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Applied Thermal Engineering 48 (2012) 367e377

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Minimization of the LCA impact of thermodynamic cycles using a combinedsimulation-optimization approach

Robert Brunet a, Daniel Cortés a, Gonzalo Guillén-Gosálbez a,*, Laureano Jiménez a, Dieter Boer b

aDepartament d’Enginyeria Quimica, Escola Tecnica Superior d’Enginyeria Quimica, Universitat Rovira i Virgili, Campus Sescelades, Avinguda Paisos Catalans 26,43007 Tarragona, SpainbDepartament d’Enginyeria Mecanica, Escola Tecnica Superior d’Enginyeria, Universitat Rovira i Virgili, Campus Sescelades, Avinguda Paisos Catalans 26, 43007,Tarragona, Spain

a r t i c l e i n f o

Article history:Received 15 November 2011Accepted 13 April 2012Available online 26 April 2012

Keywords:Process simulationOptimizationRankine cycleAbsorption cycleCost analysisLife cycle assessment

* Corresponding author. Tel.: þ34 977558618.E-mail address: gonzalo.guillen@urv.cat (G. Guillé

1359-4311/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.applthermaleng.2012.04.032

a b s t r a c t

This work presents a computational approach for the simultaneous minimization of the total cost andenvironmental impact of thermodynamic cycles. Our method combines process simulation, multi-objective optimization and life cycle assessment (LCA) within a unified framework that identifies ina systematic manner optimal design and operating conditions according to several economic and LCAimpacts. Our approach takes advantages of the complementary strengths of process simulation (in whichmass, energy balances and thermodynamic calculations are implemented in an easy manner) andrigorous deterministic optimization tools. We demonstrate the capabilities of this strategy by means oftwo case studies in which we address the design of a 10 MW Rankine cycle modeled in Aspen Hysys, anda 90 kW ammonia-water absorption cooling cycle implemented in Aspen Plus. Numerical results showthat it is possible to achieve environmental and cost savings using our rigorous approach.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The energetic and economic analysis of industrial processes hasgained wider interest in recent years. This has been motivated bythe need to use the resources available nowadays more efficiently.In this context, process optimization has emerged as an effectivetool for reducing energy consumption and improving efficiency inprocess industries. Multi-objective optimization (MOO), in partic-ular, offers decision makers a suitable framework to identify theset of operating conditions and design variables that simulta-neously improve the economic and environmental performance ofa system [1].

Thermodynamic cycles are widely used in energy conversionprocesses. They are often found in daily life, but have the drawbackof requiring large amounts of energy to operate. By optimizingpower generation cycles, (e.g Rankine cycle) it is possible toincrease their efficiency and reduce the associated global warmingemissions [2]. Cooling cycles can also benefit from the applicationof rigorous optimization tools. Increments of up to 50% in their

n-Gosálbez).

All rights reserved.

coefficient of performance (COP) have been reported [3], whichleads to significant savings in primary energy sources [4].

A variety of optimization approaches have been applied tothermodynamic cycles. Some studies in power cycles focus on theminimization of a single indicator, such as the net present value(NPV), total plant cost (TPC) [5,6], and cycle efficiency [7e10]. Incooling cycles, some models were devised to optimize the COP andcooling load [3]. The application of MOO to thermodynamic cycles,however, has been quite scarce. The simultaneous optimization ofthe exergetic efficiency and the TPC in power generation systemswas studied by BecerraeLopez and Golding [11] and Dipama et al.[2]. Pelet et al. [12] optimized a superstructure of energy systemsconsidering the cost and CO2 emissions. In the context of coolingcycles, Gebreslassie et al. [13,14] proposed a multi-objective non-linear programming (moNLP) problem for the design of anammonia-water absorption cycle considering the cost and life cycleassessment (LCA) performance [15,16].

The overwhelming majority of the works mentioned abovefollow the so called simultaneous approach, which relies onformulating algebraic optimization models described in an explicitform. For simplicity, most of these formulations contain short-cutmodels that avoid the numerical difficulties associated withhandling non-linear equations. These simplified formulationsprovide ”good” approximations when certain assumptions hold,

Fig. 1. Steam Rankine cycle.

