Optimal Planning of a Biomass Conversion System Considering

ARTICLE pubs.acs.org/IECR

Optimal Planning of a Biomass Conversion System Considering Economic and Environmental Aspects Jose Ezequiel Santiba~nez-Aguilar,† J. Betzabe Gonzalez-Campos,‡ Jose María Ponce-Ortega,*,† Medardo Serna-Gonzalez,† and Mahmoud M. El-Halwagi§ †

Chemical Engineering Department, ‡Institute of Chemical and Biological Researches, Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mich, Mexico, 58060 § Chemical Engineering Department, Texas A&M University, College Station, Texas 77843, United States ABSTRACT: This paper presents a multiobjective optimization model based on a mathematical programming formulation for the optimal planning of a biorefinery, considering the optimal selection of feedstock, processing technology, and a set of products. The multiobjective optimization problem simultaneously considers the profit maximization and the environmental impact minimization. The economic objective function takes into account the availability of bioresources, processing limits, and demand of products, as well as the costs of feedstocks, products, and processing routes. On the other hand, the environmental assessment includes the overall environmental impact measured through the eco-indicator-99 based on the life cycle analysis methodology. The proposed methodology generates a Pareto curve that identifies the set of optimal solutions for both objectives, and it is applied to a case study for planning the production of a biorefinery in Mexico.

1. INTRODUCTION In recent years, there has been significant interest in the conservation of natural resources, reduction of energy consumption, and associated emissions. Furthermore, the rising prices of petroleum and the uncertainty of its availability have led to the use of biomass as a good alternative to fulfill the demands for energy and chemicals production. Nowadays, there is a positive outlook for biofuels because they are useful in reducing the dependence on fossil fuels and decreasing GHG emissions. Selection of biomass feedstock along with its processing pathway is a critical factor in the viability of biofuel production. Clark et al.1 stated that the best way to guarantee the sustainable production of chemical products and industrial materials is the use of green chemistry and low-cost renewable materials such as biomass especially available from agricultural sources, since it could reduce the use of nonrenewable fossil fuels and cleaner and safer chemicals could be produced, fulfilling the legislative and consumer requirements at the same time. Chambost et al.2 presented the definition for the enterprise transformation and product design for implementation of a forest biorefinery. Bowling et al.3 presented an approach for inclusion of supply chain and size effects in the decision-making process for locating a biorefinery. Several systematic techniques have been developed for the synthesis and screening of biorefinery configurations.37 Elms and El-Halwagi8 developed a systematic procedure for scheduling and operation of flexible biodiesel plants accounting for a variety of feedstocks. Kokossis and Yang9 showed the role of process system technologies to promote their use in biofuels production. Goyal et al.10 reported a review for production of biofuels from thermochemical conversion of renewable resources focusing on various operational parameters. A targeting approach for effective utilization of biomass combined with heat and power systems through process integration was reported by Mohan and El-Halwagi.11 Myint and El-Halwagi12 presented an r 2011 American Chemical Society

approach for the design and optimization of the biodiesel production process from soybean oil, whereas Pokoo-Aikins et al.13 addressed the design and technoeconomic analysis of an integrated system for production of biodiesel from alga oil via sequestration of carbon dioxide from the flue gas of a power plant. A multicriteria approach to screen alternatives for converting sewage sludge to biodiesel was presented by PokooAikins et al.14 Sammons et al.15 presented a flexible framework for the optimal biorefinery product allocation. Linear mixedinteger programming models for the biomass supply chain networks were reported by van Dyken et al.,16 and a decision support system for the forest biomass exploitation for energy production purposes was presented by Freppaz et al.17 Additionally, different processing technologies and feedstocks alternatives for production of a variety of biofuels have been reported. Chew and Bhatia18 obtained conversion values for hydrogen and biodiesel production from palm oil through a set of alternatives focusing on the use of different catalysts. Huang et al.19 conducted a comparative study of the manufacturing cost of ethanol from lignocellulosic materials and evaluated the dependence of ethanol production with regard to the amount of electricity used in processing, while Kaparaju et al.20 proposed production of ethanol, hydrogen, and biogas from wheat straw in a structure that implements the concept of biorefinery. On the other hand, regarding the environmental impact, Azapagic and Clift21 introduced the life cycle assessment methodology in optimization problems; they showed the advantage of life cycle evaluation in multiobjective functions problems where the economic and environmental aspects are of main concern. Received: October 28, 2010 Accepted: May 26, 2011 Revised: April 24, 2011 Published: May 26, 2011 8558

dx.doi.org/10.1021/ie102195g | Ind. Eng. Chem. Res. 2011, 50, 8558–8570

Industrial & Engineering Chemistry Research

ARTICLE

Figure 1. Superstructure proposed for optimal planning of a biorefinery production system.

Hugo and Pistikopoulos22 presented a multiobjective mathematical programming-based methodology for explicit inclusion of life cycle assessment criteria as part of the strategic investment decisions related to the planning and design of supply chain networks. Also, Guillen-Gosalbez et al.23 proposed a new structure for optimal design of chemical processes, incorporating environmental constraints through life cycle assessment, focusing on mixed-integer problems, while Guillen-Gosalbez and Grossmann24,25 presented models for the environmentally conscious design of supply chain networks under uncertainty. Tan et al.26 reported a fuzzy multiobjective approach for optimization of bioenergy system footprints, and Urban et al.27 showed a technoecological synergy networks framework for the life cycle of corn ethanol production in a typical American residential area. Ojeda et al.6 reported the integrated use of cane bagasse as a second generation for biofuel production; they used computeraided tools for the energetic and life cycle assessment to find the best configuration and conditions for the process. Additionally, they applied process integration principles to design strategies for natural resources conservation and environmental impact reduction. As it can be seen, most of the formerly reported methodologies for optimal planning of the biorefinery systems have not considered simultaneously minimization of the overall environmental impact and maximization of the total annual profit. Furthermore, the reported methodologies have oversimplified evaluation of the total environmental impact. In this work, besides resuming the integrated biorefinery concept, an optimization model through a mathematical programming formulation for the optimal selection of feedstocks, processing technology

and a set of products is proposed. It simultaneously considers the assessment of environmental and economic aspects; the objective functions are profit maximization and environmental impact minimization. The economic objective function takes into account the availability of bioresources, processing limits, and demands of the products in a specific region as well as the costs of feedstocks, products, and processing routes, while environmental assessment includes the overall environmental impact measured through the eco-indicator-99 based on the life cycle analysis methodology. The proposed methodology is applied to a case of study for planning production of a biorefinery in Mexico.

