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.

9

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

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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

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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