technical and economic feasibility of dry air...
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TECHNICAL AND ECONOMIC FEASIBILITY OF DRY AIR
COOLING FOR THE SUPERCRITICAL CO2 BRAYTON
CYCLE USING EXISTING TECHNOLOGY
Sandeep R Pidaparti, Patrick J. Hruska, Anton Moisseytsev, James J. Sienicki, Devesh Ranjan
The 5th International Symposium – Supercritical CO2 power cycles San Antonio, Texas March 28-31, 2016
Background
• Dry air cooling is an attractive option for the S-CO2 Brayton cycle • Technically feasible but is it economical? • If feasible completely eliminates the need for water, increasing the range of applicability
• Previous investigation of Dry air cooling option1 • Used Heatric Hybrid HX technology for Air-to-CO2 cooler – Significant increase in plant capital cost
per unit electrical output ($/kWe)
• Goal of the current investigation • Identify more economical Air-to-CO2 cooler to reduce the plant capital cost • Perform cycle optimization to identify optimal cycle operating conditions using the modified Air-to-
CO2 cooler
1) "Investigation of a Dry Air Cooling Option for an S-CO2 Cycle" by A. Moisseytsev, 4th S-CO2 Symposium, Pittsburgh, PA, September 9-10, 2014
Reference conditions and Assumptions
1
ABR S-CO2 CYCLE TEMPERATURES, PRESSURES, HEAT BALANCE, AND EFFICIENCIES
516.6 164.4 104.8
19.79
CO2 367.0 403.9
1360.5 kg/s 403.9 19.96 7.722
92.8% 7.751
528.0 516.6
0.100 19.80
174.6 185.0
89.7 182.0 19.97 7.696
Na 7.643 19.98
1267.0 96.3% 88.8 171.3 184.9
kg/s 7.559 90.1% 19.99 7.682
373.0
367.0
19.95
32.8 84.3 84.3 89.8
7.621 20.00 20.00 7.666
31.25
7.400 89.1%
Efficiency = 42.27 % 5%
32.7 89.6
7.628 7.635
32%
Q,MW T,oC 6,000 30.0 35.5
Input P,MPa 0.84 kg/s 0.226 0.101
250
68%
Cycle
94.6%
26.4
95.5%
137.2
156.4
338.2
95.5%
28.5
TURBINE
HTR
RHXCOMP. #2
COOLER
COMP. #1
Eff. =
LTR
Eff. =
LTR
Eff. =
Eff. =
e (TS) =
e (TS) =
e (TS) =
• 250 MWt (~105 MWe) S-CO2 cycle for a Advanced Fast Reactor (AFR) • 42.27% cycle efficiency
• 31.25oC minimum cycle temperature
• 7.4 MPa minimum and 20 MPa maximum
cycle pressures
• 30oC inlet water temperature • Assumed same for air • Atmospheric pressure
Air-to-CO2 cooler design
• Cross flow between CO2 and air • CO2 flowing through the SS316 tubes with external aluminum fins (3 passes) • 3 fans per each unit blow air (assumed uniformly) over the finned tubes
15’ wide
1” tube diameter 2.5” fin diameter 10 fins per inch
61’ long
CO2 inlet
CO2 outlet
Exploded view
Fins closer view
CO2 – solid lines Air – dashed lines
2
10.5’ tall
Air inlet
Air outlet
Outputs
Cooler modeling
Set Model Inputs
Number of cooler units CO2 mass flow rate
CO2, air inlet temperatures CO2 inlet pressure
CO2 outlet temperature
Determine air side properties Air side heat transfer coefficient Air side pressure drop
Discrete Sub-section modeling
Energy Balance
Resistance Network Effectiveness/NTU
Air, CO2 temperatures CO2 pressure drop
CO2 heat transfer coefficient
Conductance
Fan power CO2 outlet pressure
5
Cooler model verification Variable Harsco Industrial
Air-X-Changers Calculated
(EES model) Calculated
(EES model)
Inputs
Number of HEX units 86 86 86
CO2 flow rate per unit [Kg/s] 10.22 10.22 10.22
CO2 inlet temperature [oC] 89.61 89.61 89.61
CO2 inlet pressure (MPa) 7.736* 7.736* 7.635
Air flow rate per unit [kg/s] 317.2 317.2 317.2
Air inlet temperature [oC] 30 30 30
Outputs
Heat transfer capacity [MWth] 1.691 1.696 1.61
CO2 outlet temperature [oC] 32.7 33.12 32.64
CO2 pressure drop [KPa] 6.895 6.645 6.802
Air outlet temperature [oC] 52 51.2 51.11
Air pressure drop [KPa] Not provided - 0.1112
*The CO2 inlet pressure provided in the Harsco quotation didn’t match the proposed design parameter.
