Design, Integration Schemes, and Optimization of
Conventional and Pressurized Oxy-coal Power
Generation Processes
by
Hussam Zebian
S.M., Massachusetts Institute of Technology (2011)
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
ARCHNE*
MASSACHUSETTS INST"UrE
OF TECHNOLOGY
Doctor of Philosophy
at the
MAY 0 8 2014
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LIBRARIES
February 2014
© Massachusetts Institute of Technology 2014. All rights reserved.
A uth or ....
..........................................................
Department of Mechanical Engineering
November 1, 2013
Certified by.......
Alexander Mitsos
Visiting Scientist
7') Thesis SUpe;visor
Accepted by .
David E. Hardt
Chairman, Department Committee on Graduate Thesis
2
Design, Integration Schemes, and Optimization of
Conventional and Pressurized Oxy-coal Power Generation
Processes
by
Hussam Zebian
Submitted to the Department of Mechanical Engineering
on November 1, 2013, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Abstract
Efficient and clean electricity generation is a major challenge for today's world. Multivariable optimization is shown to be essential in unveiling the true potential and the
high efficiency of pressurized oxy-coal combustion with carbon capture and sequestration for a zero emissions power plant (Zebian and Mitsos 2011). Besides the increase
in efficiency, optimization with realistic operating conditions and specifications also
shows a decrease in the capital cost.
Elaborating on the concept of increasing the performance of the process and the
power generation efficiency, as part of this Ph.D. thesis, new criteria for the optimum operation of regenerative Rankine cycles, are presented; these criteria govern
the operation of closed and open feedwater heaters, and are proven (partly analytically and partly numerically) to result in more efficient cycle than the conventional
rules of thumb currently practiced in designing and operating Rankine cycles. Simply
said, the pressure and massflowrate of the bleed streams must be selected in a way
to have equal pinch temperatures in the feedwater heaters. The criteria are readily
applicable to existing and new power plants, with no associated costs or retrofitting
requirements, contributing in significant efficiency increase and major economical and
environmental advantages. A case study shows an efficiency increase of 0.4 percentage
points without capital cost increase compared to a standard design; such an efficiency
increase corresponds to an order of $40 billion in annual savings if applied to all Rankine cycles worldwide. The developed criteria allow for more reliable and trustworthy
optimization, thus, four additional aspects of clean power generation from coal are
investigated.
First, design and optimization of pressurized oxy-coal combustion at the systemslevel is performed while utilizing a direct contact separation column (DCSC) instead
of a surface heat exchanger for more reliable and durable thermal recovery. Despite
the lower effectiveness compared to a surface heat exchanger, optimization employing
newly developed optimal operating criteria that govern the DCSC allow for an efficient
3
operation, 3.8 percentage points higher than the basecase operation; the efficiency of
the process utilizing a DCSC is smaller than that utilizing a surface heat exchanger
but only by 0.32 percentage points after optimization. Optimization also shows a
reduction in capital costs by process intensification and by not requiring the first flue
gas compressor in the carbon sequestration unit.
Second, in order to eliminate performance and economical risks that arise due to
uncertainties in the conditions that a power generation process may be subjected to,
the designs and operations that allow maximum overall performance of the process
while facing all possible changes in operating condition are investigated. Therefore,
optimization under uncertainty in coal type, ranging from Venezuelan and Indonesian
coals to a lower grade south African Douglas Premium and Kleinkopje coal, and in
ambient conditions, up to 10'C difference in the temperature of the cooling water,
of the pressurized oxy-coal combustion are performed. Using hierarchic optimization
and stochastic programing, the latter shown to be unnecessary, an ideally flexible
design is attained, whereby the maximum possible performance of the process with
any set of input parameters is attained by a single design. While in general a process
designed for a specific coal has a low performance when the utilized coal is changed,
for the pressurized oxy-coal combustion process presented herein, it is demonstrated
that designing (and optimizing) while taking into consideration the different coal
types utilized, results for each coal in performance that is equal to the maximum
performance obtained by a design dedicated to that coal.
The third aspect considered is flexibility with respect to load variation. Particularly with the increase of the power generation from intermittent renewable energy
sources, coal power plants should operate at loads far from nominal, down to 35%.
In general this results in efficiency significantly lower than the optimum. Therefore,
while keeping the turbine expansion line design fixed to that of the nominal load in
order to allow for a full range of thermal load operations, an elaborate study of the
variations in thermal load for pressurized oxy-coal combustion is performed. Here
too optimization of design and operation taking into consideration that load is not
fixed results in a process that is flexible to the thermal load; the range of thermal
load considered is 30..100%.
The fourth aspect considered is a novel design for heat recovery steam generator
(HRSG), which is an essential part of coal power plants, particularly oxy-coal combustion. It is the site of high temperature thermal energy transfer, and is shown
to have potential for significant improvements in its design and operation. A new
design and operation of the HRSG that allow for simultaneous reduction in the area
and the flow losses is proposed: the hot combustion gas is splitted prior to entering
the HRSG and prior to dilution with the recycling flue gas to control its temperature as dictated by the HRSG maximum allowed temperature. The main combustion
gas flow proceeds to the HRSG inlet and requires smaller amounts of dilution and
recycling power requirements compared to the conventional no splitting operation.
The splitted fraction is introduced downstream at an intermediate location in the
HRSG; the introduction of the splitted gas results in increasing the temperature of
the flue gas and the temperature difference between the hot and the cold streams
of the HRSG, particularly avoiding small temperature differences which require the
4
most heat transfer area. Results include area reduction by 37% without change in
the compensation power requirements, or a decrease in the compensation power requirements by 18% (corresponding to 0.15 percent points of the cycle efficiency) while
simultaneously reducing the area by 12%.
Thesis Supervisor: Alexander Mitsos
Title: Visiting Scientist
5
6
Acknowledgments
First and foremost I would like to thank my advisor Professor Mitsos for all his
efforts and contributions in making this work possible. As an advisor, he is attentive,
critical, and extremely generous with his time and thoughts. He always welcomes
and encourages new thoughts and ideas, redefining the principles of teaching and
learning making work and research fun and pleasurable. He is remarkably modest,
never treated himself as superior and always took the time to understand and to
correct what I, a blabbering know-it-all kid with broken-english from half the way
across the world, is trying to say. Professor Mitsos is more than just an advisor, he
is my mentor in most aspects of life; even after four year, till this very moment, I am
still learning from him.
I would like to thank my thesis committee members, Professor Ghoniem and Professor Buonjiorno, for their help, concerns, and smart feedback. Professor Ghoniem
has remarkable knowledge in the fields of science and engineering and even more
impressive is his ability to relate his knowledge and experience and to guide both
amateur and experienced researchers; all while being very humble and supportive.
Professor Buonjiorno is very critical and gives you all his attention and concerns
when you need him.
He was able to anticipated pitfalls and point out important
issues.
Thanks to ENEL and the DOE and their research teams for sponsoring most of
this research and for their constant interest and feedback.
Thanks for Aspen for
providing AspenPlus@ free of charge for academic uses.
I would like to thank my parents, for it was originally their dream that I pursue
a Ph.D. Also, because of my parents I was never worried or afraid about my future;
not because they were supportive or reasonable, but mainly because they were always
more worried and concerned and emotionally involved in my pursuit than I was. At
several occasions I was comforting them instead of the other way around; one can say
that they handled/lived the stressful emotional aspects of being a graduate student,
leaving the bare minimum for me. I thank my brilliant brother, who I greatly admire,
7
for being the voice of reason and for his constant constructive advice. I thank my
wonderful sister for being the most calming and relaxing person I have ever known,
and for always managing to alleviate any problem or concern.
Finally, thanks to my lab-mates and friends, they made my stay at MIT fun and
entertaining, and way different than the stereotypical ideas I had about the lifestyle
at MIT.
Disclaimer
This work was partly 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.
This thesis is in part based on [28, 29, 38, 35, 671.
8
This doctoral thesis has been examined by a Committee of the
Department of Mechanical Engineering as follows:
Professor Alexander Mitsos ..........................................
Thesis Supervisor
Visiting Scientist
Professor Ahm ed Ghoniem ...........................................
Member, Thesis Committee
Ronald C. Crane (1972) Professor
Professor Jacopo Buonjiorno.........................................
Member, Thesis Committee
Associate Professor of Nuclear Science and Engineering
10
Contents
1
A Double-Pinch Criterion for Regenerative Rankine Cycles
1.1
Summary
. . . . . . . . . . . . . . . . . .
23
1.2
M otivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
1.3
Analytical Proof of Double-Pinch for Shortcut Methods . . . . . . . .
27
1.3.1
Two possibilities for pinch to occur . . . . . . . . . . . . . . .
27
1.3.2
Analytical Proof of Necessity
. . . . . . . . . . . . . . . . . .
29
1.3.3
Graphical Proof of Uniqueness and Sufficiency . . . . . . . . .
36
1.3.4
Procedure for Cycle Optimization . . . . . . . . . . . . . . . .
38
Other Feedwater Configurations . . . . . . . . . . . . . . . . . . . . .
42
. . . . . . . . . . . . . . . .
42
1.4
1.5
2
23
1.4.1
Drain to Open Feedwater Heater
1.4.2
Cascading (Downwards)
. . . . . . . . . . . . . . . . . . . . .
42
1.4.3
Pumping to Feed . . . . . . . . . . . . . . . . . . . . . . . . .
43
1.4.4
Open Feedwater Heater
. . . . . . . . . . . . . . . . . . . . .
46
. . . . . . . . . . . . .
46
Numerical Examples with a Simple Flowsheet
1.5.1
Single Feedwater heater
. . . . . . . . . . . . . . . . . . . . .
47
1.5.2
Non-Cascading, Cascading, and Common Practice . . . . . . .
56
1.6
Numerical Case Study with a Realistic Cycle Design . . . . . . . . . .
59
1.7
Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . .
62
Optimal Design and Operation of Pressurized Oxy-Coal Combustion
with a Direct Contact Separation Column
65
2.1
Sum m ary
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
2.2
M otivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
11
2.3
2.4
2.5
2.6
3
Flowsheet and Model Description
.. .. .. .. . .. .. .. ..
69
2.3.1
Power Plant Flowsheet . . . . . . . . . .
. . . . . . .
69
2.3.2
Flue Gas Pressure Losses . . . . . . . . .
. . . . . . .
70
DCSC Modeling . . . . . . . . . . . . . . . . . .
. . . . . . .
73
2.4.1
DCSC Flowsheet
. . . . . . . . . . . . .
. . . . . . .
73
2.4.2
DCSC Operation
. . . . . . . . . . . . .
. . . . . . .
77
. . . . . . . . . . . .
. . . . . . .
78
2.5.1
Objective Function . . . . . . . . . . . .
. . . . . . .
78
2.5.2
Optimization Variables and Constraints.
. . . . . . .
78
2.5.3
Integer Variables
. . . . . . . . . . . . .
. . . . . . .
81
2.5.4
Parameters Considered constant . . . . .
. . . . . . .
82
2.5.5
Active Constraint Optimization . . . . .
. . . . . . .
82
Optimization Formulation
Results . . . . . . . . . . . . . . . . . . . . . . .
84
2.6.1
Variables at Optimal Operation . . . . .
86
2.6.2
Flue Gas Pressure Losses . . . . . . . . .
88
2.6.3
Capital Cost Reduction
89
2.6.4
Validation of the Optimization Results .
. . . . . . . . .
. . . . . . . .
90
2.7
Model-Based Optimization and Effect of Design Assumptions .
91
2.8
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
Pressurized Oxy-Coal Combustion: Ideally Flexible to Uncertain-
99
ties
3.1
Summary ...................
99
3.2
M otivation ................
100
3.3
Flowsheet and Model Description . . .
101
3.4
Optimization Formulation . . . . . . .
102
3.4.1
Optimization Objective . . . . .
102
3.4.2
Design and Operation Variables
103
3.4.3
Constraints
. . . . . . . . . . .
106
3.4.4
Active Constraint Optimization
12
106
3.5
Ideally Flexible Process to Coal, FWHs Areas, Input Flows and Spec. . . . . . . . . . . . . . . . . .
110
3.5.1
Methodology for Flexibility Assessment . . . . . . . . . . . . .
110
3.5.2
Hierarchical Optimization
. . . . . . . . . . . . . . . . . . . .
114
3.5.3
Flexibility to Input Flows and Parameters, (Air Flow, Slurry
ifications, and Ambient Temperature
water Flow, atomizer Stream Flow, and Oxidizer Stream Oxy. . . . . . . . . . . . . . . . .
123
Flexibility to Ambient Conditions . . . . .
126
3.6
Conclusion . . . . . . . . . . . . . . . . . . . . . .
128
3.7
Future W ork . . . . . . . . . . . . . . . . . . . . .
131
gen Purity)
3.5.4
4
Pressurized OCC Process Ideally Flexible to the Thermal Load
4.1
Summary ......................
. . . . . . . . . . . . .
137
4.2
Motivation ..................
. . . . . . . . . . . . .
138
4.3
Turbine Performance Curves . . . . . . . .
. . . . . . . . . . . . .
140
4.4
Modeling Approach . . . . . . . . . . . . .
. . . . . . . . . . . . .
144
4.4.1
Process Operating Parameters . . .
. . . . . . . . . . . . .
144
4.4.2
Flue Gas Pressure Losses . . . . . .
. . . . . . . . . . . . . 146
Optimization Formulation . . . . . . . . .
. . . . . . . . . . . . . 149
4.5
4.6
4.7
5
137
. . . . . . . . . . . . . 150
4.5.1
Design and Optimization Variables
4.5.2
Constraints
. . . . . . . . . . . . .
. . . . . . . . . . . . . 156
4.5.3
Active Constraint Optimization . .
. . . . . . . . . . . . . 157
Results and Analysis . . . . . . . . . . . .
. . . . . . . . . . . . . 158
4.6.1
Flexibility Assessment
. . . . . . .
. . . . . . . . . . . . .
159
4.6.2
Behavior of Key Variables . . . . .
. . . . . . . . . . . . .
164
4.6.3
Standard Rankine Cycles Without Pressurized Recovery
170
4.6.4
Partload and Subcritical Operation . . . . . . . . . . . .
173
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
174
A Split Concept for HRSG with Simultaneous Area Reduction and
177
Performance Improvement
13
177
......................
5.1
Summary .....
5.2
Motivation ..............
5.3
Novel Split Concept . . . . . . . . . . . . . . . . .
180
. . . . . . . . . . . .
180
. . .
182
5.4
178
........
5.3.1
Concept Description
5.3.2
Stand Alone HRSG-Split Simulation
Optimization Formulation for Minimal Area and/or Minimal Compensation Power Requirements . . . . . . . . . . . . .
188
5.4.1
Objective Functions
. . . . . . . . . . . .
188
5.4.2
Optimization Variables . . . . . . . . . . .
194
5.4.3
Optimization Constraints
. . . . . . . . .
194
5.4.4
Pareto Front Construction . . . . . . . . .
196
5.5
Results . . . . . . . . . . . . . . . . . . . . . . . .
196
5.6
Flexibility to Uncertainties . . . . . . . . . . . . .
199
5.7
Other Applications . . . . . . . . . . . . . . . . .
202
5.8
Conclusion . . . . . . . . . . . . . . . . . . . . . .
203
A Reaction Chemistry Added to the Separation Column in the DCSC
207
flowsheet
B DCSC Recirculation Water, rhRw-sr-in, Optimality Criterion
14
209
List of Figures
1-1
Pinch diagram for illustrative feedwater heater . . . . . . . . . . . . .
28
1-2
Pinch diagram demonstrating uniqueness of double pinch . . . . . . .
38
1-3
Feedwater configurations with pumping of the drain . . . . . . . . . .
43
1-4
Flowsheet for the numerical validation of the double pinch criterion .
48
1-5
Contours of efficiency for a fixed regenerated duty . . . . . . . . . . .
50
1-6
Contours of entropy generation rate Sge, for a fixed regenerated duty
52
1-7
Contours of efficiency for a fixed FWH Area . . . . . . . . . . . . . .
54
1-8
Contours of entropy generation Sen for a fixed FWH Area . . . . . .
55
1-9
Optimal performance of four different design procedures versus total
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
1-10 Realistic cycle design with four closed feedwater heaters . . . . . . . .
60
FW Hs area
2-1
Oxycombustion cycle flowsheet based on wet recycling
. . . . . . . .
72
2-2
Direct Contact Separation Column (DCSC) operation unit . . . . . .
75
2-3
Optimization variables and constraints for the pressurized
2-4
RHE and DCSC pressure parametric optimization and pressure para-
OCC process 95
metric sensitivity result . . . . . . . . . . . . . . . . . . . . . . . . . .
96
2-5
Effect of design considerations . . . . . . . . . . . . . . . . . . . . . .
98
3-1
Evaluations performed for flexibility assessment
. . . . . . . . . . . .
113
4-1
Variables and constraints for the pressurized OCC cycle for uncertainty
in load ........
4-2
...................................
Results for flexibility to thermal load . . . . . . . . . . . . . . . . . .
15
145
163
5-1
HRSG single-split as part of a pressurized OCC process with a thermal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
182
5-2
Temperature profiles of four different operations of the flue gas . . . .
186
5-3
Results of HRSG-split multi-objective optimization
. . . . . . . . . .
197
recovery unit
16
List of Tables
1.1
Specifications of flowsheet with 4+1 FWHs in Figure 1-10
. . . . . .
60
1.2
Results of flowsheet with 4+1 FWHs in Figure 1-10 . . . . . . . . . .
61
1.3
The applicability of the proposed design criterion for various configurations and the evidence given in this chapter. . . . . . . . . . . . . .
63
2.1
Fixed Simulation Parameters for the pressurized OCC process
. . . .
71
2.2
Optimization Variables for the pressurized OCC utilizing a DCSC . .
80
2.3
Optimization Constraints for the pressurized OCC process utilizing a
DCSC ........
...................................
81
2.4
Optimization Results of the pressurized OCC utilizing a DCSC . . . .
97
3.1
Specifications of utilized coals . . . . . . . . . . . . . . . . . . . . . .
102
3.2
Design and operation variables facing fuel uncertainty . . . . . . . . .
107
3.3
Optimization constraints facing fuel uncertainty . . . . . . . . . . . .
108
3.4
The runs performed to check the flexibility of the OCC cycle, with an
RHE or DCSC thermal recovery unit, under fuel uncertainty . . . . .
112
3.5
Results for RHE flowsheet fuel flexibility A . . . . . . . . . . . . . . .
115
3.6
Results for RHE flowsheet fuel flexibility B . . . . . . . . . . . . . . .
116
3.7
Results for DCSC flowsheet fuel flexibility A . . . . . . . . . . . . . .
117
3.8
Results for DCSC flowsheet fuel flexibility B . . . . . . . . . . . . . .
133
3.9
Results for RHE flowsheet fuel and area flexibility . . . . . . . . . . .
135
3.10 Results for RHE flowsheet fuel, area, and ambient temperature flexibility136
4.1
Turbine performance data . . . . . . . . . . . . . . . . . . . . . . . .
17
143
4.2
Recycling pipes diameters and gas velocity ranges . . . . . . . . . . .
147
4.3
Design and operation variables for uncertainty in load . . . . . . . . .
155
4.4
Optimization constraints for uncertainty in load . . . . . . . . . . . .
156
4.5
Summary of results for RHE flowsheet fuel, area, and ambient temperature flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
160
4.6
60% part load flexibility
. . . . . . . . . . . . . . . . . . . . . . . . .
161
4.7
30% part load flexibility
. . . . . . . . . . . . . . . . . . . . . . . . .
162
5.1
Fixed input parameters for the HRSG-split . . . . . . . . . . . . . . .
187
5.2
Optimization variables for the HRSG-split
. . . . . . . . . . . . . . .
195
5.3
Optimization results for the HRSG-split
. . . . . . . . . . . . . . . .
200
A.1
The relevant reaction added to Separation Column of the DCSC flowsheet208
18
Nomenclature
Latin symbols
Capacity rate [kW/K]
izcp
Bleed pressure [bar]
PB
hT(Po)
Enthalpy at the turbine
outlet [kJ/kg]
hB,o
hgsat
Enthalpy of the saturated
vapor [kJ/kg]
Heat Transfer Coefficient
2
[kW/(m K)]
Outlet pressure of the turbine
A
Derivative of the extraction mass flowrate following pinch at the onset of condensation withrespect to extraction pressure [kg/(s bar)]
Enthalpy of the bleed
stream in the outlet of the
feedwater heater [kJ/kg]
Heat Transfer Area [m 2 ]
rh
Mass flowrate [kg/s]
P
Pressure [bar]
Sgen
Rate of entropy generation
Q
Regenerated
CIP
Specific liquid thermal capacity [kJ/(kg K)]
T
Temperature [C, K
WB
Power that the extraction
stream would have generated in the turbine [kW]
Pcomb
Combustion Pressure (bar)
PDeaerator
Deaerator pressure (bar)
Duty Transfer (MW)
Combustor Duty (MW)
T
qDeaerator
Temperature (OC)
Quality in Deaerator tank
FWH
MITA
Feed Water Heater
Minimum Internal Temperature Approach [C, K]
0
"PB
U
PO
Derivative of the extraction mass flowrate following pinch at the bleed outlet with respect to extraction pressure [kg/(s bar)]
)
[kW, MW]
[kW/K]
Q
Qcomb
Duty
Greek symbols
r_
Acronyms
CFWH
HX
Cycle Efficiency (%)
Closed Feed Water Heater
Heat Exchanger
19
OFWH
Open Feed Water Heater
o-pinch
p-pinch
TLoad
ASU
Pinch at onset of bleed condensation
Air Separation Unit
FG-Rec-pri
Primary Recycled Flue Gas
CCS
FG-Rec-sec
I
Cool-Gas
DCSC
CPR
HRSG
FG-DCSC-in
FW
Pinch at bleed exit from
FWH
Thermal Load
Carbon Capture and Sequestration
Secondary Recycled Flue
_Gas
Flue Gas at exit of HRSG
Direct Contact Separation
Column thermal recovery
unit
Compensation power requirements to overcome
flue gas pressure losses
(kW)
Heat Recovery Steam Generator
CSU
DCSC-HX
Carbon Sequestration Unit
Heat Exchanger in DCSC
CER
Compression enthalpy rise
due to the CPR (kW)
RHE
Flue Gas
DCSC
Feedwater
FG-RHE-in
Recovery Heat Exchanger.
Acid condensation occurs
in RHE
Flue Gas entering the RHE
entering
the
FW,Main
Main feedwater stream.
Largest working fluid flow
passing through the HRSG
and entering the expansion
line
FWH
Feedwater Heater
FW-HRSG-in
Feedwater entering the
HRSG. Same flowrate as
FW, main
FW-DCSC-in
OCC
Feedwater entering the
DCSC
Flue gas entering the
HRSG
Lower Heating Value of
Coal (MJ/kg)
Low Pressure Pump
Oxy-Coal Combustion
RW-Sep-in
Cool-Gas
Flue gas exiting the HRSG
FW-HRSG-in
Comb-Gas-in
Flue gas entering the com-
FW-Recov-out
Hot-Gas
LHV
LP-Pump
HHV
HP-Pump
BLD
OC
bustor
BLD1-stage
BLD3_stage
Higher Heating Value of
Coal (MJ/kg)
High Pressure Pump
Rankine cycle regeneration
bleed
Oxy Combustion
Recirculation water of the
DCSC entering the separation column
Feedwater entering the
HRSG
Feedwater exiting the recovery unit, RHE/DCSC
Bleedi extraction stage
Bleed3 extraction stage
BLD2-stage
C02_Cap
Bleed2 extraction stage
Ratio of CO 2 capture to total produced
20
C02...pure
Purity of CO 2 captured
MITA-FWHi
Minimum internal temperature approach of FWHj
(OC)
MITA.HRSG
PBLDi
PDeaerator
OComb
TCool-Gas
TFW-HRSG-in
HRSG pinch ('C)
MITA-RHE
RHE pinch ('C)
Bleeds extraction pressure
(bar)
PComb
Combustion Pressure (bar)
Deaerator pressure (bar)
QFWHi
TFG-RHE-out
Feedwater Heater i duty
I (kW)
Quality in Deaerator tank
Flue gas temperature at
TComb-Gas-in
RHE exit (OC)
Temperature of gas enter-
Combustor Duty (MW)
Temperature of flue gas exiting the HRSG ('C)
Temperature of feedwater
qDeaerator
entering the HRSG ('C)
ing the combustor(OC)
Subscripts
a
actual design and operating
b
conditions
basecase design and operating conditions
B
B, o
Bleed
Bleed out
B, i
F
Bleed in
Feed
F,i
Feed in
Following o-pinch
Turbine expansion line
F,o
p
Feed out
Following p-pinch
1
sat
Liquid
Saturated state
As
HRSG total surface area
D
(m2)
HRSG tube diameter (in)
o
T
Superscripts
Vapor
Evaporation
Pressure Drop Parameters
Ac
HRSG cross section area
g
lg
d
(m2)
Recycling
pipe
diameter
(in)
Dh
Hydraulic diameter (in)
ATim
Log mean temperature dif-
HRSG pressure drop (Pa)
APipe
Recycling
ference (K)
APHRSG
pipe
pressure
drop (Pa)
6
F
k
Wall roughness (m)
ATm correction factor
Thermal conductivity
f
of
Friction factor
H
L
HRSG height (i)
HRSG length (m)
r
Flue gas flowrate (kg/s)
N
Number of tube rows along
flue gas (W/m.K )
Lpipe
Recycling pipes equivalent
length
A
(m)
Dynamic viscosity (kg/m.s)
HRSG length
Nu
Nusselt Number
Re
Reynolds number
QHRSG
HRSG (W)
I_
p
21
Total transferred duty in
Density (kg/m 3
)
SL
U
HRSG longitudinal pitch
(m)
HRSG overall heat transfer
coefficient (W/m 2 K)
Vo
W
ST
HRSG transverse pitch (m)
V
Bulk flue gas velocity (m/s)
Vmax
Maximum gas velocity in
HRSG (m/s)
I
Average gas velocity at
HRSG entrance (m/s)
HRSG width (m)
22
I
I
Chapter 1
A Double-Pinch Criterion for
Regenerative Rankine Cycles
1.1
Summary
A double-pinch criterion for closed feedwater heaters (FWH) of regenerative Rankine
cycles is presented.
The FWHs are modeled as counter-current heat exchangers.
Thus, two potential pinch positions in the FWH exist: (i) at the exit of the bleed
(drain) and (ii) at the onset of condensation. For a given heat duty in the FWH, feed
inlet temperature and flowrate, the extraction flowrate and pressure should be chosen
to achieve the same minimal approach temperature at the two potential pinch points.
An analytical proof is given for a fixed pinch value for the case that the drain enters
the condenser, based on weak assumptions. Additionally, the criterion is numerically
demonstrated for fixed pinch value and for fixed heat exchanger area using the most
common configurations: drain to condenser, drain to deaerator, and drain cascaded
to next FWH. A similar criterion is developed for the case that the drain is pumped
(upwards or downwards) and mixed with the feedwater. The double pinch criterion
simplifies the optimization procedure and results in significant efficiency increase for
23
fixed heat exchanger area. For numerical reasons it is advisable to use the pressure
as the optimization variable and calculate the heat duty and mass flowrate.
1.2
Motivation
Rankine cycles are widely used in power generation, typically with features for efficiency increase such as reheat, super heat, and regeneration [1, 2, 3].
Commercial
software packages capable of high fidelity modeling of the power cycles are available,
e.g., Thermoflex@ [4], AspenPlus@, GateCycle@ [5]. These software packages offer
tools for performing parametric and optimization studies on given cycles (flowsheet
connectivity) or even construct power cycles for a given application.
All but the simplest cycles are regenerative, i.e., they include preheating of the feed
(return from the condenser) via extraction of bleed streams from the turbine [1, 2, 3].
This preheating is performed in closed and/or open feedwater heaters (CFWH and
OFWH). There are various configurations of FWHs depending on where the exit bleed
of the CFWH, i.e., the drain, is sent to. The performance of the power cycle increases
in general with the number of FWHs. Thus, typically the number of FWHs is selected
based on cost considerations, i.e., balancing capital and operating costs. A well know
approximate design criterion is to have an equal enthalpy rise across each FWH in the
regeneration section of the Rankine cycle. More precisely, under some idealizations,
for maximum efficiency in a non-reheat non-supercritical plant the enthalpy rise of
the feedwater up to the point of saturation should, to a first approximation, be the
same in all heaters and the economizer [1, 2].
CFWHs are essentially multi-phase heat exchangers (HX). The design of HX networks is a well-established field, e.g., [6, 7, 8, 9, 10, 11]. The design of both power
cycles and HX networks can be performed with either shortcut methods or more rigorous models. A very common shortcut method is the so-called pinch analysis, i.e.,
24
to select a minimal temperature approach (MITA) and then calculate the inlet conditions and heat duty for each HX. This shortcut has the advantage of decoupling the
capital costs and detailed design of the HXs from the operating costs. The implicit
assumption of the pinch method is that the required HX area is accurately characterized by the MITA. However, accurate calculation of heat transfer area is needed
for economic optimization.
The focus of this chapter is to propose a new criterion for the optimization of
regenerative power cycles and apply it to both pinch method and optimization for a
fixed heat transfer area. Throughout the chapter CFWHs will be treated as countercurrent HXs. Consequently, there are two possible pinch points, namely at the onset of
condensation and at the exit of the bleed (the drain). The main result herein is that for
most FWH configurations optimal operation is equivalent to simultaneously achieving
both pinches. In all considerations the connectivity between units (flowsheet) and
the expansion line (condenser temperature, turbine inlet pressure & temperature and
total flowrate) are kept fixed. For the working fluid a pure species with phase change
is considered.
In the pinch analysis, a MITA is selected using economic criteria as a surrogate for
HX area. Subsequently, there are three degrees of freedom for each CFWH, namely
heat duty (as a surrogate via the MITA), bleed extraction pressure (and thus temperature) and bleed extraction flowrate. Thus, at least in principle, the cycle performance
can be optimized numerically considering simultaneous variation of these degrees of
freedom, subject to the constraints of minimal approach temperature. In the rigorous
analysis, heat transfer area is selected via economic analysis; the remaining degrees
of freedom are bleed extraction pressure and bleed extraction flowrate; moreover, the
MITA is free. The proposed design criterion eliminates two of the variables for each
CFWH. Moreover, for the case of the pinch analysis, the proposal eliminates the need
to check for the pinch-violation constraints and as such the need for a spatially dis-
25
tributed model for the feedwater heater. In summary, the proposal simplifies the cycle
optimization drastically. This computational acceleration is particularly important
when Rankine cycles are not considered in isolation, but rather as a part of a complicated process, e.g., oxycombustion [241, or inside another procedure, e.g., selection
of working fluid in an organic Rankine cycle. In fact the identification of the criterion was achieved in the process of optimizing a pressurized oxycombustion cycle [24]
using deterministic local and heuristic global optimization methods. Optimization of
a Rankine cycle in isolation is relatively simple, but not trivial in general-purpose
modeling tools, which in the absence of the proposed criterion result in suboptimal
local optima. The criterion also enables a simpler use of approximate design criteria,
such as the aforementioned equal enthalpy rise across feedwater heaters.
In Section 1.3 the shortcut rule of minimum temperature approach is considered
for the simplest FWH arrangement, namely that the drain is sent to the condenser.
A precise statement is given with appropriate boundary conditions and proved analytically. Moreover, it is demonstrated how the criterion can be implemented inside
an optimization procedure resulting in a significantly simpler optimization formulation than the alternative of simultaneous optimization of all variables. In Section 1.4
the applicability of the criterion to other configurations is discussed. In Sections 1.5
and 1.6 case studies with various FWH configurations are calculated numerically both
for the shortcut calculation and for a constant area respectively, discussing also the
entropy generation in the feedwater. The proposed criterion results in significant savings compared to current design practice for both shortcut and rigorous calculation.
26
1.3
Analytical Proof of Double-Pinch for Shortcut
Methods
In the following, the double pinch design criterion is developed and proved based on
a set of nonrestrictive assumptions. First, it is demonstrated that only two points in
the pinch diagram are of interest, namely the onset of condensation and the outlet
of the bleed.
Subsequently, for the case that the drain is sent to the condenser,
it is proved that for a given heat duty a double pinch is necessary for optimality.
Moreover, there exists a unique pair of extraction pressure and flowrate that results
in a double pinch. Therefore, a double pinch is also sufficient for optimality. Then, a
reordering of variables is proposed along with a procedure for computationally efficient
optimization.
1.3.1
Two possibilities for pinch to occur
Assumption 1.3.1 (Capacity Rates). The ratio of feed flowrate to extraction flowrate
is assumed sufficiently high that the capacity rate (rhcp) of the feed is higher than that
of the bleed for both the superheated and subcooled regions.
Assumption 1.3.1 holds for typical Rankine cycles.
The following proposition shows that in the pinch diagram only two points are of
interest. For a graphical illustration, compare also Figure 1-1.
Proposition 1.3.2. Under Assumption 1.3.1 a minimum approach temperature between the feed and bleed can only occur at two points, namely the onset of condensation, and the bleed outlet.
Proof. Recall that the feedwater heater is modeled as a counter-current HX. The feed
is always subcooled and therefore a smooth curve is obtained in the pinch diagram.
In contrast, the bleed consists in general of three regions, namely, the superheated
27
region, the condensation region, and the subcooled region, giving two kinks at the
transitions.
The region of condensation results in a horizontal line for the bleed,
i.e., enthalpy decrease without temperature change. By Assumption 1.3.1, the other
two curves corresponding to the bleed have a higher slope than the slope of the curve
corresponding to the feed. Therefore, in the direction of flow of the bleed from the inlet
to the outlet, the superheated and subcooled regions result in convergence between
the bleed and the feed curves, whereas in the condensation divergence between the
two curves is observed. Consequently, the two potential points for a pinch are the
onset of condensation and the bleed outlet.
Note that if the bleed inlet is in the
two-phase region, the onset of condensation coincides with the inlet.
300
E
________
I_______I__
Bleed M=25.5kg/s P=25bar
Bleed M=30.Okg/s P=1 5bar
Feedwater M=100.Okg/s P=100bar
250
200
c
150
p-pinch
E
I100 --
50 -
0-pinch-
01'
0
1
2
3
4
5
6
Thermal Energy Transfer, Duty (kJ/s)
7
8
X 104
Figure 1-1: Pinch diagram for illustrative feedwater heater (results generated in
AspenPlus@). There are only two possibilities for pinch to occur in a heat regeneration in the FWH of a pure substance; at the cold end of the heat exchanger (drain, red
dotted bleed line, labeled o-pinch), or at onset of bleed condensation (black dashed
bleed line, labeled p-pinch).
28
1.3.2
Analytical Proof of Necessity
In this section the shortcut method of minimum temperature approach is considered
for the case that the drain is sent to the condenser. It is shown that for a given feed
flowrate rnf, feed inlet temperature T,j and heat transfer duty
Q
a double pinch is
optimal except for trivial cases. It is based on relatively weak assumptions.
Assumption 1.3.3 (Bleed saturation enthalpy). It is assumed that the enthalpy of
the saturated vapor hg,'
at the bleed pressure PB is not lower than the enthalpy at
the turbine outlet hT(Po).
h9a'(PB) > hT(P,),
where the subscript T denotes the turbine (expansion line) and Po the outlet pressure
of the turbine.
Assumption 1.3.3 is satisfied for typical expansion lines. It could only be violated if
the turbine outlet state is highly superheated and the heat duty is very small allowing
for a very low extraction pressure PB. Such an operation is suboptimal.
Assumption 1.3.4 (Bleed outlet enthalpy). It is assumed that the enthalpy of the
bleed stream in the outlet of the feedwater heater hB,0 is not higher than the enthalpy
of the turbine outlet hT(Po)
hB,o
<;
hT(Po).
Assumption 1.3.4 is satisfied for typical expansion lines and working fluids, e.g.,
water and ammonia, heptane and toluene.
Assumption 1.3.5 (Bleed pressure). It is assumed that the optimal extraction pressure PB is strictly higher than the turbine outlet pressure P.
Assumption 1.3.5 can only be violated if the heat duty of the feedwater heater is
extremely low and the outlet of the turbine is highly superheated. In other words,
recuperators are not considered herein.
29
Assumption 1.3.6 (Bleed pressure). It is assumed that the optimal extraction pressure
PB
is strictly lower than the turbine inlet pressure.
Assumption 1.3.6 holds for typical Rankine cycles.
Assumption 1.3.7 (Heat capacity and saturated vapor). The following relationship
is assumed to hold for the pressures of interest
&hg,sat
aP
&Tsat
<;
c<P(T"(PB)
-
AMITAT, PF)
PB
-
OP PB
Assumption 1.3.7 is satisfied for typical working fluids, such as water, toluene and
ammonia. For the conditions of interest, the expression of the left hand side is either
negative or slightly positive, whereas the right hand side is always positive.
Assumption 1.3.8 (Positive Pressure Dependence of Liquid Enthalpy). The derivative of the liquid enthalpy with respect to pressure is positive
-h
> 0.
aki T
Note that Assumption 1.3.8 holds for an incompressible liquid, which is a good
approximation for the liquids. Moreover, it holds for typical working fluids, such as
water, toluene and ammonia.
In the formal statement of the main result, reheats are excluded for simplicity.
Moreover, a fixed expansion line is considered, essentially assuming that the turbine
isentropic efficiency is not affected by the extraction conditions.
Theorem 1.3.9 (Double pinch necessary).
Consider a regenerative Rankine cycle
without reheats and with positive isentropic efficiency of the turbine. Let the turbine
inlet temperature, inlet pressure, outlet temperature and outlet pressure P be fixed,
i.e., not influenced by the extraction. Consider an arbitraryfeedwater heater, specified
by an arbitrary but fixed feed flowrate
rilF,
30
feed inlet temperature TFj, and a heat
transfer duty
Q.
Suppose that the feed pressure Pf is chosen so that the feed stream
remains subcooled. Suppose that the feedwater heater can be modeled as a countercurrent heat exchanger with a minimum approach temperature AMITAT and without
pressure drop. Assume that the extraction state is saturated or superheated, i.e., the
extraction temperature is not smaller than the saturationtemperature of the extraction
pressure. Suppose that the drain is sent to the condenser. Select a pair of extraction
flowrate rmB and pressure PB such that the cycle performance is optimized. Under
Assumptions 1.3.1 through 1.3.8 a double-pinch occurs, i.e., the MITA occurs both at
the condensation onset and at the outlet of the bleed stream.
Proof. The proof is done by contraposition, i.e., by considering an optimal pair nB,
PB, assuming that no double pinch occurs and concluding that the pair is not optimal. This is done in three steps, first excluding the case that no pinch occurs, then
excluding the case that a pinch occurs only at the onset of condensation and finally
excluding the case that a pinch occurs only at the bleed outlet.
Based on the assumption that no reheat exists, the power that the extraction
stream would have generated in the turbine is given by
WB
Note that
hB,i.
hT(PB)
=
(1.1)
r4B(hT(PB) - hT(Po)).
is the enthalpy of the bleed inlet to the feedwater heater
Optimal extraction minimizes this lost power
hT(PB) =
WB.
