process for both approaches are obtained and compared. The obtained results showed that the particle size plays an important role on the validity of uniform pressure approach. Due to the interparticle mass transfer resistance, there is a considerable difference between the results of the uniform pressure and non-uniform pressure approaches for the beds with small size of particles such as \(r_\mathrm{{p}} =\) 0.025 mm.

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
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

\(C_\mathrm{p}\) :

Specific heat of adsorbent (Jkg\(^{-1}\) K\(^{-1}\))

\(D_\mathrm{{eff} }\) :

Effective mass transfer diffusivity (m\(^{2}\) s\(^{-1}\))

\(D_\mathrm{K}\) :

Knudsen diffusivity (m\(^{2}\) s\(^{-1}\))

\(D_\mathrm{m}\) :

Molecular diffusivity (m\(^{2}\) s\(^{-1}\))

\(D_{\mathrm{{bed}}}\) :

Effective diffusivity of adsorptive in adsorbent bed (m\(^{2}\) s\(^{-1}\))

\(D_{\mathrm{{o}}}\) :

Reference diffusivity (m\(^{2}\) s\(^{-1}\))

\(E\) :

Diffusional activation energy (J mol\(^{-1}\))

\(K_\mathrm{{inh}}\) :

Inherent permeability of adsorbent bed (m\(^{2}\))

\(K_\mathrm{{app}}\) :

Apparent permeability of adsorbent bed (m\(^{2}\))

\(M\) :

Molecular weight of adsorptive (kg mol\(^{-1}\))

\(P\) :

Pressure (Pa)

r\(_\mathrm{{p}}\) :

Radius of adsorbent granule (m)

\(R\) :

Radius of bed, m; ideal gas constant (J mol\(^{-1}\) K\(^{-1}\))

\(T\) :

Temperature (K)

\(t\) :

Time (s)

\(V_{\mathrm{{r}}}\) :

Adsorptive velocity (m s\(^{-1}\))

\(\overline{{W}}\) :

Average adsorbate concentration (kg\(_\mathrm{{l }}\)/kg\(_\mathrm{{s}}\))

\(W_{\infty }\) :

Local adsorbate concentration (kg\(_\mathrm{{l}}\)/kg\(_\mathrm{{s}}\))

\(\rho \) :

Density (kg m\(^{-3}\))

\(\Delta H_\mathrm{{ads}}\) :

Heat of adsorption (J kg\(^{-1}\))

\(\phi \) :

Porosity

\(\phi \) :

A dependent variable

\(\lambda _\mathrm{{eff}}\) :

Effective thermal conductivity (W m\(^{-1}\) K\(^{-1}\))

\(\mu \) :

Adsorptive viscosity (Ns m\(^{-2}\))

\(\sigma \) :

Collision diameter for Lennard–Jones potential (A\(^{0}\))

\(\varOmega \) :

Collision integral

\(\tau \) :

Tortuosity

a, d:

Final and initial conditions of adsorption

i:

Inner

l:

Adsorptive

o:

Outer

s:

Adsorbent

sat:

Saturation

v:

Adsorbate

\(\infty \) :

Equilibrium

References

  • Al-Sharqawi, H.S., Lior, N.: Conjugate computation of transient flow and heat and mass transfer between humid air and desiccant plates and channels. Numer. Heat Transf. A 46, 525–548 (2004)

    Article  Google Scholar 

  • Amar, N.B., Sun, L.M., Meunier, F.: Numerical analysis of adsorptive temperature wave regenerative heat pump. Appl. Therm. Eng. 16, 405–418 (1996)

    Article  Google Scholar 

  • Bird, B.R., Stewart, E.W., Lightfoot, N.E.: Transport Phenomena, 2nd edn, pp. 189–191. Wiley, New York (2002)

  • Chahbani, H.M., Labidi, J., Paris, J.: Effect of mass transfer kinetics on the performance of adsorptive heat pump systems. Appl. Therm. Eng. 22, 23–40 (2002)

    Article  Google Scholar 

  • Chahbani, H.M., Labidi, J., Paris, J.: Modeling of adsorption heat pumps with heat regeneration. Appl. Therm. Eng. 24, 431–447 (2004)

    Article  Google Scholar 

  • Cengel, Y.A., Boles, M.A.: Thermodynamics: An Engineering Approach. McGraw-Hill Higher Education, New York (2006)

    Google Scholar 

  • Chua, H.T., Ng, K.C., Wang, W., Yap, C., Wang, X.L.: Transient modeling of a two-bed silica gel-water adsorption chiller. Int. J. Heat Mass Transf. 47, 659–669 (2004).

