Chalmers
University of
Technology
The Role of Process Integration
in Sub-ambient Processes
by
NTNU
Truls Gundersen, Department of Energy and Process Engineering
Norwegian University of Science and Technology (NTNU)
Trondheim, Norway
With significant Contributions from
Audun Aspelund, 2005-2010
Chao Fu, 2008-2012
Danahe Marmolejo Correa, 2009-2013
Bjoern Austboe, 2011-2014
20.03.13
T. Gundersen
Slide no. 1
Content of the Presentation
n 
n 
n 
n 
Special Challenges in Sub-ambient Process Design
The Failure of ΔTmin as Economic Trade-off Parameter
Extended Heat Recovery Problem Definition
The ExPAnD Methodology
♦  Extended Pinch Analysis and Design Procedure
♦  From Heuristic Rules to Superstructures and MINLP
n 
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n 
n 
What is Exergy and why Use it below Ambient?
The History of using Exergy in Pinch Analysis
New Developments in Exergy Analysis
♦  In line with the Approach of Pinch Analysis
♦  Carnot Factor replaced by the “Exergetic Temperature”
♦  New Linear Exergy Curves suitable for Targeting
n 
n 
20.03.13
Sub-ambient Process Examples (ASU and LNG)
Concluding Remarks
T. Gundersen
Slide no. 2
Special Challenges in Sub-ambient Processes
n 
n 
n 
n 
ΔTmin does not work as Economic Trade-off Parameter
Refrigeration è Expensive Cold Utilities
Power is used to produce Refrigeration è Stronger
Relationship between Thermal and Mechanical Energy
Composite Curves cannot be drawn
♦  Process Streams often act as Utilities (vague distinction)
♦  Pressurized Streams can be expanded to produce Cooling
♦  Pressure and Phase are important Design Variables and must be
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considered together with Temperature
♦  Result: The Path from Supply to Target State for Streams is
unknown è An important Part of the Optimization Problem
n 
Temperature Differences are smaller to reduce the need
for Refrigeration è More accurate Process Models
♦  Need Rigorous Simulators with Advanced Thermodynamics
20.03.13
T. Gundersen
Slide no. 3
Using ΔTmin in Sub-ambient Processes
n 
Above Ambient: ΔTmin is an Economic Parameter
♦  Trade-off between Operating Cost and Investment Cost
n 
Several Challenges above Ambient
♦  Single global ΔTmin is unrealistic due to variations in HTFs
♦  Differences in Fluids, Phases, Exchanger Configurations,
Materials of Construction, Pressure Ratings, etc.
♦  HRAT and EMAT or ΔTi (individual Stream Contributions)
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n 
Below Ambient: None of the ΔT parameters will work
♦  The Exergy of Cooling (Refrigeration) increases rapidly with
decreasing Temperatures (see later Slides)
♦  Using ΔT as a Specification (in Optimization) will not give
the minimum Power or the minimum Total Annual Cost
♦  Using UA as a Specification works better, either with Pareto
Plots while minimizing Power, or when minimizing TAC
n 
20.03.13
A simple Case Study illustrates this special Feature
T. Gundersen
Slide no. 4
Case Study: Simple PRICO Process for LNG
min(HẆ)
pH
Condenser
Compressor
ΔTdew%≥%%ΔTdew,min
pL
ΔTHX%≥%%ΔTHX,min
Throttle%
valve
MIXED%REFRIGERANT
ṁ1,'ṁ2,'ṁ3,'...,'ṁn
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NATURAL%GAS
Heat%exchanger
Throttle%
valve
LNG
Objective:
Minimize Shaftwork subject to 2 Constraints by varying
2 Pressures and 5-6 Flows of Refrigerant Components
20.03.13
T. Gundersen
Slide no. 5
Results from the Optimization
ΔTmin as Specification