Note first that if the extracted steam is saturated steam or in the two-phase
region
(hT(PB)
h9,,at(pB)), then the pinch at the onset of condensation is trivially
satisfied. Moreover, the pinch at the outlet minimizes
given pressure since
PB
ThB
thus minimizing
> P0 is assumed. Thus, we can assume
hT(PB)
WB
for a
> h9,St(PB)-
1. Suppose for contraposition that the MITA is not reached in the feedwater for
(PB, MB). Then, an infinitesimal reduction of either extraction flowrate or pres31
sure (or even both simultaneously) allows the same heat transfer duty without
a violation of the MITA. On the other hand, this reduction implies that more
power is produced in the turbine, see (1.1), or the original pair is not optimal.
2. Assume now that for (PB,
we have a pinch at the onset of condensation
MB)
but not at the bleed outlet. Maintaining the pinch at the onset of condensation
implies that a change in extraction pressure results in a change in extraction
flowrate.
This is possible without violating any constraints, given Assump-
tion 1.3.5. We denote the derivative of the extraction mass flowrate following
pinch at the onset of condensation with-respect to extraction pressure
where the subscript p stands for p-pinch.
Consider the partial derivative of the power not produced in the turbine with respect to the extraction pressure following the pinch at the onset of condensation
evaluated at (PB, TnB)
B
9PB
Oh\
- hT(Po)) + 7B (9.PB
±
PB
0hB
=(hT(PB)
-
PB
=\OPB
-B
PBn
(1.2)
where we have used the fact that the turbine inlet and outlet states are fixed.
Optimal operation implies minimal WB, or if we find that a-
0 then the
PB
pair (PB,
MB)
is not optimal.
In the right-hand side of Equation (1.2) the second term is positive
since the turbine produces work. Thus, if the derivative
PB is nonnegative, we also have
B
(f
> 0),
evaluated at
> 0 or the pair (PB, MB) is not optimal.
Note that this would imply that we can reduce both extraction pressure and
flowrate and maintain the same preheating. Note also that
directly proved.
32
(B)
< 0 can be
We thus only need to consider the case
OrhB
<0.
OPB /
(1.3)
<-
We will show that the derivative of the power lost with respect to the
extraction
pressure is negative, or increasing the extraction pressure increases
efficiency.
We will generate an expression for
in the following. The condition for
(0-)
a pinch at the onset of condensation is
rnF (hFO
- h(T sat(PB) -
AMITAT, PF
rB
(hT(PB)
-
h9 at(PB))-
Taking the derivative with respect to PB and evaluating at (PB, MB)
gives
-~FCP(Tsat(PB) -
AMITAT, PF)
OP
C
rnB
(hT(PB)
-
IPB
h9,sat (pB)) +
t
- hgB
MB OhT
PB
MB
O P
PB
or
(hT(PB) - h
\&PB )
=
-
MB
ih T
h
5 PB
t (PB)
Bsa
+- Ohgsat
+MB
-
PB
hFCP(sat(PB) - AMITAT,PF)
33
OP/(1.4)
PB
By Assumption 1.3.3 we have hT(Po) < hg'8at(PB) and therefore
hT(PB) - hg,sa t (PB)
"Tsat
h(P)
--- hT(Po).
Recalling Inequality (1.3) we thus obtain
(hT(PB) - hT(Po)) (<hB )
PBP
(h(PB) - h'sat(PB))
OPB
P
and therefore combining Equations (1.2) and (1.4) we obtain
WB-
<
s (Ts*t
FC-p(T ( PB) ~ AMITAT PF)
,sat
+mB
_PB
PB
Noting that nB < rF
B
P
PB
by Assumption 1.3.7 we obtain '9WB
0 PB ,PB < 0. By As-
sumption 1.3.6 it is possible to increase the pressure and thus we have shown
that (PB, MB) is not optimal.
3. Assume finally that for (PB, MB) we have a pinch at the bleed outlet but not
at the onset of condensation.
Similarly to the previous case we will consider variation of the extraction pressure by maintaining the pinch at the bleed outlet (
),
i.e., the derivative
of the extraction mass flowrate following pinch at the bleed outlet with respect
to extraction pressure, where the subscript o stands for o-pinch.
Equivalently to the previous case we obtain
09WB
-
PB
(hT(PB) - hT(Po)) + MB
(hB
B
PB
(1.5)
B
and
(0mB)
PB
< 0.
(1.6)
PB
We then show that the derivative of the power lost with respect to the extraction
is positive, implying that the extraction pressure should be decreased.
34
We will generate an expression for
(2)
in the following. The heat transfer
duty maintaining a pinch at the outlet can be calculated as
Q
(hT(PB) - h1 (Ti
= rB
+ AMITAT,PB))
Noting that the total heat transfer is constant, the derivative with respect to
PB is zero. Evaluating the derivative of the right hand side at
(PB, MB)
thus
gives
0
=
OPB
O-B
SPB
(hT(PB) - h'(T,i + AMITAT, PB))
±MB
9PB PB
-
;,i+AMITAT,PB
or
O(nB
OPB /
-
(hT(PB)
Ohl
OhT
- h'(Ti + AMITAT, PB))
B
PB
~
+mB OPB
TT+AMITATPB
(1.7)
By Assumption 1.3.4 we have hl(Ti + AMITAT, PB) = hB,0 <! hT(P) and
therefore
hT(PB) - h'(Tri + AMITAT,PB)
hT(PB) - hT(P).
Recalling Inequality (1.6) we thus obtain
(hT(PB) - hT(Po)) (0riB)
h(PB) - h'(Ti + AMITAT,PB))
B
(
OB
PB
and therefore by (1.7)
(hT(PB) - hT(Po))
ohi
> -BMB
B
O
PB
OPP
+rnB
T,I±AMTAT,PB
35
)
PB
which together with (1.5) gives
-
9WB
B
B
PB
TT,i+AMITAT,PB
and by Assumption 1.3.8 we obtain
> 0. By Assumption 1.3.5 it is
possible to decrease the pressure and thus we have shown that (PB, MB) is not
optimal.
1.3.3
Graphical Proof of Uniqueness and Sufficiency
Theorem 1.3.9 proves that a double pinch is a necessary condition for optimality. In
principle, it allows for multiple double pinches, out of which some may be suboptimal.
Under two additional assumptions it is possible to prove that for a given heat duty
there exists a unique pair (PB, rnB) that gives a double pinch.
Assumption 1.3.10 (Weak Pressure Dependence of Subcooled State). The derivative of the liquid enthalpy with respect to pressure is smaller than the derivative of the
enthalpy in the expansion line
O
<
hT
(1.8)
PB
T,PB
Moreover, the heat capacity in the subcooled region is assumed to be a weak function
of pressure for the temperatures and pressures of interest, or more precisely for any
two pressures PB1, PB2 such that PBl> PB2 we have
c (T, PB1)
hT(PB1) - h1(T, PBj)
<T(B)-hl(,P2
B2--hTB2
h
cip (T,PB2)
36
(1.9)
Both clauses of Assumption 1.3.10 hold unless the turbine efficiency is extremely
low.
Assumption 1.3.11 (Enthalpy of Vaporization Decreasing). The derivative of the
enthalpy of vaporization with respect to pressure is negative
&hg
< 0.
Assumption 1.3.11 holds for pure substances [12].
Lemma 1.3.12 (Double pinch unique). Consider the conditions and assumptions of
Theorem 1.3.9.
Under the additional Assumptions 1.3.10 and 1.3.11 there exists a
unique pair of extraction flowrate 71B and pressure PB that gives a double pinch.
Proof. Consider a pair
pair
PB2, rnB2
with
(PBi, rnBl)
PB2
that results in a double pinch. Consider a second
< PBi that results in a pinch at the outlet. We will show
that it violates the minimal approach temperature at the onset of condensation.
Consider the pinch diagram, Figure 1-2, noting that no linearity is assumed (which
would require constant heat capacity in some regions). By Assumption 1.3.1 the slopes
of the subcooled curves are bigger than that of the feed for both bleeds.
Let the points Bli, B gj',
B'sat and Bio denote respectively the inlet of the bleed,
the onset of condensation, the onset of subcooling and the outlet of the bleed. Moreover, let Bis""
denote the intersection of the saturation temperature at pressure
with the subcooled curve of bleed 1.
Finally, let Bg~mt
the saturation temperature at pressure
PB2
PB2
denote the intersection of
with a parallel to the subcooled curve of
bleed 1 going through Bfi"a.
For bleed 2 to achieve pinch at the outlet, its outlet coincides with Bi0 . Note that
37
pinch at the outlet implies
=
Q
nB
(hT(PB1) - h1 (Ti
+ AMITAT, PB1))
=rnB2 (hT(PB2) - h'(T, i + A MITAT, PB2))
We will now employ the two inequalities in Assumption 1.3.10.
conditions for Q directly imply that
rnB2 >
rnBl.
By (1.8) the two
Moreover, by (1.9) the same
assumption, the onset of subcooling of bleed 2 is to the left of Beal. Finally, together
with Assumption 1.3.11, the onset of condensation is to the left of B
l
Recalling
that the slope of the bleed is higher than that of the feed, this point is to the left of
the minimum temperature approach.
Figure 1-2: Pinch diagram demonstrating uniqueness of double pinch
Since the bleed pressures
PB1, PB2
are arbitrary, we can also exclude the case of
a double pinch with higher pressure than
a double pinch for the bleed pressure
PB1
PB3.
say
PB3.
Indeed, suppose that we have
By the above arguments
PB1
violates the
minimal approach temperature leading to a contradiction.
E
Theorem 1.3.13. Under the assumptions of Theorem 1.3.9 and Lemma 1.3.12 the
unique pair (PB, rnB) that gives a double pinch is optimal.
The proof of Theorem 1.3.13 is trivial and is omitted. Note that we take existence
for granted; this is justified by the change of variables in the next subsection.
1.3.4
Procedure for Cycle Optimization
Theorems 1.3.9 and 1.3.13 prove that a double pinch is optimal for a fixed heat duty.
However, it is computationally more efficient to vary the extraction pressure in both
shortcut of pinch analysis and fixed area approach.
38
Procedure for Pinch Analysis
For the pinch analysis approach, it is possible to directly calculate the pair of extraction flowrate
rnB
and heat duty
.
mF
Q =
Q that leads to double pinch
- AMITAT, PF) - h'(TFi, PF)
hgsat(PB) - hi (TFi
+ AMITAT, PB)
hi(Tsat(PB)
hB(hT(PB)
(1.10)
h(TFi ± AMITAT, PB))
-
Note that since the expressions are explicit in
pinch for a given extraction pressure PB.
raB
and
Q
there is a unique double
One of the advantages of this change
of independent variable is that the explicit equations for the occurrence of pinches
eliminate the need for a spatially distributed model of the feedwater heater. However,
we have not proved whether a double pinch is optimal for a fixed pressure. It is
therefore necessary to demonstrate that the change in variables does not result in
convergence to spurious solutions when used inside an optimization algorithm. In the
following it will be shown that a global/local optimum in the pressure space following
the double-pinch implies a global/local optimization of the design and operation.
Proposition 1.3.14 (Extraction pressure as independent variable does not introduce
complications). Let the superscript k = 1,.
. . ,n
denote the feedwater k. Suppose that
optimization is performed with respect to the extraction flowrates Pk with the heat
duty Qk and extractionflowrate rhk specified by (1.10) and that Pk is found optimal
in a set 'pk.
Denote the corresponding extraction flowrates rik and heat duties
If 'pk contains all possible extraction pressures, then the triplets
a globally optimal power cycle efficiency.
If 'k
(PB
,I )
Qk.
ge
is a neighborhood with Pk in the
interior,the triplets give a locally optimal power cycle efficiency.
Proof. Consider first the case that the sets 'Pk encompass all possible extraction pressures. This implies that the triplets
P,
Mi,
Qk) are optimal over all triplets leading
to a double pinch, and therefore by Theorem 1.3.9 also optimal over all triplets.
39
Consider now the case that 'Pk are neighborhoods with PL in the interior. Assume
first that there is a single feedwater heater k = n = 1. Let the solution to (1.10)
as a function of the extraction pressure Pk be denoted as
rhkd(PA),
Q(Pk). Local
optimality implies
S(P, rnBd(B,
(p
k
k)
v
'Pk,
The continuity of the mappings in (1.10) implies that the image of
Qk on ',k is an
interval. Proposition 1.3.12 ensures a unique double pinch for a fixed heat duty and
thus
Qk
is not at the boundary of the interval. By Theorem 1.3.9 for any Pwe
Thus, there exists a neighborhood with (Pk,
ri,
have
Q ) in the interior for which (Pt, i,
is optimal. This is the definition of a local minimum.
Assume now multiple FWHs for the case of local optimality. Recall that the
flowsheet has one or multiple points with fixed temperature, e.g., the condenser.
Move in direction of the feed and between each of these points divide the feedwater
heaters in pairs and if needed an additional feedwater heater. For the pairs consider
a variation of the extraction pressure Pk in a neighborhood containing PB interior
for the first and adjust the second P+1 such that the sum of the heat duties remains
constant 0k+1 +
k =
+ Qk. Similarly to the case of a single feedwater heater
±k+I
we can use uniqueness and continuity (with respect to extraction pressure and feed
inlet temperature) to construct a neighborhood with Qk,
Qk+1
in the interior and
prove local optimality. Given that the pair has a constant sum of heat duties, we can
treat the odd (separate) feedwater heater similarly to the case of a single feedwater
heater.
0
40
Qk)
Procedure for Fixed Area
The double-pinch criterion can also be applied in the case of fixed heat transfer area,
but some iterative procedure is required. The optimal procedure somewhat depends
on the flowsheeting software used.
There are several plausible choices, and here
only the more promising are discussed. The general recommendation is to have the
extraction pressure
PB
as the main optimization variable. Then, for a given heat
transfer area and extraction pressure the double-pinch criterion fully specifies the
operation of the FWH, by eliminating one variable, e.g., the bleed flowrate. Note
that the value of the pinch is an unknown and that the operation is only implicitly
specified.
The first main choice is to either let the optimizer control an additional variable
to satisfy a nonlinear constraint, or mask this pair from the optimizer and embed it as
a design specification inside the objective function evaluation. The former procedure
is recommended by the recent excellent treatment of chemical plants by Biegler [131.
However, in the computational experience herein and in [241, the use of embedded
design specifications was found more favorable, because it avoid failures at the simulation level.
The second consideration is which pair of variable and constraint to select. Herein,
the bleed flowrate
fTB
is adjusted to meet the double-pinch criterion. This requires a
calculation of the heat transfer in the FWH for each iteration ("HX analysis"). Once
this calculation is performed, the values of the two pinch points can be obtained from
the temperature profiles or from solving (1.10).
of the pinch
AMITAT
An alternative is to vary the value
to meet the given heat transfer area. In this alternative the
bleed flowrate and heat transfer duty can be calculated explicitly from (1.10) but the
calculation of the heat transfer area is required ("HX design").
41
1.4
Other Feedwater Configurations
As aforementioned there are several FWH configurations.
For most configurations
the double pinch criterion seems plausible but it is outside the scope of this paper
to prove analytically. For some configurations the criterion is not applicable. For a
summary, see Table 1.3.
1.4.1
Drain to Open Feedwater Heater
In the above analytical proofs it was assumed that the drain is sent to the condenser.
For high-pressure CFWHs an obviously better choice is to send the drain to the next
possible deaerator or OFWH, since this allows the recovery of some of the remaining
availability and reduces the load on the condenser and the pumps. The proof employed
in Theorem 1.3.9 assumes that the drain does not affect the temperature of the feed
inlet and therefore is not directly applicable to the case that the drain is sent to the
condenser. A claim of this chapter is that the double pinch criterion is applicable to
this feedwater configuration. An analytical proof is outside the scope of this chapter
and instead numerical examples are given in Section 1.6.
1.4.2
Cascading (Downwards)
In high-efficiency cycles with multiple CFWHs it is customary to cascade the bleeds
downwards, namely send the drain to the next CFWH (immediately lower pressure)
and mix it with the bleed inlet. Similarly to sending to an OFWH some of the remaining availability is captured. As demonstrated in numerical examples, Section 1.5 and
Section 1.6, the double pinch criterion is promising. However, the analytical proofs
given in Section 1.3 are not directly applicable, and an analytical proof is outside the
scope of this study.
42
1.4.3
Pumping to Feed
One flowsheet configuration is to pump the drain to the feed pressure and mix the
feed, see Figure 1-3. One alternative is to mix at the inlet of the CFWH, which is
referred to as pumping backwards (or downwards). The other alternative is to pump
forward (or upward), i.e., to mix with the feed at the outlet of the CFWH. For either
of the pumping configurations, double pinch is an optimal selection of bleed pressure
and flowrate for the pinch analysis but not the unique optimum. For the constant
area approach, double pinch is not advisable. In general, an optimal selection is to
achieve pinch at the onset of condensation and just enough subcooling at the outlet to
ensure that no technical difficulties arise for pumping. Similarly to the double pinch
criterion, this gives two constraints which can be used to eliminate two of the three
variables.
FWH
JFWH
ump
Pump
Figure 1-3: Feedwater configurations with pumping of the drain; left pumping backwards/downwards, right pumping forward/upwards.
Assumption 1.4.1 (Feed inlet enthalpy). It is assumed that the enthalpy of the feed
inlet to the feedwater heater hF'i is not higher than the enthalpy of the turbine outlet
hT(Po)
hFi <; hT(Po).
Assumption 1.3.4 is satisfied for typical expansion lines and working fluids, e.g.,
water and ammonia, heptane and toluene.
43
Theorem 1.4.2 (p-pinch for pumping configuration). Consider a regenerative Rankine cycle without reheats and with positive isentropic efficiency of the turbine. Let
the turbine inlet temperature, inlet pressure, outlet temperature and outlet pressure
P be fixed, i.e., not influenced by the extraction. Consider an arbitraryfeedwater
heater, specified by an arbitrarybut fixed feed flowrate mF, feed inlet temperature TFi
and a heat transfer duty
Q.
Suppose that the feed pressure Pf is chosen so that the
feed stream remains subcooled. Suppose that the feedwater heater can be modeled as a
counter-current heat exchanger with a minimum approach temperature AMITAT and
without pressure drop. Assume that the extraction state is saturated or superheated,
i.e., the extraction temperature is not smaller than the saturation temperature of the
extraction pressure. Suppose that the drain is pumped to Pf and mixed with the feed
in the inlet or outlet of the FWH. Select a pair of extractionflowrate 7B and pressure
PB such that the cycle performance is optimized. Under Assumption
1.4.1
the MITA
occurs at the condensation onset. Moreover, subcooling of the drain to achieve the
double pinch adds heat transfer area without increase of efficiency.
Proof. We first show the necessity of pinch at the onset of condensation by contraposition. Suppose that the pair (PB,
MB)
is optimal and the pinch does not occur at
the onset of condensation. For any pair (PB,
rnB)
the first law neglecting the pump
power gives
rnF,ihF,i+ iBhT(PB) = rhFohFo,
where the inlet state i is before mixing and the outlet state o after mixing. Similarly,
the mass balance gives
TfF,i + rnB =
mpo-
Combining the last two equations we obtain
(T-F,o
~ fnB)hFi + rnBhT(PB)
44
= r
hF0
and therefore
rhB(hT(PB) - hFi)=
,o(hFo
- hFi)
We differentiate and evaluate at (P, rnB)
(PB
(Or'B)
To
(h,(PB)
-
-
By Assumption 1.4.1 we have hFi
hi)
B
M
.OhT
0
PB PB
hT(PO) and thus
hT(PB) - hFi > hT(PB) - hT(P o )
and therefore
(
&WB
O
&rnB~)
PB
(hT(PB) - hT(Po)) ±
PB )To PB
Similarly to the proof of Theorem 1.3.9 we have OWB
mB
hT
M
B
(111)
PB
> 0 and therefore PB is not
optimal.
We will now demonstrate that a double pinch is not advisable in terms of the
heat transfer area. Suppose that the pair (PB, MB) is optimal and the pinch occurs
at the onset of condensation and at the drain outlet. Keep the extraction conditions
and partition the heat exchanger into two segments: (i) for cooling the vapor and
condensation and (ii) for the subcooling. If we eliminate the second segment, we
still achieve complete condensation: in the case of pumping backward the inlets to
segment (i) are unchanged; in the case of pumping forward, the feed inlet to segment
(i) is colder resulting in higher heat transfer rate (the effect of lower flowrate on the
heat transfer rate is neglected). Moreover, eliminating the second segment does not
change the state of the feed outlet (after mixing); this is obvious by the first law and
mass balance. In conclusion, the heat transfer area can be reduced without loss in
45
performance.
1.4.4
El
Open Feedwater Heater
For the sake of completeness, OFWHs are also considered. Clearly, OFWHs do not
fall in the same category as CFWHs and thus the double pinch criterion is not directly applicable. On the other hand, it is still worthwhile to optimize the extraction
pressure and flowrate. There are still three optimization variables for each OFWH,
namely the operating pressure and the bleed pressure and flowrate. Following the
same procedure as in the proof of Theorem 1.4.2, one can show that the optimal
extraction pressure is equal to the deaerator operating pressure. Moreover, the bleed
flowrate is given by the desired temperature increase and the requirement for saturation at the feed outlet. Thus similarly to the CFWHs only one variable has to be
optimized for.
1.5
Numerical Examples with a Simple Flowsheet
In this section the validity of the design criterion is demonstrated for a single FWH
and multiple FWHs numerically. Power cycles with cascading and non-cascading
FWHs are considered. In addition to a prespecified minimum temperature approach,
the design criterion is demonstrated for the case of prespecified area. For the sake of
simplicity and compactness the same cycle is used to validate the criterion for both
single and multiple feedwater heaters.
A simple Rankine cycle implemented in AspenPlus® is shown in Figure 1-4 and
used to explain the importance of the double-pinch criterion. Feedwater exiting the
condenser, at the condenser pressure of 0.04bar and with a flowrate of 100kg/s, is
compressed to the boiler pressure 100bar, before entering the FWHs. Note that the
pressure in the condenser is below atmospheric which implies the need for a deaerator,
46
not modeled herein for simplicity; this does not affect the results and deaerator is
considered in Section 1.6.
The temperature of the feedwater increases as thermal
energy is transferred from the bleeds passing through the heaters. Feedwater is then
heated in the boiler to a fixed outlet temperature of 500'C before entering the steam
expansion line where power is produced from the steam turbine. Two extractions,
one for each bleed, are present in the expansion line. Two bleed configurations are
shown, cascading and non-cascading. In both configurations, the bleed stream exiting
FWH2 is mixed with the main feedwater stream at the condenser. In the cascading
configuration (marked by x in Figure 1-4), the bleed at the exit of FWH1 is mixed
with the lower pressure bleed before entering the FWH2. In contrast, in the noncascading configuration (marked by o in Figure 1-4), the exiting bleed from FWH1
proceeds directly to the condenser. The cycle efficiency reported is the ratio of the
net produced power (turbine power minus pump power), to the heat transfer rate
in the boiler. For the sake of simplicity no pressure drops are considered and the
turbomachinery is assumed to be irreversible. Note that this nonrealistic assumption
does not affect the qualitative results and a more realistic case study is given in
Section 1.6.
1.5.1
Single Feedwater heater
Recall that the regeneration scheme, shown in Figure 1-4 has two closed FHWs. Only
the non-cascading configuration is discussed in this subsection and only FWH1 (highpressure) is analyzed. In contrast, the FWH2 (low-pressure) is considered fixed as
follows
PB2 = 0.158bar,
rnB2 = 4.73kg/s,
Q2 = 9.50MW
The specifications for FWH2 are chosen to result in a double pinch with a value of 3YC.
This arbitrary specification does not affect the results presented in this subsection,
47
Turbine
Boiler
Bleed2
Bleedi
Condense
Cascading
FWH1
FWH2
N~on-Cascading
Pump
Figure 1-4: Flowsheet for the numerical validation of the double pinch criterion.
Cascading bleed configuration marked by x and non-cascading bleed configuration
marked by o.
since they only affect the overall efficiency.
Minimal Approach Temperature
As aforementioned a common shortcut method in system-level analysis and optimization is the pinch analysis. The proposed double-pinch criterion is validated numerically for this shortcut calculation. The heat transfer duty in FWH1 is fixed to
Q, = 60.7MW. This value is selected based on approximately optimal performance
of the cycle. As aforementioned this heat transfer duty can be achieved for different combinations of bleed flowrate and pressure, resulting in different MITA and heat
transfer area required. The bleed flowrate and pressure are discretized with 200 points
each, in the range
PB,
E [13, 15]bar,
rnB E [22, 24]kg/s
48
and the aforementioned flowsheet is simulated in AspenPlus@ for each value. The
results are illustrated in Figure 1-5, which shows contours of efficiency as a function
of the two variables. This corresponds to the optimization objective function and is
increasing with decreasing extraction pressure and flowrate. The figure also shows
the optimization constraints, namely the two possible pinch points, at the onset of
condensation and at the feedwater outlet for two given MITA. These pairs of lines
define the feasible region for higher pressure and/or flowrate (region to the upper
right), and the infeasible operation, i.e., operation violating a given MITA (region
to the lower left). The pairs of lines intersect at the double-pinch operation for a
given MITA and the figure shows the union of all intersection points. For a given
MITA the double pinch is at a higher contour line compared to either of the two
pinch lines. Mathematically, this can be expressed as the gradient of the objective
function lying in the feasible cone defined by the constraints. In other words if one
follows either of the pinch lines the efficiency increases towards the double pinch and
decreases away from it. From the graph two more facts are evident that can be also
proved analytically: (i) the pressure of the bleed at the double pinch is the smallest
extraction pressure that allows for a pinch at the outlet of the FWH; and (ii) the
flowrate of the bleed at the double pinch is the smallest flowrate that allows for a
pinch at the onset of phase change.
Maximizing the efficiency is equivalent to minimizing total entropy generation in
the system, or total exergy destruction. It is well-known that minimal system entropy generation is not necessarily equivalent to minimal entropy generation for each
component. For instance, for a minimal entropy generation in the FWH a zero heat
transfer duty is preferable which results in a suboptimal cycle performance. However,
the numerical results suggest that for this simple flowsheet optimal design & operation of the FWH coincides with minimal entropy generation in the FWH for fixed
heat transfer duty and MITA. This is demonstrated in Figure 1-6 which plots the con49
24
23.9
23.8
23.7
23.6
-I
23.4
23.3
23.2
23.1
13
c-
0.1 C
-K
Efficiency
Double pinch
C
s
-p-pinch
.
0'
o-pinch
feabibleI
0 ,
23.5
1
P
p-pinch
'.E
C
00
0.1
Double pinch
1
s o-pinch
1%
Tlwtv....
13.5
14
14.5
Bleed extraction pressure (bar)
2.5
H
15
Figure 1-5: Contours of efficiency for regenerated duty Qi = 60.7MW for Flowsheet 14. Pinch lines super imposed: pinch at onset of condensation with a MITA of 0.10 C
and 2.5 0 C (black line, labeled p-pinch); pinch at outlet of FWH with a MITA of
0.1 0 C and 2.5'C (purple line, labeled o-pinch); double-pinch with variable MITA
values (intersection of two pinch lines).
tours of entropy generation rate along with the aforementioned constraints. Minimal
entropy generation seems intuitively correct since the double-pinch seems to result in
smaller average temperature between the feed and bleed. However, as is evident from
Figure 1-1 (crossing of bleed lines) there is a tradeoff between extraction pressure
and flowrate, so that proving the validity of entropy generation would not be a trivial
task. Note also that minimizing for the entropy generation inside the cycle design is
not practical since it would require a constrained optimization problem, embedded
in the cycle simulation or optimization. For instance, the cycle optimization could
set/select the heat transfer duty and the entropy generation would be minimized by
varying the extraction pressure and flowrate subject to the MITA. Embedded optimization problems are extremely challenging and only recently have they been solved
for nonconvex problems [14]. In other words minimizing entropy generation is deemed
more complicated than the original system-level optimization problem. The double
pinch approach on the other hand eliminates two degrees of freedom and satisfies the
design constraints at each iteration performed by the optimizer while eliminating the
need for a spatially distributed model. Finally, in the case of fixed heat transfer area,
minimal entropy generation in the FWH is not a good criterion as discussed in the
following.
Fixed Area
The results presented in the previous subsection validate the analytical proof derived
for the shortcut method of pinch analysis. This analysis in principle ignores capital
costs associated with increasing the heat transfer area by reaching the MITA in two
positions. To address capital costs, the flowsheet given in Figure 1-4 is now analyzed
for a given (constant) heat transfer area of FWH2, assumed equal to 2,516m 2 . To
demonstrate the generality of the results, this area is selected different than the
one corresponding to the selected heat transfer duty in the MITA. Similarly to the
51
24
p-pinch
p-pCh
2. 5 S
23.8 23.7--
gen
G
0.1
3.-
Double pinch
p-pinch
2.23.7-o-pinch
feasible
23.6-
-
23.5
0
23.4
-
Q
23.3
apinch
Double pinch
C
-p; c
'S-pinch
7
2.5
23.2
23.1
23
13
-
-
teas
13.5
14
14.5
_
15
Bleed extraction Pressure (bar)
Figure 1-6: Contours of entropy generation rate $gen for regenerated duty Qi =
60.7MW for Flowsheet 1-4. Pinch lines super imposed: pinch at onset of condensation
with a MITA of 0.1'C and 2.5'C (black line, labeled p-pinch); pinch at outlet of FWH
with a MITA of 0.1'C and 2.5'C (purple line, labeled o-pinch); double-pinch with
variable MITA values (intersection of two pinch lines).
previous analysis the bleed flowrate and pressure are discretized with 200 points each,
in the range
PBI E
[11, 13]bar,
rhB1 E
[21,23]kg/s.
This range is similar but not identical to before to account for a different heat transfer
area/duty. The results are shown in Figure 1-7 where the contours of efficiency are
plotted. The efficiency is maximal for middle values of the extraction pressure and
flowrate. For every extraction pressure there exists an extraction flowrate that maximizes cycle efficiency (green line); these pairs are near optimal. The difference is in
the order of 10
5
(10-
3
percentage points), i.e., noticeable numerically but insignifi-
cant compared to model and/or numerical inaccuracies. In mathematical terms there
exists a linear manifold in the optimization variable space along which the directional
derivative is very small. In practical terms this allows the optimization of the cycle
even if the pressure cannot be selected with arbitrary accuracy. This is for instance
important for potential retrofit of existing cycles; therein it may not be possible to
change the extraction pressure but only the extraction flowrate. The small difference
in performance between the double-pinch pairs and the absolute optimum implies
that retrofiting may get almost the same performance increase as optimal design.
For low extraction pressures and high extraction flowrates (upper left corner) the
approach temperature at the onset of condensation is much smaller than the approach
temperature at the outlet and the opposite is true for high extraction pressures and
low extraction flowrates (lower right corner). Figure 1-7 also shows the line of (approximate) double pinch (red line), which results in an efficiency within 10-5 (10-3
percentage points) of the aforementioned near-optimal efficiency line. The difference
is so small that could be attributed to model/numerical inaccuracies and is not significant from a practical perspective. It is also noteworthy that efficiency seems to
favor large pinch at the outlet versus large pinch at the onset of condensation. This is
a possible explanation for the current design practice of only slightly subcooling the
53
23
22.8
22.6
-45.79
45.74
22.846.011
4
45.97
45.89 45.92
460
region
22.4 46.03
22.2 +
22
0
--
e
. .
218
46.01
45.98
21.6
-p-
21.4
21
11
11.5
12
12.5
45.92
13
Bleed Extraction Pressure (bar)
Figure 1-7: Contours of efficiency for a fixed FWH Area 2,516 m3 . The green line
shows the optimal extraction flowrate for a given extraction pressure, while the red
curve shows the pairs that result in double-pinch; operation points on the two lines
give efficiency differences less than 10- 5 (10-3 percentage points). The blue cross
shows the optimal solution, while the black cross shows the best double-pinch point.
drain, see the following discussion. However, both unbalanced approach temperatures
are inferior to balanced MITA.
Figure 1-8 plots contours of entropy generation rate in FWH2 as a function of the
two bleed variables. The same lines as in Figure 1-7 are superimposed on the figure.
It is evident that minimal entropy generation in the FWH is not a good criterion for
maximal cycle efficiency. Recall that this is in contrast to the case of pinch analysis
for a given heat transfer duty. More concretely, minimal entropy generation occurs for
low heat transfer duty, which occurs at low extraction pressure and flowrate. In other
words, entropy generation minimization in the FWH ignores the benefits of increased
regeneration prior to the boiler. In contrast, the proposed double pinch criterion is a
good criterion for optimal efficiency.
54
23
22.8 22.6.
146
149
151
p-pinch
region
22.4
max efficiency on
22.2
double pinch line
22 -
150
double pinch
dblinh
+
~
max efficiency
21.8
21.6
21.4
21.2
21
2- 141
11
141
11.5
12
12.5
Bleed Extraction Pressure (bar)
142
13
Figure 1-8: Contours of entropy generation gen for a fixed FWH Area 2,516 m
The green line shows the optimal extraction flowrate for a given extraction pressure,
while the red curve shows the pairs resulting in double-pinch; operation points on the
two lines give efficiency differences less than 10-5 (10-3 percentage points). The blue
cross shows the optimal solution, while the black cross shows the best double-pinch
point.
1.5.2
Non-Cascading, Cascading, and Common Practice
High-efficiency regenerative Rankine cycles have cascading bleeds in a FWH train,
i.e., combine the drain from a FWH with the inlet bleed of the preceding FWH (next
lower pressure). In Figure 1-4 the outlet from FWH1 is mixed with the inlet to FWH2
(line marked by x). The advantage of this arrangement is that the outlet bleed still
has significantly higher temperature than the following deaerator or the condenser
and thus the availability of the stream can be used to preheat the feedwater and thus
reduce the required bleed flowrate to the preceding FWH. Typically, the cascading
FWH are designed and operated to achieve the MITA in the onset of condensation
and subcool the outlet bleed by a few K. This seemingly reduces the heat transfer area
needed without loss in performance, since the bleed will be further used. However,
this analysis may be misleading since further subcooling the bleed would imply that
the preceding FWH needs to preheat the feed to a lower temperature.
Recall that no analytical proof for the optimality of cascading double pinch is
given herein. Instead, the criterion is examined numerically for the flowsheet given
in Figure 1-4. Comparing the efficiency with the pinch analysis approach could be
seen as unfairly favoring the proposed double-pinch criterion due to potentially larger
heat transfer area. Consequently, the comparison is done for a constant total heat
transfer area. The following four configurations/designs are compared: (i) cascading
configuration with the proposed double-pinch criterion; (ii) noncascading configuration with the proposed double-pinch criterion; (iii) cascading configuration with the
current design practice of slight subcooling at outlet for the FWH1 and the proposed
double-pinch criterion for FWH2 (low pressure); (iv) cascading configuration with
the current design practice of slight subcooling at outlet for both FWHs. For each
case, a cycle-level optimization of the efficiency is performed by varying the fraction
of heat transfer area between the two FWHs as well as the extraction pressures. For
the double-pinch criterion, for a given pressure and heat transfer area, the FWH is
56
fully specified, by (1.10). In the current design practice, for a given operating pressure the bleed outlet temperature is specified as Tt(PB) - 2K; therefore, for a given
heat transfer area the FWH is fully specified. A simple thought experiment to verify
this is to note that the inlet temperature of the feed is fixed, and so is the inlet and
the outlet temperature of the bleed; the feed flowrate is also given, so if we select
the bleed flowrate we obtain the heat transfer duty and feed outlet temperature by
energy balance; heat transfer correlations result in calculating the heat transfer area.
In AspenPlus@ the bleed flowrates and heat transfer duty for each FWH are implemented by design specifications embedded into the optimization. For a motivation
for this decomposition, see [24].
The calculations are performed for heat transfer coefficients accounting for the different regimes, i.e., for the vapor-fluid section U = 0.709kW/(m 2 K), for the condensation section U = 3.975kW/(m 2 K), and subcooling section U = 1.704kW/(m 2 K), as
taken from an example in [15]. Note that the values of the heat transfer coefficients
are actually dependent on the heater's geometry and flow conditions but here are
taken as constant for simplicity. Additionally, calculations for a constant overall heat
transfer coefficient are performed, but since these result in very similar qualitatively
results, they are not shown for the sake of compactness.
Figure 1-9 plots the optimal efficiency for each of the four design procedures as
a function of the total area of the FWHs. As expected all four curves are monotonically increasing indicating the tradeoff of capital costs and efficiency, including the
asymptote to a finite value for infinite heat transfer area. Moreover, as expected,
the cascading flowsheet with double pinch outperforms the noncascading equivalent.
The main finding is that the cascading cycle with double pinch in both feedwater
heaters outperforms significantly the standard practice. For large values of the heat
transfer area, the efficiency improvement is in the order of 2 percentage points compared to slight subcooling in both FWHs and in the order of 0.5 percentage points
57
47 r
46.8-
Co
46.4
o
46. -
T
-
dp cas
practice pinch
-N-dp non
e
practice cas
F9p.E
46 -
O
~
45.8
45.6
500
1000
1500
2000
2500
Total Regeneration Area
3000
3500
4000
(MPf)
Figure 1-9: Optimal performance of four different design procedures versus total
FWHs area for flowsheet given in Figure 1-4: cascading with double-pinch for both
FWHs (green solid curve, labeled "2pinch-2pinch cascading"); cascading with subcooling of 2K for FWH1 and double-pinch for FWH2 (purple dashed-doted line, labeled "ppinch-2pinch cascading"); noncascading with double-pinch for both FWHs
(blue line with x marks, labeled "2pinch-2pinch noncascading"); cascading with subcooling of 2K for both FWHs (red line with triangle marks, labeled "ppinch-ppinch
cascading").
for the case that the double pinch criterion is applied to the low-pressure FWH and
slight subcooling is applied to the high-pressure FWH. For small values of the heat
transfer area, the efficiency improvements are not as dramatic but still substantial.
Moreover, the noncascading cycle with a double pinch outperforms the cascading cycle without double pinches, and is very close to the cascading configuration with a
double pinch in FWH2. Finally, the difference in performance among the different
procedures increases with increasing area, or the proposed design criterion becomes
more important for large heat exchanger areas.
58
1.6
Numerical Case Study with a Realistic Cycle
Design
In this section a realistic Rankine cycle is considered, illustrated in Figure 1-10. It
contains four CFWHs and an OFWH acting as the deaerator.
are arranged in two pairs, above and below the deaerator.
The four CFWHs
For each of the two
pairs of CFWHs cascading is used, i.e., the drain of the high temperature CFWH
is combined with the bleed entering the CFWH. The drain of the lowest pressure
is pumped upwards. The cycle specification are shown in Table 1.1. For simplicity
the expansion line is considered to have a constant isentropic efficiency. Otherwise,
the optimization is significantly complicated, see the discussion on integer variables
in [24].
The proposed optimization criterion is compared with the current design practice
of small subcooling in the drain. Initially, the bleeds are optimized following a MITA
specification of 2K for each CFWH (FWH1,2,4&5) and with an subcooling of the
drain of 2K. Then the area of each CFWH is fixed and used for optimization of the
flowsheet with the proposed double-pinch approach for three of the four CFWHs.
Since the drain of the last CFWH is pumped upward, the double-pinch is not optimal
and the drain is subcooled by 2K.
