Optimization of Pathways for Biorefineries Involving the Selection of

Article pubs.acs.org/IECR

Optimization of Pathways for Biorefineries Involving the Selection of Feedstocks, Products, and Processing Steps Pascual Eduardo Murillo-Alvarado,† José María Ponce-Ortega,*,† Medardo Serna-González,† Agustín Jaime Castro-Montoya,† and Mahmoud M. El-Halwagi‡,§ †

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

S Supporting Information *

ABSTRACT: This paper presents a systematic approach to identify the optimal pathway configurations of a biorefinery while incorporating technical, economic, and environmental objectives. This problem is formulated as a generalized disjunctive programming model which accounts for the simultaneous selection of products, feedstocks, and processing steps. The optimal solution can involve multiproduct and multifeedstock biorefineries. The optimization model takes into account two potentially conflicting objectives, the maximization of the net profit and the minimization of the greenhouse gas emissions, while considering the number of processing steps. The environmental criterion is measured using the life cycle assessment methodology. The εconstraint method is used to determine the Pareto curves of this multiobjective optimization problem and to show the trade-offs between the competing objectives. A case study is presented to illustrate the applicability of the proposed methodology for the optimal selection of the biorefinery configuration for the conditions of Mexico under several scenarios. The results show that the optimal combination of different feedstocks and products allows for proper trade-off between the economic and environmental objectives. Results also show that bioethanol, biodiesel, and biohydrogen usually appear as products, whereas sugar cane, jatropha, and microalgae appear as feedstocks in the optimal pathways.

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INTRODUCTION Recently, there has been a growing interest in developing renewable energy technologies to address the escalating problems associated with greenhouse gas (GHG) emissions related to the use of fossil fuels and to extend the useful life of fossil fuel reserves. In this context, biofuels (i.e., fuels obtained from biomass) offer the potential to achieve these objectives. Nonetheless, several factors must be considered for the sustainable production of biofuels. For example, there is a critical need for optimizing the selection of the feedstocks, the preprocessing stages, the processing technologies, and the manufactured products. Within the biorefinery, where biomass is processed through physical, chemical, and/or biological technologies to obtain biofuels and other value-added chemicals, there are numerous possibilities, as can be seen in Figure 1. Different types of feedstocks, processing pathways, and products are possible and must be carefully screened. Issues pertaining to the selection of feedstocks have been discussed in the literature (e.g., Huber et al.,1 Saxena et al.,2,3 Goyal et al.,4 and Daoutidis et al.5). Kamm and Kamm,6 Fernando et al.,7 and Fatehi and Ni8 showed that different products can be obtained from different lignocellulosic feedstocks. Werpy and Petersen9 and Holladay et al.10 reported a list of the top-value bioproducts. You et al.11 presented a synthesis method to obtain ethanol from cellulosic biomass involving the life cycle assessment technique. Previous works show that the chemical route to produce a desired bioproduct can be quite complicated. To solve this problem, several pathway synthesis methods have been reported in the literature. © 2013 American Chemical Society

Figure 1. Schematic representation for biorefinery configurations.

Agnihotri and Motard12 and Nishida et al.13 presented approaches for the reaction pathway synthesis. Govind and Received: Revised: Accepted: Published: 5177

December 12, 2012 March 2, 2013 March 13, 2013 March 13, 2013 dx.doi.org/10.1021/ie303428v | Ind. Eng. Chem. Res. 2013, 52, 5177−5190

Industrial & Engineering Chemistry Research

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Figure 2. Generation of a superstructure for a biorefinery pathway configuration according to the addressed problem.

