Thermoeconomic Evaluation of a High-Performance Solar Biogas Polygeneration System
Abstract
:1. Introduction
- Analysis of a high-efficiency polygeneration system that recovers waste energy from an engine and a set of photovoltaic panels;
- Detailed application of the Theory of Exergy Cost to the polygeneration plant;
- Presentation of sensitivity assessments to verify the impacts of the variation in different costs.
2. Materials and Methods
2.1. Polygeneration System
2.2. System Components
2.2.1. Internal Combustion Engine
2.2.2. Absorption Chiller
2.2.3. Photovoltaic Solar Panels
2.2.4. Thermal Storage System
2.3. Thermodynamic Analysis
- (1)
- Changes in kinetic and potential energy are negligible;
- (2)
- Pressure drops and heat dissipation through the pipes are insignificant;
- (3)
- A complete combustion process occurs in the ICE.
2.4. Thermoeconomic Analysis
2.5. Theory of the Exergetic Cost
2.6. Parameter Variation Study
3. Results and Discussion
3.1. Energy Assessment
3.1.1. Average Plant Energy Consumption
3.1.2. Thermoeconomic Evaluation
3.2. Results of the Parameter Variation Study
3.2.1. Variation in the Operation Cost Rate of ICE
3.2.2. Variation in the Cost of Fuel (Biogas)
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value | Unit |
---|---|---|
Mechanical efficiency | 40.6 | % |
Rated power | 546 | kW |
Biogas flow | 0.088 | kg/s |
Temperature of jacket water | 90 | °C |
Temperature of exhaust gas | 450 | °C |
Mass flow of exhaust gas | 0.83 | kg/s |
Parameter | Value | Unit |
---|---|---|
Cooling capacity | 35.16 | kW |
Waste energy absorbed | 116.06 | kW |
Coefficient of performance (COP) | 0.59 | - |
Water outlet temperature in the chiller | 7.0 | °C |
Water inlet temperature in the chiller | 12.0 | °C |
Parameter | Value | Unit |
---|---|---|
Peak power | 80.00 | W |
Operating temperature | −40.0 to 85.0 | °C |
Monthly energy conversion rate (panel without heat exchanger) | 28.24 | kWh/m2 |
Monthly energy conversion rate (panel with heat exchanger) | 30.34 | kWh/m2 |
Area of PV panels | 20.90 | m2 |
Rated power | 630 | kWh |
Inverter | 3 | kW |
Electrical efficiency | 12.52 | % |
Cooling fluid inlet temperature | 35.0 | °C |
Cooling fluid outlet temperature | 58.0 | °C |
Average rate of solar radiation | 800.00 | kWh/m2 |
Cooling fluid mass flow (Panel with 0.52 m2 surface area) | 0.012 | kg/s |
Equipment | Mass Balance | Energy Balance | Exergy Balance |
---|---|---|---|
ICE | m1 = m2 + m10 (1) m8 = m9 (4) | Q1(biogas) = (m2 + m10)·h2 + m8·(h8 − h9) + W6 (2) | Ex1 + Ex9 = Ex2 + Ex6 + Ex8 + Ex10 + Exdestroyed (3) |
