Optimization of Cascade Cooling System Based on Lithium Bromide Refrigeration in the Polysilicon Industry
Abstract
:1. Introduction
2. Problem Statement
3. Model Formulation
3.1. Heat Exchanger Formulation
3.2. Pump Formulation and Pipe Formulation
3.3. Air Cooler Formulation
3.4. Absorption Refrigeration Cycle Formulation
3.5. Compression Refrigeration Cycle Formulation
3.6. Cooling Tower Formulation
3.7. Objective Function
4. Solution Technique Employed
5. Case Study
5.1. The Base-Case Cooling System of Hot Streams
5.2. The Cascade Cooling System of Hot Streams
5.3. The Sensitivity Analysis for the Cascade Cooling System
5.4. The Comparison of Optimization Method with Using MATLAB Only
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Nomenclature
a, b, c | Constants of heat exchanger capital cost |
A | Area of heat exchanger, m2 |
A1, A2, A3, A4 | Parameters of pipe capital cost |
Af | Annualized factor |
Approach | Temperature difference between cooling tower outlet temperature and air bulb temperature, °C |
Bblowdown | Mass flowrate of blowdown water in cooling tower, kg·s−1 |
CC | Capital cost, USD |
Cfactor | Tower fan factor |
COP | Coefficient of performance for refrigeration cycle |
CpCW | Specific heat capacity of cooling water, kJ·(kg·°C)−1 |
Cpm | Specific heat capacity of cooling medium, kJ·(kg·°C)−1 |
dtin | Inlet temperature difference of heat exchanger, °C |
dtout | Outlet temperature difference of heat exchanger, °C |
Din | Pipe inner diameter, m |
Dout | Pipe outer diameter, m |
Dtin | Inner diameter of heat exchanger, m |
Dtout | Outer diameter of heat exchanger, m |
Evop | The amount of water evaporation in cooling tower, kg·s−1 |
Fair | Mass flowrate of air in cooing tower, kg·s−1 |
ffriction | Factor of friction |
ft | Total mass flowrate of cooling water, kg·s−1 |
g | Gravitational constant |
G | Mass velocity rate of air, kg·(m2·s)−1 |
Gmax | Maximum mass velocity rate of air, kg·(m2·s)−1 |
ha | Film transfer coefficient of air, W·(m2·°C)−1 |
hin | Film transfer coefficient inside of the heat exchanger, W·(m2·°C)−1 |
hout | Film transfer coefficient outside of the heat exchanger, W·(m2·°C)−1 |
ht | Film transfer coefficient, W·(m2·°C)−1 |
Hy | Plant operation time, s·y−1 |
∆HEVAP | Enthalpy change of evaporator in compression refrigeration cycle, kJ·kg−1 |
K | Total heat transfer coefficient, W·(m2·°C)−1 |
Kt | Constant for heat exchanger tube side pressure drop |
L | Transmission distance, m |
i | Hot streams |
I | Annual interest rate |
Iin | Inlet specific enthalpy of hot stream, kJ·kg−1 |
Iout | Outlet specific enthalpy of hot stream, kJ·kg−1 |
j | Cooling medium |
m | Mass flow rate of cooling medium, kg·s−1 |
M | Mass flow rate of hot stream, kg·s−1 |
MAR-CW | Mass flow rate of cooling water in absorption refrigeration, kg·s−1 |
MLiBr | Mass flow rate of working fluid in absorption refrigeration, kg·s−1 |
Mmakeup | Mass flowrate of make-up water in cooling tower, kg·s−1 |
Mref | Mass flowrate of refrigerant in compression refrigeration cycle, kg·s−1 |
MWair | Molecular weight of air |
MWw | Molecular weight of water |
n | Lifetime of equipment, y |
Nb | Number of bundles |
OC | Operation cost, USD·y−1 |