Powers14 proposed the retro-synthesis approach for synthesizing reaction pathways. May and Rudd15 presented an approach for synthesizing reaction pathways based on thermodynamic feasibility, and Rotstein et al.16 and Fornari et al.17 proposed graphical methods for synthesizing reaction pathways. Crabtree and El-Halwagi18 presented an approach for the synthesis of chemical pathways considering the associated environmental effects. In addition, Pistikopoulos et al.19 and Buxton et al.20 presented methodologies for minimizing the environmental impact in reaction pathways. Li et al.21 and Ng et al.22 presented hierarchical optimization methods for synthesizing reaction pathways. Sammons et al.,23 Bao et al.,24 and Marvin et al.25 presented optimization-based approaches for synthesizing integrated biorefineries. Recently, some works have proposed systematic analysis to determine the optimal route for a biorefinery considering a given feedstock and the desired product; in this context, Pham and El-Halwagi26 presented a method to determine the optimal pathway for a biorefinery configuration based on dynamic programming. Later, PonceOrtega et al.27 extended this approach to include a formal optimization model based on disjunctive programming for the automatic optimization of the biorefinery pathway. Notwithstanding the usefulness of the above-mentioned approaches, they have at least one of the following limitations for the pathway optimization of biorefineries: • A preselected feedstock was used without the optimal selection of the type of feedstock. In general, there may be several types of feedstocks to be screened. • The manufactured product is preselected prior to the optimization approach. There are merits for the consideration of candidate products with the objective of determining the optimal value-added product(s). • Only one product and one feedstock have been considered. Nonetheless, to determine the optimal pathway for the biorefinery configuration, it is necessary to account for the optimal selection of different types of products and feedstocks. In addition, previous approaches did not take into account the availability of different feedstocks and the specific demands for the desired products simultaneously. • Previous approaches to solve the biorefinery pathway configuration problem have only considered the optimal selection of the pathway based on economic and/or environmental criteria. The number of processing steps

has not been taken into account. The number of processing steps is an important issue that should be taken into account for process simplification and safety issues (see Ponce-Ortega et al.28 and Gopalakrishnan et al.29). To overcome the aforementioned limitations of the previous approaches proposed to solve the biorefinery pathway configuration problem, this paper presents a systematic approach based on a mathematical programming model to address the optimal synthesis of biorefinery configurations while allowing the simultaneous handling of multiple feedstocks, products, and processing routes involving different numbers of processing steps. The proposed model accounts for the selection of several feedstocks and products while taking into account the availability and demands. Also, the approach enables the systematic trade-off for the simultaneous maximization for the total net profit and the minimization for the net GHG emissions accounting for the number of processing steps (see Figure 2). Superstructure Formulation. The first step of the proposed approach is to develop a superstructure to identify the set of pathways that are able to contain the optimal one. In this paper, the proposed approach by Pham and El-Halwagi26 is used for this task. In this regard, first the biomass that will be used as feedstock is identified and characterized, and then the target products are identified. In this step, there are several products that can be obtained from the feedstocks using different chemical reactions; there are also several reactants than can be used to produce the main product through different reactions. The problem here is to identify the interconnections between these compounds through different chemical routes. First, the approach involves the forward synthesis of biomass, where all potential intermediate products and their corresponding conversion technologies are identified. The second stage consists of the backward synthesis of desired products, where, for a given final product, the required preceding compounds as well as their corresponding technologies are determined. The next step corresponds to the matching of two intermediate compounds obtained in the forward and backward steps. The final step for the superstructure generation is the interception of two intermediate compounds obtained in the forward and backward steps identifying the set of conversion technologies required to connect these compounds. Using this approach, a superstructure like the one shown in Figure 3 is obtained for 5178

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Figure 3. Example of a superstructure for a biorefinery pathway configuration involving multiple feedstocks and products.

each specific problem (i.e., given available feedstocks and desired products). Notice in Figure 3 that there are several possibilities for the pathway biorefinery configuration and that it is not obvious to identify the pathway with the lowest cost, lowest GHG emissions, and minimum processing steps; in addition, the solution with the minimum cost may not correspond to the solution with the lowest environmental impact or the minimum GHG emissions (and remember that this is one of the purposes for the use of biofuels). Furthermore, the solution with the minimum cost may not correspond to the solution with the minimum number of processing steps. Notice that the number of processing steps has important implications on the safety of the biorefinery, since the number of processing units and storage tanks of intermediate compounds are proportional to the number of processing steps (Ponce-Ortega et al.28 and Gopalakrishnan et al.29). On the basis of the generated superstructure, the following step corresponds to apply the optimization formulation presented in the next section.

