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An Equation-Based Parallel Column Model Jingsong Zhou, Harry Kooijman, and Ross Taylor Department of Chemical and Biomolecular Engineering Clarkson University Potsdam, NY 13699 10/26/2017
An Equation-Based Parallel Column Model
Jingsong Zhou, Harry Kooijman, and Ross Taylor
Department of Chemical and Biomolecular Engineering Clarkson University Potsdam, NY 13699
10/26/2017
2
DWCs with three products
Dejanović, I., Matijašević, L., & Olujić, Ž. (2010). Dividing wall column—a breakthrough towards sustainable distilling. Chemical Engineering and Processing: Process Intensification, 49(6), 559-580.
Dividing Wall Columns: Not New Anymore
3
DWCs with more than three products
Kaibel, B. Dividing-Wall Columns, in Distillation: Equipment and Processes pp 183–199, Academic Press, 2014
Dividing Wall Columns: Not New Anymore
4
Dividing Wall Columns: Not New Anymore
– Dejanović, I., Matijašević, L. & Olujić, Ž. Dividing wall column—a breakthrough towards sustainable distilling. Chem. Eng. Process. Process Intensif. 49, 5 pp 59–580, 2010
– Yildirim, Ö, Kiss, A.A., Kenig, E.Y., Dividing wall columns in chemical process industry: A review on current activities, Separation and Purification Technology, 80, pp 403-417, 2011
– Kiss, Anton A. Advanced distillation technologies: design, control and applications. John Wiley & Sons, 2013.
– Kaibel, B. Dividing-Wall Columns, in Distillation: Equipment and Processes pp 183–199, Academic Press, 2014
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Dejanović et al. (2010) wrote:
Carrying out DWC performance simulations requires great experience and these are more or less computationally very demanding. … well established commercial software packages still do not contain a DWC as a standard model. This however will occur sooner or later, most probably as a simultaneous, equation based model.
Kaibel (2014) wrote:
Due to the potential variability of complex internal configurations, there is no dedicated software package for this purpose. … As there are strong interactions between the parameters, a rather stiff system of equations has to be solved. The convergence behavior of programs with sequential operation is sometimes problematic. Equation-based programs normally show better convergence characteristics.
But, so far, nobody has provided any evidence that that is true!
Dividing Wall Columns: What They Said
6
Outline
Introduction
Existing simulation strategies and challenges
An equation-based parallel column model
Examples
Validation with Pilot DWC Data
Conclusions
Coming soon…
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Existing Simulation Strategy
Dejanović et al. Aromatics DWC
Dejanovic, I., Matijaševic, L., Jansen, H., & Olujic, Z. (2011). Designing a packed dividing wall column for an aromatics processing plant. Industrial & Engineering Chemistry Research, 50(9), 5680-5692.
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Existing Simulation Strategy
Dejanović et al. Aromatics DWC
Dejanovic, I., Matijaševic, L., Jansen, H., & Olujic, Z. (2011). Designing a packed dividing wall column for an aromatics processing plant. Industrial & Engineering Chemistry Research, 50(9), 5680-5692.
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Existing Simulation Strategy
Generally modeled as multi-column systems
Dejanović et al. Aromatics DWC Four-column model
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Existing Simulation Strategy
Generally modeled as multi-column systems
Dejanović et al. Aromatics DWC Four-column model in UNISIM Design
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Existing Simulation Strategy
Generally modeled as multi-column systems
Dejanović et al. Aromatics DWC Four-column model in COCO
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Existing Simulation Strategy
Generally modeled as multi-column systems
Dejanović et al. Aromatics DWC Two-column model
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Existing Simulation Strategy
Generally modeled as multi-column systems
Dejanović et al. Aromatics DWC Two-column model in COCO
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Satellite Column System
Satellite Column Schematic
Tututi-Avila, S., Domínguez-Díaz, L. A., Medina-Herrera, N., Jiménez-Gutiérrez, A., & Hahn, J. (2017). Dividing-wall columns: Design and control of a kaibel and a satellite distillation column for BTX separation. Chemical Engineering and Processing: Process Intensification, 114, 1-15.
