A Multi-Objective Optimization Model for the Design of Biomass Co-Firing Networks Integrating Feedstock Quality Considerations
Abstract
:1. Introduction
2. Problem Definition
- planning horizon which consists of time intervals ;
- A set of biomass sources , with a maximum available amount of in period t with bulk density, , moisture content, , ash content, , and higher heating value ;
- The biomass has an associated cost of ;
- The biomass has to be transported from source i to pre-treatment facility j a distance of and that the biomass quality degrades with a damage factor of ;
- The transport of biomass from source i to pretreatment facility j has a weight capacity of and volume capacity of in period t, an associated cost of and emission of ;
- A set of biomass pre-treatment facilities which can process with a capacity of and store a capacity of in period t;
- Pre-treatment facility j can improve the biomass properties based on the facility’s ash improvement efficiency, , and moisture content improvement efficiency, , and improve bulk density to ;
- There are associated costs for the operation of the pretreatment facility (), the processing of biomass ();
- The biomass stored in the pre-treatment facility degrades with a damage factor of and increases in moisture content by in period t;
- The processed biomass has to be transported from pre-treatment facility j to coal power plant l a distance of and that the processed biomass degrades by a factor during transport;
- Transport from pretreatment facility j to coal power plant l has a weight capacity of and volume capacity in period t;
- A set of coal sources which can provide a maximum amount of coal in period t with bulk density, , moisture content, , ash content, , and lower heating value, ;
- The coal has an associated cost of ;
- The coal should be transported from coal source k to coal power plant l a distance of ;
- The transport of coal from source k to powerplant l has a transport weight capacity of and transport volume capacity of , an associated cost of and emission of ;
- A set of coal-fired power plants with combustion capacity which can be retrofitted for biomass co-firing to meet the total demand of energy for period t;
- The coal power plant l will have an efficiency of in period t;
- The coal power plant l will have upper () and lower () coal displacement limits if retrofitted, maximum allowable ash content (), and upper () and lower () moisture content limits;
3. System Definition
3.1. Biomass Co-Firing Network
3.2. Economic Considerations
3.3. Environmental Considerations
4. Model Formulation
4.1. Constraints
4.2. Objective Function
4.2.1. Cost Component
4.2.2. Emissions Component
5. Model Implementation
5.1. Base Case
5.1.1. Minimizing Cost
5.1.2. Minimizing Emissions
5.1.3. Full Model Run
6. Scenario Analysis
6.1. Impact of Feedstock Properties Consideration
6.2. Biomass Properties
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
PF 1 | PF 2 | PF 3 | |
---|---|---|---|
B 1 | 15 | 20 | 25 |
B 2 | 25 | 20 | 20 |
B 3 | 25 | 18 | 17 |
PP 1 | PP 2 | PP 3 | |
---|---|---|---|
PF 1 | 10 | 17 | 9 |
PF 2 | 15 | 20 | 15 |
PF 3 | 18 | 18 | 18 |
PP 1 | PP 2 | PP 3 | |
---|---|---|---|
C 1 | 15 | 15 | 15 |
C 2 | 10 | 15 | 12 |
C 3 | 15 | 20 | 18 |
B 1 | B 2 | B 3 | |
Biomass Price (US$/kg) | 2.5 | 1.75 | 1.5 |
C 1 | C 2 | C 3 | |
Coal Price (US$/kg) | 3 | 1.75 | 2 |
PP 1 | PP 2 | PP 3 | |
Retrofitting Cost (US$) | 5000 | 7000 | 4300 |
Fixed Operating Cost (US$) | Fixed Biomass Option (US$) | |||||
Period 1 | Period 2 | Period 3 | Period 1 | Period 2 | Period 3 | |
PP 1 | 350 | 300 | 350 | 20 | 24 | 35 |
PP 2 | 300 | 450 | 375 | 60 | 45 | 30 |
PP 3 | 385 | 375 | 385 | 35 | 30 | 45 |
Biomass Combustion Cost (US$/kg) | Coal Combustion Cost (US$/kg) | |||||
