Subcritical

1. ':"
.
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

2. -, .."
..
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 Engineering Power, AS ME Transactions 84(1), 83,
for
January 1962.
Power Cycles
1. Rankine Cycle Limitations
-utilization vs. cycle efficiency (11u 11c)
vs.
-"Carnotizing" to approach 2nd law limit of performance
-mechanical component efficiencies 11, 11 < 1 for turbines and feed pumps
t ~
(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 vs. subcritical operation with steam
-decrease turbine exhaust pressure/condensingtemperature
r!!~r;'.~":

3. --~--~-~-- _f~::':'"
.
-regenerative feed water heating/interstage moisture extraction
-topping and bottoming cycles using non-aqueousfluids
(topping -Hg, Cs, K; bottoming -NH3, halocarbons)
-combined cycles (gas turbine cycle linked to steam cycle)
3. 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, and C;
p:;~
correlations
-effect cycle pressure on performance with an R-115 and a 150°C resource
-irreversibility analysis of performance as function of turbine inlet pressure
-11u vs. temperature for several fluids
-correlation of "degree of superheat" for optimal performance vs. C;lR
4. ThennodynamicAnaiysu of Fluid Flow in a Duct or Nozzle
-thermodynamic analysis of fluid flow in a duct or nozzle
-conversion of KE into rotating shaft work
-sonic limitations in choked flow (pressure ratio, isentropic AH)
5. Turbine, Pump and CompressorSizingand Perfonnance
-Balje analysis of performance (11 = ffNs' Ds, Re, Mal)
-generalized approach to turbine exhaustand requirements
-sizing figure of merit
2

4. ':~~;~r:;!_- ?~~:
.
Power Cycle Terminology
I ffi .net work W net
11
C= cyC e e Clency = = -
primary heat exchanged QH
11
net work Wnet Wnet
U ==-=­
maximum possible work W max AB
AB = availability change = ill -T oAS = Wmax
To = ultimate sink temperature for heat rejection
Po = ambient pressure
For emmpie,for geothermal.systems, steadystate
at
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 11u favored. See Chapters 3 and 4
is
of Milora and Tester (1976) for further discussion.
3

5. " ~ '}~'~?:
c
200
R-717(NH3)
Qh
15 ..f: .;
:;...:.:::::::.,
HO
T 5Y5T E M ..
"
..;;:::
- Turbine
~IOO BOILER
Ws
(.)
Wp t
*1 Condensate return
.I
... pump
Wp.- _.w
~
CONDENSATE
50 RETURN
PUMP r T'-'.~S.I
'E
Qc C'ONCt;NSER
Boiler
-- Condenser
0
0 5 10 15 Hot system
20
*Y Cold system
Cp/R=
Y-I
General Rankine Cycle Schematic
:
.:;i:~::.. COLD
~:
SYSTEM
':::;:~:i:~:~
'.::;:
,.
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 MIT OCW.
availability as a function of ideal gas state reduced heat capacity.
Figure 1. General Rankine cycle schematic.

6. .
" ""c ,'::, ,~!~~~~~
"
c 1000
..
900
200
1000
800
900
SATURATED STEAM, HEAT REJECTION
TEMPERATURE = 26.7oC (BOOF)
. 700
R-717(NH3)
I
BOO
15
Maximum useful work (kW-sec/kg)
600
700
'"Ci
~
500
- ~
~
~
~
I
c:
600
~IOO
~400 0
-J 500
:J(.)
...
w
V)
:J
*1 ~300 SATURATED STEAM, HEAT
~ ... -(120OF)
x
400 REJECTION TEMPERATUf~E = ~C.90C
41:
~
200
300
50
100 SATURATED WATER, HEAT REJECTION
200 TEMPERATURE = 26.7oC (60°F)
0
0
100 50 100 150 200 250
o
Geothermal fluid temperature ( c)
SATURATED
WATER,
HEAT REJECTION
0 TEMPERATURE #
0 0 Saturated steam, heat rejection temperature f1200FI
5 10 15
4B.90C 20
0 50 26.7 co 100
*Y
(80oF) 48.9oc
150 (120oF)
200 250
Cp/R=
GEOTHERMAL FLUID TEMPERATURE (OCI
Y-I
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. for optimum utilization of geothermal fluid
critical temperature
Image by MIT OCW.
availability as a function of ideal gas state reduced heat capacity.

