The Effects of Quartic Term Mathematical Model on The Concentration Profile of Fixed Bed Gas Adsorber

Ary Mauliva Hada Putri(1*)

(1) Research Center for Chemistry-Indonesian Institute of Sciences (LIPI), Kawasan PUSPIPTEK, Serpong, 15314 Tangerang Selatan
(*) Corresponding Author


The need for a reliable mathematical model depicting the process inside a column adsorber has become a requisite in designing an effective gas adsorber. Even though this task can be done by using commercial software, it is still important to get an understanding of how the entire process happens.  In this paper, we discuss a new way to approximate the concentration profile inside the porous solids. It is an extension of the work of Liaw et al., who adopted a parabolic (i.e., quadratic) profile, which is a function of pellet radius while retaining the spherical symmetry. We extend their work by adding the quartic term. The inclusion of this new term still preserves the form of linear driving force approximation with some correction to Glueckauf’s parameter (i.e., the effective diffusivity coefficient). The addition of the correction will affect the breakthrough curve so that it affects the saturation time. In the binary system of hydrogen/methane discussed in this study, we found that a negative correction to the diffusivity coefficient will make the saturation happen earlier compared to that of the parabolic case, and vice versa. This study may help us design an efficient gas purifier, in particular when we set out for the regeneration of the adsorbent.

Keywords: activated carbon; effective diffusivity coefficient; hydrogen; linear driving force; methane; parabolic profile



Kebutuhan model matematis yang dapat menggambarkan proses penyerapan dalam kolom adsorpsi telah menjadi kebutuhan yang tak terelakkan dewasa ini. Walaupun kini telah tersedia berbagai perangkat lunak komersial, namun tidak dapat dipungkiri bahwa memahami bagaimana proses tersebut terjadi tetap menjadi suatu hal yang berguna. Paper ini bertujuan untuk menampilkan cara baru dalam pemodelan konsentrasi adsorbat di dalam adsorben padat berpori. Kami memperluas metode yang dikembangkan Liaw et al. dengan menambahkan suku pangkat empat (kuartik). Penambahan ini akan mengoreksi koefisien difusivitas efektif dari persamaan linear driving force (LDF). Koreksi yang bernilai negatif, misalnya, akan mengurangi nilai koefisien difusivitas tersebut sehingga akan menghambat kemampuan adsorpsi. Hasil perhitungan kami pada sistem biner hidrogen/ metana menunjukkan bahwa suatu koreksi bernilai negatif dapat menyebabkan saturasi berlangsung lebih cepat dari kasus profil parabolik. Begitu pula sebaliknya, koreksi positif akan menambah daya adsorpsi sehingga saturasi dapat diperlambat. Studi ini kami harapkan dapat diterapkan untuk mendesain suatu kolom adsorpsi yang efisien, terutama dalam perencanaan proses regenerasi adsorben.

Kata kunci: hidrogen; karbon aktif; koefisien difusivitas efektif; linear driving force; metana; profil parabolik


activated carbon; effective diffusivity coefficient; hydrogen; linear driving force; methane; parabolic profile

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Bird, R.B., Stewart, W.E. and Lightfoot, E.N., 2006, Transport Phenomena, 2nd ed., Wiley, New York

Do, D.D. and Rice, R.G., 1986, Validity of the parabolic profile assumption in adsorption studies, AIChE J., 32 (1), 149–154.

Glueckauf, E., 1955, Theory of chromatography. Part 10. Formulæ for diffusion into spheres and their application to chromatography, Trans. Faraday Soc., 51 (0), 1540–1551.

Glueckauf, E. and Coates, J.I., 1947, Theory of chromatography. Part IV. The influence of incomplete equilibrium on the front boundary of chromatograms and on the effectiveness of separation, J. Chem. Soc., 1315–1321.

Kärger, J. and Ruthven, D.M., 1992, Diffusion in Zeolites and Other Microporous Solids, Wiley, New York

LeVan, M. ~D., Carta, G. and Yon, C. ~M., 1997, Adsorption and ion exchange, in Perry, R. and Green, D. (Eds.), Perry’s Chem. Eng. Handb., 7th ed., McGraw-Hill, New York, p. 16.

Liaw, C.H., Wang, J.S.P., Greenkorn, R.A. and Chao, K.C., 1979, Kinetics of fixed-bed adsorption: A new solution, AIChE J., 25 (2), 376–381.

Park, J.-H., Kim, J.-N., Cho, S.-H., Kim, J.-D. and Yang, R.T., 1998, Adsorber dynamics and optimal design of layered beds for multicomponent gas adsorption, Chem. Eng. Sci., 53 (23), 3951–3963.

Patton, A., Crittenden, B.D. and Perera, S.P., 2004, Use of the linear driving force approximation to guide the design of monolithic adsorbents, Chem. Eng. Res. Des., 82 (8), 999–1009.

Rosen, J.B., 1952, Kinetics of a Fixed Bed System for Solid Diffusion into Spherical Particles, J. Chem. Phys., 20 (3), 387–394.

Ruthven, D.M., 1984, Principles of Adsorption and Adsorption Processes, Wiley, New York.

Tsai, M.C., Wang, S.S. and Yang, R.T., 1983, Pore-diffusion model for cyclic separation: Temperature swing separation of hydrogen and methane at elevated pressures, AIChE J., 29 (6), 966–975.

Yang, J., Lee, C.-H. and Chang, J.-W., 1997, Separation of hydrogen mixtures by a two-bed pressure swing adsorption process using zeolite 5A, Ind. Eng. Chem. Res., 36 (7), 2789–2798.

Yang, R.T., 1987, Gas Separation by Adsorption Processes, Elsevier, available at:

Yang, R.T. and Doong, S.J., 1985, Gas separation by pressure swing adsorption: A pore-diffusion model for bulk separation, AIChE J., 31 (11), 1829–1842.


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