Introduction
Literature
Cultivation systems
First-generation technology
Second-generation technology
Third-generation technology
References | Biofuel generation | Objective function | Uncertainty | Technology | |||
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First | Second | Third | Economic | Environmental | |||
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[47] | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | |||
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[29] | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | ||||
[25] | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | ||||
[38] | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | ||
[2] | \(\checkmark \) | \(\checkmark \) | |||||
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[13] | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | ||||
[28] | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | |||
[42] | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | |||
[46] | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | ||
This paper | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) | \(\checkmark \) |
Problem statement
Methodology
Macro-stage
Micro-stage
Model formulation
Deterministic model
Index | Definition |
---|---|
F | Set of fresh water sources |
W | Set of waste water sources |
K | Set of nutrient fertilizer markets |
V | Set of methane markets |
P | Set of power plants |
J | Set of final products |
M | Set of markets |
T | Set of time stages |
Variable | Definition |
---|---|
\(\hbox {xow}^t_f\) | Transported fresh water from source f to cultivation stage in period t |
\(\hbox {xow}^t_w\) | Transported waste water from source w to cultivation stage in period t |
\(\hbox {xw}^t\) | Transported water from lipid extraction to cultivation stage in period t |
\(\hbox {xof}^t_k\) | Purchased nutrient fertilizer from market k in period t |
\(\hbox {xc}^t\) | Transported carbon dioxide from drying to cultivation stage in period t |
\(\hbox {xc}^t_1\) | Transported carbon dioxide from lipid extraction to cultivation stage in period t |
\(\hbox {xc}^t_2\) | Transported carbon dioxide from conversion to cultivation stage in period t |
\(\hbox {xc}^t_p\) | Transported carbon dioxide from power plant p to cultivation stage in period t |
\(\hbox {xm}^t\) | Transported methane from digestion to conversion stage in period t |
\(\hbox {xom}^t_v\) | Transported methane from market v to cultivation stage in period t |
\(v^t_j\) | Inventory level of product j in period t |
\(x^t\) | Amount of micro-algae in period t |
\(y^t_{jm}\) | Quantity of final product j sent to market m in period t |
\(l_f\) | 1 if a pipeline is constructed between source f and cultivation stage, otherwise 0 |
\(l_p\) | 1 if a pipeline is constructed between power plant p and cultivation stage, otherwise 0 |
\(l_w\) | 1 if a pipeline is constructed between source w and cultivation stage, otherwise 0 |
Parameter | Definition |
---|---|
\(\hbox {oh}^t\) | Unit of operational cost in harvesting stage in period t |
\(\hbox {od}^t\) | Unit of operational cost in drying stage in period t |
\(\hbox {ol}^t\) | Unit of operational cost in lipid extraction stage in period t |
\(\hbox {oe}^t\) | Unit of operational cost in digestion stage in period t |
\(\hbox {ov}^t\) | Unit of operational cost in conversion stage in period t |
\(\hbox {pow}^t_f\) | Unit of fresh water purchasing cost from source f in period t |
\(\hbox {pof}^t_k\) | Unit of nutrient fertilizer purchasing cost from market k in period t |
\(\hbox {pom}^t_v\) | Unit of methane purchasing cost from market v in period t |
\(T_f\) | Unit of pipeline construction cost between the source of fresh water f and the cultivation stage |
\(T_w\) | Unit of pipeline construction cost between the source of waste water w and the cultivation stage |
\(T_p\) | Unit of pipeline construction cost between power plant p and the cultivation stage |
n | Nutrient required for unit of biomass |
\(\alpha \) | Water required for unit of biomass |
\(\hbox {Co}_2\) | Carbon dioxide required for unit of biomass |
\(m_j\) | Required methane to produce product j |
\(n_i\) | Amount of nutrient fertilizer obtained from unit of waste water |
\(\mu _j\) | Amount of product j produced in the conversion stage |
\(C^t_f\) | Capacity of sources f in period t |
\(C^t_w\) | Capacity of sources w in period t |
\(C^t_p\) | Capacity of power plant p in period t |
\(\eta _1\) | Conversion rate of biomass to carbon dioxide at drying stage |
