Application of Life Cycle Assessment to the Structural Optimization of

Ind. Eng. Chem. Res. 2008, 47, 777-789

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Application of Life Cycle Assessment to the Structural Optimization of Process Flowsheets Gonzalo Guille´ n-Gosa´ lbez* Department of Chemical Engineering, Carnegie Mellon UniVersity, 5000 Forbes AVenue, Pittsburgh, PennsylVania 15213

Jose´ Antonio Caballero Department of Chemical Engineering, UniVersity of Alicante, E-03080 Alicante, Spain

Laureano Jime´ nez Department of Chemical Engineering, UniVersity RoVira i Virgili, AV. Paı¨sos Catalans 26, 43007, Tarragona, Spain

This work proposes a novel framework for the optimal design of chemical processes whose main novelty lies in the incorporation of environmental concerns based on the principles of the Life Cycle Assessment (LCA) methodology. The approach presented applies mixed-integer modeling techniques to the superstructure optimization of sustainable chemical process flowsheets. As such, the resulting mathematical formulation simultaneously accounts for the minimization of the environmental impact and the cost. The environmental impact is measured through the Eco-indicator 99, which reflects the advances in the damage-oriented method recently developed for Life Cycle Impact Assessment. The incorporation of this environmental performance measure at the modeling stage causes a multiobjective mixed-integer nonlinear problem (moMINLP) that can be addressed by standard techniques for multiobjective optimization. The main advantages of our approach are highlighted through its application to a well-known design problem (the hydrodealkylation (HDA) of toluene), for which the set of trade-off solutions, in terms of cost and environmental criteria, is computed. The obtained results show that an inherent tradeoff naturally exists between both objectives and also suggest that significant environmental improvements can be achieved if decision makers are willing to compromise the economic benefit of the process. 1. Introduction Traditionally, the optimization models devised by the process systems engineering (PSE) community to assist in the operation and design of chemical processes have concentrated on finding the solution that maximizes a given economic performance indicator while satisfying a set of mass balances and capacity constraints imposed by the plant topology. Recently, however, there has been a growing awareness of the importance of including environmental concerns along with traditional economic criteria within the optimization procedure. This trend has been motivated by several issues, the main one probably being the pressure placed on governments and regulatory agencies to tighten environmental regulations. The development of these environmentally conscious optimization techniques has also been supported by recent advances in optimization theory and software applications. The progress made in these areas has furnished practitioners with powerful tools capable of tackling complex multicriteria optimization problems that were computationally intractable a few decades ago. Nevertheless, the core idea of the recent approaches that involve the design of sustainable chemical processes is not new. In fact, the concept of implementing pollution prevention techniques into process design dates back to the 1970s. The first pioneer works in this area focused on minimizing the energy consumption by applying methods for heat and power integration. These methods, which were originally developed in * To whom correspondence should be addressed. Tel.: +1 412 268 3775. E-mail: [email protected].

response to the energy crisis in the 1970s, led to great reductions in operating and capital costs in industrial scenarios. The success achieved with these tools motivated the application of the same type of methodologies for materials integration. Thus, the original idea of heat exchange networks was later expanded in scope with the objective of addressing the design of mass exchange networks,1 which were used to reduce pollutant emissions.2-4 Although these techniques led to significant environmental improvements, they still had a rather limited scope. Thus, they sometimes provided solutions that reduced the emissions of a plant at the expense of increasing burdens elsewhere in the life cycle (or even in a different section of the plant), in such a manner that the overall environmental impact was increased.5 Furthermore, most of them focused on minimizing the mass of pollutants generated in a chemical process, instead of concentrating on the more appealing objective of decreasing its environmental impact. Thus, the solutions that were found reduced the emissions of those chemicals considered in the analysis, but they did not provide any control over the potential negative effects that the chemical process could have on the biological, physical, cultural, and socio-economic aspects of the environment. Life-cycle assessment (LCA) was developed in response to this situation. LCA is an objective process for evaluating the environmental loads associated with a product, process, or activity.6 During the application of LCA, the energy and materials used in a process are first identified and quantified, along with the wastes released to the environment. This

10.1021/ie070448+ CCC: $40.75 © 2008 American Chemical Society Published on Web 01/01/2008

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Figure 1. Boundaries of the study in Life Cycle Assessment (LCA).

information is further translated into a set of environmental impacts that can be aggregated into different groups. These impacts are finally used to assess diverse process alternatives that may be implemented to achieve environmental improvements. Today, LCA can be said to be the main instrument in environmental chemical process design, because it can be effectively used to restructure any chemical process to improve its environmental performance.7-11 Specifically, the application of LCA to the design of sustainable chemical processes has two main advantages, compared to mere pollution prevention and/or waste minimization. First, it applies a system analysis to the problems of environmental management in such a manner that it covers the entire life cycle of the product, process, or activity. For this reason, this type of holistic approach is able to identify solutions that decrease the global environmental impact, instead of alternatives that reduce the impact locally and ignore other negative effects over the entire life cycle. To achieve this goal, the boundaries of the study must be expanded to include the upstream and downstream activities related to the main process itself. Thus, the essence of LCA is that it considers all material and energy flows from the “cradle” of primary resources (such as oil or ore deposits) to the “grave” of final disposal (such as stable inert material in a landfill) (see Figure 1). Second, LCA aggregates the environmental burdens into a limited set of recognized environmental impact categories, such as global warming, acidification, ozone depletion, etc. Thus, the initial limited indexes based on pollutants released or waste generated are replaced by a new set of damage-oriented indicators that can be easily used in the quantitative evaluation of chemical processes. As mentioned previously, the main goal of LCA is to provide criteria and quantitative measures that may be used to compare different process operation and design alternatives. After evaluating all the solutions from an environmental perspective, the best option can be selected, provided that they all fulfill the operational constraints. The main drawback of LCA lies in the