Pa | Local atmospheric pressure, Pa |
Pcond | Pressure of condenser in compression refrigeration cycle, MPa |
Pevap | Pressure of evaporator in compression refrigeration cycle, MPa |
Pfan | Air cooler fan power consumption, kW |
Ps | Vapor pressure, Pa |
Pcul | Capital cost of pope per unit length, USD·m−1 |
Pe | Unit cost of electricity, USD·(kWh)−1 |
Pw | Unit cost of fresh water, USD·t−1 |
∆pair | Air cooler fan pressure drop, Pa |
∆P | Pump pressure drop, Pa |
∆Pt | Tube side pressure drop, Pa |
qGEN | Heat load of generator when working fluid flowrate is 1 kg·s−1, kW |
Q | Heat load of heat exchanger, kW |
Range | Difference between cooling tower inlet and outlet temperature, °C |
Re | Reynolds number |
tin | Inlet temperature of cooling medium, °C |
tout | Outlet temperature of cooling medium, °C |
TAC | Total annual cost, USD·y−1 |
TCC | Total capital cost, USD |
TOC | Total operation cost, USD·y−1 |
Tambient | Ambient temperature, °C |
Tcin | Cooling water inlet temperature of cooling tower, °C |
Tcout | Cooling water outlet temperature of cooling tower, °C |
TCW1 | Inlet temperature of cooling water of absorber, °C |
TCW2 | Outlet temperature of cooling water of absorber, °C |
TCW3 | Outlet temperature of cooling water of condenser, °C |
Tmean | Mean temperature of cooling tower, °C |
Twb | Air bulb temperature, °C |
Tin | Inlet temperature of hot stream, °C |
Tout | Outlet temperature of hot stream, °C |
∆Tm | Logarithmic mean temperature difference of heat exchanger, °C |
∆Tmin | Minimum temperature approach difference of heat exchanger, °C |
u | The flow velocity, m·s−1 |
U | Total heat transfer coefficient of heat exchanger, kW·(m2·°C)−1 |
Vair | Volumetric flow rate of air, m3·s−1 |
VF | Face velocity of air cooler, m·s−1 |
VNF | Actual face velocity of air cooler, m·s−1 |
win | Air inlet humidity of cooling tower |
wout | Air outlet humidity of cooling tower |
WComp | Non-isentropic work of compressor, kW |
Wt | Pipe weight per unit length, kg·m−1 |
Greek letter | |
α, β, γ | Parameters of pump capital cost |
ηel | Electrical efficiency |
ηfan | Air cooler’s fan efficiency |
ηfan-tower | Cooling tower fan efficiency |
ηisen | Isentropic efficiency for compressor |
ηmech | Mechanical efficiency |
ηPump | Pump efficiency |
κ | Heat conductivity, W·(m·K)−1 |
λ | Friction factor |
μ | Viscosity, Pa·s |
ρ | Density of cooling medium, kg·m−3 |
ρair | Density of air, kg·m−3 |
πc | Cycle of concentration for cooling tower |
Subscripts | |
ABS | Absorber |
AC | Air cooler |
AR | Absorption refrigeration cycle |
Comp | Compressor |
COND | Condenser |
CR | Compression refrigeration cycle |
CT | Cooling tower |
EVAP | Evaporator |
fan-tower | Fan for cooling tower |
GEN | Generator |
HEX | Heat exchanger |
Pipe | Pipeline |
Pump | Pumps for cooling mediums |
Pump-CW | Pump for cooling water used in absorption refrigeration cycle |
Pump-LiBr | Pump for LiBr/H2O solution in absorption refrigeration cycle |
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Ts (°C) | Tt (°C) | M (kg·s−1) | hH (W·(m2·°C)−1) | Components (Mass Fraction) | |
---|---|---|---|---|---|
H1 | 132.19 | −5.8 | 34.0 | 500 | HCl: 0.00036, DCS: 0.00615, TCS: 0.19751, STC: 0.78222, H2: 0.01376 |