Fans efficiency is calculated by using the estimated pressure drop from EES (built in finned tube geometry)
6
η𝒇𝒂𝒏𝒔𝑾 𝒇𝒂𝒏 =𝒎 𝒂𝒊𝒓∆𝑷𝒂𝒊𝒓
ρ𝒂𝒊𝒓
Using, 𝑾 𝒇𝒂𝒏=32.95hp per fan → η𝒇𝒂𝒏𝒔=41%
S-CO2 air cooled cycle optimization
• Parameters for optimization Cycle minimum pressure Cycle minimum temperature
•
•
• Cycle maximum pressure (Limited by pressure containment capability of heat exchangers)
• Cycle conditions demand mechanical design changes •
•
•
•
•
Reactor heat exchanger (RHX) High temperature recuperator (HTR) Low temperature recuperator (LTR) Piping Turbomachinery components (Not implemented in this study)
Restricted to along the pseudo-critical line to take benefit of high fluid density
Minimum pressure (MPa)
Minimum Temperature (oC)
Maximum pressure (MPa)
7.4 31.25 18-30
7.628 32.5 18-30
8 35 18-30
8.864 40 19-30
9.688 45 20-30
Selected conditions for optimization study
Pressure containment capabilities of Heatric PCHEs (From their website)
3
PCHE design methodology
• Heatric design methodology was used to estimate the plate thickness (t2), ridge thickness (t3) as maximum pressure changes
• Semicircular channels are approximated as rectangular channels for design purposes • ASME 13-9
Parameters RHX HTR LTR
HEX type Z/I PCHE Platelet PCHE Platelet PCHE
Unit length (m) 1.5 0.6 0.6
Unit width (m) 0.6 1.5 1.5
Unit height (m) 0.6 0.6 0.6
Design temperature (oC) 550 450 300
Design pressure (MPa) 16-30 16-30 16-30
Hot side (Na) Cold side (CO2) Hot side (CO2) Cold side (CO2) Hot side (CO2) Cold side (CO2)
Channel diameter (mm) 6.0 2.0 1.3 1.3 1.3 1.3
Channel depth (mm) 4.0 1.0 0.65 0.65 0.65 0.65
Pitch to diameter ratio 1.083 Variable Variable Variable Variable Variable
Plate thickness (mm) Variable Variable Variable Variable Variable Variable
PCHE design methodology
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
Pit
ch/D
iam
ete
r
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Design pressure (MPa)
Channel Pitch to diameter ratios vs Design pressure
RHX
HTR
LTR
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
Pla
te t
hic
kne
ss (
mm
)
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Design pressure (MPa)
Plate thickness vs Design pressure
RHX
HTR
LTR
9
• Estimation of heat exchangers cost
𝑼𝒏𝒊𝒕 𝒄𝒐𝒔𝒕 = 𝑼𝒏𝒊𝒕 𝒗𝒐𝒍𝒖𝒎𝒆. 𝝆𝒔𝒔𝟑𝟏𝟔.𝑴𝒂𝒕𝒆𝒓𝒊𝒂𝒍 𝒄𝒐𝒔𝒕 + 𝑭𝒂𝒃𝒓𝒊𝒄𝒂𝒕𝒊𝒐𝒏 𝒄𝒐𝒔𝒕
𝑯𝑬𝑿 𝒄𝒐𝒔𝒕 = 𝑼𝒏𝒊𝒕 𝒄𝒐𝒔𝒕. 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒖𝒏𝒊𝒕𝒔
Material cost – 7.64 $/kg 𝝆𝒔𝒔𝟑𝟏𝟔 – 8,000 kg/m3 Unit volume – 0.54 m3
10
Piping design methodology
• Minimum wall thickness is estimated using ASME B31.1 design procedure