fact that it provides neither a systematic way of generating possible alternatives for improving the process being analyzed nor a way to determine the best one according to the preferences of the decision maker and the applicable legislation. Thus, the process of proposing environmental improvements and adopting more-sustainable structural alternatives usually relies on the intuition of the decision makers, and a systematic way of addressing this problem is still lacking. In this context, the application of traditional methods such as rules of thumb and/ or tailormade heuristics may lead to suboptimal solutions that do not take full advantage of the capabilities offered by LCA. To avoid the need for a random trial-and-error procedure and to allow the search of sustainable alternatives to be automated, optimization tools based on mathematical programming theory can be applied in conjunction with LCA principles. Thus, within this framework, LCA is used to evaluate process alternatives in terms of environmental criteria, whereas multiobjective mathematical programming tools find, among the entire set of feasible solutions of the problem, the best ones according to the specific economic and environmental concerns addressed in the problem formulation. Formulating the design of sustainable chemical processes as a multiobjective optimization problem is quite appealing to decision makers. The main advantage of this approach is that it provides not only one solution, but a set of efficient or Pareto alternatives that represent the optimal compromise between the criteria considered in the analysis and from which decision makers can further explore interesting tradeoffs. Therefore, the combined use of the aforementioned tools, which exhibit complementary strengths, results in a powerful formal quantitative environmentally conscious process design and optimization framework. This framework is intended to facilitate decision making in the field of sustainable chemical process design. Although the potential benefits of applying LCA to process optimization have been already acknowledged in the literature,7,11 only a limited number of case studies have been reported to date. Nevertheless, the works of Azapagic and Clift7 and

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Figure 2. Phases of the LCA methodology.

generation of design alternatives and identify among them the best ones, in terms of economic and environmental criteria. The present paper is organized as follows. Section 2 presents a formal definition of the problem of interest. In section 3, the corresponding mathematical formulation is derived, along with the solution procedure. The main advantages of our approach are illustrated through a case study in section 4, and the conclusions of the work are finally drawn in section 5. 2. Problem Statement

Figure 3. Inventory analysis phase.

Pistikopoulos and co-workers11,12 are appreciated contributions to the field. Unfortunately, the combined use of LCA and optimization tools generally has been quite rare. In fact, LCA has been traditionally used in an isolated way, which has restricted its application to cases where a reduced set of different processes or alternatives, often radically different, were evaluated. Thus, the lack of optimization skills, which can be seen as one of the main disadvantages of this sort of approach, still represents a major shortcoming. With the objective of increasing the LCA capabilities and further exploring the benefits of merging LCA and optimization theory, this work integrates LCA principles and mixed-integer nonlinear programming (MINLP) to address the structural optimization of sustainable chemical process flowsheets. The environmentally conscious chemical process design task is mathematically formulated as a multiobjective mixed-integer nonlinear programming problem (moMINLP) that is solved by applying standard methods available in the literature for multiobjective optimization. The integration of LCA and mathematical programming theory allows one to automate the

Given is a superstructure that embeds a set of potential structural alternatives of a chemical process. This superstructure may be based on a preliminary screening, engineering insights, and/or thermodynamic targets. Given are also a time horizon; the demand of the final products; the cost of the raw materials, utilities, and equipment units; and the prices of the final products. The problem then consists of selecting the optimal flowsheet structure, as well as the parameters that describe the process operation such that both the total cost (which includes the investment and operation costs) and the environmental impact of the process are minimized over the entire time horizon. 3. Mathematical Formulation The synthesis problem with environmental concerns can be formulated as a multiobjective mixed integer nonlinear problem (moMINLP) of the following form:

min U(x,y) ) {f1(x,y);f2(x)} x,y

(P1)

s.t. h(x,y) ) 0 g(x,y) e 0 x ∈ Rn, y ∈ {0,1}m The continuous variable x that appear in problem P1 represents state or design variables (i.e., flows, operating

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Figure 4. Pareto curve.

conditions, and sizes of equipment units). The binary variable y denotes the potential existence of process units, and typically appears linearly in the objective function and also in the constraints. The nonlinear performance of the system (i.e., mass and heat balances) and the sizing equations correspond to h(x,y) ) 0. On the other hand, the inequality constraints g(x,y) e0 include the design specifications, which are usually linear inequalities. With regard to the objective function, let us note that two different objectives are considered. The first one, which is denoted by f1(x,y), is the total cost of the process and includes the cost of the process equipments, the raw materials, and utility costs, as well as the byproduct sales revenues. The term f2(x) represents the environmental impact of the process. In this work, such term is measured through the Eco-indicator 99 value,13 which reflects the current state of the art in LCA methodology and application. The solution to the aforementioned problem consists of a set of Pareto optimal flowsheet configurations and their corresponding operating conditions. 3.1. Methodology: LCA and Computation of the Ecoindicator 99 Value. Here, we follow the general LCA methodology14-16 and, more specifically, the mathematical formulation described by Hugo and Pistikopoulos,11 regarding the incorporation of environmental performance measures based on LCA in the decision-making process. The LCA methodology that enables the computation of the environmental impact of the process is normally applied in four phases (see Figure 2). 3.1.1. Goal and Scope Definition. In this phase, the system boundaries, the impact categories, and the functional unit are defined. With regard to the boundaries of the system, let us note that these should include the entire life cycle of the product or process being analyzed. However, our approach focuses on decreasing the environmental impact of the manufacturing stage, and, for this reason, the analysis is restricted to this life cycle stage. Thus, the downstream processes such as secondary processing, product use, and disposal are neglected, whereas the upstream/input processes are included within the system boundaries. Therefore, the life cycle study can be regarded as a “cradle-to-gate” analysis. Nevertheless, this approach could easily be extended to include other stages in the life cycle of the product. With regard to the impact categories, let us note that the Ecoindicator 99 proposes the following 11 impact categories: (i) carcinogenic effects on humans, (ii) respiratory effects on humans that are caused by organic substances, (iii) respiratory effects on humans that are caused by inorganic substances, (iv) damage to human health that is caused by climate change, (v)