    Google Scholar 

  • Close, D.J., Dunkle, R.V.: Use of adsorbent beds for energy storage in drying and heating systems. Sol. Eng. 19, 233 (1977)

    Article  Google Scholar 

  • Cussler, E.L.: Diffusion Mass Transfer in Fluid Systems, 2nd edn, pp. 104–109. Cambridge University Press, Cambridge (1997)

  • Demir, H., Mobedi, M., Ülkü, S.: A review on adsorption heat pump: problems and solutions. Renew. Sust. Eng. Rev. 12, 2381–2403 (2008)

    Article  Google Scholar 

  • Demir, H., Mobedi, M., Ülkü, S.: Effects of porosity on heat and mass transfer in a granular adsorbent bed. Int. Commun. Heat Mass Transf. 36, 372–377 (2009)

    Article  Google Scholar 

  • Golubovic, M.N., Worek, W.M.: Influence of elevated pressure on sorption in desiccant wheels. Numer. Heat Transf. A 45, 869–886 (2004)

    Article  Google Scholar 

  • Hajji, A., Lavan, Z.: Numerical solution of nonlinear hyperbolic equations governing a regenerative closed-cycle adsorption cooling and heating system. Numer. Heat Transf. A 21, 1–19 (2007)

    Article  Google Scholar 

  • Ilis, G.G., Mobedi, M., Ülkü, S.: A parametric study on isobaric adsorption process in a closed adsorbent bed. Int. Commun. Heat Mass Transf. 37, 540–547 (2010)

    Article  Google Scholar 

  • Ilis, G.G., Mobedi, M., Ülkü, S.: A dimensionless analysis of heat and mass transport in an adsorber with thin fins;uniform pressure approach. Int. Commun. Heat Mass Transf. 38, 790–797 (2011)

    Article  Google Scholar 

  • Incropera, P.F., DeWitt, P.D.: Fundamentals of Heat and Mass Transfer, 4th edn. Wiley, New York (1996)

    Google Scholar 

  • Karger, J., Ruthven, M.D.: Diffusion in Zeolites and Other Microporous Solids. Wiley, New York (1992)

    Google Scholar 

  • Leong, K.C., Liu, Y.: Numerical study of a combined heat and mass recovery adsorption cooling cycle. Int. J. Heat Mass Transf. 47, 4761–4770 (2004a)

    Article  Google Scholar 

  • Leong, K.C., Liu, Y.: Numerical modeling of combined heat and mass transfer in the adsorbent bed of a zeolite/water cooling system. Appl. Therm. Eng. 24, 2359–2374 (2004b)

  • Leong, K.C., Liu, Y.: System performance of a combined heat and mass recovery adsorption cooling cycle: a parametric study. Int. J. Heat Mass Transf. 49, 2703–2711 (2006)

    Article  Google Scholar 

  • Leong, K.C., Liu, Y.: Numerical modeling of a zeolite/water adsorption cooling system with non-constant condensing pressure. Int. Commun. Heat Mass Transf. 35, 618–622 (2008)

    Article  Google Scholar 

  • Li, Y., Sumathy, K.: Comparison between heat transfer and heat mass transfer models for transportation process in an adsorbent bed. Int. Commun. Heat Mass Transf. 47, 1587–1598 (2004)

    Article  Google Scholar 

  • Liu, Y., Leong, K.C.: The effect of operating conditions on the performance of zeolite/water adsorption cooling systems. Appl. Therm. Eng. 22, 1403–1418 (2005)

    Article  Google Scholar 

  • Maggio, G., Gordeeva, L.G., Freni, A., Aristov, Y.I., Santori, G., Polonara, F., Restuccia, G.: Simulation of a solid sorption ice-maker based on the novel composite sorbent “lithium chloride in silica gel pores”. Appl. Therm. Eng. 29, 1714–1720 (2009)