Moreover, the bleed is two-phase liquid (not
superheated) and thus a pinch occurs at the inlet of the bleed. The results are shown
in Table 1.2; the proposed criterion results in a significant efficiency increase, in the
order of 0.45 percentage points. Note that this is achieved merely by changing the
bleed pressures and flowrates, without any increase in heat transfer area, without
addition of components, and without changing the flowsheet connectivity. Moreover,
the area of each FWH is selected based on optimization of the conventional design
criterion; allowing for a redistribution of the heat transfer area would result in further
savings for the proposed criterion.
59
Turbine
Boiler--
Bleed3
BleedB
Bleed2
Bleed4
Bleed5
FWH1
FWH4
Condes
FWH2H
FWH2
~
Deaerator
F H
LP Pump
FWH(p)
Bleed Pump
HP Pump
Figure 1-10: Realistic cycle design with four closed feedwater heaters
Table 1.1: Specifications of flowsheet with 4+1 FWHs in Figure 1-10
Unit Name
Feedwater main flowrate
Boiler pressure
Boiler superheat temperature
Turbine efficiency
Deaerator pressure=bleed3 pressure
Condenser pressure
Condensate temperature
Pumps Efficiency
LP Pump discharge pressure
Specification
Unit specifications
108 kg/s
150.3 bar
542.9 0 C
Isentropic 0.7 - Mechanical 1
17.53 bar
0.05 bar
33.0 0 C
Isentropic 1 - Mechanical 1
20.31 bar
Double-pinch
Conventional
FWH1
MITA = 20 C
Area = 2165 m 2
FWH2
FWH4
FWH5
MITA = 2'C
MITA = 20 C
MITA = 2'C
Area = 1667.8 m 2
Area = 1486.8 m 2
Area = 1048 m 2
Table 1.2: Results of flowsheet with 4+1 FWHs in Figure 1-10
Optimization results
Conventional
Double-pinch
38.56 %
Efficiencyqr38.11%
PM'
71.3 bar
82.87 bar
rm)
14.9 kg/s
15.81 kg/s
p(2 )
36.0 bar
35.21 bar
7h(2
6.26 kg/s
6.736 kg/s
7h(3
6.221 kg/s
8.418 kg/s
p(4 )
5.883 bar
4.619 bar
rh()
9.120 kg/s
8.212 kg/s
p(5)
1.080 bar
0.7478 bar
mh(5
7.162 kg/s
6.621 kg/s
1.7
Conclusion and Future Work
A new design criterion is proposed for the design and operation of feedwater heaters
in regenerative Rankine cycles.
The basis is to have the same pinch in the onset
of condensation of the bleed and in the outlet of the bleed. The criterion is proved
analytically for a simple configuration and illustrated numerically in case studies for
various configuration, see Table 1.3. Application of the criterion results in significant efficiency improvements for a constant heat transfer area (representing capital
costs). Moreover, a procedure is proposed that drastically simplifies the design and
optimization of regenerative Rankine cycles.
In the pinch analysis, for each feed-
water heater the pinch value and extraction pressure (design variable), are fixed or
optimized for; the bleed flowrate and heat transfer rate (operational variables) are
adjusted to achieve the double pinch. In the rigorous calculation, the extraction pressure and heat transfer area (design variables) are fixed or optimized for; the bleed
flowrate and pinch value are adjusted to achieve the double pinch. The case studies
demonstrate that under the proposed double-pinch criterion, the cycle performance is
not very sensitive to the design and substantial improvements to performance can be
achieved by adjusting only the operational variables. If local solvers are used for the
optimization, the criterion increases the chances to find a global optimum; if global
solvers are used the number of variabls and constraints is reduced which typically results in significantly faster CPU times. Regenerative Rankine cycles are very common
in industry and novel energy systems and thus the presented criterion has important
implications for research & development.
Future work should include experimental validation for both existing and new
cycles.
Additionally, consideration of controlability of the proposed operation and
second law analysis is of interest. Moreover, the double pinch criterion could be
applied to different systems, such as boilers and heat recovery steam generators, and
cases where both streams exhibit phase change. Finally, it would be interesting to
62
consider splitting the drain and use in both cascading and non-cascading way.
Table 1.3: The applicability of the proposed design criterion for various configurations
and the evidence given in this chapter.
Pinch analysis with fixed
and MITA
double pinch unique optimum (analytical proof +
numerical case studies)
double pinch unique optimum (numerical case
studies)
double pinch unique optimum (numerical case
studies)
double pinch non-unique
optimum
(analytical
proof)
double pinch not applicable; optimal extraction
pressure equals to operating pressure (analytical
proof)
Q,
Drain to condenser
Drain to OFWH
Cascading
CFWH
drain
Pumping
ward/forward
wards/upwards)
OFWH
to
back(down-
63
Fixed heat transfer area
double pinch unique optimum (numerical case
studies)
double pinch unique optimum (numerical case
studies)
double pinch unique optimum (numerical case
studies)
double pinch not optimal
(analytical proof)
double pinch not applicable; optimal extraction
pressure equals to operating pressure (analytical
proof)
64
Chapter 2
Optimal Design and Operation of
Pressurized Oxy-Coal Combustion
with a Direct Contact Separation
Column
2.1
Summary
Simultaneous multi-variable gradient-based optimization is performed on a 300 MWe
wet-recycling pressurized oxy-coal combustion process with carbon capture and sequestration. A direct contact separation column is utilized for practical and reliable
low-temperature thermal recovery. The models for the components include realistic behavior like heat losses, steam leaks, pressure drops, and cycle irreversibilities.
Moreover, constraints are used for technoeconomical considerations.
Optimization
involves 17 optimization variables and 10 constraints, with the objective of maximizing the thermal efficiency. The optimization procedure utilizes recent design rules
and optimization procedures for optimal Rankine cycle performance, as explained in
65
Chapter 1, speeding up the plant optimization process by eliminating variables and
avoiding constraint violations. Moreover, the procedure partially alleviates convergence to suboptimal local optima. The basecase of the study is a comprehensively
optimized cycle that utilizes a surface heat exchanger, a more thermodynamicallyeffective form of thermal recovery which however bears significant materials challenges. Upon optimization, the cycle utilizing the direct column is seen to be very
attractive regarding efficiency and performance. Moreover, the optimization results
unveil potential for reducing capital costs by eliminating the first carbon sequestration
intercooled compressor and by showing possibilities of process intensification between
the separation column and the carbon sequestration purification columns.
2.2
Motivation
The importance of emissions free power generation is motivated and discussed extensively in literature [16, 17]. Clean and renewable power production are of high
interest to both academic and industrial research aiming to make such technologies
more affordable and reliable. However, the world's dependence on fossil fuels for power
generation, especially coal due to its cheap price and abundance of reserves [181, is
expected to continue at least till renewable power generation becomes more economically attractive.
Pressurized Oxy-Coal Combustion (OCC) with Carbon Capture and Sequestration (CCS) mitigates the emissions problem while relying on the cheapest fossil fuel
[19, 20, 21, 22, 23, 24]. In OCC the flue gas is mainly carbon dioxide and water vapor,
and the latter can be separated by condensation. Flue gas cooling and condensation
can be integrated to recover thermal energy, particularly latent, into the low temperature section of the power cycle, [20, 21, 23, 24, 25]. As flue gas pressure increases, the
vapor dew point in the flue gas increases allowing for condensation to occur earlier
66
and at a higher temperature. This increases the amount of recovered latent energy
and increases its quality since it occurs at a higher temperature. Pressurizing the
combustion process increases the compression requirements of the air separation and
oxygen delivery process while reducing those for the carbon sequestration process,
but also contributes in increasing the pressure losses and irreversibilities within the
flue gas; the tradeoffs signify a presence of an optimum operation.
Simultaneous
multi-variable optimization, like the one dealt with in [24], is required to obtain the
optimum operation and achieve an attractive cycle performance. Optimization in [24]
contributes in significant efficiency increase, 0.76% points over the literature proposal
of 10bar combustor pressure, [211, while simultaneously reducing the combustor's operating pressure, to the range of 7.41 bar, thus making the process more attractive
and practical. Efficiency is 3.12% points higher than that of the atmospheric operation. Results also show the importance of the 15 other optimization variables in
obtaining such efficiency improvements.
The pressurized OCC cycle presented in [24] utilizes a recovery heat exchanger
(RHE), which is a surface heat exchanger, for recovering thermal energy from the
water vapor present in the flue gas. However, this type of heat exchanger is subjected
to considerable amount of fouling and damage from the contaminated flue gas. While
the surface heat exchanger is thermodynamically more efficient, it requires relatively
more care and maintenance. A more practical form of thermal heat recovery which is
less susceptible to fouling is a direct contact separation column (DCSC). Comparison
of the capital and operating costs between the two recovery units is out of the scope
of this work.
Separation columns are used in various engineering and chemical processes [26],
and in fact are used as part of the Carbon Sequestration Unit (CSU) in the OCC
cycle, where the dry flue gas is purified from nitrogen and sulfur oxides and other
contaminants. In general the separation process is performed by having two streams
67
in a vertical counter flow arrangement where undesired substances in one stream are
transferred to the other stream. In this study, a DCSC is used instead of a surface
heat exchanger to condense water vapor from the flue gas and recover some of the
latent and sensible energy.
Replacing the RHE with a DCSC changes the cycle's performance substantially.
The DCSC utilizes an intermediate stream between the flue gas and the working
fluid of the power cycle for the recovery process, leading to a less effective thermal
recovery compared to a RHE. Therefore, the efficiency of the cycle with the DCSC
is expected to decrease. The difference in the operation and performance of the two
units mandates optimization of the operating conditions for the DCSC flowsheet,
which are expected to be noticeably different than those for the RHE flowsheet.
Herein, multi-variable gradient based optimization is performed for the model
presented in [27, 24] with a DCSC replacing the RHE. A similar methodology and
approach are followed as those explained in [27, 24], the optimization results of which
are taken as the basecase of the current work. Recent design rules and optimization
procedures, [27, 24, 28, 29] and Chapter 1, are incorporated and automated within
the model. Detailed and high fidelity modeling of components and irreversibilities
are also considered to accurately assess the advantages and tradeoffs compared to the
original RHE flowsheet and compared to other coal CCS technologies. The details of
the model and the specifications are presented in Section 2.3. Section 2.4 describes
the DCSC unit and presents its modeling approach and simulation analysis for the
proper integration within the pressurized OCC flowsheet. Section 2.5 deals with the
optimization formulation and describes the objective function, optimization variables,
and optimization constraints. Results are shown in Section 2.6 where the influence
of the critical variables on the cycle are analyzed. Results also suggest possibilities of
capital cost reductions.
68
2.3
2.3.1
Flowsheet and Model Description
Power Plant Flowsheet
The flowsheet and model specifications studied here are identical to those of [24]
with the exception of utilizing a DCSC instead of a RHE. Aspen Plus@ is also
used for modeling the work presented here. Figure 2-1 shows the schematic of the
flowsheet with the different sections, Air Separation Unit (ASU), Combustor, Rankine
Cycle, DCSC, and CSU. Oxygen is separated from air by the ASU and provided at
an elevated pressure to the combustor as an oxidizer. The combustor is based on
the ISOTHERM PWR® technology, [30], patented by ITEA [31, 32, 33]. Prior to
combustion, the pressurized oxygen is mixed with the primary recycled flue gas stream
(FG-Rec-pri) to control the combustion to a temperature to 1550'C. Combustion
gas (Comb-Gas) exiting the Combustor is mixed with a secondary recycling stream
(FG-Rec-sec), forming Hot-Gas, before entering the Heat Recovery Steam Generator
(HRSG) to maintain a temperature of 800 0 C specified by the metallurgic properties
of the HRSG. The HRSG is based on a proprietary ITEA/Ansaldo Caldaie design,
developed with the support of ENEL. The HRSG is the site of main thermal energy
transfer from the flue gas to the Rankine cycle working fluid. Upstream of the DCSC,
the flue gas temperature should remain above the acid condensation temperature.
Sulfur and nitric oxides resulting from the combustion of coal cause damage to the
material and components if they condense outside the DCSC. Therefore, constraints
on Cool-Gas and on the feedwater entering the HRSG, FW-HRSG-in, are placed with
safety margins to avoid condensation in the flue gas and on the tubes of the feedwater
respectively. A large fraction of the Cool-Gas exiting the HRSG is recirculated for the
temperature control processes utilizing fans that compensate for the flue gas pressure
drops. The flue gas pressure losses occur mainly in the HRSG and the recirculating
pipes. The non recirculated fraction of Cool-Gas proceeds to the DCSC where acids
69
are condensed from the flue gas before the CCS process.
Moreover, low quality
thermal energy, approximately 40'C to 220'C latent and up to 300'C sensible, is
recovered by cooling the flue gas and condensing the water vapor. FG-DCSC-out exits
the DCSC and proceeds to the CSU where it is further purified, compressed to 80bar,
liquefied and pumped to 110 bar. The high pressures used allow the liquefaction at
the ambient temperature eliminating the expensive operation and capital cost that
would otherwise be needed for cooling and storage.
The power cycle utilized is a supercritical, single reheat, regenerative Rankine
cycle.
Only high-pressure feedwater heaters (FWHs) are utilized for regeneration;
the thermal recovery from the DCSC and the thermal energy absorbed from the
combustor's losses reduce the benefits of adding low-pressure FWHs preceding the
deaerator. The steam expansion line is accurately represented by twelve stages with
specified isentropic efficiency for each stage, [21, 24]. Four extractions are required
from the expansion line, one for each bleed (two closed FWHs and one open FWH
or deaerator) and one for the combustor's atomizer stream. A detailed description of
the flowsheet and model is found in [24]. Table 2.1 summarizes the flowsheet's fixed
parameters.
2.3.2
Flue Gas Pressure Losses
For the accurate assessment of the cycle and in order to find realistic optimum operating conditions, losses and irreversibilities have to be accounted for. As detailed in
[24], the pressure losses in the recycling pipes are calculated as:
APp
= pf
70
(2.1)
Table 2.1: Fixed Simulation Parameters. The superheat pressure is lower than the
highest pressure in the cycle due to pressure losses through feedwater heaters, connection pipes, and the HRSG.
Simulation-Parameter
Name
Coal HHV
Coal LHV
Coal mass flowrate
Slurry water input mass
fraction
Atomizer Stream weight ratio (steam/Coal)
Atomizer stream pressure
Oxygen purity
Oxygen molar fraction in
flue gas
ASU specific work for 95%
purity at 1.238bar
SuperHeat stream pressure
SuperHeat stream temperature
Reheat stream pressure
Reheat stream temperature
Condenser operating pressure
Condenser operating temperature
HP-Pump pressure (maximum water pressure)
Parameter Value
31.09MJ/kg
29.88MJ/kg
30kg/s
35.48%
8.33%
30 bar
95%
3%
837kJ/kg
250bar
600 0C
55.67bar
610 0C
0.04bar
29.7 0C
266.2bar
ASU
Pressurized
02
02
Compressor
r
02
02
sep
N2
a-
-G-Rec-pri
FG-Rec-se tW-HRSG-in
Reheat
CSU
HRSG
CombustioSe
CoalT Wati
Slurry
ot-G
.. Gs
ure
.... Te
estrated C2
o-Gas
i
-C
-o
FG-DCSC -in---.....
vented gas
Ash
FW-DCSC-in
Controller
Atomizer
Condensate
H P
Bleed
IPT
LPT
Bleed
Bleed3
Cooling Water
Reheat
FW-HRSG-in
FWHD
FWH
Deaerator
Condenser
HP-Pump
LP-Pump
Figure 2-1: Oxycombustion cycle flowsheet based on wet recycling utilizing a DCSC.
Note that this schematic does not represent entirely the modeling, e.g., turbines
were modeled with multiple stages in Aspen Plus. The DCSC flowsheet is shown in
Figure 2-2
where V is the bulk gas velocity in the pipe, d is the pipe diameter, Lp is the pipe
equivalent length, p is the gas density, and
f
is the friction factor calculated by:
-
= "1 -2.0log
2 l
fpe
. 2 log
2/d)_
[7.4
where e is the pipe roughness, Red
Red
= PVd
7.4
+ 13
Red
}
-2
is the Reynolds number based on the pipe
diameter, p is the flue gas density, and p is the dynamic viscosity of the gas.
The HRSG pressure drop is calculated as:
APHRSG,a
-
APHRSG,b
QHRSG,aPaTib
(2.2)
QHRSG,bp~rha
where subscripts a and b stands for actual and the basecase of the initial RHE
flowsheet optimization respectively.
QHRSG
is the thermal energy transferred in the
HRSG, and mh is the flowrate of the flue gas. A detailed derivation of the equation is
provided in [24].
2.4
2.4.1
DCSC Modeling
DCSC Flowsheet
Flue gas enters the bottom of the eight
The DCSC unit is shown in Figure 2-2.
stage separation column and exits from the top stage. Eight stages are selected to
achieve acceptable separation; a detailed design of the column is outside the scope
of this work. Meanwhile, a recirculating water stream, Rec-Wtr-Sep-in, flowing in
the opposite direction, from top to bottom, cools down the flue gas and absorbs the
condensate.
The condensate is mainly water vapor along with sulfuric and nitric
acids; despite the sulfuric and nitric acids condensation in the separation column, the
73
flue gas still requires purification in the CSU to fit sequestration standards. Although
the acid condensation does not result in high acidity in the circulation water as it
passes through the separation column, NaOH is introduced gradually into the stages
of the different stages to maintain a neutral pH. The amount of NaOH needed is
very small compared to the large flowrate of the condensed water and much larger
flowrate of the recirculation water, and thus does not affect the mass and energy
balance.
Also, the concentration of salt is much smaller than the solubility limit
and thus no precipitation occurs. The recirculation water stream itself heats up and
increases in mass flowrate, as it collects the condensing water, forming RW-Sep-out.
Flue gas exits the separation column with a reduced temperature and vapor fraction
depending on the flue gas pressure and the recirculation water stream temperature
and flowrate. The separation column is modeled by a RadFrac column in Aspen Plus
with no condenser nor reboiler.
The ability of the DCSC to cool and dehumidify the flue gas is expected to be
less than that of a RHE. In more details, the temperature of the recycling stream
in the DCSC recovery unit, the cold stream in the separator, is always greater than
the temperature of the working fluid of the Rankine cycle exiting the low-pressure
pump, which is the cold stream of the RHE in the RHE cycle. This is because the
recirculating water and the Rankine cycle working fluid exchange thermal energy in
the DCSC-HX which has a positive minimum internal temperature approach (MITA)
specification as explained later. This in principle causes smaller temperature decrease
of the flue gas and smaller condensation rates for the DCSC compared to the RHE.
Moreover, in the separation column, the condensed water increases the capacity of
the cold stream causing a smaller temperature rise of the recirculating water.
As a result of the expected higher temperature and larger humidity of the flue gas,
a flue gas cooler interacting with the atmosphere is introduced after the separation
column. The cooler is allowed to reduce the flue gas temperature to 36.9'C, which
74
7FG-Sep-out
FG-DCSC-out
Flue Gas Cooler/
Chiller Condensed Water
Condensate
ChiN
_RW-Sep-in
Separation
Column
ain
Clp
(nlow
t
RW-HX-out/RW-Split-in
FW-HX-outS-H
FG-Sep-in
-.
RW-Sep-out
I
FW-HX-in
R-Xi
PUMP
Figure 2-2: Direct Contact Separation Column (DCSC) operation unit for the low
quality thermal energy recovery
is the minimum flue gas temperature obtained in the RHE flowsheet, [241, without
introducing a cooler. This temperature is obtained based on the MITA on the RHE
(7.1'C [24]) and the temperature of the water in the Rankine cycle at the exit of the
low-pressure pump. The temperature at the exit of the low-pressure pump is defined
by the condenser's fixed operating pressure and the specifications of the pump itself.
Cooling close to atmospheric temperature is achievable and attractive because it
reduces the CSU compression power requirements.
Moreover, the chiller prevents
unacceptably large humidity in the flue gas entering the CSU. Since the air and the
coal flowrates are fixed input parameters, the flowrate of the flue gas entering the
CSU changes only due to a change in humidity, which is relatively small.
Thus,
the flue gas pressure and its pressure losses are the dominant factors in the CSU
power requirements. The chiller temperature is limited to 36.9*C because a lower
temperature requires a larger, more expensive, cooler to drive the thermal energy
across a low temperature gradient, and because no further cooling across the same
temperature gradient is considered for the RHE flowsheet.
The recirculating water stream exits the separator column from the bottom stage
75
carrying the excess water and flows through a pump that compensates for any pressure
losses. Then recirculating water enters the heat exchanger (DCSC-HX) where thermal
energy is transferred to the working fluid of the Rankine cycle. DCSC-HX is defined
by a MITA of 5'C. The recirculating water stream exits the DCSC-HX where a splitter
is responsible for controlling the flowrate back to its original value and closing the
recirculating water loop while rejecting the Excess-stream. DCSC-HX is introduced
before the splitter in order to allow for a larger thermal energy transfer from the
recirculating water stream and the carried condensate as opposed to the recirculating
water stream only. In other words, the excess stream separated by the splitter exits
the loop at a lower temperature when the splitter is after the DCSC-HX as opposed
to being before.
No pressure losses are considered in the DCSC since losses in this section are minor;
the flue gas operating pressure is expected to be relatively large, so the pressure loss
within the separator column which is of the order of 0.lbar is not significant compared
to an operating pressure of the order of 10bar, and thus barely affects the CSU power
requirements. Moreover, the recirculating water stream is a liquid, so the pump power
requirements required to compensate for the liquid losses are also insignificant. Note
that in the RHE flowsheet [24], the thermal recovery did not include pressure losses
and therefore it is consistent to do the same for the DCSC.
For all units in the DCSC flowsheet the Electrolyte NRTL property method is
used. The DCSC-HX handles the Rankine cycle working fluid (cold side of the heat
exchanger) with the Steam Tables physical property. A set of reactions describing
the nitrogen and sulfur oxides formation and reactions are used in the Separation
Column and are given in Appendix A.
76
2.4.2
DCSC Operation
A detailed design and sizing of the DCSC requires thorough modeling of phase and
chemical equilibrium and possibly kinetic and residence time. However, herein only
the aspects that are relevant to the power plant operation need to be considered. By
evaluating extreme cases of species' chemical reactions, it is found that kinetics in
the separator column play a minor role on the overall energy and mass balance. The
extreme cases of flue gas with no
S0 2 /SO
3
conversion versus a complete conversion
has minor effects on the temperature of the involved streams and thus insignificant
effect on the amount of thermal energy recovered into the Rankine cycle. Therefore,
kinetics and separator column sizing are not incorporated in the integrated flowsheet
of the total pressurized OCC cycle.
The main variables influencing the DCSC and the amount of thermal energy recovered are the flue gas pressure, specifying the separation column operating pressure,
and the characteristics of the recirculating water stream. Due to the active constraint
optimization approach, explained in Section 2.5.5, the recirculating water characteristics are not independent. The stream pressure is equal to the flue gas/separation
column pressure since pressure losses in the unit are considered minor and neglected.
Any other specification of the recirculating water stream, e.g. the recirculating water temperature or a species concentration is enough to define the DCSC behavior.
Changes to the flowrate of the recirculated water result in the easiest convergence of
the stream's specifications within the recirculation loop and thus considered as the
optimization variable associated with the DCSC. The recirculating water flowrate is
also the simplest characteristic to measure and implement during actual operation.
Section 2.6.1 explains how the stream flowrate specifies the state of the recirculating
water.
The operating pressure of the DCSC flowsheet is expected to be larger than that
of the RHE flowsheet in order to allow for enough water condensation and thermal
77
recovery. The flowrate of the recirculating water, which dictates the stream's own
temperature, is another important variable in thermal recovery. It also determines
the flue gas temperature at the exit of the separation column where the chiller is
initially seen important in order to lower the CSU power requirements.
2.5
Optimization Formulation
The importance of simultaneous multi-variable optimization is illustrated in [24],
where significant improvements are obtained compared to a single variable sensitivity
analysis. Therefore, for the DCSC pressurized
OCC cycle a similar methodology is
applied.
The basecase of the DCSC model is the optimum operation of the RHE
model.
Optimization is performed within Aspen Plus using the built-in SQP op-
timizer. Multi-start, similar to that in [24, 27], is performed here to increase the
probability of finding the global optimum, and disregard suboptimal local solutions.
2.5.1
Objective Fanction
The objective considered is to maximize the thermal efficiency of the cycle. The
fuel flowrate and specifications are fixed, therefore, the objective is equivalent to
maximizing the net power output. The net power is equal to the total power produced
from the Rankine cycle minus the power consumption of the pumps, the recirculating
fans, the ASU, and the CSU. Economical concerns are accounted for by considering
reasonable HRSG size, recycling pipe diameters, MITA for heat exchangers, etc.,
similar to the procedure in [24].
2.5.2
Optimization Variables and Constraints
Implementing the DCSC instead of the RHE adds to the complexity of the cycle
on both levels, simulation and optimization.
78
At the simulation level, convergence
is required for the separator column and the recirculating stream. More critically,
at the optimization level, the unit adds to the variable count. The RHE flowsheet
model consists of 10 constraints and 13 optimization variables, and an additional three
integer variables are required for the accurate representation of the steam expansion
line. The DCSC flowsheet model incorporates 10 constraints and 14 optimization
variables, in addition to the three integer variables. As discussed in Section 2.5.5,
some constraints and variables were coupled in design specifications to accelerate
convergence, avoid constraints' violations, and avoid suboptimal solutions. Figure 2-3
shows the optimization variables in purple circles marked by (o) and the optimization
constraints in green circles marked by (x).
Optimization Variables
The DCSC flowsheet has 15 optimization variables in common with the RHE flowsheet, including the three integer variables required for defining the bleeds extraction
stages. The variable initially associated with the RHE, TRHE, the temperature of flue
gas at the exit of the RHE which specifies the amount of thermal recovery in the
RHE, is replaced with the DCSC variables: (i) thermal energy transferred in DCSCHX, QDCSC-HX, and (ii) recirculation water flowrate,
72RW-SePin.
These two variables
essentially determine how much thermal energy is transferred from the flue gas into
the recirculating water stream and eventually into the working fluid of the Rankine
cycle. Table 2.2 shows the optimization variables as they appear in Figure 2-3. The
optimization variables are all independent, for example the bleeds' extraction pressures, PBLD, and flowrates,
rnBLD,
can be manipulated separately. In contrast, the
temperature of the bleed is not independent of the extraction pressure and therefore
not considered as a variable. Similarly, the duty transfer in the feedwater heaters,
QFWH, are independent variables that define the regeneration from the bleeds to the
feedwater. The recirculating water flowrate in the DCSC, nRec-Sep-n, and the duty
79
transfer in the DCSC-HX,
QDCSC-HX,
are optimization variables but not the temper-
ature of the recirculating water because it is defined by the recirculation flowrate, the
flue gas conditions entering the separation column especially the flue gas pressure,
and the amount of thermal energy transferred in the DCSC-HX.
Table 2.2: Optimization Variables. The deaerator operating pressure should be above
atmospheric, but here the lower bound was intentionally taken sub-atmospheric to
examine if it would lead to any advantage in performance.
Number
Range
Base-case default value
[1.283 - 30] bar
[1 - 30] MW
7.41 bar
Variable
1
PComb
2
3
QComb
mFW,Main
[240-340] kg/s
4
PBLD1
[30 - 250] bar
5
6
7
8
9
10
rnBLD1
11
12
13
14
15
16
17
QFWH2
1 MW
306 kg/s
99.0 bar
62.2 kg/s
rnBLD2
60] kg/s
[10 - 120] bar
[0 - 30] kg/s
PBLD3
[4.5 - 30] bar
16.8 bar
rnBLD3
[0
30] kg/s
9.27 kg/s
138 MW
37.7 MW
PBLD2
QFWH1
PDeaerator
QDCSC-HX
maec-sep-in
BLDILstage integer variable
BLD2-stage integer variable
BLD3_stage integer variable
[0
-
-
[0 - 200] MW
[0 - 200] MW
[0.1 - 30] bar
[20 - 130]
[50 - 500]
Stages:
Stages:
Stages:
MW
kg/s
1-4
3-6
5-7
26.0 bar
14.7 kg/s
14.7 bar
44.9 MW
100 kg/s
Stage: 3
Stage: 5
Stage: 6
Optimization Constraints
Constraints define the allowable limits of operation. The limits are dictated by physical, practical, or economical considerations.
Nine optimization constraints in the
DCSC flowsheet are identical to those in the RHE flowsheet. The MITA constraint
on DCSC-HX replaces the MITA constraint on the RHE. Table 2.3 states the DCSC
constraints as they appear in Figure 2-3.
80
Table 2.3: Optimization Constraints for the pressurized OCC process
utilizing a DCSC.
Nu mber
1
2
5
MITAHRSG
MITAFWH1
MITAFWH2
MITADCSC-HX
qDeaerator
6
Tcool-Gas
7
TFW-HRSG-in
8
Tcomb-Gas-in
9
CO 2 -Cap
CO 2 -Pur
3
4
10
Value
Value
3.70 C a
Constraint
2.1 0C
2.1 0 C
5.0 0 C
Saturated Liquid
20 0 C above acid condensation temperature
5YC above acid condensation temperature
20 0 C above acid condensation temperature
94% of total CO 2 produced
96.5% purity
a The
temperature of the flue gas is initially high as it enters the HRSG, 800'C;
it is guaranteed that the temperature difference between the flue gas and the
water/stream of the Rankine cycle, which reach a maximum of 610'C, is large
in the superheat of the main feedwater and the reheat sections; the
temperature approach in the lower temperature sections of the HRSG is
limiting due to the flue gas temperature drop. A temperature approach
around 4C is common, [34]
2.5.3
Integer Variables
The realistic representation of the steam expansion line in a comprehensive optimization study requires including integer variables to define the stage at which each bleed
is being extracted. The steam expansion line constitutes of different turbine stages
with different isentropic and mechanical efciencies, as well as steam leaks. Therefore,
modeling the expansion line requires taking into account for each stage separately,
and integer variables are required in order to specify the extraction stage of each
bleed. A detailed explanation of the procedure and proof of its validity is presented
in [24].
81
2.5.4
Parameters Considered constant
Similar to the arguments presented in [24, 271, for the realistic representation of the
operating units in the power cycle, some variables were excluded from optimization.
The behavior of some components, like the expansion turbines, change in a complicated and component-specific manner when their inputs change. The model here does
not include these dependencies mainly because they are very difficult to estimate. As
a result, parameters like the temperature and pressure of the feedwater exiting the
HRSG/entering the turbine, and more importantly, the reheat extraction pressure
and the reheat delivery temperature are not incorporated as optimization variables.
Moreover, the purity of the oxygen stream resulting from the ASU affects efficiency
and capital cost significantly and thus would be interesting to optimize, but requires
a more elaborate model for each of the ASU and CSU which is beyond the scope of
this work.
2.5.5
Active Constraint Optimization
This study utilizes recent methodological proposals in [24, 28, 29, 27] and in Chapter 1, where it is proven analytically that optimal operating conditions of the cycle
are obtained at some active constraints. More specifically, [24, 27] proves that heat
exchangers need to operate at the MITA specification for optimal performance. A
more dedicated proof for the optimum operation of regenerative Rankine cycles is
presented in [28, 29] and Chapter
1 along with elaborate numerical case studies.
The optimum regeneration necessitates the existence of a double-pinch, i.e. MITA
encountered at the onset of the bleed condensation and simultaneously at the drain
outlet. Therefore, variables can be manipulated at the simulation level to achieve
the desired value of the constraint. The advantages are numerous including reducing
violations and fatal errors in the simulation, constraint violations in the optimization,
and the size of the optimization problem. More importantly, the procedure partially
82
avoids convergence to suboptimal local optima or, even worse, saddle points by guarantying that the manipulated variables are set to the values that are obtained at the
global optima. Moreover, the procedure developed is based on explicit equations and
assignments eliminating the need for a spatially distributed model further reducing
computational expense [28, 29].
The variables and constraints coupled in this study are:
1. MITADCSC-HX/DCSC-HX
2. MITAHRSG/rhFW,Main
3. Double-pinchFWH(1 & 2)/QFWH(1 & 2) and
rnBLD(1
& 2). The double pinch con-
dition is made up of two simultaneous pinch occurrences requiring the manipulation of two variables. Therefore, both the duty transfer within each closed
FWH and the flowrate of the respective bleeds are defined in terms of the bleed
extraction pressure according to the following equations, [28, 29] and Chapter 1:
r.BLD
=
M hL(T"'"(PBLD) - AMITAT, PF) - h'(TFi, PEF)
hg,sat(PBLD) - h'(TFi ± AMITAT, PBLD)
Q
=
rnBLD(hT(PBLD) - h(TFi ±
Note that since the expressions are explicit in
AMITAT, PBLD))
mBLD
and
Q there is a unique
double pinch for a given extraction pressure PBLD4. qDeaerator/mBLD3. The equality constraint of saturation at the deaerator tank is
satisfied by the deaerator bleed flowrate as proven in [28, 29] and Chapter 1
5. PDeaerator: For optimal operation, the deaerator pressure has to be equal to
the pressure of the deaerator bleed, BLD3, at the deaerator inlet; [28, 29] and
Chapter 1.
Therefore, PBLD3 and Pbeaerator are coupled to be equal at the
level of the deaerator, i.e., after accounting for friction and hydrostatic pressure
changes. The deaerator bleed blowrate also plays a role in the optimum value
83
of the deaerator pressure since it affects the amount of pressure loss in the
connection pipes
6. MITADCSC-HX/QDCSC-HX: The allowed minimum internal temperature approach
on the DCSC-HX is achieved by the amount of thermal energy transfer in the
DCSC-HX
7. Balanced DCSC-HX/rhRWSep-in: For optimal operation, the DCSC-HX has to
be thermally balanced and this is satisfied by selecting the recirculating water
flowrate entering the separation column, as proven in Appendix B. There is
no underlying technical or economical limitation for this condition, instead the
constraint is imposed and targeted to ensure the optimal flowrate
2.6
Results
Simultaneous multi-variable optimization of the DCSC flowsheet is performed with
initial conditions set identical to the optimized results of the RHE flowsheet, i.e.
the basecase. Table 2.4 summarizes the optimal RHE, the DCSC basecase, and the
optimal DCSC operation. As expected, changing the thermal recovery unit from a
RHE to a DCSC without optimization reduces the performance substantially, to an
efficiency of 30.9%, a 3.5% points lower than the optimized RHE flowsheet. However,
upon multi-variable optimization the DCSC achieves a surprisingly high performance
of 34.10%, very close to the optimum RHE performance, with considerable difference
in some variables.
To better assess the effect of the operating pressure and importance of thermal
recovery, a pressure parametric optimization is performed and results are plotted in
Figure 2-4. Starting from the optimum found at 12.8bar, operating pressure is incrementally varied while optimizing for all variables except pressure. Figure 2-4 also
shows the pressure sensitivity of the DCSC as well as the pressure parametric opti84
mization and pressure sensitivity of the RHE, obtained from [24, 27] with an update
to the physical properties of the condensing flue gas. Pressure sensitivity without
optimization does not utilize the complete advantages of the cycle and masks the optimal operating conditions. With multi-variable optimization of the DCSC flowsheet
the cycle performance is significantly higher than that of the parametric sensitivity
at any operating pressure. Multi-variable optimization for the DCSC cycle is even
more important than that for the RHE cycle, deduced from the larger improvement
in efficiency of the parametric optimization compared to the parametric sensitivity
in the case of the DCSC cycle. This is because in the DCSC, besides the combustor's operating pressure, the recirculating water flowrate is another very important
optimization variable that play a huge role in achieving the optimal thermal recovery. The other optimization variables also contribute in attaining this high efficiency
performance as explained later.
Compared to the RHE parametric optimization, the DCSC parametric optimization is more sensitive to operating pressure near the optimum. The RHE allows for
significant flue gas recovery at low operating pressures, coinciding with the minimum
compression power pressure range. The power requirements in a RHE flowsheet are
insensitive to the operating pressure near the minimum compression requirements
range, [24, 27], resulting in an insensitive range of optimum operating pressure. However, in the DCSC flowsheet at relatively high operating pressures, where recovery
is significant, pressure losses and compression requirements are very sensitive to the
operating pressure resulting in a more sensitive parametric curve. Prior to the RHE
optimum, the efficiency of the RHE parametric optimization increases rapidly due
to the simultaneous decrease in compression requirements and increase in recovery.
Post the RHE optimum, the efficiency decreases as a result of increase in pressure
losses while recovery plateaus. Prior to the DCSC optimum, the recovery and pressure losses contributions are in opposite directions resulting in the slow increase in
85
efficiency. Post the DCSC optimum, recovery reaches a plateau and the increase in
the pressure losses results in a decrease in the efficiency in almost the same manner
as seen in the RHE at the same operating pressures.
Note that at pressures higher than approximately 12.8bar the performance of
both cycles is very similar. This is because both configurations experience identical
pressure losses and the two different recovery units transfer most of the flue gas's
recoverable latent energy. In fact, at these high pressures the DCSC model marginally
outperforms the RHE model. This is attributed to the temperature of the flue gas
exiting the separator column being lower than that exiting the RHE resulting in
marginally lower compression requirements as discussed in Section 2.6.3.
2.6.1
Variables at Optimal Operation
The high performance of the DCSC flowsheet is achieved by finding the optimum
value of the variables as discussed below.
Combustor Pressure, PComb
The most significant change in the optimal variable values is the combustor operating
pressure. Unlike the RHE, at low operating pressure the amount of water condensed
and thermal energy recovered by the separation column is very small.
Therefore,
increasing the operating pressure allows more condensation by increasing the flue
gas dew point leading to higher recovery in the separation column. The optimum
operating pressure for the DCSC flowsheet is found to be 12.8bar, a tradeoff between
recovery and pressure losses.
Recirculating Water Flowrate,
rhRW-Sep-in,
and Recovered Thermal Energy,QDCSC-HX
The recirculating water flowrate also increases from 100kg/s in the basecase to 190kg/s
in the optimized DCSC flowsheet. This flowrate contributes in effectively condensing
86
the water vapor from the flue gas in the separation column and efficiently transferring
the absorbed thermal energy into the working fluid of the Rankine cycle. The amount
of condensed water vapor in the separation column increases from 10.5kg/s in the
basecase to 33.5kg/s in the optimized results. At optimum operating conditions the
DCSC-HX is balanced i.e., the hot and cold streams have equal thermal capacity rates,
allowing for better thermal matching and larger recovery, as proven in AppendixB.
The recirculating water and the feedwater florwates at the DCSC-HX are 223kg/s.
The former is the sum of the recirculation water original flowrate, 190kg/s, and the
condensed water flowrate, 33.5kg/s. The optimality criteria of a balanced DCSC-HX
while operating at the MITA allow for a high thermal energy recovery by the DCSC
unit,
QDCSC-HX =
118MW, close to that recovered in the optimized RHE model,
QRHE
= 121MW.
Combustor Duty,
QComb
The duty transferred from the combustor to the working fluid of the Rankine cycle,
QComb, again attains the minimum allowed value, 1MW. As detailed in [24, 271, the
combustor losses are of high quality. Minimizing the losses results in higher heat
addition to the high temperature section of the Rankine cycle/ HRSG as opposed to
the low temperature section. Consequently, irreversibilities due to large temperature
differences between the source and the destination are minimized.