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Satellite Column Schematic Satellite Column System in COCO (easy to converge)
Satellite Column System
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Satellite Column Schematic Satellite Column System in COCO (no convergence)
Satellite Column System
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Satellite Column Schematic Satellite Column System in UNISIM Design
Satellite Column System
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Kaibel Column
Kaibel Column Kaibel Column
in UNISIM Design
Ashrafian, R. (2014). Using Dividing Wall Columns (DWC) in LNG Production: deviding wall column, double dividing wall column, prefractionator arrangement, Petlyuk column, NGL recovery, distillation (Master's thesis, Institutt for energi-og prosessteknikk).
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Multiple Wall Column
Multiple Wall Column
Multiple Wall Column in UNISIM Design
Ashrafian, R. (2014). Using Dividing Wall Columns (DWC) in LNG Production: deviding wall column, double dividing wall column, prefractionator arrangement, Petlyuk column, NGL recovery, distillation (Master's thesis, Institutt for energi-og prosessteknikk).
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Divided Top Column
Divided Top Column Divided Top Column in COCO
Dai, X., Ye, Q., Qin, J., Yu, H., Suo, X., & Li, R. (2016). Energy-saving dividing-wall column design and control for benzene extraction distillation
via mixed entrainer. Chemical Engineering and Processing: Process Intensification, 100, 49-64.
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Divided Top Column
1
6
11
16
21
26
31
36
300 350 400 450 500 550
Stag
e
Flowrate, kmol/h
Liquid
Vapor
Divided Top Column in COCO (false convergence)
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Divided Top Column
Divided Top Column in UNISIM Design (No convergence)
Divided Top Column
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The Challenges
Considerable effort needed to set up a multi-column model
Difficult to provide adequate initial guesses of linking streams
Slow, no, or false convergence
Some desirable specifications cannot be used (e.g. recovery)
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Equation-Based Parallel Column Model
MESH equations:
M: Material balance
𝑀𝑖𝑗 ≡ 𝐿𝑗−1𝑥𝑖,𝑗−1 + 𝑉𝑗+1𝑦𝑖,𝑗+1 + 𝐹𝑗𝑧𝑖𝑗 − 𝐿𝑗 + 𝑈𝑗 𝑥𝑖𝑗 − 𝑉𝑗 +𝑊𝑗 𝑦𝑖𝑗 = 0
𝐻𝑗 ≡ 𝐿𝑗−1𝐻𝑗−1𝐿 + 𝑉𝑗+1𝐻𝑗+1
𝑉 + 𝐹𝑗𝐻𝑗𝐹 − 𝑉𝑗 +𝑊𝑗 𝐻𝑗
𝑉 − 𝐿𝑗 + 𝑈𝑗 𝐻𝑗𝐿 − 𝑄𝑗 = 0
H: Energy balance
E: phase Equilibrium
𝐸𝑖𝑗 ≡ 𝑦𝑖𝑗 − 𝐾𝑖𝑗𝑥𝑖𝑗 = 0
S: mole-fraction Summations
𝑆𝑗𝐿 ≡ 𝑥𝑖𝑗 − 1
𝐶
𝑖=1
= 0 𝑆𝑗𝑉 ≡ 𝑦𝑖𝑗
𝐶
𝑖=1
− 1 = 0
Phase From Stage To Stage Split Ratio
Liquid
27 28 0.5
50 0.5
49 50 0
72 1.0
Vapor
72 49 0.5
71 0.5
50 49 0
27 1.0
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All equations for all stages solved simultaneously
Equation-based ChemSep PCM Dejanović et al. Aromatics DWC
Equation-Based Parallel Column Model
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Dejanović et al. Aromatics DWC Modelled Using ChemSep PCM
Equation-Based Model
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Satellite Column Schematic Equation-based ChemSep PCM (very easy to converge)
(Agrawal arrangement)
Satellite Column System
1
98 72 99
109
110
55
14
15 41
24
47
73 48
65 40 66
85
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1
11
21
31
41
51
320 340 360 380 400 420
Stag
es
Temperature, K
M
L
R
1
11
21
31
41
51
0 0.2 0.4 0.6 0.8 1
Stag
es
Liquid mole fraction
Benzene Toluene m-Xylene 1,3,5-trimethylbenzene
right column
left column
Satellite Column System
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Kaibel Column
