Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter November 19, 2021

Development of a CFD-based simulation model and optimization of thermal diffusion column: application on noble gas separation

  • Hamed Eghbalahmadi , Parissa Khadiv-Parsi EMAIL logo , Seyed Mohammad Ali Mousavian and Mohammad Hosein Eghbal Ahmadi ORCID logo


In this study, numerical simulations were carried out to investigate the separation of the helium-argon gas mixture by thermal diffusion column. This research determined the significant parameters and their effects on the process performance. Effects of feed flow rate, cut ratio, and hot wire temperature in a 950 mm height column with an inner tube of 9.5 mm radius were examined through the simulation of the thermal diffusion column. For minimizing the number of simulations and obtaining the optimum operating conditions, response surface methodology (RSM) was used. Analysis of separative work unit (SWU) values as a target function for helium-argon separation clearly showed that the maximum amount of SWU in thermal diffusion column was achieved, when hot wire temperature increased as large as technically possible, and the feed rate and cut ratio were equal to 55 Standard Cubic Centimeters per Minute (SCCM) and 0.44, respectively. Finally, the SWU value in optimum conditions was compared with the experimental data. Results illustrated that the experimental data were in good agreement with simulation data with an accuracy of about 90%.

Corresponding author: Parissa Khadiv-Parsi, School of Chemical Engineering, 4th floor, College of Engineering, University of Tehran, Tehran 11155-4563, Iran, E-mail:


I thank Mr. Saeed Yaghoobi and Mr. Shahab Golshan for assistance for writing assistance, and my colleagues for comments that greatly improved the manuscript.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


1. Wang, QM, Shen, D, Bülow, M, Lau, ML, Deng, S, Fitch, FR, et al.. Metallo-organic molecular sieve for gas separation and purification. Microporous Mesoporous Mater 2002;55:217–30. in Google Scholar

2. Yang, B, Yuan, W, Gao, F, Guo, B. A review of membrane-based air dehumidification. Indoor Built Environ 2015;24:11–26. in Google Scholar

3. Qi, R, Dong, C, Zhang, LZ. A review of liquid desiccant air dehumidification: from system to material manipulations. Energy Build 2020;215:109897. in Google Scholar

4. Baker, RW, Low, BT. Gas separation membrane materials: a perspective. Macromolecules 2014;47:6999–7013. in Google Scholar

5. Geankoplis, CJ, Hersel, AA, Lepek, DH. Transport processes and separation process principles. Boston, MA: Prentice-Hall; 2018.Search in Google Scholar

6. Iulianelli, A, Drioli, E. Membrane engineering: latest advancements in gas separation and pre-treatment processes, petrochemical industry and refinery, and future perspectives in emerging applications. Fuel Process Technol 2020;206:106464. in Google Scholar

7. Ismail, AF, Khulbe, KC, Matsuura, T. Gas separation membranes. Switz Springer 2015;10:978–3. in Google Scholar

8. Ghoreishi, SM, Dastgerdi, ZH, Dadkhah, AA. Numerical analysis and optimization of oxygen separation from air via pressure swing adsorption. Chem Prod Process Model 2011;6. in Google Scholar

9. Bum Park, H. Gas separation membranes. Encycl Membr Sci Technol 2013;3:1–32. in Google Scholar

10. Ward, TL, Dao, T. Model of hydrogen permeation behavior in palladium membranes. J Membr Sci 1999;153:211–31. in Google Scholar

11. Burggraaf, AJ. Important characteristics of inorganic membranes. Membr Sci Technol 1996;4:21–34. in Google Scholar

12. Nezami, HM, Babaluo, AA, Bayati, B. Modified solution approach in modeling of separation of gaseous hydrocarbons using nanostructure MFI zeolite membranes with MS formulation and DSL and IAST assumptions. Chem Prod Process Model 2011;6. in Google Scholar

13. Kancherla, R, Kumar, VR, Reddy, GP, Sridhar, S. Nitrate removal studies on polyurea membrane using nanofiltration system–membrane characterization and model development. Chem Prod Process Model 2020;20200041.10.1515/cppm-2020-0041Search in Google Scholar

14. Teplyakov, VV, Okunev, AY, Laguntsov, NI. Computer design of recycle membrane contactor systems for gas separation. Separ Purif Technol 2007;57:450–4. in Google Scholar

15. Zhanat, U, Sharipzhan, E. Mechanism of gases transfer through polymer membranes and membrane module calculation model to separate gases. Procedia Technol 2012;1:356–61. in Google Scholar

16. Castle, WF. Air separation and liquefaction: recent developments and prospects for the beginning of the new millennium. Int J Refrig 2002;25:158–72. in Google Scholar

17. Xu, G, Li, L, Yang, Y, Tian, L, Liu, T, Zhang, K. A novel CO2 cryogenic liquefaction and separation system, Energy. 2012;42:522–9. in Google Scholar

18. Zanganeh, KE, Shafeen, A, Salvador, C. CO2 capture and development of an advanced pilot-scale cryogenic separation and compression unit. Energy Procedia 2009;1:247–52. in Google Scholar