2. OUTLINE OF THE PROPOSED MODEL The problem addressed in this paper can be described as follows: given a set of m available feedstocks, which can be converted into k different products and several byproducts b through different processing routes r, where there is not necessarily a single option to obtain the required products. Thus, each processing route is associated to an efficiency of feedstocks to products and an efficiency for feedstocks to byproducts identified as conversion factors (R). The optimal solution arises with the best combination of these sets of variables with the highest benefit from the standpoint of economic and environmental aspects. The superstructure for the general problem addressed in this paper is presented in Figure 1. Notice that this superstructure represents different options to select the best choice. It is important to note that the decision is more complicated when 8559

dx.doi.org/10.1021/ie102195g |Ind. Eng. Chem. Res. 2011, 50, 8558–8570


ARTICLE

Figure 2. Pareto solution for the case studied.

the number of possible options increases, which is the case for the biorefinery production problem addressed in the present paper.

3. MODEL FORMULATION The indexes used are defined prior to presenting the model formulation. m represents the type of feedstock, r represents the processing route employed for products yielded from bioresources, k is associated to the type of product, and b is the byproduct produced. The model formulation is described as follows. Mass Balances. Most of the formulations that involve the processing of feedstocks to products have nonlinearities, giving rise to nonconvex problems. By considering the conversion of feedstocks to products as a black box, the mass balance can be associated with an efficiency (conversion) factor for each processing technology, and then it is possible to linearize the mass balance. The number of equations for these balances depends on the number of possible feedstocks, processing routes, products, and byproducts. For the main product k produced from the raw material m through route r, the mass balance can be stated as follows Pkmr ¼ Rkmr Fkmr , k ∈ K, m ∈ M, r ∈ R

ð1Þ

where Rkmr is the conversion factor for product k from bioresource m through route r. The conversion factors Rkmr are based on the amount of product produced with regard to a given amount of the main raw material. It should be noted that Rkmr could be greater than 1 when the processing route r requires other raw materials in addition to the main raw material to yield a specific amount of product. Pkmr and Fkmr are the flow rates of products and raw materials, respectively. For byproduct b yielded when product k is produced from raw material m through route r, the following material balance is required Bkmrb ¼ βkmrb Fkmr , k ∈ K, m ∈ M, r ∈ R

ð2Þ

In the previous equation, βkmrb is the conversion factor for the amount of byproduct b produced when bioresource m is processed through route r to produce main product k. Notice also in this case that these conversion factors βkmrb could be greater than 1 when additional raw materials are required in the processing route r. Bkmrb is the flow rate of byproduct b generated. Maximum Available Raw Materials. Besides the mass balances, a set of inequality constraints are considered for the maximum availability of feedstocks, since it is not possible to use more than the existing quantity for its processing to the corresponding final products. The availability is restricted by the data for the specific region where the model is applied, and it is different for each feedstock. The maximum availability constraints can be stated as the sum of the quantities of the feedstock used in the manufacture of each product through each processing route, and it must be lower than the total amount of the feedstock available. These constraints are stated as follows

∑k ∑r Fkmr e Fmmax , m ∈ M

ð3Þ

In previous constraints, Fmax m is the maximum amount available for bioresource m and is a parameter known prior to the optimization process. Maximum Products Demand. Another constraint considers the product demand to prevent higher production rates than necessary to avoid waste of sources and also to guarantee its consumption

∑m ∑r Pkmr e Pkmax , k ∈ K

ð4Þ

Pmax is a parameter that represents the maximum demand from k product k. Maximum Processing Limits. Finally, further constraints involve processing feedstock limits associated with a processing route and, as a consequence, to specific equipment. These 8560



ARTICLE

constraints are only for upper limits which are the maximum amount of feedstock for each processing technology max Pkmr e Pkmr , k ∈ K, m ∈ M, r ∈ R

ð5Þ

Pmax kmr is the maximum amount of product k that can be produced from bioresource m through technology r. Objective Function. The objective function considers simultaneously maximization of the total profit and minimization of the overall environmental impact as follows objective function ¼ ½max profit; min EI

ð6Þ

where profit is the total net revenue obtained for sales of products and byproducts minus the costs for the raw materials and processing, whereas EI is the total environmental impact with respect to use of bioresources, use of products, and processing. The overall environmental impact is calculated through the processing route because this considers the use of resources and wastes generated. Notice here that both objectives contradict each other, that is, the maximum gain corresponds to the highest environmental impact (point C of Figure 2), whereas the solution corresponding to minimum environmental impact represents the minimum gain (point A of Figure 2). Between these two extreme solutions there are a set of optimal solutions (set of Pareto optimal solutions) that compensate both objectives, which can be used for the decision makers to choose the solution that best fits the requirements for the specific case addressed. Prior to presenting the optimization procedure, the economic and environmental objectives are described. Economic Objective. The economic objective function is formulated in terms of the total annual profit. This function takes into account the costs of feedstocks, products, byproducts, and processing routes and is stated as follows profit ¼

þ ∑ ∑ ∑ ∑ Bkmrb Cvalue ∑k ∑m ∑r Pkmr Cvalue k b k m r b

processing ∑k ∑m ∑r Fkmr Ccost m ∑ ∑ ∑ Pkmr Ckmr k m r

ð7Þ

where Cvalue is the net price for product k including transportation, k is the net price for byproduct b, Ccost is the cost for Cvalue b m bioresource m including transportation from the cropland to the is the processing cost for processing facility, and Cprocessing kmr route r from m to k. In the profit objective function, the ) includes the overall processing cost component (Cprocessing kmr operating and annualized capital costs associated with processing. The operating cost involves the associated cost of the chemical supplies (besides the main feedstock), energy and other utilities consumed during processing, as well as labor, supervision, lab charges, royalties, catalyst, solvents, taxes, and insurance. The annualized capital costs refer to the annualized investment of the required facilities. Usually these processing costs follow nonlinear relationships to account for the economies of scale; however, under the given limits these processing costs can be linearized and become directly proportional to the product obtained. To obtain this information, experimental data or previously reported results can be used. For the specific case of Mexico, this information was obtained from recent studies developed. In addition, for cases where the economies of scales represent important variations, this situation must be considered in the model using the approach shown in Appendix A. Finally, the costs for