Bleeds' Extraction Pressures and Flowrates,
PBLD(1,2,3)
& rnBLD(1,2,3)
The deaerator operating pressure, PDeaerator, decreases slightly because the thermal
recovery at the low temperature section for the DCSC is a little lower than that of the
RHE. With the slightly cooler feedwater entering the deaerator, the deaerator bleed
flowrate,
rnBLD3,
increases to ensure saturation at the deaerator tank. Bleed3 extrac-
tion pressure increases slightly due to the larger pressure drop associated with the
87
larger bleed flowrate within identical connection pipes. As expected, the extraction
pressures for the closed FWHs decrease since the temperature of the feedwater exiting
the deaerator is now lower. The bleed flowrates and duty transferred in the closed
FWHs are those that guarantee a double pinch following [28, 29] and Chapter 1.
Main Working Fluid Flowrate,
rnFW,Main
The temperature of the feedwater entering the HRSG in the DCSC is slightly lower
than that obtained in the RHE flowsheet due to the changes in the recovery section
(lower bleeds extraction pressures). Lower extraction pressures of bleeds in general
allow lower temperature rise of the feedwater, which is initially colder at the inlet
of the closed FWH compared to the RHE flowsheet. As a result of the cooler FWHRSG-in, a unit flowrate of the feedwater entering the HRSG now requires more
thermal energy from the flue gas to elevate its temperature to the high pressure
turbine delivery temperature (600'C). Thus, the amount of working fluid able to
circulate in the power cycle without violating the HRSG pinch specification is lower
for the DCSC than that of the RHE. The optimum value of
ThFW,Main
drops form 306
kg/s in the RHE optimum operation to 286kg/s in the DCSC optimum operation.
Smaller working fluid flowrate results in lowering the work output.
2.6.2
Flue Gas Pressure Losses
The pressure losses in the recirculation pipes and in the HRSG are higher with the
higher operating pressure of the DCSC flowsheet as seen from the pressure drop
equations, equations (2.1) & (2.2). This translates in higher recirculating fans and
ASU+CSU compression requirements. Thus, the efficiency of the DCSC is somewhat
lower as compared to that of the RHE even at optimum conditions. Note that the
ASU and CSU compression requirements are considered together when comparing the
two flowsheets which operate at different optimum pressures. The ASU requirements
88
in the DCSC flowsheet is larger since it delivers the oxygen at a significantly higher
pressure, but the CSU requirements in the DCSC flowsheet is smaller since it is
compressing the flue gas starting from a significantly higher pressure. However, the
sum of the ASU and the CSU requirements are higher for the DCSC flowsheet due
to the larger pressure losses occurring between the two compression processes (in the
HRSG).
2.6.3
Capital Cost Reduction
Another interesting result is that at optimum operating conditions the DCSC flowsheet does not require a chiller. The temperature of the flue gas exiting the separator
column is even lower than that obtained in the RHE model.
This result depends
on the specified MITA specification of the RHE (7.1 0 C) and the DCSC-HX (5C),
which is the shortcut method of specifying the acceptable size constraints of heat
exchanges. Heat transfer between two liquids, like the one seen in DCSC-HX, is more
effective than that between a liquid and a gas, like the one in the RHE, and therefore,
a smaller MITA for the former is possible without a larger surface area and additional capital costs; it follows that a MITA of 5YC for the DCSC-HX is considered
conservative.
Note that optimal performance does not require a chiller signifying
lower capital costs of the DCSC, a result that is not likely to be discovered without
a comprehensive optimization.
The DCSC behavior suggests more chances for capital cost reduction. The operating pressure of the cycle at optimum operating conditions is close to the design
pressure of the NOx and SOx purification columns in the CSU. This provides two
additional benefits. First, the first CSU compressor and its intercooling can be eliminated since the flue gas pressure is already suitable for the purification processes.
Second, process intensification is possible (at least in principle), whereby purification can occur simultaneously with the recovery process in the separator column of
89
the DCSC eliminating the need for additional purification columns and reducing the
capital cost and size of the CSU and the power plant. The increase in practicality
and reduction in the capital cost associated with the DCSC model increases the competitiveness and interest in this pressurized OCC process, and is a topic of future
work.
2.6.4
Validation of the Optimization Results
The validation of the results is performed by perturbing the values of the optimization
variables and examining the objective function. Notice that numerical errors are only
relevant to variables that are not governed by criteria of optimal operation. Meanwhile, the variables that are defined by the active constraints and optimal criteria are
automatically set to their exact optimal value. Error analysis shows that the perturbation of the variables does not increase the value of the objective function and that
the results are indeed optimal. Moreover, results also show that the objective function is insensitive to the extraction pressures close to optimum, a similar behavior is
observed in [28, 291 and in Chapter 1. For example, even a 10% change in the value of
the bleeds' extraction pressures results in less 0.03 percentage points decrease in the
overall efficiency; the insensitivity to the extraction pressures motivated a detailed future work study of the pressurized OCC process's flexibility, [35] and Chapters 3&4,
and suggests that retrofitting may be viable. The sensitivity of the objective to the
other variables is also studied. Around the optimum solution, the variables that are
most influential are the combustion pressure, PComb, the bleeds flowrates,
feedwater heaters and DCSC-HX duty transfer, QFWH &
QDCSC-HX,
mhBLD,
the
and the recycling
water flowrate. Note that among the sensitive variables, only the combustion pressure
is not governed by an optimal criterion of operation.
90
2.7
Model-Based Optimization and Effect of Design Assumptions
It is very important to state that the design considerations and assumptions, i.e.,
the parameters that are considered fixed in the process, are crucial in determining
the behavior and the response of the cycle. In this study a fixed design and a set
of economical considerations for the HRSG and the recycling pipes are enforced,
Section 4.4.2, and the pressure losses are calculated by similarity analysis.
This
causes an increase in the pressure losses at an accelerating rate with the increase
the operating pressure above 6.25 bars,
[27, 24]. Therefore, the increased flue gas
recovery at higher pressures is faced with increased pressure losses, and after reaching
almost full thermal recovery the efficiency of the process starts to decrease rapidly,
as seen in the parametric optimization curve of Figure 2-4.
On the other hand, changing the design considerations results in altering the
response of the process with increasing the pressure. For example, in [68] a similar
flowsheet is studied but with different design parameters. Therein, the pressure losses
for the HRSG and the recycling pipes are assumed to be a constant fraction of the
operating pressure and in contrast to this chapter do not increase at an accelerated
rate. Therefore, therein, the parametric optimization curve exhibits a different behavior, presented in Figure 2-5; first, below 20 bar the efficiency of the process increases
rapidly with an increase in the operating pressure due to the increased thermal recovery. Second, in the range of 20 to 30 bar, the efficiency is almost constant. Finally,
above 30 bar, the efficiency decreases at a very slow rate with increasing pressure.
In addition, in [68] two other recycling configurations are studied. The first is
dry-recycling, where flue gas is recycled after thermal recovery and water condensation. If safety measures against particulate agglomeration in the recycling pipes are
not considered, then dry-recycling requires significantly lower recycling flowrates and
91
power consumption by the recycling-fans because the recycled flue gas is cooler, has
a smaller flowrate, and contains almost no water vapor. However, the flue gas from
dry-recycling is heated by at least 60'C as a safety measure against particulate agglomeration. This reduces the savings in the compression power of the recycling-fans
by increasing the temperature, the flowrate, and the pressure losses of the recycled
flue gas in the recycling pipes. The heating of the dry-recycled flue gas is performed
by the flue gas exiting the HRSG/entering the DCSC. Moreover, compared to the
wet-recycling, results show that in dry-recycling a larger fraction of flue gas enters
the DCSC and transfers a larger fraction thermal energy at the low-temperature section on the account of the thermal energy transfer at the high-temperature section;
the exergy of the heat transfer process to the working fluid in dry-recycling is lower
than that of the wet-recycling.
As a result, dry-recycling configuration has lower
efficiency than that of wet-recycling; also dry-recycling requires a larger separation
column increasing to the capital cost. Note that the Isotherm combustor requires high
rates of flue gas recycling for the mild combustion process, [30], which may not be
satisfied by dry-recycling, and therefore a dual-recycling configuration is presented as
a compromise between the wet and dry-recycling configurations. The second studied
configuration is appropriately named by the authors dual-recycling, where the recycled flue gas to the combustor is in the wet-recycling form, while the flue gas recycled
to the HRSG is in the dry-recycling form.
The exergy of the heat transfer to the
working fluid, and the power requirements of the recycling fans for the dual-recycling
is between those of the wet-recycling and dry-recycling configurations. However, for
the assumption of fixed fraction of pressure losses in [68] the power savings on recycling are not sufficient to compensate for the exergy reduction of the heat transfer;
therefore, the efficiency of the dual-recycling is less than that of the wet-recycling.
Although not evaluated, dual-recycling is more promising when considering the design
criteria herein because pressure losses are larger and more sensitive to the operating
92
pressure. This stresses again on the importance of the design criteria and assumptions
considered for the process.
Comparing the different behavior and response of the process for the different
design criteria helps realize a very important fact: Model-based optimization is of
utter most importance. Optimization is not only needed to discover the optimal performance of a given process, but also to assess the influence of the different design
assumptions and considerations. Without optimization, different design criteria may
misleadingly result in similar performance but masking the behavior, response, and
sensitivity of a certain process. Optimization allows discovering (i) the most favorable design consideration for a given application, (ii) the optimal operation for the
considered design conditions. and (iii) the overall behavior, response, and sensitivity
of the process at any given operation particularly the optimal operation. Ideally,
deciding on the set of design criteria to implement should come after the conclusions
derived from the optimization of all the candidate sets of design criteria. While this
seems computationally very demanding, it comes with a relatively small additional
effort. The model setup of the process and the optimization formulation are almost
identical between the different sets of the considered design criteria.
2.8
Conclusion
Pressurized OCC can mitigate the problem of emissions accompanying the combustion
of an abundant and cheap fuel. Moreover, the comprehensive optimization applied
to the process results in performance and efficiency much higher than those of simulations and single variable manipulations and at operating pressures more attractive
than that proposed in literature.
With the help of recently proposed active con-
straint optimization concepts, this study evaluates the performance using a separator
column, a more practical heat recovery unit than a surface heat exchanger/RHE.
93
Upon comprehensive optimization, a pressurized
OCC process utilizing a direct con-
tact separation column/DCSC does not suffer large efficiency decrease compared to
an optimized pressurized OCC utilizing an RHE. Optimization results in attractive
performance of the OCC process utilizing a DCSC along with lower capital cost than
what simulations or sensitivity analysis result in. The combustor operating pressure
increases from the optimum range of 7.41 bar for the RHE flowsheet to 12.8bar for the
DCSC flowsheet. The larger operating pressure mainly increases the cost of the combustor and the recycling pipes, however, capital costs may be offset by the major cost
reductions in the flue gas drying and cleaning processes by eliminating a no-longerneeded compressor with intercooling and by process intensification. All optimization
variables play an important role in achieving the attractive process performance when
simultaneous multi-variable optimization is performed.
Moreover, the study results in an important conclusion that model-based optimization is essential.
Different design assumptions lead to significantly different
response and behavior, and optimization is not only needed to discover the optimal
performance of a given process, but also to assess the influence of the different design
assumptions and considerations. The important lesson learned is that deciding on the
set of design criteria to implement should come after the conclusions derived from
the optimization of all the candidate sets of design criteria.
94
ASU
Pressurized -
02
ompressorH
02
N2
FW-HRSG-in
-r c-pri
- -
FG- ec-seEr-
om-Gas-in
k
fo th
Recf
RHE
Cfmbustio
16f1
Sequestrated C02
-
-7_+
vented gas
ad
Controller
su
r
G-Recov-out
FG-Recov-in
ure
Te
P.kc
-e
as
G
Gaoo-
Ash
or DCSC
Recovery Unit
t
c
at
Coa
Slurry
with (x
FW-Recov-in
AtomizerCondensate
i HT
RZ
.-
leed1
Rehjeat
FWHRG-n
-
I
-
1
Bleed
IP
--
FW
FW
9zmr
Deaerator
Cooling Water
Condenser
HP-Pump
LP-Pump
Figure 2-3: 17 Optimization variables in purple marked with (o), and 14 constraints
in green marked with (x) for the DCSC configuration. The RHE configuration is used
for later chapters.
X: 7.41
Y: 34.41
34.5 r
X: 12.8
Y: 34.1
34 F
33.5
Direct contact separation column (DCSC)
parametric optimization
- Surface heat exchanger (RHE)
parametric optimization
Direct contact separation column
sensitivity analysis
Surface heat exchanger
sensitivity analysis
I M i MI M j M I ft I M I I
33
0
-J
32.5
32
u.w
31.5
31
-
30.5
0
/
\#
5
~
10
15
Combustor Pressure (bar)
20
25
Figure 2-4: RHE and DCSC pressure parametric optimization and pressure parametric sensitivity result
Table 2.4: Key results of the base-case, the pressure only parametric study, and optimization runs
Optimization RHE
Variable
DCSC with RHE variables
Optimization
DCSC
(no
chiller needed)
Fuel Flowrate
30.00kg/s
30.00kg/s
30.00kg/s
water
Slurry
flowrate
Atomizer
Stream flowrate
Air flowrate
16.50kg/s
16.50kg/s
16.50kg/s
2.50kg/s
2.50kg/s
2.50kg/s
311.2kg/s
7.41bar
34.4%
311.2kg/s
7.41bar
30.9%"
311.2kg/s
12.8bar
34.1%
1MW
mFW,Main
306kg/s
1MW
277kg/s
1MW
286kg/s
PBLD1
99.Obar
99.0bar
65.7bar
rnBLD1
62.2kg/a
26.Obar
14.7kg/s
16.8bar
62.2kg/s
26.Obar
14.7kg/s
16.8bar
36.8kg/s
25.2bar
17.0kg/s
14.7bar
9.27kg/s
14.7bar
138MW
37.7MW
36.9 0 C
N/A
N/A
N/A
122MW
9.27kg/s
14.7bar
138MW
37.7MW
N/A
123.7 0 C
9.52kg/s
12.2bar
78.4MW
44.1MW
N/A
35.8 0 C
190kg/s
118MW
N/A
PComb
Objective Function (LHV)
QComb
PBLD2
rnBLD2
PBLD3
rnBLD3
PDeaerator
QFWH1
QFWHM2
TFG-RHEout
TFG-Sep-out
RW-Sep-in
QDCSC-HX
QRHE
100kg/sb
44.9MW
N/A
TFW-HRSG-in
Dependent Variables
289 0 C
327 C
0
283 0 C
322 C
Tcomb-Gas-in
309 0C
279 0 C
Flue gas flowrate
1,138kg/s
1,069kg/s
in HRSG
Condensed Wa-
33.2kg/s
N/A
N/A
10.5kg/s
APHRSC
0.265bar
0.275bar
0.8654bar
APpip, primary
0.054bar
0.046bar
0.088bar
sec-
0.035bar
0.039bar
0.088bar
Prim. recycling
pipe flowrate
recycling
Sec.
pipe flowrate
281kg/s
274kg/s
276kg/s
737kg/s
675kg/s
684kg/s
292 0C
2870C
0
TCool-Gas
290 0 C
1,081kg/s
N/A
ter RHE
Condensed Wa-
33.5kg/s
ter Sep-Col
AP,
ondary
a A Chiller is required for this choice of variables. If no chiller was incorporated the objective
function would be even lower, 30.27%
b If
~
i,
~
+'
1'9llr
/~pcc
rn+___indf-~
mrrdncf
1~TC~
33.0
11
jj111111111111111111
32.0
C
0 31.0
30.0
29.0
0
10
40
30
20
Process operating pressure (bar)
50
Figure 2-5: Parametric optimization results for the pressurized OCC utilizing a DCSC
with different set of design assumptions and considerations, namely the pressure losses
are a constant fraction of the operating pressure, [68]
60
Chapter 3
Pressurized Oxy-Coal Combustion:
Ideally Flexible to Uncertainties
3.1
Summary
Simultaneous multi-variable gradient-based optimization with multi-start is performed
on a 300 MWe wet-recycling pressurized oxy-coal combustion process with carbon
capture and sequestration, subject to uncertainty in fuel, ambient conditions, and
other input specifications. Two forms of flue gas thermal recovery are studied, a surface heat exchanger and a direct contact separation column. Optimization enables
ideal flexibility in the processes: when changing the coal utilized, the performance
is not compromised compared to the optimum performance of a process specifically
designed for that coal. Similarly, the processes are immune to other uncertainties like
ambient conditions, air flow, slurry water flow, atomizer stream flow and the oxidizer
stream oxygen purity. Consequently, stochastic programming is shown to be unnecessary. Close to optimum design, the processes are also shown to be insensitive towards
design variables such as the areas of the feedwater heaters. Recently proposed thermodynamic criteria are used as embedded design specifications in the optimization
99
process, rendering it faster and more robust.
3.2
Motivation
Besides performance and capital cost, another characteristic that favors adopting a
power generation process is its flexibility regarding changes in inputs, operation parameters, and desired output. Coal type and specifications vary significantly from one
source to another, or even from different batches of the same source. A process that is
optimized for a given coal type would be unattractive if its performance deteriorates
or suffers when that specific coal is not economically attainable. With the change
of coal type, other input specifications and parameters need to change accordingly,
like the oxidizer flowrate, the flowrate of slurry water responsible for transferring the
coal into the combustor, and the atomizer stream flowrate, which contribute to the
alteration of the cycle's behavior. Other forms of uncertainty are due to the ambient conditions, in particular that the cooling temperature may vary significantly.
Additionally, it is desirable to have a process that is insensitive in the selection of
feedwater heaters (FWHs) areas, which is of high interest for retrofitting. Finally,
change of load is also a significant form of uncertainty and is discussed in Chapter 4.
The aim of this chapter is to find a flexible design for the pressurized OCC processes presented in [24, 27, 38] and in Chapter 2 with respect to changes in coal type,
ambient conditions, input streams flowrates, and oxidizer stream's oxygen purity. The
models involve rigorous accounting of irreversibilities and losses in order to accurately
assess the performance compared to other CCS technologies and in order to accurately
evaluate the pressurized OCC flexibility. Section 3.3 summarizes the flowsheets and
the models of two aforementioned pressurized OCC processes. Section 3.4 discusses
the implemented optimization formulation: the objective, variables, and constraints,
in particular the active constraint optimization process based on thermodynamic cri-
100
teria. Section 3.5 evaluates the processes' flexibility, demonstrating ideal flexibility
regarding coal and FWHs areas.
3.3
Flowsheet and Model Description
The RHE and the DCSC processes and models studied here are identical to the ones
presented [24, 27, 38] and in Chapter 2, and should be referred to for further details.
AspenPlus@ is used for modeling the flowsheets.
Figure 2-3 shows a schematic of the processes and includes tags for the variables
and constraints required for the following sections.
The RHE is a counter-current surface heat exchanger where the hot stream is the
flue gas and the cold stream is the working fluid of the Rankine cycle. In contrast
the DCSC, seen in Figure 2-2, utilizes an intermediate recirculating water stream
between the flue gas and the working fluid of the Rankine cycle. The recirculating
water transfers the thermal energy from the flue gas to the Rankine cycle in a liquidliquid heat exchanger (DCSC-HX). The figure also includes tags for the variables
and constraints required for following sections. Refer to Section 2.3 for a detailed
explanation of the DCSC recovery unit.
The coal variations are represented by using two substantially different coals shown
in Table 3.1. CoalA, used in [19, 20, 21, 23, 24, 27, 38], is a typical bituminous coal
with composition similar to Venezuelan and Indonesian coals. CoalB, a south African
coal almost identical to Douglas Premium or Kleincopje coal, is of a substantially
lower quality. The flowrates of coal are set to keep the heating rate (the product of the
the flowrate and the lower heating value) constant. The properties and constituents
of each coal are important since they specify the amount of coal needed for a given
heating load, the amount of oxidizer needed, the flowrates of slurry water and atomizer
streams, and the composition of the flue gas.
101
Table 3.1: Mass dry basis specifications of high, (CoalA), and low, (CoalB), quality
coals. Moisture is based on moisture-included basis.
Coal Type
30.00kg/s
31.09MJ/kg
29.88MJ/kg
26.42MJ/kg
25.23MJ/kg
6.4
7.4
Ash
Carbon
7.479
75.962
14.7
71.2
Hydrogen
Nitrogen
5.021
1.282
3.9
1.7
Sulfur
0.534
0.6
Oxygen
9.722
7.9
Coal HHV
Coal LHV
Moisture
3.4.1
CoalB
35.53kg/s
Coal mass flowrate
3.4
CoalA
Optimization Formulation
Optimization Objective
As aforementioned, several sources of uncertainty are considered.
For simplicity,
the methodology followed is first described for the coal input uncertainty and then
repeated for the other sources of uncertainties.
To find the optimal design and operation, the uncertainty of the coal input must
be accounted for. The uncertainty influences, at least in principle, both the optimal
design and the optimal operation. A common design has to be used for all coals, while
operation can be adjusted from coal to coal. One method to address this is stochastic
optimization, [41, 42].
The objective is to obtain a flexible cycle that maximizes
the expected value of efficiency for an expected distribution of the uncertain input
specifications and parameters. The optimal process depends, at least in principle,
on the distribution of uncertain parameters, and therefore care has to be applied in
identifying this distribution.
In the ideal case, the optimal performance of the flexible process for each coal is
as good as the performance of the best process for this coal. In that case, not only
102
maximal performance is achieved, but also there is no need to estimate an expected
distribution of the uncertain specifications.
The values of the design variables in
that ideal scenario coincide with solutions for the stochastic optimization problem.
Moreover, they are also solutions for the hierarchical optimization problem, presented
in [43, 44, 451, where the objective functions are the performance of each coal.
As will be explained in further details later, herein, first, the processes are designed
for each of the two coals, then the coal is changed.
Subsequently, optimization,
using recently proposed optimality criteria, of the operation is performed on the
fixed design; the obtained performance is compared to that of the process designed
specifically to the implemented coal. As will be demonstrated, some designs that do
not take flexibility into account can results in significantly suboptimal performance
with the change in the input specifications, while other designs satisfy the desired
ideal scenario within a maximum discrepancy of 0.02%. Although this discrepancy
is already very small, hierarchical optimization performed in Section 3.5.2 eliminates
the discrepancy and also uncovers flexibility regarding parameter specifications like
FWHs areas; ideal flexibility regarding the other uncertainties are also presented and
the results are presented and discussed.
3.4.2
Design and Operation Variables
The decision variables are characterized as design or operation. Each design variable
acquires a unique value invariant among the different plant operations. In contrast,
an operation variable can change, within a certain range, between the different plant's
operations. Table 3.2 summarizes the variables while Figure 2-3 marks the variables
on the flowsheet. The methodology of implementing active constrains depends on the
variables' characterizations and is discussed in Section 3.4.4.
The combustor's operating pressure, PComb, ., is an operation variable while the
maximum allowed pressure or the design pressure, PComb, d is a design variable.
103
Herein, an upper bound of 30bar is considered on the design pressure but substantially lower optimal pressures are expected and observed. With a lower quality coal,
the water content in the flue gas increases, and therefore the pressure is favored to
increase in order to enhance the thermal recovery. The design pressure is the maximal
pressure among all operating pressures.
The combustor's duty, QComb, is a design variable since it relates to the design
of the combustor and the refractory insulation installed. Note that the combustor
temperature is fixed.
In principle, the main feedwater flowrate can be changed anytime during the operation, however, the efficiency of the turbines deteriorates, usually very substantially,
if the flowrate is varied significantly from the design flowrate. Therefore, rFWMain
is considered to be an operation variable under the condition that the optimal value
does not vary a lot between the different operations. The optimal results show that
the flowrate change is acceptably small, within few percent demonstrating that there
is no need for performance curves of the turbine.
The bleeds' flowrates can change with different coals and thus considered as operation variables. However, the bleeds' extraction pressures are fixed with the initial design of the turbine expansion line and thus are design variables. Similar to
[24, 27, 38] and Chapter 2, integer variables are used to select the extraction stage,
extraction positions; these are also design variables.
The duty transferwithin each FWH is an operationvariable. It varies with changes
in other operation variables like bleed and feed flowrates, as well as changes in design
variables like extraction pressures. Constraint specifications and their values also play
a role in the value assigned to the FWHs duty, like the minimum internal temperature
approach (MITA) and/or area specifications.
The deaerator operating pressure is an operation variable determined primarily
by the low pressure pump delivery pressure and the deaerator bleed pressure at des104
tination.
The pump and deaerator pressures are allowed to vary but also within
relatively small ranges. The maximum allowable deaerator pressure is a design variable dictated by material and structural properties, but the optimum is safely below
the maximum allowed pressure. The deaerator pressure is not expected to vary significantly since the deaerator bleed pressure is a design variable, and since the deaerator
bleed flowrate is an operation variable. In optimization, an excessively large range
of the deaerator pressure is implemented [0.1-30] in order to investigate any performance improvements. However, results show only minor variations in the optimum
deaerator pressure with the different operating conditions and all are well within the
practical ranges of [1.5-20]bar.
Additional Variable Specific for the RHE Flowsheet
The temperature of the flue gas exiting the RHE,
TFG-RHE-out,
is also an operation
variable dictating the amount of recovered thermal energy. However, it is not expected
to vary between the two coals especially since the exchanger operates under a fixed
MITA specification of 7.5'C. For simplicity the RHE is modeled assuming a constant
MITA instead of a constant area. This is acceptable bevause the variations in the
streams of the RHE are relatively minor at optimal conditions. Moreover, the MITA
is relatively large resulting in small variations in the required area with the minor
changes in the streams conditions.
Additional Variables Specific For the DCSC Flowsheet
The duty transfer in the DCSC-HX, QDCSC-HX, is an operation variable. Similar
to the RHE the MITA is used for the specification on the DCSC-HX. Moreover,
similar to the main feedwater flowrate, the recirculating water flowrate, TRW-Sep-in, is
an operation variable as long as its value does not change significantly between the
different operations; the flowrate affects the sizing of the heat exchanger, separation
105
column, pump, connection pipes etc. The values of
QDCSC-HX
and
rnRW-Sep-in
axe not
expected to change between the different operations of the DCSC flowsheet especially
since both variables are shown to have their optimum value at active constraints (see
Section 3.4.4); the results validate this assumption.
To accurately model the operating units in the power cycle, some variables like
the oxygen purity, feedwater temperature and pressure at the exit of the HRSG, and
Reheat temperature and pressure, are excluded from optimization, similar to [24, 38].
Constraints
3.4.3
Constraints on the admissible design and operation are imposed based on physical,
practical, and economical considerations. Each process has ten constraints, nine of
which are common. The constraints are listed in Table 3.3 and illustrated in Figure 2-
3.
3.4.4
Active Constraint Optimization
In [24, 27, 28, 29] and Chapters 1&2 it is proven that optimal operating conditions
occur at some active constraints. Enforcing these constraints as operation specifications facilitates the optimization in several aspects: (i) avoid constraints violations,
(ii) avoid simulation errors and failures, (iii) accelerate convergence, (iv) avoid convergence to suboptimal local optima. The desired active constraints can be satisfied
at the simulation level by manipulating the main influencing variables.
The following constraints and variables are coupled:
1. MITAHRSG/rhFW, Main: The allowed minimum internal temperature approach
constraint on the HRSG is achieved by manipulating the main feedwater flowrate
2. & 3. Double-pinchFWH(1&2)/QFWH(1&2) and
106
rnBLD(1&2).
Both the duty trans-
Table 3.2: Design and Operation Variables. The deaerator operating pressure should be above atmospheric, but here the lower bound was intentionally taken sub-atmospheric to examine if it would lead to any advantage
in performance. The variables, ThFW, Main & PDeaerator & ?nRW-Sep-in, are
considered operation variables but expected to vary a little between the
different coals; results satisfy this condition
Number
Variable
Range
Variable Type
1
2
PComb, d
[1.283 - 30] bar
[1.283 - PComb, d] bar
Design
Operation
3
QComb
4
TnFW, Main
5
BLD1_stage
variable
6
7
8
PBLD1
9
10
11
PBLD2
12
13
14
15
PBLD3
16
17
18
19
PComb, o
[1 - 30] MW
Design
[240-340] kg/s
Operation
integer
Stages: 1-4
Design
integer
[250 - 30] bar
[0 - 60] kg/s
Stages: 3-6
Design
Operation
Design
integer
[120 - 10] bar
[0 - 30] kg/s
Stages: 5-7
Design
Operation
Design
ThBLD1
BLD2-stage
variable
ThBLD2
BLD3_stage
variable
[30 - 4.5] bar
[0 - 30] kg/s
rnBLD3
[0 - 200] MW
QFWH1
[0 - 200] MW
QFWH2
[0.1 - 30] bar
PDeaerator
Variables specific for the RHE
[30 - 150] 0C
TFG-RHEout
Variables specific for the DCSC
[50 - 150] MW
QDCSC-HX
[50 - 400] kg/s
rnRW-Sep-in
Design
Operation
Operation
Operation
Operation
Operation
Operation
Operation
Table 3.3: Optimization Constraints, [24, 27]. For the initial design
purposes MITAs are taken as the FWHs' constraint. However, for flexibility assessment, fixed sizes are imposed on the FWHs, Section 3.5;
for generality two different sets of FWHs areas, obtained from the independent design of each coal with MITA specifications on the FWHs,
are assessed for each process.
Number
Constraint
Value
1
MITAHRSG
3.7'C economizer section
2
MITAFwH1
2.1 0 C
2
RHE-AreaA=7,069m
AreaFWH1
RHE-AreaB=6,728m 2
MITAFWH 2
DCSC-AreaA=6,158m 2
DCSC-AreaB=5,552m 2
2.1 0 C
AreaFWH2
RHE-AreaA=5,254m 2
RHE-AreaB=4,525m 2
3
4
5
6
7
8
9
10
10
DCSC-AreaA=4,227m 2
DCSC-AreaB=3,561m 2
Saturated Liquid
20'C above acid condensation temperature
5C above acid condensaTFW-HRSG-in
tion temperature
20'C above acid condensaTCom-Gas-in
tion temperature
94% of total CO 2 produced
C02-Cap
required to be captured
captured CO 2 is 96.5% pure
CO 2 -Pur
Constraint specific to the RHE
7.5 0 C
MITARHE
Constraint specific to the DCSC
qDeaerator
TCool-Gas
MITADrCSCHX
10 MIT~nf
Qt" -T5C
50 C
fer within each closed FWH and the flowrate of the respective bleeds are utilized
and defined in terms of the bleed extraction pressure according to the following
equations, [28, 29] and Chapter 1:
hl(Tsat(PBLD)
-
AMITA,FWHT, PEW) - h'(TFW,i, PEW)
- h'(TFWi ± AMITA,FWHT, PBLD)
mBLD
=
mW
QFWH
=
rBLD(hT(PBLD) - h(TFwi +
hg,sat(pBLD)
AMITA,FWHT, PBLD))
where h is the specific enthalpy, h' is the specific enthalpy of the liquid,
the saturation temperature, and
hT
Tsat
is
is the specific enthalpy at a certain point
along the steam expansion line.
4. PDeaerator: For optimal operation, the deaerator pressure has to be equal to
the pressure of the deaerator bleed, BLD3, at the deaerator inlet; [28, 29] and
Chapter 1.
Therefore,
PBLD3
and
PDeaerator
are coupled to be equal at the
level of the deaerator, i.e., after accounting for friction and hydrostatic pressure
changes. The deaerator bleed blowrate also plays a role in the optimum value
of the deaerator pressure since it affects the amount of pressure loss in the
connection pipes
5.
qDeaerator/rBLD3.
The mixture inside the tank deaerator has to reach the satu-
rated liquid state for the effective removal of dissolved air in the working fluid.
This constraint is satisfied by the low pressure bleed to the deaerator
Additionally for the RHE
7.
MITARHE/TFG-RH-out:
The allowed minimum internal temperature approach
on the RHE achieved by manipulating the temperature of the flue gas exiting
the RHE
Additionally for the DCSC
109
7. MITADCSC-HX/QDCSC-HX: The allowed minimum internal temperature approach
on the DCSC-HX is achieved by the amount of thermal energy transfer in the
DCSC-HX
8. Balanced DCSC-HX/RW-Sep,-in: For optimal operation, the DCSC-HX has to
be balanced and this is satisfied by the recirculating water flowrate entering the
separation column, [38] and Chapter 2.
3.5
Ideally Flexible Process to Coal, FWHs Areas,
Input Flows and Specifications, and Ambient
Temperature
3.5.1
Methodology for Flexibility Assessment
In this section, the method for coal variations flexibility assessment is presented but
the same applies to all the addressed uncertainties. The performance of the process
differs when operating with the different coals due to the different specifications,
particularly in the heating value and the water content. The total heat rate input
of the fuel based on the LHV is held constant for reasons explained later.
More
specifically, when operating with CoalB the coal flowrate is set to 35.53kg/s to obtain
a heat rate input into the cycle equal to that provided by a 30.00kg/s of CoalA. A
direct consequence of the coal flowrate are adjustments of several other flowrates to
maintain the proper operation of the combustor and the coal-water slurry delivery.
In Section 3.5.2 results show that this approach leads to maintaining the
mFW, Main
close to nominal, as intended, validating that the behavior of the turbine expansion
line, with fixed specifications, is accurately represented.
Deterministic optimization is performed in three steps to assess flexibility; then,
110
hierarchical optimization is performed. It is demonstrated that stochastic optimization is not needed. The performed series of runs are summarized in Table 3.4 and
illustrated graphically in Figure 3-1. First in Stepi, optimization is performed with
a MITA specification of 2.1 0 C on the FWHs for each of the two coals; the runs for
CoalA are essentially those presented in [24, 27, 38] and Chapter 2. Second in Step2,
the process is optimized for each coal with the areas of the FWHs fixed to the optimal values from Stepi for the other coal; Step2 determines the optimal design and
performance of the process with the given coal and area specification. Third in Step3,
the processes and designs of Stepi are optimized using only the operation variables
while holding the design variables and FWHs areas fixed to the optimum value of the
other coal. Finally, comparing the efficiency of each coal in Step2 and in Step3, the
flexibility of the process is evaluated.
In other words, the comparison shows whether using a coal in a cycle designed for
a different coal can reach the same performance as one designed specifically for the
former coal. Note that the comparison is performed for two different FWHs' area to
avoid favoring one of the two coals as well as showing that the flexibility results are
not specific to a given FWH size.
Results of Flexibility Assessment
Tables 3.5 through 3.8 show the results of the runs performed for cases RHE-A, RHEB, DCSC-A, DCSC-B respectively as defined in Table 3.4. Upon changing the coal
type in a cycle designed for a given coal without changing the operation, the performance is significantly lower than the highest possible performance for the given coal.
These results are omitted for brevity. Considering RHE-A-3 in Table 3.6, by optimizing the operation variables while holding the design variables identical to those
of CoalB's optimum performance, the cycle efficiency is essentially the optimum performance attainable by CoalA. However, not all optimum designs of one coal can
111
Table 3.4: The runs performed to check the flexibility of the OCC cycle, with an RHE
or DCSC thermal recovery unit, under fuel uncertainty
Step number
Stepi
Case Identification
RHE-A-1
Case Description
RHE Flowsheet, CoalA, Optimization of design
and operation variables, FWHs' MITA constraint
of 2.1 C
RHE-B-1
DCSC-A-1
DCSC-B-1
RHE Flowsheet, CoalB, Optimization of design
and operation variables, FWHs' MITA constraint
of 2.1 C
DCSC Flowsheet, CoalA, Optimization of design
and operation variables, FWHs' MITA constraint
of 2.1 C
DCSC Flowsheet, CoalB, Optimization of design
and operation variables, FWHs' MITA constraint
of 2.1'C
Step2
RHE-A-2
RHE Flowsheet, CoalA, Optimization of design
and operation variables, FWHs' areas from case
RHE-B-1
RHE-B-2
RHE Flowsheet, CoalB, Optimization of design
and operation variables, FWHs' areas from case
RHE-A-1
DCSC-A-2
DCSC Flowsheet, CoalA, Optimization of design
and operation variables, FWHs' areas from case
DCSC-B-1
DCSC-B-2
DCSC Flowsheet, CoalB, Optimization of design
and operation variables, FWHs' areas from case
DCSC-A-1
Step3
RHE-A-3
RHE-B-3
DCSC-A-3
DCSC-B-3
RHE Flowsheet, CoalA, Optimization of operation
variables, Design Variables and FWHs' areas from
case RHE-B-1
RHE Flowsheet, CoalB, Optimization of operation
variables, Design Variables and FWHs' areas from
case RHE-A-1
DCSC Flowsheet, CoalA, Optimization of operation variables, Design Variables and FWHs' areas
from case DCSC-B-1
DCSC Flowsheet, CoalB, Optimization of operation variables, Design Variables and FWHs' areas
from case DCSC-A-1
Stepl
Power Plant designed for Coal A
Coal A
max {efficiency I inputs = CoalA specs}
Get: opt designA, opt operationA, AreaA
'2i
00
Coal
B
V
Step2
Power Plant wit IAreasA, Optimized
(all variables) for coalB
Max {efficiencyIinputs =- CoaIB
areaA}
Coal B
Compare and
}evaluate flexibility
(
Step3
Power Plant designed for Coal A (area
specification fixed to AreaA), operation
optimized for CoalB
Max{efficiency I inputs CoalBopt designA,
areaA}
Figure 3-1: Evaluations performed for flexibility assessment of the RHE process while
using areas favoring the design for CoalA. The same 3-steps procedure is repeated for
areas favoring the design for CoalB and for the DCSC process; (four times in total).
attain the optimum operation when changing the coal as seen in Table 3.5. These
tables signify that the RHE cycle can be ideally flexible. Similarly, Tables 3.7 and
3.8 show that the DCSC process can also also be ideally flexible (discrepancies within
0.02%). For the flexibility evaluations of both processes and for the hierarchic optimization presented next, with current optimization solvers, it is necessary to utilize
the optimality criteria (proposed in [28, 29, 38] and Chapters 1&2) to obtain this
ideal flexibility.
3.5.2
Hierarchical Optimization
The above evaluations show that the cycle is nearly ideally flexible.
Hierarchical
optimization is performed to find a set of values for the design variables that minimizes/eliminates the discrepancies between the multi-coal design and the two single
coal designs. Only ideally flexible designs, within the specified allowable tolerances,
are feasible in the hierarchy optimization formulation. This is achieved by introducing
a constraint on the objective function in the formulation below. rq is the efficiency, A
and B stand for the coal type, g is the set of constraints. e is the allowed discrepancy
from the optimum. x is the set of design variables that have to be common among
the different operations of the flexible process, and y is the set of operation variables
that can change between the different operations The results from Section 3.5.1 are
feasible for e > 0.02%.
Table 3.9 shows results of the hierarchical optimization.
The procedure is re-
peated for the two processes and for the two respective sets of FWHs area. The
performance of all four optimization cases shown match the maximum performance
of the respective identical cycles deterministically optimized for a single coal. Note
that Column2's performance is higher than that of RHE-A-1 because the former is
optimized with fixed areas specification while the latter with fixed MITAs. The same
Table 3.5: Results for RHE flowsheet fuel flexibility. Area 'favoring' the design of
CoalA; AFWH1=7,069m 2 AFWH2=5,254m 2 . The changes in the values of mFW Main
and PDeaerator are acceptably small, Section 3.4.2.