human health effects that are caused by ionizing radiations, (vi) human health effects that are caused by ozone layer depletion, (vii) damage to ecosystem quality that is caused by ecosystem toxic emissions., (viii) damage to ecosystem quality that is caused by the combined effect of acidification and eutrophication, (ix) damage to ecosystem quality that is caused by land occupation and land conversion (x) damage to resources caused by the extraction of minerals, and (xi) damage to resources that is caused by extraction of fossil fuels. These groups can be further aggregated into three damage categories: human health, ecosystem quality, and resources. Finally, with regard to the functional unit chosen for the overall system, let us note that this is defined as the desired production rate of the main product. 3.1.2. Inventory Analysis. This second phase provides the inputs and outputs of materials and energy associated with the process (Life Cycle Inventory). From these values, the set of environmental burdens of the process can be calculated. In our problem, all the environmental burdens are expressed as a function of the continuous decision variable x and, specifically, as a function of the flows of raw materials and byproducts and the energy consumed by the system. Such variables are regarded as free variables by the optimization algorithm. The sources of emissions and waste from the main chemical process include byproducts, reaction agents, and separation agents that contribute to waste generation as they degrade over time, and leaks (i.e., “fugitive emissions”) that occur anywhere in the system. Furthermore, the emissions of the systems that provide utilities to the main process must be considered. Thus, the consumption of raw materials and energy must be further converted to the corresponding environmental burdens (see Figure 3). These emissions could be obtained by including the equations that describe the processes involved in the energy generation, as well as the production of raw materials, in the model. Generally, the insertion of these new constraints may lead to very complex models. To avoid this situation, it is possible to resort to specific databases that contain the inventory of emissions of a wide range of chemical processes found in Europe.17-19 In the latter case, the optimization strategy will act regarding these upstream environmental burdens as input parameters. It is important to remark that all the burdens calculated by the optimization algorithm are expressed per unit of reference flow of the main product. This reference flow value is imposed to the problem formulation through the insertion of a hard constraint that forces one to attain the desired production rate of the principal product. 3.1.3. Impact Assessment. In this stage, the process data are converted to environmental information. As mentioned in phase I, three different damage categories are considered in the calculation of the Eco-indicator 99 value. The human health damages are specified in terms of disability adjusted life years (DALYs). A damage of 1 means that one life year of one individual is lost, or one person suffers four years from a disability with a weight of 0.25. On the other hand, the ecosystem quality damages are specified in terms of PDF m2 yr, where PDF denotes the potentially disappear fraction of species. A damage of 1 means that all species disappear from 1 m2 over one year, or 10% of all species disappear from 1 m2 over 10 years. With regard to the damages to resources, these are specified in terms of megajoules (MJ) of surplus energy. A damage of 1 means that, because of a certain extraction of resources, further extraction of the same resources in the future will require an additional 1 MJ of energy, because of the lower resource concentration or other unfavorable characteristics of


Figure 5. Superstructure for the hydrodealkylation (HDA) process synthesis problem.

the remaining reserves. The specific point in the future is chosen arbitrarily as the time at which 5 times the cumulative extraction of the resource before 1990 is extracted.13 Thus, each impact factor i belonging to a specific damage category d (θi) is calculated from the environmental burdens associated with the chemical process (βb) and the set of damage factors related to them (Rbi), as stated in eq 1.

θi )

∑b βbRbi

∀i

(1)

As mentioned previously, the environmental burdens associated with the process are given by the direct emissions, the energy generation (i.e., generation of steam and electricity), and the production of raw materials: energy + βrm βb ) βdirect b b + βb

∀b

(2)

The reader should note that the calculation of the environmental burdens associated with the generation of energy and raw materials requires the expansion of the system boundaries, to include the upstream processes associated with the main one. As mentioned previously, the data associated with these upstream activities generally will be taken from standard databases.17-19 The specific technologies used for the generation of energy and raw materials may drastically affect the results of the superstructure optimization, as will be further discussed in the case study section. Thus, to obtain realistic LCA results, it is necessary to choose them according to the specific features of the scenario in which the plant will operate. The damage factors, which are the link between the results of the inventory phase and the damage categories, are given by specific damage models available for each damage category. For instance, for the human health damage category, the corresponding damage model includes (i) a fate analysis, to link any emission, which is expressed in terms of mass, to a temporary change in concentration; (ii) a exposure analysis, to link this temporary concentration to a dose; (iii) an effect analysis, to link the dosage to a number of health effects; and

finally (4) a damage analysis, to convert the health effects in terms of DALYs. Furthermore, there are three different damage models available in the Eco-indicator 99 framework. Each of them corresponds to a specific perspective that is based on cultural theory.13 For instance, in the Egalitarian perspective, which is a long-time perspective, even a minimum of scientific proof justifies the inclusion of effects. In the Individualist perspective (a short-time perspective), only proven effects are included. In the Hierarchist perspective (balanced time perspective), consensus among scientists determines the inclusion of effects. Finally, the damages of each category d (θi|i ∈ I(d)) are normalized and aggregated into a single impact factor, as stated in eq 3.

f2(x) ) Eco-Indicator 99 )

∑d ∑

δdωdθi

(3)

i∈ I(d)

This equation makes use of normalization and weighting factors (δd and ωd, respectively). The normalization set is based on a damage calculation of all relevant European emissions, extractions, and land uses. Because there are three damage models, there are also three normalization sets. With regard to the weighting method, let us note that there are four versions of the weighting setsone average for all panelists, and three versions for subgroups of the panelsthat could be regarded as adhering to a perspective. Specifically, this work applies the Hierarchist perspective combined with the default (average) weighting factors. Nevertheless, in principle, many other combinations are possible and could be easily implemented, such as the Hierarchist damage model and normalization with the Average weighting (H,A), the Egalitarian damage model and normalization with the Egalitarian weighting (E,E), and the Individualist damage model and normalization with the Individualist weighting (I,I). 3.1.4. Interpretation. Finally, in the fourth phase, the results are analyzed and a set of conclusions or recommendations for the system are formulated. Specifically, in the context of the proposed approach, it will be essential to perform a detailed

