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Design of Air Separation Units for Advanced Combustion
via Equation Based Optimization
Alexander W. Dowling Lorenz T. Biegler
Carnegie Mellon University
AIChE Annual Meeting November 4th, 2013
Process Systems Engineering
Motivation
Develop framework for full oxycombustion power plant optimization
– Estimate cost of electricity with carbon capture – Balance trade-offs between systems
2
Oxycombustion Power Plant 1. Air Separation Unit 2. Boiler 3. Steam Turbines 4. Pollution Controls 5. CO2 Compression Train
1 2
3
4 5
Methodology: Equation Oriented – High fidelity models (approaching first principles)
– Accurate derivative information efficient large
scale optimization algorithms (100,000+ variables)
– Consider integer decisions (MINLP)
– Low cost sensitivity information
– Optimality guarantees
3
Motivation
Develop framework for full oxycombustion power plant optimization
– Estimate cost of electricity with carbon capture – Balance trade-offs between systems
4
Start with cryogenic ASU
Cryogenic Air Separation
Boiling Points @ 1 atm Oxygen: -183 °C Argon: -185.7 °C Nitrogen: -195.8 °C
Multicomponent distillation with tight heat
integration
5
Photo from wikipedia.org
Low pressure section
High pressure section
Challenging to systematically optimize in AspenPlus.
Double Column Configuration
6
Column Cascade
Total Condenser
Partial Reboiler
Flash
Valve
Splitter
Multistream Heat Exchanger
ASU Superstructure
• Many different column configurations realizable
• NLP optimizer selects the
best configuration
7
Optimization Formulation
Note: Upper and lower bounds not shown above are considered for many variables including stream/equipment temperatures and pressures. 8
Cubic Equation of State
Z Z
Ex: Peng-Robinson Kamath, R. S., Biegler, L. T., & Grossmann, I. E. (2010). An equation-oriented approach for handling thermodynamics based on cubic equation of state in process optimization. Computers & Chemical Engineering, 34(12), 2085–2096.
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Mole balance
Energy Balance Equilibrium
Cascade Models
Group Method MESH Model with Bypass
10
Simpler approximation
Complex & rigorous
𝜀𝜀 = 𝑉𝑉𝑖𝑖∗
𝑉𝑉𝑖𝑖−1 = 𝐿𝐿𝑖𝑖
∗
𝐿𝐿𝑖𝑖+1
Tray i
Vi-1
Vi Li+1
Li
Vi* Li
*
Cascade Models
11
• Continuous number of ideal stages
• Based on the work of Kremser and Edmister
• Modified for general distillation by Kamath
• New distillation model
• Mass, Equilibrium, Summation and Heat equations
• Model discrete trays
• Bypass allows for tray (de)activation with only continuous variables
Kamath, Grossmann & Biegler (2010). Aggregate models based on improved group methods for simulation and optimization of distillation systems. Computers & Chemical Engineering.
Group Method MESH Model with Bypass
12
Yeomans, H., & Grossmann, I. E. (2000). Disjunctive Programming Models for the Optimal Design of Distillation Columns and Separation Sequences. Industrial & Engineering Chemistry Research, 39(6), 1637–1648.
Tray i
Tray i-1
Tray i+1
MESH with Bypass
Yeomans & Grossmann (2000) – Disjunctive model to
(de)activate trays – Logic based solution algorithm
MESH with Bypass
Yeomans & Grossmann (2000) – Disjunctive model to
(de)activate trays – Logic based solution algorithm
New model
– Use generic NLP solver – Equilibrium calculated with Vi-1
and Li+1 to avoid degeneracies
13
𝜀𝜀 = 𝑉𝑉𝑖𝑖∗
𝑉𝑉𝑖𝑖−1 = 𝐿𝐿𝑖𝑖
∗
𝐿𝐿𝑖𝑖+1
Tray i
Vi-1
Vi Li+1
Li
Vi* Li
*
Splitter
Mixer
Pinch Based Heat Integration
14
Tem
pera
ture
Heat Qw Cold Utility
Qs Hot Utility
Hot Composite Curve
Cold Composite Curve
Shift curves horizontally until ΔTmin is limiting
Flowsheet Optimization
Heat Integration
Hohmann, E.C. (1971). Optimum Networks for Heat Exchangers. PhD Thesis, University of So. Cal. Linnhoff, B. (1993). Pinch analysis – A state-of-the-art overview. Trans. IChemE., 71(A), 503.