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UA as Specification
ΔTmin
UA
W
UA
ΔTmin
W
Savings
(K)
(MW/K)
(kJ/kg)
(MW/K)
(K)
(kJ/kg)
(%)
1
3.101
896.5
3.101
0.57
882.8
1.5
2
1.658
979.2
1.658
0.87
947.7
3.2
3
1.110
1062.3
1.110
1.13
1006.0
5.3
4
0.812
1147.1
0.812
1.33
1060.9
7.5
5
0.632
1235.3
0.632
1.52
1111.1
10.1
UA is a better Specification than ΔTmin
and it is all related to Exergy
20.03.13
T. Gundersen
Slide no. 6
A new Process Synthesis Methodology
for Sub-ambient Processes
ExPAnD = Extended Pinch Analysis and Design
n 
The Classical Heat Recovery Problem has been Extended
w  ”Given a Set of Process Streams with a Supply and Target
State (Temperature, Pressure and the resulting Phase), as
well as Utilities for Power, Heating and Cooling  Design
a System of Heat Exchangers, Expanders, Valves, Pumps
and Compressors in such a way that Irreversibilities (or
Cost functions) are minimized”
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n 
n 
Notice that the Path from Supply to Target State is not fixed,
it is an important Part of the Optimization Problem
10 Heuristic Rules developed in early version of ExPAnD
A. Aspelund, D.O. Berstad, T. Gundersen, ”An Extended Pinch Analysis and Design procedure utilizing
pressure based exergy for sub-ambient cooling”, Applied Thermal Engng., vol. 27, pp. 2633-2649, 2007
20.03.13
T. Gundersen
Slide no. 7
Application: A Liquefied Energy Chain (LEC)
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n 
Key Features of the “LEC” Concept
♦ 
♦ 
♦ 
♦ 
♦ 
Utilization of Stranded Natural Gas for Power Production
High Exergy Efficiency of 46.4% (vs. 42.0% for traditional)
Innovative and Cost Effective solution to the CCS Problem
CO2 replaces Natural Gas injection for EOR
Combined Transport Chain for Energy (LNG) and CO2
Aspelund A. and Gundersen T. ”A Liquefied Energy Chain for Transport and Utilization of Natural Gas for Power
Production with CO2 Capture and Storage − Part 1”, Journal of Applied Energy, vol. 86, pp. 781-792, 2009.
20.03.13
T. Gundersen
Slide no. 8
Developing the Liquefied Energy Chain
− Manual and Automated Design Procedures
n 
The ExPAnD Methodology was used
♦  Original version uses 10 Heuristic Rules
♦  Combines Pinch & Exergy Analyses
TH1,out
§  Composite & Grand Composite Curves in
Idea Generation for Process Improvements
§  Exergy Efficiency to Quantify Improvements
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TC3,out
TC2,in
♦  Optimization has also been included
§  New Superstructure allows Simultaneous
Optimization of Networks with heat
Exchangers, Pumps, Compressors and
Expanders using Math Programming
(MINLP)
A. Wechsung, A. Aspelund, T. Gundersen and P.I. Barton,
”Synthesis of Heat Exchanger Networks at Sub-Ambient
Conditions with Compression and Expansion of Process
Streams”, AIChE Jl., vol. 57, no. 8, pp. 2090-2108, 2011.
20.03.13
T. Gundersen
E-2
TC3,in
C-2
E-3
TH4,out
TC2,out
TC1,in
TC1,out
TH2,out
TH2,in
TH3,out
TC4,in
TH1,in
C-1
E-1
TH3,in
TC4,out
TH4,in
C-3
Slide no. 9
The Onion Diagram revisited
The “forgotten” Onion
The “traditional” Onion
R
S
H
U
R
Smith and Linnhoff, 1988
S
C
&
E
H
The User Guide, 1982
The “sub-ambient” Onion
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R
S
HEN
C&E
U
A. Aspelund, D.O. Berstad, T. Gundersen, ”An Extended Pinch Analysis and Design procedure utilizing
pressure based exergy for sub-ambient cooling”, Applied Thermal Engng., vol. 27, pp. 2633-2649, 2007
20.03.13
T. Gundersen
Slide no. 10
What is Exergy (or “Availability”)?
