.
':"
Supplementary
Notes for
Chapter 14 Energy and Power Production,
Conversion, and Efficiency
1. Fundamental principles
-energy conservation
and the 1 stLaw of thermodynamics
-entropy production and the 2nd Law of thermodynamics
-reversible Carnot heat engines
-maximum work I availability I exergy concepts
2. Efficiencies
-mechanical device efficiency for turbines and pumps
-heat exchange efficiency
-Carnot efficiency
..
-cycle efficiency
-fuel efficiency
-utilization efficiency
3. Ideal cycles
-CarnQt with fixed THand Tc
-Carnot with variable TH and fixed Tc
-Ideal Brayton with variable THand Tc
"
4. Practical power cycles
-an approach to Carnotizing cycles
-Rankine cycles with condensing steam or organic working fluids
-sub and supercritical operation
-feed water heating
-with reheat
-Brayton non-condensing gas turbine cycles
-Combined gas turbine and steam Rankine cycles
-Topping and bottoming and dual cycles
-Otto and diesel cycles for internal combustion engines
5. Examples of power conversion using a natural gas or methane energy source
-sub-critical Rankine cycle
-gas turbine open Brayton cycle
-combined gas turbine steam Rankine cycle
-electrochemical fuel cell
-,
.."
..
r!!~r;'.~":
For further information, refer to:
1.
Milora, S.L. and Tester, J.W. GeothermalEnergyas a Source of Electric
Power. Cambridge, MA: MIT Press, 1976, especiallychapters 3-5.
2.
Balje, C.E. Turbomachines. New York: John Wiley and Sons, 1981.
3.
Balje, C.E. Journal of Engineeringfor Power, AS ME Transactions 84(1), 83,
January 1962.
,
Power Cycles
1.
Rankine Cycle Limitations
-utilization
vs. cycle efficiency (11uvs. 11c)
-"Carnotizing"
to approach 2nd law limit of performance
-mechanical
component efficiencies 11
t , 11
~ < 1 for turbines and feed pumps
(effect of moisture to decreaseefficiency)
-heat
transfer irreversibilities (AT> 0 in primary heat exchangerand
condenser)
-materials
limitations (metallurgical limit for steel in steam Rankine cycle
600°C (1100°F)
2.
Improvement to Rankine Cycle (fossil or nuclear-fired)
-reheat
-supercritical
-decrease
vs. subcritical operation with steam
turbine exhaust pressure/condensingtemperature
--~--~-~--
_f~::':'"
.
-regenerative
feed water heating/interstage moisture extraction
-topping
and bottoming cycles using non-aqueousfluids
(topping -Hg, Cs, K; bottoming -NH3, halocarbons)
-combined
3.
cycles (gas turbine cycle linked to steam cycle)
Power Generation with Low TemperatureHeat So~es (solar, geothennal, etc.)
-cycle
configurations possible
-analysis
of single and multi-single flash systems
-single
(binary), sub- and supercritical cyclesusing non-aqueousworking fluids
-derived
thermodynamic property estimation from BOS, P/iquid,
p:;~ and C;
correlations
-effect
cycle pressure on performance with an R-115 and a 150°C resource
-irreversibility
-11u
vs. temperature for several fluids
-correlation
4.
of "degree of superheat" for optimal performance vs. C;lR
ThennodynamicAnaiysu of Fluid Flow in a Duct or Nozzle
-thermodynamic
-conversion
-sonic
5.
analysis of performance as function of turbine inlet pressure
analysis of fluid flow in a duct or nozzle
of KE into rotating shaft work
limitations in choked flow (pressure ratio, isentropic AH)
Turbine, Pump and CompressorSizingand Perfonnance
-Balje
analysis of performance (11 = ffNs' Ds, Re, Mal)
-generalized
-sizing
approach to turbine exhaustand requirements
figure of merit
2
\':~~;~r:;!_-
?~~:
.
Power Cycle Terminology
I
11
C=
cyC
ffi
e
e
.net
Clency
work
=
primary heat exchanged
net work
U ==-=­maximum possible work
11
AB = availability change = ill
Wnet
W max
=
W net
-
QH
Wnet
AB
-T oAS = Wmax
To = ultimate sink temperature for heat rejection
Po = ambient pressure
For emmpie,for geothermal.systems,
at steadystate
AB = AH-ToAS
I
Tgf'P gf
To'P 0
where
Tgf = geothermal fluid inlet temperature
P gf = geothermal fluid inlet pressure
As the cost of producing the geothermal fluid (drilling wells, etc.) increases relative to
the cost of the power conversion equipment itself (heat exchangers, turbines, pumps,
etc.), cycle operation at conditions approaching max 11uis favored. See Chapters 3 and 4
of Milora and Tester (1976) for further discussion.