7. ,.,
. ,
200
J
Supercritical Rankine Cycle
R-717(NH3)
Geofluid
B
15
1 SUPERCRITICAL RANKINE CYCLE
)
Temperature
1
..
C B
- l.LJ
a:
::)
~
E
A
D
Working
~IOO a: fluid
l.LJ Cooling water
, C-
(.) or air
~ NG
I- Enthalpy 0
*1
...
CO
Turbine
Geofluid ENTHALPY
B C Cooling water
50
GEOFLUIO TURBINE or air
B
D C COOLI NG
Condenser
Heat exchanger WATERORAI R
Desuperheater
,
HEAT
EXCHANGER 0
A E CONDENSER/
DESUPERHEATER
Working
A E
Production
0 fluid Feed
well
0 5
WORKING pump PUMP 15
10
ED
20
PRODUCTION ~ pump
FLUID *Y
Cp/R=
WELL PUMP
Reinjection Y-I
well
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 MIT OCW.
availability as a function of ideal gas state reduced heat capacity.
Figure 3. Supercritical
Rankinecycle operatingstatepoints on a temperature-
enthalpy(T-H) diagram.

8. ; , .~;~7'"
"
.
c
200
"
,.
R-717(NH3)
Tgf
.' .'
" ..,.
15 �T1
'.
T,gf - �T1 9 f
..I,
"
.
AT
I
,," Tgf-LT, i "
- .
Temperature
Qin
t ~IOO:
..Turbine
OJ (.)
-.
='
c *1
.expanslon
... ...
T0 + �T1 + �T2
Q)
.Co E ...
..'. '. .
�T1
.Q) TO+6lj+h.T2 T
.- Qout
50 �T2"~ .Heat rejection .
T0
6Tz ~ Qout ..
TO L-ot) ..
Coolant
.
0 Entropy
0 5 10 15 20
Turbine expansion *Y Entropy
Coolant
~ Heat rejection
Cp/R=
Geothermal fluid cooling path Y-I 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. Generalized correlation for the degree of superheat above the
Figure 4. Temperature-entropy for -S) plot for an idealized geothermal fluid
critical temperature (T optimum utilization of or "Carnotized"
availability Image thatMIT AT1 and ATstate reduced heat capacity.
Note by as OCW.
power cycle.as a function of ideal gas 2 go to zero that maximum
work output is achieved.
c:';;':

9. .~ c...",.
" ""c ,'::, ,~!~~~~~
160 A B
P = 27.5 bar (398.9 psia) P = 39.26 bar (569.4 psia)
"
140
Pr = 0.87 15oC Pr = 1.24
�u = 46.5% B �u = 56.5% B
c �cycle = 9.0% �cycle = 11.2%
120 C2FSCI
MW = 154.5 g/mol
100 C
at
I Pc = 458 psia (32 bar) llt = 85% dry
he
200 8GoG (175oC )
10 C'
r
pe
T = goF IIp = 80%
Su
80 c .R-115 Chloropentofluoroethane
Tgt=150.C C
Evaporation
ing
T. =26.7. C
60 at
He
uid
16 @ @
Liq
P=27.5 bar (398.9 psio) p. 39.26 bar (569.4 pslo)
40
A 14
Condensation
F}=0.87 A Pr=I.24
Condensation
E
'Iu=46.5 %
D
R-717(NH3) E
'1.=56.5 %
D
20 'ICYCII-'.'
Temperature (oC)
12 'Icycl.=90o;. _112,.
Pumping Pumping
0 1 15
160 8
C D
P = 80.1 bar (1161.8 psia) P = 114.4 bar (1659.2 psia)
Pr = 2.54
6 Pr = 3.62
140
I
B
�u = 63.2% �u = 54.6% B
�cycle = 11.9% 4
�cycle = 10.6%
120
. -
u2
100 !!
I .2
80
~
0
~IOO
g-16 @
4J
I- (.) P=114.4 (1659.2 psla)
bar
60 14 P,=3.62
*1 '1.=54.6 %
40 A
12
... C
'Icyci. =10.6%
A
1
Condensation Condensation
20 E D E D
Pumping
8 Pumping
0
50 6 100 50 150 200 50 100 150 200
Enthalpy (J/g)
4
C2F5Cl 2 R-115 Chloropentafluoroethane �t = 85% dry
Tgf = 15.0o C �p = 80%
MW = 154.5 g/mol
To = 26.7o C
PC = 458 psia (32 bar) 200
TC = 80oC psia (175.9oF) Enthalpy (JIg)
Geothermal Fluid Cooling Path Supercritical Heating Path
0
0 5 10 15 20
Turbine Expansion Sensible Heat Rejection
*Y
Cp/R=
Approach to thermodynamically optimized Rankine cycle for R-115 with a 150oC liquid
Y-I
Figure 5 Approach to rejection at 26.7oC (80oF). Temperature-enthalpy (T-H)
geothermal fluid source and heat thermodynamically optimized Rankine cycle for R-115
diagrams shown at different 150°Cliquid geothermal fluid source and heat rejection at
with a reduced cycle pressures.
26.7°C (80°F). Temperature-enthalpy (T -H) diagrams shown at
Adapted from Tester, J. W. anddifferentchael. Thermodynamics and Its Applications. Upper Saddle River, NJ: Prentice
Modell, Mi reduced cycle pressures.
Hall PTR, 1997, p. 49, Fig. 14.10.Generalized correlation for the degree of superheat above the
Figure 8.
critical temperature for optimum utilization of geothermal fluid
Image by MIT OCW.
availability as a function of ideal gas state reduced heat capacity.
!~!~~~