Figure 4. Chemical routes for connecting two adjacent nodes.

First, the following logical relationship states that, when compound j is selected to appear in the optimal pathway, then one technology tj to produce it must be used. This is modeled using binary variables as follows: yj =

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∑ zj , t , j

∀ j ∈ J , j ≠ feedstock

t j ∈ Tj

(1)

In the previous equation, yj is a binary variable used to model the existence of the compound j in the optimal pathway (if yj is 1, the compound j exists, and when yj is zero, the compound does not exist), whereas zj,tj is a binary variable used to select the technology tj to produce the compound j (when zj,tj is 1, it means that the technology tj is used to produce j, whereas, when zj,tj is zero, it means that the technology tj is not used to produce j). When one technology tj is used to produce j from i, then an additional constraint is required to state that the preceding compound i must exist, and this is modeled as follows:

OPTIMIZATION FORMULATION On the basis of the generated superstructure, first the following scripts are defined: i represents a subscript for any compound preceding the compound j in the superstructure. To yield any compound j, several preceding compounds i can be used. Notice also that for any pair of two adjacent compounds i and j could be more than one chemical route (see Figure 4); therefore, the subscript t is used to represent any chemical route that connects any pair of compounds. After developing the superstructure for a given problem (like the one shown in Figure 3) and based on the representation shown in Figure 4, the mathematical programming formulation for the optimal biorefinery pathway configuration is presented as follows.

(1 − zj , t j) + yi ≥ 1,

∀ j ∈ J , j ≠ feedstock, ∀ t j ∈ Tj (2)

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If compound j exists in the optimal pathway, then the associated flow rate must be greater than zero as well as the associated cost and environmental impact; also, one preceding compound i must be selected to produce j through a chemical route tj available for this step that has to be optimized. The existence for the compound j in the optimal pathway is modeled as follows: f j ≤ M max f yj ,

j∈J

t

Notice here that the unit cost (Mcostj) and unit environmental impact (MEIj) for any feedstock are determined prior to the optimization process; such unit costs can be obtained from reported data, by experimentation or simulation. For other compounds different than the feedstocks, when the chemical route tj is selected to yield j, the corresponding conversion factor αi,tj(Otj) is applied to calculate the yield of j. In this case, the corresponding cost costj and environmental impact EIj have to be determined properly. Notice that these terms depend on the vector of operating variables Otj for each technology tj. On the other hand, when the component j is not present in the optimal pathway, then the associated flow rate, cost, and environmental impact must be zero. This situation is modeled through the following disjunctive formulation for the compounds different from the feedstocks.

(3)

When a given compound j of the set of feedstocks is selected to appear in the optimal solution (i.e., the binary variable yj is set as 1), then the amount selected must be lower and upper than given limits (i.e., Mmin and Mmax fj f j ); in addition, the associated unit cost (Mcostj) and unit environmental impact (MEIj) are selected accordingly. On the other hand, when the feedstock j is not selected (i.e., yj is set as zero), the associated amount, unit cost, and environmental impact are set as zero. This is modeled through the following disjunctive formulation:

∨

⎡ ⎤ ⎡ ¬Y ⎤ Yj j ⎢ ⎥ ⎢ ⎥ min max ⎢M ⎥ ⎢ f =0 ⎥ fj ≤ f j ≤ M fj j ⎢ ⎥ ⎢ ⎥ ⎢ cos t = M ⎥ ∨ ⎢ cos t = 0 ⎥ , j j cos t j ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ EI = 0 ⎥ = M EI ⎦ j EIj ⎣ ⎦ ⎣ j

t j ∈ Tj


Previous disjunction can be reformulated as an algebraic problem as follows. First, the Boolean variable zj,tj is reformulated as a binary variable Zj,tj. This means that, when the Boolean variable is true, the associated binary variable must be 1 and the equations inside the disjunction must be applied; otherwise, when the Boolean variable is false, the associated binary variable must be zero and the relationships inside do not apply. Previous relationships generally involves nonlinear relationships, so for this case the big M reformulation is more convenient to use, since the problem size (i.e., number of variables and constraints) is smaller compared to the convex hull reformulation. Therefore, in this case, the big M reformulation is implemented (see Raman and Grossmann30 and Ponce-Ortega et al.33). When a technology is selected to produce a specific compound j that appears in the optimal pathway, then the associated amount, cost, and environmental impact must be determined according to the operating conditions (Otj) as follows:

∀ j ∈ J , j = feedstock

where the Boolean variable Yj is true when the corresponding binary variable yj is 1 and, in this case, the corresponding relationships of the left-hand side of the previous disjunction apply; otherwise, when the Boolean variable Yj is false, the associated binary variable yj is zero and the corresponding relationships of the right-hand side of the previous disjunction apply. To reformulate previous logical disjunction as a set of algebraic constraints, different reformulation approaches can be implemented (including the convex hull or the big M). For this case, due to the fact that the relationships are linear and the right-hand side of the disjunction involves only equalities to zero, then the convex hull reformulation yields the same number of relationships and equations. In addition, this reformulation works better than the big M (for details about reformulations, see Raman and Grossmann,30 Lee and Grossmann,31 Vecchietti et al.,32 and Ponce-Ortega et al.33). Therefore, previous disjunction is reformulated using the convex hull reformulation as follows. If the feedstock j appears in the optimal pathway, then the amount for this compound must be greater than zero and lower than an upper limit: max M min f yj ≤ f j ≤ M f yj , j

j


f j ≤ αi , t j(Ot j )fi + M f (1 − zj , t j), j

∀ j ∈ J , j ≠ feedstock, i precedes j through t j


j

∀ j ∈ J , j ≠ feedstock, i precedes j through t j


(8)

cos t j ≤ c t j(Ot j )f j + Mcos tj(1 − zj , t j),

(5)


And the unit environmental impact for the feedstock j is calculated as follows: EIj = MEIjyj ,

(7)

f j ≥ αi , t j(Ot j )fi − M f (1 − zj , t j),

(4)

Similarly, the unit cost for the feedstock j is calculated as follows: cos t j = Mcost jyj ,

⎡ ⎤ Zj , t j ⎢ ⎥ ⎢ f = α (O )f , i precedes j through t ⎥ i ,tj tj i j ⎢ j ⎥ ⎢ ⎥, = cos t ( O ) c f j t t j j j ⎢ ⎥ ⎢ ⎥ EIj = ei j(Οt j)f j ⎢⎣ ⎥⎦

(9)

cos t j ≥ c t j(Ot j )f j − Mcos tj(1 − zj , t j), ∀ j ∈ J , j ≠ feedstock

(6) 5180

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can be measured through the Eco-indicator 99 (see Guinée et al.34). The total number of processing steps (PS) is measured as follows:

EIj ≤ ei j(Οt j)f j + MEIj(1 − zj , t j), ∀ j ∈ J , j ≠ feedstock

(11)