n 
The Definition of Exergy:
♦  ”The Maximum Amount of Work that can be produced
if a “System” is brought to Equilibrium with its natural
Environment through ideal i.e. Reversible Processes”
n 
The Word Exergy:
♦  Suggested by Rant (1953/1956)
♦  Greek Language: Exergy means External Work
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§  Ex (εξ) means “External”
§  Ergon (εργον) means “Work”
n  Exergy in Thermodynamics:
♦  Linked to Entropy and the 2nd Law of Thermodynamics
♦  Entropy Production in Processes due to Irreversibilities
is Equivalent to Exergy Losses (thus Lost Work)
20.03.13
T. Gundersen
Slide no. 11
Why use Exergy?
n 
Advantages with Exergy
♦ 
♦ 
♦ 
♦ 
Unified Treatment of different Energy Forms
Quality of Processes measured with Thermodynamics
Exergy Losses increase Energy Consumption
Obvious in Processes with Focus on Work (“pure” Exergy)
§  Power Stations and CHP Systems
§  Subambient Processes (Refrigeration produced by Work)
♦  Uncertainties in Cost – Thermodynamics is “safe” and will
never “let us down”
§  Says a Thermodynamics Lecturer …  …
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n 
Disadvantages with Exergy
♦ 
♦ 
♦ 
♦ 
20.03.13
Need to distinguish Internal and External Losses
Difficult to distinguish Inevitable and Avoidable Losses
Exergy is often in “Conflict” with Investment Cost
Lack of Expertise
§  Chemical Engineers “do not know” Exergy
§  Mechanical Engineers “hate” Exergy
T. Gundersen
Slide no. 12
Air Separation Unit (ASU)
Linde’s Classical Coupled Column Design
N2
MAC
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N2
O2
LP
MHE
PPU
Air
HP
CW
CW
DCA
C. Fu, T. Gundersen, ”Using Exergy Analysis to reduce Power Consumption in Air
Separation Units for Oxy-Combustion Processes”, Energy, vol. 44, pp. 60-68, 2012.
20.03.13
T. Gundersen
Slide no. 13
Recuperative Vapor Recompression Cycle (RVRC)
A15-1
Compressor3
Expander
A15-2
A5-1
A15-3
Compressor1
Fu C., Gundersen T. and Eimer D., “Air
Separation”, GB Patent, Application
number GB1112988.9, July 2011
A15-4
A15-5
A5-2
N2
A4
A5-3
A5-5
Condenser1
A5-4
A7-3
A7-4
A7-5
A7-6
A7-1
A7-2
O2
A1-5
A13-2
A14
A1-4
Impurities
Distillation
column
A7-7
Compressor2
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A5-6
A2-1
A2-2
Reboiler2
A12-2
Reboiler1
A12-1
PPU
A13-1
DCA
A1-3
Blower
A1-2
A1-1
Air
A0
Single Column, Distributed Reboiling, Heat Pumping (RVRC)
20.03.13
T. Gundersen
Slide no. 14
Natural Gas
Liquefaction
(NG  LNG)
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Linde & Statoil
”Mixed Fluid
Cascade” (MFC®)
used at ”Snøhvit”
Hammerfest
Norway
E. Berger, W. Förg, R.S. Heiersted, P. Paurola, ”The Snøhvit Project”,
Linde Technology, no. 1, pp. 12-23, 2003.
20.03.13
T. Gundersen
Slide no. 15
Exergy Representations in Pinch Analysis
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Carnot Factor:
ηC = 1−
T0
T
⎛ T ⎞
E = H ⋅ ⎜ 1− 0 ⎟
⎝
T⎠
Linnhoff B., Dhole V.R., “Shaftwork Targets for Low-Temperature
Process Design”, Chem. Engng. Sci., vol. 47, no. 8, pp. 2081-2091, 1992.
20.03.13
T. Gundersen
Slide no. 16
Total Site Sink Source Profiles for Targeting
Fuels, Cogeneration, Emissions, Cooling
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Dhole V.R., Linnhoff B., “Total Site Targets for Fuel, Co-generation, Emissions and Cooling”,
European Symp. on Comp. Aided Process Engng., CACE, Suppl. vol. 17, pp. S101-S109, 1993.