), byproducts (Cvalue ), and raw materials products (Cvalue k b cost (Cm ) accounts for the unitary costs as well as transportation and storage costs. For the case where the economies of scale play an important role in the transportation costs, the amount transported must be considered. For the case of Mexico, the economies of scale for the transportation costs were not significant because the distances are quite short; however, for cases when the economies of scale are important, the approach shown in Appendix A can be used to properly consider this behavior. Since eq 7 uses a huge CPU time for problem solution, eq 2 is combined with eq 7 to yield the following expression profit ¼

þ ∑ ∑ ∑ ∑ βkmrb Fkmr Cvalue ∑k ∑m ∑r Pkmr Cvalue k b k m r b

processing ∑k ∑m ∑r Fkmr Ccost m ∑ ∑ ∑ Pkmr Ckmr k m r

ð8Þ

Equation 8 decreases the number of variables by kxm rxb, which helps to reduce significantly the CPU time required to solve this problem. Environmental Objective. The environmental assessment includes the overall environmental impact measured through the eco-indicator-99 based on the life cycle analysis methodology. Even though this methodology has regional and term limitations, it is an objective measure of the environmental impact caused by a specific substance, process, or activity since it is standardized, actualized, and accepted by the scientific community. The eco-indicator-99 is based on the life cycle analysis methodology and takes into account 11 impact categories, which are classified into three main damage categories. These categories and subcategories are as follows: 1 Damage to the human health 1.1 Carcinogenic effects on humans 1.2 Respiratory effects on humans caused by organic substances 1.3 Respiratory effects on human caused by inorganic substances 1.4 Human health effects caused by ionizing radiation 1.5 Human health effects caused by ozone layer depletion 1.6 Damages to human health caused by climate change 2 Damage to the ecosystem quality 2.1 Damage to the ecosystem quality caused by ecotoxic emissions 2.2 Damage to the ecosystem quality caused by the combined effects of acidification and eutrophication 2.3 Damage to the ecosystem quality caused by land occupation and land conversion 3 Damage to the resources 3.1 Damage to the resources caused by extraction of minerals 3.2 Damage to the resources caused by extraction of fossil fuels The method to determine the eco-indicator-99 weights different impact categories. This weighting is based on the ISO 14042 and ISO 14000 standards. There are three different perspectives to determine the eco-indicator-99 (i.e., hierarchical, egalitarian, and individualist), and each one has its weight for each damage category. In the hierarchical perspective the elected time is large and the substances are included if there is a consensus with respect to their effect. In the hierarchical perspective it is assumed that damage can 8561



ARTICLE

Table 1. Conversion Factors rkmr for Different Technologies for Biofuels Production Given as the Mass Ratio of the Amount of Produced Biofuel and Input Feedstock3035 product

raw material

processing route

mass ratio

ethanol

wood chips

pretreatment acid hydrolysis and fermentation

0.1669

ethanol ethanol

wood chips wood chips

gasification and biosynthesis gasification and chemical synthesis

0.2625 0.1887

ethanol

wheat straw


0.2723

ethanol

wheat straw

production of ethanol with hydrogen from dark fermentation

0.1314

hydrogen

oil palm shell

catalytic pyrolysis La/AL2O3

2.6000

hydrogen

oil palm shell

catalytic pyrolysis gama/Al2O3

hydrogen

rice straw

catalytic pyrolysis Cr2O3

22.8700

hydrogen

sawdust

catalytic pyrolysis Cr2O3

25.7000

hydrogen hydrogen

sawdust commercial wood

catalytic pyrolysis nickel catalytic pyrolysis Cu-MCM-41

5.3000 0.8700

ethanol

sugar cane


0.0592

ethanol

wheat


0.2857

ethanol

corn grain


0.3149

ethanol

sorghum grain


0.2999

ethanol

cassava root


0.2999

ethanol

sugar beet


0.0868

ethanol biodiesel

sweet sorghum soy

pretreatment acid hydrolysis and fermentation extraction and transesterification with methanol

0.0553 0.1763

biodiesel

African palm oil

extraction and transesterification with methanol

0.2064

biodiesel

sunflower


0.2950

biodiesel

castor


0.3543

biodiesel

cotton


0.1668

biodiesel

rapeseed


0.3595

biodiesel

jatropha


0.3268

biodiesel

sawflower


0.2850

2.6200

Table 2. Conversion Factors βkmrb for Different Technologies for Biofuels Production Given as the Mass Ratio of the Amount of Produced Byproduct and Input Feedstock3035 product

raw material

processing route

byproduct

mass ratio

ethanol

wheat straw


hydrogen

ethanol

wheat straw


acetic acid

0.0315

ethanol

wheat straw


carbon dioxide

0.1400

ethanol

sugar cane


carbon dioxide

0.0607

ethanol ethanol

wheat wheat

pretreatment acid hydrolysis and fermentation pretreatment acid hydrolysis and fermentation

grain distillery carbon dioxide

0.4300 0.2560

ethanol

corn grain


grain distillery

0.3333

ethanol

corn grain


carbon dioxide

0.2850

ethanol

sorghum grain


grain distillery

0.3333

ethanol

sorghum grain


carbon dioxide

0.2850

ethanol

cassava root


green foliage

1.5000

ethanol

sugar beet


dry pulp

0.0125

biodiesel biodiesel

soy African palm oil

extraction and transesterification with methanol extraction and transesterification with methanol

cattle cake oil palm

0.8000 0.0310

biodiesel

sunflower


cattle cake

0.6130

biodiesel

rapeseed


cattle cake

0.5000

biodiesel

jatropha


cattle cake

0.6510

biodiesel

sawflower


cattle cake

0.7280

be avoided using good actions. With respect to the fossil fuels, there is the assumption that they cannot be easily replaced. In the egalitarian perspective the time elected is large. The substances

