1 Detailed simulation of dual-reflux pressure swing adsorption process 1 2 Tushar S. Bhatt a , Giuseppe Storti b , Renato Rota a, * 3 4 a Politecnico di Milano, Chemistry, Materials and Chemical Engineering Department “Giulio Natta”, Via Mancinelli 7, 20131 Milan, Italy 5 b ETH Zürich, Department of Chemistry and Applied Biosciences, Vladimir-Prelog-Weg 1-5/10, HCI F 125, 8093 Zürich, Switzerland 6 7 Highlights 8 9 • Aspen Adsim ® model for simulating realistic DR-PSA process scenarios is presented. 10 • 19 experimental runs reported by McIntyre et al. (2010) are simulated. 11 • Model predictions are in good agreement with experimental results. 12 • Effect of feed position on process performance is assessed via simulations. 13 14 Abstract 15 16 A model for the detailed simulation of dual-reflux pressure swing adsorption process developed in the frame of the 17 commercial software Aspen Adsim ® is presented. For validation purposes, simulations were performed and model 18 predictions were compared with published experimental results. At cyclic steady-state, model predictions were found 19 to be in good agreement with reported experimental results in terms of: (i) average ethane mole fraction in heavy 20 product, (ii) average nitrogen mole fraction in light product, (iii) instantaneous heavy product composition profiles, 21 and (iii) instantaneous column composition profiles. The predicted and experimental trends obtained by analyzing the 22 effect of various operating parameters (light reflux flowrate, duration of feed/purge step, heavy product flowrate and 23 mole fraction of heavy component in binary feed gas mixture) on process performance are also comparable. Overall, 24 this simulation technique of dual-reflux pressure swing adsorption can serve as an effective tool for process design, 25 cost reduction of laboratory and/or plant trails, and enhanced process understanding. 26 27 Keywords: Pressure swing adsorption; Dual-reflux; Mathematical modeling; Gas purification; Process simulation; 28 Cyclic adsorption process 29 30 * Corresponding author. Tel.: +39 0223993154; Fax: +39 0223993180. 31 E-mail: [email protected]32 https://doi.org/10.1016/j.ces.2014.09.013
49
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1
Detailed simulation of dual-reflux pressure swing adsorption process 1
2
Tushar S. Bhatta, Giuseppe Stortib, Renato Rotaa,* 3
4 a Politecnico di Milano, Chemistry, Materials and Chemical Engineering Department “Giulio Natta”, Via Mancinelli 7, 20131 Milan, Italy 5 b ETH Zürich, Department of Chemistry and Applied Biosciences, Vladimir-Prelog-Weg 1-5/10, HCI F 125, 8093 Zürich, Switzerland 6
7
Highlights 8
9
• Aspen Adsim® model for simulating realistic DR-PSA process scenarios is presented.10
• 19 experimental runs reported by McIntyre et al. (2010) are simulated.11
• Model predictions are in good agreement with experimental results.12
• Effect of feed position on process performance is assessed via simulations.13
14
Abstract 15
16
A model for the detailed simulation of dual-reflux pressure swing adsorption process developed in the frame of the 17
commercial software Aspen Adsim® is presented. For validation purposes, simulations were performed and model 18
predictions were compared with published experimental results. At cyclic steady-state, model predictions were found 19