EIj ≥ ei j(Οt j)f j − MEIj(1 − zj , t j), ∀ j ∈ J , j ≠ feedstock

PS =

j ∈ jproducts

j ∈ jfeedstock

OF = {max profit; min totEI; PS}

To solve this multiobjective optimization problem, the constraint method can be used (see Diwekar35) to determine the trade-offs between the considered objectives. Case Study. A case study is presented to show the applicability of the proposed mathematical programming model for the optimal pathway configuration of a biorefinery involving multiple feedstocks and products. Several scenarios are identified (i.e., with different objective functions) attending to economic and environmental aspects. This case study considers the feedstocks, processing routes, and products shown in Figure 3. The input data is given in Table 1 available in the Supporting Information, which includes the values for the efficiency of each processing step considered in Figure 3. This information was reported previously in the literature (see sugar cane bioethanol,36 BIOENERCEL,37 Lopez and Lopretti,38 OlivaDominguez,39 Aden et al.,40 Zhu and Jones,41 Philip et al.,42 Dutta et al.,43 Kazi et al.,44 Pokoo-Aikins et al.,45,46 Myint and El-Halwagi,47 Pham et al.,48 Chouinard-Dussault et al.,49 and Santibañez-Aguilar et al.50). The efficiency is expressed in terms of kg of the product obtained per kg of raw material for each processing step, the cost of each processing step is presented in units of US$ per kg produced, and the GHG emissions generated for each processing step are presented in units of CO2 eq. per kilogram of produced product. The model takes into account the GHG emissions associated with the raw materials, the processing steps, and the produced products due to the use of biofuels or other materials. The raw materials available as feedstocks, costs, and GHG emissions per kg are shown in Table 2, which is also available in the Supporting Information, where the most important raw materials available in Mexico to obtain biofuels are presented. These raw materials were selected due to their chemical composition that allows one to extract fermentable sugars or lipids to obtain biofuels or some high value products. The values reported in Table 2 (Supporting Information) were obtained from SENER.51 Table 3 (available in the Supporting Information) shows the data for the products considered in the representation of Figure 3 for the specific case of Mexico. This table includes the data for the demand, the sale price, and the associated GHG emissions for each product (SENER,51 Oliva-Dominguez,39 and ExpósitoFernández52). The GHG emissions are based on the complete life cycle of products which takes into account that a sustainable product is made, used, and disposed of in a way that can lower its overall impact on the environment. This cradle-to-grave approach is data-intensive, since it requires data for such elements as raw materials, processing stages (consumption of utilities, emissions into air, water, and oil, and solid waste), and use of products. The model for this case study has 158 continuous variables, 66 binary variables, and 409 constraints; this model was coded in the GAMS software, and the solver CPLEX was used to solve the associated MILP problem (Brooke et al.53). Several

(13)

(14)

To incorporate the ideas of process intensification, the proposed model considers a multiobjective optimization approach, in which the objective function consists of the simultaneous maximization of the net profit and the minimization of the environmental impact accounting for the number of processing steps. These objective functions are formulated as follows. First, the total cost consists of the sum of the costs for all the compounds present in the optimal pathway, including the cost for the feedstocks as well as the cost for the processing steps, which are modeled as follows:

totcost = HY ∑ cost j (15)

j∈J

where costj is the overall cost for the production of j. The value for the sales of products is determined as follows: sales = HY

∑

pricejf j

j ∈ jproducts

(16)

where pricej is the unit price for the product j. And the net profit is given by the sales minus the costs: profit = sales − totcost

(17)

where profit is the total net profit. The total environmental impact for the pathway is calculated as follows:

totEI =

∑ EIj j∈J

(19)

Finally, the objective function is stated as follows:

There is a maximum amount for the availability of feedstocks for a given problem; thus, the following constraint must be applied: f j ≤ availabj ,

j

j ∈ J t j ∈ Tj

(12)

In previous relationships, Mf j, Mcostj, and MEIj are upper bounds for the relationships to avoid infeasibilities for the cases when the binary variables yj,tj are equal to zero. When the binary variables zj,tj are 1, then the relationships apply properly because the relaxations are eliminated (i.e., M is multiplied by zero). In previous relationships, the conversion factor αi,tj(Otj), unit cost ctj(Otj), and unit environmental impact eij(Otj) depend on the operating conditions for each technology. Notice that the operating conditions must be optimized simultaneously because of the interactions between the different reaction steps. Product demand constraints are stated as follows: f j ≤ demand j,

∑ ∑ zj , t

(18)

where EIj is the overall unit environmental impact for the production of j. It is noteworthy that the unit environmental impact must be measured through the life cycle analysis technique, and it can consider the overall GHG emissions or it 5181