Pinch Based Heat Integration
15
Tem
pera
ture
Heat Qw Cold Utility
Qs Hot Utility
ΔTmin
Hot Composite Curve
Cold Composite Curve
Shift curves horizontally until ΔTmin is limiting
Pinch point
Flowsheet Optimization
Heat Integration
Hohmann, E.C. (1971). Optimum Networks for Heat Exchangers. PhD Thesis, University of So. Cal. Linnhoff, B. (1993). Pinch analysis – A state-of-the-art overview. Trans. IChemE., 71(A), 503.
Heat Integration Model
16
Pinch candidates Available heating and cooling above pinch Utility calculations
Flowsheet Optimization
Heat Integration Duran, M. A., & Grossmann, I. E. (1986). Simultaneous optimization and heat integration of chemical processes. AIChE Journal, 32(1), 123–138.
Heat Exchanger Decomposition
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2-phase
vapor
liquid
Q
T
HX3 HX2
HX1
Decomposition for Validation
2-phase
vapor
liquid
Q
T
HX3b
HX2b & HX2a
HX3a HX1b HX1a
Implementation Details
• Non-convex problem – 12,000 variables &
constraints
• Automated initialization – Simple complex models – Custom multistart procedure
• Solved using CONOPT3 in
GAMS – 12 CPU minutes on Intel i7
desktop for one initial point
18
Initialization Procedure
19
Ideal Thermo & Shortcut Cascade
CEOS Thermo & Shortcut Cascade
CEOS Thermo & MESH Cascade
Decompose Heat Exchange Units &
Reoptimize
Repeat with different combinations of initial
values and bounds
Sort local solutions by final obj. function value
1.80 mol/t (.78, 0.21, 0.01)
300 K, 3 bar 6 stages
30 stages
O2 enriched recycle
81.4 K 90% liquid
N2 enriched reflux
88.7 K liquid
0.20 mol/t (.78, 0.21, 0.01) 333 K, 40 bar
1.58 mol/t (.978, .013, .009) 298 K, 1.01 bar
0.42 mol/t (.036, .950, .014) 315 K, 1.01 bar
Mole fractions (N2, O2, Ar)
Optimal ASU
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Validation with Aspen Plus® Specifications: • Peng-Robinson thermodynamics model • R2 feed conditions match GAMS results • R2 outlet: 74.7% vapor • Pressure: 1.053 bar
Stream Prop GAMS Aspen
S18 (vapor)
N2 11.03% 11.05% O2 86.33% 86.31% Ar 2.64% 2.64%
S15 (liquid)
N2 3.07% 3.09% O2 95.00% 94.96% Ar 1.93% 1.95%
Temp. 89.42 K 89.39 K
Discrepancy likely due to mismatch with input data for thermodynamic models 21
Heat Integration Results
Heat integrated separately
ΔTmin = 0.4 K
Hot Curve
Cold Curve
Pinch Points
ΔTmin = 1.5 K 0.185 kWh/kg O2 product (86% eff. compressors)
Industrial Optimized Design (NETL, 2010) 0.179 kWh/kg O2 product (possible 86% eff.) 22
y = 0.0359x + 0.1051 R² = 0.9994
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.75 1.25 1.75 2.25 2.75 3.25
Spec
ific
Ene
rgy
(kW
h/kg
)
ΔTmin
Heat Integration Sensitivity
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Optimized: Low Energy
Optimized: Low Capital
Am. Air Liquide NETL (2010)
100% efficient compressors
O2 Purity Sensitivity
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y = 0.3338x - 0.1579 R² = 0.9975
0.14
0.145
0.15
0.155
0.16
0.165
89% 90% 91% 92% 93% 94% 95% 96% 97%
Spec
ific
Ene
rgy
(k
Wh/
kg)
O2 Purity (mol%) 100% efficient compressors
KKT Multiplier 0.36 kWh/kg/mole frac.
Future Work
25
Oxycombustion Power Plant 1. Air Separation Unit 2. Boiler 3. Steam Turbines 4. Pollution Controls 5. CO2 Compression Train
1 2
3
4 5
Optimize trade-offs across systems in oxycombustion power plant
Conclusions
Optimized ASU with equation-based model: – Cubic equation of state & simultaneous heat integration
– New distillation model: MESH with bypass
– Pure nonlinear program – no discrete variables
– Comparison with NETL/industry report
Acknowledgements:
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
Heat Integration Reformulation
27
Consider contribution of single unit hgu