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Article
Strategic Planning for the Supply Chain of Aviation
Biofuel with Consideration of Hydrogen Production
Saul Domínguez-García, Claudia Gutiérrez-Antonio, Julio Armando De
Lira-Flores, José María Ponce-Ortega, and Mahmoud M El-Halwagi
Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02632 • Publication Date (Web): 24 Oct 2017
Downloaded from http://pubs.acs.org on October 28, 2017
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Industrial & Engineering Chemistry Research is published by the American Chemical
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Published by American Chemical Society. Copyright © American Chemical Society.
However, no copyright claim is made to original U.S. Government works, or works
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Industrial & Engineering Chemistry Research
Strategic Planning for the Supply Chain of
Aviation Biofuel with Consideration of Hydrogen
Production
Saúl Domínguez-García, 1 Claudia Gutiérrez-Antonio, 2 Julio
Armando De Lira-Flores, 2 José María Ponce-Ortega 1* Mahmoud M.
El-Halwagi 3,4
1
Chemical Engineering Department, Universidad Michoacana de San
Nicolás de Hidalgo, Morelia, Michoacán, 58060, México.
2
Faculty of Chemistry, Universidad Autónoma de Querétaro, Querétaro,
Querétaro, 76010, México.
3
Chemical Engineering Department, Texas A&M University, College Station,
TX, 77843, USA.
4
Adjunct Faculty at the Chemical and Materials Engineering Department,
King Abdulaziz University, Jeddah, 21589, Saudi Arabia
* Corresponding author: J.M. Ponce-Ortega
E-mail: [email protected]
Tel. +52 443 3223500 ext. 1277
Fax. +52 443 3273584
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Abstract
Substitution of petro-based aviation fuel with biomass-derived aviation fuel is an emerging
strategy to reduce the carbon footprint associated with the aviation sector. There are several
pathways for the production of aviation biofuel, and most of them require the use of
hydrogen. Therefore, the analysis of the aviation biofuel supply chain must incorporate the
production of hydrogen. This paper presents an optimization approach for the strategic
planning of aviation fuel supply chains, which considers hydrogen production from fossil
and renewable raw materials. The approach also considers extraction of fossil materials,
growth of biomass, selection and several processing routes of the feedstock, along with the
distribution of products. As case study, the strategic planning of aviation biofuels in
Mexico considering the generation of biomass and the hydrogen production is selected. The
results show that significant decreases in producing costs and CO2 emissions can be
obtained if aviation fuel is generated from renewable raw materials. This finding is quite
important, since in Mexico 90% of the consumed energy proceed from fossil sources.
Several scenarios are addressed to assess the key factors in the design of the supply chain,
reconciling the economic and environmental objectives; and also an analysis for the
integration of the infrastructures of the fossil fuels and biorefineries is presented.
Keywords: Aviation biofuel, biohydrogen, supply chain, optimization.
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1. Introduction
The climate change has caused a number of natural disasters around the world,
which includes floods, tsunamis, and droughts. Several scientific studies have indicated that
the main cause of climate change is the excessive emission of greenhouse gases (GHGs),
particularly carbon dioxide. In order to address the climate change crisis, the Paris
Agreement (or Paris Climate Accord) sets the objective of substantial reduction in GHG
emissions.1
One of the main sources of CO2 emissions is the use of fossil fuels for
transportation. While automotive transportation is the largest source of emissions, aviation
transport of passengers and goods account for 2% and 3% of the global CO2 emissions,
respectively.2-4 Furthermore, a forecast indicates that by 2050, the aviation sector
(domestic, international and shipping) is expected to contribute between 10%–32% of the
total CO2 emissions.4 In this context, the relatively large contribution of fossil-based
aviation fuels to CO2 emissions has promoted a growing trend to identify other fuels with
lower carbon footprints. Towards this objective, it has been recommended to use blends of
conventional jet fuels with other fuels. For instance, Al-Nuaimi et al.5 proposed an
optimization-based framework for blending jet fuel with synthetic fuel derived from gas-toliquid (GTL) operation. Hong et al.6 suggested the use a mixture with different ratios of
conventional aircraft fuel with a biofuel, which satisfies the physicochemical properties
required for the aviation fuel. There are several pathways for converting biomass to
aviation fuel, and most of them require the use of hydrogen. Since the objective of
substituting fossil-based fuel with biofuel is to reduce the carbon footprint, it is important to
identify hydrogen production routes with low carbon footprints. The hydrogen is usually
production through reforming of natural gas; however, this processing route is associated
with substantial CO2 emissions.7-9 On the other hand, the use of biomass to produce
hydrogen offers a lower carbon footprint. Different processes have been proposed to
produce biomass-derived hydrogen or “biohydrogen”.10,11 Pan et al.12 investigated the
production of biohydrogen through the fermentation of wheat bran, while Fan et al.13
analyzed the conversion of corn to biohydrogen by anaerobic cultures.
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In order to produce renewable aviation fuel with low carbon footprint, all the
required raw materials must to be generated through production processes with low carbon
footprint. Here lies the importance of considering the production of hydrogen, along with
the biomass generation in the aviation fuel supply chain. Thus, an effective supply chain for
the aviation biofuel, and the assessment of the economic, environmental, and safety metrics
can be obtained.14-16 Regarding the determination of the optimal supply chain for biofuels
production several works have been reported in the literature. An analysis of several raw
material crops for the production of biofuels was carried out by Sepulveda-González.17
Later, Moraes et al.18 carried out a comparative analysis of different types of raw materials
to offer a methodical basis for screening and selection. El-Halwagi et al.19 used a multiobjective optimization framework for designing hydrogen production biorefineries and
supply chains, while accounting for safety and economic objectives. Also, El-Halwagi20
proposed a metric for reconciling economic and other sustainability metrics in the design of
processing facilities. The exploration of various processing routes for the production of
aviation biofuel was reported by Chiaramonti et al.21 Santibañez-Aguilar et al.22-24
presented a study on the strategic planning of bioethanol and biodiesel supply chains.
Moreover, several studies related to production of hydrogen have been carried out.
Guillén-Gonsálbez et al.29,30 developed an optimization model for the supply chain of
hydrogen production considering the market uncertainty. Martín et al.28 analyzed the
production of hydrogen from switch grass, in Spain, using an optimization model. Also,
Martín and Grossman28,31 analyzed the integrated production of biohydrogen and liquid
biofuels.
All the previously presented works are valuable research efforts; however, they lack
in at least one of the following issues:
•
The strategic planning for the supply chain associated with the aviation biofuels
does not account for the needed hydrogen in the production process. It should be
noticed that most of the reported processes for the aviation biofuel production
require significant usage of hydrogen. This hydrogen can be fossil-based hydrogen
or biohydrogen. This synergic relationship has not been properly addressed in the
previous works.
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•
Minimization of the carbon footprint on a life-cycle basis for the whole supply
chain for aviation biofuels.
• The consideration of feedstock type, availability, selection and processing routes for
the production of biohydrogen.
In order to address the foregoing limitations, the present paper introduces an
optimization approach for the strategic planning of the aviation biofuel supply chain while
incorporating the use and production of renewable and fossil hydrogen. The supply chain to
produce hydrogen is integrated with the aviation biofuel supply chain. Several biomass
sources and processing routes are considered for the production of biohydrogen. Finally,
economic and environmental objectives are used to optimize the design of the supply chain.
2. Problem statement
Given a certain region with the following known information:
•
Demands for biomass-based aviation fuel. Production over the minimum
demand may be exported and shortages to meet the minimum demand may
be compensated through importation.
•
Amount of hydrogen required for the production of aviation fuels.
•
Available supply of fossil aviation fuels in the region.
•
Available land for the production of different types of biomass feedstock
that can be used for aviation biofuel and biohydrogen production.
•
Candidate pathways for the processing of biomass to produce aviation fuels.
•
A transportation roadmap which can facilitate the transfer of feedstock,
intermediates, byproducts, and main product.
The objective is to design a supply chain that utilizes biomass and fossil materials to
produce cost-effective and environmentally friendly solutions.
3. Methodology
Figure 1 shows a schematic representation of the addressed problem, which shows
the reserves of fossil energy and the production of biomass in the considered region (e.g.,
Mexico). This representation considers the possibility of installing new biorefineries and
biohydrogen production plants. The excess production of aviation biofuel can be exported,
whereas the deficiency in meeting the regional demand can be overcome through
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importation. The following section describes the key building blocks of the optimization
model.
3.1 Use of land for cultivation
Area of cultivation
The total used area ( Ai ,m ) for cultivation of any raw material ( m) in the site ( i) is
equal to the sum of the existing area used for cultivation ( AiExist
plus the new area ( AiNew
,m )
,m )
needed to produce the biomass demand in each biorefinery.
New
Ai ,m = AiExist
, m + Ai , m , ∀ i ∈ I , m∈ M
(1)
Production of biomass
The amount of produced biomass (seeds) ( Pi , m ) in the cultivation sites ( i) for the
raw material ( m) depends on the production factor ( βi ,m ) and the used area
(A )
i ,m
as
follow:
Pi , m = β i , m Ai , m , ∀ i ∈ I , m ∈ M
The production factor for the biomass
(2)
(β )
i ,m
is determined by environmental
conditions and land composition.
Delivery of biomass to biorefineries and biohydrogen plants
The amount of produced biomass ( Pi , m ) is equal to the sum of the raw materials sent
to the biorefineries ( FMBTi ,i1,m ) and biohydrogen plants ( FMBH i ,i 2,m ) :
Pi ,m = ∑ FMBTi ,i1, m + ∑ FMBH i ,i 2,m , ∀ i ∈ I , m ∈ M
i1
(3)
i2
3.2 Production and distribution of biohydrogen
Balance of biomass sent to each biohydrogen production plant
The raw material delivered to each biohydrogen production plant ( FMBHtotali 2,m )
is equal to the sum of the amount of biomass ( FMBH i ,i 2,m ) sent to the installation site of
the plants.
FMBHtotali 2, m = ∑ FMBH i ,i 2, m , ∀ i 2∈ I 2, m∈ M
i
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Balance of biomass delivered to each processing route in any biohydrogen production
plant
The total amount of raw material processed in each biohydrogen plant
) processed in each route (rbh) .