3
"
~
'}~'~?:
c
200
R-717(NH3)
Qh
T 5Y5T E M
:;...:.:::::::.,
HO
..f:
15
.;
..
"
..;;:::
-
Turbine
~IOO
BOILER
(.)
Ws
t
Wp
*1
.I
Condensate return
pump
...
Wp.-
_.w
CONDENSATE
RETURN
PUMP
50
Qc
r
C'ONCt;NSER
0
T'-'.~S.I
'E
Boiler
-0
~
Condenser
5
10
15
*Y
Cp/R=
Hot
20 system
Cold system
Y-I
':::;:~:i:~:~
~:
'.::;:
General
Rankine Cycle Schematic
:
,.
.:;i:~::.. COLD
SYSTEM
Adapted from Tester, J. W. and Modell, Michael. Thermodynamics and Its Applications.
Upper Saddle River, NJ: Prentice Hall PTR, 1997, p. 606, Figure 14.7.
Figure 8.
Generalized correlation for the degree of superheat above the
critical temperature for optimum utilization of geothermal fluid
Image
by MITofOCW.
availability as
a function
ideal gas state reduced heat capacity.
Figure 1. General Rankine cycle schematic.
.
" ""c
,'::,
,~!~~~~~
"
1000
c
..
\
900
200
1000
800
900
SATURATED STEAM, HEAT REJECTION
TEMPERATURE = 26.7oC (BOOF)
.
R-717(NH3)
700
I
Maximum useful work (kW-sec/kg)
BOO
15
600
700
'"Ci
~
500
~
I
~
~
600
~
c:
~IOO
~400
0
-J
500
:J(.)
...
w
V)
:J
*1~
~300
...
SATURATED STEAM, HEAT
400
REJECTION
TEMPERATUf~E
= ~C.90C
-(120OF)
x
41:
~
200
300
50
100
SATURATED WATER, HEAT REJECTION
TEMPERATURE = 26.7oC (60°F)
200
0
0
100
50
100
150
200
250
o
Geothermal fluid temperature ( c)
0
0
0
SATURATED
WATER,
HEAT REJECTION
0
TEMPERATURE
10
15 f1200FI
Saturated5steam, heat rejection
temperature
4B.90C
50
o
26.7 c
*Y
oF)
100
(80
Cp/R=
150
48.9oc
GEOTHERMAL FLUID TEMPERATURE
Y-I
200
(120oF)
#
20
250
(OCI
Saturated water, heat rejection temperature
o
o
26.7 c (80 F)
48.9oc (120oF)
Availability or maximum useful work as a function of geothermal
fluid temperature.
Figure 2.
Availability or maximum useful work as a function of geothermal
Figure 8.
Generalized correlation for the degree of superheat above the
fluid
temperature.
critical
temperature for optimum utilization of geothermal fluid
Image
by MITofOCW.
availability as
a function
ideal gas state reduced heat capacity.
,.,
.
,
200
J
Supercritical Rankine Cycle
R-717(NH3)
Geofluid
B
15
1
SUPERCRITICAL RANKINE CYCLE
1
..
-
Temperature
)
~IOO
,
C
A
l.LJ
a:
E
::)
~
a:
D
~
NG
Enthalpy
I-
*1
Working
fluid
Cooling water
or air
l.LJ
C-
(.)
B
0
...
CO
Geofluid
50
Turbine
ENTHALPY
B
GEOFLUIO
TURBINE
B
Heat exchanger
HEAT
EXCHANGER
A
0
Production
0
well
Cooling water
or air
C
D
C
COOLI NG
Condenser
WATERORAI R
Desuperheater
,
0
E
Working
A
fluid
CONDENSER/
E
5
WORKING
FLUID
pump
*Y
PRODUCTION~
Cp/R=
WELL
PUMP
Reinjection
well
DESUPERHEATER
Feed
10
15
pump
ED PUMP
20
Y-I
REINJECTION WELL
Supercritical Rankine cycle operating state points on a temperature-enthalpy
(T-H) diagram.
/
Figure 8.
Generalized correlation for the degree of superheat above the
(
critical temperature for optimum utilization of geothermal fluid
Image
by MITofOCW.
availability as
a function
ideal gas state reduced heat capacity.