H2 | 131.82 | −6.7 | 33.5 | 500 | HCl: 0.00036, DCS: 0.00619, TCS: 0.19828, STC: 0.78122, H2: 0.01394 |
H3 | 131.82 | −7.1 | 33.4 | 500 | HCl: 0.00037, DCS: 0.00619, TCS: 0.19828, STC: 0.78122, H2: 0.01394 |
tin (°C) | tout (°C) | ρ (kg·m−3) | Cp (kJ·(kg·°C)−1) | μ (Pa·s) | κ (W·(m·K)−1) | hC (W·(m2·°C)−1) | |
---|---|---|---|---|---|---|---|
1 (HW) | 90~110 | 100~120 | 950 | 4.200 | 0.0003 | 0.68 | 2500 |
2 (AIR) | 35~35 | 60~65 | 1.169 | 1.004 | 0.0011 | 0.024 | 475.93 |
3 (CW) | 20~25 | 45~50 | 995 | 4.182 | 0.001 | 0.62 | 2500 |
4 (CHW) | 7~12 | 12~17 | 1000 | 4.182 | 0.0015 | 0.57 | 2500 |
5 (EG) | −15~−10 | −5~0 | 1082.45 | 2.582 | 0.007 | 0.39 | 2500 |
Items | Data |
---|---|
Air coolers capital cost (USD) [1] | 4778·A0.525 |
Other heat exchangers capital cost (USD) [43] | 8500 + 409·A0.85 |
Pump capital cost (USD) | 8600 + 7310(M·∆P/ρ)0.2 |
Air cooler fan efficiency | 70% |
Cooling tower fan efficiency | 70% |
Pump efficiency | 70% |
Compressor isentropic efficiency | 70% |
Compressor mechanical efficiency | 80% |
Compressor electrical efficiency | 90% |
Price of electricity (USD·kWh−1) | 0.15 |
Price of fresh water (USD·t−1) | 0.5 |
Plant operation time (h·y−1) | 8000 |
Plan lifetime (y) | 5 |
Interest rate | 15% |
Annualized factor | 0.298 |
Items | Data | |
---|---|---|
Minimum temperature approach difference of heat exchanger ΔTmin | Waste heat recovery cooler | 10 °C |
Water cooler/air cooler | 10 °C | |
Absorption refrigeration cooler | 3 °C | |
Allowable outlet temperature of air cooler | 50~65 °C | |
Allowable outlet temperature of water cooler | 25~35 °C | |
Allowable outlet temperature of absorption refrigeration heat exchanger | 10~15 °C | |
Ambient temperature Tambient | 25 °C | |
Wet bulb temperature Twb | 12 °C | |
Air saturated humidity at wet bulb temperature | 0.011 kgw·kga−1 | |
Atmospheric pressure | 101,325 Pa | |
Air cooler face velocity | 3 m·s−1 | |
Air cooler friction factor | 0.95 | |
Air cooler number of bundles | 4 | |
Cycle of concentration | 4 | |
ARC condensation temperature | 35~45 °C | |
ARC evaporation temperature | 5~10 °C | |
ARC cooling water initial temperature | 30~32 °C | |
ARC cooling water final temperature | 32~42 °C | |
CRC condensation temperature | 35~45 °C | |
CRC evaporation temperature | −20~−15 °C | |
CRC cooling water initial temperature | 27~37 °C | |
CRC cooling water final temperature | 32~42 °C |
Items | Base-Case Cooling System | Cascade Cooling System |
---|---|---|
TAC (USD·y−1) | 4,505,811 | 3,574,786 |
TCC (USD) | 4,773,854 | 6,029,170 |
TOC (USD·y−1) | 3,083,203 | 1,778,093 |
CCHEX (USD) | 760,560 | 970,190 |
CCPUMP (USD) | 203,819 | 384,554 |
CCPIPE (USD) | 2,894,782 | 3,961,743 |
CCAR (USD) | - | 208,396 |
CCCR (USD) | 893,692 | 481,577 |
CCCT1 (USD) | 10,267 | 10,026 |
CCCT2 (USD) | - | 7282 |
CCCT3 (USD) | 10,734 | 5403 |
OCPUMP (USD·y−1) | 188,834 | 267,727 |
OCAC (USD·y−1) | 77,193 | 65,583 |
OCAR (USD·y−1) | - | 68 |
OCCR (USD·y−1) | 2,514,212 | 1,178,940 |
OCCT1 (USD·y−1) | 78,092 | 78,946 |
OCCT2 (USD·y−1) | - | 98,258 |
OCCT3 (USD·y−1) | 224,873 | 88,572 |
Fan power (kW) | 316 | 276 |
Compressor power (kW) | 1509 | 982 |
