Abstract
With the increasing attention to the environmental impact of discharging greenhouses gases, there has been a growing public pressure to reduce the carbon footprint associated with the use of fossil fuels. In this context, one of the key strategies is the substitution of fossil fuels with biofuels such as biodiesel. The design of biodiesel production facilities has traditionally been carried out based on technical and economic criteria. Greenhouse gas (GHG) policies (e.g., carbon tax, subsidy) have the potential to significantly alter the design of these facilities, the selection of the feedstocks, and the scheduling of multiple feedstocks. The objective of this article is to develop a systematic approach to the design and scheduling of biodiesel production processes while accounting for the effect of GHG policies in addition to the technical, economic, and environmental aspects. An optimization formulation is developed to maximize the profit of the process subject to flowsheet synthesis and performance modeling equations. Furthermore, the carbon footprint is accounted for with the help of a life cycle analysis (LCA). The objective function includes a term which reflects the impact of the LCA of a feedstock and its processing to biodiesel. A multiperiod approach is used to discretize the decision-making horizon into time periods. During each period, decisions are made on the type and flowrate of the feedstocks, as well as the associated design and operating variables. A case study is solved with several scenarios of feedstocks and GHG policies.
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Abbreviations
- GHG:
-
Greenhouse gas
- LCA:
-
Life cycle analysis
- FAME:
-
Fatty acid methyl esters
- GREET:
-
Greenhouse gases regulated emissions and energy use in transportation
- EIO-LCA:
-
Economic input–output life cycle assessment
- N f :
-
Number of feedstock alternatives f
- f :
-
Index for feedstock alternatives
- \( E_{\text{feedstock}}^{{{\text{CO}}_{2} }} \) :
-
CO2 emissions for a given feedstock
- U :
-
A set of pretreatment units
- u :
-
Index for pretreatment units
- N T :
-
Number of pretreatment units, u
- INPUT u :
-
The set of input streams for pretreatment unit u
- i u :
-
Index to represent input streams for pretreatment unit u
- N in u :
-
Number of input streams for pretreatment unit u
- OUTPUT u :
-
The set of output streams for pretreatment unit u
- j v :
-
Index to represent output streams for pretreatment unit u
- N out u :
-
Number of output streams for pretreatment unit u
- \( F_{{i_{u} }} \) :
-
Flowrate of input stream i u
- \( X_{{i_{u} ,q}} \) :
-
Composition of component q in input stream i u
- \( G_{{j_{u} }} \) :
-
Flowrate of output stream j u
- \( Y_{{j_{u} ,q}} \) :
-
Composition of component q in output stream j u
- V :
-
A set of common process units
- v :
-
Index for common process units
- N PU :
-
Number of common process units v
- INPUT v :
-
The set of input streams for common process unit v
- i v :
-
Index to represent input streams for common process unit v
- N in v :
-
Number of input streams for common process unit v
- OUTPUT v :
-
The set of output streams for common process unit v
- j v :
-
Index to represent output streams for common process unit v
- N out v :
-
Number of output streams for common process unit v
- \( F_{{i_{v} }} \) :
-
Flowrate of input stream i v
- \( X_{{i_{v} ,q}} \) :
-
Composition of component q in input stream i v
- \( G_{{j_{v} }} \) :
-
Flowrate of output stream j v
- \( Y_{{j_{v} ,q}} \) :
-
Composition of component q in output stream j v
- P :
-
A set of product discharges
- p :
-
Index for product discharges
- N p :
-
Number of product discharges p
- W :
-
A set of waste discharges
- w :
-
Index for waste discharges
- N w :
-
Number of waste discharges
- B :
-
A set of intermediate streams that are redirected back into the process
- b :
-
Index for intermediate streams that are redirected back into the process
- N b :
-
Number of intermediate streams that are redirected back into the process
- i b :
-
Index to represent input stream for the “intermediate block”
- \( F_{{i_{b} }} \) :
-
Flowrate of input stream i b
- \( X_{{i_{b} ,q}} \) :