Chiller | m2 = m3 (5) m4 = m5 (8) | m2·(h2 − h3) Qabsorber + W1(pump) = Qchiller (6) | Ex2 + Ex5 + W1(pump) + Exabsorber = Ex4 + Ex3 + Exdestroyed (7) |
Water cooling (PV) | m12 = m13 (9) | Q16 + W2(pump) + m12 · (h13 − h12) = Qpcs (10) | Ex13 + Ex16 + W2(pump) = Ex12 + Expcs + Exdestroyed (11) |
Tank (hot water) | - | m14 · (h14 − h15) = m12 · (h12 − h13) + m10·(h10 − h11) + m8 · (h8 − h9) + W3(pump) (12) | Ex8 + Ex10 + Ex12 + Ex15 + W3(pump) = Ex14 + Ex13 + Ex11 + Ex9 + Exdestroyed (13) |
Proposition | Equation | Description |
---|---|---|
Proposition 01 | ∑Ex*(in) = ∑Ex*(out) (16) | Conservation of flows |
Proposition 02 | (Exi*/Exi) = (Exo*/Exo) → ki = ko (17) | Input proposition |
Proposition 03 | (Exi*/Exi) = (Exo′*/Exo’) →ki = ko′ (18) | Product proposition |
Proposition 04 | Exi*/Exi = 0 (19) | Loss proposition |
Proposition 05 | Exi* = Exi (20) | Proposition of lack of valuation |
Equipment | Value (USD/h) | Reference |
---|---|---|
Cost of biogas: C1 | 6.54 | [30] |
ICE: Z1 | 1.30 | [31] |
Evaporator (chiller): Z4 | 0.48 | [31] |
PV cooling system (Pump and heat exchanger): Z12 | 0.09 | Adapted from [23] |
Heat recovery: Z14 | 0.55 | [31] |
Equipment | P(1) 01 | P(1) 02 | P(1) 03 | P(1) 04 | P(1) 05 |
---|---|---|---|---|---|
Internal combustion engine | Ex1* = Ex2* + Ex6* +(Ex8* − Ex9*) + Ex10* (22) | (Ex1* + Ex9*)/(Ex1 + Ex9) = (Ex2* + Ex10* +Ex8* + Ex6*)/(Ex2* + Ex10* + Ex8* + Ex6*) (23) | (Ex2* + Ex10*)/ (Ex2 + Ex10) = (Ex8*-Ex9*)/ (Ex8-Ex9) (24) | Ex11* = 0 (25) | Ex1* = Ex1 (26) |
Chiller | (Ex2* − Ex3*) + Ex5* + Exw1* = Ex4* (27) | - | - | Ex3* = 0 (28) | Ex5* = Ex5 (29) |
Photovoltaic panels | Ex12* = Ex16* + Exw2* +Ex13* (30) | - | (Ex12*/Ex12) = (Ex13*/Ex13) (31) | - | Ex12* = Ex12 (32) |
Hot water tank | Ex14* − Ex15* = Exw3 + (Ex8* − Ex9*) + (Ex10* − Ex11*) + (Ex12* − Ex13*) (33) | - | - | Ex15* = 0 (34) | - |
Equipment | Cost (USD/h) | Auxiliary eq.R |
---|---|---|
Internal combustion engine | C1 + Z1 = C2 + C10 + C8 + C6 (35) | (C8 − C9)/(Ex8 − Ex9) = (C2 + C10)/(Ex2 + Ex10) (36) |
Chiller | C2 + C5 + Z4 = C4 (37) | C4/Ex4 = (C2 + C5)/(Ex2 + Ex5) (38) |
Photovoltaic panels | C12 + Z12 = C13 (39) | C12/Ex12 = C13/Ex13 (40) |
Hot water tank | C10 + (C12 − C13) + (C8 − C9) Z14 = C14 (41) | - |
Cost Rate | Reference [USD/h] | −10% [USD/h] | +10% [USD/h] |
---|---|---|---|
Biogas | 6.54 | 5.886 | 7.194 |
Operation: ICE | 1.30 | 1.170 | 1.430 |
Operation: Chiller | 0.48 | 0.432 | 0.528 |
Operation: Tank | 0.11 | 0.099 | 0.121 |