Fig. 2. Ammonia-water absorption cycle.

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377368

but can lead to large numerical errors otherwise. Sequential processsimulation models are more difficult to optimize due to the pres-ence of non-convexities of different types, but have the advantageof producing more accurate results. Another limitation of theworksmentioned above is that those that account for environmentalconcerns restrict the analysis to a single environmental indicator,neglecting the effects caused in other environmental damages.

This work applies a combined approach for the design of ther-modynamic cycles that takes advantage of the complementarystrengths of sequential modular process simulators (e.g. AspenHysys and Aspen Plus), optimization tools (e.g. SNOPT and CPLEX)and LCA. The pivotal idea of our method is to optimize modularsimulation models of thermodynamic cycles using an externaldeterministic optimizer that is guaranteed to converge to anoptimal solution. Our approach is inspired by other simulation-optimization methods used in a variety of chemical engineeringapplications, including the design of systems such as: heatexchangers and chemical reactions [17e19], chemical plants[20,21], distillation columns [22], and biotechnological processes[23]. An efficient solution method is presented for tackling theseproblems based on decomposing them into two sub-levels betweenwhich an algorithm iterates until a stopping criterion is satisfied.This algorithm performs the calculations using both a processsimulation and an external optimizer.

The final goal of our analysis is to identify the design andoperating conditions of different thermodynamic cycles thatsimultaneously minimize the total annualized cost (TAC) andenvironmental impact (EI). We demonstrate the capabilities of thismethodology through its application to the design of two cycles:a steam Rankine cycle and an ammonia-water absorption cycle. Theoptimization of the steam Rankine cycle is formulated as a moNLPproblem, which is optimized with a Successive QuadraticProgramming (SQP) solver that interacts at each iteration with theprocess simulator of choice. The optimization of the absorptioncycle gives rise to a multi-objective mixed-integer non-linearprogramming (moMINLP) problem, in which binary variables areemployed to model the number of trays in the desorber.

2. Problem statement

As previously mentioned, we will focus herein on two energyconversion cycles: a steam Rankine cycle for power generation andan ammonia-water absorption cooling cycle. Note, however, thatthe approach presented is general enough to be adapted to anyother energy system. We provide next a brief description of each ofthese systems before immersion into a detailed mathematicalformulation.

2.1. Rankine cycle

We consider a reheat-regenerative power cycle with one closedand one open feedwater heater (see Fig.1). The system contains oneboiler, one turbine, a condenser, two pumps, and two shell-tubeheat exchangers. Water is used as working fluid in the cycle. Theboiler is assumed to operate with natural gas. The combustiongases behave as air. For the condenser as well as the heatexchangers, we use shell-tube heat exchangers.

2.2. Absorption cycle

We consider the single effect ammonia-water absorption cool-ing cycle described by Gebreslassie et al. [13,14] (see Fig. 2). Theabsorption cycle provides chilled water at 5 �C. The equipmentunits are the absorber (A), condenser (C), rectification column (RC),evaporator (E), subcooler (SC), refrigerant expansion valve (VLV1),

solution heat exchanger (SHX), solution pump (P), and solutionexpansion valve (VLV2). It is assumed that the systemworks understeady state conditions. Heat and pressure losses are neglected.Adiabatic valves are considered. The refrigerant leaves thecondenser, absorber and bottom of the generator as saturatedliquid.

2.3. Problem definition

The problems can be formally stated as follows. In the case of theRankine cycle, we are given the flowsheet arrangement, net poweryield, turbines and pumps efficiencies, overall heat transfer coef-ficients, thermodynamic properties, cost estimation correlations,economic parameters and environmental indicators. For theabsorption cycle, we need to specify as well the cooling capacity,and inlet and outlet temperatures of the external fluids.

The goal of our study is to identify the optimal design andoperating conditions that simultaneously minimize the TAC andthe following damage impact indicators: damage to humanhealth (HH), damage to ecosystem quality (EQ) and depletion ofresources (DR).