Figure 3.
SupercriticalRankinecycle operatingstatepoints on a temperatureenthalpy(T-H) diagram.
.
;
"
,
.~;~7'"
c
c:';;':
200
"
,.
R-717(NH3)
.'
Tgf
.'
15
" ..,.
�T
. 1
f
T,gf..I,- �T
" 19
'.
AT
I
Temperature
,," Tgf-L\T,
t
-.='c
.Q)
.
"
Qin
~IOO:
OJ
...
.Co
i
..Turbine
(.)
.expanslon
*1
...
Q) + �T + �T
T
0
1
2
E
..'.
...
.-
TO+6lj+h.T2
�T1
'.
T
Qout
�T2"~
50
T0
.
.Heat rejection
6Tz
TO
.
~ Qout
L-ot)
..
..
Coolant
.
0
Entropy
0
5
Turbine expansion
10
*Y
Cp/R=
Geothermal fluid cooling path
15
Entropy
Coolant
Y-I
~
20
Heat rejection
Supercritical heating path
Temperature-entropy (T-S) plot for an idealized or "Carnotized" power cycle. Note
that as �T1 and �T2 go to zero that maximum work output is achieved.
Figure 8.
Figure 4.
Generalized correlation for the degree of superheat above the
Temperature-entropy
(T -S)
plot forutilization
an idealized
or "Carnotized"
critical temperature for
optimum
of geothermal
fluid
Image
by
MIT
OCW.
power
cycle.as
Note
that asofAT
1 andgas
AT2
go toreduced
zero that
maximum
availability
a function
ideal
state
heat
capacity.
work output is achieved.
.~
" ""c
160
"
15oC
120
,~!~~~~~
B
P = 39.26 bar (569.4 psia)
Pr = 1.24
�u = 56.5%
B
�cycle = 9.0%
c
,'::,
A
P = 27.5 bar (398.9 psia)
Pr = 0.87
�u = 46.5%
140
c...",.
B
�cycle = 11.2%
C2FSCI
MW = 154.5 g/mol
Pc
Temperature (oC)
!~!~~~
20
uid
Liq
A
E
at
12
'Icycl.=90o;.
1
15
Pumping
C
T. =26.7. C
@
p. 39.26 bar (569.4 pslo)
A
R-717(NH3)
D
E
C
8
B
�cycle = 11.9%
.2
g-16
B
@
4J
(.)
I-
60
P=114.4bar (1659.2 psla)
14
P,=3.62
'1.=54.6 %
'Icyci. =10.6%
*1
12
A
1
0
50
D
~IOO
0
~
80
20
D
Pumping
!!
I
40
Condensation
�cycle = 10.6%
.u2 -
100
Pr=I.24
'1.=56.5 %
_112.'
'ICYCII-'
,.
P = 114.4 bar (1659.2 psia)
Pr = 3.62
�u = 54.6%
4
120
IIp = 80%
Chloropentofluoroethane
@
P=27.5 bar (398.9 psio)
F}=0.87
Condensation
'Iu=46.5 %
= 85% dry
Tgt=150.C
P = 80.1 bar (1161.8 psia)
6
Pr = 2.54
�u = 63.2%
I
140
llt
Evaporation
ing
He
16
14
0
160
.R-115
Su
pe
r
c
60
40
= 458 psia (32 bar)
10oC
200= 8GoG (175
T
goF )
80
C
C'
he
at
100
I
E
...
C
Condensation
D
Pumping
8
6
100
50
A
E
150
200
Condensation
Pumping
50
100
D
150
200
Enthalpy (J/g)
4
C2F5Cl 2
�t = 85% dry
�p = 80%
R-115 Chloropentafluoroethane
Tgf = 15.0o C
To = 26.7o C
MW = 154.5 g/mol
PC = 458 psia (32 bar)
TC = 80oC psia (175.9oF)
200
Enthalpy (JIg)
Geothermal
0 Fluid Cooling Path
Supercritical Heating Path
Turbine Expansion
Sensible Heat Rejection
0
5
10
*Y
Cp/R=
15
20
Y-Icycle for R-115 with a 150oC liquid
Approach to thermodynamically optimized Rankine
oF). Temperature-enthalpy
Figure
5
Approach
to rejection
thermodynamically
optimized
Rankine cycle for (T-H)
R-115
geothermal
fluid source
and heat
at 26.7oC (80
with
a
150°C
liquid
geothermal
fluid
source
and
heat
rejection
at
diagrams shown at different reduced cycle pressures.