Period 1 | Period 2 | Period 3 | Period 1 | Period 2 | Period 3 | |
PP 1 | 2 | 3 | 1.5 | 2 | 2.25 | 2.5 |
PP 2 | 5 | 4 | 1 | 3 | 2.75 | 2.8 |
PP 3 | 4 | 3.5 | 5 | 2.6 | 2.5 | 3 |
Fixed Expansion Costs (US$) | Unit Expansion Costs (US$/kg) | |||||
Period 1 | Period 2 | Period 3 | Period 1 | Period 2 | Period 3 | |
PP 1 | 300 | 295 | 325 | 1 | 1 | 1 |
PP 2 | 500 | 375 | 350 | 1.25 | 1.25 | 1.5 |
PP 3 | 475 | 388 | 420 | 1.75 | 1.5 | 1 |
Fixed Operating Cost (US$) | Biomass Pretreatment Cost (US$/kg) | |||||
Period 1 | Period 2 | Period 3 | Period 1 | Period 2 | Period 3 | |
PF 1 | 50 | 75 | 80 | 3 | 1 | 1.5 |
PF 2 | 80 | 69 | 78 | 2 | 2 | 2 |
PF 3 | 68 | 80 | 75 | 1.7 | 2.15 | 1.85 |
Fixed Expansion Costs (US$) | Unit Expansion Costs (US$/kg) | |||||
Period 1 | Period 2 | Period 3 | Period 1 | Period 2 | Period 3 | |
PF 1 | 200 | 350 | 300 | 1 | 1.25 | 1.5 |
PF 2 | 500 | 400 | 450 | 1.75 | 1.5 | 1.1 |
PF 3 | 200 | 375 | 425 | 1.25 | 1 | 1.35 |
Fixed Holding Costs (US$) | Unit Holding Costs (US$/kg) | |||||
Period 1 | Period 2 | Period 3 | Period 1 | Period 2 | Period 3 | |
PF 1 | 50 | 35 | 75 | 0.5 | 0.15 | 0.3 |
PF 2 | 100 | 65 | 45 | 0.15 | 0.2 | 0.25 |
PF 3 | 50 | 50 | 50 | 0.3 | 0.25 | 0.2 |
Biomass Pretreatment Emissions | 0.03 kg CO2/kg |
Transportation Emissions | 0.12 kg CO2/km |
Biomass Combustion Emissions | 0.08 kg CO2/kg |
Coal Combustion Emissions | 0.50 kg CO2/kg |
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Indices | Definition | |
i | Biomass source locations | |
j | Pretreatment facilities | |
k | Coal source locations | |
l | Coal power plants | |
t | Time period | |
Parameters | Definition | Units |
Cost value when environmental emissions is minimized | Million US$ | |
Minimum achievable cost | Million US$ | |
Environmental emissions value when cost is minimized | kt CO2 | |
Minimum achievable environmental emissions | kt CO2 | |
Amount of energy demanded on period t | MJ | |
Amount of biomass available at biomass source location i in period t | kt | |
Amount of coal available a coal source location k in period t | kt | |
Upper coal displacement limit of coal power plant l | % | |
Lower coal displacement limit of coal power plant l | % | |
Storage capacity in pretreatment facility j in period t | kt | |
Bulk density of raw biomass from source i in period t | kg/m3 | |
Bulk density of pretreated biomass in pretreatment facility j in period t | kg/m3 | |
Bulk density of coal | kg/m3 | |
Moisture content of raw biomass from source i in period t | % wt. | |
Moisture content of coal | % wt. | |
Lower heating value of coal | MJ/kg | |
Higher heating value of biomass | MJ/kg | |
Ash content of raw biomass from source i in period t | % wt. | |
Ash content of coal | % wt. | |
Maximum allowable ash content in coal power plant l | % wt. | |
Maximum allowable moisture content in coal power plant l | % wt. | |
Minimum allowable moisture content in coal power plant l | % wt. | |
Ash content improvement efficiency in pretreatment facility j | % | |
Moisture content improvement efficiency in pretreatment facility j | % | |
Biomass damage factor from storing in pretreatment facility j | % | |
Biomass damage factor from transporting raw biomass from source i to pretreatment facility j | % | |
Biomass damage factor from transporting pretreated biomass from pretreatment facility j to coal power plant l | % | |
Increase in moisture content due to storage in pretreatment facility j in period t | % | |
Distance from biomass source i to pretreatment facility j | km | |
Distance from pretreatment facility j to coal power plant l | km | |
Distance from coal source k to coal power plant l | km | |
Transport weight capacity from biomass source i to pretreatment facility j in period t | kt | |
