The Effect of Kernel on the prediction of Energy Distribution Function in a Heterogeneous Solid Adsorbent

Ghorbani, M.R.; Haghighi Asl, A.; Shahsavand, A.; Ahmad Pour, A.

doi:10.30501/jamt.2012.129242

Authors

¹ MSc graduate from School of Chemical Gas and Petroleum Engineering, Semnan University

² School of Chemical Gas and Petroleum Engineering, Semnan University, Semnan, I.R. IRAN

³ Department of Chemical Engineering, Ferdowsi University of Mashhad

https://doi.org/10.30501/jamt.2012.129242

Abstract

In this article, the effect of different adsorption isotherms on the prediction of energy distribution function was considered. It is known that the adsorption integral equation has two parts, kernel (isotherm) and distribution function, in which the energy distribution function can be obtained from the solution of this equation. The important isotherms (kernels) such as Sips, Toth and Unilan were considered. The above isotherms have substituted in the integral equation as kernels and then by using the linear regularization method and inverse theory, the prediction of energy distribution function was performed. The results illustrated that the Sips isotherm have negative effect on the prediction of energy distribution function and the Toth isotherm has performed very well at high levels of stochastic errors. Also, the Unilan isotherm can predict the energy distribution function successfully in all cases.

Keywords

Main Subjects

Organic composition

References

[01] Losi. A and Secchetti. A., “First-Kind Fredholm Integral with Kernel of Hancel Type”, Inverse Problems 15, PP. 281-290, 1999.

[02] William. H. et al,"Numerical Recipes (The art of scientific computing)", Cambridge University Press 2^ndEd. 1992.

[03] Szombathely. M. V., Brauer. P. and Jaroniec. M., “The Solution of Adsorption Integral Equations by Means of the Regularization Method”, Journal of Computational Chemistry, Vol.13, No. 1, PP. 17-32, 1992.

[04] Glob and Loan.,"Matrix computation",third edition, 1996.

[05] Venkatesh. P. K., “On Tikhonov Regularisation”, Physica A, ELSEVIER, Vol. 284, PP. 448-460, 2000.

[06] Merz. P. H., “Determination of Adsorption Energy Distribution by Regularization and a Characterization of Certain Adsorption Isotherms”, Journal of Computational Physics, Vol. 38, PP. 64-85, 1980.

[07] Hansen. O.¹, Fischer. S.² and Ramlau. R.² “Regularization of Mellin–type Inverse Problems with an application to oil engineering”, 1- Johannes Gutenberg–University Mainz and 2- University of Bremen, 2003.

[08] Lamm. P. K., “Variable-Smoothing Regularization Methods for Inverse Problems”, Michigan State University, East Lansing, MI 48824-1027, USA, 2000.

[09] Doung. D. Do., "Adsorption Analysis :Equilibria and Kinetics",Imperical college press, Singapore, 1998.

[10] Ahmadian. H., Mottershead. J. E. and Friswell. M. I., “Regularisation Methods for Finite Element Model Updating”, Mechanical systems and Signal Processing, AP, Vol.12, No. 1, PP. 47-64, 1998.

[11] YAGOLA. A. and TITARENKO. V.," NUMERICAL METHODS AND REGULARIZATION TECHNIQUES FOR THE SOLUTION OF ILL-POSED PROBLEMS", Department of Mathematics, Faculty of Physics, Moscow State University Moscow 119899 Russia, 2000.

[12] Yeun. Y. S., Lee. K. H., Han. S. M. and Yang. Y. S., “Smooth Fitting With a Method for Determining the Regularization Parameter Under the Genetic Programming Algorithm”, Information Sciences, ELSEVIER, Vol. 133, PP. 175-194, 2001.

Journal of Advanced Materials and Technologies

The Effect of Kernel on the prediction of Energy Distribution Function in a Heterogeneous Solid Adsorbent

References

References

Volume 1, Issue 1
October 2012
Pages 69-78

The Effect of Kernel on the prediction of Energy Distribution Function in a Heterogeneous Solid Adsorbent

References

References

Volume 1, Issue 1October 2012Pages 69-78

Volume 1, Issue 1
October 2012
Pages 69-78