0.0220

are included if there is no indication about their effect. In the egalitarian perspective, damage cannot be avoided and catastrophic effects can be produced. With regard to fossil fuels, the assumption 8562



ARTICLE

Table 3. Processing Cost for Different Raw Materials, Processing Routes, and Products3035 product

a

raw material

processing route

cost (USD/ton processed)

ethanol

wood chips


a

ethanol

wood chips

gasification and biosynthesis

a

ethanol

wood chips

gasification and chemical synthesis

a

ethanol

wheat straw


38.29

ethanol

wheat straw

production of ethanol with hydrogen from black fermentation

a

hydrogen

oil palm shell

catalytic pyrolysis La/Al2O3

a

hydrogen

oil palm shell

catalytic pyrolysis gamma/Al2O3

a

hydrogen hydrogen

rice straw sawdust

catalytic pyrolysis Cr2O3 catalytic pyrolysis Cr2O3

a

hydrogen

sawdust

catalytic pyrolysis nickel

a

hydrogen

commercial wood

catalytic pyrolysis Cu-MCM-41

a

ethanol

sugar cane


30.40

ethanol

wheat


50.68

ethanol

corn grain


55.86

ethanol

sorghum grain


53.20

ethanol ethanol

cassava root sugar beet


88.20 27.50

a

ethanol

sweet sorghum


16.10

biodiesel

soy


47.02 55.05

biodiesel

oil palm


biodiesel

sunflower


78.67

biodiesel

castor


94.50

biodiesel

cotton


44.50

biodiesel biodiesel

rapeseed jatropha


95.87 87.16

biodiesel

sawflower


76.01

Accurate data is not available for the specific case of Mexico; therefore, this route has been excluded from analysis.

Table 4. Availability and Cost of Feedstocks Used for Biofuels Production in Mexico3035 raw material wood chips

cost (USD/ton)

availability (ton/year)

86.60

190 600.57

wheat straw

38.85

52 559.77

oil palm shell

367.89

0.00

rice straw sawdust

0.00

13 672.93 69 005.34

sugar cane wheat

28.98 286.10

51 090 720.79 1 902 794.67

corn grain

207.40

1 573 914.77

sorghum grain

167.77

6 593 050.48

cassava root

230.71

13 639.50

sugar beet

150.29

167.00

31.11

5 032 396.62

330.58

153 022.20

66.31 12.66

307 756.87 111 208.00

sweet sorghum soy oil palm sunflower

product

castor

533.84

8.50

cotton

361.89

365 226.98

rapeseed

227.08

503.86

jatropha

110.40

529.80

sawflower

269.07

95 831.27

cost

demand

proposed

(USD/ton)

(ton/year)

scenario

ethanol

696.82

3 616 888

considering 10% of

hydrogen

2470

375 482 918

considering that it is 20% of

biodiesel

841

814 000

considering 5% of

ethanol in total gasoline

0.00 60.62

commercial wood

Table 5. Cost and Demand of Products for the Proposed Scenario3035

demand of natural gas biodiesel in diesel

that they cannot be substituted is considered. In the individualist perspective, the elected time is short (100 years or less) and the substances are included if they have a possible effect. In the individualist perspective it is assumed that the damages are subject to changes because of technological improvements. For the case of fossil fuels, it is assumed that the fossil fuels cannot be exhausted. These different perspectives provide diverse values for the unitary eco-indicators-99 for each damage category, and the hierarchical perspective is the one used in the proposed methodology because it allows replacing the fossil fuels in a reasonable time. In this paper, the environmental objective function considers the global environmental impact and the life cycle is involved when the eco-indicators for resources extraction, products 8563



ARTICLE

Table 6. Cost of Byproducts Produced from Different Feedstocks3035 byproducts

raw material

Table 7. Eco-Indicator-99 for Each Feedstock raw material

cost of byproducts (USD/ton)

eco-indicator-99/ton

wood chips

211.12

grain distillery

wheat

140.06

wheat straw

146.09

grain distillery grain distillery

corn grain sorghum grain

140.06 140.06

oil palm shell

14.61

dry pulp

sugar beet

112.04

sawdust

169.32

green foliage

cassava root

9.80

commercial wood

169.32

oil palm african

palm oil

634.92

sugar cane

12.14

cattle cake

jatropha

72.92

cattle cake

soy

201.21

wheat corn grain

146.09 199.78

cattle cake

rapeseed

93.37

sorghum grain

250.56

cattle cake cattle cake

sawflower sunflower

40.43 60.97

cassava root

62.47

sugar beet

48.33

hydrogen

wood chips

2470

sweet sorghum

rice straw

0.00

41.84

soy

444.06

disposal, and feedstock processing are considered.

oil palm

14.61

þ ∑∑∑ ∑k ∑m ∑r Fkmr eco-indicatorresource m k m r

sunflower castor

2.04 631.69

cotton

245.08

rapeseed

404.00

EI ¼

þ

disposal Pkmr eco-indicatork

∑k ∑m ∑r Pkmr eco-indicatorprocessing kmr

ð9Þ

In this expression, EI is the overall environmental impact and eco, eco-indicatordisposal , and eco-indicatorprocessing are indicatorresource m k kmr the eco-indicators-99 for the resources, products, and processing, respectively. To determine these eco-indicators and to set them as parameters, it is necessary to make a life cycle analysis for bioresources, products, and processing prior to the optimization process, including these eco-indicators in the processing technologies. The methodology described by Geodkoop and Spriensma28 is used in this paper to determine the overall eco-indicators applied. ecoaccounts for the overall environmental impact for indicatorresource m feedstock production m as well as transportation from the cropland considers the overall to the processing facility, eco-indicatordisposal k environmental impact for transportation, use, and final disposal of accounts for the overall product k, and eco-indicatorprocessing kmr environmental impact for the processing route.