20.03.13
T. Gundersen
Slide no. 17
Classification &
Decomposition
of Exergy
4th class:
Origin
3rd class:
Energy Quality
Reactional
Chemical
Concentrational
Exergy < Energy
2nd
class:
Carrier
Thermo-mechanical
ETM
Carried by Matter
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Exergy
1st class:
Open/Closed
Systems
Exergy Parts or
Components
T-based ET
P-based Ep
Kinetic
Mechanical
Potential
Exergy = Energy
Electrostatic
Electrical
Flow Exergy
Electrodynamic
Nuclear
Non-flow
Exergy
Heat EQ
Exergy < Energy
Radiation
Carried by Energy
Exergy = Energy
Electrical
D. Marmolejo-Correa, T. Gundersen, ”A Comparison of Exergy Efficiency Definitions
with focus on Low Temperature Processes”, Energy, vol. 44, pp. 477-489, 2012.
20.03.13
T. Gundersen
Slide no. 18
Special Behavior of Temperature based Exergy
Thermo-mechanical
Exergy of a Stream
Exergy of Heat
.
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2.0
.
S
Exergy, E
Exergy ratio of Heat, EQ / Q
.
1.5
1.0
T < T0
E TM
(T , p )
S0
T0
p
(T0 , p )
0.5
0.0
0
0.5
1
2
3
4
5
Dimensionless Temperature, T T0
⎛ T ⎞
E = Q ⋅ ⎜ 1− 0 ⎟ for T ≥ T0
⎝
T⎠
E p
(T0 , p0 )
Enthalpy, H
TM
T
p



E =E +E
⎛T
⎞
E = Q ⋅ ⎜ 0 − 1⎟ for T ≤ T0
⎝T
⎠
20.03.13
0
p0
E T
T. Gundersen
Slide no. 19
Consider Heat and Exergy Transfer
above/below Ambient Temperature
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Exergy Transfer
Temperature (°C)
Temperature (°C)
Heat Transfer
200
1
150
Source
4
100
2
50
0
Sink
H (kW)
3
0
50
100
150
1
200
200
150
100
0
4
-50
1
4
Sink
50 2
Source
-50
Source
E (kW)
3
0
20
40
1
4
60
80
100
Sink
2
Sink
-100
-100
3
2
Source
3
-150
-150
Hot Stream (energy)
20.03.13
120
Cold Stream (energy)
T. Gundersen
Hot Stream (exergy)
Cold Stream (exergy)
Slide no. 20
Exergy Efficiency Definitions
(Internal)
Exergy
Consumed
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Process or
Unit Operation
Exergy
Produced
Brodyansky
et al. (1994)
Bejan et al.
(1996)
Kotas
(1995)
Marmolejo-Correa
and Gundersen (2013)
”Exergy
Efficiency”
”Exergetic
Efficiency”
”Rational
Efficiency”
”Exergy Transfer
Effectiveness (ETE)”
E out − E transit
ηe =
E in − E transit
E products
ε=
E fuels
E out , desired
ψ=
E in, necessary
E sinks
ε tr =
E sources
D. Marmolejo-Correa, T. Gundersen, ”Exergy Transfer Effectiveness for Low
Temperature Processes”, to be submitted to Intl. Jl. of Thermodynamics, 2013.
20.03.13
T. Gundersen
Slide no. 21
Applied to the simple PRICO Process
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Brodyansky
et al. (1994)
Bejan et al.
(1996)
E 8T
ηe = T
p
E 6 + ΔE 6−8
+ W tot
= 0.508
TM
ΔE 6−8
ε=
W tot
= 0.323
20.03.13
Kotas
(1995)
T
ΔE 6−8
ψ=
p
ΔE 6−8
+ W tot
= 0.500
T. Gundersen
Marmolejo-Correa
and Gundersen (2013)
E 8T
ε tr = T
p
E 6 + ΔE 6−8
+ W tot
= 0.508
Slide no. 22
How and When is Exergy used?