( FMBHtotali 2,m ) is equal to the sum of biomass ( fmiroute
2,m ,rbh
FMBHtotali 2, m = ∑ fmiroute
, ∀ i1∈ I1, m∈ M
2,m ,rbh
(5)
rbh
Production of biohydrogen
The amount of biohydrogen produced in each plant ( PBHi 2 ) is equal to the sum of
processed biomass ( fmiroute
) multiplied by a conversion factor (γ i 2,m ,rbh ) .
2,m ,rbh
PBH i 2 = ∑∑ fmiroute
γ
, ∀ i 2∈ I 2
2,m ,rbh i 2, m , rbh
m
(6)
rbh
Distribution of the produced biohydrogen
The biohydrogen produced in each plant is equal to the sum of the biohydrogen sent
to biorefineries ( FBHBi 2,i1 ) and refineries ( FBHRi 2,k1 ) :
PBH i 2 = ∑ FBHBi 2,i1 + ∑ FBHRi 2,k1 , ∀ i 2∈ I 2
i1
(7)
k1
Delivery of fossil fuels to refineries and hydrogen plants
The amount of fossil fuels ( Fk ,n ) obtained in each extraction site is equal to the sum
of the raw material sent to the refineries ( FfossilTk ,k1,n ) and hydrogen plants ( FfossilHk ,k 2,n ) :
Fk ,n = ∑ FfossilTk ,k1,n + ∑ FfossilH k ,k 2,n , ∀ k ∈ K , n ∈ N
k1
(8)
k2
3.3 Production and distribution of hydrogen
Balance of fossil raw materials sent to each hydrogen production plants
The raw material delivered to each hydrogen production plant ( FfossilHtotalk 2,n ) is
equal to the sum of biomass ( FfossilH k,k 2,n ) sent to the site of the plant.
FfossilHtotalk 2,n = ∑ FfossilH k,k 2,n , ∀ k 2∈ K 2, n ∈ N
(9)
k
Balance of fossil fuel delivered to each processing route in any hydrogen production
plant
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The total amount of raw material processed in each hydrogen plant
( FfossilHtotalk 2,n ) is equal to the sum of all fossil mass ( fhkroute
2,n, rh ) processed in each route
(rh) .
FfossilHtotalk 2,n = ∑ fhkroute
2,n, rh , ∀ k 2 ∈ K 2, n ∈ N
(10)
rh
Production of hydrogen
The amount of hydrogen produced in each plant ( PH k 2 ) is equal to the sum of the
fossil mass processed ( fhkroute
2, n , rh ) multiplied by a conversion factor (λk 2, n , rh ) :
PH k 2 = ∑∑ fhkroute
2, n , rh λk 2, n , rh , ∀ k 2∈ K 2
n
(11)
rh
Distribution of produced hydrogen
The hydrogen produced in each plant is equal to the sum of all flows of hydrogen
sent to biorefineries ( FHBk 2,i1 ) and refineries ( FHRk 2,k1 ) .
PH k 2 = ∑ FHRk 2,k 1 + ∑ FHBk 2,i1 , ∀ k 2∈ K 2
k1
(12)
i1
3.5 Total hydrogen supplied to biorefineries
Biohydrogen supplied to each biorefinery
The total amount of biohydrogen sent to each biorefinery ( BHBi1 ) is equal to the
sum of hydrogen produced from all biohydrogen plants ( FBHBi 2,i1 ) .
BHBi1 = ∑ FBHBi 2,i1 , ∀ i1 ∈ I1
(13)
i2
Hydrogen supplied to each biorefinery
The total amount of hydrogen sent to each biorefinery ( HBi1 ) is equal to the sum of
hydrogen flows from all hydrogen plants ( FHBk 2,i1 ) :
HBi1 = ∑ FHBk 2,i1 , ∀ i1∈ I1
(14)
k2
Total hydrogen supplied to each biorefinery
The total amount of hydrogen that arrives to each biorefinery ( HBtotali1 ) is equal to
the sum of flows of biohydrogen ( BHBi1 ) and hydrogen of fossil origin ( HBi1 ) .
HBtotali1 = BHBi1 + HBi1 , ∀ i1∈ I1
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Balance of total hydrogen consumed in each biorefinery
The total amount of hydrogen that arrives to each biorefinery must be consumed to
avoid accumulation; then it is equal to the sum of all flows of biomass transformed into
aviation biofuel ( f mroute
, r ,i1 ) multiplied by a conversion factor (φm , r , i1 ) and a stoichiometric
coefficient (υ m ,r ,i1 ) .
HBtotali1 = ∑∑ υm , r ,i1 f mroute
, r ,i1φm , r ,i1 , ∀ i1∈ I 1
m
(16)
r
3.6 Total hydrogen supplied to refineries
Biohydrogen supplied to each refinery
The total amount of biohydrogen sent to each refinery ( BHRk1 ) is equal to the sum
of hydrogen flows from all hydrogen plants ( FBHRi 2,k1 ) .
BHRk 1 = ∑ FBHRi 2,k1 , ∀ k ∈ K
(17)
i2
Hydrogen supplied to each refinery
The total amount of hydrogen sent to each refinery ( HRk1 ) is equal to the sum of
hydrogen flows coming from all hydrogen plants ( FHRk 2,k1 ) .
HRk 1 = ∑ FHRk 2,k1 , ∀ k ∈ K
(18)
k2
Total hydrogen supplied to each refinery
The total amount of hydrogen that arrives to each refinery ( HRtotalk1 ) is equal to
the sum of flows of biohydrogen ( BHRk1 ) and hydrogen of fossil origin ( HRk1 ) .
HRtotalk1 = BHRk1 + HRk1 , ∀ k ∈K
(19)
Balance of total hydrogen consumed in each refinery
The total amount of hydrogen that arrives to each refinery ( HRtotalk1 ) must be
consumed to avoid accumulation; then it is equal to the sum of all flows of fossil materials
route
transformed into aviation fuel ( ftn,rt ,k1 ) multiplied by a conversion factor (δn,rt ,k1 ) and a
stoichiometric coefficient (τ n,rt ,k1 ) .
HRtotalk 1 = ∑∑ τ n,rt ,k1 ftn,route
rt ,k1δ n, rt ,k1 , ∀ k1∈ K 1
n
rt
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3.7 Production and distribution of aviation biofuel
Balance of biomass sent to each biorefinery
The total amount of raw material delivered to each biorefinery ( FMBTtotali1,m ) is
equal to the sum of the amount of biomass ( FMBTi ,i1,m ) sent to the processing plant.
FMBTtotali1,m = ∑ FMBTi ,i1,m , ∀ i1 ∈ I1, m∈ M
(21)
i
Balance of biomass delivered to each processing route in any biorefinery
The total amount of raw material processed in each biorefinery ( FMBTtotali1,m ) is
equal to the sum of the biomass ( fmroute
,r ,i1 ) processed through each route ( r ) .
FMBTtotali1,m = ∑ f mroute
, r ,i1 , ∀ i1∈ I 1, m ∈ M
(22)
r
Production of aviation biofuel
The amount of aviation biofuel produced in each biorefinery ( Bi1 ) is equal to the
route
sum of all biomass processed ( fm,r.i1 ) multiplied by a conversion factor (φm,r ,i1 ) .
Bi1 = ∑∑ f mroute
, r .i1 φm , r ,i1 , ∀ i1∈ I 1
m
(23)
r
Distribution of produced aviation biofuel
The aviation biofuel produced in each biorefinery is equal to the sum of the flows of
the biofuel sent to the national market (bi1,a ) and international market ( FBNIi1 ) .
Bi1 = ∑ bi1, a + FBNI i1 , ∀ i1∈ I1
(24)
a
3.8 Production and distribution of aviation fuel of fossil origin
Balance of fossil raw materials sent to each refinery
The total amount of raw material delivered to each refinery ( FfossilTtotalk1,n ) is
equal to the sum of the amount of fossil raw materials ( FfossilTk,k1,n ) sent to the processing
plants.
FfossilTtotalk 1,n = ∑ FfossilTk,k1, n , ∀ k1∈ K1, n ∈ N
k
Balance of fossil raw materials delivered to each processing route in any refinery
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The total amount of raw material processed in each refinery (FfossilTtotalk1,n ) is
route
equal to the sum of the fossil raw material ( ftk1,n,rt ) processed in each route ( rt ) .
FfossilTtotalk1,n = ∑ ftkroute
1, n , rt , ∀ k1∈ K1, n ∈ N
(26)
rt
Production of aviation fuel of fossil origin
The amount of aviation fuel produced in each refinery (Tfossilk1 ) is equal to the sum
route
of all fossil raw materials processed ( ftk1,n,rt ) multiplied by a conversion factor (δ n,rt ) .
Tfossilk 1 = ∑ ∑ ftkroute
1, n , rt δ n, rt , ∀ k1 ∈ K 1
n
(27)
rt
Distribution of produced aviation fuel
The aviation fuel produced in each refinery is equal to the sum of all the flows sent
to the national ( FTk1,a ) and international markets (FTNIk1 ) .
Tfossilk 1 = ∑ FTk 1,a + FTNI k 1 , ∀ k1 ∈ K1
(28)
a
3.9 Production and distribution of byproducts
Production of byproducts
The amount of byproduct ( j ) produced in each biorefinery (Si1, j ) is equal to the
sum of the processed biomass ( fi1,route
m , r ) multiplied by a conversion factor (α m , r , j ) .
Si1, j = ∑∑ fi1,route
m , r α m , r , j , ∀ i1 ∈ I 1, j ∈ J
m
(29)
r
Distribution of byproducts
The amount of byproduct ( j ) produced in each refinery (Si1, j ) is equal to the sum
of the flows of this product sent to the national market ( si1, j ,a ) and international market
( FSNIi1, j ) .
Si1, j = ∑ si1, j ,a + FSNI i1, j , ∀ i1∈ I1, j ∈ J
a
3.10 Balances of aviation biofuel and aviation fuel in the markets
Balance of aviation biofuel in the national market
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The amount of aviation biofuel received in the national market ( BTNa ) must be
equal to the sum of the flows sent from biorefineries (bi1, a ) .
BTN a = ∑ bi1, a , ∀ a ∈ A
(31)
i1
Balance of aviation fuel of fossil origin in the national market
The amount of aviation fuel of fossil origin received in the national market (TN a )
must be equal to the sum of the flows sent from refineries ( FTk1,a ) and international market
( FTINa ) .
TN a = ∑ FTk 1,a + FTIN a , ∀ a ∈ A
(32)
k1
Total balance of aviation fuel received in the national market
The total amount of aviation fuel received in the national market (TBa ) is equal to
the sum of aviation biofuel ( BTNa ) and aviation fuel of fossil origin (TN a ) received in the
national market.