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Table 1. Cost Data for the HDA Problem Parameter

Value

cost/price of feedstock or product/byproduct hydrogen feed (95% hydrogen, 5% methane) toluene feed (100% toluene) product benzene (g99.97% benzene) diphenyl heating value hydrogen purge methane purge cost of utilities electricity heating (steam) cooling (water) fuel Investment Cost absorber

$2.50/kg-mol $14.00/kg-mol $19.90/kg-mol $11.84/kg-mol 1.08 3.37 $0.04/(kW h) $8.0 × 106/kJ $0.7 × 106/kJ $4.0 × 106/kJ

Fixed Charge Cost ($) 13

compressor stabilizing column benzene column toluene column furnace membrane separator reactor adiabatic isothermal

7.155 1.126 16.3 3.90 6.20 43.24

Linear Coefficient 1.2 × number of trays 3 × vapor rate 0.815 × brake horsepower (kW) 0.375 × number of trays 1.55 × number of trays 1.12 × number of trays 1.172 × heat duty (10 9 kJ/yr) 49 × inlet flow rate

74.30 92.88

1.257 × reactor volume (m3) 1.571 × reactor volume (m3)

Table 2. Environmental Data for the HDA Problem Impact Category

Steam (1 kg, 2.6 MJ/kg)

Electricity (1 MJ)

Hydrogen (1 kg by cracking)

Toluene (1 kg)

carcinogens (DALY) respective organics (DALY) respective inorganics (DALY) climate change (DALY) radiation (DALY) ozone layer (DALY) ecotoxicity (PDF m2 yr) acidity/eutropism (PDF m2 yr) land use (PDF m2 yr) minerals (MJ surplus) fossil fuels (MJ surplus)

4.8 × 10-9 1.0 × 10-10 6.0 × 10-8 4.9 × 10-8 8.4 × 10-11 3.0 × 10-11 3.6 × 10-3 1.6 × 10-3 1.1 × 10-3 3.8 × 10-4 5.2 × 10-1

1.7 × 10-8 7.0 × 10-11 1.6 × 10-7 3.2 × 10-8 4.7 × 10-9 5.2 × 10-11 2.1 × 10-3 3.6 × 10-3 6.0 × 10-3 2.4 × 10-4 5.1 × 10-2

4.8 × 10-9 1.2 × 10-9 7.0 × 10-7 2.6 × 10-7 1.2 × 10-12 3.3 × 10-14 4.7 × 10-4 2.9 × 10-2 1.4 × 10-5 3.2 × 10-4 9.0 × 100

6.6 × 10-9 2.8 × 10-9 1.0 × 10-6 3.4 × 10-7 1.7 × 10-12 4.6 × 10-14 5.6 × 10-4 3.9 × 10-2 2.2 × 10-5 5.5 × 10-4 9.8 × 100

analysis of the efficient solutions calculated by the optimization strategy. As a result of this analysis, the best compromise solution will be chosen. Let us note that the selection of the final alternative requires some articulation of preferences. However, as opposed to other techniques that account for environmental concerns by adding constraints on operations, in our work, the preferences are articulated in the post-optimal analysis of all the Pareto solutions. This type of approach has the advantage of providing further insights into the design problem, thus allowing a better understanding of the tradeoff between the objectives considered. In this regard, upon analysis of the tradeoff solutions, decision makers should try to operate in those regions where significant environmental improvements can be achieved at a marginal increase in cost. 3.2. Solution to the Multiobjective Problem. Every chemical process flowsheet has an associated cost and a certain Ecoindicator 99. Structural alternatives that have lower cost values are expected to lead to higher environmental impacts. Therefore, for a specific range of values, cost and Eco-indicator 99 have a tendency to be contradictory objectives, and the solution of problem P1 results in a set of Pareto-optimal chemical process flowsheets operating under specific conditions. A significant number of methodologies have been proposed to calculate the Pareto-optimal or non-inferior solution set of multiobjective optimization problems.20 Among them, the weighted-sum method, the constraint method, and the goal-programming method, which are based on the conversion of the original

multiobjective model into a set of single-objective problems,7,21,22 are the most widely used in process engineering. To be able to suggest a specific point of this set, some attempts have been made to compare the objectives between them, for example, optimizing a Nash-type function,23 defining the objectives as fuzzy sets22 or adding the consideration of the decision-maker input in the problem formulation.24 Specifically, the constraint method, which was first introduced by Haimes et al.,25 is applied in this work to generate these solutions. This method is based on maximizing one objective function and regarding the other objectives as constraints bounded by some allowable levels. The levels then may be altered to generate the entire Pareto-optimal set. Therefore, the following single MINLP optimization problem is used to obtain the Pareto solutions:

f1(xj*,yj*) ) min {f1(x,y)} x,y

(P2)

s.t. f2(x) e h(x,y) ) 0 g(x,y) e 0 x ∈ Rn, y ∈ {0,1}m Thus, if problem P2 is solved for all possible values of and the resulting solutions (xj*,yj*) are unique, then these solutions


Figure 6. Trade-off solutions of the problem.

represent the entire Pareto set of solutions of the original multiobjective problem (problem P1). The extreme points of the interval [, j] within which the value must fall, ∈ [, j], can be determined by solving the following single objective problems:

) f2(xj*)

(P3)

xj* ) arg min {f2(x)} x,y

s.t. h(x,y) ) 0 g(x,y) e 0 x ∈ Rn, y ∈ {0,1}m If the solutions to problem P2 are not unique for some value-

j ) f2(xj*)

