Optimization of the Supply Chain Associated to the Production of

Article pubs.acs.org/IECR

Optimization of the Supply Chain Associated to the Production of Bioethanol from Residues of Agave from the Tequila Process in Mexico Pascual Eduardo Murillo-Alvarado,† José Ezequiel Santibañez-Aguilar,† José María Ponce-Ortega,*,† Agustín Jaime Castro-Montoya,† Medardo Serna-González,† and Mahmoud M. El-Halwagi‡,§ †

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, México 58060 Chemical Engineering Department, Texas A&M University, College Station, Texas, United States 77843-3122 § Adjunct Faculty at the Chemical and Materials Engineering Department, King Abdulaziz University, Jeddah, Saudi Arabia ‡

S Supporting Information *

ABSTRACT: The Mexican economy is highly dependent on the tequila industry, where there are associated several residues of agave (i.e., the plant used to make tequila), which is lignocellulosic matter that can be used as feedstock for bioethanol production. The residues of agave are obtained in the harvesting sites located in several states of Mexico and from the tequila factories that are mainly located in two places in Mexico. This paper presents an optimization framework for designing a supply chain for the bioethanol production from residues of agave bagasse obtained in the tequila processing in Mexico, where central and distributed bioethanol processing plants are considered. The bioethanol production process in the central and distributed plants is modeled according to conversion factors for the different processing steps obtained from experimental data. The proposed optimization formulation also considers the total available agave and the bioethanol demand in Mexico. Several scenarios are analyzed for the bioethanol production from agave bagasse in Mexico, where positive results are obtained from the reuse of residues of agave bagasse for bioethanol production, obtaining considerable profits and satisfying a significant demand of the gasoline required in the area.

1. INTRODUCTION The agave is a perennial arid plant that consists of thin sheets around a pineapple (or plant head), whose main elements are fibers, sugars, minerals, and water. Juice with high concentration of fructose and other vitamin properties is naturally produced in the center of the pineapple; also, agave has some fat particles that yield its distinctive taste and smell. This way, a large number of products can be obtained from agave as honey water, paper, textiles, mezcal (i.e., a fermented beverage similar to tequila), and tequila. Mexico is one of the areas with the greatest diversity of species of agave in the world. For this reason, agave is one of the most important industries associated to tequila and mezcal production, where the agave plant is used as source of fermentable sugars. The agave is mainly cultivated in the central-western part of Mexico (in the states of Jalisco, Guanajuato, and Michoacán), and most of the factories associated to the tequila industry are located in this region. During the processing of agave to yield tequila, several lignocellulosic residues from the agave are produced. These residues correspond to the stalks that are obtained in the cultivation areas because these are not used for the tequila process, and also, there are other lignocellulosic residues obtained in the factories associated to the tequila processing from the plant heads after the fermentation process. Nowadays, the residues from the agave generated in this region represent a considerable pollution problem because these residues are not used at all. However, these lignocellulosic residues can be used as raw material to produce several value-added products, including bioethanol and solid fuel. Furthermore, satisfying the © 2014 American Chemical Society

fuel requirements is a serious problem due to the reduction of oil reserves around the world and the associated greenhouse gas emissions. In this regard, biofuels are expected to decrease the negative environmental impact for energy use. These biofuels are produced from biomass and organic wastes with high carbon content; for example, bioethanol is one of the most accepted biofuels that can be used as substitution of gasoline. Furthermore, there are several routes to produce bioethanol, most of them through fermentation. Huang et al.1 studied the effect of biomass species and plant size on cellulosic ethanol. Dutta et al.2 presented an economic comparison of different fermentation configurations to obtain ethanol using various microorganisms to observe the advantages with respect to the configuration of the production process. Also, a technoeconomic analysis comparing several routes for bioethanol production from corn stover and lignocellulosic materials was reported by Kazi et al.3 In addition, several chemical and biochemical routes have been proposed for the bioethanol production from lignocellulosic materials such as wheat straw, wood chips, different bagasse, and others. Kaparaju et al.4 proposed the utilization of wheat straw to obtain different biofuels as ethanol, hydrogen, and biogas via hydrothermal pretreatment. Cardona et al.5 discussed the profitability of bioethanol production from lignocellulosic materials considerReceived: Revised: Accepted: Published: 5524

September 24, 2013 February 17, 2014 March 5, 2014 March 5, 2014 dx.doi.org/10.1021/ie4031715 | Ind. Eng. Chem. Res. 2014, 53, 5524−5538

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic representation of the addressed problem for the supply chain of bioethanol production in Mexico from agave bagasse.

bioethanol and sugar production with economic and environmental concerns. In addition, Mele et al.23 presented a systematic optimization approach for designing and planning supply chains for the sugar cane industry involving economic and environmental aspects. Akgul et al.24 presented MILP models for designing bioethanol supply chains, and Shabani and Sowlati25 proposed the supply chain configuration of a typical forest biomass power plant, whereas Ng and Ng26 and Ng et al.27 presented a systematic method for synthesizing integrated palm oil-based biorefineries. A determinant factor for the assessment of the supply chain is the effect of the economies of scale, which was considered by Bowling et al.28 You and Wang29 synthesized biomass to liquid supply chains involving economic and environmental criteria. Tay et al.30 presented an optimization approach for synthesizing integrated biorefineries accounting for uncertainties. Also, uncertainties through stochastic optimization models have been taken into account in the supply chain optimization by Gebreslassie et al.31 and Guillén-Gosálbez and Grossmann.32 Recently, some approaches for accounting sustainability criteria in the supply chain optimization during the biofuels production have been proposed. In this regard, Santibañez-Aguilar33 proposed a multiobjective optimization formulation for the supply chain associated to a biorefinery involving economic and environmental aspects, whereas You et al.34 proposed an approach for the optimal planning of biofuel supply chains considering economic, environmental, and social objectives. An alternative way to consider sustainability is the utilization of waste because residues cause a serious environmental problem. In this context, Santibañez-Aguilar et al.35 proposed an optimization formulation for using water hyacinth as feedstock in a biorefinery in

ing pretreatment and biological transformations. Alex-Marvin et al.6 presented an optimization study focusing on the net present value of five types of lignocellulosic biomass for ethanol production. Furthermore, a simulation study involving thermochemical routes to produce bioethanol from cellulosic and lignocellulosic materials was presented by Gonzalez et al.7 Additional approaches have been proposed to determine the optimal pathway of biorefineries (see Pham and El-Halwagi,8 Ponce-Ortega et al.,9 Murillo-Alvarado et al.,10 Moncada et al.,11 and Martin and Grossmann12). Furthermore, process integration was included in the bioethanol production by ChouinardDussault13 and Martinez-Hernandez et al.14 For the specific case of agave, Hernandez-Salas et al.15 reported experimental data to support the use of agave bagasse for saccharification to obtain value-added fermentation products. Davis et al.16 studied the potential of agave as a biofuel feedstock in the context of eco-physiology, agronomy, and land availability. Holtum and Chambers17 reported a study for the feasibility of agave growing in Australia for bioethanol production, and SaucedoLuna et al.18 presented a study for the chemical and enzymatic saccharification of the lignocellulosic residue from agave to produce bioethanol. Finally, Núñez et al.19 explored the economic viability of producing biofuels from agave in Mexico. Furthermore, recently several approaches for the supply chain optimization for bioethanol production have been proposed. In this context, Sammons et al.20 proposed a systematic framework for optimizing the product portfolio and process configuration in integrated biorefineries. Van Dyken et al.21 presented a mixed-integer linear programming model (MILP) for designing biomass-based supply chains. Mele et al.22 presented the optimal planning of supply chains for 5525

dx.doi.org/10.1021/ie4031715 | Ind. Eng. Chem. Res. 2014, 53, 5524−5538


Article

Figure 2. Bioethanol processing from agave bagasse.