3. Methodology

This section describes the approach proposed to tackle theproblems described above. A general mathematical formulation isfirst presented. We then describe how the economic and environ-mental objective functions are calculated. The solution procedureand the computer implementation are finally discussed.

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377 369

3.1. Mathematical formulation

The design of thermodynamic cycles with economic and envi-ronmental concerns can be expressed in mathematical terms asa moMINLP. We solve this model using the ε-constraint method[24,25]. This technique is based on calculating a set of single-objective models in which one objective is kept in the objectivefunction while the others are transferred to auxiliary constraintsand forced to be lower than a set of epsilon parameters:

minxD

z ¼ ff1ðx;u; xDÞgs:t: foðx;u; xDÞ � εo o ¼ 2; :::; n

h1ðx;u; xDÞ ¼ 0hEðx;u; xDÞ ¼ 0gEðx;u; xDÞ � 0

(1)

Where f1 is the economic objective function, and f2 to fn denote theLCA metrics used to assess the environmental performance of thecycle. ε is an auxiliary parameter that bounds the values of theobjectives transferred to the auxiliary inequality constraints.Equations hI are implicit equations implemented in the processsimulator, whereas hE and gE are explicit constraints that ensurecertain process conditions. The form of these equations depends onthe system under study.

The design variables are denoted by xD, while other processvariables are represented by x. Finally, u denotes parameters notmodified during the calculations. It is important to note that xDinclude only continuous variables in the case of the Rankine cycle,while in the case of the absorption cycle it includes both, contin-uous and integers (i.e., number of trays and feed tray in theabsorber).

Fig. 3. Flowchart of the proposed outer-approximation algorithm.

3.2. Objective functions

The model presented, seeks to optimize simultaneously the TACand environmental impact. We describe next how these indicatorsare calculated.

3.2.1. Economic indicator (total annualized cost)The TAC of the thermodynamic cycles is given by Eq. (2).

TAC ¼ COþ CF$crf (2)

Where CO and CF are the operating and fixed costs, and crf is thecapital recovery factor, which is a function of the interest rate(parameter i) and the lifetime of the cycle (parameter t) expressedin years (see Eq. (3)).

crf ¼

ið1þ iÞtð1þ iÞte1

!(3)

The operation cost, denoted by CO, accounts for the cost of theenergy and electricity required to operate the cycle.

CO ¼Xu˛U

ðQu$cqþWu$cwÞ$top (4)

In this equation, Qu [MW] is the thermal power supplied toequipment unit U, Wu [MW] is the electrical power required byequipment unit, top [h] is the total annual operation time and cq[V/MWh] and cw [V/MWh] are the unit costs for heat and elec-tricity respectively. Note thatQu andWu are provided by the processsimulator.

Eq. (5) determines the total fixed cost (CF) which accounts forthe cost of the main equipment units of the cycle (Cu) including the

equipment and maintenance cost, which are determined using thecosting correlations described in sections 4.1 and 4.2.

CF ¼Xu˛U

Cu (5)

3.2.2. Environmental indicator (damage categories)The environmental impact is quantified following LCA princi-

ples, similarly as done before by the authors in other works [23].Further details on the calculations are provided in the Appendix.

3.3. Solution procedure

3.3.1. ε-Constraint methodologyThe solution of the multi-objective model is given by a set of

Pareto points representing the optimal compromise between theobjectives considered. These points are generated combining theε-constraint method [24,25] with a tailored decomposition algo-rithm that integrates simulation and optimization tools. The solu-tion method proposed is shown in Fig. 3. It comprises two nestedloops: an outer loop in which epsilon values are defined for theenvironmental impacts, and an inner loop that solves each single-objective problem. We provide next details on the inner loop ofthe algorithm.

3.3.2. Simulation-optimization approachThe solution strategy for solving each single-objective problem

relies on an outer-approximation [26] scheme that decomposeseach model into two hierarchical levels: a primal non-linearprogramming (NLP) sub-problem and a master mixed-integer

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377370

linear programming (MILP) sub-problem. The algorithm iteratesbetween these levels until a termination criterion is satisfied.