n 
Exergy Analysis is used as a Post-Design Tool
♦  Existing Plants or Complete Grassroot Designs
n 
Exergy Analysis requires substantial Information
♦  Calculated from Enthalpy and Entropy Data
n 
Exergy Analysis is done on the Equipment Level
♦  Exergy Losses or Exergy Efficiency for each Unit
♦  Not suited to study Connection between Units
♦  Very few (if any) Guidelines for Design/Retrofit
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n 
Our Objective:
♦  Move Exergy from Post-Design to Conceptual Design
♦  Develop Graphical Tools similar to Pinch Analysis
§  Exergy Composite Curves and Exergy Cascades
§  Targeting, Conceptual Design and Optimization
20.03.13
T. Gundersen
Slide no. 23
Exergy
Composite
Curves
(ECCs)
Carnot Factor, ηC
Limitations of Existing Exergy Diagrams
Q Deficit ,min
ηC = 1−
E Destruction,min
ηC , T = 0
Q Surplus,min
Similar Diagrams:
n 
n 
n 
20.03.13
T0
T
⎛ T ⎞
E = H ⋅ ⎜ 1− 0 ⎟
⎝
T⎠
Heat
Recovery
0
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Carnot Factor:
Heat
Pinch
Enthalpy, H
Exergy Grand Composite Curve (EGCC)
Exergy Column Grand Composite Curve (ECGCC)
The Curves are Non-Linear (of course)
Simulations required to generate Curves
Targets not explicitly available from the Graphs
T. Gundersen
Slide no. 24
Developing “Exergetic Temperatures” (1)
Gouy-Stodola Theorem: −W max = ΔE = ΔH − T0 ⋅ ΔS
Thermo-mechanical Exergy can be decomposed:
eTM = ⎡⎣ h (T , p ) − h (T0 , p0 ) ⎤⎦ − T0 ⋅ ⎡⎣ s (T , p ) − s (T0 , p0 ) ⎤⎦ = eT + e p
Exergy Components: (NB: Not Unique)
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eT = ⎡⎣ h (T , p ) − h (T0 , p ) ⎤⎦ − T0 ⋅ ⎡⎣ s (T , p ) − s (T0 , p ) ⎤⎦
e p = ⎡⎣ h (T0 , p ) − h (T0 , p0 ) ⎤⎦ − T0 ⋅ ⎡⎣ s (T0 , p ) − s (T0 , p0 ) ⎤⎦
Differential Form of Thermo-mechanical Exergy:
TM
de
20.03.13
⎛ ∂eTM ⎞
⎛ ∂eTM ⎞
=⎜
⋅ dT + ⎜
⋅ dp and deTM = deT + de p
⎟
⎟
⎝ ∂T ⎠ p
⎝ ∂p ⎠T
T. Gundersen
Slide no. 25
Developing “Exergetic Temperatures” (2)
More Differential Forms
Required Partial Derivatives
⎛ ∂h ⎞
⎜⎝
⎟ = cp
∂T ⎠ p
⎡⎛ ∂h ⎞
⎛ ∂eTM ⎞
⎛ ∂s ⎞ ⎤
de = ⎜
⋅
dT
=
−
T
⋅
⎢⎜⎝
⎟⎠
⎟⎠ ⎥ ⋅ dT
0 ⎜
⎝
∂T
∂T
⎝ ∂T ⎟⎠ p
p
p⎦
⎣
T
⎡⎛ ∂h ⎞
⎛ ∂eTM ⎞
⎛ ∂s ⎞ ⎤
de = ⎜
⋅
dp
=
−
T
⋅
⎢⎜ ⎟
0 ⎜
⎟⎠ ⎥ ⋅ dp
⎝
⎠
⎝
∂
p
∂
p
⎝ ∂ p ⎟⎠ T
⎣
T
T ⎦
p
⎛ ∂h ⎞
⎛ ∂v ⎞
=
v
−
T
⋅
⎜⎝
⎟⎠
⎜⎝ ∂ p ⎟⎠
∂T
p
T
cp
⎛ ∂s ⎞
=
⎜⎝
⎟
∂T ⎠ p T
⎛ ∂s ⎞
⎛ ∂v ⎞
=
−
⎜⎝
⎟⎠
⎜⎝ ∂ p ⎟⎠
∂T
p
T
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T-based and p-based Exergy Components
T
⎛ T ⎞
e = ∫ c p ⋅ ⎜ 1− 0 ⎟ ⋅ dT
⎝
T⎠
T
T
0
⎡
⎛ ∂v ⎞ ⎤
e = ∫ ⎢ v − (T − T0 ) ⋅ ⎜
⎟⎠ ⎥ ⋅ dp
⎝
∂T
p⎦
p0 ⎣
p
p
20.03.13
T. Gundersen
Slide no. 26