19. Platten, JK. The Soret effect: a review of recent experimental results. J Appl Mech 2006;73:5–15. in Google Scholar

20. Yeh, HM. Recovery of deuterium from the separation of H–D gas mixture in concentric-tube thermal diffusion columns with transverse sampling streams. Fusion Eng Des 2009;84:2174–7. in Google Scholar

21. Yamakawa, H, Mori, S, Takenaga, Y, Kobayashi, N, Enokida, Y, Yamamoto, I. Effect of cold wall temperature of thermal diffusion column on 14N15N—14N2 isotope separation. J Nucl Sci Technol 2000;37:710–5. in Google Scholar

22. Mason, EA, Munn, RJ, Smith, FJ. Thermal diffusion in gases. Adv At Mol Phys 1966;2:33–91. in Google Scholar

23. Yeh, HM. Enrichment of heavy water in flat-plate thermal diffusion columns inclined for improved performance. Separ Purif Technol 2002;26:227–36. in Google Scholar

24. YEH, HM. Enrichment of heavy water by thermal diffusion. Chem Eng Commun 1998;167:167–79. in Google Scholar

25. Reith, D, Müller-Plathe, F. On the nature of thermal diffusion in binary Lennard-Jones liquids. J Chem Phys 2000;112:2436–43. in Google Scholar

26. Platten, JK, Bou-Ali, MM, Dutrieux, JF. Enhanced molecular separation in inclined thermo-gravitational columns. J Phys Chem B 2003;107:11763–7. in Google Scholar

27. Ryzhkov, II, Stepanova, IV. On thermal diffusion separation in binary mixtures with variable transport coefficients. Int J Heat Mass Tran 2015;86:268–76. in Google Scholar

28. Heines, TS, Larson, OA, Martin, JJ. Separation of benzene and n-heptane in continuous thermal diffusion columns. Ind Eng Chem 1957;49:1911–20. in Google Scholar

29. VanVaerenbergh, S, Srinivasan, S, Saghir, MZ. Thermodiffusion in multicomponent hydrocarbon mixtures: experimental investigations and computational analysis. J Chem Phys 2009;131:114505. in Google Scholar PubMed

30. Yeh, HM. Design of batch-type flat-plate thermal diffusion columns for recovery of deuterium from water–isotopes mixture with energy consumption rate fixed. Fusion Eng Des 2008;83:752–8. in Google Scholar

31. Bindeman, IN, Lundstrom, CC, Bopp, C, Huang, F. Stable isotope fractionation by thermal diffusion through partially molten wet and dry silicate rocks. Earth Planet Sci Lett 2013;365:51–62. in Google Scholar

32. Richter, FM, Watson, EB, Mendybaev, RA, Teng, FZ, Janney, PE. Magnesium isotope fractionation in silicate melts by chemical and thermal diffusion. Geochem Cosmochim Acta 2008;72:206–20. in Google Scholar

33. Hoang, H, Nguyen, P, Pujol, M, Galliero, G. Elemental and isotopic fractionation of noble gases in gas and oil under reservoir conditions: impact of thermo-diffusion. Eur Phys J E 2019;42:1–10. in Google Scholar PubMed

34. Yeh, HM, Lin, WH. Thermal diffusion in an ideal column. Separ Sci Technol 1991;26:395–407. in Google Scholar

35. Simon, R. Performance of a hot wire Clusius and Dickel column. Phys Rev 1946;69:596. in Google Scholar

36. Clusius, K, Dickel, G. New process for separation of gas mixtures and isotopes. Naturwissenschaften 1938;26:546. in Google Scholar

37. Furry, WH, Jones, RC. Isotope separation by thermal diffusion: the cylindrical case. Phys Rev 1946;69:459. in Google Scholar

38. Srivastava, BN, Srivastava, RC. Investigation of the performance of thermal diffusion column. Physica 1954;20:237–42. in Google Scholar

39. McInteer, BB, Reisfeld, MJ. Thermal‐diffusion‐column shape factors for the Lennard‐Jones (12–6) potential. J Chem Phys 1960;33:570–3. in Google Scholar

40. Saxena, SC, Raman, S. Theory and performance of thermal-diffusion column. Rev Mod Phys 1962;34:252. in Google Scholar

41. Yamamoto, I, Makino, H, Kanagawa, A. Optimum pressure for total-reflux operated thermal diffusion column for isotope separation. J Nucl Sci Technol 1990;27:149–56. in Google Scholar

42. Yamamoto, I, Kanagawa, A. Similarity in pressure dependence among separation factors of thermal diffusion column in total-reflux operation. J Nucl Sci Technol 1993;30:831–3. in Google Scholar

43. Yamamoto, I, Makino, H, Kanagawa, A. Optimum feed point for isotope separating thermal diffusion column. J Nucl Sci Technol 1995;32:200–5. in Google Scholar