The master MILP is constructed using information provided bythe primal NLP. This primal NLP is solved integrating a determin-istic gradient-based method with the process simulator. The binaryvariables are thus handled by the MILP, while the NLP provides theoptimal values of the continuous variables for a fixed set of binaries.This strategy is inspired by previous simulation-optimizationapproaches applied in chemical engineering [17e23]. The mainadvantage of this method is that it ensures convergence to a local(or global) optimum, as opposed to heuristic-based approaches thatare unable to guarantee the optimality of the solutions calculated.

3.3.2.1. Primal NLP sub-problem. This level optimizes the contin-uous decision variables of the NLP sub-problem for fixed values ofthe binary variables predicted by the master sub-problem (Eq. (6)).This procedure is repeated iteratively for different values of thebinary variables until a termination criterion is met. The NLP sub-problems are solved using a gradient-based SQP solver that iter-ates with the simulation package in order to obtain information onthe derivatives of the decision variables with respect to the objec-tive function and constraints.

Slack variables are used to relax the external equality andinequality constraints, which avoids unconvergencies in the slaveproblem. Potential intermediate unfeasible points are thus handledexternally by the optimization algorithm. These slacks are penal-ized in the objective function. This approach avoids unfeasiblesimulation runs, preventing the algorithm from ending prema-turely. The modified objective function is expressed as follows.

minxD

z ¼ f1ðx;u; xDÞ þQðs1 þ s2 þ s3 þ s4Þ

s:t: foðx;u; xDÞ � εo þ s1 o ¼ 2; :::;nε0 � εo � εo o ¼ 2; :::;n

hIðx;u; xDÞ ¼ 0hEðx;u; xDÞ þ s2es3 ¼ 0gEðx;u; xDÞ � s4s1 � 0; s2 � 0; s3 � 0; s4 � 0;

(6)

WhereQ

is a penalty parameter vector, and s1, s2, s3 and s4 arevectors of positive slack variables.

3.3.2.2. Master MILP sub-problem. The master sub-problemprovides new values for the binary variables that are expected toyield better results than previous solutions. Note that this masterMILP is only required in the case of the absorption cycle, in whichthe number of trays of the desorber must be decided. In contrast,the optimization of the Rankine cycle can be solved as an NLP.

To construct the master MILP, we use the derivatives of theobjective function and constraints of the NLP sub-problem at theoptimal NLP solution of the previous iteration. Due to the presenceof non-convexities in the NLP, the master MILP is not guaranteed toprovide a rigorous lower bound on the global optimum. Thefollowing notation is defined in the MILP at iteration k of thealgorithm:

T ¼ {iji is a potential column configuration}Tk ¼ {iji is a rectification column configuration, entailing a given

number of trays and a specific feed stage, which can be obtainedperforming one single modification on the design calculated atiteration k}

EQ ¼ {jjj is an external (explicit) equality constraint}IEQ ¼ {jjj is an external (explicit) inequality constraint}Dobjki;o ¼ Difference between the objective function o at itera-

tion k of the NLP and the objective function associatedwith the newrectification column design i

Dgki;j¼Difference between the values of the inequality constraintj for the new rectification column design i and constraint j in theoriginal NLPk problem.

DhkEi;j ¼ Difference between the values of the external equalityconstraint j in the new rectification column design i and constraint jin the original NLPk problem.

The master MILP takes the following form:

min aþQ Pn

o¼2s1o

þ Pj˛IEQ

s2jþ P

j˛EQs3j

!

s:t: fo�xk;uk; xkD

�þP

n

�vfovxDn

�xDn¼xiDn

�xDn

� xkDn

�

þXi˛Tk

yi$Dobjki;o � a o ¼ 1

fo�xk;uk; xkD

�þXn

�vfovxDn

�xDn¼xiDn

�xDn

� xkDn

�

þXi˛Tk

yi$Dobjki;o � εo þ s1o

o ¼ 2; :::;n

gj�xk;uk; xkD

�þXn

�vgjvxDn

�xDn¼xiDn

�xDn

� xkDn

�

þXi˛Tk

yi$Dgki;j � s2j

cj˛IEQ

sign�lkj

�hEj�xk;uk; xkD

�þXn

�vhEjvxDn

�xDn¼xiDn

�xDn

� xkDn

�

þXi˛Tk

yi$DhkEi;j

� s3jcj˛EQ

k ¼ 1;2;3; :::;K264s1o

� 0 s2j� 0 s3j

� 0Pi˛T

yi ¼ 1

yi˛f0;1g

375 (7)