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analysis for the reduction of the associated GHG emissions is presented in Figure 6, where the problem is solved using the

scenarios are analyzed to identify the applicability of the proposed methodology: Scenario A considers the best economic solution, scenario B accounts for the case when the demand of bioethanol is fully satisfied, scenario C satisfies the full demand of biodiesel, scenario D studies the case when the demands for bioethanol and biodiesel are completely satisfied, scenario E takes into account the case when 50% of the demand of bioethanol and 100% of the demand of biodiesel are satisfied, scenario F considers the case when 100% of the demand of bioethanol and 50% of the demand of biodiesel are satisfied, and finally scenario G accounts for the case when 50% of the demands of bioethanol and biodiesel are satisfied. For each scenario, Pareto curves are presented to account for the tradeoffs between the economic and environmental objectives. Scenario A (Economic Solution). This scenario corresponds to the best economic solution without considering any specific demand for the given products (only considering the upper bound for the demand of products). The optimal solution is shown in Figure 5. As can be observed, in this case, the best

Figure 6. Pareto curve for scenario A.

constraint method (see Diwekar35) for the maximization of the net profit and the minimization of the associated GHG emissions. As can be seen in this figure, the net profit decreases when the GHG emissions decrease, whereas the pathway is the same along the Pareto curve. Scenario B (Production of Bioethanol). For this scenario, the same values for scenario A are considered, but the demand of the bioethanol needs to be totally satisfied (i.e., the production of bioethanol must be 150 000 kg/day). Figure 7

Figure 5. Optimal pathway for scenario A.

pathway gives biodiesel as a product using microalgae as raw material due to the high content of lipids in this feedstock and its high processing efficiency. This solution only selects one product (biodiesel). Notice that the model involves only the maximization for the profit without any restriction to satisfy the demands for the products considered. Notice in Figure 5 that 546 190 kg of microalgae per day are needed to produce 175 000 kg of diesel per day; also, notice that the demand of biodiesel is completely satisfied in this economic scenario. The optimal solution has a net profit of US $17,638,614.74/year, which represents the difference between the total sales and the total production costs, whereas the associated net GHG emissions are 1.8139 × 108 kg of CO2 eq./ year considering the CO2 captured for the growth of microalgae, the CO2 produced in the processing steps, and the CO2 produced in the combustion of the biodiesel. An

Figure 7. Optimal economic pathway for scenario B.

shows the optimal economic pathway to produce the desired amount of bioethanol; as can be observed in this figure, the optimal economic solution also includes the production of biodiesel. The optimal values for the net profit and the GHG emissions for this solution are 1,170,988.55 US$/year and 2.732 × 108 kg/year, respectively. Additionally, Figure 8 shows the Pareto curve for scenario B representing the objectives profit versus GHG emissions; notice 5182



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× 108 kg/year, respectively. Figure 10 shows the Pareto curve for scenario C. Notice in this figure that there is a section with a

Figure 8. Pareto curve for profit versus GHG emissions for scenario B.

that the profit decreases when the emissions decrease which, in turn, reduces the produced amount of biodiesel. For section A of Figure 8, the corresponding optimal pathway configuration is shown in Figure 9a, whereas, for section B of Figure 8, the corresponding optimal pathway is shown in Figure 9b. In both sections A and B of Figure 8, the demand of bioethanol is fully satisfied; however, in section A of Figure 8, biodiesel is also produced, whereas, in section B of Figure 8, biohydrogen is also produced instead of biodiesel. This production scheme is required to satisfy the bioethanol demand with the highest profit and, at the same time, to meet the constraint imposed on the GHG emissions associated with the Pareto curve of Figure 8. Scenario C (Production of Biodiesel). For this scenario, the same values of scenario A are considered, but the demand of the biodiesel needs to be completely satisfied. The optimal economic pathway is the same as that for scenario A shown in Figure 5; in this case, the optimal values for the net profit and the net GHG emissions are US$17,638,614.74/year and 1.8139

Figure 10. Pareto curve for scenario C.