TBa = BTN a + TN a , ∀ a ∈ A
(33)
Balance of aviation biofuel sent to international market
The amount of aviation biofuel sent to international marker (BTNItotal ) is equal to
the sum of all aviation biofuel sent to international market from each biorefinery ( FBNIi1 ) .
BTNItotal = ∑ FBNI i1
(34)
i1
Balance of aviation fuel of fossil origin sent to international market
The amount of aviation fuel of fossil origin sent to international marker (TNItotal ) is
equal to the sum of the aviation fuel of fossil origin sent to the international market from
each refinery ( FTNI k1 ) .
TNItotal = ∑ FTNI k1
(35)
k1
Total balance of aviation fuel sent to international market
The total amount of aviation fuel sent to international market (TI ) is equal to the
sum of aviation biofuel ( BTNItotal ) and aviation fuel of fossil origin (TNItotal ) sent to
international market.
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TI = BTNItotal + TNItotal
(36)
3.11Balance of byproducts in national and international markets
Balance of byproducts received in the national market
The amount of byproduct ( j ) received in the national market (TS j ,a ) is equal to
sum of amounts of byproduct coming from each biorefinery (si1, j , a ) and those from
international market ( FSIN j ,a ) .
TS j , a = ∑ si1, j ,a + FSIN j ,a , ∀ a ∈ A, j ∈ J
(37)
i1
Balance of byproducts sent to international market
The amount of byproduct ( j ) sent to international market ( SI j ) is equal to the
sum of all the amount of this byproduct sent from each biorefinery ( FSNI j ,i1 ) .
SI j = ∑ FSNI j ,i1 , ∀ j ∈ J
(38)
i1
3.12 Constraints
Area constraint
The used area for the production of biomass ( Ai ,m ) is constrained by the available
area ( Aimax
, m ) . It means that only it is possible to consider a limited area of land for the
cultivation of raw material ( m) without a high environmental impact.
Ai ,m ≤ Aimax
,m , ∀ i ∈ I , m ∈ M
(39)
Aviation fuel demand
The amount of aviation fuel received in the national market (TBa ) must be lower or
equal than the total demand of this fuel in the national market ( DBamax ) .
TBa = DBamax , ∀ a ∈ A
(40)
Byproduct demand restrictions
The amount of byproduct ( j ) received in the national market (TS j ,a ) must be
lower or equal than the total demand of this byproduct in the national market ( DS max
j ,a ) .
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TS j ,a ≤ DS max
j ,a , ∀ j ∈ J , a ∈ A
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(41)
Constraint for fossil reserves
The amount of fossil raw material ( n ) extracted in each site ( Fk ,n ) is limited by the
available reserves in the site ( Fkmax
,n ) .
Fk ,n ≤ Fkmax
,n , ∀ k ∈ K , n∈ N
(42)
3.13 Capacity constraints of processing plants
Binary variables for the activation of biorefineries
The capacity of any biorefinery ( Bi1 ) has to be greater or equal than the minimum
capacity of aviation biofuel production ( Bimin
1 ) , and lower or equal than the maximum
capacity of aviation biofuel production ( Bimax
1 ) . The binary variable ( yi1 ) is used to
associate the capital cost with the dimension of biorefinery.
max
Bimin
1 yi1 ≤ Bi1 ≤ Bi1 yi1 , ∀ i1∈ I 1
(43)
Binary variables for the existence of processing routes in each biorefinery
The capacity of any processing route in each biorefinery ( fi1,route
m , r ) has to be greater or
min
) , and lower or
equal than the minimum capacity of processing of raw material ( fi1,route
m,r
) . The binary
equal than the maximum capacity of processing of raw material ( fi1,routemax
m,r
variable ( zi1, m ,r ) is used to associate the capital cost with the capacity of biorefinery.
min
route max
fi1,route
zi1,m,r ≤ fi1,route
zi1,m, r ∀ i1∈ I1, m∈ M , r ∈ R
m,r
m , r ≤ f i1, m , r
(44)
Binary variables for existence of refineries
The capacity of any refinery (Tfossilk1 ) has to be greater or equal than the minimum
capacity of aviation fuel production (Tfossilkmin
1 ) , and lower or equal than the maximum
capacity of aviation fuel production (Tfossilkmax
1 ) . The binary variable (uk1 ) is used to
associate the capital cost with the capacity of refinery.
max
Tfossilkmin
1 uk 1 ≤ Tfossilk1 ≤ Tfossilk1 uk 1 , ∀ k1∈ K1
Binary variables for the activation of processing routes in each refinery
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route
The capacity of any processing route in each refinery ( ftk1,n,
rt ) has to be greater or
routemin
equal than the minimum capacity of processing of raw material ( ftk1,n,
rt ) , and lower or
route max
equal than the maximum capacity of processing of raw material ( ftk1,n,
rt ) . The binary
variable (vk1,n,rt ) is used to associate the capital cost with the dimension of refinery.
routemin
route
routemax
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vk1,n,rt ∀ k1∈K1, n∈N , rt ∈RT
rt vk1,n,rt ≤ ftk1,n,rt ≤ ftk1,n,rt
(46)
Binary variables for activation of the hydrogen production plants
The capacity of any hydrogen plant ( PH k 2 ) has to be greater or equal than the
minimum capacity of hydrogen of fossil origin ( PH kmin
2 ) , and lower or equal than the
maximum capacity of hydrogen of fossil origin ( PH kmax
2 ) . The binary variable ( d k 2 ) is
used to associate the capital cost with the capacity of process plant.
max
PH kmin
2 d k 2 ≤ PH k 2 ≤ PH k 2 d k 2 , ∀ k 2∈ K 2
(47)
Binary variables for activation of processing routes in each hydrogen production plant
The capacity of any processing route in each hydrogen plant ( fhkroute
2,n, rh ) has to be
greater or equal than the minimum capacity of processing of raw material ( fhkroutemin
2,n, rh ) , and
max
lower or equal than the maximum capacity of processing of raw material ( fhkroute
2,n, rh ) . The
binary variable (ek1,n,rh ) is used to associate the capital cost with the dimension of process
plant.
route
routemax
fhkroutemin
2,n, rh ek 2,n, rh ≤ fhk 2,n,rh ≤ fhk2,n,rh ek1,n, rh ∀ k 2∈K 2, n∈ N , rh∈RH
(48)
Binary variables for activating the biohydrogen production plants
The capacity of any biohydrogen plant ( PBH i 2 ) has to be greater or equal than the
minimum capacity of biohydrogen production ( PBH imin
2 ) , and lower or equal than the
maximum capacity of biohydrogen production ( PBH imax
2 ) . The binary variable ( wi 2 ) is used
to associate the capital cost with the dimension of process plant.
max
PBH imin
2 wi 2 ≤ PBH i 2 ≤ PBH i 2 wi 2 , ∀ i 2∈ I 2
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Binary variables for activation of processing routes in each production plant of
biohydrogen
The capacity of any processing route in each biohydrogen plant ( fmiroute
2, m, rbh ) has to be
min
greater or equal than the minimum capacity of processing of raw material ( fmiroute
2, m, rbh ) , and
max
lower or equal than the maximum capacity of processing of raw material ( fmiroute
2, m, rbh ) . The
binary variable ( xi 2,m,rh ) is used to associate the capital cost with the dimension of process
plant.
route
routemax
fmiroutemin
2,m,rbh xi 2,m,rbh ≤ fmi 2, m, rbh ≤ fmi 2,m,rbh xi 2, m, rh ∀ i 2∈I 2, m∈M , r ∈RBH
(50)
3.13 Costs
Feedstock cost
The total feedstock cost (Cost feedstock ) is equal to the sum of all biomass processed
( Pi , m ) multiplied by the unitary cost of biomass (UCi feedstock
) , plus the sum of all fossil mass
,m
).
processed ( Fk ,n ) multiplied by the unitary cost of fossil mass (UCfossilkfeedstoks
,n
Cost feedstock = ∑∑ Pi ,m UCi ,feedstock
+ ∑∑ Fk ,nUCfossilkfeedstoks
m
,n
i
m
k
(51)
n
Processing cost of biomass for producing aviation biofuel
proces sin g
) is
The processing cost of biomass for aviation biofuel production (Costavitionbiofuel
equal to the sum of the processed biomass ( fi1,route
m , r ) multiplied by the unitary processing cost
sin g
(UCbtiproces
).
1.m.r
proces sin g
proces sin g
Costaviationbiofuel
= ∑∑∑ fi1,route
m, rUCbti1.m.r
i1
m
(52)
r
Processing cost of biomass for biohydrogen production
proces sin g
) is equal
The processing cost of biomass for biohydrogen production (Costbiohydrogen
to the sum of the processed biomass ( fmiroute
2, m, rbh ) multiplied by the unitary cost of processing
sin g
(UCbhiproces
).
2.m.rbh
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proces sin g
proces sin g
Costbiohydrogen
= ∑∑∑ fmiroute
2, m, rbhUCbhi 2.m.rbh
i2
(53)
m rbh
Processing cost of fossil mass for producing aviation fuel
proces sin g
The processing cost of fossil mass for aviation fuel production (Costaviation
fuel ) is
equal to the sum of the processed fossil mass ( ftkroute
1,n, rt ) multiplied by the unitary cost of
sin g
).
processing (UCtkproces
1.n.rt
proces sin g
route
proces sin g
Costaviation
fuel = ∑∑∑ ftk1,n, rtUCtk 1.n.rt
k1
n
(54)
rt
Processing cost of fossil mass for hydrogen production
proces sin g
) is equal
The processing cost of biomass for biohydrogen production (Costhydrogen
to the sum of the processed biomass ( fhkroute
2,n, rh ) multiplied by the unitary cost of processing
sin g
(UChkproces
).
1.n.rh
proces sin g
proces sin g
Costhydrogen
= ∑∑∑ fhkroute
2,n, rhUChk 2,n, rh
k2
n
(55)
rh
Total cost of processing
proces sin g
) is equal to the sum of biomass
The total cost of feedstock processing (Costtotal
processing cost and fossil mass processing cost for hydrogen and aviation fuel production.
proces sin g
proces sin g
proces sin g
proces sin g
proces sin g
Costtotal
= Cost jet
+ Costhydrogen
+ Costbiohydrogen
+ Costbiojet
fuel
fuel
(56)
Transportation cost for biomass to biorefineries
The transportation cost of biomass to biorefineries (CTMB) is equal to the sum of
the biomass sent to biorefineries ( FMBTi ,i1,m ) multiplied by the unitary transportation cost
between the cultivation site and processing sites (UCTMBi ,i1,m ) .