Developing “Exergetic Temperatures” (3)
Assuming constant cp
⎡
⎛ T ⎞⎤
⎛ To ⎞
e = c p ⋅ ∫ ⎜ 1− ⎟ ⋅ dT = c p ⋅ ⎢(T − T0 ) − T0 ⋅ ln ⎜ ⎟ ⎥
⎝
T⎠
⎝ T0 ⎠ ⎦
T
⎣
T
T
0
T
⎡T
T⎤
eT = c p ⋅T0 ⋅ ⎢ - 1 - ln ⎥ = c p ⋅T E
T0 ⎦
⎣ T0
Assuming Ideal Gas and constant cp
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p
⎡
⎤
⎡ RT
∂v
R⎤
⎛
⎞
e p = ∫ ⎢ v − (T − T0 ) ⋅ ⎜
⋅
dp
=
−
T
−
T
⋅
(
)
⎥
⎟⎠
0
⎢ p
⎥ ⋅ dp
∫
⎝
∂T
p
⎦
p⎦
p0 ⎣
p0 ⎣
p
e p = R ⋅T0 ⋅ ln
⎛ p⎞
p
k -1
p
= c p ⋅T0 ⋅
⋅ ln = c p ⋅T0 ⋅ ln ⎜ ⎟
p0
k
p0
⎝ p0 ⎠
k-1
k
= c p ⋅T E
p
 Linear Relationships
20.03.13
T. Gundersen
Slide no. 27
A small illustrating Example
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Energy Targets:
Exergy Targets:
ΔTmin = 0°C
T0 = 15°C , p0 = 1 bar
E Surplus,miin = ?? MW , E Deficit ,miin = ?? MW
Q H ,min = 3.5 MW
Q C,min = 6.0 MW
E Destructed,min = ?? MW
E Required,min = ?? MW , E Rejected,min = ?? MW
D. Marmolejo-Correa, T. Gundersen, ”A new Graphical Representation of Exergy
applied to Low Temperature Process Design”, submitted to I&EC, 2012.
20.03.13
T. Gundersen
Slide no. 28
Heat and Exergy Cascades
Exergy Deficit
Heat Deficit
T
T (°C) and T E (K)
3.50
250°C
3.00
230°C
6.50
4.50
-4.50
200°C
2.00
230°C
5.00
180°C
2.00
4.00
6.00
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H2
30.00 kW
10.00
Pinch
140°C
9.00
15.00
80°C
6.00
40°C
-4.00
0.00
12.00
54.38K
2.43
H1
9.32 kW
1.89
34.54K
H2
8.93 kW
Pinch
3.34
Pinch
21.17K
2.22
12.00
3.70
80°C
C1
32.00 kW
6.39K
0.80
8.00
40°C
4.00
3.69
0.58
0.76
42.10K
Corresponding
Intervals
& Pinch
1.03K
-1.34
34.54K
4.01
2.67
21.17K
0.00
2.96
6.39K
1.03K
0.20
0.04K
0.04K
6.00
2.49
Heat Surplus
Exergy Surplus
T. Gundersen
C1
6.90 kW
1.07
2.69
-0.20
Pinch
2.96
2.96
-0.27
C2
9.96 kW
2.26
1.34
2.01
8.00
140°C
-1.85
54.38K
1.13
12.00
20°C
20°C
20.03.13
180°C
10.00
-4.00
C2
27.00 kW
6.00
12.00
-2.0
1.32
42.10K
200°C
63.15K
1.32
1.84
9.00
3.00
H1
31.50 kW
63.15K
250°C
3.00
1.11
Slide no. 29
New Linear Exergy Composite Curves
70
T
ET
E Deficit ,min = 1.11 MW
60
50
40
30
E Required,min = 1.47 MW
E Surplus,min = 2.49 MW
20
NTNU
E T
10
0
8
4
E Rejected,min = 0.80 MW
16
20
E Destructed,min = (1.47 − 1.11) + (2.49 − 0.80) = 2.05 MW
E Required = E Deficit + E Destructed
20.03.13
12
and
T. Gundersen
E Rejected = E Surplus − E Destructed
Slide no. 30
Small Industrial Case Study – LNG Process
κ=
cp
cv
ΔH
Stream
Type
Ts
Tt
ps
pt
 p
mc
(ID)
Energy
(°C)
(°C)
(bar)
(bar)
(kW/ºC)
(–)
(MW)
NG
Hot
25
-168
65.0
1.0
varying
varying
-13.84
N2a
Hot
25
-168
120.0
6.3
121.6
1.48
-23.46
N2b
Cold
-168
25
6.3
120.0
121.6
1.48
23.46
!