10. "
c
200
65
12 60
�u, % of �B
11 R-717(NH3) 55
10 50 20
15 R - 115 chloropentafluoroethane
I, Specific irreversibility (J/g)
9 T = 150oC geothermal fluid temperature 45 18
To = 26.7oC condensing temperature
8 40 16
IT, Total irreversibility (J/g)
7 14
6 - 12
5 ~IOO 10
(.)
4 8
*1
3 ... 6
2 4
1 50 2
0 0
0.8 0.9 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0
Pr, reduced cycle pressure
Utilization factor I Heat exchanger I Total
I Heat rejection
0 I Turbine
0 5 10 15 20 I Residual fluid
I Pump *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 MIT OCW.
availability as a function of ideal gas state reduced heat capacity.

11. "
--~~:fi
c
.
200
656 R-717(NH3)
15
606
-
~
55
!...5
Utilization efficiency �u (%)
~
~
>-
50
u5
Z
-
~
~IOO .R- 717 (NH3)
~ (.) ..R -115
lJ..
45
lJ.. 4 .R -32
w *1 0 R- 22
Z
0
... 6. RC -318
~404 x R -114
~ .R -600 a (ISOBUTANE)
~ 50
§353 Optimum Thermodynamic Performance
OPJIMUM THERMODYNAMICPERFORMANCE
To = 16.7oC
T = 16.7°C
Tcond = 26.7oC
T = 267°C
303
�t = 85=%
0
TI, 85% �p TIp = %
= 80 80%
cond.
�T~Tplnch10oC
pinch = = 10°C
100 150
150 200
200 250
250 300
300
0 GEOTHERMAL FLUID TEMPERATURE (OC)
Geothermal fluid temperature (oC)
0 5 10 15 20
R - 717 (NH3) *Y
R - 115 R - 32 R - 22
Cp/R=
RC - 318 R - 114 Y-I R - 600a (Isobutane)
Utilization efficiency �u as a function of geothermal fluid (initial heat source)
temperature for optimum thermodynamic operating conditions.
Figure 8. Generalized correlation for the degree of superheat above the
critical temperature for optimum utilization of geothermal fluid
Figure 7. Utilization efficiency 11u ofaideal gas state reduced heat capacity.
Image by MIT function of geothermal fluid (initial
as
availability as a function OCW.
heat source) temperature for optimum thermodynamic operating
conditions.

12. " ""c ,'::, ,~!~~~~~
"
c
200
200
R - 717 (NH3)
R-717(NH3)
150
15
R - 22
R - 32
- 100
T* - Tc (oC)
790
~IOO
C* /R
p
(.)
R - 600a
*1
... R - 114
R - 115
50
50
RC - 318
0
00 5 10 15 20
0 5 10 � 15 20
C* *Y =
/R
Cp/R= � - 1
P
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 MIT OCW.
availability as a function of ideal gas state reduced heat capacity.