CTMB = ∑∑∑ FMBTi ,i1, mUCTMBi ,i1, m
i
i1
(57)
m
Transportation cost of biomass to biohydrogen production plants
The transportation cost of biomass to biohydrogen production plants (CTMH ) is
equal to the sum of the biomass sent to the hydrogen production plants ( FMBH i ,i 2, m )
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multiplied by the unitary transportation cost between the cultivation site and installation
site of hydrogen production plants (UCTMH i ,i 2,m ) .
CTMH = ∑∑∑ FMBHi ,i 2,mUCTMH i ,i 2,m
i
i2
(58)
m
Transportation cost for fossil mass to refineries
The transportation cost of fossil resources to refineries (CTNR) is equal to the sum
of all fossil mass sent to all refineries ( FfosilTk ,k1,n ) multiplied by the unitary transportation
cost between the extraction site and installation site of refineries (UCTNRk ,k1,n ) .
CTNR = ∑∑∑ FfosilTk ,k1,nUCTNRk , k1,n
k1
k
(59)
n
Transportation cost for fossil resources to hydrogen production plants
The transportation cost of fossil resources to hydrogen production plants (CTNH ) is
equal to the sum of all fossil mass sent to all hydrogen production plants ( FfossilH k .k 2.n ) ,
multiplied by the unitary transportation cost between the extraction site and installation site
of hydrogen production plant (UCTNH k ,k 2,n ) .
CTNH = ∑∑∑ FfossilH k .k 2.nUCTNH k ,k 2,n
k2
k
(60)
n
Transportation cost for aviation biofuel to national market
The transportation cost for the aviation biofuel to national market (CTB) is equal to
the sum of the aviation biofuel sent to national market (bi1, a ) multiplied by the unitary
transportation cost between the installation site of biorefineries and the market (UCTBi1,a ) .
CTB = ∑∑ bi1,aUCTBi1,a
i1
(61)
a
Transportation cost for byproducts to national market
The transportation cost of byproducts to national market (CTS ) is equal to the sum
of the byproducts sent to the national market (si1, j , a ) multiplied by the unitary
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transportation cost between the installation site of biorefineries and the final site of
consumption (UCTSi1, j ,a ) .
CTS = ∑∑∑ si1, j ,aUCTSi1, j ,a
i1
j
(62)
a
Transportation cost of aviation fuel of fossil origin to national market
The transportation cost of aviation fuel of fossil origin to national market (CTT ) is
equal to the sum of the aviation fuel sent to national market ( FTk1,a ) multiplied by the
unitary transportation cost between the refineries and the market (UCTTk1, a ) .
CTT = ∑∑ FTk1,aUCTTk1,a
k1
(63)
a
Transportation cost of aviation fuel from international to national market
The transportation cost of aviation fuel from international market to national market
(CTBI ) is equal to the sum of all aviation fuel received in each national market ( FTINa )
multiplied by unitary transportation cost (UCTTI a ) .
CTBI = ∑ FTINaUCTTI a
(64)
a
Transportation cost of byproducts from international to national market
The transportation cost of byproducts from international to national market (CTSI )
is equal to the sum of all byproducts received in each national market ( FSIN j ,a ) multiplied
by unitary cost of transportation (UCTSI j ,a ) .
CTSI = ∑∑ FSIN j ,aUCTSI j ,a
j
(65)
a
Transportation cost of aviation biofuel sent to international market
The transportation cost of aviation biofuel sent to international market (CTBE ) is
equal to the sum of the aviation biofuel sent from biorefineries to international market
( FBNIi1 ) multiplied by unitary transportation cost (UCTBEi1 ) .
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CTBE = ∑ FBNIi1UCTBEi1
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(66)
i1
Transportation cost of aviation fuel of fossil origin sent to international market
The transportation cost of aviation fuel of fossil origin sent to international market
(CTTE ) is equal to the sum of the aviation fuel sent from each refinery to international
market ( FTNI k1 ) multiplied by unitary transportation cost (UCTTEk1 ) .
CTTE = ∑ FTNI k1UCTTEk1
(67)
k1
Transportation cost of byproducts sent to international market
The transportation cost of byproducts sent to international market (CTSE ) is equal
to the sum of all byproducts sent from each biorefinery to international market ( FSNI j ,i1 )
multiplied by the unitary transportation cost (UCTSE j ,i1 ) .
CTSE = ∑∑ FSNI j ,i1UCTSE j ,i1
j
(68)
i1
Transportation cost of biohydrogen to biorefineries
The transportation cost of biohydrogen to biorefineries (CTBHB) is equal to the
sum of the biohydrogen sent to biorefineries ( FBHBi 2,i1 ) multiplied by the unitary
transportation cost (UCTBHBi 2,i1 ) .
CTBHB = ∑∑ FBHBi 2,i1UCTBHBi 2,i1
i2
(69)
i1
Transportation cost of biohydrogen to refineries
The transportation cost of biohydrogen to refineries (CTBHR) is equal to the sum of
the biohydrogen sent to refineries ( FBHRi 2,k1 ) multiplied by the unitary transportation cost
(UCTBHRi 2,k1 ) .
CTBHR = ∑∑ FBHRi 2,k1UCTBHRi 2,k1
i2
k1
Transportation cost of hydrogen of fossil origin to biorefineries
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The transportation cost of hydrogen of fossil origin to biorefineries (CTHB) is
equal to the sum of the hydrogen sent to the biorefineries ( FHBk 2,i1 ) multiplied by the
unitary transportation cost (UCTHBk 2,i1 ) .
CTHB = ∑∑ FHBk 2,i1UCTHBk 2,i1
k2
(71)
i1
Transportation cost of hydrogen of fossil origin to refineries
The transportation cost of hydrogen of fossil origin to refineries (CTHR) is equal to
the sum of the hydrogen sent to the refineries ( FHRk 2,k1 ) multiplied by the unitary
transportation cost (UCTHRk 2,k1 ) .
CTHR = ∑∑ FHRk 2, k1UCTHRk 2, k1
k2
(72)
k1
Total transportation cost
transport
) is equal to the sum of costs of raw
The total transportation cost (Costtotal
material, hydrogen, aviation fuel and byproduct transportation as follows:
transport
Costtotal
= CTMB + CTMH + CTNR + CTNH + CTB + CTS + CTT + CTBI + CTSI
(73)
CTBE + CTTE + CTSE + CTBHB + CTBHR + CTHB + CTHR
Capital cost by installation of biorefineries
The capital cost for installing biorefineries (CCB) is equal to the sum of binary
variables of activation ( yi1 ) multiplied by the installation base cost (CBiB1 ) , plus the sum of
the binary variables of activation for each processing route ( zi1, m.r ) multiplied by the
installation base cost of each route (CRiB1,m ,r ) , and plus the sum of the processed raw
route
) multiplied by a sizing parameter (CDiB1,m,r ) .
material to produce aviation biofuel ( fi1,m.r
route
CCB = ∑ CBiB1 yi1 + ∑∑∑ CRiB1,m,r zi1,m.r + ∑∑∑ CDiB1,m,r fi1,m.r
i1
i1
m
r
i1
m
(74)
r
Capital cost for installing biohydrogen production plants
The capital cost for installing biohydrogen production plants (CCBH ) is equal to
the sum of binary variables of activation ( wi 2 ) multiplied by the installation base cost
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(CBiBH
2 ) , plus the sum of the binary variables of activation for each processing route
( xi 2,m,rbh ) multiplied by the installation base cost of each route (CRiBH
2,m, rbh ) , plus the sum of
the processed raw material for producing biohydrogen ( fmiroute
2, m.rbh ) multiplied by a sizing
parameter (CDiBH
2, m.rbh ) .
BH
BH
route
CCBH = ∑ CBiBH
2 wi 2 + ∑∑∑ CRi 2, m , rbh xi 2, m , rbh + ∑∑∑ CDi 2, m.rbh fmi 2, m.rbh
i2
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m rbh
(75)
m rbh
Capital cost for installing refineries
The capital cost for installing refineries (CCR) is equal to the sum of binary
variables of activation (uk1 ) multiplied by the installation base cost (CBkR1 ) , plus the sum of
the binary variables of activation for each processing route (vk1,n,rt ) multiplied by the
installation base cost of each route (CRkR1,n, rt ) , plus the sum of the processed raw material to
R
produce aviation fuel ( ftkroute
1, n , rt ) multiplied by a sizing parameter (CDk 1, n , rt ) .
CCR = ∑ CBkR1uk1 + ∑∑∑ CRkR1,n,rt vk1,n,rt + ∑∑∑ CDkR1,n, rt ftkroute
1, n , rt
k1
k1
n
k1
rt
n
(76)
rt
Capital cost for installing hydrogen production plants
The capital cost for installing hydrogen production plants (CCH ) is equal to the
sum of binary variables of activation ( d k 2 ) multiplied by the installation base cost (CBkH2 ) ,
plus the sum of the binary variables of activation for each processing route (ek 2,n,rh )
multiplied by the installation base cost of each route (CRkH2, n, rh ) , plus the sum of the
processed raw material to produce hydrogen ( fhkroute
2, n , rh ) multiplied by a sizing parameter
(CDkH2,n,rh ) .
CCH = ∑ CBkH2 d k 2 + ∑∑∑ CRkH2,n, rh ek 2,n, rh + ∑∑∑ CDkH2,n ,rh fhkroute
2, n , rh
k2
k2
n
rh
k2
n
rh
Total capital cost
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The total capital cost (CapCost ) is equal to the sum of the capital cost for installing
of biorefineries, biohydrogen production plants, refineries and hydrogen production plants
as follows:
CapCost = CCB + CCBH + CCR + CCH
(78)
Import charges for aviation fuel and byproducts
Import charges for aviation fuel and byproducts ( InternationalCost ) is equal to the
sum of all aviation fuel received in the national market from the international one ( FTINa )
multiplied by the international price of aviation fuel and byproducts (UCTI ) , plus the sum
of all amounts of byproducts received in the national market from the international one
( FSIN j ,a ) multiplied by the international price of each byproduct (UCSI j ) .