The objective function of the MILP contains an auxiliary variable(a) and a penalty value for constraint violation (

Q) that multiplies

the slack variables. The first constraint is formed by three terms: (i)the objective function value at iteration k of the algorithm, (ii) thelinearization performed on the design variables, and (iii) thecontribution of changing the current distillation column charac-teristics, by either adding or removing stages in the column orchanging the feed stage. This last term is the product of the binaryvariable yi (that is 1 if topological modification i is implemented

and 0 otherwise) with the parameter Dobjki;o. The latter accounts forthe change in the objective function value when topology i isimplemented. Fig. 4 provides an illustrative example on how theseterms are defined.

External inequality (IEQ) and equality (EQ) constraints arehandled following a similar procedure. signðlkj Þ refers to the sign ofthe Lagrange multiplier of constraint j at iteration k. This value isused to correctly relax equalities into inequalities [27]. Note thatlinear constraints are accumulated in the master MILP, so at itera-tion k, the problem includes constraints from current and previousiterations.

After determining the new set of values for the binary variables,the primal problem is solved again, and the overall procedure isrepeated until the termination criterion is satisfied. Integer cuts canbe added to the master MILP in order to avoid repetition of solu-tions explored so far in previous iterations. Implicit constraints are

Fig. 4. Details on the definition of binary variables in the MILP (inspired in the work by Caballero et al. [22]).

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377 371

handled by the process simulator and their derivatives are obtainedby finite differences.

Note that the complexity of the overall solution proceduregrows rapidly with the number of environmental objectives. Incases with a large number of objectives, we might be interested inapplying dimensionality reduction methods to keep the problem ina manageable size [28e30].

3.4. Computational implementation

We use the process simulators Aspen Hysys [31] and Aspen Plus[32] to simulate the thermodynamic cycles. These software pack-ages allow an easy modeling of the cycles, as they implementthermodynamic correlations, built-in models for a variety of unitoperations andmass and energy balances. These process simulatorswere connected with Matlab [33], in which the main code of thealgorithm was implemented. This software gets the values of thedependent variables (e.g., temperature, pressure, mass and energyflows) from the process simulators at each iteration of thealgorithm.

Fig. 5. Main steps of the solu

As NLP solver, we used SNOPT [34], which was accessed via theTomlab [35] modeling system supported by Matlab. This solver isparticularly suited for non-linear problems whose functions andgradients are expensive to evaluate [36]. The master MILP sub-problem was solved using the MIP solver CPLEX [37], accessed viaTomlab. Fig. 5 outlines the computer architecture of the solutionalgorithm proposed.

4. Case studies

Two thermodynamic cycles were studied, a steam Rankine cycleand an ammonia-water absorption cycle. Both systems weresimulated using standard commercial process simulators, therebyavoiding the definition of the thermodynamic equations in anexplicit form.

4.1. Case study I: steam Rankine cycle

4.1.1. System descriptionThe first case study addresses the design of a 10 MW steam

Rankine cycle (see Fig. 6) taken from Moran and Shapiro [38]. The

tion algorithm proposed.

Fig. 6. Steam Rankine cycle simulated in Aspen Hysys.

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377372

cycle was simulated in Aspen Hysys under steady state conditions.Heat and pressure losses were neglected. Adiabatic efficiencies inturbines and pumps were set to 75% [39]. An adiabatic expansionvalve was considered in the calculations.

4.1.2. System modelingThe properties of water, selected as the working fluid of the

cycle, were calculated using the ASME steam tables. The boiler andreboiler operate with natural gas. The composition of thecombustion gases in the boiler and reboiler is unknown, but weassume that they behave as air, which was modeled using UNI-QUAC. For the condenser, heat exchanger, boiler and reboilersimulation, we considered shell-tube heat exchangers, which weremodeled using the weighted model built-in Aspen Hysys. Theboiler and reboiler were simulated as separated heat exchangers.The same approach was applied to the turbine. The mixer wasmodeled as an open flow heat exchanger that mixes streams atdifferent temperatures.

