1

Optimization Modeling of Energy Processes

L. T. Biegler Department of Chemical Engineering

Carnegie Mellon University Pittsburgh, PA 15213

http://capd.cheme.cmu.edu

March, 2012

2

Optimization of PSA units for Carbon Capture (Alex Dowling)

Compressor

Feed ( L + H )

Pbed

L

Pbed

H

Feed Pressurization

Feed (Adsorption)

Counter-current Depressurization

Light reflux (Desorption)

3

PSA Bed Model

( ) izvC

tq

tC ii

sbi

b ∀=∂

∂+

∂

∂−+

∂

∂ 0)1( ρεε

)( *iii

i qqktq

−=∂

∂

2,1exp

11

4321

12

22

11

11*

=∀⎟⎟⎠

⎞⎜⎜⎝

⎛=+=

++

+=

∑∑==

miTkkbTkkq

Pyb

Pybq

Pyb

Pybqq

mimimimimi

smi

nc

jjj

iisi

nc

jjj

iisi

i

( ) ( ) vvCM

dv

dzP i

iw

bp

b

bp

b⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−=

∂

∂− ∑

1000175.11150332

2

εε

εεµ

Component mass balance

LDF equation

Dual-site Langmuir Isotherm

Energy Balance

Ergun equation

( ) ( ) ( )

∑

∑∑

=

==

=+++=

=−+∂

∂+

∂

∂Δ−

∂

∂⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛++−

nc

i

ipgi

ic

ic

ic

ic

ipg

wc

nc

i

iis

wpwwpss

nc

i

ipgit

TCChTdTcTbaC

TTDh

zvh

tqH

tT

DhCCRCC

1

32

11044

ρρρε

Ideal gas ∑=i

iRTCP

4

Two-bed PSA Superstructure Systematic formulation to develop, evaluate and optimize PSA cycles

Co-currentBed

(CoB)

Counter-current Bed

(CnB)

Light Product (LP)

Pressure-reducingValve

Top reflux (TR)

b(t)

Bottom reflux (BR)a (t)

Heavy Product (HP)

Heavy-product compressor

Feed compressor

Vacuum Generator

Patm

Pd(t)

Pa(t) Cd,i(t), Td(t),vd(t), Pdes(t)

f (t) Feed

Ca,i(t), Ta(t),va(t), Pads(t)

Input flux (F)

Inlet gasPfeed

Inletcompressor(optional)

Pinlet

Allows all steps (P-FD-DP-EV-EQ-HP-LP) Includes most steps with 2-bed interactions Extend to product tanks

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Motivation for CO2 Capture

Challenges

- Which Sorbent works best for CO2 capture? - Which PSA cycle for high purity CO2 capture? - Computationally efficient flowsheet simulation/optimization with PDAE-based PSA model.

IGCC Existing pulverized coal plants

Post-combustion capture Pre-combustion capture

Can we use PSA for carbon capture?

6 4/2/12 11:05 6

Reduced Order Modeling for CFD Units(Yi-dong Lang)

CFD Model

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ROM Development for CFD Models PCA-based Input-Output Mapping

Exp’l Design (e.g., LHS)

Modeling Strategy

Set of inputs

Set of solutions

PDE CFD

Input

Output

Snapshot Developing ROM

Yred

Mapping Scores

PCA

F(u)

(ROM)

Input-Output Mapping (Kriging)

?

Lang, Y-D et al., Energy and Fuels, 23, 1695 (2009)

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ROM for Turbine Combustor

FLUENT

PCA

ROM

8

Average Fluent Case ~2000 CPU sec

Each case in ROM < 1 CPU sec Lang, Y-D et al., Energy and Fuels, 23, 1695 (2009)

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ROM for Entrained-Flow Gasifier

Avg. Fluent Case 72 000 CPUs Avg. ROM Case < 1 CPUs

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TNO-IGCC Process Flowsheet

TNO-Report R98/135 (1998)

Coal Gasification

Air Separation

Unit

Water gas shift

Reactor I

CO2 Capture

TSA

Gas Turbine

Water gas shift

Reactor II

Steam Cycle and

Steam Turbines

CO2 Compressor CO2, 110 bar

CO2, 19 bar

Heat Exchangers

Heat flux Steam

Coal

Air

Combustor

•  Detailed Optimized Economic Study for IGCC with CCS •  Various CCS technologies considered (e.g., Selexol, TSA) •  Can Optimization with CFD models improve on this design?

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TNO-IGCC and integration of replaced CFD models

Water shift

TSA and CO2 compress

Gas-Combustor-Turbine

Steam cycle

Gasif

USER3

Cmbst USER3

•  Allows fast EO-based optimization with Aspen •  Leads to 7% increase in energy efficiency in IGCC process