-
Composition of component q in input stream i b
- j b :
-
Index to represent output stream for the ‘intermediate block’
- \( G_{{j_{b} }} \) :
-
Flowrate of output stream j b
- \( Y_{{j_{b} ,q}} \) :
-
Composition of component q in output stream j b
- t h :
-
Decision-making time horizon
- N t :
-
Number of time intervals or periods t
- t :
-
Time interval or period
- PERIODS:
-
A set of operation intervals or periods
- \( E_{u}^{{{\text{CO}}_{2} }} \) :
-
CO2 emitted by pretreatment unit u
- \( E_{v}^{{{\text{CO}}_{2} }} \) :
-
CO2 emitted by common process unit v
- \( E_{\text{soy}}^{{{\text{CO}}_{2} ,{\text{growth}}}} \) :
-
CO2 emitted for growth of soy feedstock
- \( E_{\text{soy}}^{{{\text{CO}}_{2} ,{\text{harvesting}}}} \) :
-
CO2 emitted for harvesting of soy feedstock
- \( E_{\text{soy}}^{{{\text{CO}}_{2} ,{\text{seedPT}}}} \) :
-
CO2 emitted for soy feedstock seed processing and transport
- \( E_{\text{soy}}^{{{\text{CO}}_{2} ,{\text{oilext}}}} \) :
-
CO2 emitted for soy feedstock oil extraction
- \( E_{\text{soy}}^{{{\text{CO}}_{2} ,{\text{BDprod}}}} \) :
-
CO2 emitted for biodiesel production from soy feedstock
- \( E_{\text{soy}}^{{{\text{CO}}_{2} ,{\text{BDtransport}}}} \) :
-
CO2 emitted transport of biodiesel produced from soy feedstock
- \( E_{\text{soy}}^{{{\text{CO}}_{2} ,{\text{BDuse}}}} \) :
-
CO2 emitted during use of biodiesel produced from soy feedstock
- \( E_{\text{soy}}^{{{\text{CO}}_{2} }} \) :
-
CO2 emitted per ton of soy oil used as a feedstock to produce biodiesel
- WCO:
-
Waste cooking oil
- \( E_{\text{WCO}}^{{{\text{CO}}_{2} }} \) :
-
CO2 emitted per ton of WCO used as a feedstock to produce biodiesel
- \( F_{{{\text{soy}},t}} \) :
-
Flowrate of soy oil feedstock into the process over time t
- \( F_{{{\text{WCO}},t}} \) :
-
Flowrate of WCO feedstock into the process over time t
- \( P_{BD,t}^{{_{{}} }} \) :
-
a given production rate of biodiesel over time t
- \( E_{\text{BD}}^{{{\text{CO}}_{2} }} \) :
-
The total quantity of CO2 emitted over time period t for biodiesel produced using soy oil and/or WCO as feedstock inputs
- \( P_{D,t}^{{_{{}} }} \) :
-
A given production rate of petroleum-based diesel over time t
- \( E_{D}^{{{\text{CO}}_{2} }} \) :
-
The total quantity of CO2 emitted over time period t for production of petroleum-based diesel
- \( S^{{{\text{CO}}_{2} }} \) :
-
Subsidy for reduction of CO2 emissions ($/ton CO2 reduced)
- \( {\text{TS}}^{{{\text{CO}}_{2} }} \) :
-
Total subsidy attained for biodiesel produced from soy oil and/or WCO feedstocks
- Net_Genu,q,t :
-
Net generation of component q in pretreatment unit u during period t
- N components :
-
Number of components q
- \( d_{u,t} \) :
-
Vectors describing the design variables of unit u during period t
- o u,t :
-
Vectors describing the operating variables of unit u during period t
- \( g_{{j_{u} ,i_{v} ,t}} \) :
-
Assigned from source j u to destination i v during period t
- \( g_{{j_{u} ,i_{u} ,t}} \) :
-
Flowrate from source j u to destination i u during period t
- \( p_{{j_{u} ,p,t}} \) :
-
Flowrate assigned from j u to the pth product stream during period t
- \( w_{{j_{u} ,w,t}} \) :
-
Flowrate from j u to the wth waste stream during period t
- \( P_{p,t}^{\text{T}} \) :
-
Total flowrate of the pth product from the N T pretreatment units in period t
- \( Z_{p,q,t}^{\text{T}} \) :
-
Composition of component q in the pth product stream coming from the N T pretreatment units during period t
- \( W_{w,t}^{\text{T}} \) :
-
Flowrate of the wth waste stream from the N T pretreatment units during period t
- \( Z_{w,q,t}^{\text{T}} \) :
-
Composition of component q in the wth waste stream coming from the N T pretreatment units during period t
- \( r_{{j_{b} ,i_{v} ,t}} \) :
-
Flowrate assigned from intermediate source j b to destination i v during period t
- Net_Genv,q,t :
-
Net generation of component q in common process unit v during period t
- \( d_{v,t} \) :
-
Vectors describing the design variables of unit v during period t
- o v,t :
-
Vectors describing the operating variables of unit v during period t
- \( w_{{j_{v} ,w,t}} \) :
-
Flowrate assigned from output stream j v to the wth waste stream during period t