4.1.3. Objective functionsThe heat cost was set to 25 V/MWh, and the operation time to

4000 h per year. The energy flows in the boiler and reboiler wereretrieved from Aspen Hysys. The cost of the expansion valves andmixer were neglected. Table 1 shows the cost estimation correla-tions used for the remaining equipment units [39e41].

The environmental impact of the operation phase was deter-mined from the energy flows imported from Aspen Hysys. Tocalculate the environmental impact of the construction phase, weconsidered only the turbine and heat exchangers (heat exchanger,

Table 1Cost correlations used in the Rankine cycle.

Equipment Correlation Reference

Boiler and reboiler CB ¼ fmð1þ fdþ fpÞ$ðQBÞ0:86 Walas [40]

Condenser andheat exchanger

CHX ¼ fd$fm$fp$Cb Evans et al. [41]

Turbine CT ¼ 4750$ðWT Þ0:75 Nafey [39]Pumps CP ¼ 3500$ðWPÞ0:47 Nafey [39]

condenser, boiler and reboiler). The mass of steel from tubes,pumps, valves and other equipments in the cycle were neglected.The amount of stainless steel contained in the heat exchangers wasdetermined from the exchange area assuming a thickness of 1/4inches. The weight of the turbine was assumed to be equal to 10tons (typical weight of a 10 MW turbine [42]).

4.2. Case study II: absorption cooling cycle

4.2.1. System descriptionThe second example studies a 90 kW single effect ammonia-

water absorption cooling cycle (see Fig. 7). This cycle is discussedin detail in Gebreslassie et al. [13,14]. The absorption cycle provideswater at 5 �C.

4.2.2. System modelingThe RedlicheKwongeSoave equation of state was selected to

model the ammonia-water mixture in vapor phase [43]. For thesimulation of the liquid mixture, the Non-Random Two Liquidmodel was employed. The absorber, condenser, evaporator, sub-cooler and solution heat exchanger were simulated using theMheatX model. The desorber was simulated with a rigorous tray-by-tray distillation column model.

4.2.3. Objective functionsThe operational costs were calculated with Eq. (4), assuming an

electricity cost of 100 V/MWh, a heat cost of 25 V/MWh, and anoperation time of 4000 h per year. The energy flows (electricity andheat) in the pump and desorber were retrieved from Aspen Plus.The cost correlations are given in Table 2 [44e46].

The energy flows were retrieved from the process simulator (inthis case Aspen Plus). The mass of steel contained in the pipes,valves and other equipments in the cycle were neglected. The massof steel contained in the heat exchangers was calculated followingthe same approach as in case study 1. The mass of steel from thedesorber was determined by approximating the distillation columnby a cylinder. The dimensions of the desorber were imported fromthe process simulator.

Fig. 7. Ammonia-water absorption cycle simulated in Aspen plus.

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377 373

5. Results and discussion

The design problem aims to determine the optimal operatingconditions of the cycle (fluid flow rates, equipment sizing andsystem pressures and temperatures) that minimize simultaneouslythe economic indicator (TAC) and different impact categories (HH,EQ and DR) given a fixed energy capacity of the cycle.

We generated in both cases a set of Pareto solutions that weobtained for simplicity minimizing the TAC versus each individualdamage category separately.

3.42

3.44

3.46

3.48 x 105

Hea

lth (P

oint

s) Q

ualit

y (P

oint

s)

sour

ces

(Poi

nts)2.95

2.925

2.9

2.975x106

5.1. Case study I: steam Rankine cycle

We first studied a 10 MW Rankine cycle. The problem wassolved as a moNLP with the following 11 design continuousvariables: mass flow passing through the cycle (mass flow 1),temperatures of streams 1 and 4, pressure of stream 1, outletpressure of the turbines (pressures 2, 3, 5 and 6) and outlettemperature of the heat exchangers (temperatures B1 and B2). Inaddition, the model includes 5 non-linear inequality constraints:power equal or higher than 10 MW, and a minimum temper-ature difference of 10 �C in the heat exchangers. The remainingprocess variables and constraints are defined in an implicit formusing the process simulator (Aspen Hysys). The algorithm takesaround 600 to 1000 CPU seconds to generate 10 Pareto solutionsof each 2-dimensional Pareto set on a computer AMD Phe-nomTM 8600B, with a Triple-Core Processor 2.29 GHz and3.23 GB of RAM.