NTNU
Stream
Type
TsE
(ID)
Exergy
(K)
NG
Sink
0.00 117.73
555.33
0.00
8.13
-27.21
N2a
Sink
0.00 117.73
462.94
177.98
14.32
-34.65
N2b
Source
177.98
462.94
-14.32
34.65
T
117.73
Tt E
T
(K)
0.00
TsE
p
(K)
Tt E
p
(K)
ΔE T
ΔE p
(MW)
(MW)
!
ΔTmin = 0°C , T0 = 25°C , p0 = 1 bar
20.03.13
T. Gundersen
Slide no. 31
Energy Composite Curves
Temperature (°C)
H 1 = 37.3 MW
TH ,1 = TC,2 = 25°C
50
0
-50
Q H ,min = 0.0 MW
Q C,min = 13.8 MW
1
-200
0
5
10
Energy Targets:
ΔTmin = 0°C
3
-150
20.03.13
2
H 3 = 0 MW
2
TH ,3 = −168°C
-100
NTNU
1
H 2 = 13.8 MW
TH ,2 = −92.5°C
TC,1 = −168°C
15
20
25
30
35
40
Enthalpy ( MW )
Cold
Hot
n 
Natural Gas is divided into Segments to account for cp = f(T)
n 
Nitrogen treated as Ideal Gas with constant cp
T. Gundersen
Slide no. 32
Exergy Composite Curves before Pressure Changes
T
E C,1
= 14.3 MW
ET
TC,1
Exergetic Temperature (K)
150
= 117.7 K
1
125
E TH ,3 = 22.4 MW
T
THE,3 = 117.7 K
3
100
NTNU
75
50
E H ,2 = 6.8 MW
25
2
0
0
T
THE,2 = 31.9 K
2
1
5
10
15
20
25
T − based Exergy ( MW )
Source
Sink
E Surplus,min = 0.0 MW , E Deficit ,min = 22.4 − 14.3 = 8.1 MW
E Destructed,min = 14.3 − 6.8 = 7.5 MW
E Required,min = 8.1+ 7.5 = 15.6 MW , E Rejected,min = 0.0 MW
20.03.13
T. Gundersen
Slide no. 33
Process Modifications to save Energy
Temperature (°C)
H 1 = 37.3 MW
TH ,1 = TC,2 = 25°C
50
0
-50
-200
u 
20.03.13
5
10
15
20
25
30
35
40
Enthalpy ( MW )
Cold
Hot
Q C,min = 13.8 MW
The “Plus/Minus” Principle applied below Pinch
u 
n 
ΔTmin = 0°C
Q H ,min = 0.0 MW
1
0
Energy Targets:
TPinch = 25°C
3
-150
n 
2
H 3 = 0 MW
2
TH ,3 = −168°C
-100
NTNU
1
H 2 = 13.8 MW
TH ,2 = −92.5°C
TC,1 = −168°C
(A) Increase Heat Sink (Exergy Source)
(B) Decrease Heat Source (Exergy Sink)
(A) means added refrigeration, (B) means utilizing the
Pressure of N2a to create cooling through Expansion
T. Gundersen
Slide no. 34
Energy Composite Curves with Pressure Changes
N2a
Temperature (°C)
-52.64°C
-168°C
120 bar
120 bar
6.3 bar
H 2 = 23.1 MW
TH ,2 = 25°C
TC,2 = 22°C
125
NTNU
25°C
75
H 1 = 70.0 MW
TH ,1 = 85.7°C 1
Energy Targets:
2
25
ΔTmin = 0°C
2
-25
-75
-125 3
1
-175
0
H 3 = 0 MW
TH ,3 = −165°C
TC,1 = −168°C
20
Q H ,min = 0.0 MW
40
60
80