Mexico. Yue et al.36 included environmental aspects into a multiobjective optimization approach for optimizing biofuelbased supply chains. Finally, water and energy are key factors involved in the supply chains associated to biofuels, which were considered by Martin et al.37 Furthermore, Ng et al.38 proposed a modular optimization approach to design integrated biorefineries involving energetic aspects. Ng et al.39 presented a systematic approach to synthesize sustainable integrated biorefineries, which involves economic, environmental, and safety issues. Additionally, El-Halwagi et al.40 proposed a multiobjective optimization model for the supply chain associated to a biorefinery involving economic and safety objectives, and Mazzetto et al.41 proposed a model for the supply chain economic optimization of bioethanol from corn. Baliban et al.42,43 proposed global optimization approaches for synthesizing liquid transportation fuels. Mansoornejad et al.44 proposed an approach for optimizing supply chains associated to forest biorefineries. Lim et al.45 presented a study for planning an integrated rice mill complex. It should be noted that currently there is not a study for the optimal supply chain associated to the bioethanol production from agave residues in Mexico. This supply chain offers particular considerations including the specific processing steps for this process, and sources for the lignocellulosic materials are obtained from the tequila and mezcal industries currently installed (because there are several residues after to yield tequila) and from the harvesting sites (because there are several parts of the agave that are not used in the tequila industry, and these are considered as wastes). Furthermore, the specific geographic location for the tequila industry in Mexico offers particular situations that need to be considered in the optimization for the supply chain, and finally, there is not an

analysis for the capacity to satisfy the bioethanol demand in Mexico using these residues as well as the land and water required to satisfy additional bioethanol demands. Therefore, this paper proposes a mathematical programming model for optimizing the supply chain associated to bioethanol production from residues of agave from the tequila industry in Mexico. The proposed optimization approach uses experimental data obtained from a pilot plant accounting for explicitly the processing steps for the bioethanol production from agave. The economies of scale are properly considered in the proposed optimization formulation. Finally, this paper presents an analysis for different scenarios for satisfying the bioethanol demand in Mexico using the agave residues from the tequila industry in Mexico, and the analysis includes the additional land and water required to satisfy a specific bioethanol demand.

2. PROBLEM STATEMENT The proposed approach is illustrated in Figure 1, which shows the most important harvesting areas of agave in Mexico. These harvesting sites produce agave that can be separated in leaves and plant heads, where the leaves are transported to processing facilities and the plant heads are distributed to the tequila industries. In addition, it is possible to obtain bagasse as waste from the tequila industries. This waste can be transported to potential bioethanol processing facilities (details for this process are shown in Figure 2) to be mixed with the bagasse from leaves according with Figure 3, where the main sources to obtain agave bagasse represent the stalks in the cultivation areas and the bagasse obtained from the tequila industry. This agave bagasse is used to produce bioethanol in processing factories (Figure 2). Figure 4 shows the steps that the biomass requires to be transformed to bioethanol. It should be noticed that there 5526



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and mezcal industries is used as feedstock in the central and/or distributed processing plants. These processing plants are illustrated in Figure 2 for bioethanol production. The differences between the central and distributed processing facilities are capacity and location. In this context, central processing facilities are located in industrialized zones where the capacity is larger and the processing is cheaper, which allows for obtaining larger volumes of bioethanol. On the other hand, distributed processing facilities are located near the cultivation areas, where there is less infrastructure and the processing capacity is lower; this way the unit processing cost is greater (due to the economies of scale). In this context, distributed processing facilities help to reduce the transportation costs for raw materials, which is the main transportation cost involved in the supply chain. However, these distributed processing facilities increase the processing cost. This way, the optimization model must determine the best compromise between these two options. In this way, there are two processing cost functions that depend on the capacity (one for the distributed plant and another for the central plant) and the location of the processing facilities. The processing to obtain bioethanol considers conversion efficiencies (α) for each step; these efficiencies are shown in Table 1 of the Supporting Information. It should be noticed that these values were calculated according to experimental data obtained from a pilot plant and represent the ratio of the outlet mass produced per the inlet total mass processed in each process step.

Figure 3. Main sources of agave bagasse.

3. MODEL FORMULATION Prior to formulating the mathematical model, definitions are needed for the following sets: i represents a set for harvesting areas, j is an index used to define the distributed processing facilities, l is used to represent the central processing facilities, the sites for the industries for tequila production are associated to the index k, locations where products (bioethanol and solid fuel) are consumed are defined by the index m, and finally, the time periods are identified by the index t. The mathematical programing formulation is based on the superstructure shown in Figure 5, whereas the considered bioethanol production facilities are based on the flowsheet presented in Figure 2. The model accounts for the optimal design of the supply chain for the bioethanol production based on residues of agave from the tequila industry in Mexico and considering the available agave residues. This is presented as follows. Mass Balances in Agave Growing Areas. From the available agave (FAgavei,t) can be obtained the plant heads (FPlantHeadsi,t), which are the main raw materials for the tequila production considering a separation efficiency of zAHi, which is modeled as follows F Agavei , t × zAHi = F PlantHeadsi , t , ∀i ∈ I , t ∈ T

(1)

Also, the stalks are important parts of the agave (FTotalLeavesBagassei,t) that currently are considered as wastes, but these can be raw materials for producing bioethanol. The amount of stalks that can be obtained from the agave is determined as follows

Figure 4. Steps for bioethanol production from agave bagasse.

is a lot of water required in the production process. Finally, the produced bioethanol can be transported to different consumption regions located in the main cities of Mexico. To identify the distribution of the processing plants, the superstructure shown in Figure 5 is proposed. In this regard, first the agave bagasse from the harvesting areas and the tequila

F Agavei , t × zALi = F TotalLeavesBagassei , t , ∀i ∈ I , t ∈ T (2)

where zALi is the separation factor for the stalks. 5527



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Figure 5. Proposed superstructure for optimizing the supply chain for a biorefinery based on residues of agave.