Table 2Cost correlations used in the absorption cooling cycle.

Equipment Correlation Reference

DesorberCRC ¼

�MS280

�ð101:9Diam1:066H0:802Þ

� ð2:18þ 2FcÞdeuro

Guthrie [44]

Heatexchangers

CHX2 ¼ Pu˛HX

ðc1Amu˛HX þ c2Þ Kizilkan et al. [45]

Pump CP ¼ c3W0:4P Siddiqui [46]

Three bi-criteria Pareto sets were generated optimizing the TACagainst each single damage impact category separately (see Fig. 8).Fig. 8 represents the Pareto solutions of the three bi-objectiveoptimization problem TAC vs HH, TAC vs EQ and TAC vs DR. Asobserved, the impact in damage category HH was reduced by 2.40%(334.89 kPoints vs 342.93 kPoints) along the Pareto curve. This wasaccomplished by increasing the heat exchanger areas, therebyreducing the natural gas consumption. This led in turn to anincrease of 3.65% in the TAC (3491 MV/yr vs. 3619 MV/yr). Inaddition, the EQ was reduced by 2.38% (336.52 kPoints vs 344.55kPoints) along the Pareto curve at the expense of increasing the TACby 3.84% (3491 MV/yr vs. 3625 MV/yr). Note that in both cases,solutions with lower TAC entail larger natural gas consumptionrates and smaller equipments. Finally we analyze the trade-offsolutions between TAC vs DR. Here, the DR was decreased by2.22% (2873.06 kPoints vs 2941.19 kPoints) while the TAC wasincreased by 4.44% (3491 MV/yr vs 3646 MV/yr). Further inspec-tion of the results reveals similar insights, regarding operatingconditions and design characteristics, as in the previous cases.

3.48 3.5 3.52 3.54 3.56 3.58 3.6 3.62 3.64x 106

3.34

3.36

3.38

3.4

Total Annualized Cost (euro/yr)

Dam

age

to H

uman

D

amag

e to

Eco

syst

em

Dep

letio

n N

atur

al R

e

HHEQDR

2.875

2.85

2.825

2.82

Fig. 8. Total annualized cost vs impact damage categories. Case study I: Rankine cycle.

1 2 3 495

95.5

96

96.5

97

97.5

98

98.5

99

99.5

100

Objective functions

Perc

enta

ge w

ith re

spec

t to

the

max

imum

val

ue (%

)

HHTAC EQ DR

Fig. 9. Parallel coordinates plot. Case study I: Rankine Cycle. Objective functions: Totalannualized cost (TAC), damage to human health (HH), damage to ecosystem quality(EQ), and depletion of natural resources (DR).

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377374

Fig. 9 depicts the Pareto solutions in a parallel coordinates plot,which is a useful graphical tool to display data sets of largedimension. The figure shows in the x axis the set of objectivefunctions (TAC, HH, EQ and DR) and in the y axis the normalizedvalue attained by each solution in every criterion. The normaliza-tion was performed by dividing each objective function value by itsmaximum over the entire set. Note that each line in the plotrepresents a different Pareto solution, entailing a set of operatingconditions. As observed, all environmental impacts seem equiva-lent, since they tend to behave similarly. Moreover, all of theimpacts are conflictive with the TAC of the cycle. This is becausereductions in the environmental impact are achieved at theexpenses of increasing the cost.