RHE-B-2
RHE-B-3
Variable
RHE-A-1
Fuel Flowrate
30kg/s
35.53kg/s
35.53kg/s
Slurry water flowrate
Stream
Atomizer
flowrate
16.50kg/s
2.50kg/s
19.22kg/s
2.96kg/s
19.22kg/s
2.96kg/s
Air flowrate
Efficiency (LHV)
311.2kg/s
34.41%
332.5kg/s
33.06%
332.5kg/s
32.82%
Input Parameters
Independent and Key Dependent Variables
7.41bar
9.67bar
7.41bar
PComb,d
7.41bar
9.67bar
QComb
1MW
1MW
mFW Main
291kg/s
80.0bar
45.4kg/s
286kg/s
77.8bar
44.2kg/s
7.41bar
1MW
285kg/s
80.Obar
44.3kg/s
rnBLD2
26.lbar
23.9kg/s
26.2bar
19.9kg/s
26.lbar
24.2kg/s
PBLD3
9.44bar
11.4bar
9.44bar
1.98kg/s
9.30bar
2.12kg/s
11.4bar
0kg/s
9.02bar
98.2MW
63.6MW
36.9 0 C
118MW
95.4MW
52.1MW
36-9 0C
129MW
95.7MW
64.6MW
64-58. 0 C
120MW
PComb,o
PBLD1
rnBLD1
PBLD2
rnBLD3
PDeaerator
Q0textFWH1
Q0textFWH2
TFG-RHEout
QRHE
Dependent Variables
TComb-Gas-in
303 0 C
297 0 C
294 0 C
307 0C
301 0C
294 0 C
307 0 C
302 0 C
289 0 C
Flue gas flowrate in
1091kg/s
1,080kg/s
1076kg/s
33.2kg/s
36.1kg/s
34.9kg/s
0.277bar
0.059bar
0.056bar
0.474bar
0.070bar
0.0690bar
0.277bar
0.044bar
0.038bar
278kg/s
705kg/s
259kg/s
690kg/s
258kg/s
687kg/s
171 0 C
163 0 C
Tcool-Gas
TFW-HRSG-in
HRSG
Condensed
water
RHE
APHRSG
APpip, primary
APpzpe secondary
mFCRec-Pri
mFG-Rec-Sec
TRHE-out
160 0 C
Table 3.6: Results for RHE flowsheet fuel flexibility. Area 'favoring' the design of
CoalB; AFWH1=6,728m 2 AFWH2=4,525m 2 . The changes in the values of rnFW Main
and PDeaerator are acceptably small, Section 3.4.2.
RHE-A-2
RHE-A-3
Input Parameters
30kg/s
35.53kg/s
16.50kg/s
19.22kg/s
2.50kg/s
2.96kg/s
30kg/s
16.50kg/s
2.50kg/s
RHE-B-1
Variable
Fuel Flowrate
Slurry water flowrate
Stream
Atomizer
flowrate
Air flowrate
Efficiency (LHV)
311.2kg/s
311.2kg/s
identical to col- 34.42%
umn 4
Variables
Dependent
Independent and Key
9.67bar
7.41bar
9.67bar
7.41bar
9.67bar
1MW
1MW
Pcomb,d
PComb, o
QComb
332.5kg/s
33.05%
284 kg/s
74.3bar
289kg/s
74.3bar
PBLD3
41.8kg/s
26.Obar
19.5kg/s
11.5bar
42.6kg/s
26.0bar
20.9kg/s
11.5bar
rnBLD3
2.57kg/s
5.30kg/s
PDeaerator
11.3bar
QFWH1
89.9MW
51.0MW
10.6bar
91.7MW
mFW Main
PBLD1
rnBLD1
PBLD2
rnBLD2
QFWH2
0
TFG-HE-out
38-3 C
QRHE
128MW
55.0MW
368 0C
118MW
Dependent Variables
290 0C
1072kg/s
303 0 C
297 0 C
288 0 C
1,091kg/s
36.1kg/s
33.2kg/s
0.460bar
0.059bar
0.056bar
258kg/s
683kg/s
170 0 C
0.280bar
0.050bar
0.038bar
276kg/s
694kg/s
160 0 C
303 0 C
TCool-Gas
TFW-HRSG-in
TComb-Ga&-in
0
297 C
Flue gas flowrate in
HRSG
Condensed
water
RHE
APHRSG
APpe primary
APpzpe secondary
mFG-rec-pri
mFG-re-sec
TRHFrout
Table 3.7: Results for DCSC flowsheet fuel flexibility. Area 'favoring' the design if
CoalA; AFWH1=6,158m 2 AFWH2=4,227m 2 . The changes in the values of rnFW,Main,
PDeaerator, and TnRW-Sepin are acceptably small, Section 3.4.2.
Variable
DCSC-A-1
DCSC-B-2
DCSC-B-3
chiller
(no
required)
chiller
(no
required)
(chiller required)
Input Parameters
Fuel Flowrate
Slurry water flowrate
Stream
Atomizer
flowrate
Air flowrate
Function
Objective
30.00kg/s
35.53kg/s
35.53kg/s
16.50kg/s
2.50kg/s
19.22kg/s
2.96kg/s
19.22kg/s
2.96kg/s
311.2kg/s
34.10%
332.5kg/s
32.48%
332.5kg/s
32.15%
(LHV)
Independent and Key Dependent Variables
12.8bar
12.8bar
OComb
12.8bar
12.8bar
1MW
16.9bar
16.9bar
1MW
mFW Main
286kg/s
274kg/s
1MW
279kg/s
PBLD1
65.7bar
57.9bar
65.7bar
36.8kg/s
25.2bar
32.1kg/s
23.6bar
36.4kg/s
25.2bar
rnBLD3
17.0kg/s
14.7bar
9.52kg/s
13.1kg/s
15.3bar
8.27kg/s
25.2kg/s
14.7bar
Okg/s
PDeaerator
12.2bar
13.5bar
7.61bar
QFWH1
78.4MW
44.1MW
35.8 0 C
68.2MW
33.5MW
38.1 0 C
127MW
77.7MW
67.4MW
96.8 0 C
116MW
PComb,d
PComb, o
rnBLD1
PBLD2
rnBLD2
PBLD3
QFWH2
TFG-Sep-out
ODCSC-HX
mRW-Sep-in
118MW
186kg/s
189kg/s
Dependent Variables
TCool-Gas
292 0 C
283 0 C
218kg/s
292 0 C
Flue gas flowrate in
287 C
290 0C
1,081kg/s
277 C
287 0 C
1,045kg/s
287 0 C
298 0 C
1,056kg/s
HRSG
Condensed
33.5kg/s
36.4kg/s
33.1kg/s
0.865bar
1.53bar
0.86bar
APpipe
primary
APpipe secondary
0.088bar
0.088bar
0.137bar
0.136bar
0.092bar
0.089bar
mFG-Rec-pri
276kg/s
684kg/s
255kg/s
658kg/s
255kg/s
668kg/s
396MW
158 0 C
420MW
165 0 C
403MW
1560C
0
TFW-HRSG-in
TComb-Gas-in
Water
0
Sep..Col
APHRSG
mFG-Rec-sec
Rankine net power
TFW-Recov-out
argument applies when comparing Column5 of Table 3.9 to RHE-B-1.
Columns2&3 represent CoalA and CoalB respectively with the first set of area
specifications and prove the ideal flexibility when operating with RHE-AreaA. Columns
four and five prove ideal-flexibility when operating with RHE-AreaB. Since Columns2&4
show that the cycle is ideally flexible to the area changes while operating with CoalA,
and columns3&5 show the same while operating with CoalB, the process is ideally
flexible to FWHs' areas. More specifically, the area specifications do not affect the
choice of other design variables. This has positive implications to turbine manufacturing, retrofitting, construction of plants with intent/uncertainty to upscaling etc. The
four columns which are introduced as belonging to two different hierarchical optimization runs, one for each FWHs area, can be presented as a single larger hierarchical
optimization problem. The bigger problem has four objectives, which are the performances of the different combinations of the two coals and the two area specifications,
instead of just the original two coals. The problem formulation is shown below where
a and b stand for the areas obtained from CoalA's initial design and CoalB's initial
design respectively.
Note that here too the only feasible solutions are ideally flexible designs within
the allowed tolerances ekL. Results in Table 3.9 show that 6 can be set essentially to
zero, i.e., the RHE process is ideally flexible to coal and FWHs areas variations. The
same behavior is encountered for the DCSC process but not shown here.
Behavior of Operation Variables
In this section, the optimal values of the operation variables are discussed for the
changes in the coal input. The values of the design variables essentially do not change
between different coal operations and thus are not discussed, yet they have a range
of near-optimal values. Unless otherwise specified, the discussion is relevant to the
118
ideally flexible design of Table 3.9.
Pressure, PComb
In the RHE flowsheet, the optimum combustor operating pres-
sure for CoalB is higher than that of CoalA in order to allow for the additional thermal
recovery carried with the larger flue gas flowrates and larger amount of water vapor.
However, with larger operating pressure the pressure losses and the compensation
power requirements increase. Recall that the optimum pressure range for CoalA in
an RHE flowsheet is determined by two main factors, [24, 27]: (i) large amount of
water condensation and thermal recovery at the RHE, and (ii) flue gas compression
power requirements being close their minimum value. With a lower quality coal,
CoalB, the advantage of increasing the operating pressure for enhancing thermal recovery is diminished by the increase in the pressure losses and the compensation
power requirements; in scenarios where the coal quality is even lower, then the optimum pressure might be lower than that providing maximum thermal recovery in
order to avoid huge pressure losses.
When the operating pressure is limited by the design pressure as an upper bound,
a lower quality coal will suffer from inadequate recovery as seen in RHE-B-3 and
DCSC-B-3 of Tables 3.5&3.7. The lower recovery results in a lower temperature of
the feedwater entering the deaerator. Therefore, the deaerator pressure decreases. In
the above scenarios, the deaerator bleed is favored to be zero because its extraction
design pressure is now considerably larger than the deaerator pressure. The losses
also include the mixing of bleedsl&2 as they exit FWHs1&2 to a lower pressure in
the deaerator, and additional power requirements by the HP pump to elevate the
feedwater pressure over a larger range. Therefore, the design of the process should
take into consideration the different coals involved and simultaneous optimization
should be performed to obtain the ideally flexible designs like in Tables 3.6& 3.8 and
particularly Table 3.9.
119
Combustor Duty, QComb
For both processes and both coals, the combustor duty
again takes on the minimum allowed value, 1MW, as expected.
It is preferable
to transfer thermal energy to the high-temperature section rather than to the lowtemperature section of the cycle.
Thermal Recovery, QRHE/QDCSC-HX
Utilizing CoalB, the flue gas contains a
larger amount of water vapor due to the increased flowrate of slurry water, atomizer
stream, and additional water content in the higher coal flowrate. The higher water
content results in a larger heat recovery at the RHE/DCSC. However, the additional
recovery at the low temperature section is at the expense of the heat transfer at the
high temperature section; transferring more thermal energy through the recovery unit
signifies transferring less thermal energy at the HRSG.
For the RHE flowsheet, the recovery section independent variable is chosen to be
the temperature of the flue gas exiting the RHE,
TFG-RHE-Out.
During the different
operations, the value of TFG-RHEout does not change because by increasing the operation pressure the pinch point of the surface heat exchanger is reached at the outlet
of the flue gas, yet the recovered duty changes due to the different constituents of the
flue gas. It is worth mentioning that the RHE experiences a double pinch, i.e., the
MITA is encountered at two locations, at optimum conditions. As operating pressure increases above atmospheric, recovery rapidly increases predominantly due to
the decreasing temperature of the flue gas leaving the RHE till the pinch is reached
at that outlet as opposed to just occurring at the dew point, [24, 27]. Any further
increase in flue gas pressure results in no change in the outlet temperature and in
very small increase in recovery and water condensation due to the increase in the
partial pressure of the water vapor. The pressure losses increase accompanied with
the operating pressure increase dominates over the insignificant additional recovery.
Therefore, optimization results in a double pinch where a higher pressure operation
120
suffers from the dominating increase in pressure losses and a lower pressure operation
suffers from significantly lower recovery.
For the DCSC process, the two liquid streams of the DCSC-HX are enforced to be
balanced, as described in Section 3.4.4. The hot end is governed by the temperature of
the recirculating water entering the DCSC-HX/leaving the separation column which
is identical to the temperature of the bottom stage of the column. The separation
column's bottom stage is the first site of condensation in the DCSC recovery unit and
therefore analogous to the point of water condensation of the flue gas in the RHE.
Main Feedwater Flowrate,
ThFW, Main
The amount of thermal energy absorbed
by the increased flow of water entering the combustor (slurry water, moisture in coal,
atomizer stream) increases. Most of this thermal energy is transferred to the Rankine
cycle at the RHE/DCSC during condensation instead of being transferred at the
HRSG. rhFW, Main decreases due to the decrease in the thermal energy available at
the HRSG, reducing the flow through the turbines and decreasing the power output.
The decrease in
mFW, Main
is analogous to results obtained in [24, 27] where water
addition into the cycle is preferred to be smaller. The oxidizer's increased flowrate also
results in a similar behavior but to a smaller extent than the increased water flowrate.
The main stream flowrate is not significantly affected because of the compression
enthalpy rise (CER) of the flue gas. The CER is the enthalpy added to the flue gas
by the compensation power requirement (CPR) of the recycling fans, [24, 27]. This
increase in enthalpy is eventually transferred to the Rankine cycle which contributes
in obtaining a working fluid flowrate close to nominal, and results in a comparable
gross power output.
Deaerator and Deaerator Bleed, PDeaerator and PBLD3 and
mBLD3
When the
design pressure is lower than the optimal pressure required for the process, recovery
suffers and the deaerator pressure decreases. However, with lower-quality coals, when
121
the design pressure allows reaching the optimal operation pressure, the increase in
thermal energy transfer at the RHE/DCSC and the lower feedwater flowrate results
in a higher temperature of the feedwater entering the deaerator. Therefore, a smaller
bleed flowrate is required to cause saturation at the deaerator tank. The lower bleed
flowrate results in a smaller pressure drop through the connection pipes, allowing for
a larger deaerator pressure.
FWH Bleeds Flowrate and FWHs Duty Transfer,
rnBLD(1&2)
and
QFWH(1&2)
Lower feedwater flowrate requires smaller amounts of heating from the FWHs, controlled by the bleeds' flowrates and FWHs' duty transfer. Therefore, the optimum
operation of CoalB requires lower bleedl&2 flowrates and smaller
DCSC recirculating water flowrate,
rhRW-Sep-in
QFWLH(1&2)-
In the DCSC, changing from
CoalA to CoalB reduces the main feedwater flowrate trough the Rankine cycle, rnMain,
as explained above, which signifies a decrease in the working fluid flowrate through the
recovery unit. According to the optimality of the active constraint, balanced DCSCHX, the flowrate of the recirculating stream in the DCSC-HX/exiting the separation
column decreases.
A smaller amount of recirculating water exiting the column is
required and a larger amount of condensed water from the flue gas within the column
means that the amount of the recirculating water entering the separation column,
rnRW-Sep-in,
decreases.
Discussion for Efficiency and Rankine cycle Power
While the heat rate
burned/consumed is constant, the gross and net power outputs are not.
Using a
lower heating value coal results in a decrease in the exergy of the heat input because
more thermal energy is transferred at the low-temperature section of the cycle rather
than the high-temperature section due to the larger flows, particularly water flow,
into the combustion process, as detailed in [24, 271. The larger water flow here is due
122
to the coal's larger moisture content and flow, larger water slurry flow, and larger
atomizer stream flow. In addition, the atomizer stream is withdrawn from the steam
expansion line contributing to further decrease the gross power output. Coupled with
larger power requirements for the larger amount of air flow input and flue gas to be
purified, the overall efficiency decreases with lower quality coals despite the presence
of thermal recovery. However, the decrease in the gross power is not large. The reason
is that the compression requirements cause the flue gas to acquire larger amounts of
enthalpy which are eventually transferred to the Rankine cycle to produce additional
gross work; but as detailed in [24, 27], the increase in the compression power requirements are larger than the extra work they contribute in producing which results in
an overall decrease in efficiency.
3.5.3
Flexibility to Input Flows and Parameters, (Air Flow,
Slurry water Flow, atomizer Stream Flow, and Oxidizer Stream Oxygen Purity)
In the above study, input parameters like the air flowrate, slurry water flowrate,
and atomizer stream flowrate are proportional to the coal flowrate as determined
by technological constraints.
It is plausible that some of these specifications are
revisited after the plant is built, in particular for technologies under development,
such as pressurized OCC. As seen above, increasing the coal flowrate when changing
from CoalA to CoalB increases each of those parameters' flowrates and results in a
total decrease of exergy of the combustion gas. Notice that the increase in flow of
each one of those parameters contributes in decreasing the exergy in different amounts
but in the identical manner: more thermal energy transferred at the low temperature
section at the expense of the thermal energy transferred at the high temperature
section. Now since the processes are able to handle the summed large decrease in
123
exergy, it is possible that they are also able to handle a decrease in exergy due to an
independent increase of one or more of these flowrate. The same flexibility applies
regarding the decrease in flowrate of those parameters due to decreasing the coal
flowrate when changing from CoalB to CoalA. Therefore, the processes are expected
to be ideally flexible to changes in the input parameters of air flowrate, slurry water
flowrate, and atomizer stream flowrate.
For brevity, the results of this flexibility
assessment are not shown here. Of course changes in flowrates must fall within the
acceptable operation ranges of the combustor, herein modeled approximately; also it
is necessary that all the utilized coal is oxidized.
The flexibility of the processes to the air flowrate has yet another positive implication regarding the ASU's oxygen purity. It is optimal for the process to operate with
the smallest possible oxidizer and air flowrates, given that all the fuel is oxidized, because it requires the least compression requirements throughout the process; therefore,
a change in purity might require a change in the input air flow. The oxygen purity
plays an important role in determining the ASU's and CSU's power requirements,
which are to a large extent independent from the energy conversion process and the
power delivered by the power cycle, but the process is considered ideally flexible to
the oxygen purity as shown next. Consider, for example, a given flowrate and purity
of the oxidizer stream that is capable of oxidizing a fixed amount of fuel. Changing the purity of the oxidizer stream while keeping the same oxidizer flowrate and
pressure, results in the same flowrate of the flue gas but a different oxygen content;
argon and nitrogen content may change too but their concentrations are insignificant
to begin with.
The effects of the change in the oxygen content in the flue gas is
insignificant; first, the range of variation of the oxygen purity in the oxidizer stream
is relatively small, within 85 to 98 vol%, [46], and even smaller after mixing with the
flowrate of the primary recycling stream, which is significantly larger than that of
the oxygen stream; second, CO 2 and then H 2 0 are the predominant species of the
124
flue gas and the recycling streams, and these species are responsible for dictating the
streams' properties particularly the thermal capacity. Even if the thermal capacity
of the flue gas is slightly affected, the effect on the power cycle is again insignificant
because much larger changes in flue gas properties and recycling flowrates, seen in the
coal flexibility, are easily accommodated. The acid condensation temperature may
change, with concerns towards an increase in acid dew point and condensation prior
to recovery; however, the optimum temperature of flue gas heading to the recovery
unit is already significantly higher than the acid dew point, hence, acid condensation
is not an issue. Also, the water condensation in the recovery unit is not affected
because the H 2 0 concentration is not significantly changed. As a result, given complete oxidation of the coal, the processes are not affected by a change in the oxidizer
stream purity for the same flowrate. Meanwhile, from the air flow flexibility above,
the processes are ideally flexible to changes in the oxidizer flowrate while maintaining
the same purity. As a conclusion, the processes are flexible to a general change in the
purity of the oxidizer stream, even when accompanied by a change in its flowrate, as
long as the fuel is completely oxidized.
In other words, the processes are flexible to the air flowrate whether the change
in the flowrate is due to a change in the coal flowrate, the preferred ratios of oxygento-coal, or due to a change in the oxygen purity of the ASU (or all three). A total
oxidation of the fuel is assumed in the above discussion which is trivially the most
efficient way to operate. It is true that the efficiency will change with different values
of oxygen purity, but these changes can be accommodated by the flexible design during
operation to achieve and maintain the maximum possible performance for any value
of oxygen purity. Here again any change should be within the acceptable operation
region of the combustor which is not modeled here in component level details.
125
3.5.4
Flexibility to Ambient Conditions
In the processes considered the condenser rejects thermal energy to cooling water from
a river or reservoir. Pressure and humidity changes of the ambient have no effect on
the condenser's operation; the condenser's operating pressure is defined by the type
of the working fluid and the condenser's temperature.
Typically, the condenser's
pressure is substantially lower than the atmospheric pressure. Also, ambient pressure
and humidity do not affect the deaerator.
However, the ambient temperature, more specifically the cooling water temperature, creates uncertainties to the processes because it affects the condenser's operating
temperature. As a result the condenser's operating pressure and the temperature of
the feedwater entering the recovery unit changes, which therefore changes the recovered thermal energy, the deaerator operation, and so on, as well as the temperature of
the flue gas entering the CSU and the CSU power requirements. To assess the flexibility towards the temperature of the cooling water, a similar methodology is followed as
the one presented above for the coal. Note that the temperature of the atmospheric
air slightly affects the ASU process, however, these effects do not propagate to the
power cycle since the oxygen pure stream is delivered by an intercooled compressor
with intercooling temperature of 60C, which is well above the ambient temperatures.
The power of the ASU can be slightly altered with ambient temperature variations,
but this is not represented here due to the limited modeling of the ASU. The initial
condenser temperature and pressure are 29.73'C and 0.042bar. A temperature rise
of 10'C, which is representative of seasonal and location variations, is evaluated resulting in a condenser pressure of 0.073bar. For brevity, only the RHE process with
CoalA and AreasA is presented.
Hierarchical optimization for changes in ambient
temperature is performed with the initial guess being that of the ideally flexible design of the above hierarchical optimization represented in Table 3.9. Optimization
results in no change in the values of the design variables even with large tolerances,
126
E, which
means that the optimal design for the high ambient temperature is identical
to that of the low ambient temperature; the ideal flexible design for the changes in
coal, input streams flows and parameters, and FWHs Areas is simultaneously ideally
flexible to ambient conditions. Other optimization runs with different initial guesses
were performed to make sure that the claimed ideally flexible design is not a local
optimal for the new high ambient temperature condition. Results of the temperature
flexibility are shown in Table 3.10.
Response to Variations in Ambient Conditions
It is obvious that the efficiency decreases with higher ambient temperature due to
the higher condenser pressure.
Moreover, with larger ambient temperatures, the
minimum value of the temperature of the flue gas exiting the recovery unit is larger
due to the higher temperature of the feedwater entering the RHE; this results in lower
recovery and larger CSU power requirements. The optimum design of the process
with a high ambient temperature is identical to that of the low ambient temperature
proving the ideal flexibility to ambient conditions, but optimization of the operation
variables is required to ensure the maximum performance with the changes in ambient
conditions.
The operating pressure increases in order to allow for a larger thermal energy
transfer at the RHE by avoiding the limitations of the pinch at the onset of flue
gas condensation.
With the initial operation pressure, the higher temperature of
the feedwater entering the RHE results in having the pinch at the onset of water
condensation and not at the cold end of the RHE (Hot-stream-out/Cold-stream-in),
and limits the amount of condensed water and the amount of recovered thermal
energy. Increasing the operating pressure allows the pinch to occur at both the point
of flue gas water condensation and at the flue gas outlet allowing for lower flue gas
exit temperature and more water condensation. Upon optimizing the process with
127
the high ambient temperature condition, the amount of water condensed reaches
33.Okg/s, slightly less than the maximum amount possible with the lower ambient
temperature conditions.
Notice that with larger operating pressures, the pressure losses increase. Further
increase in the ambient temperature may favor increasing the pressure to values that
do not acquire maximum recovery in order to save on pressure losses and compensation
power requirements.
It is worth mentioning that nine out of the 10 operation variables for the RHE
cycle, and 10 out of the 11 for the DCSC cycle are governed by active constraints.
The combustor's operating pressure is the remaining operation variable that is not
governed by an optimality criterion. Attempting to optimize for all the operation
variables instead of following the proven criteria, [24, 27, 38, 28, 29] and Chapters 1&2,
is likely to result in suboptimal solutions which do not satisfy ideal flexibility.
3.6
Conclusion
The operation of a powerplant is subject to several uncertainties in the inputs or
parameters or surrounding conditions. A realistic operation of a coal power plant
involves the utilization of different types of coals depending on several unpredictable
factors like market, environment, supply, demand, etc. Slurry water, atomizer stream,
and air flow requirements among other parameters are also subject to change. Moreover, changes in ambient conditions can significantly alter the power generation process if not properly accounted for. For profitable power generation the plant should
accommodate the different possible uncontrollable conditions with high production
efficiency.
Some process variables are design variables that cannot change during operation,
while operation variables can. Herein, using relatively detailed models, optimization
128
of two
OCC processes is performed while facing uncertainty in the input parameters,
in particular coal types and specifications and ambient temperature. Uncertainty in
input streams flowrates and in oxygen purity of the oxidizer stream are also discussed.
Results show that the studied concept of pressurized OCC is ideally flexible. More
specifically, changes in inputs can be accommodated without any compromise in the
processes' performance compared to a process specifically designed for the new values
of the inputs. The study concludes that stochastic optimization is not needed for
designing the flexible powerplant. In essence, the uncertainties in input conditions
and parameters need not to be quantified but merely the range of input conditions
needs to be taken into account during design. The ideal flexibility of the processes is
discovered with the help of the optimum criteria of operation presented in [28, 29, 381
and Chapters 1&2. These criteria allow finding the ideal flexible design, during design,
and provide straight forward guidelines, during operation.
It is particularly interesting and convenient that changes in the input specifications, which require changes to the operation variables, can be accommodated with
minimal efforts. In essence, after finding the ideally flexible design, a change in imposed conditions, even as large as using a significantly different coal, FWHs areas, and
ambient temperatures, does not require any additional modeling and optimization efforts to maintain optimum operation, but rather only a change in variables to satisfy
the relevant criteria. The same applies to other operating parameters like slurry water
flowrate, air flowrate, atomizer stream flowrate, and oxidizer stream oxygen purity.
Results also show insensitivity regarding the design variables near their optimum.
In particular, the pressurized OCC process is found to be ideally flexible regarding
the FWHs area specifications, which are also a part of the plant's design. The insensitivity towards design variables is initially observed in [28, 29] and Chapter 1. These
results strengthen the possibilities and interest in retrofitting existing powerplants.
The fixed designs of an operating powerplant, in particular fixed heat exchanger areas
129
and fixed turbine expansion line, are likely to achieve high performance as long as they
are not too far away from optimum. Also their performance will not suffer with the
unpredictable changes in the input specifications and parameters of operation. Additional positive implications are seen regarding turbine manufacturers when designing
the expansion line and extraction locations which are shown to be less contingent on
the other power plant specifications like FWHs areas.
When changing the coal, the fuel heat rate input is held fixed instead of the
net output power for three reasons. The main motivation is that the processes are
limited by the combustor's and HRSG's sizes and thermal loads.
An additional
motivation is that this allows to keep the same basecase reference conditions of the
cycle (HRSG and recycling pipes' reference/basecase pressure losses, turbine and heat
exchanger's sizing etc.). Third, this allows to maintain the working fluid flowrate close
to nominal; this achieves high performance for the turbines and also eliminates the
need for performance curves. If in contrast, the cycle operates under fixed net work
output, it has to compensate for the additional compression requirements caused
by using a lower quality coal, CoalB; i.e., the Rankine cycle is required to produce
more gross power output. Larger gross power output requires even more fuel and
inlet stream flows and result in even more compression requirements that need to
be compensated for. As a result, the feedwater flowrate through the HRSG and
turbine expansion line increases, and will result in significant deviation from design
conditions. Additionally, keeping the fuel flowrate constant when using a lower quality
coal, which forms a flue gas with lower exergy, results in lower thermal energy transfer
at the HRSG; as a result, the feedwater flowrate capable of flowing through the HRSG,
and eventually through the expansion line, will decrease, causing deviation from the
expansion line design conditions.
It is noteworthy to discuss the flexibility presented herein for the pressurized
OCC in regards to regular and pressurized coal processes. In standard, non OCC,
130
coal power plants, thermal energy is transferred from the flue gas to the working fluid
only at the boiler due to the absence of the low temperature heat transfer section, a
RHE or a DCSC. Even if a recovery section is incorporated, if the flue gas pressure
is atmospheric then an insignificant amount of thermal recovery is obtained; for a
pressurized coal process without carbon capture the compression enthalpy rise of the
high rates of recycling in the pressurized OCC process is absent. Therefore, operating
at the same boiler load, the amount of thermal energy capable of being transferred to
the working fluid decreases. As a result, the working fluid flowrates are likely to be
significantly affected, altering the turbine expansion line characteristics; the response
of the expansion line might not be suitable with the cycle's original design, extraction
positions and pressures, FWHs sizes, reheat stream pressure and temperature etc.
Therefore, non-OCC coal power generation is expected to be less flexible than the
processes considered herein; however, a detailed investigation is warranted to check
this claim.
3.7
Future Work
It is highly possible that the processes are flexible to a varying load as motivated next.
The processes are flexible to flow changes for the same heat rate input, and capable of
attaining the different maximum efficiencies for the different parameters imposed; the
performance change due to the change in compression requirements and to the change
in the exergy of the flue gas; the two factors are to a large extent independent. Now
assume a CoalC with specifications in between those of CoalA and CoalB. Operating
at the same load and input specifications ratios, the input streams of CoalC and flue
gas flowrates are larger than those of CoalA but lower than those of CoalB. The exergy
of the thermal energy of the flue gas resulting from CoalC operation is lower than
that of CoalA but higher than that of CoalB. Now consider a decrease in the flowrate
131
of the CoalC in order to operate at a lower load. The streams flowrate will get closer
to the base load of CoalA, but the heatrate decreases and thus the availability of the
thermal energy will get closer to that of the base load of CoalB; such an operation
is analogous to having CoalB with base load operation but with lower input streams
flowrates, which can be accommodated by the flexible design, Section 3.5.3. The same
argument can be applied for an increase in flowrate of CoalC, considering that the
thermal load of the combustor and HRSG are not limiting. Therefore, the processes
might very well be flexible to varying load. However, load changes might be larger
than the range allocated by the two coals and that is why a detailed study is intended
for future work.
Part-load, presented in Chapter 4, is another important topic but requires an
expansion line model accounting for off-design operations. The task is to determine
how to operate optimally for part-load and more generally how to operate optimally
facing the different and uncertain load requirements. It is intriguing to consider if
the process is also ideally flexible to load changes. If not, then does the design of a
process require knowledge of the distribution of the expected load operations or just
the range of the part-load? The next chapter handles a detailed study of the process
facing variations and uncertainty in the thermal load. Using optimization the process
is designed to be flexible for the load.
132
Table 3.8: Results for DCSC flowsheet fuel flexibility. Area 'favoring' the design of
CoalB; AwrH=5,552m 2 AFWH2=3,561m 2 . The changes in the values of rnFW,Main,
PDeaerator, and rnRW-Sep-in are acceptably small, Section 3.4.2.
Variable
DCSC-B-1
DCSC-A-2
DCSC-A-3
(chiller required)
(no
chiller
required)
(no
chiller
required)
Input Parameters
Fuel Flowrate
35.53kg/s
30.00kg/s
30.00kg/s
Slurry water flowrate
Atomizer
Stream
flowrate
Air flowrate
19.22kg/s
2.96kg/s
16.50kg/s
2.50kg/s
16.50kg/s
2.50kg/s
332.5kg/s
311.2kg/s
311.2kg/s
Objective
(LHV)
32.43%
34.07%
34.05%
Function
Independent and Key Dependent Variables
rnBLD2
15.5bar
15.5bar
1MW
274kg/s
56.0bar
30.9kg/s
23.3bar
12.7kg/s
12.8bar
12.8bar
1MW
285kg/s
65.Obar
36.4kg/s
25.2bar
16.9kg/s
15.5bar
12.5bar
1MW
280kg/s
56.Obar
31.5kg/s
23.3bar
15.4kg/s
PBLD3
15.4bar
16.7bar
15.4bar
rnBLD3
9.07kg/s
13.3bar
65.5MW
32.4MW
61.1 0 C
9.12kg/s
12.4kg/s
77.7MW
43.9MW
35.0 0 C
9.56kg/s
14.1bar
66.8MW
39.8MW
35.0 0 C
PComb,d
PComb, o
QComb
mFW Main
PBLD1
rnBLD1
PBLD2
PDeaerator
QFWH1
QFWH2
TFG-Sep-out
QDCSC-HX
mRW-Sep-in
118MW
124MW
189kg/s
186kg/s
Dependent Variables
291 0C
280 0C
0
285 0 C
274 C
115MW
189kg/s
283 0C
288 0C
1,039kg/s
1,078kg/s
280 0 C
274 0 C
278 0 C
1,059kg/s
Condensed
Water
SepCol
APHRSG
APpipe primary
APpipe secondary
36.0kg/s
33.4kg/s
33.3kg/s
1.30bar
0.124bar
0. 123bar
0.86bar
0.088bar
0.088bar
0.84bar
0.087bar
0.089bar
mFG-Rec-pri
254kg/s
653kg/s
276kg/s
682kg/s
274kg/s
665kg/s
417MW
162 0C
423MW
155 0C
422MW
154 0 C
Tcool-Gas
TFW-HRSG-in
TComb-Gas-in
Flue gas flowrate in
HRSG
mFG-Rec-sec
Rankine cycle power
TFW-Recov-out
Objective
Step2
SteplA
StepiB
maxX,YA ?7A(X, YA)
maxX,YBq B(x, YB)
i
(x, YA, YB)
maxX,YA,YB
=
A or B
Constraints
Desired
0 & gB(X,yB)
gA(x,yA)
AA*-A &
0 & 7A(X,YA)
rB (X,YB) 7B* EB
A
=
xIYIYB,I7A (X)I
I=
B*
?7^, and 7B*
gB(x,yB) < 0
gA(x,yA) <
x4,y~,?A(X*,Y*)=A*
77B
*7B(XIBYB
x* YB
Results
B
(assuming
feasibility)
SteplAa
Objective
Constraints
Desired
Results
7A,a(X, YA,a)
gA,a(x, YA,a) < 0
A,,y*,a
maxX,YA,.
(assuming
feasibility)
?7A,a(XAa, YA,a) =
ra
SteplAb
maxx,YB,. ?7B,a(X, YB,a)
maxx,YAb rJA,b(X, YA,b)
0
9A,b(x, YA,b)
gB,a(X,
YB,a)
0
BaYB,a
(A
SteplBb
StepiBa
XA,b,YA,b
B~a) X
_
Ba)
77
r7B,aBB,a, yB,a) = Ba
7
Ab( Ab,
maxX,YBb ?7B,b(X, YB,b)
9B,b(X,
0
YB,b)
*B
,B,b
A,b)*7A
=
bbBb
YA,b)
'q(*b
X
b)
B
?B,b( B,b, XB,b)
Step2
Objective
maxXYAaYBabYBb
rlij(X, YA,a, YB,a, YA,b, YB,b) i = A or B and
0
gk,L(x,yk,I)
Constraints
77k,1(X, Yk,)
k,)
Ek,l
--
V k E{AB} and 1 E{ab}
Desired
x
Y YB*,bbA*b
Y,a, YB**a,
Results
(assuming
feasibility)
?7A,a(X, YAa)
=IAa
TB,a ( X, yBa)
=
,
7A,b
and 77B,b(x
y~b
, Bb
**
BPa
1
7
T|b
7
7Bb
(Aab)*
)a
b)*
(Bb)
j
=
a or b
(Bb)
bb
Table 3.9: Fuel and Area flexibility for the RHE process after hierarchic optimization. The
process is designed to be ideally flexible under fuel uncertainty while operating with the
first pair of area specifications (AFWH1 = 7, 069m 2 and AFWH2 = 5, 254m 2 ), columns2&3.
It is also ideally flexible to the fuel uncertainty while operating under the second pair of
area specifications (AFWH1 = 6, 728m 2 and AFWH2 = 4, 525m 2 ), columns4&5. The changes
in the values of TiFW,Main and PDeaerator are acceptably small, Section 3.4.2.
Area specifications
Areas favor CoalA design
new
RHE-A
Variable
RHE-B
new
variables
variables
Input Parameters
Areas favor CoalB design
RHE-A
new
RHE-B
variables
variables
Input Parameters
Fuel Flowrate
30kg/s
35.53kg/s
30kg/s
35.53kg/s
Slurry water flowrate
Stream
Atomizer
flowrate
Air flowrate
16.50kg/s
2.50kg/s
19.22kg/s
2.96kg/s
16.50kg/s
2.50kg/s
19.22kg/s
2.96kg/s
311.2kg/s
332.5kg/s
311.2kg/s
332.5kg/s
34.42%
33.07%
34.41%
33.08%
Efficiency
(based on
LHV)
Independent and Key and Varaibles
PComb, d
PComb, o
9.67bar
7.41bar
9.67bar
9.67bar
9.67bar
7.41bar
9.67bar
9.67bar
QComb
mFW Main
1MW
306kg/s
1MW
301kg/s
1MW
306kg/s
1MW
303kg/s
PBLD1
99.Obar
99.Obar
99.Obar
99.Obar
rnBLD1
62.2kg/s
61.4kg/s
62.0kg/s
61.5kg/s
PBLD2
26.0bar
14.7kg/s
26.Obar
12.8kg/s
26.Obar
16.7kg/s
26.Obar
15.2kg/s
16.8bar
16.8bar
16.8bar
16.8bar
4.57kg/s
rnBLD2
PBLD3
rnBLD3
9.27kg/s
6.77kg/s
7.11kg/s
PDeaerator
14.7bar
15.7bar
13.4bar
14.2bar
QFWH1
138MW
377MW
36.9 0 C
122MW
136MW
32.7MW
38.1 0 C
133MW
137MW
43.2MW
36.9 0 C
122MW
136MW
39.2MW
36-9 0 C
133MW
327 0 C
321 0 C
311 0 C
QFWH2
TFG-RHE-out
QRHE
Dependent Variables
327 0 C
322 0 C
328 0 C
322 0 C
327 0 C
321 0 C
309 0 C
1,138kg/s
311 0 C
1,118kg/s
309 0 C
1,137kg/s
33.2kg/s
36.1kg/s
33.2kg/s
36.1kg/s
AXPHRSG
APpi, Primary
APpi, secondary
0.265bar
0.054bar
0.035bar
0.437bar
0.055bar
0.051bar
0.266bar
0.054bar
0.035bar
0.448bar
0.055bar
0.051bar
mFG-Rec-pri
281kg/s
262kg/s
281kg/s
265kg/s
FG-Rec-sec
737kg/s
409MW
164 0 C
724kg/s
405MW
175 0 C
736kg/s
409MW
163 0 C
729kg/s
408MW
174 0 C
Tcool-Gas
TFW-HRSG-in
TComb-Gas-in
Flue gas fkiwrate in
1,125kg/s
HRSG
Condensed
water
RHE
Rankine cycle power
TFW-Recov-out
new
Table 3.10: Hierarchical optimization results for the RHE process with tem2
perature uncertainty. FWHs' areas are RHE-AreaA: AFWHi = 7,069m and
AFWH2 = 2, 524m 2 . The designed for the ideally flexible process facing coal,
areas, and flows uncertainty is also ideally flexible to the temperature uncertainty. The changes in the values of TmFW,Main and PDeaerator are acceptably
small, Section 3.4.2.