- \( p_{{j_{v} ,p,t}} \) :
-
Flowrate assigned from output stream j v to the pth product stream during period t
- \( r_{{j_{v} ,b,t}} \) :
-
Flowrate assigned from output stream j v to the bth intermediate stream during period t
- \( W_{w,t}^{\text{PU}} \) :
-
Flowrate of the wth waste stream from the N PU common process units
- \( Z_{w,q,t}^{\text{PU}} \) :
-
Composition of component q in the wth waste stream coming from the N PU common process units during period t
- \( P_{p,t}^{\text{PU}} \) :
-
Total flowrate of the pth product from the N PU common process units in period t
- \( Z_{p,q,t}^{\text{PU}} \) :
-
Composition of component q in the pth product stream coming from the N PU common process units in period t
- \( R_{b,t}^{\text{PU}} \) :
-
Flowrate of the bth intermediate stream from the N PU common process units during period t
- \( Z_{b,q,t}^{\text{PU}} \) :
-
Composition of component q in the bth intermediate stream from the N PU common process units during period t
- \( P_{p,t}^{{}} \) :
-
Flowrate of the pth product out of the process
- \( Z_{p,q,t} \) :
-
Composition of component q in the pth product stream out of the process during period t
- \( W_{w,t} \) :
-
Flowrate of the wth waste stream out of the process during period t
- \( Z_{w,q,t} \) :
-
Composition of component q in the wth waste stream out of the process during period t
- \( r_{{j_{v} ,i_{b} ,t}} \) :
-
Flowrate assigned from source j v to destination i b during period t
- \( d_{u}^{\min } ,d_{u}^{\max } \) :
-
Minimum and maximum vectors describing the design variables of unit u, respectively
- \( d_{v}^{\min } ,d_{v}^{\max } \) :
-
Minimum and maximum vectors describing the design variables of unit v, respectively
- \( o_{u}^{\min } ,o_{u}^{\max } \) :
-
Minimum and maximum vectors describing the operating variables of unit u, respectively
- \( o_{v}^{\min } ,o_{v}^{\max } \) :
-
Minimum and maximum vectors describing the operating variables of unit v, respectively
- \( P_{p,t}^{\text{Demand}} \) :
-
Demand for product p during period t
- \( F_{{i_{u} }}^{\min } ,F_{{i_{u} }}^{\max } \) :
-
Minimum and maximum flowrate for the i u th input to pretreatment unit u, respectively
- \( X_{{i_{u} ,q}}^{\min } ,X_{{i_{u} ,q}}^{\max } \) :
-
Minimum and maximum composition of component q for the i u th input to pretreatment unit u, respectively
- \( F_{{i_{v} }}^{\min } ,F_{{i_{v} }}^{\max } \) :
-
Minimum and maximum flowrate for the i v th input to common process unit v, respectively
- \( X_{{i_{v} ,q}}^{\min } ,X_{{i_{v} ,q}}^{\max } \) :
-
Minimum and maximum composition of component q for the i v th input to pretreatment unit v, respectively
- \( S^{{{\text{CO}}_{2} ,\min }} ,S^{{{\text{CO}}_{2} ,\max }} \) :
-
Minimum and maximum CO2 subsidy, respectively
- \( C_{p,t}^{\text{product}} \) :
-
Unit selling price of product p during period t
- P p,t :
-
Production rate of product p during time t
- \( C_{f,t}^{\text{feedstock}} \) :
-
Cost of feedstock f during period t
- F f,t :
-
Feed rate of feedstock f during time t
- POC t :
-
Process operating cost excluding feedstock cost (e.g. utilities labor waste treatment, etc.) during period t
- TACPretreatment :
-
Total annualized cost of retrofitted pretreatment
- AFC:
-
Annualized fixed cost
- AOC:
-
Annual operating cost
- I f :
-
A binary integer variable designating the presence or absence of the fth feedstock
- \( F_{f,t}^{{}} \) :
-
Flowrate of feedstock f during period t
- \( F_{f,t}^{\max } \) :
-
Upper bound on the allowable flowrate of feedstock f
- MINLP:
-
Mixed integer non-linear program
- MILP:
-
Mixed integer linear program
- FFA:
-
Free fatty acid
- B100:
-
Diesel fuel comprised of 100% biodiesel
- MMGPY:
-
Millions of gallons per year
- FCI:
-
Fixed capital investment
- ROI:
-
Return on investment
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Elms, R.D., El-Halwagi, M.M. The effect of greenhouse gas policy on the design and scheduling of biodiesel plants with multiple feedstocks. Clean Techn Environ Policy 12, 547–560 (2010). https://doi.org/10.1007/s10098-009-0260-1
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DOI: https://doi.org/10.1007/s10098-009-0260-1