InternationalCost = ∑∑ FSIN j ,aUCSI j + ∑ FTINaUCTI
j
a
(79)
a
3.14 Sales
Domestic sales
Domestic sales ( DomesticSales) are the result of the sum of the amounts of aviation
biofuel distributed to national market from all biorefineries (bi1.a ) , and the sum of the
amounts of aviation fuel of fossil origin distributed to national market from all refineries
( FTk1,a ) ; both sums multiplied by the national price of aviation fuel (UCaaviationbiofuel ) plus the
sum of the amounts of byproducts distributed to national market from all biorefineries
(si1, j , a ) multiplied by the national price of the byproducts (UC byproduc
) as follow:
j ,a
DomesticSales = (∑∑ bi1.a + ∑∑ FTk1,a )UCaaviationbiofuel + ∑∑∑ si1, j ,aUC byproduc
j ,a
a
i1
a
k1
i1
j
(80)
a
International sales
International sales ( InternationalSales) are the result of the sum of the amounts of
aviation biofuel distributed to international market from all biorefineries ( FBNIi1 ) and the
sum of the amounts of aviation fuel of fossil origin distributed to international market from
all refineries ( FTNI k1 ) ; both sums multiplied by the international price of aviation fuel
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(UCTI ) , plus the sum of the amounts of byproducts distributed to international market
from all biorefineries ( FSNI j ,i1 ) multiplied by the international price of the byproducts
(UCSI j ) as follows:


InternationalSales =  ∑ FTNI k1 + ∑ FBNI i1  UCTI + ∑∑ FSNI j ,i1UCSI j
i1
j i1
 k1

(81)
Total sales
The total sales (TotalSales) are equal to domestic sales plus international sales.
TotalSales = DomesticSales + InternationalSales
(82)
Economic objective function
The total profit (Pr ofit ) is equal to the total sales minus all the costs involved in the
supply chain for production of aviation fuel and hydrogen as follow:
proces sin g
Pr ofit = TotalSales − Cost feedstock − Costtotal
(83)
transport
−Costtotal
− CapCost − InternationalCost
3.15 Emissions of carbon dioxide
CO2 captured in the cultivation fields
The CO2 captured in the cultivation fields (CMPCO2 ) is equal to the sum of
cultivated areas ( Ai ,m ) multiplied by the conversion factor to produce biomass (βi ,m ) and
the parameter for carbon dioxide capture (CMPi , m ) .
CMPCO2 = ∑∑ Ai ,m CMPi , m β i ,m
i
(84)
m
CO2 released by the raw material transport
The CO2 released by the raw material transportation (TMPCO2 ) is equal to the sum
of all biomass transported to all biorefineries from all cultivation sites ( FMBTi ,i1,m )
multiplied by a unitary parameter of CO2 emissions (TMPBi ,i1, m ) , plus the sum of the
biomass transported to all biohydrogen production plants from all cultivation sites
( FMBH i ,i 2,m ) multiplied by a unitary parameter of CO2 emissions (TMPBH i ,i 2,m ) , plus the
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sum of the all fossil mass transported to all refineries from all extraction sites
( FfossilTk ,k1,n ) multiplied by a unitary parameter of CO2 emissions (TNPRk ,k1,n ) , plus the
sum of all fossil mass transported to all hydrogen production plants from all extraction sites
( FfossilH k ,k 2,n ) multiplied by a unitary parameter of CO2 emissions (TNPH k ,k 2,n ) as
follows:
TMPCO2 = ∑∑∑ FMBTi ,i1,mTMPBi ,i1,m + ∑∑∑ FMBH i ,i 2,m TMPBH i ,i 2,m
i
i1
m
i
i2
(85)
m
+ ∑∑∑ FfossilTk , k1,nTNPRk , k1,n + ∑∑∑ FfossilH k , k 2,nTNPH k ,k 2, n
k
k1
n
k
k2
n
CO2 released by the aviation fuel transportation
The CO2 released by the aviation fuel transportation (TBTCO2 ) is equal to the sum
of all aviation biofuel transported to all national markets from all biorefineries (bi1,a )
multiplied by a unitary parameter of CO2 emissions (TBTi1,a ) , plus the sum of the aviation
fuel transported to the national market from all refineries ( FTk1,a ) multiplied by a unitary
parameter of CO2 emissions (TTk1,a ) , plus the sum of the aviation fuel transported to
national market from international market ( FTINa ) multiplied by a unitary parameter of
CO2 emissions (TTINa ) , plus the sum of the aviation biofuel transported to the
international market from the national market ( FBNIi1 ) multiplied by a unitary parameter
of CO2 emissions (TBNI i1 ) , plus the sum of the aviation fuel transported to the
international market from the national market ( FTNI k1 ) multiplied by a unitary parameter
of CO2 emissions (TTNI k1 ) as follows:
TBTCO2 = ∑∑ bi1,a TBTi1,a + ∑∑ FTk1,aTTk1,a + ∑ FTIN aTTIN a
i1
a
k1
a
(86)
a
+ ∑ FBNI i1TBNI i1 + ∑ FTNI k1TTNI k1
i1
k1
CO2 released for the transportation of byproducts
The CO2 released by the byproducts transportation (TSPCO2 ) is equal to the sum of
the byproducts transported to the national market from biorefineries (si1, j,a ) multiplied by a
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unitary parameter of CO2 emissions (TSPi1, j ,a ) , plus the sum of the byproducts transported
to the national market from the international market ( FSIN j ,a ) multiplied by a unitary
parameter of CO2 emissions (TSIN j ,a ) , plus the sum of the byproducts received in the
national market form the international market ( FSNI j ,i1 ) multiplied by a unitary parameter
of CO2 emissions (TSNI j ) .
TSPCO2 = ∑∑∑ si1, j,a TSPi1, j ,a + ∑∑ FSIN j ,aTSIN j ,a + ∑∑ FSNI j ,i1TSNI j
i1
j
a
j
a
j
(87)
i1
CO2 released by the raw material processing
The CO2 released by the raw material processing ( PMPCO2 ) is equal to the sum of
the biomass processed to produce aviation biofuel ( fi1,route
m , r ) multiplied by a unitary
parameter of CO2 emissions ( PMPi1, m, r ) , plus the sum of biomass processed to produce
( fmiroute
2, m, rbh )
biohydrogen
multiplied by a unitary parameter of CO2 emissions
( PMPBH i 2,m,rbh ) , plus the sum of fossil mass processed to produce aviation fuel ( ftkroute
1, n , rt )
multiplied by a unitary parameter of CO2 emissions ( PMPTk1,n, rt ) , and plus the sum of
fossil mass processed to produce hydrogen of fossil origin ( fhkroute
2, n , rh ) multiplied by a
unitary parameter of CO2 emissions ( PMPH k 2,n ,rh ) .
route
PMPCO2 = ∑∑∑ f i1,route
m , r PMPi1, m , r + ∑∑∑ fmi 2, m , rbh PMPBH i 2, m , rbh
i1
m
r
i2
m
(88)
rbh
route
+ ∑∑∑ ftkroute
1, n , rt PMPTk 1, n , rt + ∑∑∑ fhk 2, n , rh PMPH k 2, n , rh
k1
n
rt
k2
n
rh
CO2 released by aviation fuel consumption
The CO2 released by aviation fuel consumption ( BTCO2 ) is equal to the sum of all
aviation fuel consumed in the national market (TBa ) multiplied by a unitary parameter of
CO2 emissions ( BTa ) , plus the sum of total amount of aviation fuel sent to international
market (TI ) multiplied by unitary parameter of CO2 emissions ( BTT ) .
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BTCO2 = ∑ TBa BTa + BTT TI
(89)
a
CO2 released by the consumption of byproducts
The CO2 released by the consumption of byproducts (SPCO2 ) is equal to the sum
of all byproducts consumed in the national market (TS j,a ) multiplied by a unitary
parameter of CO2 emissions ( SPj ,a ) , plus the sum of total amount of aviation fuel sent to
international market ( SI j ) multiplied by a unitary parameter of CO2 emissions (SSPj ) .
SPCO2 = ∑∑TS j,a SPj ,a + ∑ SI j SSPj
a
j
(90)
j
Environmental objective function
The total CO2 released (TOTALCO2 ) is equal to the sum of emissions by
transportation, raw material processing and consumption of products minus the carbon
dioxide captured in the fields of cultivation plus the amount of CO2 remaining (CREM ) .
TOTALCO2 = TMPCO2 + TBTCO2 + TSPCO2 + PMPCO2
(91)
+ BTCO2 + SPCO2 − CMPCO2 + CREM
The amount of CO2 remaining (CREM ) is now defined as the amount of CO2 that
was captured in the biomass crops, but was not used to produce aviation biofuel or
biohydrogen.
It is important to mention that the parameter of CO2 captured during cultivation
depends on the climatological conditions and biomass composition; in Mexico SAGARPA2
reports these parameters along with the productive potential of energy crops. On the other
hand, the CO2 release parameter is constituted of emissions by transportation, processing
and product consumption; the first one was calculated based on the consumed fuel per
kilometer for each transported ton. The emissions by consumption were estimated with
base on the carbon contain per ton of each product assuming that all products are used as
fuels. The emissions by processing consider those associated to heating and cooling
services along with those generated as byproducts for each processing route. All the CO2
emissions associated to processing were calculated using a chemical processes simulator.
These parameters are available in supplementary material section.
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3.16 Mass conservation law
Balance of CO2 captured in the biomass crops
The amount of CO2 captured in the biomass crops must be equal to the sum of
carbon dioxide released into the atmosphere by aviation and byproducts consumption, plus
the amount of CO2 released by the transformation of biohydrogen plus the amount of CO2
remaining.
CMPCO2 = ∑ BTT Bi1 + ∑∑ si1, j SSPj + ∑∑∑ fmiroute
2, m, rbhCCMPi 2, m, rbh + CREM
i1
j
i1
i2
(92)
m rbh
The amount of CO2 released by the transformation of biomass to biohydrogen
(∑∑∑ fmiroute
2, m , rbhCCMPi 2, m , rbh ) is the generated byproduct, the unitary parameter of CO2
i2
m rbh
emissions by biomass transformation to biohydrogen (CCMPi 2, m, rbh ) depends on the carbon
content in the biomass.