𝑴𝒊𝒏 𝒕𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔 =𝟎.𝟓𝑷𝒅𝒆𝒔𝒊𝒈𝒏.𝑰𝑫
𝑷𝒅𝒆𝒔𝒊𝒈𝒏.𝒀+𝑺𝒂𝒍𝒍𝒐𝒘𝒂𝒃𝒍𝒆 .𝑾 . 𝟏−𝑼𝑻𝑷−𝑪𝑨 −𝑷𝒅𝒆𝒔𝒊𝒈𝒏
𝑵𝒐𝒎𝒊𝒏𝒂𝒍 𝒕𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔 = 𝑴𝒊𝒏 𝒕𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔. (𝟏 − 𝑼𝑻𝑷 − 𝑪𝑨)
𝑺𝒂𝒍𝒍𝒐𝒘𝒂𝒃𝒍𝒆 - Allowable stress for SS316 (Table 1A of ASME B&PV code section II, Part D) 𝒀 – Coefficient from ASME B31.1 Table 104.1.2(A) 𝑾 – 0.975 (Weld joint strength reduction factor) UTP – Under tolerance allowance (12.5%) CA – Corrosion allowance (12.5%)
• As per the recent 3-D plant layout, there are 25 pipe sections connecting different components • Lengths • Inner diameters • Design pressure • Design temperature
• Estimation of piping cost 𝑶𝑫 = 𝑰𝑫 + 𝟐.𝑴𝒊𝒏 𝒕𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔
𝑴𝒂𝒕𝒆𝒓𝒊𝒂𝒍 𝒗𝒐𝒍𝒖𝒎𝒆 =𝝅
𝟒. 𝑶𝑫𝟐 − 𝑰𝑫𝟐 . 𝑳
𝑴𝒂𝒕𝒆𝒓𝒊𝒂𝒍 𝒄𝒐𝒔𝒕 = 𝑼𝒏𝒊𝒕 𝒗𝒐𝒍𝒖𝒎𝒆. 𝝆𝒔𝒔𝟑𝟏𝟔. 𝑴𝒂𝒕𝒆𝒓𝒊𝒂𝒍 𝒗𝒐𝒍𝒖𝒎𝒆
Fabrication cost is neglected assuming that it is small compared to the material cost
Cost based optimization
• Plant capital cost based optimization technique is employed
• Plant capital cost per unit net electrical output is calculated as,
• Rest of plant capital cost is calculated for the reference conditions • Minimum pressure – 7.4MPa • Minimum temperature – 31.25oC • Maximum pressure – 20MPa • Water cooling • 4480.432 $/KWe is the reference value calculated • 104.6 MWe is the reference grid power calculated
• A code was developed in Matlab to perform the optimization
Rest of plant capital cost
31
$
𝑲𝑾𝒆=
𝑹𝒆𝒔𝒕𝒐𝒇𝒑𝒍𝒂𝒏𝒕𝒄𝒂𝒑𝒊𝒕𝒂𝒍𝒄𝒐𝒔𝒕+𝑹𝑯𝑿 𝒄𝒐𝒔𝒕+𝑯𝑻𝑹 𝒄𝒐𝒔𝒕+𝑳𝑻𝑹 𝒄𝒐𝒔𝒕+𝑪𝒐𝒐𝒍𝒆𝒓 𝒄𝒐𝒔𝒕+𝑷𝒊𝒑𝒊𝒏𝒈 𝒄𝒐𝒔𝒕
𝑷𝒆𝒍𝒆𝒄−𝑷𝒇𝒂𝒏
Optimization code flow chart
START
READ THE INPUT VARIABLES (MIN, MAX PRESSURE and MIN TEMPERATURE)
SET THESE VARIABLES IN INPUT FILES FOR PDC DEPENDING ON MAX PRESSURE CHANGE RHX, HTR and LTR parameters (Pitch
to diameter ratio, plate thickness)
BEGIN THE OPTIMIZATION WITH REFERENCE NUMBER OF HEX UNITS (RHX – 96 units, HTR – 48 units, LTR – 48 units)
VARY SPLIT FRACTION BETWEEN COMPRESSORS FROM 0.6 to 0.8 in steps of 0.01
FIND OPTIMUM SPLIT FRACTION WHICH YIELDS MAXIMUM CYCLE EFFICIENCY
AND SET THE VALUE IN CYCLE INPUT FILE
VARY NUMBER OF RHX units from 32 to 272 in steps of 8 FIND OPTIMUM NUMBER OF RHX UNITS WHICH MINIMIZES PLANT $/KWe AND
SET THE VALUE IN RHX INPUT FILE
VARY NUMBER OF HTR units from 18 to 198 in steps of 6 FIND OPTIMUM NUMBER OF HTR UNITS WHICH MINIMIZES PLANT $/KWe AND
SET THE VALUE IN HTR INPUT FILE
VARY NUMBER OF LTR units from 18 to 198 in steps of 6 FIND OPTIMUM NUMBER OF LTR UNITS WHICH MINIMIZES PLANT $/KWe AND
SET THE VALUE IN LTR INPUT FILE
DID OPTIMUM SPLIT FRACTION CHANGE?