Q C,min = 46.9 MW
Enthalpy ( MW )
Cold
Hot
External Cooling increased, but moved to above Ambient
20.03.13
T. Gundersen
Slide no. 35
Exergy Composite Curves with Pressure Changes
Exergetic Temperature (K)
Above
Below
T
150
E
TC,1
= 117.7 K
125
THE,3 = 112.3 K
T
1
3
T
THE,1 = 6.1 K
100
75
E TC,2 = 4.4 MW
50
E TH ,2 = 9.4 MW
T
E
TC,2
= 0.0 K
25
1
2
0
T
THE,2 = 0.0 K
2
0
NTNU
E TC,1 = 18.8 MW
5
10
Source (above T0)
15
20
T − based Exergy ( MW )
Source (below T0)
Sink
Above
Below
E Surplus,min = 4.4 MW
E Surplus,min = E Deficit ,min = 0.0 MW
E Rejected,min = 4.4 MW
E Destructed,min = 9.4 − 4.4 = 5.0 MW (was 7.5 MW)
E Required,min = E Rejected,min = 0.0 MW
All others are 0.0 MW
20.03.13
T. Gundersen
Slide no. 36
Temperature (°C)
No Surprise:
NTNU
Exergetic Temperature (K)
We have actually
“discovered” the
Reverse Brayton
LNG Process
H a = 70.0 MW a
Ta = 85.7°C
125
75
b
25
e
-25
-75
-125
H c,d = 0 MW
Tc = −165°C
Td = −168°C
c
d
-175
0
10
E Tc,d = 18.8 MW
150
20
H b,e = 23.1 MW
Tb = 25°C
Te = 22°C
30
40
50
60
70
80
Enthalpy ( MW )
Cold
Hot
5
8
T
TdE = 117.7 K
125
T
TcE
100
= 112.3 K
d
c
LIQ-EXP-100
7
E Tb,e = 4.4 MW
75
c
d
4
TUR-100
c
T
50
E
Tb,e
= 0.0 K
25
TaE = 6.1 K
T
a
0
-25
0
b
E Tb' = 9.4 MW
T
THE,b' = 0.0 K
b'
e
5
10
15
b
HX-100
20
T − based Exergy ( MW )
Source
Sink
20.03.13
T. Gundersen
6 (Natural gas)
b
e
3 AC-100
2
1 (Nitrogen)
a
COM-100-5
Slide no. 37
Concluding Remarks: Our modest Contributions to
using Exergy Analysis in Sub-ambient Process Design
n 
n 
n 
Discussed special Challenges in Sub-ambient Design
Discussed the Classification of Exergy Forms
Illustrated the importance of Decomposition
♦  Explains behavior of Compressors/Expanders above/below T0
♦  Results in Exergy Efficiencies that measure Design Quality
n 
Discussed various Exergy Efficiencies
♦  Compared existing ones applied to LNG Processes
♦  Proposed a new Exergy Efficiency based on Sources & Sinks
NTNU
n 
n 
n 
n 
20.03.13
New Exergetic Temperature as an Energy Quality
Parameter that can replace the Carnot Factor
New Linear Graphical Diagrams for Exergy
New Targeting Procedure for Exergy
Developments + ExPAnD è New Design Procedure
T. Gundersen
Slide no. 38