to be in good agreement with reported experimental results in terms of: (i) average ethane mole fraction in heavy 20
product, (ii) average nitrogen mole fraction in light product, (iii) instantaneous heavy product composition profiles, 21
and (iii) instantaneous column composition profiles. The predicted and experimental trends obtained by analyzing the 22
effect of various operating parameters (light reflux flowrate, duration of feed/purge step, heavy product flowrate and 23
mole fraction of heavy component in binary feed gas mixture) on process performance are also comparable. Overall, 24
this simulation technique of dual-reflux pressure swing adsorption can serve as an effective tool for process design, 25
cost reduction of laboratory and/or plant trails, and enhanced process understanding. 26
27
Keywords: Pressure swing adsorption; Dual-reflux; Mathematical modeling; Gas purification; Process simulation; 28
𝑐𝑐𝑖𝑖 Bulk gas-phase concentration of component 𝑖𝑖, kmol/m3
𝐶𝐶𝑆𝑆𝑆𝑆 Cyclic steady state
𝐵𝐵𝑚𝑚𝑜𝑜𝑐𝑐𝑜𝑜𝑚𝑚𝑒𝑒 Diameter of each adsorption column, m
𝐵𝐵𝐾𝐾 Knudsen diffusion coefficient, m2/s
𝐵𝐵𝑀𝑀 Molecular diffusion coefficient, m2/s
𝐵𝐵𝐻𝐻 Macropore diffusion coefficient, m2/s
DR-PH-A dual-reflux pressure swing adsorption system with feed to high pressure bed and pressure swing using heavy gas
DR-PH-B dual-reflux pressure swing adsorption system with feed to high pressure bed and pressure swing using light gas
DR-PL-A dual-reflux pressure swing adsorption system with feed to low pressure bed and pressure swing using heavy gas
DR-PL-B dual-reflux pressure swing adsorption system with feed to low pressure bed and pressure swing using light gas
DR-PSA dual-reflux pressure swing adsorption
𝔽𝔽 represents that the interaction module is feeding back the recorded information
𝐹𝐹𝐹𝐹 Feed step
𝐻𝐻𝑃𝑃 Heavy product
𝐻𝐻𝑅𝑅 Heavy reflux
𝐻𝐻𝑅𝑅𝐹𝐹𝐶𝐶 Heavy reflux flowrate controller
𝐻𝐻𝑅𝑅𝐼𝐼 Heavy reflux interaction
𝐼𝐼 Interaction module
𝐼𝐼𝑃𝑃1 First isotherm parameter, mol/(kg.kPa)
𝐼𝐼𝑃𝑃2 Second isotherm parameter, 1/kPa
𝐾𝐾�𝐾𝐾,𝑖𝑖 Local Henry’s coefficient obtained from equilibrium isotherms, dimensionless
𝑘𝑘𝑀𝑀𝑇𝑇𝑀𝑀 Lumped, effective mass transfer coefficient, 1/s
𝑘𝑘𝑓𝑓 Film resistance coefficient , 1/s
𝐿𝐿𝑏𝑏𝑏𝑏𝑏𝑏 Length of each adsorption column, m
𝐿𝐿𝑃𝑃 Light product
𝐿𝐿𝑃𝑃𝐹𝐹𝐶𝐶 Light product flowrate controller
𝐿𝐿𝑅𝑅 Light reflux
𝐿𝐿𝑅𝑅𝐼𝐼 Light reflux interaction
𝐿𝐿𝐻𝐻𝑆𝑆 Length of rectifying section of the column, m
𝐿𝐿𝑆𝑆𝑆𝑆 Length of stripping section of the column, m
𝑀𝑀𝑚𝑚𝑏𝑏𝑎𝑎 Adsorbent weight, kg
𝑀𝑀𝑊𝑊 Molecular weight, kg/kmol
𝑁𝑁 Number of moles, kmol
𝑁𝑁𝐵𝐵𝐵𝐵 Total number of moles of gas released during Blowdown step, kmol
𝑁𝑁𝐻𝐻𝐻𝐻 Total number of moles of gas fed to the column during Pressurization step, kmol
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𝑃𝑃 Pressure, total pressure, final pressure, kPa
𝑝𝑝 Partial pressure, kPa
𝑃𝑃𝐵𝐵𝐵𝐵,𝑏𝑏𝑒𝑒𝑏𝑏 Pressure at the end of blowdown step, kPa
𝑃𝑃𝐵𝐵𝐹𝐹 Partial differential equation
𝑃𝑃𝐻𝐻 High pressure, kPa
𝑃𝑃𝐼𝐼 Pressure interaction
PID Proportional-Integral-Derivative
𝑃𝑃𝐿𝐿 Low pressure, kPa
𝑃𝑃𝑅𝑅 Pressurization step
PSA Pressure swing adsorption
𝑃𝑃𝑃𝑃 Purge step
𝑄𝑄 Flowrate, sccm
𝑄𝑄𝐵𝐵𝐵𝐵 Flowrate of gas released during blowdown step, sccm
𝑄𝑄𝐵𝐵𝐵𝐵/𝐻𝐻𝐻𝐻 Flowrate of gas released during blowdown step or flowrate of gas fed to the column during pressurization step, sccm
𝑄𝑄𝐹𝐹 Flowrate of feed gas, sccm
𝑄𝑄𝐻𝐻,𝑜𝑜𝑜𝑜𝑜𝑜 Flowrate of gas released from the low pressure column during feed step, sccm