NO
STOP
YES
12
• The cycle efficiency decreases after a certain maximum pressure due to drop in turbine and compressors efficiency
• It is required to change design of turbomachinery equipment to maintain constant efficiencies
• These values might change if the efficiencies of compressors and turbine are maintained constant
Results – Fixed turbomachinery design
42.5
42
41.5
41
40.5
40
39.5
39
38.5
38
37.5
Pla
nt
eff
icie
ncy
(%
)
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Cycle maximum pressure (MPa)
Effect of cycle maximum pressure on plant efficiency
7.4MPa, 31.25C - Water cooling 7.4MPa, 31.25C 7.628MPa, 32.5C 8MPa, 35C 8.864MPa, 40C 9.688MPa, 45C
5400
5350
5300
5250
5200
5150
5100
5050
5000
4950
4900
4850
4800
4750
4700
Pla
nt
Ca
pit
al
cost
($
/KW
e)
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Cycle maximum pressure (MPa)
Effect of cycle maximum pressure on plant capital cost
7.4MPa, 31.25C - Water cooling
7.4MPa, 31.25C 7.628MPa, 32.5C
8MPa, 35C
8.864MPa, 40C
9.688MPa, 45C
13
• Optimum conditions are • Minimum pressure – 8MPa • Minimum temperature – 35oC • Maximum pressure – 24 MPa
90.5
91
91.5
92
92.5
93
93.5
Turb
ine
eff
icie
ncy
(%
)
18 19 20 21 22 23 24 25 26 27 28 29 30
Maximum cycle pressure (MPa)
Turbine efficiency as a function of max cycle pressure
7.4MPa, 31.25C
7.628MPa, 32.5C
8MPa, 35C
8.864MPa, 40C
9.688MPa, 45C
90
89.5
89
88.5
88
87.5
87
86.5
86
85.5
Co
mp
ress
or
#1 e
ffic
ien
cy (
%)
18 19 20 21 22 23 24 25 26 27 28 29 30
Maximum cycle pressure (MPa)
Compressor #1 efficiency as a function of max cycle pressure
7.4MPa, 31.25C
7.628MPa, 32.5C
8MPa, 35C
8.864MPa, 40C
9.688MPa, 45C
90
89
88
87
86
85
92
91
Co
mp
ress
or
#2 e
ffic
ien
cy (
%)
18 19 20 21 22 23 24 25 26 27 28 29 30
Maximum cycle pressure (MPa)
Compressor #2 efficiency as a function of max cycle pressure
7.4MPa, 31.25C
7.628MPa, 32.5C
8MPa, 35C
8.864MPa, 40C
9.688MPa, 45C
Results – Fixed turbomachinery design
14
Results – Fixed turbine efficiency
• Optimum conditions didn’t significantly change compared to previous case • Minimum pressure – 8MPa • Minimum temperature – 35oC • Maximum pressure – 25 MPa
• $/kWe of air cooled plant is still about 5% higher compared to water cooled plant
37
38
39
40
41
42
43
Pla
nt
eff
icie
ncy
(%
)
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Cycle maximum pressure (MPa)
Effect of cycle maximum pressure on plant efficiency
7.4MPa, 31.25C - Water cooling 7.4MPa, 31.25C 7.628MPa, 32.5C 8MPa, 35C 8.864MPa, 40C 9.688MPa, 45C
5400
5350
5300
5250
5200
5150
5100
5050
5000
4950
4900
4850
4800
4750
4700
Pla
nt
Ca
pit
al
cost
($
/KW
e)
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Cycle maximum pressure (MPa)
Effect of cycle maximum pressure on plant capital cost
7.4MPa, 31.25C - Water cooling 7.4MPa, 31.25C 7.628MPa, 32.5C 8MPa, 35C 8.864MPa, 40C
15
Effect of cycle minimum pressure
43
42.5
42
41.5
41
40.5
40
39.5
39
38.5
38
Pla
nt
eff
icie
ncy
(%
)
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Cycle maximum pressure (MPa)
Effect of cycle maximum pressure on plant efficiency