Design
Tab
Low
(RHE-A Column2 of
Table 3.9)
Variable
Fuel Flowrate
Slurry water flowrate
Stream
Atomizer
flowrate
Air flowrate
Tcondenser
Pcondenser
Efficiency (LHV)
PComb, d
PComb, o
Input Parameters
30kg/s
16.50kg/s
2.50kg/s
High Tamb Design = optimization of operation
variables of Low Tamb
Design
30kg/s
16.50kg/s
2.50kg/s
311.2kg/s
311.2kg/s
0
39.73 0 C
29.73 C
0.073bar
0.042bar
Independent and Key Dependent Variables
33.23%
34.34%
max {PComb, oLow Tamb, PComb, 0 lligh Tamb}
8.92bar
7.41bar
QComb
1MW
1MW
rhFW,Main
306.0kg/s
99.Obar
62.2kg/s
26.0Obar
14.7kg/s
16.8bar
9.27kg/s
307.0kg/s
PBLD1
ThBLD1
PBLD2
rhBLD2
PBLD3
rhBLD3
PDeaerator
QFWH1
QFWH2
TFG-RHFrout
QRHE
99.Obar
62.5kg/s
26.Obar
13.9kg/s
16.8bar
8.15kg/s
14.7bar
15.2bar
138MW
37.7MW
36.9 0 C
122MW
139MW
35.6MW
46.9 0 C
120MW
Dependent Variables
TCJool-Gas
TFW-HRSG-in
TComb-Gas-in
Flue gas flowrate in
HRSG
Condensed Water RHE
APHRSG
APpipe primary
APpipe secondary
mFG-Rec-pri
mFG-Rec-sec
Rankine cycle power
TFW-Recov-out
327 0 C
322 0C
309 0C
1,138kg/s
327 0C
322 0C
312 0 C
1,141kg/s
33.2kg/s
0.265bar
0.054bar
0.035bar
281kg/s
737kg/s
33.0kg/s
0.385bar
0.048bar
0.046bar
282kg/s
739kg/s
409MW
401MW
0
164 C
1690C
8.92bar
Chapter 4
Pressurized OCC Process Ideally
Flexible to the Thermal Load
4.1
Summary
Pressurized oxycoal combustion process is optimized for variable thermal loading
(100% to 30%). The steam expansion line behavior is accurately represented based
on manufacturer data. Simulations with the nominal design and nominal operation
are then performed with variable loads to determine the level of performance decrease if no optimization is performed. Finally, optimization of operation for a fixed
design, and simultaneous optimization of design and operation are performed. The
design optimization for a specific load does not include the redesign of the turbines
to a process specifically designed for this load. However, the design variables of the
turbine expansion line, namely the extraction bleeds, are considered. At each load,
the performance of the process designed for nominal load is compared to the maximum possible performance obtained when designing the process for that specific load.
Thanks to the thermal recovery section, the process exhibits ideal flexibility to load
variations (not accounting for efficiency variations in the air separation unit, which
137
is accurate if oxygen storage is assumed), unlike Rankine cycles without pressurized
recovery. Consequently, there is no need to optimize for an expected distribution of
load operations. Finally, the process maintains supercritical operating conditions (no
phase change of FW in the HRSG) over larger ranges of thermal loads.
4.2
Motivation
Another very important disturbance to the process is variable loading, and is considered herein. At the time of plant design, the loading in uncertain. Load variations as
well as uncertainty in load is increasing in importance, [47, 481, especially with the rise
of the renewable but intermittent electric energy production, particularly wind and
solar. Therefore, because the process in not always operating at nominal conditions,
it is crucial to design the process for an overall maximum performance, rather than
the maximum performance at nominal conditions; in general, this is very challenging
and exhibits strong tradeoffs.
Studies regarding the performance of power generation processes at partload are
available in literature particularly for gas cycles and combined cycles, where significant
achievements in the design of the gas turbines allow them to operate flexibly to load
variations,
[49, 50].
Fewer studies of partload are available for Rankine cycles or
the bottoming cycle of a combined cycle. In [47] a combined cycle is addressed to
obtain high performance at partload and meet the emissions criteria because of the
efficiency decrease with the decrease in operation load; the addressed parameters for
optimization are those related to the gas process where the gas turbines are fitted
with guiding vanes and preheating of the gas cycle air improve the overall efficiency
at partload. However, the parameters of the Rankine cycle itself are not addressed.
Similarly pertaining to the gas cycle section of the combined cycle, [511 addresses
the importance of guiding vanes and [52] studies different types of commercial gas
138
turbines, while maintaining the conditions for the bottoming Rankine cycle at nominal
in order to prevent alterations in its behavior. Solar thermal power generation and
organic Rankine cycles are also studied under the influence of partload, [531, therein
however, the Rankine cycle design and operation are not considered but rather the
size of the solar field for the minimum levelized cost of electricity production for
a given load schedule. Judes and Tsatsaronis [54] presents a comprehensive study
of a simplified single pressure combined cycle power plant under variable loading;
there too the main variables are the choice of the gas turbines and the temperature
approach of the heat recovery steam generators. The Rankine cycle is a simple twostage turbine with no reheat or regeneration. As will be demonstrated in this study,
regeneration and thermal recovery of a complex Rankine cycle have an intertwining
and complex behavior and requires a dedicated evaluation. Other studies involving
the partload flexibility of the Rankine cycle deal with comparing the valve throttling
method to sliding pressure boilers method for partload operations, or even hybrid
methods combining both, [55, 56, 57]. However, the optimal design and operation of
the process are not addressed as herein.
Herein, the pressurized oxycoal combustion process presented in Chapters 2&3,
seen in Figure 4-1, is optimized for variable thermal loading. The first challenge in the
analysis of load variations is determining the steam turbine expansion line behavior
as the operation deviates from the nominal conditions. Experimental isentropic efficiency data are first analyzed in Section 4.3 to determine the expansion line behavior
and performance curves. Then, Section 4.4 presents the modeling approach. The
change of load also requires changes in several parameters to satisfy the operating
requirements of the units. For instance, the requirement on excess oxygen in combustion implies that the oxygen stream is proportional to the coal stream. Moreover, for
realistic representation of the process, the pressure losses in the heat recovery steam
generator (HRSG) and in the recycling pipes are evaluated and implemented. Then,
139
the optimization formulation is presented in Section 4.5, i.e., optimizing the process at
different loads (100% to 30% with 10% increments) taking care in modeling the design
variables particularly the bleeds' extraction pressures. Following proven thermodynamic criteria of optimum operation, [24, 27, 28, 29, 38] and Chapters 1&2, active
constraint optimization is utilized to simplify the optimization problem and avoid
convergence to suboptimal local optima. Finally, results are presented in Section 4.6
where the importance of optimization is reflected by the significant performance improvement of the variable load operations. Moreover, the flexibility of the process to
partload is evaluated by comparing the performance of a fixed design over the range
of loads to the maximum possible performance; the latter is the performance of the
processes designed for each of the specific loads. In designing for a specific load, the
turbines are considered to allow for the whole range of load operations, thus having
the nominal design, as justified in Section 4.5. Results show that due to the recovery
section, the process is ideally flexible to variable load, i.e., a fixed design operating at
variable load matches the maximum possible performance for each load. In contrast,
Rankine cycles without pressurized recovery do not share this favorable property.
Other important benefits of the recovery section are explained.
4.3
Turbine Performance Curves
The thermal load (TLoad) is the ratio of the coal flowrate into the combustor to
that of the full load nominal operation (TLoad=
rcoal, actual
m'koal, nominal
). As the thermal load
changes, the amount of thermal energy transported from the flue gas to the working
fluid of the Rankine cycle changes, thus changing the behavior of the working fluid.
The deviation of the turbine operation from the nominal conditions changes their
efficiency and power output. Therefore, an accurate representation of the expansion
line versus the relevant variations in the process is required. Stodala, [58], is credited
140
for one of the earliest attempts to assess the flow variations of a multistage turbine
by developing the ellipse law using experimental data. The rule is an experimentally
derived equation that relates the steam mass flowrate, inlet and outlet pressures, and
inlet temperature at off-design modes. Here however, the efficiency and power output
of the turbine are also required. Therefore, the off-design operation and performance
of the steam turbine is obtained by a different approach. Backed by experimental
data, Table 1, and rules of current practice, [59], it is well known that in an off-design
operation of a steam turbine the volumetric flowrate profile of the steam has to be
identical to the nominal volumetric flowrate profile. The reasons and implementation
of this approach are detailed next.
Experimental data from a standard Rankine cycle without carbon capture and
sequestration (CCS), with power ratings similar to those of the pressurized OCC
process, are shown in Table 4.1.
The specifications of the working fluid and the
response of each of the turbines are shown for different thermal loading. The presented
operations are not necessarily optimal, but the efficiency of the expansion line for the
particular values of the working fluid conditions at the inlet of each turbine can be
obtained from the table.
In general, the exergy of the thermal energy transferred from the flue gas to the
working fluid increases with increasing temperature of the working fluid. Therefore,
it is favorable to maintain the main stream and the reheat stream temperature at
the highest possible value, 600'C and 610'C respectively; moreover, this implies that
the inlet temperature of the turbines are at their nominal values. Now in order to
maintain the temperature of the working fluid at the exit of the HRSG/inlet of the
HPT and IPT constant despite the decrease in the thermal load, the mass flowrate
of the working fluid has to decrease as seen in Table 4.1.
Higher pressures of the working fluid increase the exergy of the process, however,
the characteristics of the turbine expansion line necessitates decreasing the working
141
fluid pressure with the decrease in thermal load. More specifically, turbines must
maintain an approximately constant flow pattern for an efficient and reliable operation, [59], where steam flows smoothly over the blades' surfaces rather than colliding
with them. The turbine angular velocities and thus the blades velocities are constant
besides during startup and shutdown. Therefore, for fixed blades design, to achieve
the constant design flow pattern, a constant volumetric flowrate of the working fluid
through any section of the turbine is required; note that the volumetric flowrate of the
working fluid increases as the steam expands through the turbine. Variations in the
volumetric flowrate profile result in deterioration of the lifetime and efficiency of the
turbines. To achieve constant volumertic flowrate profile at reduced mass flowrate,
the inlet pressures of the turbines are decreased. This can be achieved by (i) a constant pressure at the steam generation followed by throttling at the turbine inlet or
(ii) so-called sliding pressure boiler, i.e., variable pressure at the steam generation,
[60, 61]. Herein, it is assumed that the HRSG generates steam at sliding pressure.
In the data of Table 4.1, the volumetric flowrate of the working fluid at both the
inlet and exit of the turbines is constant for different loads except for exit of the low
pressure turbine which is maintained at the nominal condenser's pressure. To achieve
this in modeling, the inlet and outlet pressures of the high pressure and intermediate
pressure turbines are taken as function of the working fluid mass flowrate. In other
words, the equation V = rh x v (P,T) = constant is enforced at the inlet and outlet of
each turbine section, where V and v are the total volumetric flowrate and the specific
volume, respectively, while rh, T, &P are the mass flowrate, temperature, and pressure of the working fluid. The temperature is fixed at inlet, as explained above, and
is a dependent variable throughout the expansion process. Thus, the pressure and
the mass flowrate are no longer independent resulting in a single degree of freedom
in the above equation. Herein, the mass flowrate is chosen as the degree of freedom,
for numerical reasons. The mass flowrate is an optimization variable and its value
142
Table 4.1: Operating conditions of working fluid and turbine expansion line at different loads. Each turbine operates at a constant volumetric flowrate profile (constant
volumetric flowrate at each section of the expansion line). The outlet pressure of
the LPT, condenser pressure, is constant and equal to 0.042bar for the assumed wet
cooling condenser
Thermal Load %
Pinlet bar
inlet temperature 'C
7nFW,
FW,
actual
nominal
7
lactual
lnominal
Pinlet
Poutlet
100
99.44
99.33
98.20
4.2888
4.177
4.093
4.058
100
5.204
t
High Pressure Turbine (HPT)
250
169.9
120.1
84.62
100
70
50
35
100
600
600
600
600
100
64.7
45.6
32.0
Reheat - Intermediate Pressure Turbine(IPT)
100
610
52.90
70
50
35
36.91
26.55
18.95
610
610
610
69.8
50.3
35.8
98.75
98.75
98.75
4.98
4.80
4.68
100
70
50
35
10.44
7.60
5.67
4.15
Low Pressure Turbine(LPT)
-
100
72.9
53.9
39.3
100
99.25
98.18
96.79
239.5
174.4
130.2
95.3
is determined by energy balance during optimization of each thermal load. For each
turbine section, the efficiency ratio, the inlet pressure ratio, and the outlet pressure
ratio are mapped versus the mass flowrate ratio, wherein each ratio is taken relative
to the nominal. With very high accuracy, the inlet and outlet pressure ratios are
affine linear functions of the mass flow ratio, as a direct consequence of the physical
properties of the water particularly in the very superheated state after the reheat
where temperature is relatively high and pressure is relatively low. The efficiency ratio is considered as a piecewise linear function versus the working fluid mass flowrate
ratio because it does not seem to follow any particular continuous function versus the
mass flowrate ratio.
143
4.4
4.4.1
Modeling Approach
Process Operating Parameters
Similar to [24, 27, 38, 35] and Chapters 2&3, the model is implemented in AspenPlus. Figure 4-1 represents the process where a surface heat exchanger (RHE) is
used for sensible and latent heat recovery from the water in the flue gas. Note that
the analysis is pseudo-steady state, i.e., does not consider the transition dynamics
between different power levels. The variables and constraints on Figure 4-1 are used
for optimization.
For the scope of the current work, the air separation unit (ASU) is accounted
for by its power requirements and is not modeled rigorously. Operating the ASU at
partload increases the specific power requirement for producing the oxygen stream.
However, herein the power demand and specifications of the ASU are considered
constant (for any design and operation) for two reasons: first, a design specific to a
certain load is required to operate within the complete range of operation of the power
plant (30%-100%), thus the ASU should be capable of supplying the full load oxygen
requirements; therefore, the ASU design is the nominal/full-load design. Second, it
is assumed that oxygen storage is possible; therefore, for any dedicated design the
specific power demand of the ASU is identical to that of the nominal operation and
design. It is worth mentioning that even if storage is not practical then the ASU is
still required to have the full load design, and therefore using an elaborate model for
the ASU leads to changing the results in terms of values but not in the terms of the
trend or relative behavior. In particular, the comparison of the flexible design to the
dedicated designs will not be affected, which is the aim of this study. In conclusion,
the power demand and specifications of the ASU are considered constant for any
design and operation. In other words, the effects of load variation on the ASU are
not accounted for without jeopardizing the conclusions of flexibility to the thermal
144
load.
ASU
Pressurized
02
02
o pressor
I
IP
4-
02+Ar
L
Air
separat
N2
-R
c-prn
FW-HRSG-1n
FG-Rec-sec
om-Gas-in
"ReheatRH
o
Contrller
Ah
dSequestrated C02
Unit
mbustionre-Recovery
ot-G
Gas
Coa Wat
Slurry
vou
aG-e
C
ITvented
gas
A
FW-Recov-in
Condensate
P~
IBL
~~
ra
atio.
Stage3 ., Bleed
leed
DI .Flw
-B
IBLD3 Flowl
Bleed-
Reheatq
FW-HRSG-in
Cooling Water
rtor
FW
FW
,
Condenser
HP-Pump
LP-Pump
Figure 4-1: Oxycombustion cycle flowsheet based on wet recycling. Note that this
schematic does not represent entirely the modeling, e.g., turbines were modeled with
multiple sections in AspenPlus®
Table 2.1 shows the fixed parameters of the process, pertaining to the operation
of the Isotherm® combustor, [30], and other components.
To satisfy these while
varying the load requires adjustments to several streams in order to satisfy the ope
ration requirements. First of all, changing the thermal load requires a change in the
amount of coal and thus the amount of slurry water needed to transport the coal
keeping the required water ratio in the coal water slurry mixture.
Moreover, the
amount of oxygen required to oxidize the fuel also changes, and therefore, the air
flowrate entering the air separation unit changes. Also, the amount of the atomizer
145
stream needed to atomize the coal water slurry entering the combustor changes. In
the Rankine cycle, the steam leaks from the turbines are assumed to scale linearly
with the working fluid flowrate. Now that the atomizer stream flowrate, which is
extracted from the steam expansion line, and the turbine leaks change, the amount of
makeup water also changes. All of the dependent variations are modeled in calculator
blocks or design specifications in order to maintain the operation constraints of the
process at any load.
4.4.2
Flue Gas Pressure Losses
Another important aspect of the model is the calculation of the flue gas pressure
losses as it passes through the HRSG and the recycling pipes. Pressure losses are
calculated by utilizing standard pressure loss equations [62, 631, and similarity analysis [24, 27, 35, 38] and Chapters 2&3. The losses depend on the designs of the HRSG
and the recycling pipes, which depend on the process design pressure and economical
considerations [24, 271. Therefore, at a given thermal load, the pressure drops depend
on whether the HRSG and pipes are designed for that specific load, or are operated at
a load different than their design load. In the case of the former, the process pressure
and the HRSG and pipe designs are allowed to change upon design
(PComb, design
is
a design variables, Section 4.5.1), and the representation of the pressure losses are
identical to those of [24, 271:
Design specific for a particular load
For the recycling pipes upon design:
AP,3e=p
=
146
L
V2
where V is the bulk gas velocity in the pipe, d is the pipe diameter, LP is the pipe
equivalent length, p is the gas density, and
f
is the friction factor calculated by
-
-2
2 E/d)
L(2log)(2e/d)
= 'p-2. log
2o)J13
Red
7.4
where E is the pipe roughness, Red
= PVd
7.4
Red
is the Reynolds number based on the pipe
diameter, p is the flue gas density, and p is the dynamic viscosity of the gas.
The pipe diameter, d, and the gas velocity, V, are related by mh = pV-2-,
where
ni is
the recycled gas mass flowrate through each of the two pipes. Note that for practical
considerations the pipes diameters and the gas velocities in the pipes have to fall
within fixed ranges. The acceptable ranges are shown in Table 4.2 similar to those
considered [21, 24, 27]. The equivalent length is obtained by considering a 63.5 mbar
pressure drop in each pipe at an operating pressure of 10 bar based on experimental
data from ENEL.
Table 4.2: Recycling pipes diameters and gas velocity ranges, [21, 24]
Diameter Range (m)
Velocity Range (m/s)
[1-6]
[1-4.15]
[4-25]
[14-30]
Primary Recycling Pipe
Secondary Recycling Pipe
The larger the pipe diameter, the smaller the gas flow velocity, and the smaller
the pressure drop. Thus, a larger pipe is always favored in terms of efficiency but not
necessarily from an economical point of view as the capital, installation, and maintenance costs would increase. However, very large flow velocities can cause structural
failure and acoustic resonance.
Herein, at each iteration within the optimization
study, the largest allowable diameter, for each of the two pipes, is chosen such that
the gas velocity remains within the velocity range. In the case that the flowrate is
too high, the upper bound on the diameter is chosen and the velocity range is violated.
147
For the HRSG upon design:
where
QHRSG
APHRSG,a
_HRSG,a
APHRSG,b
QHRSG,bPb
a hb
a
is the rate of thermal energy transferred in the HRSG,
rh
is the flue gas
mass flowrate, and a and b stand for actual design and basecase design respectively.
Operation with a fixed design
On the other hand, when the process operates at a load while designed for a different
load, the specifications of the HRSG and the recycling pipes are identical to those
of the design load. Moreover, the design pressure is the maximum allowed pressure
of any operation. The losses are computed based on similarity analysis between the
actual, a, and design, d, operating conditions:
The recycling pipes
APpipe, a
A
pipe, d
d'
_(
22
)a
y
(f
(
p
Lp &,
7
h2)a
(
(d3d
2)d
_
d
aPd
fadPa
The pipes lengths, Lp, and the pipes diameters, d, are constant and equal to those
of the design load, therefore, do not appear in the final expression.
For the HRSG:
APHRSG, a
(fNp2)a
APHRSG, d
(fNp vj,)
m
fp
dPa
148
y__2_a
d
2 p
2A d
(fPV6) d
The HRSG design and size are invariant from those of the design load, therefore, the
number of rows N, and the cross sectional area Ac, are constant. Moreover, the tube
diameters D, the transverse and longitudinal distance between the tubes ST&SL, are
also constant leading to
_
=
.
f is the friction factor, which is approximately
constant for the ranges of Reynolds numbers involved. The pressure losses at a given
operation load are inversely proportional to the density of the flue gas.
In other
words, optimization of operation while the process is designed for a different load
results in the maximum allowable value of the operating pressure, since it decreases
pressure losses and does not decrease thermal recovery; also the tradeoff between the
02 and the CO 2 compression is insensitive within those ranges of pressures. However,
since the operation pressure cannot exceed the design pressure of the design load, the
optimum operating pressure is expected to be equal to the design pressure; this is
verified by the results.
4.5
Optimization Formulation
The objective of the study is to achieve a high performance for the pressurized OCC
process subject to variable loading. In particular, it is first desired to determine the
flexibility of the process. If the performance of the process designed for the nominal
load but operating at a different load is lower than the performance of the process
designed specifically for the non-nominal load, then the process is not ideally flexible.
In that case, the original design needs to be revisited, such that a maximum overall
performance is achieved rather than maximum performance at nominal conditions. To
examine the ideal flexibility, two families of optimization processes are required over
the range of possible thermal load; first, optimization of operation under the nominal
design, and second, simultaneous optimization of design and operation at the specific
thermal load.
Similar to the study of uncertainties at nominal loading, [351 and
149
Chapter 3, a classification of the optimization variables as design and as operation
is required.
Operation variables can change with load variations, whereas, design
variables are fixed. As described in Section 4.5.2, load variations impose additional
constraints compared to nominal operation.
As mentioned above, the redesign of the process for a specific load is considered to
allow for the same range of load operation; therefore, the turbines are ones that can
accommodate the nominal load operation, without reaching unrealistic working fluid
pressures, thus have the nominal load design. Recall that an expansion line design
requires maintaining the design flow pattern for maintaining high turbine performance
and reliability. More specifically, the inlet pressures and pressure ratios of the turbines
are adjusted as a function of the working fluid flowrate in order to maintain the
fixed volumetric flowrate profile of the working fluid in the turbines. Operating at a
load lower than the design is possible by decreasing the turbines' inlet pressures and
pressure ratios, and vice versa. Conversely, to operate at higher than design load, the
pressure would have to be increased. But to achieve high performance at nominal
conditions, the pressure is typically set at the maximal allowed limit, thus further
increase is not possible. So if the expansion line is designed for a partload operation,
then the plant is incapable of providing the initial full load power rating. However,
since a power plant is expected to operate for the majority of its lifetime under the
initial full load power rating, then the full load design of the expansion line is the
desired design for any partload.
4.5.1
Design and Optimization Variables
Table 4.3 characterizes the variables as design or operation and provides their range,
and Figure 4-1 marks the variables on the flowsheet. The basecase default values are
the optimized results of the design that is ideally flexible to uncertainties in coal, ambient conditions, and input stream specifications of the process at nominal load [35].
150
The classification of the variables is similar to that in [35] and Chapter 3 with few additions and differences. The methodology of implementing active constrains depends
on the variables' characterizations and is discussed in Section 4.5.3.
Combustor Pressure, PComb, o & PComb, d
As discussed in Section 4.4.2, the conbustor's operating pressure, PComb, o, is an operation variable, while the upper bound on its range, equal to the design pressure of
the design load,
is a design variable. It is also seen that for a fixed design,
PComb, d,
the pressure losses are smaller with increasing operation pressure, and therefore, optimization is expected to choose the maximum allowed value i.e., the design pressure.
This is verified by the results.
Combustor's Duty,
QComb
In [35] where only the nominal load is considered, the combustor's duty, QComb, is
treated as a design variable. However, the combustor's specifications and insulation
are fixed with the design, and the value of QComb for a given design changes with the
operating load. At a given design with a
combustor duty, QComb,
a,
QComb, d,
the resulting actual operational
is assumed to scale with the design duty according to
the ratio of the thermal loads of the design, d, and operation, o; in other words,
Note that the linear dependence is consistent with the extreme
Comb,.
cases: for a fixed design, at zero load there is zero transferred duty, and at design
load the transferred duty equals to the value at design. Similarly, the range of QComb,
d
is assumed to depend on the nominal duty QComb, n according the following equation,
QComb, d _
TLoadd _ TLoadd
QComb, n
TLoadn
1
Feedwater Flowrate, rnFW, Main
The performance curves of the turbines are available as discussed in Section 4.4. The
pressures of the working fluid are set to accommodate the turbine expansion line con-
151
straints. The main feedwater flowrate is an operation variable with no restrictions on
the range of its variation. It is trivial to deduce that the optimal flowrate decreases
with decreasing load. Therefore, bounding the range of the feedwater flowrate from
above at the nominal value facilitates the problem without constraining the optimization; a slightly larger upper bound is used nevertheless to make sure that the problem
is not constrained.
Bleeds' Flowrates,
rnBLD1,2,&3
The bleeds' flowrates can, and should, change with different thermal loads since the
amount of regeneration required for the varying feedwater flowrate changes. Moreover, the effectiveness of regeneration changes due to the change in the expansion line
pressures, as explained later, and require a different optimum flowrate. Therefore,
rnBLD1,2,&3
are considered as operation variables.
Bleeds' Pressures,
PBLD1,2,&3
In [35], where only the nominal load is considered, the bleeds' extraction pressures
are fixed with the initial design of the turbine expansion line, representing a fixed
position of extraction within a turbine stage, and thus are design variables. Here
however, fixed bleed extraction position is not equivalent to fixed extraction pressure
since at different loads the pressure ranges of each turbine stage change. Therefore,
a fixed extraction position is the required design variable, and this results in different
bleed pressures at different loads. Recall that for a given design, the turbines operate
with a fixed volumetric flowrate throughout in order to maintain the efficient flow
pattern. Therefore, a fixed extraction position is one that has a fixed volumetric
flowrate of the working fluid passing through the turbine at the section of extraction.
Modeling the bleed extraction positions by specifying the bleed pressure that
satisfy the volumetric flowrate constraint would result in a highly iterative procedure
and in an extremely complicated optimization process.
152
Fortunately, it is possible to eliminate the need for iteration and reproduce the
fixed extraction position by simple formulas.
To achieve this, the above iterative
procedure is separately implemented on an isolated expansion line, and the results
are compared to fixing the ratio of the extraction pressure relative to the inlet and the
outlet turbine pressures. The comparison is performed over a range of the working
fluid flowrate, representing a range of operation load. At the range of interest, keeping
the simple ratio of bleed extraction pressure, namely
Pex"r"ctionPo"t"et as
constant over
a range of 100% to 30% load, results in less than a 0.5% difference in the volumetric
flowrate of the working fluid at the point of extraction. This implies that keeping the
pressure ratio fixed according to the dimentionless variable proposed, corresponds to
a fixed extraction position. Keeping the pressure ratio fixed is easy to implement and
makes optimization tractable.
Extraction Stage, Integer Variables
Similar to [24, 38, 351, integer variables are used to select the extraction stage, where
each stage has different ranges of operation and different performance properties. The
discrete variables representing the extraction stage are also design variables.
FWH Duty Transfer,
QFWny&2
The duty transfer within each FWH is an operation variable.
Deaerator Pressure,
PDeaerator
The deaerator operating pressure is an operation variable determined primarily by
the low pressure pump delivery pressure and the deaerator bleed pressure at destination. Due to load variation the bleeds' pressures are not constant, and thus the
deaerator pressure is subject to change. However, upper and lower bounds on the
deaerator pressure should be respected.
A deaerator operating temperature range
of 101 to 200'C is common practice [64]. This temperature range is equivalent to a
153
pressure range of 1.076 to 15.55 bar. In other words, the pressure should be higher
than atmospheric (1.013bar), and lower than 15.55bar, the pressure of the maximum
allowed saturation temperature of 200*C, which is a material constraint. Regarding
the low-pressure feedwater pump, the pressure range of 5-15 bar obtained in the results, Section4.6, is considered within the acceptable range of operation. To achieve
variable pressure, a variable-speed driven (VSD) pump could be utilized. If instead a
fixed-pressure pump is utilized, then the pressure of the low-pressure pump can be set
to around 15 bar (maximum pressure required for any operating load, Section 4.6) and
the feedwater would be throttled into the deaerator tank (if and when needed). The
power requirement increase due to always operating at 15bar is minor, less than 0.01
percentage points change in efficiency of the cycle, because the pumping requirements
are relatively low.
Temperature of Flue Gas Exiting the RHE,
The temperature of the flue gas exiting the RHE,
TFG-RHE-out
TFG-RHE-OUt,
is also an operation
variable dictating the amount of recovered thermal energy. However, the optimal
value is not expected to vary with different operating loads because the optimum flue
gas operating pressure is high enough to allow the pinch point to occur at the flue gas
exit from the RHE. This expectation is confirmed by the obtained results. Note that
even if the value of
TFG-RHEOut
is invariant, the amount of recovered thermal energy
at the RHE, QRHE, changes because different loads have different flue gas flowrates
and different amounts of energy to recover.
Additional Integer Variables Required for Partload Optimization
Finally the process has three additional binary variables, each denoting the activation
or deactivation of a bleed flow. In principle, deactivating the bleed flow is identical to
setting the bleed flow to zero, however, the binary variables are required for modeling
purposes: zero flowrates cause convergence and mass balance errors in AspenPlus.
154
Table 4.3: Design and operation variables. The integer variables BLDAflow
inhibit or allow a bleed flow; inhibiting a flow by a BLD-flow value of zero is,
in practice, equivalent to setting 7hBLD to zero, but required here for modeling
purposes
Number
Variable
1
PComb, operation
2
PComb, design
3
(c)omb
4
mFW, Main
5
BLD1_stage
variable
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Range
Variable Type
[1 - PComb, design] bar
[1 - 10] bar
[1 - 30] x TLOAD MW
Operation
[20-300]
integer
Stages: 1-4
PBLD1--BLD.stage, outlet
PBLD1..-tage, inlet -PBLDL.stage, outlet
integer
-
1]
Stages: 3-6
DM2-PBLD2-stage, outlet
PBLD2.stage, inlet -PBLD2..stage, outlet
rnBLD2
BLD3_stage
variable
[0
[0 - 60] kg/s
ThBLD1
BLD2..stage
variable
kg/s
integer
PBLD2-PBLD3.stage, outlet
BLD3..stage, inlet -PBLD3.stage,
outlet
[0
-
1]
Design
Design
Operation
Design
Design
Operation
Stages: 5-7
Design
[0
-
1]
QFWH2
[0 - 200] MW
PDeaerator
[2 - 15.55] bar
[30 - 200] 0C
TFG-RHEout
Design
Operation
[0 - 30] kg/s
[0 - 30] kg/s
[0 - 200] MW
mBLD3
QFWH1
Design
Required for partload optimization
BLD1-flow
binary
{0,1}
variable
BLD2-flow
binary
{0,1}
variable
BLD3-flow
binary
{0,1}
variable
Design
Operation
Operation
Operation
Operation
Operation
Operation
Operation
Operation
The three integer variables are BLDiflow, one for each bleed, and are operation
variables, i.e., can be activated depending on the load. Physically these variables are
controlled in the same manner the bleed flow is controlled.
155
4.5.2
Constraints
Constraints on the admissible design and operation are imposed based on physical,
practical, and economical considerations. The turbines' volumetric flowrate profile
is a major constraint which is satisfied by automating the turbines' inlet pressures
and pressure ratios. Twelve constraints are accounted for explicitly at any operation
load. The constraints are listed in Table 4.4 and illustrated in Figure 4-1. Further,
active constraints presented in Section 4.5.3 allow satisfying the constraints at the
simulation level, while providing optimal performance.
Table 4.4: Optimization constraints, [24, 27, 35] and Chapter 3. The
most challenging constraints are eliminated by setting the bounds on
the variables and automating the turbine inlet pressures, turbines pressure ranges, and bleeds extraction pressures, and thus not shown here
Nu mber
Constraint
Value
1
2
MITAHRSG
AreaFWH1
> 3.7 0C
7,069m 2
equivalent
0
3
AreaFVWH2
4
5
qDeaerator
6
PDeaerator
7
TCool-Gas
8
TFW-HRSG-in
9
TCom-Gas-in
10
11
MITARHE
CO 2 -Cap
12
CO 2 _Pur
MITAFWH1=2.1 C
nominal
equivalent
5,254m 2
MITAFWH2=2.1'C
nominal
Saturated Liquid
to
at
to
at
* 2bar
; 15.55bar
PDeaerator
20'C above acid condensation temperature
50 C above acid condensation temperature
20'C above acid condensation temperature
> 7-5 0 C
94% of total CO 2 produced
required to be captured
captured CO 2 is 96.5% pure
156
4.5.3
Active Constraint Optimization
In [24, 27, 28, 29] and Chapter 1 it is proven that optimal operating conditions occur
at some active constraints. Enforcing these constraints as operation specifications,
facilitates the optimization in several aspects: (i) avoid constraints violations, (ii)
avoid simulation errors and failures, (iii) accelerate convergence, (iv) avoid convergence to suboptimal local optima. The desired active constraints can be satisfied at
the simulation level by manipulating the main influencing variables.
The following constraints and variables are coupled:
1. MITAHRSG /ThFW, Main: The allowed minimum internal temperature approach
constraint on the HRSG is achieved by manipulating the main feedwater flowrate
2. MITARHE/TF-HE-out:
The allowed minimum internal temperature approach
on the RHE achieved by manipulating the temperature of the flue gas exiting
the RHE
3. & 4. Double-pinch.FWH(1&2)/FWH(1& 2) and
rnBLD(1&2).
Both the duty trans-
fer within each closed FWH and the flowrate of the respective bleeds are utilized
in order to guarantee equal values of the temperature approach at the feedwater
heater outlet, and at the position of phase change of the bleed,
[28, 29] and
Chapter 1. Note that the areas of the feedwater heaters are fixed and thus the
value of the double-pinch is not necessarily equal at different loads:
5.
PDeaerator:
For optimal operation, the deaerator pressure has to be equal to
the pressure of the deaerator bleed, BLD3, at the deaerator inlet; [28, 29] and
Chapter 1.
Therefore, PBLD3 and
PDeaerator
are coupled to be equal at the
level of the deaerator, i.e., after accounting for friction and hydrostatic pressure
changes. The deaerator bleed flowrate also plays a role in the optimum value
of the deaerator pressure since it affects the amount of pressure loss in the
connection pipes
157
6.
qDeaerator/nBLD3-
The mixture inside the tank deaerator has to reach the satu-
rated liquid state for the effective removal of dissolved air in the working fluid.
This constraint is satisfied by the low pressure bleed to the deaerator
Note that the last two items are relevant only when the deaerator bleed is active,
i.e., BLDJflow3=1; otherwise when BLD.flow3=0, the constraint on the quality of
the mixture inside the dearator is satisfied by manipulating the deaerator pressure.
Moreover, the combustor operation pressure is not equated to the design pressure in
an active constraint, in order to show that indeed the optimum operation pressure is
the process's design pressure.
4.6
Results and Analysis
Three steps are performed to examine the partload performance of the pressurized OC
process. First, a given partload is operated with the nominal design and operating
conditions, [35] and Chapter 3, with changes in the values of the deaerator pressure,
feedwater flowrate, and FWHs' duty, in order to satisfy the constraints set on the
deaerator pressure and satisfy the FWHs areas. Then, optimization of the operation
is performed while keeping the same fixed design. Third, the process is redesigned for
that specific partload by simultaneous optimization of design and operation. Recall
that the turbine expansion line design is kept fixed in this step, but not the design
of the extraction bleeds' positions. The latter optimization obtains the maximum
possible performance at that specific load (for the given turbines). Comparing the
results of steps two and three, the flexibility of the process to varying load is obtained.
The results show that the process is ideally flexible to load variations. The flexibility
eliminates the need for a prior knowledge of the operation schedule. The reasons
behind the ideal flexibility are shown in Sections 4.6.2, 4.6.3 & 4.6.4. The comparison
of steps 1 and 2 shows that optimization of operation is required even for a flexible
158
design, to achieve high performance. Comparing Steps 2 and 3 show that a flexible
design can match the optimum performance of the process at the evaluated variable
loads.
In the case study considered, the lowest thermal load is 35%, see Table 4.1. Herein,
flexibility assessment is performed om thermal loads reaching down to 30%, to account
for extreme scenarios.
Table 4.5 summarizes the results of the RHE configuration
of [351 and Chapter 3, which is the ideal flexible design to uncertainties of coal,
ambient conditions, and input streams specifications at nominal load, and serves
as the basecase of this study. Tables 4.6&4.7 present the results of the flexibility
evaluations for the 60% and 30% thermal loads, respectively.
4.6.1
Flexibility Assessment
The results of the flexibility assessment, Tables 4.6 & 4.7, show that the process
designed for full load is ideally flexible to large load changes.
By optimizing the
operation of a design specific for the full load while under a partial thermal load
(columns 3 in Tables 4.6 & 4.7), the process performance matches the maximum
possible performance obtained when the process is designed specifically for that load
-apart from the turbines- (columns 4 in Tables 4.6 & 4.7). The discrepancy is approximately 0.02% and as such insignificant. In contrast, maintaining the nominal
load operating conditions when at a partload operation (simulations in columns 2 in
Tables 4.6 & 4.7), results in a drastic decrease in the efficiency of the process, around
8 percentage points decrease at the 60% TLoad, and 30 percentage points 30% load.