4. SOLUTION STRATEGY The constraint method is implemented in this paper (see Diwekar29) to determine the set of optimal solutions that compensate for both objectives and are used to construct the Pareto curve. The addressed problem can be stated as follows objective f unction ¼ ½max prof it; min EI ð10Þ

s:t: eqs 15

jatropha

14.61

sawflower

614.38

Table 8. Eco-Indicator-99 for Product Amount Produced and Used as Biofuel According to the Proposed Scenario product


ethanol

32.12

hydrogen

0

biodiesel

10.15

Then to determine point A of Figure 2, minimization of the EI without taking into account the profit is solved as follows min EI s:t: eqs 15 Solution of the problem by eq 12 usually produces the minimum profit in the Pareto curve, because this model does not consider the profit. These two extreme solutions (solutions C and A given by relationships 11 and 12, respectively) then are used as limits to build the Pareto curve by solving the following problem

where profit and EI are defined in eqs 8 and 9, respectively. First, to determine point C of Figure 2, maximization of the profit is carried out without considering the EI as follows

max prof it s:t: EI e ε

max Prof it s:t:

ð12Þ

ð13Þ

eqs 15 ð11Þ

eqs 15 It is worth noting that solution of previous model usually yields the maximum EI in the Pareto curve.

To yield the Pareto curve, the previous problem given by eq 13 is solved for different values of ε. The limits for ε are the EI obtained from solutions C and A given by eqs 11 and 12 that correspond to the maximum and minimum EI, respectively. 8564



ARTICLE

Table 9. Eco-Indicator-99 for Processed Feedstock Amount for Biofuel Production product

raw material

processing route


ethanol

wood chips


ethanol

wood chips

gasification and biosynthesis

39.31

ethanol

wood chips

gasification and chemical synthesis

10.39

ethanol

wheat straw


11.84

ethanol

wheat straw

production of ethanol with hydrogen from black fermentation

hydrogen

oil palm shell

catalytic pyrolysis La/Al2O3

hydrogen

oil palm shell

catalytic pyrolysis gamma/Al2O3

hydrogen hydrogen

rice straw sawdust

catalytic pyrolysis Cr2O3 catalytic pyrolysis Cr2O3

hydrogen

sawdust

catalytic pyrolysis nickel

hydrogen

commercial wood

catalytic pyrolysis Cu-MCM-41

ethanol

sugar cane


1.84

ethanol

wheat


13.10

ethanol

corn grain


17.16

ethanol

sorghum grain


5.85

ethanol ethanol

cassava root sugar beet


42.05 2.75

ethanol

sweet sorghum


5.85

biodiesel

soy


9.02

biodiesel

oil palm


10.56

biodiesel

sunflower


15.09

biodiesel

castor


18.13

biodiesel

cotton


8.54

biodiesel biodiesel

rapeseed jatropha


18.39 16.72

biodiesel

sawflower


14.58

9.90

0.70

Table 10. Solution of Case B (profit equal to 1394 Million U.S. Dollars and EI equal to 51 107 PTS) raw material (ton/year)

product (ton/year)

processing route

wheat straw

52 559.77

ethanol

14 312.025

P. acid hydrolysis and fermentation

sugar cane

2.97 1007

ethanol

1.76 1006


sawdust

1.37 1004

hydrogen

3.51 1005

catalytic pyrolysis with Cr2O3

commercial wood

6.90 10

hydrogen

6.00 1004

catalytic pyrolysis with Cu-MCM-41

African palm

3.08 1005

biodiesel

63 521.018

P. extraction and transesterification

sunflower jatropha

1.11 1005 529.8

biodiesel biodiesel

32 806.36 173.139

P. extraction and transesterification P. extraction and transesterification

04

Table 11. Solution of Case C (profit equal to 1853 Million U.S. Dollars and EI equal to 225 107 PTS) raw material (ton/year)

product (ton/year)

processing route

wood chips

1.91 1005

ethanol

50 032.65

P. gasification and biosynthesis

wheat straw

52 559.77

ethanol

14 312.025


sugar cane

2.66 1007

ethanol

1 575 300


sorghum grain

6.59 1006

ethanol

1.98 1006


sawdust

1.37 1004

hydrogen

3.51 1005

catalytic pyrolysis with Cr2O3

commercial wood african palm

6.90 10 3.08 1005

hydrogen biodiesel

6.00 1004 63 521.018

catalytic pyrolysis with Cu-MCM-41 P. extraction and transesterification

sunflower

1.11 1005

biodiesel

32 806.36


rapeseed

503.86

biodiesel

181.138


jatropha

529.8

biodiesel

173.139


04

8565



ARTICLE

Figure 3. Flow diagrams for (a) solution B and (b) solution C of the Pareto curve.

Table 12. Solution of Case D (profit equal to 1600 Million U.S. Dollars and EI equal to 145 107 PTS for sugar cane availability equal to 40% of maximum allowable) raw material (ton/year)

product (ton/year)

processing route

wood chips

1.91 1005

ethanol

31 811.14

P. gasification and biosynthesis

wheat straw

52 559.77

ethanol

14 312.023


sugar cane

2.04 1007

ethanol

1 207 680


grain sorghum sawdust

3.95 1006 1.37 1004

ethanol hydrogen

1 184 605 3.51 1005

P. acid hydrolysis and fermentation catalytic pyrolysis with Cr2O3

commercial wood

6.90 1004

hydrogen

6.00 1004

catalytic pyrolysis with Cu-MCM-41

african palm

3.08 1005

biodiesel

63 521.02


sunflower

1.11 1005

biodiesel

32 806.36


jatropha

529.80

biodiesel

173.14


4. RESULTS AND DISCUSSION To test the proposed methodology, a case study to establish a biorefinery system in the central region of Mexico is used. This case involves 21 bioresources available in the central region of Mexico that can be used as feedstocks to obtain 3 products and 8 byproducts; furthermore, there are available 10 different processing routes. It is worth noticing here that despite the fact that this problem corresponds to a specific region of Mexico, the model formulation can be applied to any region anywhere. The efficiency (conversion) factors for the 10 different processing technologies were taken from previous results obtained by Horta-Nogueira, 30 Trindade, 31 Lazcano-Martínez,32 and M€uller-Langer et al.33 and from existing technologies for biofuels production developed in Brazil, the United States, the European

Union, and some Latin-American and Asian countries that have developed and implemented innovative technologies for this matter. The aforementioned data are presented in Table 1, while Table 2 shows the processing costs for different processing routes from different available raw materials to the desired products used for the example presented. Notice that some processing routes have conversion factors greater than 1; this is explained by the fact that additional chemical supplies are required in the processing routes besides the main raw material. Additional required data such as feedstock, products, and byproducts costs, availability, and demand could be taken from governmental institutions depending on the region where the model will be applied. In the case of Mexico, these data can be taken from institutions such as the Ministry of 8566



ARTICLE

Figure 4. Sensitivity analysis for different values of the availability for the sugar cane.