positive net profit (which corresponds to the pathway shown in Figure 11a), but also there is a section with a negative profit that requires a different pathway (i.e., the pathway shown in Figure 11b) to decrease the GHG emissions. As can be seen in Figure 11, for both sections A and B, the biodiesel is produced from microalgae and also is produced biohydrogen from sugar cane bagasse. However, for section A, with a positive profit and huge GHG emissions, only microalgae is used to produce the biodiesel, whereas, for section B, with a negative profit and low GHG emissions, the biodiesel is produced from jatropha and microalgae simultaneously. Scenario D (Production of Bioethanol and Biodiesel). This scenario states that the demands for bioethanol and biodiesel must be fully satisfied. Figure 12 shows the optimal economic pathway for the production of bioethanol and biodiesel; the net profit for this solution is US$1,170,988.55/year, and the

Figure 9. Optimal pathways for sections A and B of Figure 8. 5183



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Figure 13 shows the Pareto curve for scenario D. Notice that most of the region represents positive profits, which means that

Figure 13. Pareto curve for scenario D.

the combination of two products allows one to decrease the net GHG emissions and, at the same time, to obtain significant economic benefits. In this figure, two main sections are identified that have associated the pathways presented in Figure 14. In both sections A and B, biodiesel and biohydrogen are obtained from microalgae and sugar cane bagasse, respectively; in addition, in both cases, bioethanol is produced. However, for section A, bioethanol is obtained from sugar beet, whereas, for section B, it is obtained from jatropha. Scenario E (Production of 50% of the Demand of Bioethanol and 100% of the Demand of Biodiesel). In this scenario, it is set that 50% of the demand of bioethanol and 100% of the demand of biodiesel must be satisfied (i.e., 75 000 and 175 000 kg/day for bioethanol and biodiesel, respectively). Figure 15 shows the optimal economic pathway, which has an

Figure 11. Pathways for sections identified in the Pareto curve of scenario C.

associated GHG emissions are 2.7323 × 108 kg/year. Notice in Figure 12 that bioethanol is obtained from sugar beet and biodiesel is obtained from microalgae.

Figure 12. Optimal economic pathway for scenario D. 5184



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Figure 14. Pathways for scenario D for sections identified in the Pareto curve of Figure 13.

Figure 15. Optimal economic pathway for scenario E.

produce biohydrogen to obtain positive profits, as shown in Figure 17. Scenario F (Production of 100% of the Demand of Bioethanol and 50% of the Demand of Biodiesel). This scenario considers the production of 100 and 50% of the demands of bioethanol and biodiesel, respectively (i.e., 150 000 and 87 500 kg/day, respectively). The optimal economic

optimal net profit of $9,404,801.65 US$/year and GHG emissions of 2.2731 × 108 kg/year. Figure 16 shows the Pareto curve for different constraints on the net GHG emissions. As can be observed, there is a section with positive net profits, but it has considerable GHG emissions. It is noteworthy that the pathway is changed along the Pareto curve and, for section A of this figure, it is needed to 5185



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Figure 16. Pareto curve for scenario E.

pathway is shown in Figure 18 which has a net profit and GHG emissions of $7,648,318.81 US$/year and 1.8253 × 108 kg/ year, respectively. Notice in Figure 18 that bioethanol is produced from sugar beet, whereas biodiesel is obtained from microalgae. Figure 19 shows the Pareto curve for this scenario, where no positive profit is observed. Scenario G (Production of the 50% of the Demands of Bioethanol and Biodiesel). This scenario considers the production of 50% of the demands of bioethanol and biodiesel (i.e., 75 000 and 87 500 kg/day, respectively). The optimal economic pathway is shown in Figure 20; in this case, the net profit and GHG emissions are US$585,494.27/year and 1.3661 × 108 kg/year, respectively. Similarly to the previous case, the bioethanol and biodiesel are obtained from sugar beet and microalgae, respectively. Additionally, Figure 21 shows the Pareto curve for scenario G. As can be seen in this figure, there is a section for positive profits and high GHG emissions on the right-hand side and a section with negative profit and low GHG emissions on the left-hand side of this figure. Finally, Figure 22

Figure 18. Optimal economic pathway for scenario F.

shows the pathways for sections A and B of the Pareto curve shown in Figure 21; it is noteworthy that, for section A (positive profit and high GHG emissions), bioethanol and biodiesel are produced from jatropha and microalgae, respectively, whereas, for section B (negative profits and low

Figure 17. Pathways for optimal economic solution and for section A of Figure 16. 5186



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Figure 19. Pareto curve for scenario F.