26.7°C (80°F). Temperature-enthalpy (T -H) diagrams shown at
reduced
cycle pressures.
Adapted from Tester, J. W. anddifferent
Modell, Michae
l. Thermodynam
ics and Its Applications. Upper Saddle River, NJ: Prentice
Hall PTR,
1997,
p.
49,
F
i
g.
14.10.
Figure 8.
Generalized correlation for the degree of superheat above the
critical temperature for optimum utilization of geothermal fluid
Image
by MITofOCW.
availability as
a function
ideal gas state reduced heat capacity.
"
c
200
65
12
R-717(NH3)
I, Specific irreversibility (J/g)
10
R - 115 chloropentafluoroethane
T = 150oC geothermal fluid temperature
To = 26.7oC condensing temperature
15
9
8
7
6
5
55
50
20
45
18
40
16
14
-
12
~IOO
10
(.)
4
3
8
*1
...
6
2
IT, Total irreversibility (J/g)
11
�u, % of �B
60
4
1
2
50
0
0.8 0.9 1.0
1.5
2.0
2.5
3.0
Pr, reduced cycle pressure
Utilization factor
I0Heat rejection
0
I Pump
I Heat exchanger
5
10
I Turbine
15
3.5
4.0
5.0
0
I Total
20 I Residual fluid
*Y
Cp/R=
Y-I
Component irreversibility and �u as a function of reduced cycle pressure
for R-115 for the condition shown in the figure above.
Adapted from Tester, J. W. and Modell, Michael. Thermodynamics and Its Applications. Upper Saddle
River, NJ: Prentice Hall PTR, 1997, p. 613, Fig. 14.11.
Figure 8.
Generalized correlation for the degree of superheat above the
critical temperature for optimum utilization of geothermal fluid
Image
by MITofOCW.
availability as
a function
ideal gas state reduced heat capacity.
"
--~~:fi
c
.
200
R-717(NH3)
656
15
606
-~
Utilization efficiency �u (%)
!...5
55
~
-
~
>-
50
u5
Z
~IOO
~
~
lJ..
lJ..
454
w
(.)
*1
...
Z
0
~404
~
.R..R
.R
0
717 (NH3)
-115
-32
R- 22
6.
x
RC -318
R -114
.R
~
50
§353
-600 a
(ISOBUTANE)
Optimum
OPJIMUMThermodynamic
THERMODYNAMICPerformance
PERFORMANCE
o
oC
= 26.7
C
Tcond
To =T 16.7
= 16.7°C
T
= 267°C
0
cond.
�t =TI,85=%85%
�p TIp
= 80= %
80%
o
�T~Tplnch
C
pinch = 10
= 10°C
303
100
0
0
150
200
250
150
200
250
GEOTHERMAL
TEMPERATURE
(OC)
GeothermalFLUID
fluid temperature
(oC)
5
R - 717 (NH3)
RC - 318
10
15
R*Y
- 115
Cp/R=
R - 114
R - 32
Y-I
300
300
20
R - 22
R - 600a (Isobutane)
Utilization efficiency �u as a function of geothermal fluid (initial heat source)
temperature for optimum thermodynamic operating conditions.
Figure 8.
Figure 7.
Generalized correlation for the degree of superheat above the
critical temperature for optimum utilization of geothermal fluid
Utilization
asofOCW.
aideal
function
of geothermal
fluidcapacity.
(initial
Image
by11u
MIT
availabilityefficiency
as
a function
gas state
reduced heat
heat source) temperature for optimum thermodynamic operating
conditions.
" ""c
,'::,
,~!~~~~~
"
c
200
200
R - 717 (NH3)
R-717(NH3)
150
15
R - 22
R - 32
T* - Tc (oC)
-
100
~IOO
(.)
790
C*p /R
R - 600a
*1
...
R - 114
R - 115
50
50
0
00
0
RC - 318
5
5
10
C* *Y
/R =
P
10 �
15
15
20
20
Cp/R= � - 1
Y-I
Generalized correlation for the degree of superheat above the critical
temperature for optimum utilization of geothermal fluid availability as
a function of ideal gas state reduced heat capacity.
Figure 8.
Generalized correlation for the degree of superheat above the
critical temperature for optimum utilization of geothermal fluid
Image
by MITofOCW.
availability as
a function
ideal gas state reduced heat capacity.