Mass Balances in Tequila Industry. This balance determines the inlet flow rate to the tequila processing facilities (FPlantHeadsTequilaIndustry ). In this way, the amount of agave i,k,t plant heads from the harvesting areas i (FPlantHeadsi,t) is equal to the agave plant heads distributed for the tequila production in all facilities k at any period t. The inlet flow rate to the tequila processing factories is used to determine the bagasse that is possible to obtain as waste from the tequila industry at any period of time

The total amount of agave bagasse obtained from the stalks in the agave growing areas is sent to the distributed and central processing facilities for bioethanol production F TotalLeavesBagassei , t =

∑ F LeavesBagasseiDistributed ,j,t j∈J

+

∑ F LeavesBagasseCentral i , l , t , ∀i ∈ I , t ∈ T l∈L

(3)

F PlantHeadsi , t =

Maximum Available Agave. The maximum agave that can be used is limited by the following constraint F Agavei , t ≤ F AgaveiMAX , t , ∀i ∈ I , t ∈ T

k∈K

(6)

The total flow rate of plant heads (FTotalPlantHeadsTequilaIndustry ) from growing areas i that is processed by k,t the tequila industry k for yielding tequila at any time period t is stated as follows

(4)

where FAgaveMAX represents the maximum agave available in i,t the agricultural areas. In this paper, the maximum available agave in the cultivation areas is considered as an optimization variable. This is because the proposed model includes the possibility to increase the cultivation area to satisfy a greater demand based on the available area in the zone. Therefore, FAgaveMAX is calculated considering the current available agave i,t AVAILABLE in this area at any period of time (FAgaveCURRENTLY ) i,t Possible increasing as follows multiplied by a possible increment Inci,t CURRENTLY

Possible increasing

F AgaveiMAX = F AgaveiAVAILABLE (1 + Inci , t ,t ,t

, ∀ i ∈ I, t ∈ T ∑ F PlantHeadsiTequilaIndustry ,k ,t

F TotalPlantHeadskTequilaIndustry ,t =

, ∀k ∈ K , t ∈ T ∑ F PlantHeadsiTequilaIndustry ,k ,t i∈I

(7)

Residues of Agave Bagasse from the Tequila Industry. This balance determines the total amount of tequila bagasse (FTequilaBagassek,t) that is obtained from the tequila processing factories. The obtained bagasse depends on the total agave plant heads in the tequila industry (FTotalPlantHeadsTequilaIndustry ) and an efficiency factor (zCookedk) as k,t follows

), ∀i ∈ I , t ∈ T

(5)

It should be noted that the variable is fixed to zero for the case when the possibility of increasing is not considered, and for other cases, it is limited to the available area in the zone at each period of time t. increasing IncPossible i,t

F TequilaBagassek , t = F TotalPlantHeadskTequilaIndustry ,t × zCookedk , ∀k ∈ K , t ∈ T 5528

(8)



Article Plant F Reactor Plant = F Filtered1Plant p, t × α Filtered1p p , t , ∀p ∈ P , t ∈ T

The total amount of agave bagasse from the tequila industry (FTequilaBagassek,t) is sent to the distributed (FBagasseTequiDistributed Central lak,j,t ) and central (FBagasseTequilak,l,t ) processing facilities for producing bioethanol at any time period t F TequilaBagassek , t =

(14) Plant F Reactor Plant = F Filtered2Plant p, t × α Filtered2 p p , t , ∀p ∈ P , t ∈ T

(15)

∑ F BagasseTequila kDistributed ,j,t

There is another filtering section to treat the effluent from the second hydrolysis reactor, the fermentable material (FFilteredSecondPlant p,t ) obtained from eq 17 is conducted to one fermentation process, and the other part is considered as a solid fuel (FFuelSolidPlant p,t ) that is a byproduct in the global bioethanol production process and is given by eq 18

j∈J

+

∑

F BagasseTequila Central k ,l ,t ,

∀k ∈ K , t ∈ T

l∈L

(9)

Mass Balances in Distributed Processing Plants for Bioethanol Production. These balances take into account the total amount of bagasse in the distributed processing plants (FTotalBagasseDistributed ), which is equal to the flow rate of the j,t stalk bagasse (FLeavesBagassei,t) and the plant heads bagasse (FBagasseTequilaDistributed ) to obtain bioethanol k,j,t

Plant = F Reactor2Plant F filtered2Plant p , t × α Reactor2 p p , t , ∀p ∈ P , t ∈ T

(16) Plant F Reactor2Plant p , t × α FilteredSecond1p

= F FilteredSecondPlant p , t , ∀p ∈ P , t ∈ T

F TotalBagasse Distributed j,t =

∑

F BagasseTequila kDistributed ,j,t

Plant F Reactor2Plant p , t × α FilteredSecond2 p

k∈K

+

, ∀j ∈ J , t ∈ T ∑ F LeavesBagasseiDistributed ,j,t i∈I

(17)

= F FuelSolidPlant p , t , ∀p ∈ P , t ∈ T (10)

(18)

materials (FFermentationPlant p,t ) bagasse (FJuicePlant p,t ) effluents

Fermentable are juices from primary agave from the first Plant (FFiltered1Plant p,t ) and second (FFilteredSecondp,t ) hydrolysis reactors (here only is considered the hydrolyzed part). These fermentable materials are directed to a fermentation process to obtain bioethanol from sugar, and the produced bioethanol is sent to a distillation column that is known as concentrator column

The total bagasse flow rate in the distributed and processing facilities is considered for the bioethanol production, and the production is according to the process shown in Figure 2. All the considered steps have efficiency factors (αstepPlant p ) shown in Table 1 of the Supporting Information, which are based on the data obtained from the pilot plant. The involved steps in the bioethanol production are described in eqs 11−23. These equations are similar for central and distributed processing facilities. For this reason, these equations are grouped using the index “Plant” for both facilities. This way, the set P is the union of J and L (P = J∪L). This way, the agave bagasse in the plants is preprocessed to decrease the particle size through a milled process because a small particle size is required to improve the process to obtain carbohydrates that can be transformed to bioethanol

Plant Plant F Fermentation Plant p , t = F Juice p , t + F Filtered1p , t

+ F FilteredSecondPlant p , t , ∀p ∈ P , t ∈ T (19)

F Fermentation Plant p,t =

Plant F TotalBagassePlant = F Mill Plant p, t × α Mill p p, t , ∀p ∈ P , t ∈ T

×

F Column1Plant p,t ,

α Fermentation Plant p,t

∀p ∈ P , t ∈ T

(20)

Materials from the concentrator column are sent to a second column that is used to dehydrate the bioethanol because one of the most important problems to using bioethanol as fuel is the humidity content. After the dehydrator column, the product is stored in a tank that allows for distributing adequately the product to the consumers

(11)

On the other hand, during the milling process it is possible to obtain juices rich in sugars that then can be processed to produce bioethanol Plant F TotalBagasse Plant = F JuicePlant p, t × α Juice p p , t , ∀p ∈ P , t ∈ T

Plant F Column1Plant p, t × α Distillation p

(12)

= F Column2Plant p, t , ∀p ∈ P , t ∈ T

In addition, the flow rate from milling is treated in a hydrolysis reactor to break the chain of cellulose and hemicellulose. This step is associated to an efficiency factor to process the lignocellulosic material to yield a mix of compounds that can be separated.

(21)

Plant F Column2Plant = F StockPlant p , t × α Dehydrated p p , t , ∀p ∈ P , t ∈ T

(22)

Finally, to take into account the storage of bioethanol in the plants at any time period t (FTankPlant p,t ), this considers the stored bioethanol in the previous time period t − 1 (FTankPlant p,t−1) plus the bioethanol obtained from any processing facility (FStockPlant p,t ) minus the bioethanol sent to markets (FprodBioethanolPlant p,t ), which is stated as follows

Plant F Mill Plant = F Reactor Plant p, t × α Reactor p p , t , ∀p ∈ P , t ∈ T

(13)

After the first reactor, a mix of hydrolyzed and no hydrolyzed compounds is separated through a filter, where the hydrolyzed part is sent to a fermentation tank and the no hydrolyzed part is directed to a second hydrolysis reactor to obtain additional fermentable materials. The separation after the first reactor is modeled through eqs 14 and 15:

Plant Plant F TankPlant p , t = F Tank p , t − 1 + F Stock p , t

− F ProdBioethanolPlant p , t , ∀p ∈ P , t ∈ T (23) 5529



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Distribution of Products from Processing Plants to Markets. These balances take into account the total flow rate of bioethanol obtained from distributed and central processing plants. Furthermore, the flow rate of solid fuel that is obtained in the processing is considered, and this solid fuel is a byproduct that can be economically attractive. The total products obtained from the processing plants Plant (FprodBioethanolPlant p,t , FFuelSolidp,t ) are collected and sent to Plant the markets for sale (gprodBioethanolPlant p,m,t , gprodSolidFuelp,m,t ), and these relationships are stated as follows

∑ U CostPlant pOpMill

CoperPlantMill p =

t∈T

× F TotalBagasse Plant p , t , ∀p ∈ P CoperPlantReactor = p

(33)

× F MillPlant ∑ U CostPlantOpReactor p p , t , ∀p ∈ P t∈T

(34)

∑ U CostPlantOpReactor2 p

CoperPlantReactor2 = p

t∈T

F prodBioethanolpPlant ,t =

∑

× F Filtered2Plant p , t , ∀p ∈ P

g prodBioethanolPlant p , m , t , ∀p ∈ P , t ∈ T

CoperPlantSieve2 = p

(24)

m∈M

(35)

× F Reactor2Plant ∑ U CostPlantOpSieve2 p p , t , ∀p ∈ P t∈T

F FuelSolidPlant p,t =

∑

(36)

g prodSolidFuelPlant p , m , t , ∀p ∈ P , t ∈ T

m∈M

CoperPlantSieve = p

(25)

× F Reactor Plant ∑ U CostPlantOpSieve p p , t , ∀p ∈ P t∈T

(37)

Additional equations are required to establish that the products in markets (GBioethanolm,t, GSolidFuelm,t) are equal to the products obtained from distributed (gprodBioetha, gprodSolidFuelDistributed ) and central (gprodBioenolDistributed j,m,t j,m,t Central thanoll,m,t , gprodSolidFuelCentral l,m,t ) processing facilities

CoperPlantTank = p

∑ U CostPlant pOpTank t∈T Plant × (F Filtered1Plant p , t + F Juice p , t ), ∀p ∈ P

(38)

∑ g prodBioethanolDistributed + ∑ g prodBioethanolCentral j,m,t l ,m,t j∈J

CoperPlantTank2 = p

l∈L

= G Bioethanol m , t , ∀m ∈ M , t ∈ T

∑

g prodSolidFuelDistributed j,m,t

j∈J

+

∑

∑ U CostPlantOpTank2 p t∈T

(26)

× F Fermentation Plant p , t , ∀p ∈ P

g prodSolidFuelCentral l ,m,t

∑ U CostPlantOpColumn p

CoperPlantColumn = p

l∈L

= GSolidFuel m , t , ∀m ∈ M , t ∈ T

t∈T

(27)

× F Column1Plant p , t , ∀p ∈ P

Product Demands. Equations 28−31 impose limits for the MIN maximum (GMAX m,t ) and minimum (Gm,t ) limits for demands in the markets

CoperPlantColumn2 = p

G Bioethanol m , t ≥

CoperPlantTankA = p

(29)

GSolidFuel m , t ≥

The total capital cost accounts for the fixed and variable costs for each unit in the distributed and central processing plants

(31)

Cost of Distributed Bioethanol Processing Plants. The operational cost for the distributed and central processing plants is calculated according to the cost of the involved equipment in the plants as follows

OP

CostPlant

⎛ CoperDistMill + CoperDistReactor ⎞ p p ⎜ ⎟ ⎜ Reactor2 Sieve ⎟ + CoperDist p ⎟ ⎜ + CoperDist p ⎜ ⎟ Sieve2 + CoperDistTank = ∑ ⎜ + CoperDist p ⎟ p ⎟ j∈J ⎜ Tank2 Column ⎜ + CoperDist p ⎟ + CoperDist p ⎜ ⎟ ⎜+ CoperDistColumn2 + CoperDistTankA ⎟ p p ⎝ ⎠

× F StockPlant ∑ U CostPlantOpTankA p p , t , ∀p ∈ P (42)

∀m ∈ M , t ∈ T

∀m ∈ M , t ∈ T

(41)

t∈T

(30)

GSolidFuel mMIN ,t ,

∑ U CostPlantOpColumn2 p × F Column2Plant p , t , ∀p ∈ P

(28)

G BioethanolmMIN ,t ,

(40)

t∈T

G Bioethanol m , t ≤ G Bioethanol mMAX , t , ∀m ∈ M , t ∈ T GSolidFuel m , t ≤ GSolidFuel mMAX , t , ∀m ∈ M , t ∈ T

(39)

CostPlantCAP = KF

∑ p∈P

⎛ CPlantMill + CPlantReactor ⎞ p p ⎜ ⎟ ⎜ Reactor2 Sieve ⎟ + CPlant + CPlant p p ⎜ ⎟ ⎜ ⎟ Sieve2 Tank + CPlant + CPlant ⎜ ⎟ p p ⎜ ⎟ Column2 ⎟ ⎜+ CPlantColumn + CPlant p p ⎜ ⎟ TankA ⎜ ⎟ + Cplant p ⎝ ⎠

∀p ∈ P

(43)

Additional constraints in distributed and central plants are needed to calculate the capacity that is used to obtain the variable part of the capital cost for the processing units. This should be considered into a disjunctive formulation because the fixed part of the cost only is considered when the unit exists. Furthermore, the capacity for each unit must consider the maximum flow rate for all the time periods considered in the supply chain

∀p ∈ P

(32)

where the individual cost for each unit depends on a unitary cost for the amount of processed material in each unit 5530



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F TotalBagasseCAPPlant ≥ F TotalBagassePlant p p , t , ∀p ∈ P , t ∈ T

F Column1CAPPlant ≥ F Column1Plant p p , t , ∀p ∈ P , t ∈ T (44)

F MillCAPPlant p

≥

F MillPlant p,t ,

∀p ∈ P , t ∈ T

(50)

(45)

F Column2CAPPlant ≥ F Column2Plant p p , t , ∀p ∈ P , t ∈ T

F Filtered2CAPPlant ≥ F Filtered2Plant p p , t , ∀p ∈ P , t ∈ T

(51) (46)

F ReactorCAPPlant p

≥

F Reactor Plant p,t ,

∀p ∈ P , t ∈ T

F StockCAPPlant ≥ F StockPlant p p , t , ∀p ∈ P , t ∈ T

For the optimal location of processing facilities, the following disjunction is proposed (where the unit data are shown in Table 2 of the Supporting Information; these costs include the capital and operating costs). The binary variable yPlant is used to p determine the optimal location for the distributed and central plants.