Agriculture (SAGARPA), Ministry of Energy (SENER), Ministry of Economy (SE), and Ministry of Environment (SEMARNAT), and in the case of the United States this information could be taken from the Department of Energy (DOE) and the Department of Agriculture (USDA). For the case study presented in this paper, the data taken from the SAGARPA-SIAP34 and SEMARNAT35 were used (see Table 3). Table 4 shows the cost and availability for bioresources for the proposed scenario (based on the data from the SENERBioenergetics Production Program), whereas Tables 5 and 6 show the costs and demands for the products and byproducts in the proposed scenario. Notice in these tables that the economies of scale are considered in this example by the limits imposed for each technology; in addition, if the economies of scale were significant, the approach shown in Appendix A can be used. Moreover, notice that some interesting technologies considered as an alternative for biofuels production in Mexico34,35 (i.e., thermochemical and catalytic processing routes) are not reported in Table 3 because there is not accurate information for their implementation in Mexico. These routes can be included in the model when the required information is available. The impact factors data were obtained by applying the life cycle analysis methodology by considering the products, processes, and associated activities (transportation, waste production, etc.) from cradle to grave. It was quantified by the ecoindicator-99.28,36 As mentioned above, an eco-indicator-99 was determined for each feedstock, products, and processing route and the eco-indicators for bioresources, products, and processing technologies from cradle to grave are reported in Tables 7, 8, and 9, respectively.

Figure 5. Economies of scale for the unitary costs (Cvalue , Cvalue , Ccost k b m , and Cprocessing ). kmr

The problem was formulated in the General Algebraic Modeling System (GAMS) software.37 The model consists of 1262 variables and 664 constraints, and each of the Pareto solutions was solved using the solver CPLEX in no more than 0.016 s of CPU time in a computer with an i7 at 2.67 GHz processor with 9 GB of RAM. First, the solution for the minimum environmental impact (point A of Figure 2) was obtained by solving the model formulation given by eq 12. This solution provides values of EI and profit equal to zero points and zero million dollars, respectively (which means that nothing is produced, and therefore, the minimum environmental impact is equal to zero). Then, the problem for the maximum profit (point C of Figure 2) given by 8567


Industrial & Engineering Chemistry Research eq 11 was solved to obtain the values of EI and profit equal to 2.2546 109 points and 1.8539 109 million dollars, respectively. Notice here the significant gap between the minimum and the maximum EI identified in the Pareto curve. Then the problem given by eq 13 was solved for different values of ε between the minimum EI (given by solution A) and the maximum EI (given by solution C) to determine the Pareto curve, as it can be seen in Figure 2. It is worth noticing that the Pareto curve represents a set of optimal solutions that compensate for both objectives simultaneously and from which the decision maker can take the one that best fits the specific requirements. In this case, we identify solution B (see Figure 2) that corresponds to a quarter of the maximum environmental impact and 80% of the maximum profit. Tables 10 and 11 show solutions for points B and C identified in the Pareto curve of Figure 2. It is noteworthy that none of the optimal solutions involve the use of food-grade feedstocks. With respect to ethanol production, the comparison between the chosen point and the maximum profit shows that in the first one 50% of ethanol demand is satisfied using 10% wood chips and 60% of sugar cane. Nonetheless, for the second case, besides wood chips and sugar cane, sorghum is needed to fulfill 50% leftover of ethanol demand; however, the sorghum yielded per hectare is lower than the sugar cane. Regarding biodiesel, rapeseed appears in the optimal set of solutions but its production is extremely low and does not increase the biodiesel demand fulfillment. On the other hand, it can be seen that in both cases the non-food-grade feedstock jatropha is part of the optimal solution. In spite of the fact that there are no official records for jatropha before 2009 in Mexico, it is expected to obtain an update of the records for this crop in 2011 since it takes about 5 years to stabilize its seed production. Consequently, it is expected that the compliance of biodiesel demand will increase from 30% to 50%. Focusing on production of hydrogen, note that there is no change in the first part of the Pareto curve where hydrogen production is performed and its demand is not totally fulfilled according to the proposed scenario. However, a sudden increase in profit is observed with no environmental impact change. This is a good indication that hydrogen is a cleaner biofuel than ethanol and biodiesel previously discussed. Nonetheless, it does not mean that there is no environmental impact, because environmental impact could be involved during feedstock extraction, processing, or hydrogen combustion. Finally, Figure 3 shows diagrams for solutions of cases B and C identified in the Pareto curve of Figure 2. Sensitivity Analysis. A sensitivity analysis was done based on the availability for the sugar cane, considering a decrease from 100% to 0% of sugar availability using intervals of 20% points. For each analyzed scenario, it was observed that when the availability of sugar cane decreases also the overall profit decreases proportionally, whereas the opposite occurs for the overall environmental impact. This happened because to increase ethanol production, different raw materials (i.e., sorghum, wood, etc.) have to be used since the sugar cane can be used only for ethanol production (see Table 12); however, use of these different raw materials yields a decrease in the overall profit and a simultaneous increase in the overall environmental impact. Figure 4 shows the results for the sensitivity analysis for the case when the availability of the sugar cane decreases. The line for 100% of sugar cane availability is the base case, whereas the other cases represent lower availability of sugar cane. Notice that when the availability of the sugar cane decreases, the Pareto curve

ARTICLE

shifts to suboptimal solutions. As an example of these solutions, Table 12 presents the result for the case when the availability of the sugar cane is 40% of the original one required for the case when EI must be lower than 145 107 points for the eco-indicator-99; this solution is identified as point D of Figure 4, and the overall profit corresponds to $1600 106/year. These results show that the proposed methodology can be used to analyze different scenarios considering simultaneously the economic and environmental aspects.