Figure 4-2 represents the results of all the operation ranges graphically, where the
optimum operation of the full load design at a particular load matches the respective optimal design of that load, while without optimization the performance suffers
significantly and may even be infeasible. Note that the 90% load has an efficiency of
159
Table 4.5: Summary of optimal design and operation of the RHE process for coal and ambient conditions variations and FWH area specification, [35] and Chapter 3 Table 3.10. Results shown are for the coal considered herein
Fuel Flowrate
Slurry water flowrate
Stream
Atomizer
flowrate
Air flowrate
Efficiency (based on
30kg/s
16.50kg/s
2.50kg/s
311.2kg/s
34.41%
LHV)
Independent and Key Dependent /araibles
7.41bar
PComb
ThBLD2
1MW
306kg/s
99.Obar
62.2kg/s
26.Obar
14.7kg/s
PBLD3
16.8bar
ThBLD3
9.27kg/s
PDeaerator
14.7bar
rnFW Main
PBLD1
mBLD1
PBLD2
138MW
37.7MW
36.9 0 C
122MW
OFWH1
QFWH2
TFG-RHE-out
RHE
Depend ent Variables
TComb-Gas-in
327 0 C
3220 C
3090 C
Flue gas fkiwrate in
1,138kg/s
Tcool-Gas
TFW-HRSG-in
HRSG
water
Condensed
33.2kg/s
RHE
0.265bar
0.054bar
0.035bar
APHRSG
APp,
APp,
Primary
secondar
281kg/s
737kg/s
rnFG-Rec-pri
rnFG-Rec-sec
Rankine
power
cycle
TFW-Recov-out
PHPT
PReheat
net
409MW
1640C
250bar
53.5bar
Table 4.6: 60% thermal load flexibility
60% thermal load
simulation
Variable
60% thermal load
of
optimization
with
operation
load
nominal
design
Fuel Flowrate
Slurry water flowrate
Atomizer Stream flowrate
Air flowrate
Input Parameters
18kg/s
18kg/s
9.9kg/s
9.9kg/s
1.5kg/s
1.5kg/s
191.7kg/s
191.7kg/s
Efficiency (based on LHV)
23.70%
PComb
31.59%
Independent and Key Dependent Varaibles
7.41bar
7.41bar
thermal
60%
load optimization
and
of
design
operation
18kg/s
9.9kg/s
1.5kg/s
191.7kg/s
31.61%
7.41bar
OComb
0.6MW
0.6MW
0.6MW
mFW Main
ThBLD2
179kg/s
64. Ibar
99.Obar
62.2kg/s
16.3bar
26.Obar
14.7kg/s
168kg/s
60.4bar
99.Obar
27.9kg/s
17.Obar
26.Obar
7.27kg/s
169kg/s
64.6bar
105bar
29.3kg/s
18.8bar
28.0bar
8.60kg/s
PBLD3
8.17bar
11.0bar
11.2bar
equivalent PBLD3 at nominal
16.8bar
9.27kg/s
16.8bar
4.33kg/s
10.3bar
17.0bar
4.10kg/s
67.2MW
19.0MW
67.9MW
22.7MW
93.8 0 C
36-90 C
36-9 0 C
58.2MW
70.1MW
70.1MW
PBLD1
equivalent PBLD1 at nominal
rhBLD1
PBLD2
equivalent PBLD2 at nominal
rhBLD3
PDeaerator
FWHV1
QFWH2
TFCRHE-out
RHE
TCool-Gas
TFW-HRSG-in
TComb-Gas-in
Flue gas fkiwrate in HRSG
Condensed water RHE
APHRSG
APpipe Primary
APpi,, secondary
mFG-Rec-pri
FG-Rec-sec
Rankine cycle net power
TFW-PRecov-out
PHPT
PReheat
8.16bar
87.0MW
27-4MW
Dependent Variables
2960 C
2 311 0C
0
291 0C
306 C
296 0 C
665kg/s
283 0 C
648kg/s
10.6bar
301 0 C
296 0 C
288 0 C
637kg/s
17.1kg/s
19.9kg/s
19.9kg/s
0.334bar
0.334bar
0.334bar
0.035bar
0.009bar
0.034bar
0.008bar
0.03bar
0.008bar
167kg/s
165kg/s
166kg/s
426kg/s
196MW
173 0C
161bar
42.6bar
411kg/s
242MW
157 0 C
151bar
39.7bar
416kg/s
239MW
158 0 C
152bar
40.Obar
Table 4.7: 30% thermal load flexibility
Variable
30% thermal load
simulation
30% thermal load
of
optimization
with
operation
load
nominal
design
Input Parameters
9kg/s
9kg/s
Fuel Flowrate
4.95kg/s
4.95kg/s
Slurry water flowrate
0.75kg/s
0.75kg/s
Atomizer Stream flowrate
102kg/s
102kg/s
Air flowrate
24.48%
Infeasible
Efficiency (based on LHV)
Independent and Key Dependent Varaibles
7.41bar
7.41bar
PComb
0.3MW
QComb
mFW
Main
thermal
30%
load optimization
and
design
of
operation
9kg/s
4.95kg/s
0.75kg/s
102kg/s
24.48%
7.41bar
0.3MW
0.3MW
74.5kg/s
74.5kg/s
31.8bar
PBLD1
equivalent PBLD1 at nominal
ThBLD1
PBLD2
equivalent PBLD2 at nominal
99.Obar
99.Obar
9.41kg/s
106bar
8.75kg/s
8.66bar
10.3bar
rhBLD3
26.Obar
3.23kg/s
NA
16.8bar
0kg/s
29.9bar
4.19kg/s
NA
NA
0kg/s
PDeaerator
5.04bar
5.23bar
24.6MW
8.93MW
22.7MW
11.8MW
36-9 0 C
369 0 C
33.1MW
33.3MW
26.Obar
ThBLD2
PBLD3
equivalent PBLD3 at nominal
QFWH1
QFWH2
TFGRiHE-out
RHE
16.8bar
Dependent Variables
TFW-HRSG-i
TComt-Gas-in
253 0 C
247 0 C
246 0C
256 0 C
250 0 C
248 0C
Flue gas fkiwrate in HRSG
Condensed water RHE
APHRSG
APi, Primary
302kg/s
9.96kg/s
0.334bar
0.008bar
304kg/s
9.96kg/s
0.334bar
0.008bar
0.002bar
80.2kg/s
0.002bar
80.3kg/s
186kg/s
188kg/s
TFW-Recov-out
110MW
157 0 C
109MW
1500C
PHPT
72.lbar
72.4bar
PReheat
19.8bar
19.9bar
TCool-Gas
AP
2,
secondary
hFCRec-pri
FG-Rec-sec
Rankine cycle net power
34.55%, larger than the full load efficiency because the benefits of smaller pressure
losses and smaller flue gas flows outweigh the disadvantages of the turbines expansion
and turbines bleeds reduction in performance; this validates that the full load design
takes economic consideration into account for the sizing of the HRSG and recycling
pipes [24, 271.
35
32.5 -
30
S27.525-
-
40
22.5
.0
4
20'
17.5-
x
...
I
of design and operation
Optimization of operation
15 -
for a fixed (full-load) design
12.510
0.2
Simultaneous optimization
Simulation of the fixed
4-
(full-load) design
0.4
0.6
Thermal Load
0.8
1
Figure 4-2: Simulation and optimization of the operation for the full load optimal
design at different partloads, in dashed and solid lines respectively. Optimization of
the operation of the full load design matches the performance of the optimal design of
the specific part load, in (x)'s. The full load design is ideally flexible but optimization
is required, while simulation of the full load operation suffers significantly and is even
infeasible at relatively small loads. In all designs, the design of the turbine expansion
line is fixed to allow for the complete range of load operations.
163
4.6.2
Behavior of Key Variables
Analyzing the behavior of the variables is crucial to understand the reasons behind
the flexibility of the process with respect to loading, in particular the variables related
to regeneration and the recovery sections. The behavior of key variables is discussed
in this subsection. In the following subsection, Rankine cycles without pressurized
thermal recovery and CCS are discussed to argue that they do not exhibit ideal
flexibility.
Combustor Pressure,
PComb, operation
&
PComb, design
As mentioned above, the operating pressure at optimum is equal to the upper bound
of its range, which is the pressure of the design load. Moreover, the design pressure
does not change from the nominal design pressure value because the same tradeoff
between thermal recovery and pressure losses that exists at full load, [24, 27], also
occurs here; although higher operating pressures result in more recovery, it results
in larger pressure losses. Also, lower operating pressures reduces the pressure losses,
but achieves smaller thermal recovery at the HRSG. First, the thermo-economical
optimum design occurs at the same range as that of the nominal design. The pressure
is sufficient to allow for the condensation of the majority of the water in the flue gas,
by allowing the minimum temperature approach to occur at the outlet of the flue
gas; note that the pinch also occurs at the onset of water condensation of the flue gas
because a lower pressure eliminates the outlet pinch and a higher pressure results in
larger pressure drop of the designed HRSG and recycling pipes with no change in the
outlet pinch.
Combustor Duty, QComb
QComb
is favored to be the minimum allowed value as it reduces the irreversibilities
associated with the heat transfer across a large temperature gradient.
164
Feedwater Flworate, rnFW Main
As expected, the optimal mFW Main decreases with decreasing thermal load.
The
amount of thermal energy available for transfer from the HRSG to heat the working
fluid upto the nominal working fluid temperatures, 600'C for the main stream, and
610'C for the reheat stream, results in a smaller working fluid flowrate compared to
the full load operation. At any fixed thermal load, a larger main feedwater flowrate
in general signifies a larger power output and a larger efficiency, columns 3 & 4 of
Tables 4.6 & 4.7. However, this is not the case looking at Column 1 of the same
tables. The main feedwater flowrate is large but the working fluid flowrate decreases
significantly through the expansion line due to the suboptimal high bleeds flowrates,
resulting in a significant decrease of efficiency. Notice that the pressure at the inlet
to the high pressure turbine and the intermediate pressure turbine,
PHPT
&
PReheat
respectively, decrease with the decrease in working fluid flowrate in order to satisfy
the turbines constraints of constant volumetric flowrates. At 60% and 30% thermal
load, the process is subcritical, i.e., there is a phase change of the feedwater in the
HRSG, see Section 4.6.4. It is important to realize that in the two optimized runs of
each load, optimization of operation and optimization of design and operation, the
.npW Main, pload is almost equal to the thermal load;
ratio of the working fluid flowrate, mFW
Main, nominal
this fact is due to the thermal recovery section, and is fundamental in explaining the
reasons behind the flexibility. The argument that the recovery section is responsible
for the working fluid ratio relative to nominal being proportional to the thermal load
is proven in Section 4.6.3, but considered as an observation/result in what follows.
Recovery Section (condensed water, QRHE,
TFG-RHE.out, TFW-R.H-out)
Before discussing the behavior of the regeneration bleeds, it is important to understand the thermal recovery section (after the condenser, before the deaerator),
which the working fluid passes through prior to regeneration. The overall flue gas
165
flowrate scales according to the thermal load and has almost identical composition
with the flue gas at nominal conditions; the fuel flowrate, the oxygen flowrate, and
the added water flowrate scale from their nominal values according to the operation thermal load. Similarly, the overall thermal energy available for transfer also
scales proportionally with the thermal load.
Now, due to the invariant flue gas
composition in particular water fraction, the ratio of the low grade thermal energy,
transferred at the RHE/recovery, to the total thermal energy transferred into the
Rankine cycle is almost constant (and equal to the same ratio at nominal load);
note that in the pressurized OCC process the temperature of the flue gas exiting
the HRSG/entering the RHE, Tcbo-Gas, is almost equal in the optimum operations
at different loads.
As a result, the amount of recovered thermal energy, at any
load, relative to the nominal load is proportional to the thermal load; in summary,
T*t*1,TI.*d
QTotal,100%
-
Tload &
9RHE
QTta
__
QRHETload
Q
QRHE,100%
=
=
Tload. This is validated
by comparing the results of QRHE in the optimized runs, or comparing the amount
of water condensed from the flue gas in the RHE (33.2kg/s, 19.9kg/s & 9.96kg/s at
100%, 60% & 30% thermal loads respectively).
Recall that the working fluid mass flowrate in the optimized partload operations
and optimized partload designs above scales with the thermal load and that the condenser temperature is constant at any load. Therefore, the extensive properties of
the thermal recovery section at the optimized partloads is almost identical to the
recovery section at nominal load, which is verified by the results; namely the temperature of the flue gas exiting the RHE,
feedwater exiting the RHE,
TFW-ReC-oUt.
TFCRHEout,
and the temperature of the
Therefore, a unit mass of the working fluid
leaving the condenser and before reaching the deaerator always experiences identical
conditions irrespective of the load, the turbine expansion line pressure ranges, or the
regeneration bleeds extraction pressures and flowrates. The nominal load recovery is
suited for a power plant with supercritical pressures and large pressure ranges equal
166
to those of the basecase nominal load operation; yet, at partload the recovery is
operating within smaller pressure ranges. In other words, the scaled version of the
thermal recovery section is more than adequate in heating the working fluid during
partload and takes over relatively larger and larger fractions of the working fluid's
gradual preheating processes with decreasing load; thus compensates for the regeneration process which inherently and independently faces diminishing performance as
explained next. In conclusion, the thermal recovery in a pressurized OCC process
results in two advantages: first, the maximum efficiency of partload is only slightly
lower than the maximum efficiency of the nominal load, and second, the process designed for nominal load can attain a performance that matches the maximum possible
performance at any load.
Another way to explain the importance of the recovery section is by realizing
that at nominal loading the recovery, with the help of the dearator bleed, is able to
sustain a deaerator pressure of around 14bar, and thus bleed3 is extracted from the
turbine expansion line withing the same range of pressure. At partload, the recovery
is unaffected, and able to deliver the working fluid with similar conditions as those of
nominal, i.e., sustaining the high deaerator pressure; however, at partload, the same
value of pressure for the dearator bleed resembles earlier extraction positions, signifying that the recovery section is contributing to a larger fraction of the working fluid
preheating, and is taking over the regeneration which faces diminishing effectiveness
with decreasing load.
Recall that initially the recovery section replaces a number of low pressure feedwater heaters and regeneration bleeds found in standard Rankine cycles without pressurized recovery. Unlike the recovery section, the regeneration section is highly affected
by the turbines' pressure ranges and bleeds' extraction pressures. Therefore, a standard Rankine cycle without a pressurized recovery section is expected to be inflexible
to variable loading, and has a partload performance, whether optimized operation
167
or optimized design, significantly lower than that of the nominal, as elaborated in
Section 4.6.3.
Regeneration Section, Bleeds pressures and flowrates
With the.decrease in the expansion line inlet pressures and pressure ranges, the pressure of a bleed withdrawn from the fixed extraction position decreases, and so does
its saturation temperature. The decrease of the bleed's saturation temperature limits
the temperature rise of the feedwater in the feedwater heater decreasing the quantity
and quality of regeneration. Therefore, with decreasing thermal load and decreasing
expansion line pressure ranges, a unit mass of regenerative bleed extracted from a
fixed position is relatively less beneficial to the unaltered temperature of the feedwater entering the regeneration section; in the pressurized OCC considered herein
the regeneration section starts with the deaerator while in non-pressurized OCC processes it starts at the exit of the low pressure pump after the condenser. The high
temperature source of thermal energy, the flue gas in the HRSG, is still operating at
approximately the same temperature ranges; therefore in general, a decrease in the
effectiveness of regeneration reduces the temperature of the feedwater entering the
HRSG, and causes a decrease in the exergy of the transferred thermal energy at the
HRSG, reducing the efficiency of the process. The effect of the decrease in recovery effectiveness on the Rankine cycle performance is alleviated when a pressurized
recovery section is present as explained next.
The reduction of the regeneration effectiveness at partload is one of the reasons
why in the simultaneous optimization of design and operation of the pressurized
OCC the extraction pressures of the bleeds increase compared to those obtained by
the nominal extraction positions operating at the same load. This signifies that the
extraction positions shift to earlier sections along the expansion line; the smaller the
load, the earlier the designed extraction position is. The second reason behind the
168
earlier extraction positions of the bleeds is that the recovery section covers a relatively larger preheating portion and therefore higher quality regeneration is required;
(as if additional feedwater heaters are introduced before FWH1&2, thus FWH1&2
move upwards in pressure). For example, for bleedi, the nominal extraction position
of 99.Obar at nominal load results in a 60.4bar at 60% partload. After redesigning
for the 60% load, the extraction pressure is 64.6bar equivalent to 105bar at nominal
conditions. Similarly for the 30% load, the optimal design extraction position occurs
even earlier with an equivalent pressure of 106bar at nominal conditions. However,
due to the behavior of the recovery section, which is independent of the thermal load,
there is not much advantage in redesigning the regeneration and extractions for a
specific partload. In other words, while the regeneration effectiveness of the bleeds
and feedwater heaters decrease with smaller loads, which here necessitates earlier and
earlier extraction positions, the effectiveness of the recovery section, relative to the
smaller working fluid pressure ranges, increases and takes over the regeneration section. The independence of the thermal recovery section to the turbine expansion line
pressure ranges is the main reason behind the flexibility of the process. This behavior
is best explained by the response of the deaerator bleed/BLD3, where at partload
there is very little interest in a deaerator bleed. In particular, the 30% load requires
no deaerator bleed. This is a definite illustration of how the recovery section takes
on a larger role with the decrease in the thermal load till eventually eliminating one
bleed altogether. Another reason for flexibility, also in favor of the recovery section,
is that the recovery section replaces the low temperature feedwater heaters where the
bleeds' saturation temperatures, and thus bleeds' quality, are highly sensitive to the
bleeds' pressures and the turbine pressure ranges; while the saturation temperature
of the high pressure bleeds, namely bleedsl&2 of FHW1&2 in the pressurized OCC
process, are relatively less sensitive to the pressure ranges. Note that if the conditions
of the feedwater entering the FWHs are altered significantly, like what would be the
169
case if low pressure feedwater heaters are present instead of the recovery section, then
the high pressure feedwater heaters and bleeds require significant change in design
and result in a significantly different performance.
The behavior of the bleeds' flowrates are justified for similar reasons. As the load
decreases the bleeds' flowrates decrease; first, the working fluid has a lower flowrate
and thus requires smaller regeneration. Second, the recovery section takes a larger
portion of the working fluid preheating and less regeneration is required.
Finally,
with the decrease in saturation temperature of the bleeds, due to the decrease in the
pressure ranges of the turbines, the possible temperature rise of the working fluid is
smaller and thus smaller bleeds flowrates are required.
4.6.3
Standard Rankine Cycles Without Pressurized Recovery
In Section 4.6.2 it was argued that in the OCC process considered the thermal recovery
section allows ideal flexibility with respect to thermal load. A key to achieve this was
that the mass flowrate of the working fluid is proportional to the load. Herein, it is
argued that this proportionality is enabled by the thermal recovery section and that
Rankine cycles without pressurized recovery section do not show this ideal flexibility.
In Rankine cycles without pressurized recovery, where the boiler is the only site of
thermal energy transfer from the flue gas, the amount of thermal energy transferred
to the working fluid relative to that at nominal approximately scales with the thermal
load; (as seen later, the temperature of the flue gas at the outlet of the boiler in a
partload operation is generally smaller than that at nominal and thus the proportionality is not exact). However, unlike the pressurized OCC process, the working
fluid flowrate does not scale linearly with the thermal load because the quality of the
transferred thermal energy decreases compared to the nominal operation. The argument is illustrated by contraposition; assume in a Rankine cycle without pressurized
170
recovery that the flowrate of the working fluid scales with the thermal load. The
decrease in the fluid mass flowrate at partload from its nominal value results in lower
turbines' pressure ranges due to the requirement of constant volumetric flowrate. The
regeneration section, which is the only section responsible for the gradual preheating
of the working fluid, decreases in effectiveness relative to the nominal conditions due
to the decrease in the expansion line and bleeds' pressures (even if regeneration is
redesigned for that specific load). As a result, the temperature of the working fluid
entering the boiler is lower than that of the nominal operation. Therefore, part of
the thermal energy transfer at the boiler is required to compensate for the deficiency
in the working fluid's temperature, and therefore by conservation of energy, the mass
flowrate of the working fluid has to be smaller than that originally assumed. The even
smaller flowrate results in even smaller turbines' pressure ranges, smaller regeneration
effectiveness, and smaller temperature of the working fluid entering the boiler, etc.
As mentioned above, this behavior can be considered as a decrease in the quality
of the transferred thermal energy because the average temperature of the feedwater
in the boiler is smaller due to the lower temperature of the feedwater entering the
boiler/exiting the less effective regeneration. To be more rigorous, note that since the
temperature of the working fluid entering the boiler decreases, the temperature of the
flue gas exiting the boiler can decrease too. However, the increased amount of thermal energy transfer due to the larger flue gas temperature drop is smaller than the
amount of thermal energy required to elevate the smaller temperature of the working fluid entering the boiler because the thermal capacity of the flue gas is smaller
than that of the working fluid, guaranteeing that the mass flowrate of the working
fluid relative to the nominal scales sublinearly with the thermal load. The fact that
the thermal capacity of the flue gas is smaller than that of the working fluid can be
deduced in several ways, (i) the pinch inside the HRSG occurs at the cold end of the
exchanger (flue gas exit, feedwater inlet), (ii) the temperature drop of the flue gas is
171
much larger than the temperature increase of the feedwater and the reheat streams,
(iii) regeneration increases efficiency, (iv) and of course can be seen by comparing
the temperature profiles of the streams in the HRSG where the hot stream profile is
steeper than that of the cold stream, etc.
Coal-fired Rankine cycles without pressurized recovery have another limitation
for partload operation. At some thermal load the temperature of the working fluid
entering the boiler will fall below the acid condensation temperature, thus further
limiting the heat transfer from the flue gas. This further deteriorates the performance
of the Rankine cycle subject to variable loading.
Moreover, Rankine cycles without pressurized recovery have larger number of
FWHs, particularly low pressure FWHs, compared to the pressurized OCC process
of the same size.
The sensitivity of the larger regeneration section to the turbine
pressure ranges, especially at the low pressures, results in a large difference between
the designs of the non pressurized recovery process at different loads. Thus, rendering
the process inflexible and further deteriorating the performance when a fixed design
is operated under variable loading.
In contrast, due to the recovery section in the pressurized OCC process, which
increases in effectiveness and takes over the regeneration section with decreasing load,
the temperature of the working fluid entering the HRSG barely changes, resulting in
the aforementioned linear relation of the working fluid to the thermal load.
Nev-
ertheless, the process remains unconstrained by the acid condensation temperature
constraints, and therefore operates at the unconstrained optimum and maintains a
high performance. For further elaboration, using the same argument used for processes without pressurized recovery, it can be shown that the optimal ratio of the
flowrate in the pressurized OCC process is actually sustainable, and the results seen
in the optimized runs in the above tables are not coincidental. The increased effectiveness of the recovery section compensates for the decrease in the effectiveness of
172
the recovery section, thus maintaining the temperature of the feedwater entering the
HRSG close to nominal and allows for the scaled ratio of the working fluid.
4.6.4
Partload and Subcritical Operation
As the load and the mass flowrate of the working fluid decrease, the turbine inlet
pressures and pressure ranges decrease to satisfy the turbine expansion line constraints
of constant volumetric flowrate profile. At some flowrate the required working fluid
pressure falls below critical and the process becomes subcritical, where there is a
phase change of the feedwater in the HRSG, and through out that phase change a
constant saturation temperature is maintained.
The lower the feedwater pressure,
the lower the saturation temperature, and the larger the enthalpy of vaporization. A
larger enthalpy of vaporization signifies that more thermal energy is transferred to
the relatively low temperature of saturation, decreasing the exergy of the transferred
thermal energy. Moreover, the presence of a larger range where the temperature of the
feedwater is constant results in decreasing the temperature difference at the cold end
of the HRSG and in reaching the minimum allowed temperature difference, which
limits the flow of the feedwater. The efficiency of the 30% load is relatively small
compared to the efficiencies of the 60% load, relatively high saturation temperature,
and to the 100% loads, supercritical, which are not that different from each other.
Note that in non pressurized recovery Rankine processes, the subcritical conditions
are reached earlier/at larger partloads, and the saturation temperatures for a given
subcritical load are lower, than those of the pressurized OCC process; this is due to
the fact that the flowrate of the feedwater decreases at a faster rate in conventional
Rankine cycles compared to the pressurized OCC process.
173
4.7
Conclusion
The flexibility of the ENEL/ITEA pressurized OCC process to variable load is evaluated with an accurate representation of unit operations particularly the turbine expansion line. The turbines operate at constant volumetric fluid flowrate profile which
requires changing the turbine inlet pressures and pressure ranges with the change in
load. The results show that the process is ideally flexible for variable load due to the
characteristics of the thermal recovery section. The performance of the nominal load
design when operating at a given partload matches the maximum performance of the
process designed specifically for that partload. When designing the process specific to
a partload, the turbines are maintained at the nominal load design in order to allow
for a full range of load operations. The ideally flexible behavior is owed to the thermal recovery section, which is not affected by the reduction of the pressure ranges of
the turbine expansion line with decreasing thermal load. The recovery section always
provides adequate preheating to the working fluid. In particular, a unit flowrate of
working fluid always receives the same preheating from the flue gas at the thermal
recovery section independent of the operating load. This signifies a relatively larger
preheating duty with the decrease in the turbine pressure ranges; the recovery section
compensates the decrease in the effectiveness of the inflexible regeneration section,
and therefore, the OCC process is ideally flexible. This flexibility is in contrast to
Rankine cycles without pressurized recovery, wherein the performance significantly
deteriorates compared to the nominal operation. Moreover, as the thermal load and
the working fluid flowrate decrease, the required turbine pressures fall below the critical pressure, and the working fluid in the HRSG pass through the saturation region.
However, this transition occurs at a larger load for Rankine processes without pressurized recovery compared to the pressurized OCC processes which are able to maintain
supercritical conditions at smaller thermal loads.
Due to the increasing effectiveness of the recovery section, the working fluid enter-
174
ing the HRSG is high enough such that the flue gas of the pressurized OCC process
never violates the acid condensation constraints even at extremely low loads.
In
contrast, due to the reduction in the effectiveness of regeneration, conventional coal
Rankine cycles are constrained by the acid condensation temperatures at certain part
loads, and therefore operate sub-optimally with a low performance.
175
176
Chapter 5
A Split Concept for HRSG with
Simultaneous Area Reduction and
Performance Improvement
5.1
Summary
A split concept for boilers and heat recovery steam generators (HRSG), where flue gas
recycling is required for controlling the maximal temperature, is proposed for reducing
the heat exchange area and/or the recycling power requirements.
The concept is
demonstrated in the context of an HRSG of a pressurized oxy-coal combustion process,
where the hot flue gas entering the HRSG is diluted by recycled flue gas to comply
with the temperature constraint. The split concept proposes splitting the hot flue gas
prior to dilution, and introducing the splitted fraction, with or without a secondary
recycling stream, at an intermediate point in the HRSG. As a result, the split allows
for lower recycling power requirements (lower diluent flowrate) and a smaller heat
exchange area because the average temperature difference between the hot and cold
streams in the heat exchanger is increased. Multi-objective optimization, for area and
177
power requirements, is performed and the Pareto front is constructed. Results include
a reduction by 37% without a change in the compensation power requirements, or a
decrease in the power requirements by 18% (corresponding to 0.15 percentage points
in cycle efficiency increase) while simultaneously reducing the area by 12%.
5.2
Motivation
Reducing the capital cost and/or increasing the efficiency of power generation is
highly desirable especially given the ever growing market of electric power [36]. Besides economic concerns, efficiency in power generation is also important because the
dominating majority of electric energy production is from non-renewable fossil fuels, and there are increasing concerns and regulations regarding their emissions, [37].
Flexibility to uncertain parameters, like fuel specifications, ambient conditions, and
thermal load is another important characteristic required from the implemented technologies.
In thermal power generation there are several forms of unavoidable losses as well
as several operational constraints and economic considerations. For example, the area
of heat exchangers areas are limited by capital cost consideration, resulting in less
effective heat transfer and/or larger pressure drops of the streams due to the packed
and constrained pathways; thus, the efficiency of the cycle decreases.
Metallurgic
properties pose temperature constraints on combustors, boilers, heat recovery steam
generators (HRSG), turbines, etc., [40, 22], thus resulting in exergy destruction and
reduction of power output. For example, flue gas recycling (FGR) in coal boilers is
required in order to quench the combustion gas to limit the radiative-dominant (high
temperature) heat transfer regiment and enables a convective-dominant heat transfer;
FGR is applied because radiation is more expensive than convection for the same
degree of thermal energy transfer, [65]. FGR also increases the boiler efficiency and
178
reduces emissions, and is applied in almost all relatively recent (younger than 30 years
old) coal fired powerplants, [65, 66]. The FGR require compression to compensate for
losses in the boiler and the recycling pipes; moreover, throughout the heat exchange
process, the temperature gradient between the hot and cold streams decreases as flue
gas moves from away from the inlet, which increases the heat exchange area required
close to the cold end of the heat exchanger.
One of the promising concepts of carbon-capture and sequestration is pressurized
oxy-coal combustion (OCC). Pressurizing the flue gas increases the effectiveness of
the convective heat transfer. In [20, 21, 23, 25, 24, 27, 38, 35, 67] and Chapters 2-4, a
pressurized OCC concept is considered with an HRSG with relatively high FGR that
relies on convective heat transfer. Note that in general the combustion process occurs
in a section, that may or may not be physically connected to the HRSG, referred to
as a combustor. The capital cost of the HRSG is a relatively large portion of the
capital cost of the powerplant, e.g., [68], and reducing its size results in significant
savings.
Herein, a novel split concept for the HRSG is introduced in order to enhance the
rate of thermal energy transfer by increasing the average temperature between the
involved streams, and reduce the compression requirements by reducing the recycling
flow rates and/or pressure losses compared to the conventional operation. The concept
is applicable to coal boilers and other heat exchange processes that require quenching
of the hot fluid. Section 5.3 applies the concept to a standalone model of an HRSG of
the aforementioned pressurized OCC. Section 5.4 deals with minimizing the area of
the exchanger and the compensation power requirements while keeping fixed the input
streams conditions and the total transferred thermal energy. A detailed explanation of
the two objectives, variables, and constraints are presented, and the Pareto front of the
multi-objective optimization is constructed. The results are discussed in Section 5.5,
where the Pareto front illustrates the achievable reductions in the area and power
179
requirements, allowing for lower capital costs and/or higher efficiencies. Section 5.6
shows that the split concept preserves the ideal flexibility of the pressurized OCC
process.
5.3
5.3.1
Novel Split Concept
Concept Description
Figure 5-1 illustrates the split concept applied to the HRSG of a pressurized OCC
process, [24, 27, 38, 35, 67] and Chapters 2-4. In pressurized OCC, oxygen is delivered
to the combustor at an elevated pressure. Primary recycling flue gas, FG-Rec-pri,
is mixed with the oxygen stream for dilution in order to control the temperature
of the combustor to acceptable levels, [40]; a temperature of 1550*C is considered
here. Combustion gas is mixed with secondary recycling flue gas, FG-Rec-sec, to
achieve an acceptable temperature at the entry of the HRSG. In the HRSG, thermal
energy is transferred to the working fluid of a Rankine cycle. Flue gas is recycled for
controlling the critical temperature of the combustors and the HRSG in two possible
configurations, wet or dry recycling. In wet recycling flue gas is recycled directly
after the HRSG exit, while in dry recycling flue gas is recycled after condensing and
separating the water. Figure 5-1 illustrates the wet recycling case, but the split design
can be equivalently applied to dry recycling. Recycling fans are used to compensate
for the pressure losses encountered by the flue gas mainly in the HRSG and the
recycling pipes.
The concept proposes splitting the hot combustion gas prior to its dilution by the
secondary recycling stream. The flue gas entering the HRSG decreases in temperature as it exchanges thermal energy with the working fluid of the Rankine cycle; flue
gas acid condensation in the HRSG is not allowed as discussed later in the operation
constraints, Section 5.4.3. In essence, the mixing of the splitted stream in the HRSG
180
is intended to elevate the flue gas temperature. The primary flue gas is mixed with a
recycling stream similar to the HRSG without splitting. The splitted flue gas is (potentially) mixed with another secondary recycling stream. The secondary recycling to
the split allows larger ranges and larger feasible combinations of the mixing positions
and the mixing temperatures. The specific amount of recycling to the split, if any,
is determined by optimization. The results in Section 5.5 demonstrate that minimal
area does not require any recycling to the split, whereas minimal compensation power
requirements requires. The additional split pipe, the pipe of the recycling to the split
(if used), and the recycling to the split recycling fan (if used) add some capital cost,
however, it is insignificant compared to the savings in the HRSG. Note that even
when two recycling streams are used, a single fan can be installed by introducing
some throttling at the outlet of the split recycling stream; obviously this results in
higher compensation power requirements. For a given HRSG thermal load, the splitting process can increase the overall temperature difference between the streams of
the exchanger, particularly avoiding small temperature differences which require the
most heat transfer area. Moreover, the split allows for lower rates of recycled flue
gas compared to regular HRSG: the required amount of recycling to the inlet of the
HRSG is smaller because it needs to dilute a smaller amount of the combustion gas.
Also, at the mixing position, the flue gas within the HRSG acts as a diluent to the
split stream, thus a relatively small amount of the recycling to the split is required
(if any).
The higher average temperature differences imply smaller exchanger area, and
the lower recycling requirements imply lower pressure drops and lower compensation
power requirements (CPR). The CPR consists of two components; the first is the
power needed by the recycling fans to re-pressurize the recycling streams to compensate for the pressure losses encountered in the HRSG and the recycling pipes. The
second component of the CPR is the power needed to maintain the main flue gas
181
FG-Rec-pri
to combustor
TMix
FW-HRSG-in
Rec-FanO
Combustion
Split
Hot- as
'Ht
GsGaso
T
FG-Rec-sc
c-s rr 0
FG-R
Reheat
plte r
Tempe~r.'0
th
91jt
~~Controller
Thermal
ool-Gas
a
WRvynC
F-cr
plit
basi
-Rec-sec 1
Split-Rec
Rec-Fani
Mixerl1c
Mixm
ecl
Figure 5-1: HRSG single-split as part of a pressurized OCC process with a thermal
recovery unit. Optimization variables in purple circles marked with (o). Constraints
are on the maximum allowed temperature in the HRSG and safety margins against
acid condensation.
flow as it faces pressure losses while passing through the HRSG, Section 5.4.1. For
simplicity, only one split is illustrated and tested here. Multiple splits, that would
be introduced sequentially at different intermediate locations, are possible and would
further increase performance and decrease the heat transfer area, but would add
structural complexity. Note that in general the split can be extracted from any point
along the HRSG and not limited to the inlet combustion gas, and the recycling can
also be withdrawn from any point along the HRSG and not limited to the outlet CoolGas; however, such processes are less practical to implement and more complicated
to model and optimize.
5.3.2
to CS
FG-Rcvry nRecovery
split
TiX
-Rcvry-out
Stand Alone HRSG-Split Simulation
To illustrate the possible advantages, Figure 5-2 shows the profiles of four cases of
HRSG operation as a standalone unit with an identical set of input parameters.
182
ondensate
As shown in Table 5.1, the input parameters are the specifications of the hot and
the cold input streams, the outlet specifications of the cold stream, and fractional
thermal losses; the fixed specifications signify that the total amount of thermal energy
transferred in the HRSG is fixed.
Table 5.1 shows two sets of input parameters
as obtained from an optimized pressurized OCC with wet recycling, [35, 67] and
Chapters 3&4; the specifications titled CoalA are the operating conditions that the
HRSG encounters when the basecase OCC process utilizes a high quality coal, while
those titled CoalB are relevant to combusting a lower quality coal, where CoalA
and CoalB are identical to those utilized in [35] and Chapter 3. The specifications
titled CoalA are used here upto Section 5.5, and then for the flexibility assessment
(Section 5.6) both coals are used. Both sets of input specifications of the streams
are for the nominal full load operation. The cold stream profile is that of the main
feedwater and the reheat streams.
The maximum allowed HRSG temperature is
800*C equal to that considered in [24, 27, 38, 35, 67] and Chapters 2-4. Similar to the
basecase the HRSG is considered to face a 0.75% fractional heat duty losses. First,
note that in Figure 5-2 although the input streams specifications, CoalA specifications
of Table 5.1, and the total duty transfer in the HRSG are constant among all four
operations, the temperature of the flue gas at the exit of the HRSG, Cool-Gas, might
not be. The different pressure losses and recycling requirements for each operation
result in different CPR which causes different amounts of compression enthalpy rise
(CER) carried by the flue gas, [24, 27]; therefore, the temperature of the Cool-Gas
exiting the HRSG is slightly different between the four profiles.
The first profile in Figure 5-2 is without splitting or recycling, i.e., all the combustion gas enters the exchanger directly without dilution; this operation violates the
maximum temperature constraint on the HRSG, and is only shown for illustration.
The infeasible operation of Profilel theoretically requires the smallest heat exchanger
area due to the largest temperature differences between the hot and cold streams, and
183
requires zero recycling and zero second component of the CPR; (the CPR components
are described in Section 5.4.1).
The second profile in Figure 5-2 represents the standard basecase operation where
all the combustion gas is mixed with enough recycling to result in Hot-Gas entering
the HRSG at precisely the maximum allowed temperature. The flue gas temperature
then drops to the exit temperature as thermal energy is transferred to the working
fluid. The flue gas has approximately constant thermal capacity as inferred by the
nearly linear temperature profile versus thermal energy transferred.
A lower inlet
temperature for the Hot-Gas into the HRSG requires higher recycling flowrate, which
results in larger flue gas flowrates in the HRSG, a flatter temperature profile of the
hot stream, and smaller temperature differences between the streams of the HRSG. If
thermal energy transfer and pressure losses are independent of the flow conditions in
the HRSG, then lower inlet temperatures, leading to smaller temperature differences
and larger recycling flow rates, are clearly unfavorable regarding both exchanger area
and the CPR. However, as described in Section 5.4, the heat transfer, pressure losses,
and flow conditions of the flue gas are not independent, so larger flows and smaller
entry temperatures might be favorable in some cases, especially when CPR is of a
higher priority than area, since larger flowrates may contribute in smaller HRSG
pressure losses.
The third profile in Figure 5-2 represents a theoretical operation while respecting
the maximum temperature constraint; this graph is only given for illustrative purposes. The profile is achieved by an infinite number of splits, and an infinitesimal
recycling to the inlet required to decrease the temperature of the infinitesimal inlet
combustion gas from 1550'C to 800'C. The splitted combustion gas is introduced
infinitesimally into the HRSG maintaining for as long as possible a constant temperature equal to the maximum allowed. When all the combustion gas is introduced, the
temperature profile is only infinitesimally flatter than that of Profilel, and the two
184
profiles seem indistinguishable.
The fourth profile in Figure 5-2 represents an operation with a single split. First a
certain amount of combustion gas is split, and just enough recycling to the inlet of the
0
HRSG is used to obtain a Hot-Gas temperature of 800 C. The split is then introduced
to the HRSG without any recycling at a point where the resulting flue gas mixture in
0
the HRSG attains a temperature of 800 C. Compared to the conventional operation
of Profile2, the split can provide larger average temperature differences between the
steams of the HRSG, therefore, smaller areas. Moreover, lower recycling flowrates,
and possibly smaller CPR, are required since respecting the maximum temperature
constraints are attained not only by recycling but also by the gradual heat transfer
(note that pressure losses in the HRSG, which might increase, are another factor
in determining the CPR). Lower flue gas flowrates can also be inferred from the
steeper slopes of Profile4 compared to those of Profile2. Introducing the split further
downstream and/or adding recycling to the split, neither of which are shown here but
considered in later sections for optimization, result in a lower mixture temperature
inside the HRSG. Also, adding recycling to the split can allow earlier mixing positions
while satisfying the maximum temperature constraint.
It can be proven geometrically that for a given split flowrate, the largest temperature differences between the hot and cold streams are attained when the inlet and the
mixing temperatures are at the maximum allowed and when there is no recycling to
the split. Also, by comparing the slopes of the temperature profiles, it can be proven
that for any split flowrate, operating with the mixing temperatures at the maximum
possible value minimizes the flowrate of the recycling streams. It is tempting to say
that for a given split flowrate the least area requirements and the least recycling
requirements are obtained when the constraints on the maximum allowable temperatures are active; as the optimization shows, in fact the area is minimized when the
maximum temperature constraints are active, however, this is not always true for the
185
Mn.NIRW=Ok/,r~,N
,iswn=Ogs
50
Prfll
Profile1: Tuiw,0 = 1550* C, 7hsyntj = Okg/s, Tmi., =NA, 7hac.0 =
No Split, Constraint Violated
la=
1
400 --
Profile2: TMjO = 800*C, 7hspam = Okg/s, &.,I
Okg/s, 7hjz.