F Reactor2CAPPlant ≥ F Reactor2Plant p p , t , ∀p ∈ P , t ∈ T (48) F FermentationCAPPlant p

≥

F Fermentation Plant p,t ,

(52)

(47)

∀p ∈ P , t ∈ T (49)

⎡ ⎤ Y pPlant ⎢ ⎥ ⎡ ⎤ ¬Y pPlant ⎢ ⎥ ⎢ ⎥ PlantMIN Plant ≤ F F TotalBagasseCAP TotalBagasseCAP ⎢ ⎥ ⎢ p p ⎥ Plant ⎢ ⎥ ⎢ F TotalBagasseCAP p = 0 ⎥ PlantMAX ⎢ ⎥ ⎢ ≤ F TotalBagasseCAPPlant F TotalBagasseCAP ⎥ p p ⎢ ⎥ ⎢ C PlantMill ⎥ p = 0 ⎢ C PlantMill = C FixPlantMill + C VarPlantMill × F TotalBagasseCAP Plant ⎥ ⎢ ⎥ p p p p ⎢ ⎥ ⎢ ⎥ = C PlantReactor 0 p ⎢ ⎥ ⎢ Reactor Reactor Reactor Plant ⎥ = + × C C C F Plant FixPlant VarPlant MillCAP p p p p ⎢ ⎥ ⎢ Reactor2 ⎥ = C Plant 0 p ⎢ ⎥ ⎢ ⎥ Reactor2 Reactor2 Reactor2 Plant = C FixPlant p + C VarPlant p × F Filtered2CAP p ⎥ ⎢ ⎢ C Plant p ⎥ Sieve = C Plant 0 ⎢ ⎥∨⎢ p ⎥ , ∀p ∈ P ⎢ ⎥ ⎢ = C FixPlantSieve + C VarPlantSieve × F ReactorCAP Plant C PlantSieve ⎥ p p p p ⎢ ⎥ ⎢ =0 C PlantSieve2 p ⎥ ⎢ C PlantSieve2 = C FixPlantSieve2 + C VarPlantSieve2 × F Reactor2CAPPlant ⎥ ⎢ ⎥ p p p p ⎢ ⎥ ⎢ =0 C PlantTank ⎥ p ⎢ Tank Tank Tank Plant ⎥ ⎢ ⎥ = + × C C C F Plant FixPlant VarPlant FermentationCAP p p p p ⎢ ⎥ ⎢ Column ⎥ = C Plant 0 p ⎢ ⎥ ⎢ ⎥ Column Column Column Plant = C FixPlant p + C VarPlant p × F Column1CAP p ⎢ C Plant p ⎥ ⎢ Column2 ⎥ =0 C Plant p ⎢ ⎥ ⎢ ⎥ Column2 Column2 Column2 Plant ⎢C Plant p = C FixPlant p + C Varplant p × F Column2CAP p ⎥ ⎢ ⎥ TankA ⎢ ⎥ ⎣ =0 C Plant p ⎦ TankA TankA TankA Plant ⎢ ⎥ = C FixPlant p + C VarPlant p × F StockCAP p C Plant p ⎣ ⎦

The previous disjunction is reformulated as follows. The binary variable yPlant is one when the distributed or central plant p is installed; otherwise the binary variable is zero. Then, the distributed or central plant is installed when the amount of treated agave bagasse is between the given upper and lower limits MIN

F TotalBagassePlant p

where there is not a linear relationship between the capacity and cost. However, this formulation may represent numerical complications for solving large nonlinear and no convex optimization problems. In the analyzed case study, the abovementioned formulation yields problems that are difficult to solve without good initial guesses. It should be noticed that there is not simple to obtain these good initial guesses. Instead of that, the nonlinear behavior for the capital cost functions can be linearized in several segments, as was presented by Bowling et al.28 To obtain these linear relationships, only upper and lower bounds with respect to the capacity for the linear segments are required. This way, in this paper, proper upper and lower bounds for the capacity for the units involved were considered to obtain linear relationships for the capital cost functions (it should be noticed that these limits for central processing plants are greater than the ones for distributed processing plants). This way, the model accounts for the economies of scale, and at the same time, this model formulation can be easily solved.

× ypPlant ≤ F TotalBagasseCAPPlant , ∀p ∈ P p (53)

F TotalBagasseCAPPlant p MAX

≤ F TotalBagasseCAPPlant p

× ypPlant , ∀p ∈ P

(54)

yPlant p

The binary variable is used to calculate the capital cost for each processing unit, where the fixed part of the capital cost is multiplied by the binary variable and the variable part is equal to a unitary cost multiplied by the greatest flow rate processed in all periods of time. It should be noted that the capital cost function usually has an exponent between 0.6 and 0.8 in the variable part to account for the economies of scale. This is the economies of scale state 5531



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Mill Plant C PlantMill + C VarPlantMill p = C FixPlant p × yp p

× F TotalBagasseCAPPlant , ∀p ∈ P p

CostTranspBagasse Plant Teq =

(55)

k∈K p∈P t∈T

C PlantReactor = C FixPlantReactor × ypPlant + C VarPlantReactor p p p ×

F MillCAPPlant , p

∀p ∈ P

× F BagasseTequila kPlant ,p,t

C PlantReactor2 = C FixPlantReactor2 × ypPlant + C VarPlantReactor2 p p p (57)

C PlantSieve = C FixPlantSieve × ypPlant + C VarplantSieve p p p × F ReactorCAPPlant , ∀p ∈ P p C PlantSieve2 p

=

C FixPlantSieve2 p

×

ypPlant

+

C PlantTank p

=

C FixPlantTank p ×

×

ypPlant

+

CostTranspProdBioethanol =

(58)

× U CostTransBioethanolDistributed × djDist j,m,t ,m +

(59)

∀p ∈ P

Cent × U CostTransBioethanolCentral l , m , t × dl , m

(60)

=

× U CostTranspSolidDistributed × djDist j,m,t ,m

(61)

+

×

∀p ∈ P

Cent × U CostTranspSolidCentral l ,m,t × dj ,m

(63)

TotCost = (CostPlantOP + CostPlant CAP + CostTranspLeavesPlant + CostTranspBagasse Plant Teq + CostTranspProdBioethanol + CostTranspProdSolidFuel)

(68)

On the other hand, the total sales include the sales for bioethanol and solid fuel in the markets. In this case, the sold amount in each market over each time period is multiplied by the unitary price

CostTranspLeavesPlant Plant ∑ ∑ ∑ U CostTranspLeavesiPlant , p × di , p i∈I p∈P t∈T

× F LeavesBagasseiPlant ,p,t

(67)

To annualize the transportation cost for bagasse and products, the sum of all time periods is considered. Objective Function. The objective function is maximizing the profit, which accounts for the sales minus the costs. The total cost takes into account all the cost involved into the proposed model, including the operational cost, capital cost, and transportation cost for distributed and central processing plants

The operational cost of the central processing plants is calculated in a similar way as the the distributed processing facilities. The main differences between distributed and central processing plants are their capacity because the economies of scale are considered. In addition, the central processing facilities are associated to a different binary variable to identify if any central plant should be installed. The capital costs for the central processing plants are calculated as a sum of the capital costs for each unit, and this has a fixed part and a variable part that depends on the amount of processed material. Transportation Cost for Stalks to Distributed and Central Plants. This cost involves a unitary charge for bagasse transportation (UCostTranspLeavesPlant i,p ) and the distance from the growing areas to the plant (dPlant i,p ): =

∑ ∑ ∑ g prodSolidFuelCentral l ,m,t l∈L m∈M t∈T

(62)

C PlantTankA = C FixPlantTankA × ypPlant + C VarPlantTankA p p p F StockCAPPlant , p

∑ ∑ ∑ g prodSolidFuelDistributed j,m,t j∈J m∈M t∈T

C PlantColumn2 = C FixPlantColumn2 × ypPlant + C VarPlantColumn2 p p p × F Column2CAPPlant , ∀p ∈ P p

(66)

CostTranspProdSolidFuel

C PlantColumn = C FixPlantColumn × ypPlant + C VarPlantColumn p p p × F Column1CAPPlant , ∀p ∈ P p