𝑄𝑄𝐻𝐻𝐻𝐻 Flowrate of heavy product, sccm
𝑄𝑄𝐻𝐻𝐻𝐻 Flowrate of heavy reflux, sccm
𝑞𝑞�𝑖𝑖 Particle-average concentration of species 𝑖𝑖 in adsorbed phase per unit mass of solid, kmol/kg
𝑞𝑞𝑖𝑖∗ Adsorbent loading of component 𝑖𝑖 which is in equilibrium with the gas-phase composition, kmol/kg
𝑄𝑄𝐿𝐿,𝑜𝑜𝑜𝑜𝑜𝑜 Flowrate of gas released from the column during purge step, sccm
𝑄𝑄𝐿𝐿𝐻𝐻 Flowrate of light product, sccm
𝑄𝑄𝐿𝐿𝐻𝐻 Flowrate of light reflux, sccm
𝑄𝑄𝐻𝐻𝐻𝐻 Flowrate of gas fed to the column during pressurization step, sccm
𝑅𝑅 Universal gas constant, (kPa.m3)/(kmol.K)
ℝ represents that the interaction module is recording information
𝑅𝑅𝐵𝐵 Reynolds number, dimensionless
𝑟𝑟𝐻𝐻 Radius of adsorbent particle, mm
𝑟𝑟𝐻𝐻 ,𝑚𝑚𝑚𝑚𝑚𝑚 Radius of macropores in adsorbent particle, m
𝑅𝑅𝑆𝑆 Rectifying section
s represents time in seconds
sec represents time in seconds
sccm represents flowrate in standard cubic centimeters per minute, std cm3/min
𝑆𝑆ℎ Sherwood number, dimensionless
𝑆𝑆𝑐𝑐 Schmid number, dimensionless
𝑆𝑆𝑆𝑆 Stripping section
𝑅𝑅 Temperature, K
𝜕𝜕 Time, s
𝜕𝜕𝑚𝑚𝑐𝑐𝑚𝑚𝑐𝑐𝑏𝑏 Time of one DR-PS-A cycle, s
𝜕𝜕𝐹𝐹𝐹𝐹 Feed step duration, s
𝜕𝜕𝐹𝐹𝐹𝐹/𝐻𝐻𝑃𝑃 Feed or purge step duration, s
𝜕𝜕𝐻𝐻𝑃𝑃 Purge step duration, s
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 Adsorbent bed volume, m3
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𝑉𝑉𝐹𝐹 represents the valve through which feed material flows
𝑣𝑣𝑔𝑔 Gas-phase superficial velocity, m/s
𝑉𝑉𝑚𝑚𝑏𝑏𝑎𝑎𝑜𝑜+𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑜𝑜 Mesoporous and macroporous volumes, m3/kg
𝑦𝑦 Mole fraction of heavy component in any stream, final composition (in terms of mole fraction of heavy component), specific concentration value, dimensionless
𝑦𝑦𝑀𝑀2𝐻𝐻6 Mole fraction of 𝐶𝐶2𝐻𝐻6, dimensionless
𝑦𝑦� Average mole fraction of heavy component in any stream, dimensionless
𝑦𝑦𝑖𝑖 Bulk gas-phase mole fraction of component 𝑖𝑖, dimensionless
𝑦𝑦𝐹𝐹 Mole fraction of heavy component in binary feed gas mixture, dimensionless
𝑦𝑦�𝐻𝐻𝐻𝐻 Average mole fraction of heavy component in heavy product stream, dimensionless
𝑦𝑦𝐻𝐻𝐻𝐻 Mole fraction of heavy component in heavy product stream, dimensionless
𝑦𝑦�𝐿𝐿𝐻𝐻 Average mole fraction of heavy component in light product stream, dimensionless
(1 − 𝑦𝑦�𝐿𝐿𝐻𝐻) Average mole fraction of light component in light product stream, dimensionless
𝑍𝑍 axial co-ordinate normalized with respect to column length, dimensionless
𝑧𝑧 position along the length of the adsorption column, axial co-ordinate, m
𝑍𝑍 = 0 Stripping section end of the column, light material is either injected-in or is released at this position during the process, dimensionless
𝑍𝑍 = 1 Rectifying section end of the column, heavy material is either injected-in or is released at this position during the process, dimensionless
𝑍𝑍𝐹𝐹 Feed injection position along the length of the adsorption column, dimensionless 618 619 Greek letters 620 621 𝜀𝜀𝑖𝑖 Interstitial (or external) porosity of the adsorbent, dimensionless
𝜀𝜀𝐻𝐻 Adsorbent particle porosity, dimensionless
𝜀𝜀𝑇𝑇 Total bed voidage, dimensionless
𝜓𝜓 Shape factor of adsorbent particle, dimensionless
𝜌𝜌 Density, kg/m3
𝜌𝜌𝐵𝐵 Bulk density of adsorbent, kg/m3
𝜌𝜌𝑔𝑔 Molar gas-phase density, kmol/m3
𝜌𝜌𝑆𝑆 Solid density of adsorbent, kg/m3
𝜏𝜏 Tortuosity of adsorbent particle, dimensionless
represents open valve at designated or controlled flowrate 626
627
628