7.7MPa, 32.5C
8.2MPa, 35C
9.2MPa, 40C
5200
5100
5000
4900
4800
5400
5300
Pla
nt
ca
pti
al
cost
($
/kW
e)
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Cycle maximum pressure (MPa)
Effect of cycle maximum pressure on plant captial cost
7.7MPa, 32.5C
8.2MPa, 35C
9.2MPa, 40C
16
39.5
40
40.5
41
41.5
42
42.5
43
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Pla
nt
effi
cien
cy (
%)
Cycle maximum pressure (MPa)
Effect of cycle maximum pressure on the plant efficiency
7.8MPa
7.9MPa
8MPa
8.1MPa
8.2MPa
4800
4850
4900
4950
5000
5050
5100
5150
5200
5250
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Pla
nt
cap
tia
l co
st (
$/k
We)
Cycle maximum pressure (MPa)
Effect of cycle maximum pressure on the plant captial cost
7.8MPa7.9MPa8MPa8.1MPa8.2MPa
Water vs Air cooled optimal conditions
17
ABR S-CO2 CYCLE TEMPERATURES, PRESSURES, HEAT BALANCE, AND EFFICIENCIES
516.6 164.4 104.8
19.79
CO2 367.0 403.9
1360.5 kg/s 403.9 19.96 7.722
92.8% 7.751
528.0 516.6
0.100 19.80
174.6 185.0
89.7 182.0 19.97 7.696
Na 7.643 19.98
1267.0 96.3% 88.8 171.3 184.9
kg/s 7.559 90.1% 19.99 7.682
373.0
367.0
19.95
32.8 84.3 84.3 89.8
7.621 20.00 20.00 7.666
31.25
7.400 89.1%
Efficiency = 42.27 % 5%
32.7 89.6
7.628 7.635
32%
Q,MW T,oC 6,000 30.0 35.5
Input P,MPa 0.84 kg/s 0.226 0.101
250
68%
Cycle
94.6%
26.4
95.5%
137.2
156.4
338.2
95.5%
28.5
TURBINE
HTR
RHXCOMP. #2
COOLER
COMP. #1
Eff. =
LTR
Eff. =
LTR
Eff. =
Eff. =
e (TS) =
e (TS) =
e (TS) =
About 1-2% increase in the plant $/kWe compared to the water cooled cycle
Summary and Conclusions
• More economical Air-to-CO2 cooler was identified and commercially available
• The cooler was modeled and the calculations were verified with the vendor specifications
• Using this cooler design, air cooled cycle optimization was performed in reference to the water cooled cycle
• New optimal conditions were calculated which results in only about 1-2% increase in the plant $/kWe compared to water cooled cycle
• Shows that dry air cooling is both technically and economically feasible
Questions?
Thank you for your time!
Piping design methodology
Section Pipe ID (m) Pipe length (m)
1 0.68302 29
2 0.68302 2
3 0.68302 12
4 0.68302 30
5 0.5 9.25
6 0.5 5.5
7 0.5 13
8 0.5 9.25
9 0.5 5
10 0.5 55
11 0.5 21
12 0.5 5
13 0.5 10
14 0.5 10
15 0.68302 10
16 0.68302 15
17 0.68302 2
18 0.5 12
19 0.45 38
20 0.25 17
21 0.25 21
22 0.25 11
23 0.25 11
24 0.25 12
25 0.25 25
0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.2
Pip
e t
hic
kne
ss (
m)
RHX to turbine pipe thickness vs cycle maximum pressure
7.4MPa, 31.25C
7.628MPa, 32.5C
8MPa, 35C
8.864MPa, 40C
9.688MPa, 45C
0.05
0.048
0.046
0.044
0.042
0.04
0.038
0.036
0.034
0.032
0.03
Pip
e t
hic
kne
ss (
m)
18 19 20 21 22 23 24 25 26 27 28 29 30
Cycle maximum pressure (MPa)
18 19 20 21 22 23 24 25 26 27 28 29 30
Cycle maximum pressure (MPa)
turbine to HTR hot side pipe thickness vs cycle maximum pressure
7.4MPa, 31.25C
7.628MPa, 32.5C
8MPa, 35C
8.864MPa, 40C
9.688MPa, 45C
10
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