\(\eta _2\) | Conversion rate of biomass to carbon dioxide at lipid extraction stage |
\(\eta _3\) | Conversion rate of biomass to carbon dioxide at conversion stage |
\(\lambda \) | Conversion rate of biomass to water at lipid extraction stage |
\(\theta \) | Achievable methane from digestion stage |
\(\beta \) | Productivity of cultivation stage |
\(\beta _1\) | Productivity of harvesting stage |
\(\beta _2\) | Productivity of drying stage |
\(\beta _3\) | Conversion rate of lipids to oil |
\(\beta _4\) | Conversion rate of oil to final product |
\(\beta _5\) | Conversion rate of biomass to solid waste |
\(R_{\hbox {CO}_2}\) | Released carbon dioxide |
\(R_{\hbox {N}_2\hbox {O}}\) | Released Nitrogen |
\(R_{\hbox {CH}_4}\) | Released Methane |
\(d^t_j\) | Demand for final product j in period t |
\(h^t_j\) | Unit of inventory cost of final product j in period t |
\(p^t_j\) | Sale price of final product j in period t |
Robust model
Variable | Definition |
---|---|
\(\hbox {xow}^{ts}_f\) | Transported fresh water from source f to cultivation stage in period t and under scenario s |
\(\hbox {xow}^{ts}_w\) | Transported waste water from source w to cultivation stage in period t and under scenario s |
\(\hbox {xw}^{ts}\) | Transported water from lipid extraction to cultivation stage in period t and under scenario s |
\(\hbox {xof}^{ts}_k\) | Purchased nutrient fertilizer from market k in period t and under scenario s |
\(\hbox {xc}^{ts}\) | Transported carbon dioxide from drying stage to cultivation stage in period t and under scenario s |
\(\hbox {xc}^{ts}_1\) | Transported carbon dioxide from lipid extraction stage to cultivation stage in period t and under scenario s |
\(\hbox {xc}^{ts}_2\) | Transported carbon dioxide from conversion stage to cultivation stage in period t and under scenario s |
\(\hbox {xc}^{ts}_p\) | Transported carbon dioxide from power plant p to cultivation stage in period t and under scenario s |
\(\hbox {xm}^{ts}\) | Transported methane from digestion stage to conversion stage in period t and under scenario s |
\(\hbox {xom}^{ts}_v\) | Transported methane from market v to cultivation stage in period t and under scenario s |
\(v^{ts}_j\) | Inventory level of product j in period t and under scenario s |
\(x^{ts}\) | The amount of micro-algae in period t and under scenario s |
\(y^{ts}_{jm}\) | Quantity of final product j sent to market m in period t and under scenario s |
\(l_f\) | 1 if a pipeline is constructed between source f and cultivation stage, otherwise 0 |
\(l_p\) | 1 if a pipeline is constructed between power plant p and cultivation stage, otherwise 0 |
\(l_w\) | 1 if a pipeline is constructed between source w and cultivation stage, otherwise 0 |
Results
Parameters
Final Product | Market | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 |
---|---|---|---|---|---|---|
Biodiesel | \(m=1\) | 0.3 | 1.1 | 2.3 | 3 | 3.2 |
\(m=2\) | 0.9 | 2.0 | 3.1 | 3 | 4.2 | |
\(m=3\) | 0.8 | 0.9 | 1.6 | 4 | 4.6 | |
Glycerin | \(m=1\) | 0.08 | 0.05 | 0.25 | 0.39 | 0.21 |
\(m=2\) | 0.04 | 0.15 | 0.27 | 0.44 | 0.69 | |
\(m=3\) | 0.06 | 0.2 | 0.18 | 0.17 | 0.3 |
Stages | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 |
---|---|---|---|---|---|
Harvesting | $31.2 | $34.3 | $37.8 | $41.5 | $45.7 |
Drying | $139.1 | $153 | $168.3 | $185.1 | $203.6 |
Lipid extraction | $42.2 | $46.4 | $51 | $56.1 | $61.7 |
Digestion | $14.5 | $15.9 | $17.5 | $19.2 | $21 |
Conversion | $17.2 | $19 | $20.8 | $23 | $25.3 |
Macro-stage
Cost | Efficiency (%) | Pollution (%) | Land use | |
---|---|---|---|---|
Open pond | 415 | 11 | 33 | 301 |
Flat-plate photobioreactor | 596 | 27 | 15 | 50 |
Tubular photobioreactor | 495 | 25 | 23 | 14.6 |
Open pond | Flat-plate photobioreactor | Tubular photobioreactor | |
---|---|---|---|
Total score | 253 | 303.9 | 276.19 |
Micro-stage
Sources | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 |
---|---|---|---|---|---|
Power plant | 540.2 | 607.1 | 486.8 | 634.4 | 675.8 |
Drying | 186.8 | 175.6 | 172.1 | 215.2 | 191.3 |
Lipid extraction | 12.1 | 22 | 19.8 | 29.1 | 22.3 |
Conversion | 8.8 | 11.7 | 9.6 | 8.7 | 10.6 |
Sources | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 |
---|---|---|---|---|---|
Market-first source | 0 | 0 | 0 | 0 | 25.3 |
Market-second source | 0 | 0 | 0 | 0 | 0 |
Waste water-first source | 299.5 | 131.5 | 125.2 | 252.5 | 270.1 |
Sources | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 |
---|---|---|---|---|---|
Market-first source | 0 | 0 | 0 | 0 | 0 |
Digestion | 0.21 | 0.41 | 0.35 | 0.46 | 0.49 |