∑ ∑ ∑ grodBioethanolCentral l ,m,t l∈L m∈M t∈T

C VarPlantTank p

F FermentationCAPPlant , p

∑ ∑ ∑ g prodBioethanolDistributed j,m,t j∈J m∈M t∈T

C VarPlantSieve2 p

× F Reactor2CAPPlant , ∀p ∈ P p

(65)

Transportation Cost for Products. This cost involves the transportation cost for the products obtained in the distributed and central processing plants that are sent to the markets. Two products are obtained, bioethanol and solid fuel, and the cost is calculated as follows

(56)

× F Filtered2CAPPlant , ∀p ∈ P p

Plant ∑ ∑ ∑ U CostTranspBagassekPlant , p × dk , p

TotSales = ( ∑

(64)

∑ GBioethanol m,t × βmBioethanol

m∈M t∈T

Transportation Cost from Tequila Industries to Distributed and Central Bioethanol Processing Plants. The transportation cost associated to the bagasse transported from the tequila industries to the central and distributed processing plants accounts for the unit transportation cost (UCostTranspBagasse), the associated distance (d) and the transported bagasse (FBagasseTequila):

+

∑ ∑ GSolidFuel m,t × βmSolidFuel) m∈M t∈T

(69)

Finally, the total annual profit is determined by the difference between total sales and costs. PROFIT = TotSales − TotCost 5532

(70)



Article

Figure 6. Optimal economic solution for Scenario A.

4. CASE STUDY The proposed optimization formulation is applied to a case study of Mexico, considering the main region where the agave is cultivated and where the tequila and mezcal industries are located (Figure 1). Table 3 of the Supporting Information shows the available agave in this region. This information has been reported by the Mexican government through its Web site with the current reports of agricultural species (see SAGARPA46). The demand of gasoline in the States of Mexico is shown in Table 4 of the Supporting Information. These data represent the total consumption, but the mathematical model is able to find the demand that can be satisfied considering that the gasoline can be replaced by bioethanol (see SENER47). The model considers nine agricultural areas for agave cultivation (Guanajuato, Zacatecas, Jalisco, Michoacán, Morelos, Nayarit, Oaxaca, Puebla, and Zacatecas). The current tequila factories are located in six places (Tequila 1, Tequila 2, Pénjamo, Oaxaca, Morelos, and Zacatecas). Three central processing facilities for bioethanol production have been considered (Tequila, Oaxaca, and Irapuato) and six distributed bioethanol processing facilities (Chilpancingo, Morelia, Cuernavaca, Tepic, Puebla, and Fresnillo). According with these data and taking into account the possible installation of distributed and central bioethanol processing plants, the next step is to solve the model to find the optimal distribution for the supply chain of bioethanol from agave residues in Mexico. The model for this case study has 12,534 continuous variables, 9 binary variables, and 7189 constraints. This model was coded in the GAMS software and solved through the solver CPLEX (Brooke et al.48). Several scenarios were analyzed to identify the applicability of the proposed methodology. Scenario A considers the economic solution with a constraint for the satisfied demand of bioethanol equal to 1% of the total demand of gasoline in each consumption site. Scenario B considers the case where the bioethanol demand is not limited in any market. For each scenario, the Pareto curves are presented to take into account the behavior between the agave consumption versus the net annual profit. In addition, a comparison of both

scenarios is presented to show the best economic solution between the profit and demand of bioethanol. Furthermore, Scenario C considers the case of when it is possible to increase the cultivation area to satisfy a greater bioethanol demand. In Scenario C, the additional land and water for agave cultivation is considered. Scenario A: Economic Solution with a Constraint of 1% for Bioethanol Demand in Each Consumption Site. The optimal solution for Scenario A includes the installation of two central plants (Central 1 at the city of Tequila in the State of Jalisco and Central 2 at the city of Oaxaca in the State of Oaxaca), and no distributed plants were selected. Central Processing Plant 1 receives bagasse from Cultivation Area 3 (located in the State of Jalisco) with a flow rate of 4.32 × 108 kg of bagasse per year and from Cultivation Area 6 (located in the State of Nayarit) with a flow rate of 1.11 × 107 kg/year. Central Processing Plant 2 is fed from Growing Area 7 (near the city of Oaxaca) with a flow rate of 1.32 × 108 kg/year. Also, the central processing plants are fed with tequila bagasse. Tequila Industry 1 (located in the city of Tequila) and Tequila Industry 2 (located also in the city of Tequila) feed flow rates of bagasse to Central Processing Plant 1 with 1.12 × 108 and 1.21 × 107 kg/ year, respectively. Central Processing Plant 2 is fed with a flow rate of 3.08 × 108 kg/year of tequila agave from Tequila Industry 4 (located in the city of Oaxaca). In this case, the bioethanol production is 1.79 × 108 and 1.38 × 108 kg of bioethanol/year for Central 1 and 2 Processing Plants, respectively. The obtained bioethanol is sent to all considered markets (flow rates are shown in Table 5, Supporting Information). In addition, Figure 6 shows the graphical representation for the supply chain. The optimal distribution was generated with the constraint of 1% for the satisfied demand. This constraint is subjected to the demand stated in each market. Therefore, the bioethanol is consumed in all markets, but the portion consumed in each market is different due to the demand. For the best economic solution for Scenario A, 85% of the total available agave bagasse was consumed. The optimal distribution presents a total annual 5533



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profit of 1.5337 × 108 USD/year, where the sales and costs are 3.72646 × 108 and 2.1927 × 108 USD/year, respectively. In the bioethanol production, the agave waste can be used as solid fuel, adding an important monetary value. This waste provides 2.1645 × 106 USD/year of the total sales. It should be noted that the major contribution for the costs is the operational cost in the central processing plants with a value of 1.9630 × 108 USD/year. This is because the residual bagasse cost is not considered for this case. Furthermore, the transportation cost for biomass and products is lower than the operational cost in central processing plants, and this is 7 × 105 to 9 × 106 USD/ year. This is due to the lower density of the agave bagasse, and the transportation cost for products through duct is lower. Also, it should be noted that the distribution for the supply chain states that the bioethanol production is cheaper in central processing facilities, although this configuration is not sufficient to obtain the total bioethanol consumed. In this way, Scenario A was chosen because this scenario allows for satisfying the biofuel demands in all markets, which represents a geographically distributed solution. Additionally, this scenario only considers the current available agave, which is a realistic solution. Furthermore, the proposed approach can obtain a set of Pareto solutions like is shown in Figure 7 to trade-off the profit

Figure 8. Distribution of bioethanol for Case 1 of Scenario A.

respectively. Furthermore, Tequila Industries 1 and 2 provide bagasse flow rates of 2.83 × 108 and 6.26 × 107 kg/year to Central Processing Plant 1. Tequila Industry 3 provides a bagasse flow rate of 3.52 × 107 kg/year to Central Processing Plant 3. According with the total flow rate in each central processing plant, it is possible to obtain 1.13 × 108 kg/year of bioethanol from Central Processing Plant 1 and 1.66 × 108 kg/ year of bioethanol from Central Processing Plant 3. Figure 9 shows the distribution of the bioethanol obtained for the considered markets for Case 2, where the associated profit is 1.3949 × 108 USD/year.