3.17 Sustainability indicators
The sustainability of an activity is a measure of its reversibility; it means how much
feasible is that this activity is continued for the following generations. The sustainability is
based on the following three aspects: the economic benefit, the environmental affectation
and the social benefit associated with such activity. Nevertheless, it does not exist a
measure patron to quantify the degree of sustainability of activities, being its interpretation
relative and arbitrary. This research proposes two sustainability indicators which are
defined below:
Economic-environmental density ( DS )
The economic-environmental density is the ratio between the economic benefit and
the amount of greenhouse gases emissions (CO2). This indicator determines how much
money is possible to gain by one ton of greenhouse emission in such activity. This
indicator is represented by the symbol ( DS ) and it is calculated as follow:
DS =
Economic benefit ($)
Greenhouse emissions (tons of CO2 released)
Coefficient of mass integration in coupled supply chains (CIM )
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The coefficient of mass integration in coupled supply chains is the ratio between the
amounts of recycled mass and the amount of processed mass. This indicator determines
how efficient is the integration of coupled supply chains, and for the specific case of
supply chain to produce aviation fuel from biomass and fossil mass it is represented by
the symbol (CIM ) and calculated as follow:
CIM =
CO2 captured in the biomass crops ( ton ) − CREM (ton)
CO2captured in the biomass crops ( ton )
(94)
If a large amount of biomass is cultivated, transported, and processed but it is not
transformed into fuel, hydrogen or byproducts, this represents a passive system, which does
not produce energy but it consumes energy and it produces pollution. On the other hand,
sustainability is based on savings of economic cost, pollution and other issues; so, a passive
system is not sustainable, in other words, a supply chain with CIM equal to 1 is more
sustainable.
Finally, the model formulation is stated as a multi-objective optimization approach,
where the problem consists in maximizing equation (83) and minimizing equation (91)
subject to the rest of equations.
4. Case studies
In this paper, a case study from Mexico is presented. The problem considers the
satisfaction of the aviation fuel in the national marker while accounting the use of aviation
biofuel under several scenarios. The considered data were taken from Dominguez-García et
al.23 and Gutiérrez-Antonio et al.24 (see Tables S1 - S4 available in the supporting
information section). Then, the model is a Mixed-Integer Linear Programming (MILP)
problem, which consists of 358,127 continuous variables, 22,520 binary variables and
108,477 constraints; this model was implemented in the software GAMS® and solved
through CPLEX in a computer with an Intel processor at 3.0 GHz with 32 GB of RAM.
The average CPU time required to solve each point of the Pareto curve using the epsilon
constraint method was of 100 seconds.
The supply chain to produce aviation fuel is analyzed from an integral point of
view, involving the production and consumption of hydrogen to produce aviation biofuel.
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Thus, with the aim of determining the convenience of separating the hydrogen production
from the aircraft fuel production plants along with the use of fossil and biomass raw
material simultaneously, different scenarios are studied. Therefore, Scenario 1 considers the
exclusive use of fossil raw materials to produce both hydrogen and aviation fuel, Scenario 2
considers the exclusive use of biomass to produce hydrogen and aviation fuels (also called
biohydrogen and aviation biofuel). Scenario 3 considers the use of fossil mass and biomass
in an integrated mode to produce hydrogen and aviation fuel; this scenario is quite
interesting since it could be the starting case for the energetic transition in aviation sector.
Finally, Scenario 4 considers the use of fossil mass and biomass in an integrated mode to
produce hydrogen and aviation fuel, but involving environmental and economic aspects
simultaneously. In the four scenarios, there is possible to import and export aviation fuel.
Next, a more detailed description of each scenario is provided.
Scenario 1. In this case the aim is determining the supply chain in Mexico that
maximizes the profit with the following conditions. The demand of aviation fuel in each
state of Mexico must be completely satisfied, and only the existing refineries can be used to
produce hydrogen and aviation fuel from fossil resources (petroleum). The surplus of
aviation fuel and byproducts can be exported; moreover it is possible import aviation fuel.
Scenario 2. In this case, the goal is generating the supply chain in Mexico that
maximizes the profit with the following conditions. The demand of aviation fuel in each
state of Mexico must be completely satisfied. The cultivation sites are all the states of
Mexico, in each state is possible to install one biorefinery; furthermore the needed
hydrogen to produce the aviation fuel may be obtained from biomass. In each biorefinery is
possible to install five different processing routes with different gains and byproducts; also,
in each biohydrogen production plant is possible to install three processing routes to
convert biomass to biohydrogen. The surplus of aviation biofuel and byproducts can be
exported; moreover it is possible to import aviation fuel.
Scenario 3. In this case, the focus is to determine the supply chain in Mexico that
maximizes the profit with the following conditions. The demand of aviation fuel in each
state of Mexico must be completely satisfied, and the resulting fuel must be a mixture with
50% from biomass and 50% from fossil mass. The cultivation sites are all the states of
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Mexico. In each state is possible to install one biorefinery and one biohydrogen production
plant; these plants can be linked together with refineries already installed in an integrated
mode to produce aviation fuel and hydrogen from biomass and fossil mass (petroleum). In
each biorefinery is possible to install five different processing routes with different gains
and byproducts; furthermore in each biohydrogen production plant is possible to install
three processing routes to convert biomass to biohydrogen. The surplus of aviation fuel and
byproducts can be exported; moreover it is possible to import aviation fuel.
Scenario 4. In this case the goal is to determine the supply chain in Mexico that
maximizes the profit with the following conditions. The epsilon constrain method is used to
determine a Pareto
solution considering
economic and
environmental aspects
simultaneously. The demand of aviation fuel in each state of Mexico must be completely
satisfied, and the resulting fuel must be a mixture with 50% from of biomass and 50% from
fossil mass. The cultivation sites are all states of Mexico; in each state it is possible to
install one biorefinery and one biohydrogen production plant, these plants can be linked
together with refineries already installed in an integrated mode to produce aviation fuel and
hydrogen from biomass and fossil resources (petroleum). In each biorefinery, it is possible
to install five different processing routes with different gains and byproducts; furthermore
in each biohydrogen production plant is possible to install three processing routes to
convert biomass to biohydrogen. The surplus of aviation fuel and byproducts can be
exported; moreover it is possible import aviation fuel.
5. Results
In this section, the obtained results are analyzed for each one of the defined
scenarios.
Scenario 1. This scenario corresponds to the maximum economic benefit using
exclusively fossil resources to produce both, hydrogen and aviation fuel. The yearly
production of aviation fuel and hydrogen is shown in Table 1, and the economic results for
this case are shown in Table 2, which correspond to transportation cost of 225.45 M$/year,
processing cost of 246.91 M$/year and the raw material cost of 2,490.50 M$/year. The
export sales are 2,388.00 M$/year and the national sales are 3,087.00 M$/year, so that the
profit is 2,512.10 M$/year. The total emissions and the sustainability indicators are shown
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in Table 3. The economic-environmental density has a value of 112.16 $/t, which means
that for every ton of CO2 produced $112.16 are achieved. The coefficient of mass
integration in coupled supply chains for this case is equal to zero, since the biomass is not
used as raw material. Figure 2 shows the schematic representation of distribution of
aviation fuel for this case.
Scenario 2. In this case, there was considered the maximum economic benefit using
exclusively biomass to produce biohydrogen and aviation biofuel. The yearly production of
aviation biofuel and biohydrogen is shown in Table 1, and the economic results for this
case are shown in Table 2, which correspond to transportation cost of 205.32 M$/year,
processing cost of 2,652.30 M$/year and raw material cost of 21,530.00 M$/year. The
export sales are 27,460.00 M$/year and the national sales are 6,629.80 M$/year, so that the
profit is 7,269.70 M$/year; the economic benefit for this case is almost three times greater
than the Scenario 1, it means the use of biomass could be more profitable than the exclusive
use of fossil fuels. The total emissions and sustainability indicators are shown in Table 3.
The economic-environmental density has a value of 107.75 $/ton, which means that for
every ton of CO2 produced $107.75 are achieved, which is a smaller amount of money than
the one of Scenario 1; it means the use of biomass could be more profitable but less
sustainable. The coefficient of mass integration in coupled supply chains for this case is
0.60, it means 40% of biomass captured in the crops is returned to the atmosphere. Figure
3 shows the schematic representation of distribution of aviation biofuel for this case.
Scenario 3. In this scenario, the consideration was given to the maximum economic
benefit using fossil resources and biomass to produce hydrogen and aviation fuel. The
yearly production of aviation biofuel and biohydrogen are shown in Table 1, and the
economic results for this case are shown in Table 2, which correspond to transportation
cost of 330.1 M$/year, processing cost of 2,894.90 M$/year and raw material cost of
24,030.00 M$/year. The export sales are 32,320.00 M$/year and the national sales are
7,259.50 M$/year. So, the profit is 9,908.70 M$/year, the economic benefit for this case is
greater than the one of Scenario 2; it means using biomass and fossil mass in an integrated
mode could be more profitable than the production of aviation fuel from exclusively
biomass or exclusively fossil resources. The total emissions and sustainability indicators
are shown in Table 3. The economic-environmental density has a value of 111.42 $/ton,
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which means that for each ton of CO2 produced $111.42 are achieved, which is a greater
amount of money than the one of Scenario 2; it means using biomass combined with fossil
resources could be more sustainable than using exclusively one of them. The coefficient of
mass integration in coupled supply chains for this case is 0.61, 1% greater than the one of
Scenario 2, and it means that using biomass combined with fossil mass can raise the
efficiency of the supply chain. As was mentioned before, this scenario could represent the
initial point to begin the energetic transition in the aviation sector. Figure 4 shows the
schematic representation of distribution of aviation fuel for this case.
Scenario 4. In this case, the economic benefit using fossil mass and biomass to
produce hydrogen and aviation fuel is addressed with the epsilon constrain method, to
determine a Pareto Solution considering economic and environmental aspects
simultaneously. It should be noted that the Pareto curve represents the overall tradeoffs
between the economic and environmental objectives. This way, any point along this curve
can be seen as a trade-off solution. Furthermore, the solution presented in Tables 1-3 for
scenario 4 is the one remarked in blue color in Table S5, and this was selected because this
shows a good compromise between the considered objectives. In this solution the yearly
production of aviation biofuel and biohydrogen are shown in Table 1, and the economic
results for this case are shown in Table 2, which correspond to transportation cost of
196.45 M$/year, processing cost of 1,421.30 M$/year and raw material cost of 22,190.00
M$/year. The export sales are 11,310.00 M$/year and the national sales are 22,320.00
M$/year, so that the profit is 7,299.30 M$/year. The total emission and sustainability
indicators are shown in Table 3. The economic-environmental density has a value of
346.77 $/ton, which means that for each ton of CO2 produced $ 311.76 are achieved; this is
a greater amount of money than the one of Scenario 3, it means that using biomass
combined with fossil mass could be more sustainable than using exclusively one of them,
and the epsilon constrain method allows determining a more sustainable solution. The
coefficient of mass integration in coupled supply chains for this case is 1.00, it means 100%
of biomass captured is used to produce aviation fuel.