Transport weight capacity from pretreatment facility j to power plant l in period t | kt | |
Transport weight capacity from coal source k to coal power plant l in period t | kt | |
Transport volume capacity from biomass source i to pretreatment facility j in period t | m3 | |
Transport volume capacity from pretreatment facility j to power plant l in period t | m3 | |
Transport volume capacity from coal source k to coal power plant l in period t | m3 | |
Cost to retrofit coal power plant l | Million US$ | |
Fixed cost to operate coal power plant l on period t | Million US$ | |
Fixed cost to use biomass option in coal power plant l on period t | Million US$ | |
Biomass combustion cost in coal power plant l on period t | US$/kg | |
Coal combustion cost in coal power plant l in period t | US$/kg | |
Fixed cost to operate pretreatment facility j in period t | Million US$ | |
Biomass pretreatment cost in facility j in period t | US$/kg | |
Fixed cost to expand the capacity of pretreatment facility j in period t | Million US$ | |
Unit capacity expansion cost of pretreatment facility j in period t | US$/kg | |
Fixed cost to expand the capacity of power plant l in period t | Million US$ | |
Unit capacity expansion cost of coal power plant l in period t | US$/kg | |
Fixed cost to store in pretreatment facility j in period t | Million US$ | |
Unit holding cost in pretreatment facility j in period t | US$/kg | |
Cost to transport raw biomass from source i to pretreatment facility j in period t per trip | US$/kg-km | |
Cost to transport pretreated biomass from pretreatment facility j to coal power plant l in period t per trip | US$/kg-km | |
Cost to transport coal from source k to coal power plant l in period t per trip | US$/kg-km | |
Cost of biomass from source i in period t | US$/kg | |
Cost of coal from source k in period t | US$/kg | |
Emissions due to biomass pretreatment in facility j in period t | kg CO2/kg | |
Emissions due to biomass combustion in coal power plant l in period t | kg CO2/kg | |
Emissions due to coal combustion in power plant l in period t | kg CO2/kg | |
Emissions due to transporting raw biomass from source i to pretreatment facility j in period t | kg CO2/kg-km | |
Emissions due to transporting pretreated biomass from pretreatment facility j to coal power plant l in period t | kg CO2/kg-km | |
Emissions due to transporting coal from source k to power plant l in period t | kg CO2/kg-km | |
System Variables | Definition | Units |
Ending biomass inventory in pretreatment facility j in period t | kt | |
Weight of biomass received and pretreated in pretreatment facility j in period t | kt | |
Lower heating value of biomass in coal power plant l in period t | MJ/kg | |
Lower heating value of the mixed feedstock in coal power plant l in period t | MJ/kg | |
Moisture content of pretreated biomass from source j in period t | % wt. | |
Moisture content of all biomass in pretreatment facility j in period t | % wt. | |
Moisture content of biomass in coal power plant l in period t | % wt. | |
Moisture content of mixed feedstock in power plant l in period t | % wt. | |
Ash content of pretreated biomass from source j in period t | % wt. | |
Ash content of all biomass in pretreatment facility j in period t | % wt. | |
Ash content of biomass in coal power plant l in period t | % wt. | |
Ash content of mixed feedstock in coal power plant l in period t | % wt. | |
Accumulated excess moisture content of feedstock in power plant l in period t | % wt. | |
Accumulated lack in moisture content of feedstock in power plant l in period t | % wt. | |
Accumulated excess ash content of feedstock in coal power plant l in period t | % wt. | |
Accumulated feedstock processed in power plant l in period t | kt | |
Efficiency loss of equipment in coal power plant l in period t | - | |
