# Mathematical Modeling of Natural Gas Separation Using Hollow Fiber Membrane Modules by Application of Finite Element Method through Statistical Analysis

• Javad Aminian Dehkordi , Seyed Saeid Hosseini , Prodip K. Kundu and Nicolas R. Tan

## Abstract

Hollow fiber membrane permeators used in the separation industry are proven as preferred modules representing various benefits and advantages to gas separation processes. In the present study, a mathematical model is proposed to predict the separation performance of natural gas using hollow fiber membrane modules. The model is used to perform sensitivity analysis to distinguish which process parameters influence the most and are necessary to be assessed appropriately. In this model, SRK equation was used to justify the nonideal behavior of gas mixtures and Joule-Thomson equation was employed to take into account the changes in the temperature due to permeation. Also, the changes in temperature along shell side was calculated via thermodynamic principles. In the proposed mathematical model, the temperature dependence of membrane permeance is justified by the Arrhenius-type equation. Furthermore, a surface mole fraction parameter is introduced to consider the effect of accumulation of less permeable component adjacent to the membrane surface in the feed side. The model is validated using experimental data. Central Composite Designs are used to gain response surface model. For this, fiber inner diameter, active fiber length, module diameter and number of fibers in the module are taken as the input variables related to the physical geometries. Results show that the number as well as the length of the fibers have the most influence on the membrane performance. The maximum mole fraction of CO2 in the permeate stream is observed for low number of fibers and fibers having smaller active lengths. Also results indicate that at constant active fiber length, increasing the number of fibers decreases the permeate mole fraction of CO2. The findings demonstrate the importance of considering appropriate physical geometries for designing hollow fiber membrane permeators for practical gas separation applications.

## References

1. Xiao Y, Low BT, Hosseini SS, Chung TS, Paul DR. The strategies of molecular architecture and modification of polyimide-based membranes for CO2 removal from natural gas – A review. Prog Polym Sci 2009;34:561–80.10.1016/j.progpolymsci.2008.12.004Search in Google Scholar

2. Hosseini SS, Peng N, Chung TS. Gas separation membranes developed through integration of polymer blending and dual-layer hollow fiber spinning process for hydrogen and natural gas enrichments. J Membr Sci. 2010;349:156–66.10.1016/j.memsci.2009.11.043Search in Google Scholar

3. Najari S, Hosseini SS, Omidkhah M, Tan NR. Phenomenological modeling and analysis of gas transport in polyimide membranes for propylene/propane separation. RSC Adv 2015;5:47199–215.10.1039/C5RA05556CSearch in Google Scholar

4. Hosseini SS, Chung TS. Carbon membranes from blends of PBI and polyimides for N2/CH4 and CO2/CH4 separation and hydrogen purification. J Membr Sci 2009;328:174–85.10.1016/j.memsci.2008.12.005Search in Google Scholar

5. Hosseini SS, Chung TS, Polymer blends and carbonized polymer blends, US Patent 8,623,124, 2014.Search in Google Scholar

6. Kaldis SP, Kapantaidakis GC, Sakellaropoulos GP. Simulation of multicomponent gas separation in a hollow fiber membrane by orthogonal collocation – hydrogen recovery from refinery gases. J Membr Sci 2000;173:61–71.10.1016/S0376-7388(00)00353-7Search in Google Scholar

7. Scholz M, Harlacher T, Melin T, Wessling M. Modeling gas permeation by linking nonideal effects. Ind Eng Chem Res 2012;52:1079–88.10.1021/ie202689mSearch in Google Scholar

8. Hosseini SS. Membranes and Materials for Separation and Purification of Hydrogen and Natural Gas: PhD Thesis, National University of Singapore; 2009.Search in Google Scholar

9. Weller S, Steiner WA. Separation of gases by fractional permeation through membranes. J Appl Phys 1950;21:279–83.10.1063/1.1699653Search in Google Scholar

10. Hosseini SS, Roodashti SM, Kundu PK, Tan NR. Transport properties of asymmetric hollow fiber membrane permeators for practical applications: Mathematical modelling for binary gas mixtures. Can J Chem Eng 2015;93: 1275–87.10.1002/cjce.22215Search in Google Scholar

11. Hosseini SS, Najari S, Kundu PK, Tan NR, Roodashti SM. Simulation and sensitivity analysis of transport in asymmetric hollow fiber membrane permeators for air separation. RSC Adv. 2015;5:86359–70.10.1039/C5RA13943KSearch in Google Scholar

12. Rastegar S, Mousavi S, Rezaei M, Shojaosadati S. Statistical evaluation and optimization of effective parameters in bioleaching of metals from molybdenite concentrate using Acidianus brierleyi. J Ind Eng Chem 2014;20:3096–101.10.1016/j.jiec.2013.11.049Search in Google Scholar

13. Myers RH, Montgomery DC, Anderson-Cook CM. Response surface methodology: process and product optimization using designed experiments, 3rd ed. Hoboken, New Jersey, USA: John Wiley & Sons, Inc., 2009.Search in Google Scholar

14. Tranchino L, Santarossa R, Carta F, Fabiani C, Bimbi L. Gas separation in a membrane unit: experimental results and theoretical predictions. Sep Sci Tech 1989;24:1207–26.10.1080/01496398908049898Search in Google Scholar

15. Feng X, Ivory J, Rajan VSV. Air separation by integrally asymmetric hollow-fiber membranes. AIChE J 1999;45:2142–52.10.1002/aic.690451013Search in Google Scholar