=NA, hR.,I =
Original operation
Okg/s
(1-1d) = ekg/S,
Profile3: imi.O = 800*C, 7sj,
Infenitesimal Splitting, e recycling to inlet
1
000 -
Profile4: fusj.0 =
Single
a
O*C, hsoit,
150kg/s, mi, = 800*C, rhRcj
Split
=NA
R,,O = e, he,
(,-,of
=
Ok
= Okg/s
0.
a
400
Cold streams (main Feed Water and Reheat streams) temperature profile common
among all four hot stream profiles
1
2M
1
2
1
4
1
3
1
5
HRSG Duty Transfer, QHRSC (W)
1
6
7
8
XO'
Figure 5-2: Temperature profiles of four different operations of the flue gas with identical cold streams profile (and heating duty requirement). Profilel has no recycling or
dilution and violates the maximum temperature constraints. Profile2 is the original
basecase operation. Profile3 has infinite number of split. Profile4 is an un-optimized
example of the flue gas with a single split, where the overall temperature differences
between the streams of the HRSG can be higher than the original operation, and the
recycling flowrates are lower.
CPR.
It also can be proven that any split operation with a certain total amount of recycling, regardless of the number of splits, the splits flowrates, or the mixing positions,
can at most reach the boarders outlined by a profile with no split and the same total
amount of recycling introduced all at once to the inlet; as an example Profile3 and
Profflel with an infinitesimal recycling to the inlet, respectively.
186
Table 5.1: Fixed input parameters for the HRSG. Two different flue gas
conditions are presented, each relevant to a different coal type. The conditions titled CoalA are used up to Section 5.5, and both the conditions of
CoalA and CoalB are used for the flexibility assessment of Section 5.6.
Input Parameter
Flue Gas Conditions
Combustion gas flowrate
Combustion gas temperature
Combustion gas pressure
Combustion gas mole fraction Composition
With CoalB
With CoalA
394kg/s
402kg/s
155b C
7.41bar
H2 0 = 0.479; 02
=0.030; N 2=0.008;
9.67bar
H 2 0 = 0.478; 02
=0.030; N 2 =0.009;
C0 2=0.457;
C0 2=0.458;
S0 2 =0.001;
S0 2 =0.001;
AR=0.024;
800 0 C
AR=0.025;
Maximum allowed HRSG
temperature
HRSG fractional heat loss
Flue Gas flowrate to recovery unit
Feedwater and Reheat Conditions
Feedwater flowrate
Feedwater inlet temperature
Feedwater inlet pressure
Feedwater outlet temperature
Feedwater outlet pressure
Reheat flowrate
Reheat inlet temperature
Reheat inlet pressure
Reheat outlet temperature
Reheat outlet pressure
Compressors Specifications
Primary recycling fan
0.75%
120kg/s
132kg/s
306kg/s
322 0 C
301kg/s
322.0 0 C
265bar
600 0C
250bar
I
233kg/s
260kg/s
358OC
53.5bar
610 0 C
53. ibar
0.83
misentropic =
77mecbanical =
Thermal spec =
Secondary recycling fanO&1
nisentropic
=
7
7mechanical =
Thermal spec =
0.99
Adiabatic
0.90
Main stream compensation
77isentropic
compressor
?7mechanical =
Thermal spec
0.99
Adiabatic
0.8338
=
0.98
Adiabatic
5.4
Optimization Formulation for Minimal Area
and/or Minimal Compensation Power Requirements
5.4.1
Objective Functions
The purpose of the split is to reduce the capital cost by utilizing smaller surface
area of the heat exchanger and reduce the CPR by reducing pressure drops and/or
recycling flowrates. The two objectives are neither equivalent, nor mutually exclusive,
and have to be accounted for simultaneously; smaller exchangers in general lead to
larger pressure losses, and the flow properties affect the heat transfer coefficient, the
HRSG pressure drop, and the recycling losses. Herein, a multi-objective approach is
taken and the Pareto front, or set of non dominated solutions is obtained. This is
constructed using a weighted sum approach, [69], and hierarchic optimization, [44, 43],
as explained later.
Objective Functions Calculation
Computing the objectives is not trivial and herein, they are based on similarity analysis for calculating the area and pressure losses.
Area of the Heat Exchanger
The HRSG area is calculated according to the logarithmic mean temperature difference, and discretized heat exchanger (1000 elements). For each discretized region, i,
we have:
Aa,i
oa,i Ub,i Fb,i ATLM,
Abi
Qbi Uai Fai ATLM, a,i
b,i
where subscripts a and b stand for actual and basecase respectively. A is the area,
U is the equivalent heat transfer coefficient,
188
Q is the heat transfer duty, and F is its
correction factor.
Compensation Power Requirement, CPR
The CPR consists of two components: the first component of the CPR is the power
needed by the recycling fans to re-pressurize the recycling streams after experiencing
pressure losses from the HRSG and the recycling pipes. The second component is the
power needed to maintain the main gas flow and overcome the HRSG pressure losses.
The extra compression needed to overcome the main flow losses can be introduced
prior to combustion or after the HRSG. For example, in standard coal power plants,
the same fans or compressors that drive the inlet streams to the combustor force the
flow through the main stream pressure losses. But in pressurized OCC combustion,
since a compressor is already present after thermal recovery and needed for the carbon
sequestration unit (CSU), the compensation power requirement is less costly to be
accounted for by compressing a cooler stream with a lower flowrate post the thermal
recovery.
Similar to the basecase, the pressure loss of each recycling pipe, APpjp, is estimated by the following equations [62, 63]:
2
APipe = pf L V
where V is the bulk gas velocity in the pipe, d is the diameter of the pipe, Lp is
the equivalent length of the pipe, p is the gas density, and
f
is the friction factor
calculated by
-
fpipe
2.-20Olog
(2e/d)
_5.02
(2~)
7.4
where c is the pipe roughness, Rea
.2log
Red
PVd
-2
\
(2e/d) + 13
13
7.4
Red
is the Reynolds number based on the pipe
diameter and M is the dynamic viscosity of the gas. The pipe diameter, d, and the
189
where
gas velocity, V, are related by n = pVd,
is the recycled gas mass flowrate
fr
through each pipe. The diameters, d, and equivalent length of the each recycling pipe,
LP, are identical to those of the basecase, optimized results of [24, 27], where practical
and economic considerations and experimental data are incorporated in obtaining the
diameters and the equivalent length; therefore,
APipe,a
APpipe, b
Pa fa Lp, adb
_
2
Pb fb Lp, b da V
faaKPb
fbaPa
The subscripts a and b stand for actual and base-case, respectively. For deriving
the final equality in the above equation the gas mass flowrate is
ii
= L. Each split
adds a secondary recycling pipe and therefore for the single split considered here two
secondary recycling pipes are present, one to the inlet of the HRSG and the other
to the split at some intermediate point in the HRSG. Both secondary recycling pipes
are considered to have the same specifications, which is a conservative approximation
since the recycling pipe to the split may be shorter than that to the inlet.
The primary recycling is also considered but treated a little differently in order to
preserve the inlet combustion gas conditions for the stand alone model. The primary
pipe losses and compression requirements are evaluated for a free-open-end stream
without reintroducing that stream into the combustor that outputs the combustion
gas, which is considered as a fixed input parameter. This is intended to maintain
the inlet stream conditions of the stand alone model and reduces the simulation
complexity by eliminating the need to converge an additional outer-most recycling
stream. The pressure losses and power requirements of the free-open-end stream are
very close to those of a closed loop stream, less than 1% difference. Similarly, the
properties of the flue gas are not significantly different with the open-ended stream
in the standalone model compared to those when including the combustor.
basecase recycling conditions are: APpd
1 ,b
=
190
0.058bar, APse, b = 0.035bar,
The
Tpri, b =
281.lkg/s,
hsec, b
= 736.5kg/s, and the density of the flue gas at the exit of the
HRSG/inlet to recycling pipes is pb = 4.47kg/M 3
The pressure drop in the HRSG is more complicated to evaluate and is expressed
as, [62, 63]:
=
APHRSG
Npf
V2
max
2
where Vmax = V S$D is the maximum velocity between the tubes and V is the average face velocity [62]. N is the number of tube bundles/rows along the longitudinal
direction, and the constant parameters D and ST are the tube diameter and the
transverse pitch of the fixed design heat exchanger, respectively. The friction factor,
f, is a function of Reynold's number. All operating conditions considered herein result in high Reynold's numbers and thus an approximately constant friction factor.
Therefore,
APHRSG, a
APHRSG, b
NaPa 0 a
NbpbV
(5.1)
(5.
N is directly and linearly proportional to L, the length of the heat exchanger, by
a factor of 1/SL, where SL is the longitudinal pitch and is also constant for a fixed
design.
The heat exchanger surface area is A. = irD x W x
ST
x
-S,
SL
where H is the
height of the exchanger and H/ST represents the number of tubes in the transverse
direction.
W is the width of the exchanger which is also the length of the tubes
through which water/steam pass. Therefore A. = constant x AcL where A, = x 2 is
the HRSG cross sectional area when, for simplicity, a square cross section of side x
is assumed (H = W = x). Also Vo0 =
A.
r= xcpA. stant, therefore
threor
which implies
La
_rbPaAs,
Lb
-
aV, a
raPbAs, bVo, b
191
,,Vb
=
7rnbpaAs, aLb
and as a result
As, aP Vc0
APHRSG, a
APHRSG, b
As, bPb
arnb
0 , bra
The Reynolds number based on the hydraulic diameter Dh is given by ReDj
PVOD,
where Dh
=
p
Db = x = A=h
-Ae. For the square cross sectional area considered,
Weted Peremeter
C(M
VOP )1/
2
Reh "
which means that ~~ReDh
,b
-
Vi
VbP
0,
Reynolds number is approximately related to Nusselt number by
where Nu
=
hDh.
=
ReL,
,a
_
ReDh,
b
N
Ih~
h and K are the gas heat transfer coefficient and thermal conduc-
tivity respectively. h is usually the limiting factor in U and therefore for simplicity
can be considered comparable. Moreover, the other resistances of U are constant due
to the fixed parameter specifications of the stand alone model. Usually a = 0.8, [62].
This leads to
VO, 2
VO, b
a+1
_hc'kbanaSL1
2PaPb
hkaarhb 2LbPa
2
substituting in the pressure drop equation
APHRSG,
a
As, a
APHRSG,
b
As,
ha)
b (ha
60
Kb)
(Ila)2
Ka
\j#b/
6a
(-a")
\nb/
\PPa/
Where APHRSG, b=0.265bar. Two simplifying and justifiable approximations can
be used. Introducing the split does not require changing the internal design of the
heat exchanger. Therefore, the heat transfer coefficient on the gas side, h, and the
equivalent heat transfer coefficient, U, can be considered equal between the actual
and the basecase operations. Second, the logarithmic mean temperature difference
correction factor F, can also be considered constant. F is a function of the design
and the temperatures at the extremities of each discretization, but in the range of the
optimum temperatures obtained in the results, the correction factor is comparable to
that of the basecase. In fact, Fa is smaller than Fb prior to introducing the split so the
approximation of Fa = Fb contributes in an underestimation of the actual area prior
192
to mixing the split, but larger after introducing the split so the same approximation
contributes in an overestimation of the actual area post mixing of the split. Since
the optimization results in Section 5.5 show that the split is introduced closer to
the inlet than to the outlet of the exchanger, then the assumption of constant F is
conservative. Finally we can write the objective functions as follows:
Minimize the ratio of the actual area to that of the basecase:
1000 Aa,i
Aa,i
mi
Ab,i
Ab
ATLM,
a,i
-
b,i
Qb,i ATLM, a,i
and minimize the ratio of the actual compensation power requirements relative to
that of the basecase:
. CPRa s.t.:
mm
CPRb
CPRi
=
nRec-pri (h(TFRec-pri, PComb-Gas)
-
h(TCool-Gas, PComb-Gas
-
APHRSG
-
A
pipe pri))i
CPRpri, i
"
Rec-sec0 (h(TFG-Rec-seco, PComb-Gas) -
h(TCool-Gas,
Comb-Gas -
APHRSG
-
APpipe secO))i
APHRSG
-
APpipe seci
CPRseco, i
± ThRec-seci (h(TFG-Rec-sec1, PFG-HRSG)
-
h(Tool-Gas, PComb-Gas
-
CPRs.c, i
±
mRecov-out
(h(TCo2-OUt,
PCO2-0 t)
-
h(TRecov-out, PComb-Gas
-
APHRSG)).
CPR main flow, i
i E {a, b}
where h is the enthalpy of the flue gas. Note that the temperatures of the streams
exiting the compressors,TFGRec-pri & TFG-Rec-sec & TFG-ReC-seC1 & TCO2-0
1t,
are depen-
dent variables and defined by the respective streams entering each compressor and
the characteristics of the compressor. The pressure losses are:
APpipe, a
pa fa Lp, a db V
APpipe, b
Pb fb
2
Lp, b da Vb
193
fa
Tl
Pb
fb 72Pa
and
APHRSG,
a
APHRSG, b
5.4.2
_
As, aK
6a
6
"*a
+1Tha"a+1
6Ha
6
As, bKa".' 1"
ba [b
2(a-2)
Pb
2(a-2)
h
Ak+
mb
Pa
a
Optimization Variables
As aforementioned, a single split is considered herein. The independent decision variables are chosen to facilitate optimization, since they allow satisfying some constraints
by properly setting their ranges as shown in Section 5.4.3. Also, these variables are
considered the simplest to monitor and set to their desired values during operation.
The optimization variables are: (i) the split flowrate, riiht, 1 , (ii) the temperature at
the inlet of the HRSG, TMiX, 0, (iii) the flowrate of the recycling stream to the split,
7hRp, 1, (iv) and finally the temperature of the flue gas in the HRSG after introducing
the split, TMiX, 1. The variables are illustrated in Figure 5-1 and the ranges are defined
in Table 5.2.
Based on this choice of independent variables, important variables are now dependent. For example, the flowrate of the recycling stream to the inlet,
hRc, 0,
is
dependent once the split flowrate and the inlet temperatures are specified; i.e. the
stream entering the HRSG is fully specified. Further, the position of introducing
mixture of the split and its recycling in the heat exchanger, Mix-Pos=
befre mxng
is
dependent once the split flowrate, the flowrate of the recycling to the split, and the
mixing temperature are specified.
5.4.3
Optimization Constraints
The operation of the heat exchanger is subject to physical limitations. Introducing
the split provides better performance while still satisfying these constraints. The
temperatures of the streams inside the heat exchanger are a major concern. De194
Table 5.2: Optimization variables, their ranges and the basecase default values,
for a single split. Because most of the basecase variables values are far from the
optimum (zero split, no recycling to split, and no mixing within the exchanger),
several initial guesses are implemented in order to exclude suboptimal convergence.
The boundaries of the ranges of the temperature variables are set to avoid constraint violations. TMiX, o lower bound is set to the maximum temperature of the
cold streams, i.e., the reheat stream exiting the HRSG at 610'C; also, the upper
bound on mixing temperatures, TMix, O & TMix, 1, are set to the maximum allowable temperature in the HRSG 800'C; and the lower bound of TMiX, 1 is set to the
temperature of feedwater entering the HRSG 321.7 C.
Number
Variable
Range
Base-case and/or default value
1
rnSpliti
[0 - 300] kg/s
0/set to 100 kg/s
2
TMix, o
m ec, 1
[TFW, out
3
[0
-
600] kg/s
4
Tuix, 1
[TFW, in
-
THRSG,
-
THRSG, max] 'C
max]
800'C
THRsG, max =
N/A /0
0
C
N/A set to THRSG,
max =
800'C
fined by the metallurgic properties, the maximum temperature allowed in the HRSG
is limited to THRSG, max = 800'C. In essence, the constraint has to be satisfied at
every point within the heat exchanger; but because the temperature monotonically
decreases along the HRSG (apart from the mixing point), the constraint needs only
be imposed at the inlet and at the mixing position. For the addressed values of the
input streams, the temperature of the cold stream entering the HRSG is safely above
the acid condensation temperature of the flue gas, [24, 27], therefore, there is no need
to include constraints on the minimum allowed temperature for avoiding condensation of acids in the flue gas or on the feedwater tubes in the HRSG. In contrast,
it is beneficial to include constraints on the MITA to avoid temperature crossovers
and ensure a realistic operation. The physical limit on MITA is zero, but a value of
0.5'C is used to speed the optimization process. In other words, the intuition that
small MITAs are clearly undesirable since they result in huge area requirements, is
communicated to the optimizer. The results show that the constraint on MITA is not
active along the Pareto front and thus does not limit the minimum CPR operations,
195
or the Pareto front profile.
5.4.4
Pareto Front Construction
The two objective functions are dependent and accounted for simultaneously by finding the Pareto front curve. Optimization is performed by combining the two objectives
in a weighted sum approach with modifications. First, two independent optimization
runs are performed to determine the value of the minimum area ratio, min A and
minimum CPR ratio, min 8
, respectively. Then, two hierarchic optimization runs,
[44, 43], are performed to determine the two ends of the Pareto front, Point A and
Point B. Point A is a result of the hierarchic optimization that minimizes
CPRp
CPRb
sub-
ject to minimal area Aa. Point B is due to that of minimizing L subject to minimal
CPRa. The additional constraints are imposed with a tolerance of 0.01. Afterwards,
multi-variable optimization is performed using the weighted sum approach combining
both objectives in order to construct the intermediate points of the Pareto curve.
Fifty steps are used in the weighted sum, each with ten multi-start points. Figure 5-3
shows the Pareto front of the HRSG-split where the x-axis is the ratio of the actual
area to the basecase area,
basecase CPR,
CPR.
CPRb
, and the y-axis is the ratio of the actual CPR to the
For validation, 5000 additional simulation runs picked up from
a grid spanning the variable space are evaluated and 225 points close to the Pareto
front are shown in blue dots; all lie to the right and above the Pareto curve. The original no-split/zero-split flowrate basecase operation has the coordinates (1, 1) where
CPRbase = 8115kW.
5.5
Results
The Pareto front clearly shows the tradeoff between the two objectives:
a small
surface area results in a large pressure drop due to the flow constrictions. Starting
196
1.25
I
I
I
i
I
I
I
1.2
1.15
W0
1 .1
Point A
U 1.05F -7.
2
basecase
1
0 95F
0.9
- *Point B
0.85
0.8
0.7
0.8
0.9
1
1.1
Aactual/Abase
1.2
1.3
1.4
Figure 5-3: The ratio of the compensation power requirements versus the ratio of the
areas, both relative to the basecase operation. The Pareto front, obtained using discretized weighted sum approach, multi-start optimization in each step, and hierarchic
optimization, of the single-split HRSG is shown in the red dashed line. Additional
225 simulation runs are plotted in blue points. The basecase power requirement is
8.1MW for a net electric power output of 300MW.
from point A of coordinates (0.63, 1.05), as area increases the compensation power
requirements decrease rapidly at first since in the region of small areas the HRSG
pressure drop is the predominant form of loss. For further increase in the surface
area, the CPR decreases at a much smaller rate and becomes almost insensitive to
the area changes.
In the range of large surface areas the recycling pipes pressure
losses are predominant, and therefore the CPR are not noticeably effected by the
HRSG size. Beyond an area ratio of 0.88 the CP
cannot be reduced any lower than
0.82 leading to point B of coordinates (0.88, 0.82).
The range of variation in the
CPR for this HRSG contribute around 0.15 percentage points in the efficiency of the
powerplant. Larger savings in area and in CPR can be encountered depending on the
input parameters and operating conditions, as explained in Section 5.7.
The detailed results of the two ends of the Pareto front, points A and B are shown
in Table 5.3. Designing for the minimum area, Point A, requires the largest split
flowrate of all designs on the Pareto curve, rhSpiit, = 180kg/s, requires zero recycling to the split, mhR,,ci, and mixes the furthest away from the inlet, where the MixPos=Abefore
mixing
=0.173; the mixing position along the Pareto curve is always closer to
the inlet than to the outlet, therefore, the approximations considered in Section 5.4.1
are conservative. The large split ensures that the temperature of the flue gas within
the HRSG and at a point relatively far from the inlet is increased to the maximum
allowed, so that most of the HRSG is operating with large temperature differences
between the hot and cold streams. Dilution by recycling is minimal in order to maintain the largest temperature gradients, but results in low flue gas flowrates leading to
the largest HRSG pressure drop, and therefore the largest CPR. For higher area on
the Pareto front, the split flowrate decreases and mixes closer to the inlet. Lower split
flowrate requires higher recycling to the inlet which increases the flowrate of the flue
gas in the HRSG and reduces the HRSG pressure drop. The area increases because a
smaller portion of the HRSG is operating with large temperature differences between
198
the hot and the cold streams, while the CPR decreases because a larger portion of
the HRSG is operating with larger flue gas flowrates. With further emphasis on the
CPR, the recycling to the split increases in order to increase the flue gas flowrate in
the HRSG. Note that the recycling to the split requires just enough compensation
power to achieve the pressure of the flue gas at the mixing position which is slightly
less than that of the HOT-Gas entering the HRSG at the inlet, and this is why the
mixing position is close to but not exactly at the inlet of the HRSG. On the Pareto
front, Point B has the smallest split flowrate, the smallest mixing position, and the
largest recycling to the split.
For this specific study, all the Pareto optimal designs and operations have both
mixing temperatures at the upper bound; i.e., the constraints on the maximum HRSG
temperatures are active.
Larger mixing temperatures result in larger temperature
differences between the stream of the HRSG and in lower recycling flowrates, helping
minimize both objectives. This is in general not true; based on the similarity analysis,
the HRSG pressure drop is inversely proportional to the flue gas flowrate.
Other
values of the input parameters of the HRSG-split result in Pareto optimal points that
do not have the maximum temperature constraints active particularly at large weights
for the
CPR,;
increasing the flowrate of the flue gas in the HRSG, mha, by increasing
dilution from recycling, reduces the pressure losses in HRSG at the expense of the
streams' temperature difference, thus reduces the CPR at the expense of the area.
These results are not shown here for conciseness.
5.6
Flexibility to Uncertainties
The operation of a power plant is subject to several uncertainties, and without optimizing for a flexible design the performance of the process can suffer significantly,
[35, 67] and Chapters
3&4. The basecase of this study, pressurized OCC process
199
Table 5.3: Optimization results for the operating conditions of streams resulting from the
combustion of CoalA
Variable
C
CMh
Basecase
Design A
Design B
1
1
0.63
1.05
0.88
0.82
180kg/s
91.8kg/s
800 0C THRSG, max
169kg/s
800 C THRSG, max
Independent Variables
nSplit1
TMix, O
rnRec, 1
TMix,
1
0kg/s
800 0C
NA
NA
8000C
THRsG,
max
Okg/s
800'C = THRsG,
max
Key Dependent Variables
rhRec,
o
Mix-Pos (
m")
mibU"o )
ATOtal
APHRSG, before mixing
APHRSG,
after mixing
APpri pipe
737kg/s
NA
NA/Obar
0.265bar= APHRSG,
0.058bar
total
411kg/s
0.173
0.119bar
0.321bar
0.055bar
570kg/s
0.003
0.001bar
0.231bar
0.054bar
APsec pipeO
0.035bar
0.011bar
0.013bar
APsec pipel
NA
NA/Obar
0.001bar
utilizing the standard HRSG design, is ideally flexible to fuel specifications and thermal load, [35, 67] and Chapters 3&4. It is demonstrated here that the HRSG split
concept also has this favorable property. A change in coal is addressed here because
among the uncertainties mentioned, the variations in coal have the largest effect on
the streams of the HRSG. Therefore, designing for coal flexibility seems most challenging. Also, design for variable load flexibility pertains more to the expansion line,
regeneration, and heat recovery sections rather than the HRSG.
A coal powerplant utilizes different types of coals during its lifetime. The advantages of the split concept are not limited to the type of coal used; for any coal utilized
for power generation, the HRSG-split can be designed accordingly in order to reduce
the area and/or the CPR. Since during the operation of the powerplant the utilized
coal is expected to change, it is extremely important that the optimal design of the
HRSG-split for one coal is flexible to changing the coal; i.e., the design is also optimal
200
for the other coal.
Assessing the flexibility of the HRSG-split in general requires characterizing the
variables as design or operation variables, [35, 67] and Chapters 3&4. Design variables are fixed upon design while operation variables can change with the different
operations of the HRSG. The four independent variables chosen in Section 5.4.2 for
the optimization of the standalone HRSG-split, TMIxo, Thspliti, TMIxi, & rhRecl, are
all operation variables. However, dependent variables of the standalone model, in
particular the split mixing position, Mix-Pos, and the resulting HRSG area, A, are
design variables and have to be common between the different operations. Luckily,
based on the following approach, there is no need to reformulate the problem to include design variables as decision variables, which pose a lot of difficulties in solving
for the objective function which would require complicated numerical methods, and
result in large domains of infeasible operations.
The ideal flexibility is demonstrated herein by a much simpler approach; the same
optimization above is performed on a standalone HRSG-split but with the a new
specifications of the input streams which are relevant to a coal different from the
original. The input streams specifications used above are a result of the pressurized
OCC process designed for ideal flexibility to uncertainties when operating with a
typical bituminous coal with composition similar to Venezuelan and Indonesian coals
(referred to as CoalA), while the new streams' specifications result from operating
with a lower quality south African coal almost identical to Douglas Premium or
Kleincopje coal (referred to as CoalB), as presented in [35] and Chapter 3. The multiobjective optimization of the HRSG-split operating with the streams conditions of
CoalB results in a Pareto front curve very similar to that seen for HRSG-split multiobjective optimization (presented above) operating with the conditions of CoalA.
More specifically, equal areas on the two Pareto fronts have identical mixing positions,
therefore, a given Pareto optimal design of the HRSG-split for one coal is also a
201
Pareto optimal design for the second, therefore, the HRSG is thermodynamically
ideally flexible. Moreover, equal areas between the original and new Pareto curves
are a result of equal weight vectors for the multi-objective optimization, therefore,
the HRSG-split is also economically ideally flexible; determining the most profitable
design does not require to consider the coal distribution because any optimal design
for one operation is optimal for the other, and has the same tendencies/preferences
towards each of the two objectives. A similar behavior to that of the coal variation
is encountered for the other uncertainties. As a conclusion, the HRSG-split is ideally
flexible to uncertainties, and at least capable of maintaining the flexibility of the
process it is incorporated in.
5.7
Other Applications
The application of the HRSG-split is not limited to the OCC process. The split concept can be applied to any heat exchange process that requires a recycling stream to
control the temperature of the main stream; for example, in conventional boilers, both
the FGR rates and the heat exchange area, particularly radiative, can be reduced.
The concept can be readily applied to new power plants; moreover, the retrofit of
existing plants is conceivable.
Although not shown here, the benefits of the HRSG-split in subcritical power
cycles can have larger magnitudes than those obtained here for a supercritical. Recall
that the smaller the temperature differences between the streams, the larger the area
required for the same amount of heat transfer, and therefore, the exchanger area is
directly related to the value of the MITA. In the case study above, the feedwater
conditions are those from an optimized supercritical Rankine cycle, where the pinch
in the HRSG is located at the cold end; the feedwater temperature entering the
HRSG is relatively large, by utilizing the FWHs regeneration, allowing higher rates
202
of feedwater through the HRSG while respecting the MITA specifications, and thus
larger flowrates through the expansion line to increase the power output and efficiency.
Since the pinch is at the cold end, introducing the HRSG-split cannot avoid the pinch
because the flue gas temperature at the exit of the HRSG varies only slightly due to
the variations in the CPR. Also, the feedwater temperature profile in the HRSG is
smooth due to the absence of phase transitions. On the other hand, with subcritical
feedwater, the transition from the subcooled liquid state to the two-phase state is
marked by a sharp kink, and usually the pinch point occurs at that location rather
than at the cold end. Since in an HRSG-split the temperature of the flue gas after
mixing is larger than that of the basecase operation, except very close to the exit of
the HRSG where the temperature might be slightly lower depending on the CPR,
then the temperature difference at the location of the pinch is larger than that of the
basecase. Now since in subcritical operations the pinch is alleviated, the reduction in
area and pressure losses are significantly larger compared to the supercritcal scenario.
Note that the increase in the temperature approach due to the split in the subcritical
process allows, upon process optimization, for even larger feedwater flowrate through
the HRSG which increases the power output and the efficiency; i.e., compared to
the supercritical scenario, in a subcritical process the savings on area and CPR are
larger, and there is a possibility of increased power output and further increase in the
efficiency.
5.8
Conclusion
A new split concept applicable to heat exchangers that require recycling of the hot
stream for temperature control, e.g., coal boilers and HRSGs, is presented herein.
The concept proposes splitting the hot stream, which has a temperature higher than
that allowed in the heat exchanger, before its dilution and its introduction into the
203
heat exchanger. At the inlet of the flue gas, a lower amount of dilution is required
to control the temperature of the now smaller fluid flowrate. The splitted fraction
is then introduced into the heat exchanger at an intermediate point downstream,
increasing the temperature of the hot stream and enhancing the temperature gradient
of the heat exchange process. The concept is able to reduce the cost by reducing the
area requirements and/or increase the efficiency by decreasing the power required to
compensate for the pressure losses of the flue gas. The concept is illustrated in a
standalone model of an HRSG in the context of a pressurized oxy-coal combustion
process. Multi-objective optimization is performed by constructing the Pareto front
of minimal area and minimal power requirements.
Both the heat exchange area
and the compensation power requirements are shown to be reduced compared to the
conventional operation; in the illustrated case, the area can be reduced down to 0.63
the original size, and the compensation power requirements can be reduced down to
0.82 the original requirements. The design and operation is not limited to new heat
exchangers and retrofitting is considered easily possible because no changes in the
internal structure of the heat exchanger is required.
Moreover, facing uncertainty in input parameters and operating conditions, the
split concept is shown to be ideally flexible and preserves the flexibility of the process
it belongs to.
Herein, the heat exchange process is enhanced by a slight modification to the
design of heat exchanger while holding the input streams and the total transferred
thermal energy constant. However, the input streams to the exchanger are variables
of the process it belongs to. Therefore, the overall performance of the process and
the performance of the HRSG and the capital cost savings can be enhanced by simultaneous optimization of the HRSG-Split and the powerplant deign.
204
Appendices
205
206
Appendix A
Reaction Chemistry Added to the
Separation Column in the DCSC
flowsheet
A set of reactions are implemented in the Separation Column chemistry in order
to properly evaluate the behavior of the condensates in involved streams.
Of the
elaborate and relatively large set of possible reactions, only a few are show to be
influential to the scope and assessments of the current work. Table A. 1 presents those
important reactions where their equilibrium constants are evaluated using Gibbs free
energy.
207
Table A.1: The relevant reaction added to Separation Column of the DCSC flowsheet
Stoichiometry
N20 4
Reaction type
Equilibrium
Equilibrium
Equilibrium
Equilibrium
Salt
Salt
Salt
2 NO 2
SO 2 + NO 2
-
SO 3 + H 2 0
H 2 SO4
HSO- + H2 0
Na 2 SO 4
Na 2 SO 4 .(H2 0)10
Na 2 SO 4 .NaOH
SO 3 + NO
-
SO2- + H3 0+
2 Na++ SO2 Na++ SO- + 10 H 2 0
3 Na + SO2- + OH
Appendix B
DCSC Recirculation Water,
rnRW-Sep-in, Optimality Criterion
The optimization of the DCSC flowsheet can be simplified by manipulating the recirculating water flowrate to obtain a balanced DCSC-HX. The criterion is justified
after two observations.
First, the temperature of the bottom stage of the separa-
tion column, which is equal to the temperature of the recirculating water exiting
the column (RW-Sep-out), is highly insensitive to the flowrate and the temperature
of the recirculating water entering the top stage (RW-Sep-in).
For example a 50%
change in flowrate, and/or temperature, in 'C, of the RW-Sep-in results in less than
a 0.01% change in the temperature, in 'C, of the bottom stage/the temperature of
RW-Sep-out.
The bottom stage temperature is almost only dependent on the flue
gas entering the separation column (FG-Sep-in) conditions particularly pressure and
constituents because they define the temperature at which water in the flue gas is
transitioning from vapor to liquid. Second, the temperature of the top stage which is
equal to the temperature of the flue gas exiting the separation column (FG-Sep-out),
decreases with the decrease in the temperature and/or increase in the flowrate of
RW-Sep-in; the effect of the RW-Sep-in temperature on the temperature of the top
209
stage is significantly larger than that of the stream's flowrate. On average, within
the practical ranges of operation, a 10% change in TRw-Sep-in, in 'C, results in around
5% change in the top stage temperature, in 'C, while a 10% change in
RW-Ser-in,
in kg/s, results in a 3% change in the stage's temperature, in 'C. Analyzing the top
stage temperature is needed since the amount of thermal energy transferred from the
flue gas to the recirculating water and the amount of the water condensed increase
with the decrease in the temperature of FG-Sep-out (and vice versa).
The criterion proposed herein is to have the thermal capacity rate of the recirculating water entering DCSC-HX, i.e., stream RW-HX-in, equal to that of the working
fluid at that section (WF-HX-in), thereby obtaining a balanced heat exchanger. The
specific thermal capacities of the two streams are almost identical and neither are significantly affected by the temperature change encountered in the DCSC-HX, therefore, the principle is equivalent to matching the flowrates of the streams involved.
The criterion is proven by examining the flowrate and temperature of the splitter's
excess condensed water which is rejected outside the recirculating loop (Split-E-CW),
where a lower temperature and/or a larger flowrate of Split-E-CW signify larger recovery and thus better performance. The proof is performed in two parts; first, the
case where
i2RW-HX-in < nFW-HX-in
is considered and it is shown that an increase in
nRw-HX-in gives an increase in the recovered thermal energy and thus an improvement
in performance; second, the case where
rhRW-HX-in > mFW-HX-in is
considered and it
is shown that a decrease of nRW-HX-in is favorable. For each case, four general scenarios might occur, i.e., the flowrates of RW-Split-in and Split-E-CW can increase or
decrease. It will be shown that the flowrate of RW-HX-in should increase when it is
lower than that of WF-HX-in, and should decrease when it is higher.
First, in the region where the
mRW-HX-in
is less than
hFW-HX-in,
the pinch point
occurs at the cold end of the heat exchanger; recall that an initial criterion for optimality is for the heat exchanger to operate at the allowed MITA. In this domain,
210
increasing the rnRW-HX-in does not change the temperature of the recirculating water exiting the DCSC-HX i.e., the temperatures of Split-E-CW & RW-Sep-in.
As
rnRW-HX-in increases, the following four scenarios are conceivable, but only the last is
possible:
1. Both the flowrate of Split-E-CW and of RW-Sep-in decrease; this scenario violates the mass balance of the splitter and thus is not possible.
2. (&3.) The flowrate of Split-E-CW increases (decreases), and the flowrate of RWSep-in decreases (increases); this scenario leads to a contradiction. A decrease
(increase) in rnRWSep-in increases (decreases) the separation column top stage
temperature resulting in a higher (lower) temperature and water fraction of
FG-Sep-out. This means a smaller (larger) amount of water condensation which
contradicts with the larger (smaller)
rhsplit-ECW-
4. Both the flowrate of Split-E-CW and of RW-Sep-in increase; this is the only
remaining scenario out of the four general combinations and doesn't lead to
any contradictions.
The increased flowrate of RW-Sep-in, while having the
same temperature, increases the amount of condensed water in the separation
column which is in agreement with the increase in
mSpjit-E-CW.
Second, in the region where rnRW-HX-in > rnFW-HX-in, the pinch point occurs at the
hot end of the heat exchanger. Decreasing the flowrate of RW-HX-in decreases the
temperature of RW-Split-in, Split-E-CW, and RW-Sep-in. Again, four scenarios are
conceivable, but only one is possible:
1. Both the flowrate of Split-E-CW and of RW-Sep-in increase; this scenario violates the mass balance of the splitter and thus not possible.
2. The flowrate of Split-E-CW decrease, and the flowrate of RW-Sep-in increases;
this scenario leads to a contradiction. An increase in hRW-Sep-in and a decrease in
211
its temperature reduces the temperature of the separation column's top stage.
Therefore, the temperature and water fraction of FG-Sep-out decrease. This
means larger amount of water condensation in the separation column which
contradicts with the smaller amount of Split-E-CW.
The two remaining scenarios require first to show that
than
rnRW-HX-out
TRW-HX-Out
is more sensitive
with respect to a change in the flowrate of RW-HRSG-in.
First
consider the energy balance on the hot stream of the DCSC-HX neglecting pressure
effects:
nRW-HX-inCp (TRW-HX-in - TRW-HX-out) :
Consider a fixed cycle operation and thus a constant
notation, differentiate relative to
TiRW-HX-in,
QDCSC-HX
QDCSC-HX-
With an abuse of
then multiply by drhRW-HX-in to get:
dIRW-HX-inCp (TR-HX-in - TRW-HX-out) + rRW-HX-incp d(TRW-HX-in - TR-HX-out) = 0
Assuming a constant c, and rearranging:
dhRW-HX-in
mRW-HX-in
_
d(TRW-HX-in
-
TRW-HX-out)
(TRW-HX-in - TRW-HX-out)
keeping in mind that TRW-HX-in is equal to the temperature of the bottom stage of the
separation column, which as discussed is independent of the flowrate of RW-Sep-in.
Finally rearrange and divide by
dTRW-HX-out
TRW-HX-out
_
TRW-HX-out:
TRW-HX-in
- TRW-HX-out
TRW-HX-out
drhRW-HX-in
mRW-HX-in
Considering that all temperature are given in 'C, TRW-HX-.Out is less than (TRW-HX-in - TRW-HX-out),
so the percentage change in the temperature, in 'C, of RW-HX-out is larger than the
percentage change of its flowrate, in kg/s (rhRW-HX-in
212
= TnRW-HX-out).
3. Both the flowrates of Split-E-CW and of RW-Sep-in decrease; this scenario leads
to a contradiction. The percent decrease in TRW-Ser-in (equal to TRw-split-in/TRw-HX-out
is larger than the percent decrease in rnRWSep-in, with the former being more effective in changing the temperature and vapor fraction of FG-Sep-out than the
latter as discussed above. Therefore, in this scenario, the temperature and water
fraction of FG-Sep-out decrease. This means larger amount of water condensation in the separation column which contradicts with the smaller Split-E-CW;
thus this scenario is not possible.
4. The flowrate of Split-E-CW increases, and the flowrate of RW-Sep-in decreases;
this is the only remaining scenario and doesn't lead to any contradictions. The
decrease in
TRW-Sep-in
reduces the temperature of FG-Sep-out despite the for-
mer' s decrease in flowrate (percent change of flowrate is singificantly smaller
than the change in temperature and has significantly smaller effect even for the
same percent change). Therefore, the amount of condensed water from the flue
gas increases, which is in agreement with the increase of Split-E-CW.
In conclusion, the largest amount of thermal recovery occurs when the stream flowrates
at the DCSC-HX are matched.
213
214
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