(P4)

xj* ) arg min {f1(x,y)} x,y

s.t. h(x,y) ) 0 g(x,y) e0 x ∈ Rn, y ∈ {0,1}m (s) of , then the Pareto point(s) must be picked by direct comparison, i.e., by applying the Pareto definition (i.e., the dominance concept). Let us note that some important sampling techniques exist to minimize the number of single-objective optimization problems to generate a true representation of the entire Pareto surface, such us the Hammersley sequence sampling (HSS) technique, which is based on quasi-random generation.26-28 These methods could be used, in the context of our work, to reduce the computational burden associated with the generation of the Pareto set. The general concept of Pareto frontier is depicted in Figure 4. Here, two objectives are considered: cost and environmental impact. The points that lie in the Pareto curve are the Pareto optimal solutions of the problem. Notice that no solution exists below the Pareto curve, because this would violate the definition of Pareto optimality (i.e., this solution would dominate some of the Pareto optimal ones, which, by definition, cannot be dominated by anyone). Finally, the decision maker should

choose, from the set of Pareto solutions, the one that maximizes his/her particular preferences and also satisfies the applicable legislation at the same time. Generally, some constraints of problem P2 will be nonconvex,29 and a strategy based on global optimization theory will be required to guarantee the global optimality of the solution that is found. These strategies usually lead to large computer processing unit (CPU) times; thus, for this reason, one may want to apply local optimizers that are less computationally intensive. Specifically, in this work, the outer approximation method30 is used to sequentially solve different instances of problem P2 for different values of . This method is guaranteed to converge to the global optimal solution of the original problem, provided both the objective function and the feasible region are convex. However, its extension to problems with nonconvex feasible regions through the use of slack variables and penalty parameters in the objective function of the master problem provides solutions whose global optimality cannot be guaranteed. Furthermore, although problem P2 could be solved to optimality for every value of , the -constraint method could still yield some non-Pareto solutions. This would happen if some values of were not explored.25 Because of the aforementioned issues, the solutions of problem P1 that are obtained by following the previously described procedure are labeled in this paper as tradeoff solutions, instead of Pareto optimal solutions, because their Pareto optimality cannot be guaranteed with the optimization strategy used. Therefore, by changing the weights , a set of solutions can be obtained. Each of them represents a chemical process flowsheet operating under certain conditions and with a specific cost and Eco-indicator 99. The set of tradeoff solutions may be represented in a two-dimensional chart (where the dimensions are cost and Eco-indicator 99). It is worth noting, at this point, that problem P1 can be solved by any standard algorithm for multiobjective optimization. Moreover, the problem could also be reformulated as a multiparametric mixed-integer programming problem31 and can be solved using recently developed algorithms for parametric optimization,32 although this would greatly increase the CPU time required to generate the Pareto frontier. Let us note that there is one issue that may attract considerable interest in the context of analyzing the results of the Pareto curve. This issue is that of identifying the limits of an objective fluctuation within which the integer part of the optimal solution keeps its optimal status. In other words, it may be interesting to know under which conditions a flowsheet configuration represented by a set of binary variables remains optimal. Mathematically, if yj* denotes the set of binary variables associated with an optimal flowsheet, it may be interesting to identify the values of the target imposed to the Eco-indicator 99 that delimit the interval [, j], within which (xj*(), yj*) remains optimal. Generally, it is interesting to select flowsheets with the appealing property of maintaining their structural optimality, even for large fluctuations of the target imposed to the environmental impact. These structural alternatives are able to operate under a wide range of conditions and be adjusted according to the prevalent environmental needs to be met. 4. Case Study The process chosen to illustrate the methodology previously described is the hydrodealkylation (HDA) of toluene. The superstructure selected for this problem and all the associated data have been taken from the work of Kocis and Grossmann33 (see Figure 5 and Table 1). Specifically, we consider the

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Figure 7. Optimal solution in the interval [3.40 × 108, 3.10 × 108] (minimum cost solution).

production of 1060 tons of benzene per year during a time horizon of 10 years. The desired reaction in the HDA process is the following:

toluene + hydrogen f benzene + methane An undesired reversible reaction also occurs:

2benzene f diphenyl + hydrogen The conditions for these gas-phase reactions are as follows: pressure, 3.45 MPa; temperature, 895-980 K. At lower temperatures, the toluene reaction is too slow and at higher temperatures hydrocracking occurs. Also, a hydrogen:aromatics molar ratio of at least 5:1 is required to prevent coking. Kinetic data for the toluene reaction34 indicate that the reaction is firstorder in toluene and one-half order in hydrogen. Because hydrogen is present in excess, its concentration can be assumed to be constant and the rate then reduces to a first-order reaction. A hydrogen raw material stream is available at a purity of 95% (the remaining 5% is methane). A membrane separator can be used to yield a higher-purity feed stream by removing methane. A toluene fresh feed is also available. Both feed streams are combined with recycle hydrogen and toluene and heated before being fed to the reactor. The exothermic reaction can be conducted in a plug-flow reactor operating either adiabatically or isothermally (this last one is more expensive, because of the need for heat removal). The reactor product stream must be quenched immediately and cooled further to condense the aromatics that will then be separated from the noncondensable hydrogen and methane in a flash separator. Part of the vapor stream from the flash separator can be purged to avoid the accumulation of methane. Alternatively, a membrane separator can be used to decrease the