Additional data of sustainable indicators for the analyzed points in the Pareto curve
are presented in Table S5 as supporting information; while Figure 5 shows the location of
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a trade-off solution according with the epsilon constrain method, but this solution is not the
most sustainable depending on the economic-environmental density. On the other hand,
Figures 6 and 7 show that the economic-environmental density behavior as a function of
CO2 emissions and economic benefit, which present a maximum point of this indicator of
sustainability equal to 360.04 $/ton, while the economic-environmental density indicator
for the trade-off solution has a value of 311.76 $/ton. Figures 8 and 9 show the schematic
representation of distribution of aviation fuel for trade-off solution and maximum
economic-environmental density solution, respectively. Also, Table S6 contains a summary
of the production activity of each state of Mexico, which is marked with X.
6. Conclusions
This paper has presented an optimization approach to design supply chains for the
production of aviation fuels. The approach integrates the use of biomass and fossil
resources to produce hydrogen and aviation fuel taking synergistic advantages of both types
of feedstocks. The model incorporates several decision-making factors including the
optimal selection of the bioresources and fossil resources, cultivation sites for biomass,
extraction sites of fossil resources, processing routes and technologies, and integration of
new biorefineries with existing infrastructures. Furthermore, the model incorporates the
optimal distribution and transportation of materials through the supply chain. Two
objective functions have been considered simultaneously: the maximization of the overall
profit and the minimization of the associated emissions.
A case study has been solved for Mexico with several scenarios and conditions. In
this case study, it was determined that the transportation cost associated with the use of
biomass to produce biohydrogen and aviation biofuel is cheaper than the use of fossil
resources. This is attributed to the good condition of the transportation infrastructure of
biomass in Mexico compared to the transportation of fossil resources, and the better
distribution of biomass resource in the country. The model results suggest installing small
processing facilities distributed through the supply chain. A gasification pathway to
produce biohydrogen has been found to be meritorious. It is important to mention that in
the production of aviation fuel, the required amount of hydrogen is small; therefore, the
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cost of transportation is lower than the capital costs for installation of the production plants.
This can be observed in Table S5 of the supplementary material.
The recommended raw materials have been found to be Jatropha Curcas and
Higuerilla, whereas Camelina was the worst option. Finally, attractive solutions have been
generated to balance the economic and environmental objectives. The production of
aviation fuel from biomass and fossil resources simultaneously has been found to be more
profitable than the production of aviation fuel from exclusively one of them. This proposal
is very useful for countries or territories with suitable distribution of potential production of
biomass, furthermore bioresources could be combined with solar or wind energy to produce
any other liquid fuels thus broadening the horizon to combat climate change.
7. Nomenclature
7.1 Indexes
a
Location of national market
i
Location of cultivation sites
i1
Location of biorefineries
i2
Location of biohydrogen production plants
j
Byproducts
k
Fossil resources extraction sites
k1
Location of refineries
k2
Location of hydrogen production plant
m
Type of biomass
n
Type of fossil mass
r
Processing routes to produce aviation biofuel
rt
Processing routes to produces aviation fuel
rbh
Processing routes to produces biohydrogen
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rh
Processing routes to produce hydrogen
7.2 Variables
Ai , m
Total used area for cultivation of any raw material
AiNew
,m
New area needed to produce and supply the biomass demand in each
biorefinery
Bi1
Amount of aviation biofuel produced in each biorefinery
bi1, a
Aviation biofuel sent to national market
BHBi1
Flows of biohydrogen that arrives to each biorefinery
BTN a
Amount of aviation biofuel received in the national market
BHBi1
Total amount of biohydrogen sent to each biorefinery
BTCO2
CO2 released by aviation fuel consumption
BHRk1
Total amount of biohydrogen sent to each refinery
BTNItotal
Amount of aviation biofuel sent to international market
BTNItotal
Amount of aviation biofuel sent to international market
Cost feedstock
Total cost of feedstock
proces sin g
Costavitionbiofuel
Processing cost of biomass for aviation biofuel production
proces sin g
Costbiohydrogen
Processing cost of biomass for biohydrogen production
proces sin g
Costaviation
fuel
Processing cost of fossil mass for aviation fuel production
proces sin g
Costhydrogen
Processing cost of biomass for hydrogen production
proces sin g
Costtotal
Total cost of feedstock processing
CTM B
Cost of transportation of biomass to biorefineries
CTM H
Cost of transportation of biomass to biohydrogen production plants
CTNR
Cost of transportation of biomass to refineries
CTNH
Cost of transportation of fossil mass to hydrogen production plants
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CTB
Cost of transportation of aviation biofuel to national market
CTS
Cost of transportation of byproducts to national market
CTT
Cost of transportation of aviation fuel of fossil origin to national market
CTBI
Cost of transportation of aviation fuel from international market to national
market
CTSI
Cost of transportation of byproducts from international market to national
market
CTBE
Cost of transportation of aviation biofuel sent to international market
CTTE
Cost of transportation of aviation fuel of fossil origin sent to international
market
CTSE
Cost of transportation of byproducts sent to international market
CTBHB
Cost of transportation of biohydrogen to biorefineries
CTBHR
Cost of transportation of biohydrogen to refineries
CTHB
Cost of transportation of hydrogen of fossil origin to biorefineries
transport
Costtotal
Total cost of transportation
CCB
Capital cost by installation of biorefineries
CCBH
Capital cost by installation of biohydrogen production plants
CCR
Capital cost by installation of refineries
CCH
Capital cost by installation of hydrogen production plants
CapCost
Total capital cost
CIM
Coefficient of mass integration in coupled supply chains
CREM
Amount of CO2 that was captured in the biomass crops but was not used to
produce aviation biofuel or biohydrogen
CMPCO2
CO2 captured in the fields of cultivation
DS
Economic-environmental density
DomesticSales
Domestic sales
FBHRi 2,k1
Hydrogen flow from any hydrogen plants
ftn,route
rt ,k1
Flows of fossil mass transformed into aviation fuel
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FMBTtotali1,m
Total amount of raw material delivered to each biorefinery
FMBTi ,i1, m
Amount of biomass sent to the installation site of biorefinery
FMBTtotali1,m
Total amount of raw material processed in each biorefinery
FBNIi1
Aviation biofuel sent to international market
FfossilTtotalk1,n
Total amount of raw material delivered to each refinery
FSNIi1, j
Flows of byproducts sent to international market
FTINa
Aviation fuel of fossil sent to international market
FTk1,a
Aviation fuel of fossil origin sent to national market
FTNIk1
Aviation fuel of fossil origin sent to international market
FfossilTk,k1,n
Fossil mass sent to the installation site of any refinery
fm iroute
2 ,m ,rbh
Biomass processed in each biohydrogen production plant
FBHBi 2,i1
Biohydrogen sent to biorefineries
FBHRi 2,k1
Biohydrogen sent to refineries
Fk ,n
The amount of fossil mass extracted in each extraction site
FfossilTk , k1,n
Raw material sent to the refineries
FfossilH k ,k 2,n
Raw material sent to the hydrogen plants
FfossilHtotalk 2,n
Raw material delivered to each plant of hydrogen production
FfossilH k,k 2,n
Amount of biomass sent to the site of installation of the plant
fhkroute
2,n, rh
Fossil mass processed in each route (rh)
fhkroute
2, n , rh
Fossil mass processed in each hydrogen production plant
FHBk 2,i1
Hydrogen sent to biorefineries
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FHRk 2,k1
Hydrogen sent to refineries
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Hydrogen flow from any biohydrogen plant
FHBk 2,i1
Hydrogen flow from any hydrogen plant
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, r ,i1
Flows of biomass transformed into aviation biofuel
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Aviation biofuel sent to international market from each biorefineries
FTNI k1
Aviation fuel of fossil origin sent to international market from each
refineries
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Byproducts from any biorefinery
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Byproducts sent to international market from any biorefinery
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Raw material sent to the biorefineries
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Raw material sent to the biohydrogen plants
FMBHtotali 2, m
The raw material delivered to each plant of production of
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FMBHi ,i2,m
Biomass sent to the installation site of the plants
fm iroute
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Biomass processed in each route (rbh)
FHRk 2,k1
Hydrogen flow coming from any hydrogen plants
HBi1
Total amount of hydrogen sent to each biorefinery
HRk1
Total amount of hydrogen sent to each refinery
HBtotali1
Total amount of hydrogen that arrives to each biorefinery
HBi1
Flows of hydrogen of fossil origin that arrives to each biorefinery
HRtotalk1
Total amount of hydrogen that arrives to each refinery
InternationalCost
Import charge for aviation fuel and byproducts
InternationalSales
International sales
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PBH i 2
The amount of biohydrogen produced in each plant
Pr ofit
Total profit
Pi , m
Biomass produced
PHk 2
Amount of hydrogen produced in each hydrogen production plant
PMPCO2
CO2 released by the raw material processing
Si1, j
Amount of byproduct ( j ) produced in each biorefinery
si1, j ,a
Flows of byproducts sent to national market
SI j
Amount of byproduct ( j ) sent to international market
SPCO2
CO2 released by byproduct consumption
TMPCO2
CO2 released by the raw material transportation
TBTCO2
CO2 released by the aviation fuel transportation
TSPCO2
CO2 released by the byproducts transportation
TotalSales
Total sales
TI
Total amount of aviation fuel sent to international market
TS j ,a
Amount of byproduct ( j ) received in the national market
TOTALCO2
Total CO2 released
Tfossilk1
Amount of aviation fuel produced in each refinery
TNa
Amount of aviation fuel of fossil origin received in the national market
TNItotal
Amount of aviation fuel of fossil origin sent to international market
TBa
Amount of aviation fuel received in the national market
7.3 Binary variables
dk 2
Binary variable to associate the capital cost with the dimension of hydrogen
of fossil origin production plant
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ek 2,n,rh
Binary variable to associate the capital cost with the dimension of processing
route (rh)
uk 1
Binary variable to associate the capital cost with the dimension of refinery
vk1,n,rt
Binary variable to associate the capital cost with the dimension of processing
route (rt )
wi 2
Binary variable to associate the capital cost with the dimension of
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xi 2,m, rh
Binary variable to associate the capital cost with the dimension of processing
route (rbh)
yi1