Number of trips to transport raw biomass from source i to pretreatment facility j in period t | Trips | |
Number of trips to transport pretreated biomass from pretreatment facility j to coal power plant l in period t | Trips | |
Number of trips to transport coal from source k to coal power plant l in period t | Trips | |
Combustion capacity of coal power plant l in period t | kt | |
Pretreatment capacity in facility j in period t | kt | |
Decision Variables | Definition | Units |
Amount of biomass transported from biomass source locations i to pretreatment facilities j in period t | kt | |
Amount of biomass transported from pretreatment facilities j to power plant l in period t | kt | |
Amount of coal transported from coal source location k to power plant l in period t | kt | |
Capacity expansion for pretreatment facility j in period t | kt | |
Capacity expansion for coal power plant l in period t | kt | |
Binary variable, 1 if coal power plant l is retrofitted | - | |
Binary variable, 1 if biomass option of coal power plant l is used in period t | - | |
Binary variable, 1 if storage in pretreatment facility j is used in period t | - | |
Binary variable, 1 if pretreatment facility j is operating in period t | - | |
Binary variable, 1 if coal power plant l is operating in period t | - | |
Binary variable, 1 if pretreatment facility j undergoes capacity expansion in period t | - | |
Binary variable, 1 if coal power plant l undergoes capacity expansion in period t | - |
Period 1 | Period 2 | Period 3 | |
---|---|---|---|
Demand (MJ) | 47,000 | 48,500 | 49,000 |
Biomass Supply (kt) | |||
B 1 | 800 | 900 | 1050 |
B 2 | 1000 | 750 | 1200 |
B 3 | 1200 | 1050 | 850 |
Coal Supply (kt) | |||
C 1 | 1550 | 1350 | 1000 |
C 2 | 800 | 1000 | 900 |
C 3 | 3000 | 2250 | 2500 |
Bulk Density (kg/m3) | Moisture Content (% wt.) | Ash Content (% wt.) | |||||||
---|---|---|---|---|---|---|---|---|---|
Period 1 | Period 2 | Period 3 | Period 1 | Period 2 | Period 3 | Period 1 | Period 2 | Period 3 | |
B 1 | 50 | 30 | 55 | 17 | 18 | 20 | 17 | 18 | 20 |
B 2 | 35 | 40 | 40 | 25 | 20 | 19 | 25 | 20 | 19 |
B 3 | 60 | 70 | 55 | 18 | 23 | 22 | 18 | 23 | 22 |
Ash | Moisture | Bulk Density (kg/m3) | Storage Damage Factor | Storage Capacity (kt) | |
---|---|---|---|---|---|
PF 1 | 65% | 35% | 25 | 2 | 1350 |
PF 2 | 76% | 52% | 20 | 7 | 1000 |
PF 3 | 54% | 67% | 30 | 5 | 2250 |
Displacement Limits (%) | Ash Content (% wt.) | Moisture Content (% wt.) | |
---|---|---|---|
PP 1 | [0, 40] | 0 | [10, 12] |
PP 2 | [0, 45] | 0 | [10, 12] |
PP 3 | [0, 40] | 0 | [10, 12] |
Bulk Density (kg/m3) | 78.5 |
Lower Heating Value (MJ/kg) | 30 |
Ash Content (% wt.) | 5 |
Moisture Content (% wt.) | 9 |
Potential | Minimizing Cost | Minimizing Emissions | Complete Model Run | ||
---|---|---|---|---|---|
Efficiency | |||||
Cost (Million US$) | 45,959.97 | 45,959.97 | 360,920.00 | 80,859.36 | 0.8892 |
Emissions (kt CO2) | 3491.29 | 4858.40 | 3491.29 | 3642.78 | 0.8892 |
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San Juan, J.L.G.; Aviso, K.B.; Tan, R.R.; Sy, C.L. A Multi-Objective Optimization Model for the Design of Biomass Co-Firing Networks Integrating Feedstock Quality Considerations. Energies 2019, 12, 2252. https://doi.org/10.3390/en12122252
San Juan JLG, Aviso KB, Tan RR, Sy CL. A Multi-Objective Optimization Model for the Design of Biomass Co-Firing Networks Integrating Feedstock Quality Considerations. Energies. 2019; 12(12):2252. https://doi.org/10.3390/en12122252
Chicago/Turabian StyleSan Juan, Jayne Lois G., Kathleen B. Aviso, Raymond R. Tan, and Charlle L. Sy. 2019. "A Multi-Objective Optimization Model for the Design of Biomass Co-Firing Networks Integrating Feedstock Quality Considerations" Energies 12, no. 12: 2252. https://doi.org/10.3390/en12122252