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References 629
Bhatt, T.S., Storti, G., Rota, R., 2013. Optimal design of dual-reflux pressure swing adsorption units via equilibrium theory. 630
Chemical Engineering Science 102, 42-55. 631
Diagne, D., Goto, M., Hirosi, T., 1994. New PSA process with intermediate feed inlet position and operated with dual refluxes: 632
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pressure swing adsorption process. Energy Conversion and Management 36, 431–434. 635
Diagne, D., Goto, M., Hirosi, T., 1995b. Parametric studies on CO2 separation and recovery by a dual reflux PSA process 636
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of equilateral cylindrical particles. Chemical Engineering Science, 61(24), 8060-8074. 683
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Fig. 1. DR-PL-A cycle steps and flows. 689 690
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Fig. 2. Schematic representation of DR-PL-A process simulation flowsheet. 698
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Fig. 3. Base case (Run # 1) results at 𝑪𝑪𝑪𝑪𝑪𝑪 during one DR-PL-A cycle. a) Simulation and experimental pressure profiles and b) 709 simulated flow pattern of various streams (𝑭𝑭𝑭𝑭: Feed; 𝑩𝑩𝑩𝑩: Blowdown; 𝑷𝑷𝑳𝑳: Pressurization and; 𝑷𝑷𝑷𝑷: Purge step). 710
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Fig. 4. Simulation and/or experimental (McIntyre et al., 2010) results at 𝑪𝑪𝑪𝑪𝑪𝑪 for Run # 1 to 6 showing the effect of light reflux flowrate 712 (𝑸𝑸𝑳𝑳𝑳𝑳) on: a) average 𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔 mole fraction in heavy product (𝒚𝒚�𝑯𝑯𝑷𝑷); b) average mole fraction of 𝑵𝑵𝟐𝟐 in light product (𝟏𝟏 − 𝒚𝒚�𝑳𝑳𝑷𝑷) and; c) 713 heavy reflux flowrates (𝑸𝑸𝑯𝑯𝑳𝑳). 714
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Fig. 5. Results at cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) for Run # 1 to 6 showing the effect of light reflux flowrate (𝑸𝑸𝑳𝑳𝑳𝑳) on: a) ethane mole 717 fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) measured by the experimenters (McIntyre et al., 2010) during feed step (𝑭𝑭𝑭𝑭); b) model 718 predicted ethane mole fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) during feed step (𝑭𝑭𝑭𝑭); c) ethane mole fraction profile in the column 719 �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the end of high pressure purge step (𝑷𝑷𝑷𝑷) measured by the experimenters (McIntyre et al., 2010) and; d) model predicted 720 ethane mole fraction profile in the column �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the end of high pressure purge step (𝑷𝑷𝑷𝑷). 721
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Fig. 6. Model predicted cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) column composition profiles at the beginning (start) and end of each DR-PL-A cycle 735 step for Run # 1 to 6 (𝑭𝑭𝑭𝑭: Feed; 𝑩𝑩𝑩𝑩: Blowdown; 𝑷𝑷𝑳𝑳: Pressurization and; 𝑷𝑷𝑷𝑷: Purge step). 736
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Fig. 7. Simulation and/or experimental (McIntyre et al., 2010) results at 𝑪𝑪𝑪𝑪𝑪𝑪 for Run # 7, 8, 1 and 9 to 12; showing the effect of feed or 739 purge step duration �𝒕𝒕𝑭𝑭𝑭𝑭/𝑷𝑷𝑷𝑷� on: a) average 𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔 mole fraction in heavy product (𝒚𝒚�𝑯𝑯𝑷𝑷); b) average mole fraction of 𝑵𝑵𝟐𝟐 in light 740 product (𝟏𝟏 − 𝒚𝒚�𝑳𝑳𝑷𝑷) and; c) heavy reflux flowrates (𝑸𝑸𝑯𝑯𝑳𝑳). 741