hydrogen loss in the purge stream. Another alternative is to treat the flash separator vapor stream in an absorber with toluene feed to recover the benzene lost in the flash separator. A portion of the flash separation liquid stream is used to quench the reactor product stream, and the remainder is sent to the liquid separation system. Hydrogen and methane are removed using either a stabilizing column or a second flash separator operating at a lower pressure than the first one. A distillation column then is used to yield a benzene stream with the desired purity. In this case, the benzene product stream is specified to be at least 99.97%. The split of the bottom stream, which contains primarily toluene, can be accomplished in a flash separator or a column. The purge streams that contain methane, as well as the diphenyl byproduct streams, are combusted and the heat is recovered. Specifically, it is supposed that 60% of this heat can be reutilized to produce steam, which can then be used in other parts of the plant. The superstructure for this HDA process is modeled as an MINLP in a similar way as was originally done by the authors.33 Specifically, simplified models such as Raoult’s law for phase equilibrium, the Fenske-Underwood equation for distillation columns, and the Kremser equation for the absorber are used. The model accounts for the minimization of cost and environmental impact. The cost includes raw-materials cost, utility costs (electricity, steam, cooling water), and investment costs for equipment (membrane separators, reactors, distillation columns, and compressors). Economies of scale for the investment cost are represented with linear fixed-charge cost models, based on Guthrie’s correlation.35 The environmental impact is measured using the Eco-indicator 99. The environmental data required for its calculation are retrieved from the Eco-invent database, which is integrated with the Simapro software18 (see Table 2).


Figure 8. Optimal solution in the interval [3.10 × 108, 2.70 × 108] (design 2).

Figure 9. Optimal solution in the interval [2.70 × 108, 2.03 × 108] (design 3).

Furthermore, the Hierarchist damage model and normalization with the Average weighting have been applied. The resulting moMINLP optimization problem contains 724 constraints, 710 continuous variables, and 13 binary variables, and it is solved by applying the -constraint method. Each singleobjective problem is implemented in GAMS 21.336 and solved with DICOPT.37 The NLP subproblems are solved with

CONOPT,38 whereas the MILP master problems are solved with CPLEX 9.0.39 The CPU time involved in the calculation of each tradeoff solution is in the range of 1-10 s, on a Pentium III processor operating at 1.4 GHz. The problem is first solved by minimizing cost and neglecting the environmental concerns. This calculation provides the first trade-off solution. The Eco-indicator 99 value then is reduced

786


Figure 10. Optimal solution in the interval [2.03 × 108, 2.02 × 108] (minimum Eco-indicator 99 solution).

by imposing more-restrictive limits on . Specifically, in this case study, a fixed step of 1 × 106 Eco-indicator 99 points is chosen for gradually decreasing the value. Let us note that, because of the low CPU time required to generate each tradeoff solution, it has not been necessary to resort to specific sampling techniques that are intended to reduce the number of single-objective problems required to generate the Pareto set.26-28 The aforementioned procedure is finished when problem P2 turns out to be infeasible for a specific value of . Alternatively, the value of for which the model is rendered infeasible can be known beforehand by minimizing the Ecoindicator 99 as a single objective. The results obtained by following this strategy can be observed in Figure 6. As can be observed, there is a clear tradeoff between both criteria, because a reduction in the Eco-indicator 99 value can only be achieved at the expense of an increase in the cost. The first trade-off solution represents the most profitable design (i.e., the one that yields the minimum cost), whereas the last one is the least environmentally harmful (i.e., the one with the lowest Ecoindicator 99 value). Each trade-off solution represents a chemical process flowsheet operating under a set of specific conditions. Notice that the operating conditions are given by continuous variables, whereas the plant design is represented by continuous (sizes of equipments) as well as binary variables (existence of equipments). Specifically, by analyzing the particular features of the trade-off solutions, one can see how the model is forced to seek alternatives that are less environmentally harmful to gradually meet the increasing environmental requirements imposed by the constraint. This is achieved by effectively adjusting the structure of the flowsheet as well as its operating conditions according to the environmental needs to be fulfilled in each case. Specifically, the objective of these structural and operative changes is to reduce the consumption of raw materials and energy, which, in turn, decreases the environmental loads and, thus, the impact caused.

Ideally, the raw materials and energy consumption should be minimized simultaneously to increase profitability and decrease environmental impact. However, this is not possible, because a reduction in raw materials consumption usually leads to an increase in energy needs, and vice versa. Thus, the energy consumed in the separation system, as well as the pumping of the recycle streams and the conversion of raw materials, have a tendency to be conflictive objectives. In fact, each trade-off solution involves a different compromise between both terms. To calculate this optimal balance, it is necessary to assess the contribution of each of them to the economic and environmental performance of the system. The problem is further complicated by the possibility of combusting the purge streams. The combustion of unreacted raw materials and byproducts provides surplus energy that can be used elsewhere in the plant. This extra energy increases the profit, because it decreases the overall energy needs in the plant. This term has also a positive environmental effect that must be evaluated when calculating the Eco-indicator 99 value. Specifically, one must subtract from the impact of the different parts of the plant (i.e., raw materials production, electricity generation, and direct emissions) the term corresponding to the environmental impact savings related to the surplus energy. This last term, which appears with a negative sign in the Eco-indicator 99 calculation, is computed by assuming that, in the absence of this surplus energy, the required steam would be generated via standard means. The environmental loads related to the standard production of steam for chemical processes is retrieved from the Eco-invent database. Finally, let us note that, in all the trade-off solutions, the total consumption of energy, which is used in the furnace, the reboilers, and the heaters placed in different parts of the flowsheet, is compensated by the combustion of the purge streams. With regard to the structural features of the solutions found, let us note that four different design alternatives are identified among all the trade-off solutions. Each of these solutions is

Ind. Eng. Chem. Res., Vol. 47, No. 3, 2008 787 Table 4. Materials Balance for the Minimum Eco-indicator 99 Solution Flow Rate, Based on Compound (kmol/min)

Figure 11. Contribution of different parts of the plant to the Eco-indicator 99.