Figure 7. Pareto curves for Scenarios A and B.

and satisfy the demand for this scenario. Notice that the profit increases when the satisfied demand increases. Two cases are selected for analyzing this Pareto curve. Case 1: 40% of Consumed Agave. This scenario accounts for the installation of Central Processing Plant 1. This plant receives 2.56 × 108 kg/year of bagasse from Cultivation Area 3 (Jalisco) and 1.46 × 107 kg/year from Growing Area 6 (Nayarit). Also, Tequila Industries 1 and 2 (both located in Tequila, Jalisco) feed the central processing plant with bagasse flow rates of 9.97 × 107 and 1.03 × 108 kg/year, respectively. With this total flow rate, Central Processing Plant 1 produces 1.49 × 108 kg/year of bioethanol. The distribution of the bioethanol obtained in the markets is shown in Figure 8, where the associated profit is 7.4806 × 107 USD/year. Case 2: 75% of Consumed Agave. For this scenario, the optimal distribution considers the installation of Central Processing Plants 1 and 3. Central Processing Plant 1 is fed from Cultivation Area 6 (Nayarit) with a flow rate of 1.46 × 107 kg/year of agave bagasse. Central Processing Plant 3 receives bagasse from Cultivation Areas 1, 3, and 4 with bagasse flow rates of 3.54 × 107, 4.37 × 108 , and 1.35 × 107 kg/year,

Figure 9. Distribution of bioethanol for Case 2 of Scenario A.

Scenario B: Solution without Constraint for Demand of Bioethanol in the Markets. In this scenario, the mathematical model is solved without constraints for demands in markets. The optimal economic solution for this scenario selects the installation of Central Processing Plants 1, 2, and 3, and Distributed Processing Plant 3. Table 6 of the Supporting Information shows the agave bagasse from cultivation areas and tequila industries feeding all central and distributed processing plants. In addition, Table 7 of the Supporting Information shows the obtained bioethanol by each processing plant. The flow rates of the obtained bioethanol are sent to the different markets. However, in this scenario, there is not a constraint to satisfy any demand in the markets. For this reason, in the optimal solution, the plants send bioethanol to the nearest markets, which is shown in Figure 10. In addition, the satisfied 5534



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Currently, the gasoline is mixed with bioethanol to be used in vehicles. The most common composition is 90−10%, although this concentration depends on the country. In this context, the satisfied demand is almost 40% of the total bioethanol demand. However, the increase in cultivation areas requires more used land, land conversion, irrigation water, and water due to the increase in bioethanol production. Table 8 of the Supporting Information shows the required surface for the increase in agave cultivation as well as bioethanol production. It is important to note that the model incorporates constraints for the additional cultivation areas depending on the available cultivation land; also the model can determine the additional water required for cultivating the additional agave. Table 9 of the Supporting Information presents the amount of water that is needed to produce bioethanol when the possibility of increasing the agave production is considered. The used water was obtained according to the produced bioethanol from each plant. The water for irrigation was approximated with the monthly precipitation water for a good agave production, which is around 600−800 mm of water. Results for this scenario show that the needed water is from 365 × 103 to 122 × 106 m3. In this case, the needed water depends mainly on the increased area for agave production. The water required for processing is shown in Table 10 of the Supporting Information. In this case, the amount of utilized water does not change importantly because the processing plants are operating to the maximum allowed capacity to obtain the largest amount of bioethanol for the economic solution.

Figure 10. Optimal economic solution for Scenario B.

demand in some market is around 50% in some periods. Nonetheless, the satisfied demand during the entire horizon is around 10−20%. The obtained profit is 1.8541 × 108 USD/ year for the given configuration of the supply chain. Figure 7 shows the Pareto curve for this scenario. It should be noticed that the profit increases when the satisfied demand increases. In this regard, Figure 7 also shows the comparison between both Pareto curves. The main difference between both solutions is the configuration of the supply chains. The amount of harvested agave is very similar as well as the obtained profit. However, a change in the supply chain should affect the transportation cost of raw materials and products. The behavior of both Pareto curves is very similar. Consequently, the transportation cost does not have an important effect on the net profit for the analyzed case study. Scenario C: Increasing the Cultivation Area. A third scenario has been considered. In this case, the possibility to increase the agave cultivation areas in order to increase the satisfied bioethanol demand is included. Also, this scenario provides an analysis about the profitability of the use of the agave bagasse in bioethanol production. This scenario was considered because agave production is not sufficient to satisfy the total bioethanol demand. Also, agave is a perennial plant and requires five years for growing. In this context, it is necessary to implement optimal planning to determine the location where agave cultivation is feasible or required. To consider a change in the availability of agave, the upper increasing limit for the variable IncPossible (eq 5) was changed from i,t 1 to 6. With this change, the amount of available agave was increased from 100% to 600% more of the currently available agave. It is important to note that the amount of utilized agave can be different to the available agave for given harvesting sites. Also, the cost for production of the new agave was taken into account. An example of this variable is given as follows: (1) If it takes the value of zero, the increment is 0% (the available agave is equal to the current amount of agave). (2) If it takes the value of one. The increment is 100% (the available agave is equal to the double of the current amount of agave). (3) The parameter should be changed up to 6 for this case study. In other words, the available agave can be up to 7 times the current amount of agave. According to the obtained results, the maximum bioethanol demand that can be satisfied is about 3.8% of the total demand of gasoline with an increment of 400% of the available agave.

5. CONCLUSIONS This paper has presented a study for the optimal planning of the sustainable use of agave residues obtained in tequila production in Mexico. This paper proposes to use the lignocellulosic residues from the processing of tequila to obtain biofuels (bioethanol and solid fuel). The study includes the development of an optimization formulation for the supply chain, where several harvesting sites, tequila factories, and markets for the biofuels have been considered. Furthermore, the optimization model involves the optimization for the selection of distributed and central processing plants, transportation, and economies of scale associated to the supply chain. Experimental data from a pilot plant for obtaining bioethanol from agave residues have been included in the optimization formulation. The optimization formulation considers the maximization for the profit accounting the sales for the bioethanol and solid fuel in the markets minus the total costs associated to harvesting, processing, and transportation in the supply chain. Several scenarios have been analyzed. Results show that the bioethanol production from agave bagasse is a feasible way for obtaining biofuels. For the current situation, the results show that it is possible to satisfy around the 10% of the total demand of bioethanol of Mexico, and for some specific cities, it is possible to satisfy about 40% and 50% of the bioethanol demand in some seasons of the year, with a considerable obtained profit for processing this residue from the tequila industry. Furthermore, the proposed approach has been applied to determine the additional agave as well as land and water required to satisfy a greater bioethanol demand in Mexico. Results show that the possible satisfied bioethanol demand is around 40% in most of the considered markets, although this 5535