5. CONCLUSIONS This paper presents a new mathematical formulation for optimal planning of a biorefinery considering simultaneously maximization of the total net profit and minimization of the total environmental impact. The profit accounts for sales of products and byproducts minus costs of raw materials and costs for processing, whereas the environmental impact is measured through the eco-indicator-99 that is based on life cycle analysis for the raw materials, processing, and products. An efficient method is presented in this paper to adequately consider the objective function because these two objectives contradict each other. The resulting model is an LP problem that can be easily solved for global solution. The model is applied to a case study for planning of production of a biorefinery in the central part of Mexico accounting for the specific bioresources available in that region. ’ APPENDIX A: CONSIDERATION OF THE ECONOMIES OF SCALE To account for the economies of scale in the profit objective function of the proposed model, the unitary cost of eqs 7 and 8 can be calculated as follows C ¼ C a þ Cb P C c

ðA1Þ

where Ca, Cb, and Cc are constant coefficients. The previous relationship is nonlinear and nonconvex, and it can be linearized in different segments as can be seen in Figure 5. The following disjunction can be used then to yield linear relationships 2 3 Yn ∨ 6 6 Pmin e P e Pmax 7 7 n 5 "n ∈ N 4 n C ¼ C an þ C b n P r The previous disjunction can be reformulated as follows 1¼ P ¼ C¼

8568

∑

yn

ðA2Þ

∑

pn

ðA3Þ

∑

cn

ðA4Þ

n∈N

n∈N

n∈N

Pnmin yn e pn e Pnmax yn , n ∈ N

ðA5Þ

cn ¼ Can yn þ Cbn pn , n ∈ N

ðA6Þ

cn e Cmax yn , n ∈ N

ðA7Þ


Industrial & Engineering Chemistry Research This way, the model remains linear and the economies of scale can be properly considered.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ NOMENCLATURE Rkmr feedstock conversion to products through different processing routes feedstock conversion to byproduct from βkmrb different processing routes and products cost coefficient (fixed charge) Ca cost coefficient (variable charge) Cb cost coefficient (exponent) Cc sales price for byproduct b Cvalue b sales price for product k Cvalue k purchase price for feedstock m Ccost m processing cost for product k, from feedCprocessing kmr stock m, thorough processing route r eco-indicator-99 for processing feedstock eco-indicatorprocessing kmr m, to produce product k through processing route r eco-indicator-99 for feedstock extraction eco-indicatorresource m eco-indicator-99 for use and disposal of eco-indicatordisposal k products maximum availability of feedstock m Fmax m maximum demand of product k Pmax k upper limit for processing for each Pmax r processing route ’ VARIABLES Bkmrb mass rate for byproduct b from feedstock m and product k through processing route r c disaggregated variable for C EI global environmental impact mass flow rate for feedstock m to produce product k Fkmr through processing route r mass flow rate for product k from feedstock m and Pkmr processing route r p disaggregated variable for P profit total annual profit y binary variable for the segments ’ INDEXES b byproduct k product M feedstock n segment r processing route

’ REFERENCES (1) Clark, J. H.; Budarin, V.; Deswarte, F. E. I.; Hardy, J. J. E.; Kerton, F M.; Hunt, A. J.; Luque, R.; Macquarrie, D. J.; Milkowski, K.; Rodriguez, A.; Samuel, O.; Tavener, S. J.; White, R. J.; Wilson, A. J. Green chemistry and the biorefinery: a partnership for a sustainable future. Green Chem. 2006, 8 (10), 841–928.