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Fig. 8. Results at cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) for Run # 7, 8, 1 and 9 to 12; showing the effect of feed or purge step duration �𝒕𝒕𝑭𝑭𝑭𝑭/𝑷𝑷𝑷𝑷� 745 on: a) ethane mole fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) measured by the experimenters (McIntyre et al., 2010) during feed step 746 (𝑭𝑭𝑭𝑭); b) model predicted ethane mole fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) during feed step (𝑭𝑭𝑭𝑭); c) ethane mole fraction profile 747 in the column �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the end of high pressure purge step (𝑷𝑷𝑷𝑷) measured by the experimenters (McIntyre et al., 2010) and; d) 748 model predicted ethane mole fraction profile in the column �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the end of high pressure purge step (𝑷𝑷𝑷𝑷). 749
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762
763
Fig. 9. Model predicted cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) column composition profiles at the beginning (start) and end of each DR-PL-A cycle 764 step for Run # 7, 8, 1 and 9 to 12 (𝑭𝑭𝑭𝑭: Feed; 𝑩𝑩𝑩𝑩: Blowdown; 𝑷𝑷𝑳𝑳: Pressurization and; 𝑷𝑷𝑷𝑷: Purge step). 765
766
https://doi.org/10.1016/j.ces.2014.09.013
38
767
Fig. 10. Simulation and/or experimental (McIntyre et al., 2010) results at 𝑪𝑪𝑪𝑪𝑪𝑪 for Run # 13, 1, 14 and 15 showing the effect of heavy 768 product flowrate (𝑸𝑸𝑯𝑯𝑷𝑷) on: a) average 𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔 mole fraction in heavy product (𝒚𝒚�𝑯𝑯𝑷𝑷); b) average mole fraction of 𝑵𝑵𝟐𝟐 in light product 769 (𝟏𝟏 − 𝒚𝒚�𝑳𝑳𝑷𝑷) and; c) heavy reflux flowrates (𝑸𝑸𝑯𝑯𝑳𝑳). 770
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39
771
772
Fig. 11. Results at cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) for Run # 13, 1, 14 and 15 showing the effect of heavy product flowrate (𝑸𝑸𝑯𝑯𝑷𝑷) on: a) 773 ethane mole fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) measured by the experimenters (McIntyre et al., 2010) during feed step (𝑭𝑭𝑭𝑭); b) 774 model predicted ethane mole fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) during feed step (𝑭𝑭𝑭𝑭); c) ethane mole fraction profile in the 775 column �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the end of high pressure purge step (𝑷𝑷𝑷𝑷) measured by the experimenters (McIntyre et al., 2010) and; d) model 776 predicted ethane mole fraction profile in the column �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the end of high pressure purge step (𝑷𝑷𝑷𝑷). 777
778
779
780
781
782
783
784
785
786
787
788
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40
789
790
Fig. 12. Model predicted cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) column composition profiles at the beginning (start) and end of each DR-PL-A 791 cycle step for Run # 13, 1, 14 and 15 (𝑭𝑭𝑭𝑭: Feed; 𝑩𝑩𝑩𝑩: Blowdown; 𝑷𝑷𝑳𝑳: Pressurization and; 𝑷𝑷𝑷𝑷: Purge step). 792
793
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41
794
Fig. 13. Simulation and/or experimental (McIntyre et al., 2010) results at 𝑪𝑪𝑪𝑪𝑪𝑪 for Run # 16, 17, 1, 18 and 19 showing the effect of 795 ethane mole fraction (𝒚𝒚𝑭𝑭) in binary feed gas mixture on: a) average 𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔 mole fraction in heavy product (𝒚𝒚�𝑯𝑯𝑷𝑷); b) average mole 796 fraction of 𝑵𝑵𝟐𝟐 in light product (𝟏𝟏 − 𝒚𝒚�𝑳𝑳𝑷𝑷) and; c) heavy reflux flowrates (𝑸𝑸𝑯𝑯𝑳𝑳). 797