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CFixPlantReactor2 = Fixed cost for reactor of the second stage p = Fixed cost for sieve CFixPlantSieve p CFixPlantSieve2 = Fixed cost for sieve of the second stage p = Fixed cost for tanks CFixPlantTank p CFixPlantTank2 = Fixed cost for tanks of the second stage p = Fixed cost for stock tank CFixPlantTankA p = Unit variable cost for distillation column CVarPlantColumn p CVarPlantColumn2 = Unit variable cost for dehydrated column p = Unit variable cost for mill CVarPlantMill p CVarPlantReactor = Unit variable cost for reactor p = Unit variable cost for reactors of the CVarPlantReactor2 p second stage CVarPlantSieve = Unit variable cost for sieve p = Unit variable cost for sieve of the second CVarPlantSieve2 p stage CVarPlantTank = Unit variable cost for tanks p = Unit variable cost for stock tank CVarPlantTankA p CVarPlantTank2 = Unit variable cost for tanks of the second p stage dPlant = Distance from cultivation area i to plant p i,p dPlant k,p = Distance from tequila industry k to plant p dPlant p,m = Distance from plant p to market m FAgavei,tMAX = Maximum agave available in cultivation area i GBioethanolMAX m,t = Maximum demand of gasoline in market m GBioethanolMIN m,t = Minimum demand of gasoline in market m GSolidFuelMAX m,t = Maximum demand of solid fuel in market m GSolidFuelMIN m,t = Minimum demand of solid fuel in market m KF = Factor used to annualize the capital costs UCostPlantOpColumn = Unit operating cost for distillation p column UCostPlantOpColumn2 = Unit operating cost for dehydrated p column = Unit operating cost for mills UCostPlantOpMill p UCostPlantOpReactor = Unit operating cost for reactors p = Unit operating cost for reactors of UCostPlantOpReactor2 p second stage UCostPlantOpSieve = Unit operating cost for sieves p UCostPlantOpSieve2 = Unit operating cost for sieve of second p stage of plants = Unit operating cost for tanks UCostPlantOpTank p UCostPlantOpTank2 = Unit operating cost for tanks of second p stage UCostPlantOpTankA = Unit operating cost for stock tanks p UCostTranspBagasse = Unit transportation cost from tequila industry k to plants UCostTranspBioethanol = Unit transportation cost from plants to market k UCostTranspLeaves = Unit transportation cost from cultivation area i to plants UCostTranspSolid = Unit transportation cost from plants to market k zAHi = Efficiency for agave plant heads in cultivation area i zALi = Efficiency for agave bagasse in cultivation area i zCookedk = Efficiency for agave bagasse in tequila industry k

causes the consumption of large amounts of water and a significant additional amount of cultivation land. Finally, no numerical complications were observed in the application of the proposed approach, which is general and can be applied to different biomass and biofuel types.

■

ASSOCIATED CONTENT

S Supporting Information *

Detailed data and results for the case study are included in tables. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail:[email protected]. Tel.: +52 443 3223500, ext. 1277. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS Authors acknowledge the financial support obtained from SAGARPA and CONACyT. NOMENCLATURE

Indexes

= Index for agave cultivation areas = Index for distributed bioethanol processing plants k = Index for tequila industry l = Index for central bioethanol processing plants m = Index for markets t = Index for time period p = Distributed or central processing plants i

j

Sets

I = Set for agave cultivation area i J = Set for distributed bioethanol processing plant j K = Set for tequila industry k L = Set for central bioethanol processing plant l M = Set for market m for bioethanol and solid fuel P = Set for central and distributed processing plants T = Set for time period t Parameters

αDehydrated = Efficiency for dehydration αDistillation = Efficiency for distillation αFermentation = Efficiency for fermentation αFiltered1 = Efficiency for filtration at first stage of filtration αFiltered2 = Efficiency for filtration at first stage of filtration to obtain the amount of material directed to the second hydrolysis reactor αFiltered second1 = Efficiency for second filtration process at second stage to obtain the fermentable material αFiltered second2 = Efficiency for second filtration to obtain the solid fuel αReactor = Efficiency for reaction at first stage of hydrolysis αReactor2 = Efficiency for reaction process at second stage αSieve = Efficiency for milling αSieveJuice = Efficiency for milling for the juice obtained βBioethanol = Bioethanol price in market m m βSolidFuel = Solid fuel price in market m m = Fixed cost for distillation column CFixPlantColumn p CFixPlantColumn2 = Fixed cost for dehydrated column p CFixPlantMill = Fixed cost for milling p CFixPlantReactor = Fixed cost for reactor p

Variables

CPlantColumn = Capital cost for the columns p = Capital cost for the second columns CPlantColumn2 p CPlantMill = Capital cost for the mills p CPlantReactor = Capital cost for the reactors p CPlantReactor2 = Capital cost for the second stage of reactors p 5536



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CPlantSieve = Capital cost for the sieves p = Capital cost for the second stage of sieves CPlantSieve2 p CPlantTank = Capital cost for the tanks p = Capital cost of the stock tanks CPlantTankA p CPlantTank2 = Capital cost of the second tanks p = Operating cost for the columns CoperPlantColumn p = Operating cost for the second stage of CoperPlantColumn2 p columns CoperPlantMill = Operating cost for the mills p CoperPlantReactor = Operating cost for the reactors p = Operating cost for the second stage of CoperPlantReactor2 p reactors CoperPlantSieve = Operating cost for the sieves p = Operating cost for the second stage of CoperPlantSieve2 p sieves CoperPlantTank = Operating cost for the tanks p = Operating cost for the stock tanks CoperPlantTankA p CoperPlantTank2 = Operating cost for the second stage of p tanks CostPlantCAP = Total capital cost for processing plants CostPlantOP = Total operating cost for processing plants CostTranspBagasseCentral = Cost for transportation of agave Teq bagasse from the tequila factories to central processing plants CostTranspBagasseDist Teq = Cost for transportation of agave bagasse from the tequila factories to distributed plants CostTranspLeavesCentral = Cost for the transportation of the bagasse to central processing plants CostTranspLeavesDist = Cost for the transportation of the bagasse to distributed processing plants CostTranspProdBioethanol = Transportation cost of the bioethanol to markets CostTranspProdSolidFuel = Transportation cost of the solid fuel to markets GBioethanolm,t = Total bioethanol flow rate sent to the market m gprodBioethanol = Bioethanol flow rate sent from plants to markets gprodSolidFuel = Solid fuel flow rate sent from plants to markets GSolidFuelm,t = Total solid fuel sent to the market m FBagasseTequila = Bagasse flow rate sent from the tequila industry k to processing plants FColumn1Plant = Flow rate inlet to the distillation column p,t FColumn2Plant = Flow rate inlet to the dehydrated column p,t = Flow rate inlet to the fermentation FFermentationPlant p,t process FFiltered secondPlant = Flow rate inlet to the filter of the p,t second stage FFiltered1Plant = Flow rate outlet to the fist filter p,t = Flow rate outlet to the first filter sent to FFiltered2Plant p,t second stage of hydrolysis FFuelSolidPlant = Flow rate of solid fuel obtained p,t FPlantHeadsi,t = Flow rate of agave plant heads in cultivation area i FPlantHeadsTequilaIndustry = Flow rate of plant heads from i,k,t cultivation area i in tequila industry k FMillPlant = Flow rate in mill process p,t = Flow rate of bioethanol produced in FProdBioethanolPlant p,t plants FReactorPlant = Flow rate in reaction process in plants p,t FReactor2Plant p,t = Flow rate in reaction of the second stage in plants

■

FStockPlant = Amount of bioethanol obtained in distributed p,t or central plants FTankPlant = Flow rate in stock tank in plants p,t FTequilaBagassek,t = Total flow rate of bagasse in tequila industry k FTotalBagassePlant = Total flow rate of bagasse in plants p,t = Total flow rate of plant heads in FTotalHeadsTequilaIndustry k,t tequila industry k FTotalLeavesBagassei,t = Flow rate of agave bagasse in cultivation area i FTotalLeavesBagasse = Flow rate of bagasse in cultivation area i sent to plants PROFIT = Total annual profit TotCost = Total annual cost TotSales = Total annual sales yp = Binary variable for the existence of the distributed or central processing plants

REFERENCES

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