Table 3. Materials Balance for the Minimum Cost Solution Flow Rate, Based on Compound (kmol/min) Stream

h2

ch4

ben

dip

total

hydrogen feed toluene feed toluene feed (absorber)

3.05 0 0

0.34 0 0

0 0 0

0 3.92 0.01

tol

0 0 0

3.39 3.92 0.01

total in

3.05

0.34

0

3.93

0

7.32

benzene product diphenyl byproduct column flash membrane 1 purge membrane 2 purge purge 1 purge 2

0

0

2.08

0

0

2.08

0 0 0 0 0 0

0 0 0 4.25 0 0

0 0.07 0 0.04 0 0

0 0.02 0 0 0 0

0 0.86 0 0 0 0

0 0.95 0 4.29 0 0

total out

0

4.25

2.19

0.02

0.86

7.32

represented by a different set of of binary variables, which remain optimal for different Eco-indicator 99 ranges (see Figure 6). Figures 7-10 show the flowsheet configurations that correspond to these solutions. Specifically, the first solution is optimal in the interval [, j] ) [3.40 × 108, 3.10 × 108], whereas the second and third ones perform better for values in the range of [3.10 × 108, 2.70 × 108] and [2.70 × 108, 2.03 × 108], respectively. Finally, the third one keeps its optimal status in the interval [2.03 × 108, 2.02 × 108]. Notice that the first and fourth solutions are the ones with the minimum cost and Eco-indicator 99 value, respectively. Given these results, it seems more appropriate to choose the third design, because it can operate over a wider range of environmental requirements. Figure 11 depicts the contribution of the different parts of the plant to the Eco-indicator 99, whereas in Tables 3-5, the mass and energy balances associated with the extreme designs are given. With regard to the figure, let us note that the parts of the plant that contribute to the environmental impact include the steam generation, raw materials production, electricity generation, and the direct emissions. This last term includes the impact of the diphenyl byproduct that appears in the stream of the main product (i.e., benzene) and also the carbon dioxide generated in the combustion of the purge streams. Upon analysis of these results, the first thing to notice is that, in both cases, the raw materials generation represents the highest contribution

Stream

h2

ch4

ben

hydrogen feed toluene feed toluene feed (absorber)

8.95 0 0

0.99 0 0

0 0 0

total in

8.95

0.99

benzene product diphenyl byproduct column flash membrane 1 purge membrane 2 purge purge 1 purge 2

0

total out

tol

dip

total

0 2.16 0.01

0 0 0

9.95 2.16 0.01

0

2.17

0

0.01

0

2.08

0

0

2.08

0 0 2.38 0 4.43 0

0 0 0.78 0 2.38 0

0 0.02 0 0 0.02 0

0 0.01 0 0 0 0

0 0.02 0 0 0 0

0 0.05 3.16 0 6.83 0

6.81

3.16

2.12

0.01

0.02

12.12

Table 5. Energy Balance for the Extreme Tradeoff Solutions Energy Streams

Minimum Cost (× 109 kJ/yr)

Minimum Eco-indicator 99

heat in furnace heat in reboilers heat in heaters combustion heat heat removed in reactor heat removed in condensers heat removed in coolers

143.99 122.08 29.43 -3407.53 -100.00 -73.50 -350.47

78.55 120.69 0 -1901.54 -55.24 -71.18 -156.35

to the environmental impact, followed by the direct emissions. On the other hand, the electricity generation has a low impact in the environment. In fact, the reduction in the Eco-indicator 99 value is achieved by decreasing the raw materials consumption. Specifically, the solution with minimum cost consumes more toluene than the stoichiometrically required (i.e., 3.93 kmol/min). This manner of operation is motivated by the fact that the increase in raw materials cost is compensated by the energy savings obtained through the combustion of the diphenyl byproduct. On the other hand, in the minimum Eco-indicator 99 solution, the input stream of toluene is decreased from 3.93 kmol/min to 2.17 kmol/min, which leads to a reduction in the environmental impact. However, this reduction of toluene also reduces the diphenyl byproduct, which decreases from 0.86 kmol/min to 0.02 kmol/min. The diphenyl byproduct has a high combustion energy, and, for this reason, the energy savings decrease accordingly, from 3408 × 109 kJ/yr to 1902 × 109 kJ/yr. To compensate for this effect, the model is forced to increase the purge streams by increasing the amount of hydrogen in the input stream from 3.05 kmol/min to 8.95 kmol/min. With this modifications, the Eco-indicator 99 value decreases from 3.40 × 108 to 2.02 × 108 points. With regard to the structural features of the above commented solutions, let us note that all of them use the isothermal reactor, the stabilizing column, and the second flash. However, the designs differ in the use of the membrane in the input stream and in the methane purge. Specifically, the minimum cost solution avoids the membrane in the input stream but uses the one placed in the methane purge. On the other hand, the least environmentally harmful design uses the input membrane and avoids the second one. As mentioned previously, the latter configuration increases the amount of hydrogen in the purge streams, which compensates for the decrease in the amount of diphenyl byproduct. Thus, these results illustrate how the Ecoindicator 99 value is effectively manipulated by properly

788


changing the operating conditions (i.e., the purge streams) and flowsheet topology (i.e., the existence of membranes). The reader should note that the results obtained in this case study are very sensitive to the LCA data involved in the Ecoindicator 99 calculation. Thus, the recommendations that are made may drastically change, according to the specific LCA data used in the analysis. 5. Conclusions This work has proposed a novel framework for the environmentally conscious design of sustainable chemical processes. The approach presented relies on the combined use of Life Cycle Assessment (LCA) and mixed-integer mathematical programming techniques that are integrated within a single modeling and optimization framework. Specifically, the design task is mathematically formulated as a multiobjective mixed-integer nonlinear problem (moMINLP) that accounts for the minimization of cost and the Eco-indicator 99, which is solved by standard methods for multiobjective optimization. The capabilities of our strategy have been illustrated through a case study (hydrodealkylation (HDA) of toluene) for which the set of trade-off solutions has been computed. These results have shown that significant environmental improvements can be achieved through structural modifications in the process flowsheet, as well as changes in the operating conditions. The proposed methodology provides valuable insights in the design problem and attempts to guide the decision maker toward the adoption of more-sustainable design alternatives. Nomenclature Indices b ) environmental burdens i ) impact categories d ) damage categories Sets I(d) ) set of impact categories that contribute to damage category d Variables x ) continuous variables y ) binary variables Parameters Rbi ) damage caused in impact category i per unit of chemical b released to the environment βb ) total amount of chemical b released per unit of reference flow βdirect ) amount of chemical b released per unit of reference b flow due to direct emissions βrm b ) amount of chemical b released per unit of reference flow due to raw materials generation βenergy ) amount of chemical b released per unit of reference b flow due to energy generation δd ) normalization factor for damage category d ) epsilon parameter ) lower bound on j ) upper bound on ωd ) weighting factor for damage category d θi ) impact caused in impact category i