Binary variable to associate the capital cost with the dimension of
biorefinery
zi1, m ,r
Binary variable to associate the capital cost with the dimension of processing
route ( r )
7.4 Parameters
AiExist
,m
Existing area used for cultivation
Aimax
,m
Available area to produce biomass
Bimin
1
Minimum capacity of aviation biofuel production
Bimax
1
Maximum capacity of aviation biofuel production
BTT
Unitary parameter of CO2 emissions by aviation fuel consumed in the
international market
BTa
Unitary parameter of CO2 emissions by aviation fuel consumed in the
national market
CMPi , m
Capture of carbon dioxide parameter
CDkH2,n,rh
Sizing parameter of each route (rh)
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CRkH2,n,rh
Base cost of each route (rh) installation
CBkH2
Base cost of hydrogen production plant installation
CDkR1,n,rt
Sizing parameter of each route (rt )
CRkR1,n , rt
Base cost of each route (rt ) installation
CBkR1
Base cost of refinery installation
CDiBH
2, m . rbh
Sizing parameter of each route (rbh)
CRiBH
2, m , rbh
Base cost of each route (rbh) installation
CBiBH
2
Base cost of biohydrogen production plant installation
CDiB1,m ,r
Sizing parameter of each route ( r )
CRiB1, m ,r
Base cost of each route ( r ) installation
CBiB1
Base cost of biorefinery installation
CCMPi 2, m,rbh Unitary parameter of emission by biomass transformation to biorefinery
DBamax
Total demand of aviation fuel in the national market
DS max
j ,a
Total demand of byproducts in the national market
Fkmax
,n
Available reserves of fossil mass
min
fi1,route
m,r
Minimum capacity of processing of raw material through route ( r )
max
fi1,route
m, r
Maximum capacity of processing of raw material through route ( r )
route min
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rt
Minimum capacity of processing of raw material through route (rt )
route max
ftk1,n,
rt
Maximum capacity of processing of raw material through route (rt )
min
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Minimum capacity of processing of raw material through route (rh)
max
fhkroute
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Maximum capacity of processing of raw material through route (rh)
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PH kmin
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Minimum capacity of hydrogen of fossil origin production
PH kmax
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Maximum capacity of hydrogen of fossil origin production
PBHimin
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Minimum capacity of biohydrogen production
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Maximum capacity of biohydrogen production
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Minimum capacity of processing of raw material through route (rbh)
fmiroutemax
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Maximum capacity of processing of raw material through route (rbh)
PMPH k 2, n, rh Unitary parameter of CO2 emissions by fossil mass processed to produce
hydrogen of fossil origin
PMPTk1,n,rt
Unitary parameter of CO2 emissions by fossil mass processed to produce
aviation fuel
PMPBH i 2,m,rbh Unitary parameter of CO2 emissions by biomass processed to produce
biohydrogen
PMPi1, m , r
Unitary parameter of CO2 emissions by biomass processed to produced
aviation biofuel
SSPj
Unitary parameter of CO2 emissions by byproducts consumed in the
international market
SPj ,a
Unitary parameter of CO2 emissions by byproducts consumed in the national
market
TSNI j
Unitary parameter of CO2 emissions by byproducts received in the national
market form the international market
TSIN j , a
Unitary parameter of CO2 emissions by byproducts transported to consume
sites in the national market from the international market
TSPi1, j , a
Unitary parameter of CO2 emissions by byproducts transported to consume
sites in the national market from biorefineries
TTNI k1
Unitary parameter of CO2 emissions by aviation fuel transported to
international market from national market
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Unitary parameter of CO2 emissions by aviation biofuel transported
to international market from national market
TTINa
Unitary parameter of CO2 emissions by aviation fuel transported to
national market from international market
TTk1,a
Unitary parameter of CO2 emissions by aviation fuel transported to
consume sites in the national market from refineries
TBTi1,a
Unitary parameter of CO2 emissions by aviation biofuel transported
to consume sites in the national market from biorefineries
TNPH k ,k 2,n
Unitary parameter of CO2 emissions by fossil mass transported to
hydrogen production plants from extraction sites
TNPRk , k1,n
Unitary parameter of CO2 emissions by fossil mass transported to
refineries from extraction sites
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Unitary parameter of CO2 emissions by biomass transported to
biohydrogen production plants from cultivation sites
Tfossilkmin
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Minimum capacity of aviation fuel production
Tfossilkmax
1
Maximum capacity of aviation fuel production
TMPBi ,i1,m
Unitary parameter of CO2 emissions by biomass transported to
biorefineries from cultivation sites
UCSI j
International price of the byproducts
UCTI
International price of aviation fuel
UCaaviationbiofuel
National price of aviation fuel
UC subproducto
j ,a
National price of the byproducts
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Unitary cost of transportation between the installation site of
hydrogen plants and installation site of refineries
UCTBHRi 2,k1
Unitary cost of transportation between the installation site of
biohydrogen plants and installation site of refineries
UCTBHBi 2,i1
Unitary cost of transportation between the installation site of
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UCTSE j ,i1
Unitary cost of transportation between installation sites of
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UCTTEk1
Unitary cost of transportation between installation sites of refineries
and international market
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Unitary cost of transportation between installation sites of
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UCTSI j ,a
Unitary cost of transportation between international market and the
final consumption
UCTTI a
Unitary cost of transportation between international market and the
final consumption
UCTTk 1, a
Unitary cost of transportation between the installation site of
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Unitary cost of transportation between the installation site of bio
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UCTBi1,a
Unitary cost of transportation between the installation site of bio
refineries and the final site of consumption
UCTNH k ,k 2,n
Unitary cost of transportation between the extraction site and
installation site of hydrogen production plant
UCTNRk , k1, n
Unitary cost of transportation between the extraction site and
installation site of refineries
UCTMHi,i 2,m
Unitary cost of transportation between the cultivation site and
installation site of hydrogen production plant
UCTMBi ,i1, m
Unitary cost of transportation between the cultivation site and
installation site of biorefineries
sin g
UChkproces
1.n.rh
Unitary cost of biomass processing to produce hydrogen
sin g
UCtkproces
1.n.rt
Unitary cost of biomass processing to produce aviation fuel
sin g
UCbhiproces
2.m.rbh
Unitary cost of biomass processing to produce biohydrogen
sin g
UCbtiproces
1.m.r
Unitary cost of biomass processing to produce aviation biofuel
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UCfossilkfeedstoks
,n
Unitary price of fossil mass
UCi ,feedstock
m
Unitary price of biomass
α m, r , j
Biomass to byproducts conversion factor
βi ,m
Efficient factor of biomass production
δn,rt ,k1
Fossil mass to aviation fuel conversion factor
γ i 2,m,rbh
Biomass to biohydrogen conversion factor
λk 2,n,rh
Fossil mass to hydrogen conversion factor
φm,r ,i1
Biomass to aviation biofuel conversion factor
τ n,rt ,k1
Stoichiometric coefficient of hydrogen consumption to produce
aviation fuel of fossil origin
υm,r ,i1
Stoichiometric coefficient of hydrogen consumption to produce
aviation biofuel
8. Acknowledgements
Financial support provided by CONACyT, through grants 239765 and 253660, for
the development of this project is gratefully acknowledged.
9. Supporting Information
Unit prices and costs used in the mathematical model are presented in Table S1.
Yields of different processing routes to produce aviation fuel and yields of different
processing routes to produce hydrogen are presented in Table S2. Table S3 shows the
produced hydrogen through different processing routes. Table S4 shows the unit
information for the CO2 emissions associated to different involved activities. All the points
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that conform the Pareto curve and their values can be consulted in Table S5. Sustainability
indicators for the Pareto curve, activities carried out by each state for all analyzed scenarios
are shown in Table S6. This information is available free of charge via the Internet at
http://pubs.acs.org/.
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Table 1. Production of hydrogen and aviation fuel for all scenarios
Aviation
Study
Aviation fuel,
Hydrogen,
case
kton/year
kton/year
I
6,293.10
0.63
-
-
II
-
-
15,317.00
2.65
III
15,334.00
3.28
6,293.10
-
IV
11,341.00
3.69
1,774.10
7.42
biofuel,
kton/year
Biohydrogen,
kton/year
Table 2. Economic results for all scenarios
Study
Transportation
Processing
case
cost, M$/year
I
225.45
246.91
II
205.32
III
IV
Feedstock
Capital Cost
Import cost,
Export sales,
National sales,
Profit,
M$/year
M$/year
M$/year
M$/year
M$/year
2,490.50
0.00
-
2,388.00
3,087.00
2,512.10
2,652.30
21,530.00
2,432.48
-
27,460.00
6,629.80
7,269.70
330.10
2,894.90
24,030.00
2,415.80
-
32,320.00
7,259.50
9,908.70
196.45
1,421.30
22,190.00
2,522.95
-
11,310.00
22,320.00
7,299.30
cost, M$/year cost, M$/year
Table 3. Sustainability indicators for all scenarios
Study
CO2 emissions,
CO2 captured,
CREM,
Profit,
case
kton/year
kton/year
kton/year
M$/year
I
22,397.00
-
-
II
67,467.00
103,840.00
III
88,931.00
IV
23,400.00
DS, $/ton
CIM
2,512.10
112.16
Ind.
41,081.00
7,269.70
107.75
0.60
103,840.00
40,465.00
9,908.70
111.42
0.61
103,510.00
-
7,299.30
311.76
1.00
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Figures
Figure 1. Superstructure of integrated supply chain to produce aviation fuel from fossil
resources and biomass
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Figure 2. Schematic representation of distribution of aviation fuel for Scenario 1.
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Figure 3. Schematic representation of distribution of aviation biofuel for Scenario 2
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Figure 4. Schematic representation of distribution of aviation fuel for Scenario 3
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Figure 5. Pareto curve
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Figure 6. DS Behavior as a function of CO2 emissions
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Figure 7. DS Behavior as a function of economic benefit
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Figure 8. Schematic representation of distribution of aviation biofuel for Scenario 4 (a)
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Figure 9. Schematic representation of distribution of aviation biofuel for Scenario 4 (b)
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For Table of Content Use Only
Synopsis: This paper presents an optimization approach to design supply chains for the
production of aviation fuels. The approach integrates the use of biomass and fossil
resources to produce hydrogen and aviation fuel taking synergistic advantages of both types
of feedstocks.
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