ARTICLE

(2) Chambost, V.; Mcnutt, J.; Stuart, P. R. Guided Tour: Implementing the forest biorefinery at existing pulp and paper mills. Pulp Pap.Can. 2008, 109 (78), 19–27. (3) Bowling, I. M.; Ponce-Ortega J. M.; El-Halwagi, M. M. Facility location and supply chain optimization for a biorefinery. Ind. Eng. Chem. Res. 2011, 50 (10), 62766286. (4) Pham, V.; El-Halwagi, M. M. Process synthesis and optimization of biorefinery Configurations. AIChE J. 2011, in press, DOI: 10.1002/aic.12640. (5) Bao, B.; Ng, D. K. S.; Tay, D. H. S.; Jimenez-Gutierrez, A.; El-Halwagi, M. M. A Shortcut method for the preliminary synthesis of process-technology pathways: An optimization approach and application for the conceptual design of integrated biorefineries. Comput. Chem. Eng. 2011, in press. (6) Ojeda, K. A.; Sanchez, E. L.; Suarez, J.; Avila, J., O.; Quintero, O., V.; El-Halwagi, M. M.; Kafarov, V. Application of computer-aided process engineering and exergy analysis to evaluate different routes of biofuels production from lignocellulosic biomass. Ind. Eng. Chem. Res. 2011, 50 (5), 2768–2772. (7) Sammons, N. E., Jr.; Yuan, W.; Eden, M. R.; Aksoy, B.; Cullinan, H. T. Optimal biorefinery product allocation by combining process and economic modeling. Chem. Eng. Res. Des. 2008, 86 (7), 800–808. (8) Elms, R. D.; El-Halwagi, M. M. Optimal scheduling and operation of biodisel plants with multiple feedstokes. Int. J. Process Syst. Eng. 2009, 1 (1), 1–28. (9) Kokossis, A. C.; Yang, A. On the use of systems technologies and a systematic approach for the synthesis and the design of future biorefineries. Comput. Chem. Eng. 2010, 34 (9), 1397–1405. (10) Goyal, H. B.; Seal, D.; Saxena, R. C. Bio-fuels from thermochemical conversion of renewable resources: A review. Renewable Sustainable Energy Rev. 2008, 12 (2), 504–517. (11) Mohan, T.; El-Halwagi, M. M. An algebraic targeting approach for effective utilization of biomass in cogeneration systems through process integration. Clean Technol. Environ. Policy 2007, 9 (1), 13–25. (12) Myint, L. L.; El-Halwagi, M. M. Process analysis and optimization of biodiesel production from soybean oil. Clean Technol. Environ. Policy 2009, 11 (3), 263–276. (13) Pokoo-Aikins, G.; Nadim, A.; Mahalec, V.; El-Halwagi, M. M. Design and analysis of biodiesel production from algae grown through carbon sequestration. Clean Technol. Environ. Policy 2010, 12 (3), 239–254. (14) Pokoo-Aikins, G.; Heath, A.; Mentzer, R. A.; Mannan, S. M.; Rogers, W. J.; El-Halwagi, M. M. A multi-criteria approach to screening alternatives for converting sewage sludge to biodiesel. J. Loss Prev. Process Ind. 2010, 23 (3), 412–420. (15) Sammons, Jr. N.; Eden, R. M.; Yuan, W.; Cullinan, H.; Aksoy, B. A flexible framework for optimal biorefinery product allocation. Environ. Prog. 2007, 26 (4), 349354. (16) Van Dyken, S.; Bakken, B. H.; Skjelbred, H. I. Linear mixedinteger models for biomass supply chains with transport, storage and processing. Energy 2010, 35 (3), 1338–1350. (17) Freppaz, D.; Minciardi, R.; Robba, M.; Rovatti, M.; Sacile, R.; Taramasso, A. Optimizing forest biomass exploitation for energy supply at a regional level. Biomass Bioenergy 2004, 26 (1), 15–25. (18) Chew, T. L.; Bhatia, S. Catalytic processes towards the production of biofuels in a palm oil and oil palm biomass-based biorefinery. Bioresour. Technol. 2008, 99 (17), 7911–7922. (19) Huang, H. J.; Ramaswamy, S.; Al-Dajani, W.; Tschirner, U.; Cairncross, R. A. Effect of biomass species and plant size on cellulosic ethanol: A comparative process and economic analysis. Biomass Bioenergy 2009, 33 (2), 234–246. (20) Kaparaju, P.; Serrano, M.; Thomsen, A. B.; Kongjan, P.; Angelidaki, I. Bioethanol, biohydrogen and biogas production from wheat straw in a biorefinery concept. Bioresour. Technol. 2009, 100 (9), 2562–2568. (21) Azapagic., A.; Clift, R. The application of life cycle assessment o process optimization. Comput. Chem. Eng. 1999, 23 (10), 1509–1526. (22) Hugo, A.; Pistikopoulos, E. N. Environmentally conscious longrange planning and design of supply chain networks. J. Cleaner Prod. 2005, 13 (15), 1471–1491. 8569



ARTICLE

(23) Guillen-Gosalbez, G.; Caballero, J. A.; Jimenez, L. Application of life cycle assessment to the structural optimization of process flowsheets. Ind. Eng. Chem. Res. 2008, 47 (3), 777–789. (24) Guillen-Gosalbez, G.; Grossmann, I. E. Optimal design and planning of sustainable chemical supply chains under uncertainty. AIChE J. 2009, 55 (1), 99–121. (25) Guillen-Gosalbez, G.; Grossmann, I. E. A global optimization strategy for the environmentally conscious design of chemical supply chains under uncertainty in the damage assessment model. Comput. Chem. Eng. 2010, 34 (1), 42–58. (26) Tan, R. R.; Ballacillo, J. B.; Aviso, K. B.; Culaba, A. B. A fuzzy multiple-objective approach to the optimization of bioenergy system footprints. Chem. Eng. Res. Des. 2009, 87 (9), 1162–1170. (27) Urban, R. A.; Bakshi, B.; Grubb, G. F.; Baral, A.; Mitsch, W. J. Towards sustainability of engineered processes: Designing self-reliant networks of technological-ecological systems. Comput. Chem. Eng. 2010, 34 (9), 1413–1420. (28) Geodkoop, M.; Spriensma, R. The eco-indicator 99, A damage oriented for life cycle impact assessment. Methodology report and manual for designers; Technical report, PRe Consultants, Amersfoort, The Netherlands. 2001. (29) Diwekar, U. M. Introduction to applied optimization and modeling; Kluwer Academic Press: The Netherlands, 2003. (30) Horta-Nogueira, L. A. Task 5: Ethanol and ETBE production and end-use in Mexico. Potential and Feasibility of the use of bioethanol and biodiesel for transport in Mexico SENER-IDB-GTZ, 2006. (31) Trindade, S. C. Task 7: Rationales, drivers and barriers for fuel ethanol and ETBE market introduction. Potential and Feasibility of the use of bioethanol and biodiesel for transport in Mexico SENER-IDB-GTZ, 2006. (32) Lazcano-Martínez, I. Task B: Agricultural aspects and sources for biodiesel production. Potential and Feasibility of the use of bioethanol and biodiesel for transport in Mexico SENER-IDB-GTZ, 2006. (33) M€uller-Langer, F.; Probst, O.; Thr€an, D.; Weber, M. Task C: Biodiesel production and end-use in Mexico: current and future (Scenario Building). Potential and Feasibility of the use of bioethanol and biodiesel for transport in Mexico SENER-IDB-GTZ, 2006. (34) SAGARPA-SIAP. (2010). Almanac for the sowing 20082009. SENER, Bioenergetics production program.http://www.siap.gob.mx/ index.php?option=com_wrapper&view=wrapper&Itemid=350. (35) SEMARNAT. (2006). Forest almanac 2006.http://www. semarnat.gob.mx/tramites/gestionambiental/forestalsuelos/Anuarios/ Anuario%20Forestal%202006.pdf;http://www2.ine.gob.mx/descargas/ cclimatico/e2008e_bioenergia.pdf. (36) Guinee, J. B.; Gorree, M.; Heijungs, R.; Huppes, G.; Kleijn, R.; de Koning, A.; Van Duin, R.; Huijbregts, M. A. J. Handbook on life cycle assessment. Operational guide to the ISO standards; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2002. (37) Brooke, A.; Kendrick, D.; Meeruas, A.; Raman, R. GAMS-Language guide; GAMS Development Corp.: Washington, D.C., 2006.

8570


Optimal Planning of a Biomass Conversion System Considering

Recommend Documents