Acknowledgment G.G.-G. expresses his gratitude for the financial support received from the Fulbright/Spanish Ministry of Education and Science Visiting Scholar Program. Literature Cited (1) El-Halwagi, M. M.; Manousiouthakis, V. Chem. Eng. Sci. 1990, 45, 2813-2831. (2) Ciric, A. R.; Jia, T. Comput. Chem. Eng. 1994, 18, 481-495. (3) Wang, Y. P.; Smith, R. Chem. Eng. Sci. 1994, 49, 981-1006. (4) Linninger, A. A.; Stephanopoulos, E.; Ali, S. A.; Han, C.; Stephanopoulos, G. Comput. Chem. Eng. 1995, 19 (Supplement), S7-S13. (5) Grossmann, I. E.; Drabbant, R.; Jain, R. K. Chem. Eng. Commun. 1982, 17, 151-170. (6) Guineé, J. B.; Gorreé, M.; Heijungs, R.; Huppes, G.; Kleijn, R.; de Koning, A.; van Oers, L.; Sleeswijk, A. W.; S. Suh, S.; de Haes, H. A. U.; de Bruijn, H.; 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. (7) Azapagic, A.; Clift, R. Comput. Chem. Eng. 1999, 10, 1509-1526. (8) Petrie, B. A. G. B. J.; Romagnoli, J. Comput. Chem. Eng. 2000, 24 (2-7), 1195-1200. (9) Hoffmann, V. H.; Hungerbuhler, K.; McRae, G. J. Ind. Eng. Chem. Res. 2001, 40 (21), 4513-4524. (10) Chen, H.; Shonnard, D. R. Ind. Eng. Chem. Res. 2004, 43 (2), 535552. (11) Hugo, A.; Pistikopoulos, E. N. J. Cleaner Prod. 2005, 13, 14711491. (12) Stefanis, S. K.; Livingston, A. G.; Pistikopoulos, E. N. Comput. Chem. Eng. 1997, 21, 1073-1094. (13) The Eco-indicator 99, A damage oriented method for life cycle impact assessment. Methodology Report and Manual for Designers; Technical Report, PRe´ Consultants, Amersfoort, The Netherlands, 2000. (14) ISO Standard 14040, Gestio´ n ambientalsAna´ lisis del ciclo de vidasPrincipios y marco (Environmental ManagementsLife cycle assessment. Frame of reference); International Organization for Standardization: Basel, Switzerland, 1997. (15) ISO Standard 14041, Gestio´ n AmbientalsAna´ lisis del Ciclo de vidasDefinicioń de la meta y el alcance y ana´lisis del inventario del ciclo de vida (Environmental managementsLife cycle analysis. Defining the purpose and field inventories and analysis); International Organization for Standardization: Basel, Switzerland, 1998. (16) ISO Standard 14042, Gestio´ n AmbientalsAna´ lisis del Ciclo de vidasEvaluacioń del impacto del ciclo de vida (Environmental Managements Life cycle analysis. Impact assessment lifecycle); International Organization for Standardization: Basel, Switzerland, 2000. (17) TEAM and DEAM; Ecobalance UK, The Ecobilan Group; Arundel, U.K., 1998 (www.ecobalance.com/uk_team.php). (18) SimaPro 6 LCA software; PRe´ Consultants: Amersfoort, The Netherlands, 1998 (www.pre.nl/simapro/default.htm). (19) PEMS 4 Database; PIRA International, Leatherhead, U.K., 1998 (www.pira.co.uk/pack/lca_software.htm). (20) Miettinen, K. M. Nonlinear MultiobjectiVe Optimization; Kluwer Academic Publishers: Boston, 1999. (21) Zhou, G.; Min, H.; Gen, M. Comput. Ind. Eng. 2002, 43, 251261. (22) Chen, C. L.; Wang, B. W.; Lee, W. C. Ind. Eng. Chem. Res. 2003, 42, 1879-1889. (23) Gjerdrum, J.; Shah, N.; Papageorgiou, L. G. Ind. Eng. Chem. Res. 2001, 40, 1650-1660. (24) Rodera, H.; Bagajewicz, M. J.; Trafalis, T. B. Ind. Eng. Chem. Res. 2002, 41, 4075-4084. (25) Haimes, Y. Y.; Lasdon, L. S.; Wismer, D. A. IEEE Trans. Syst., Man. Cybern. 1971, 1, 296-297. (26) Kalagnanam, J.; Diwekar, U. Technometrics 1997, 39 (3), 308319. (27) Kalagnanam, J.; Diwekar, U. Ann. Oper. Res. 2004, 132 (1-4), 109-134. (28) Baratto, F.; Diwekar, U.; Manca, D. J. Power Sources 2005, 139 (1-2), 214-222. (29) Smith, E. M. B.; Pantelides, C. C. Comput. Chem. Eng. 1999, 23, 457. (30) Duran, M. A.; Grossmann, I. E. Math. Prog. 1986, 36, 307.

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ReceiVed for reView March 27, 2007 ReVised manuscript receiVed August 23, 2007 Accepted October 17, 2007 IE070448+

Application of Life Cycle Assessment to the Structural Optimization of

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