Stochastic Programming Model Integrating Pyrolysis Byproducts in the Design of Bioenergy Supply Chains
Abstract
:1. Introduction
1.1. Literature Review
1.2. Contributions
2. Mathematical Model
- : Nodes of distribution network , for all .
- : Arcs of distribution network , for all .
- : Set of counties(suppliers) for all .
- : Set of potential locations for depots, for all .
- : Set of potential locations for biorefineries, .
- : Set of power plants (coal), .
- : Set of cities, .
- : Set of arcs from to , .
- : Set of arcs from to , .
- : Set of arcs from to , .
- : Set of arcs from to , .
- : Set of technologies for conversion, .
- : Set of scenarios, .
- : Investment cost to open a depot at node .
- : Investment cost to open a biorefinery at location utilizing technology .
- : Fixed cost of loading/unloading a unit train along arc every week for a period of one year (52 weeks).
- : Unit transportation and procurement cost charged per metric ton shipped along arc .
- : Total unit cost charged per metric ton shipped along arc .
- : Fixed unit cost charged per metric ton shipped along arc .
- : Fixed unit cost charged per metric ton shipped along arc .
- : Variable unit cost charged per metric ton per kilometer along arc .
- : Variable unit cost charged per liter per kilometer along .
- : Distance of arc (kilometers) .
- : Distance of arc (kilometers) .
- : Represents the penalty cost for demand shortage of coal.
- : Represents the penalty cost for demand shortage of bioethanol.
- : Represents the monetary value per liter of biodiesel.
- : Conversion factor for biomass/biochar supplied to power plant applying pyrolysis.
- : Conversion factor for biomass pyrolysis oil to bioethanol.
- : Conversion factor for biomass pyrolysis oil to biodiesel.
- : Maximum capacity of a unit train along arc .
- : Represents the preprocessing capacity of depot facility .
- : Production capacity of biorefinery including technology .
- : Distance from biorefinery to power plant.
- : Distance from biorefinery to city.
- : Total demand of biochar.
- : Total demand of bioethanol.
- : Byproduct share of biochar.
- : Byproduct share of bio-oil.
- : Total unit cost charged per metric ton shipped along arc under scenario .
- : Available supply in county for scenario .
- : Probability of scenario .
- : Target moisture content of conversion technology.
- : Target ash content of conversion technology.
- : Boiler maintenance cost.
- : Densification cost at .
- : Cooling cost at .
- : Electricity cost at .
- : Grinding loss in stage 1 at .
- : Grinder feed rate at .
- : Moisture-related cost under scenario for a given .
- : Grinding cost under scenario .
- : Energy consumption due to the grinder at by processing biomass delivered from farm .
- : Moisture content of biomass coming from farm for scenario .
- : Energy consumption due to the rotary shear at .
- : Moisture content of biomass after grinder at .
- : Biomass screen size after grinder at under scenario .
- : Ash removal and disposal cost under scenario for a given .
- : Ash content of biomass coming from county for scenario .
- : A binary variable, which takes the value 1 if a depot is connected with a biorefinery , and 0 otherwise.
- : A binary variable which takes the value 1 if if the potential location is used as a biorefinery utilizing technology , and 0 otherwise.
- : A binary variable which takes the value 1 if potential location is used as depot, and 0 otherwise.
- : Flow along arc under scenario .
- : Flow along arc under scenario .
- : Flow along arc under scenario .
- : Flow along arc under scenario .
- : Variable cost incurred by product shipped along arc after diesel related cost reduction under scenario .
- : Variable cost incurred by product shipped along arc after diesel related cost reduction under scenario .
- : Quantity of biodiesel allocated to shipping cost reduction along arc under scenario .
- : Quantity of biodiesel allocated to shipping cost reduction along arc under scenario .
- : Third party coal supply under scenario .
- : Third party bioethanol supply under scenario .
Costs along Arc
3. Case Study
3.1. Biomass Supply
- The available biomass.
- The biomass moisture content.
- The biomass ash content.
- The weather condition scenario.
3.2. Scenario Generation
- Gather historical data of the daily precipitation level of every county.
- Use the historical data to estimate the weighted average yearly precipitation for every county.
- Depending on the levels of daily precipitation, a county is classified as humid or dry. If the value is above average, the county is considered humid and vice-versa.
- Calculate the frequency of a county’s humid conditions for harvesting.
- Set the number of scenarios.
- Generate n random numbers to classify a county as humid or dry. A random number above the probability assigns a county as dry and a lower number assigns a county as humid.
- The moisture content of a humid county is sampled from the right-hand side of the triangular distribution and vice-versa.
- The triangular distribution is used to generate a random ash content.
3.3. Depots
3.4. Biorefineries
3.5. Transportation and Other Costs
3.6. Power Plants
3.7. Cities
4. Results
4.1. Numerical Results
4.2. Sensitivity Analysis
5. Conclusions and Future Work
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Authors | Bowling, and El-Halwagi 2011 [17] | Castillo-Villar, Eksioglu, Taherkhorsandi, 2017 [18] | Aboytes-Ojeda, Castillo-Villar Eksioglu, 2018 [19] | This Work |
---|---|---|---|---|
Hub-and-spoke network | X | X | X | X |
Considers variability in moisture and ash content | X | X | X | |
Utilizes depots to reduce transportation costs and processing variability | X | X | ||
Uses L-shape Method | X | X | X | |
Considers multiple biomass byproducts | X |
Cost | Type | Value | Units |
---|---|---|---|
Natural Gas | Variable | 10.37 | $/Mg Dry Biomass |
Chemicals | Variable | 33.17 | $/Mg Dry Biomass |
Waste | Variable | 1.04 | $/Mg Dry Biomass |
Electricity | Variable | 9.32 | $/Mg Dry Biomass |
Fixed Costs | Fixed | 39,312,000 | $/Year |
Depreciation | Fixed | 25,974,000 | $/Year |
Taxes | Fixed | 7,722,000 | $/Year |
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Keith, K.; Castillo-Villar, K.K. Stochastic Programming Model Integrating Pyrolysis Byproducts in the Design of Bioenergy Supply Chains. Energies 2023, 16, 4070. https://doi.org/10.3390/en16104070
Keith K, Castillo-Villar KK. Stochastic Programming Model Integrating Pyrolysis Byproducts in the Design of Bioenergy Supply Chains. Energies. 2023; 16(10):4070. https://doi.org/10.3390/en16104070
Chicago/Turabian StyleKeith, Kolton, and Krystel K. Castillo-Villar. 2023. "Stochastic Programming Model Integrating Pyrolysis Byproducts in the Design of Bioenergy Supply Chains" Energies 16, no. 10: 4070. https://doi.org/10.3390/en16104070