State | T [°C] | P [bar] | m [kg/s] | h [kJ/kg] | s [kJ/(kg.K)] | ex [kJ/kg] | Ex [kW] |
---|---|---|---|---|---|---|---|
1 (Biogas) | 30.1 | 1.02 | 0.0613 | 4638.00 | 11.62 | 18,570.00 | 1138.34 |
1 (Air) | 25.0 | 1.02 | 0.528 | 298.60 | 5.69 | 0 | 0 |
2 | 450.0 | 2.40 | 0.258 | 465.44 | 5.85 | 385.90 | 99.56 |
3 | 70.0 | 1.17 | 0.258 | 72.40 | 0.91 | 116.30 | 29.23 |
4 | 7.0 | 1.34 | 1.060 | 29.51 | 0.11 | 93.52 | 99.13 |
5 | 12.0 | 1.34 | 1.060 | 50.46 | 0.18 | 112.60 | 119.36 |
8 | 90.0 | 2.80 | 0.438 | 377.00 | 1.19 | 413.80 | 181.24 |
9 | 30.0 | 2.80 | 0.438 | 125.80 | 0.44 | 181.50 | 79.50 |
10 | 450.0 | 2.40 | 0.331 | 465.44 | 5.85 | 385.90 | 120.57 |
11 | 70.0 | 1.17 | 0.331 | 72.40 | 0.91 | 116.30 | 36.34 |
12 | 58.0 | 1.10 | 0.480 | 242.90 | 0.81 | 289.40 | 138.91 |
13 | 35.0 | 1.10 | 0.480 | 146.70 | 0.51 | 200.70 | 96.34 |
14 | 90.0 | 1.34 | 0.599 | 377.00 | 1.19 | 413.80 | 247.87 |
15 | 30.0 | 1.34 | 0.599 | 125.80 | 0.44 | 181.50 | 108.72 |
State | Exergy Ex [kW] | Thermoeconomic Cost Ex* [kW] | k [kW/kW] | ηex | C [USD/h] |
---|---|---|---|---|---|
1 (biogas) | 1138.34 | 1138.34 | 1.00 | 1.00 | 4.58 |
2 | 99.56 | 233.15 | 2.34 | 0.43 | 0.69 |
3 | 29.23 | 0.00 | 0.00 | - | 0.00 |
4 | 99.13 | 352.60 | 3.56 | 0.28 | 1.73 |
5 | 119.36 | 119.36 | 1.00 | 1.00 | 0.83 |
6 | 385.70 | 385.70 | 1.00 | 1.00 | 2.69 |
7 | 373.80 | 373.80 | 1.00 | 1.00 | 2.69 |
8 | 181.24 | 423.28 | 2.34 | 0.43 | 1.26 |
9 | 79.50 | 185.65 | 2.34 | 0.43 | 0.55 |
10 | 120.57 | 281.56 | 2.34 | 0.43 | 0.84 |
11 | 36.34 | 0.00 | 0.00 | - | 0.00 |
12 | 138.91 | 139.34 | 1.43 | 0.70 | 0.03 |
13 | 96.34 | 94.79 | 1.40 | 0.71 | 0.02 |
14 | 247.87 | 844.19 | 3.41 | 0.29 | 1.70 |
15 | 108.72 | 0.00 | 0.00 | - | 0.00 |
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Moreira, J.L.B.; Marques, A.d.S.; Lago, T.G.S.d.; Arruda, V.C.d.L.; Carvalho, M. Thermoeconomic Evaluation of a High-Performance Solar Biogas Polygeneration System. Energies 2024, 17, 4172. https://doi.org/10.3390/en17164172
Moreira JLB, Marques AdS, Lago TGSd, Arruda VCdL, Carvalho M. Thermoeconomic Evaluation of a High-Performance Solar Biogas Polygeneration System. Energies. 2024; 17(16):4172. https://doi.org/10.3390/en17164172
Chicago/Turabian StyleMoreira, José Luciano Batista, Adriano da Silva Marques, Taynara Geysa Silva do Lago, Victor Carlos de Lima Arruda, and Monica Carvalho. 2024. "Thermoeconomic Evaluation of a High-Performance Solar Biogas Polygeneration System" Energies 17, no. 16: 4172. https://doi.org/10.3390/en17164172