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42
798
799
Fig. 14. Results at cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) for Run # 16, 17, 1, 18 and 19 showing the effect of ethane mole fraction (𝒚𝒚𝑭𝑭) in binary 800 feed gas mixture on: a) ethane mole fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) measured by the experimenters (McIntyre et al., 2010) 801 during feed step (𝑭𝑭𝑭𝑭); b) model predicted ethane mole fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) during feed step (𝑭𝑭𝑭𝑭); c) ethane mole 802 fraction profile in the column �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the end of high pressure purge step (𝑷𝑷𝑷𝑷) measured by the experimenters (McIntyre et al., 803 2010) and; d) model predicted ethane mole fraction profile in the column �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the end of high pressure purge step (𝑷𝑷𝑷𝑷). 804
805
806
807
808
809
810
811
812
813
814
815
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43
816
817
Fig. 15. Model predicted cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) column composition profiles at the beginning (start) and end of each DR-PL-A 818 cycle step for Run # 16, 17, 1, 18 and 19 (𝑭𝑭𝑭𝑭: Feed; 𝑩𝑩𝑩𝑩: Blowdown; 𝑷𝑷𝑳𝑳: Pressurization and; 𝑷𝑷𝑷𝑷: Purge step). 819
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44
820
821 Fig. 16. Simulation results at 𝑪𝑪𝑪𝑪𝑪𝑪 showing the effect of dimensionless feed position (𝒁𝒁𝑭𝑭) on: a) average 𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔 mole fraction in heavy 822 product (𝒚𝒚�𝑯𝑯𝑷𝑷); b) average mole fraction of 𝑵𝑵𝟐𝟐 in light product (𝟏𝟏 − 𝒚𝒚�𝑳𝑳𝑷𝑷) and; c) heavy reflux flowrates (𝑸𝑸𝑯𝑯𝑳𝑳). 823
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45
824
825
Fig. 17. Model predicted results at cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) showing the effect of dimensionless feed position (𝒁𝒁𝑭𝑭) on: a) ethane 826 mole fraction profile in heavy product (𝒚𝒚𝑯𝑯𝑷𝑷) during feed step (𝑭𝑭𝑭𝑭) and; b) ethane mole fraction profile in the column �𝒚𝒚𝑪𝑪𝟐𝟐𝑯𝑯𝟔𝟔� at the 827 end of high pressure purge step (𝑷𝑷𝑷𝑷). 828
862 863 Fig. 18. Model predicted cyclic steady state (𝑪𝑪𝑪𝑪𝑪𝑪) column composition profiles at the beginning (start) and end of each DR-PL-A 864 cycle step (𝑭𝑭𝑭𝑭: Feed; 𝑩𝑩𝑩𝑩: Blowdown; 𝑷𝑷𝑳𝑳: Pressurization and; 𝑷𝑷𝑷𝑷: Purge step). 865
866
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47
867 868
Table 1. Parameter values used for all simulations. 869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
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48
885
886
Table 2. Values of the operating parameters used in Run # 1 (Base Case) to Run # 19. Parameters in bold italics in a column indicate 887 the group of runs used to study the effect of that parameter on process performance. This table is the identical to Table 2 reported by 888 McIntyre et al. (2010). 889
890
891
892
893
894
895
896
897
898
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49
899
900
Table 3. Modus operandi of various valves and interaction models during different steps in the cycle organizer. ‘’ represents closed 901 valve or nonfunctional interaction; ‘’ represents open valve at designated or controlled flowrate; ‘ℝ’ represents that the interaction 902 model is recording information and ‘𝔽𝔽’ represents that the interaction model is feeding back the recorded information. 903