    Article  Google Scholar 

  • Marletta, L., Maggio, G., Freni, A., Ingrasciotta, M., Restuccia, G.: A non-uniform temperature non-uniform pressure dynamic model of heat and mass transfer in compact adsorbent beds. Int. J. Heat Mass Transf. 45, 3321–3330 (2002)

    Article  Google Scholar 

  • Nield, D.A., Bejan, A.: Convection in Porous Media. Springer, New York (2006)

    Google Scholar 

  • Restruccia, G., Freni, A., Maggio, G.: A zeolite-coated bed for air conditioning adsorption systems: parametric study of heat and mass transfer by dynamic simulation. Appl. Therm. Eng. 6, 19–30 (2002)

    Google Scholar 

  • Restuccia, G., Freni, A., Vasta, S., Aristov, Y.: Selective water sorbent for solid sorption chiller: experimental results and modeling. Int. J. Refrig. 27, 284–293 (2004)

    Article  Google Scholar 

  • Ruivo, C.R., Costa, J.J., Figueiredo, A.R.: Analysis of simplifying assumptions for the numerical modeling of the heat and mass transfer in a porous desiccant medium. Numer. Heat Transf. A 49, 851–872 (2006)

    Article  Google Scholar 

  • Ruivo, C.R., Costa, J.J., Figueiredo, A.R.: Numerical study of the cyclic behavior of a desiccant layer of a hygroscopic rotor. Numer. Heat Transf. A 53, 1037–1053 (2008)

    Article  Google Scholar 

  • Saha, B.B., Chakraborty, A., Koyama, S., Aristov, Y.I.: A new generation cooling device employing CaCl\(_{2}\) in silica gel water system. Int. J. Heat Mass Transf. 52, 516–524 (2009)

    Article  Google Scholar 

  • Sakoda, A., Suzuki, M.: Fundamental study on solar powered adsorption cooling system. J. Chem. Eng. Japan. 17, 52–57 (1984)

    Article  Google Scholar 

  • Sakoda, A., Suzuki, M.: Simultaneous transport of heat and adsorbate in closed type adsorption cooling system utilizing solar heat. J. Sol. Eng. Eng. Trans. ASME 108, 239–245 (1986)

    Article  Google Scholar 

  • San, J., Lin, W.: Comparison among three adsorption pairs for using as the working substances in a multi-bed adsorption heat pump. Appl. Therm. Eng. 28, 988–997 (2008)

    Article  Google Scholar 

  • Sun, L.M., Amar, N.B., Meunier, F.: Numerical study on coupled heat and mass transfers in an adsorber with external fluid heating. Heat Recovery Syst. 15, 19–29 (1995)

    Google Scholar 

  • Sphaier, L.A., Worek, W.M.: Numerical solution of periodic heat and mass transfer with adsorption in regenerators: analysis and optimization. Numer. Heat Transf. A 53, 1133–1155 (2008)

    Article  Google Scholar 

  • Tchernev, D.I.: Solar applications of natural zeolites. In: Proceedings of Natural Zeolites Occurrence Properties and Use, Oxford (1976)

  • Tchernev, D.I.: The use of zeolites for solar cooling. In: Proceedings of 5th Inter Conference on Zeolites, Naples, Italy (1980)

  • Wang, X., Chua, H.T.: A comparative evaluation of two different heat-recovery schemes as applied to a two-bed adsorption chiller. Int. J. Heat Mass Transf. 50, 433–443 (2007)

    Article  Google Scholar 

Download references

Acknowledgments

The authors express their very sincere thanks to the reviewers for their valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Izmir Institute of Technology, Urla, 35430 , Izmir, Turkey

    Gamze Gediz Ilis & Moghtada Mobedi

  2. Chemical Engineering Department, Izmir Institute of Technology, Urla, 35430 , Izmir, Turkey

    Semra Ülkü

Authors
  1. Gamze Gediz Ilis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Moghtada Mobedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Semra Ülkü
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Moghtada Mobedi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ilis, G.G., Mobedi, M. & Ülkü, S. Comparison of Uniform and Non-uniform Pressure Approaches Used to Analyze an Adsorption Process in a Closed Type Adsorbent Bed. Transp Porous Med 98, 81–101 (2013). https://doi.org/10.1007/s11242-013-0134-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-013-0134-1

Keywords

Search

Navigation