Figure 21. Pareto curve for scenario G.

GHG emissions), bioethanol and biodiesel are obtained from jatropha and microalgae too, but in this case it is also produced biohydrogen from sugar cane bagasse. From previous results, one can conclude that several scenarios can be analyzed using the proposed optimization approach considering different perspectives (i.e., minimum number of processing steps, minimum GHG emissions, and minimum total cost). For the specific case of Mexico, results indicate that the main bioproducts are bioethanol and biodiesel, whereas the main feedstocks are microalgae, jatropha, and sugar cane.

are considered. The proposed approach is based on a disjunctive programming formulation that takes into account the simultaneous selection of multiple raw materials, products, and processing steps. A multiobjective (economic and environmental) optimization approach has been adopted using the εconstraint method to evolve the Pareto curves for the reconciliation of the economic and environmental objectives. The proposed approach has been applied to a case study from Mexico where different scenarios for the demands of desired products were analyzed. The results have shown that the generated Pareto curves allow the methodical trade-offs between the objectives. Additionally, the results have quantified the contradictions between the economic and environmental objectives. Solutions that simultaneously compensate the considered objectives involve the production of several products using multiple raw materials. In most of the proposed scenarios, bioethanol, biodiesel, and biohydrogen are selected

■

CONCLUSIONS This paper has presented a systematic approach for the synthesis of pathway configurations of a biorefinery. Multiple feedstocks, processing pathways, and products are considered. Additionally, technical, economic, and environmental objectives

Figure 20. Optimal economic pathway for scenario G. 5187



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Figure 22. Optimal pathways for sections A and B of the Pareto curve of scenario G.

i j min max tj

as products, whereas microalgae, jatropha and sugar cane are selected as feedstocks. Additionally, no numerical complications were observed in the application of the proposed approach which is general and can be applied to different case studies with multiple feedstocks, processing steps, and products while satisfying constraints on demands and availabilities for products and feedstocks, respectively. Finally, it should be recommended to include a flexibility aspect in the proposed model taking into consideration changes over the time for the availability of the feedstocks and demands of products.

■

Sets

I set for compounds i J set for compounds j Tj set for technology for producing j Parameters

αi,tj availabj c tj demandj eij HY Mcostj MEIj Mmax fi Mmin fj O tj pricej

ASSOCIATED CONTENT

S Supporting Information *

Tables showing data for the processing steps of the case study; available raw materials and their unit costs and GHG emissions; and demands, unit costs, and GHG emissions for the products. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

conversion factor to yield j from i availability for raw material j cost for using the technology tj demand of the product j unit environmental impact for obtaining component j time of operation maximum cost for component j maximum emissions for component j maximum flow of the component i minimum flow of the component j vector of operating variables for each technology tj sale price of the products obtained

Variables

Notes

costj EIj fj profit PS OF sales totcost totEI Yj yj

The authors declare no competing financial interest.

■ ■

index for the selection of raw material index for the obtained component j minimum value maximum value index for the selection of technology tj

ACKNOWLEDGMENTS Authors acknowledge the financial support from CONACYT and CIC-UMSNH. NOMENCLATURE

Scripts

feedstock index for the available feedstocks products index for the products obtained 5188

processing cost of the component j environmental impact of processing of component j flow of component j total annual profit per year total number of processing steps objective function total sales of the products obtained per year processing cost of the optimal pathway per year total emissions for the optimal pathway Boolean variable for the existence of the component j binary variable for the existence of the component j dx.doi.org/10.1021/ie303428v | Ind. Eng. Chem. Res. 2013, 52, 5177−5190

Industrial & Engineering Chemistry Research Zj,tj

Boolean variable for the existence of the technology tj

zj,tj

binary variable used to select the technology tj to produce the compound j

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Article

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Optimization of Pathways for Biorefineries Involving the Selection of

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