Items | CRC in Base Case | ARC in Cascade System | CRC in Cascade System |
---|---|---|---|
COP | 2.8016 | 0.7657 | 2.5768 |
Generating temperature (°C) | - | 110 | - |
Evaporating temperature (°C) | −15 | 5 | −17 |
Condensing temperature (°C) | 35 | 45 | 36 |
Evaporating pressure (Pa) | 163,940 | 873 | 150,837 |
Condensing pressure (Pa) | 886,981 | 9590 | 911,849 |
Refrigerant flow rate (kg·s−1) | 30.05 | 7.18 | 13.22 |
Secondary refrigerant flow rate (kg·s−1) | 95.34 | 71.53 | 35.64 |
Cooling water inlet temperature (°C) | 27 | 30 | 27 |
Cooling water outlet temperature (°C) | 32 | 42 | 33 |
Cooling water flow rate (kg·s−1) | 274.39 | 112.24 | 100.88 |
Items | Nanchang | Xi’an |
---|---|---|
Pe (USD·kWh−1) | 0.096 | 0.083 |
Pw (USD·t−1) | 0.344 | 0.843 |
TAC (USD·y−1) | 2,941,456 | 2,836,840 |
TCC (USD) | 6,063,125 | 5,976,545 |
TOC (USD·y−1) | 1,134,644 | 1,055,830 |
CCHEX (USD) | 968,291 | 981,735 |
CCPUMP (USD) | 385,700 | 384,757 |
CCPIPE (USD) | 213,689 | 208,396 |
CCAR (USD) | 447,170 | 447,170 |
CCCR (USD) | 10,135 | 9783 |
CCCT1 (USD) | 6827 | 7282 |
CCCT2 (USD) | 5189 | 5189 |
CCCT3 (USD) | 4,026,123 | 3,932,234 |
OCPUMP (USD·y−1) | 174,547 | 148,380 |
OCAC (USD·y−1) | 50,212 | 36,624 |
OCAR (USD·y−1) | 43 | 37 |
OCCR (USD·y−1) | 732,608 | 633,401 |
OCCT1 (USD·y−1) | 53,929 | 74,645 |
OCCT2 (USD·y−1) | 68,128 | 99,737 |
OCCT3 (USD·y−1) | 55,178 | 66,006 |
Aspen and MATLAB | MATLAB | |
---|---|---|
Population size | 30 | 300 |
Maximum generation | 500 | 5000 |
Computation time (s) | 340,471 | 1884 |
Heat Exchanger Load (kW) | Waste Heat Recovery | Air Cooling | Water Cooling | Absorption Refrigeration | Compression Refrigeration | Total Heat Load |
---|---|---|---|---|---|---|
Aspen and MATLAB | 1055.07 | 5686.41 | 1269.42 | 807.85 | 586.67 | 9405.41 |
MATLAB | 1062.51 | 5692.98 | 1402.14 | 780.49 | 560.58 | 9498.69 |
Items | Aspen and MATLAB | MATLAB |
---|---|---|
TAC (USD·y−1) | 3,574,786 | 3,475,097 |
TCC (USD) | 6,029,170 | 5,842,860 |
TOC (USD·y−1) | 1,778,093 | 1,733,924 |
CCHEX (USD) | 970,190 | 925,009 |
CCPUMP (USD) | 384,554 | 384,068 |
CCPIPE (USD) | 3,961,743 | 3,947,379 |
CCAR (USD) | 208,396 | 178,450 |
CCCR (USD) | 481,577 | 385,382 |
CCCT1 (USD) | 10,026 | 10,483 |
CCCT2 (USD) | 7282 | 6737 |
CCCT3 (USD) | 5403 | 5352 |
OCPUMP (USD·y−1) | 267,727 | 265,594 |
OCAC (USD·y−1) | 65,583 | 65,304 |
OCAR (USD·y−1) | 68 | 55 |
OCCR (USD·y−1) | 1,178,940 | 1,151,132 |
OCCT1 (USD·y−1) | 78,946 | 72,229 |
OCCT2 (USD·y−1) | 98,258 | 89,065 |
OCCT3 (USD·y−1) | 88,572 | 90,545 |
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Yang, S.; Wang, Y.; Wang, Y. Optimization of Cascade Cooling System Based on Lithium Bromide Refrigeration in the Polysilicon Industry. Processes 2021, 9, 1681. https://doi.org/10.3390/pr9091681
Yang S, Wang Y, Wang Y. Optimization of Cascade Cooling System Based on Lithium Bromide Refrigeration in the Polysilicon Industry. Processes. 2021; 9(9):1681. https://doi.org/10.3390/pr9091681
Chicago/Turabian StyleYang, Shutong, Youlei Wang, and Yufei Wang. 2021. "Optimization of Cascade Cooling System Based on Lithium Bromide Refrigeration in the Polysilicon Industry" Processes 9, no. 9: 1681. https://doi.org/10.3390/pr9091681