Kaibel Column
110
1
2
20
40
60
72
100
109
Feed
21 61
C2
C3
C5+
93 LPG
Equation-based ChemSep PCM
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Kaibel Column
1
11
21
31
41
51
61
250 300 350 400 450 500
Stag
e
Temperature (K)
1
11
21
31
41
51
61
0 200 400 600 800 1000 1200
Stag
e
Flows (kmol/h)
Liquid
Vapor
1
11
21
31
41
51
61
0 0.2 0.4 0.6 0.8 1St
age
Liquid mole fraction
Ethane
Propane
C4
C5+
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Divided Top Column
Equation-based ChemSep PCM
F
1
38
67
2
37
36 61
62
EF
Divided Top Column
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Divided Top Column
1
6
11
16
21
26
31
36
300 350 400 450 500 550
Stag
e
Flowrate, kmol/h
Liquid
Vapor
1
6
11
16
21
26
31
36
100 150 200 250 300 350
Stag
e
Flowrate, kmol/h
Liquid
Vapor
COCO (false solution)
ChemSep PCM (correct solution)
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Divided Top Column
1
6
11
16
21
26
31
36
41
320 370 420 470
Stag
e
Temperature (K)
1
6
11
16
21
26
31
36
41
0 0.2 0.4 0.6 0.8 1
Stag
e
Mole fraction
Benzene Cyclohexane
Sulfolane o-xylene
Top-left
Top-right
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Divided Top Column
1
6
11
16
21
26
31
36
41
320 370 420 470
Stag
e
Temperature (K)
1
6
11
16
21
26
31
36
41
0 0.2 0.4 0.6 0.8 1
Stag
e
Mole fraction
Benzene Cyclohexane
Sulfolane o-xylene
Top-left
Top-right
Temperature gradient across wall can be significant
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Heat Transfer
Dividing walls are not insulators
Feed
A
B
C
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Heat Transfer
Dividing walls are not insulators
Extremely difficult to include heat transfer in multi-column models
Requires many energy interlinks Feed
A
B
C
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Heat Transfer
Dividing walls are not insulators
Extremely difficult to include heat transfer in multi-column models
Very easy to include heat transfer in Parallel Column Model
𝑄𝑗 = 𝑈 ∙ 𝐴𝑗 ∙ ∆𝑇𝑗
U – Overall heat transfer coefficient Aj – Heat transfer area on stage j ∆𝑇𝑗 – Temperature difference
Feed
A
B
C
Terms added to energy balance
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Heat Transfer
System: n-pentane, n-hexane, and n-heptane
Rv = 0.6855
Uwall = 800 W/m2K
RL = 0.3641
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Heat Transfer
1
6
11
16
21
26
31
36
41
46
320 330 340 350 360 370 380 390
Stag
e
Temperature, K
1
6
11
16
21
26
31
36
41
46
320 330 340 350 360 370 380 390
Stag
e
Temperature, K
U = 800 W/m2K
(a) Without heat transfer (b) With heat transfer
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Heat Transfer
Heat transfer affects product purity
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Heat Transfer
What if Uwall goes to infinity…?
1
6
11
16
21
26
31
36
41
46
320 330 340 350 360 370 380 390
Stag
e
Temperature, K
U = 600,000,000 W/m2K
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Compared to multi-column models, the ChemSep PCM
Conclusions
Takes very little effort to set up
Requires no initial guesses from engineer
Converges much quicker
Converges to the correct solution when other simulators fail
Makes it easy to model heat transfer across the wall
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Rate-based Parallel Column Model
Other Uses for a PCM…
Coming Soon…
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Crude Column Systems
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PCM for Maldistribution
Equivalent PCM Structure Billingham and Lockett Maldistribution Model
Redistributors modeled as stages with no mass transfer