44. Cox, N, Drapala, P, Finlayson, BF. Transport limitations in thermal diffusion. In: The 2007 AIChE annual meeting, Salt Lake City, UT; 2007.Search in Google Scholar

45. Wiegand, S. Thermal diffusion in liquid mixtures and polymer solutions. J Phys Condens Matter 2004;16:R357. in Google Scholar

46. Ahadi, A, Giraudet, C, Jawad, H, Croccolo, F, Bataller, H, Saghir, MZ. Experimental, theoretical and numerical interpretation of thermodiffusion separation for a non-associating binary mixture in liquid/porous layers. Int J Therm Sci 2014;80:108–17. in Google Scholar

47. Yamamoto, I, Baba, T, Kanagawa, A. Measurement of separative characteristics of thermal diffusion column for argon isotope separation. J Nucl Sci Technol 1987;24:565–72. in Google Scholar

48. Yamamoto, I, Kanoh, K, Kanagawa, A. Numerical solution of two-dimensional axisymmetric free convection within isotope separating thermal diffusion column. J Nucl Sci Technol 1985;22:469–83. in Google Scholar

49. Yamamoto, I, Yamagishi, K, Kanagawa, A. Numerical calculation of concentration profiles within thermal diffusion column with continuous feed and draw-offs. J Nucl Sci Technol 1987;24:393–403. in Google Scholar

50. Yamakawa, H, Matsumoto, K, Enokida, Y, Yamamoto, I. Numerical analysis of dynamic behavior at start-up of the thermal diffusion column for hydrogen isotope separation. J Nucl Sci Technol 1999;36:198–203. in Google Scholar

51. Vela´ squez, JE, Chejne, F, Hill, AF. Mathematical model and simulation of a thermal diffusion column. J Heat Tran 2003;125:266–73.10.1115/1.1560150Search in Google Scholar

52. Clarke, R, Nuttall, W, Glowacki, B. Endangered helium: bursting the myth. Chem Eng 2013;870:32–6.Search in Google Scholar

53. Berezhnoi, AN, Semenov, AV. Thermal diffusion in the helium–argon gas system. Theor Found Chem Eng 2004;38:483–9. in Google Scholar

54. McCourt, FR. Thermal diffusion in binary mixtures containing molecular gases. III. The temperature dependence of αT. Mol Phys 2003;101:3223–9. in Google Scholar

55. Rufford, TE, Chan, KI, Huang, SH, May, EF. A review of conventional and emerging process technologies for the recovery of helium from natural gas. Adsorpt Sci Technol 2014;32:49–72. in Google Scholar

56. Ozsunar, A, Baskaya, S, Sivrioglu, M. Numerical analysis of Grashof number, Reynolds number and inclination effects on mixed convection heat transfer in rectangular channels. Int Commun Heat Mass Tran 2001;28:985–94. in Google Scholar

57. Bird, RB. Transport phenomena. Appl Mech Rev 2002;55:R1–4. in Google Scholar

58. Văsaru, G, Mülller, G, Reinhold, G, Fodor, T. The thermal diffusion column: theory and practice with particular emphasis on isotope separation. Berlin: VEB Deutscher Verlag der Wissenschaften; 1969.Search in Google Scholar

59. Wilke, CR. A viscosity equation for gas mixtures. J Chem Phys 1950;18:517–9. in Google Scholar

60. Rahman, MA, Saghir, MZ. Thermo-diffusion or Soret effect: historical review. Int J Heat Mass Tran 2014;73:693–705. in Google Scholar

61. Navarro, JL, Madariaga, JA, Santamarià, CM, Savirón, JM, Carriòn, JA. Thermal diffusion factor for carbon tetrachloride-cyclohexane and benzene-n-heptane mixtures from thermo-gravitational column separation. Separ Sci Technol 1985;20:335–43. in Google Scholar

62. Wood, HG, Ying, C, Zeng, S, Nie, Y, Shang, X. Estimation of overall separation factor of a gas centrifuge for different multicomponent mixtures by separation theory for binary case. Separ Sci Technol 2002;37:417–30. in Google Scholar

63. Kotz, S, Johnson, NL. editors. Breakthroughs in statistics: methodology and distribution. New York: Springer-Verlag New York, Inc.; 1992.10.1007/978-1-4612-4380-9Search in Google Scholar

64. Bezerra, MA, Santelli, RE, Oliveira, EP, Villar, LS, Escaleira, LA. Response surface methodology (RSM) as a tool for optimization in analytical chemistry. Talanta 2008;76:965–77. in Google Scholar PubMed

65. Ferreira, SLC, Bruns, RE, Ferreira, HS, Matos, GD, David, JM, Brandao, GC. EGP da. Silva, LA Portugal, PS dos. Reis, AS Souza and WNL dos. Santos, Box–Behnken design: an alternative for the optimization of analytical methods. Anal Chim Acta 2007;597:179–86. in Google Scholar PubMed

Received: 2021-08-03
Accepted: 2021-10-21
Published Online: 2021-11-19

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 27.9.2023 from
Scroll to top button