Table 3 shows the details of the corresponding extreme points(i.e., minimum TAC and minimum environmental damage). Wepresent first the decision variables values in the extreme solutions,which differ mainly in the mass flow rate and temperature ofstream 1, and the pressure in the turbines. The mass flow rate ofstream 1 in the minimum cost solution is greater than in theminimum environmental impact. This is because larger mass flowrates require more natural gas to evaporate water in the boiler andreboiler. The temperature of stream 1 in the economic optimum islower than in the environmental optimum. Moreover, the pressure

Table 3Details of the extreme solutions. Case study I: Rankine cycle.

Variable Min TAC Min HH Min EQ Min DR

Mass flow stream 1 [kg/s] 9.33 8.78 8.82 8.90Temperature of stream 1 [�C] 516.43 587.30 577.85 571.55Pressure of stream 1 [kPa] 8550.08 8878.49 8860.25 8805.51Pressure of stream 2 [kPa] 2300.00 2269.70 2274.19 2276.43Pressure of stream 3 [kPa] 737.29 698.34 703.54 707.00Pressure of stream 5 [kPa] 329.92 301.20 304.74 307.58Pressure of stream 6 [kPa] 8.80 7.00 7.23 7.40Temperature of stream 4 [�C] 496.09 493.99 494.39 494.46Temperature of stream 11 [�C] 205.19 215.15 214.66 212.94Temperature of combustion

gases B1 [�C]250.00 249.90 249.91 249.92

Temperature of combustiongases B2 [�C]

278.69 300.00 295.56 295.26

Area of the boiler andreboiler [m2]

160.82 165.47 165.73 166.59

Area of the condenser [m2] 133.14 149.11 149.96 152.63Area of the Heat Exchangers [m2] 60.41 63.44 63.60 64.17Steam [tones] 3.96.108 3.89.108 3.89.108 3.88.108

Electricity [MJ] 1.48.106 1.43.106 1.43.106 1.42.106

drop in the turbine is lower in the minimum cost solution, whichleads to smaller turbines and investment costs. Table 3 also displaysthe heat exchangers areas and the energy consumption (heat andelectricity) of the extreme solutions. As observed, the heatexchangers area in the economic optimum is between 5 and 11%smaller than in the minimum environmental impact solutions.Regarding energy consumption, the use of heat and electricity intheminimum impact designs is between 1 and 3.5% smaller than inthe economic optimum.

The objective function values of the extreme designs arecompared in Table 4. Note that impacts HH, EQ and DR can bedecreased by up to 2.40%, 2.38% and 2.22% respectively.

5.2. Case study II: absorption refrigeration cycle

A moMINLP model of the 90 kW absorption cycle was devel-oped. This formulation featured 10 design variables, 8 continuousand 2 discrete, and 4 non-linear inequality constraints. Thecontinuous variables denote the reboiler duty in the desorber, thehigh and low pressure of the system, the mass flow and massfraction of stream 1, the temperature at the outlet of the hot side ofunit SHX (temperature 5), the temperature at the outlet of the hotside of the SC unit (temperature 9), and the reflux ratio in thedesorber. Discrete variables model the number of trays and the feedtray in the desorber. Inequality constraints impose a minimumcooling capacity and minimum temperature difference betweenthe inlet and outlet external flows. The remaining process variablesand constraints were implemented in the process simulator, in thiscase Aspen Plus. The algorithm took around 2500 to 3000 CPUseconds to generate 10 Pareto solutions on the same computer asbefore.

Fig. 10 depicts the Pareto solutions of the three bi-objectiveoptimization problems: TAC vs HH, TAC vs EQ and TAC vs DR. TheHH index is reduced by 5.84% (2734 points vs 2584 points) alongthe Pareto curve. This is accomplished by reducing the steamprovided to the cycle. On the other hand, the TAC is increased by4.66% (21,917 V/yr vs. 22,940 V/yr). The steam consumption isreduced by increasing the heat exchanger areas, which leads tolarger capital investments. Concerning the EQ, this is reduced by6.82% (2740 points vs 2565 points) along the Pareto curve, whereasthe TAC is increased by 4.71% (21,917 V/yr vs. 22,951 V/yr). Finally,impact DR is decreased by 7.03% (10,497 points vs 11,228 points),while the TAC is increased by 4.73% (21,917 V/yr vs 22,954 V/yr).Note that all the Pareto solutions involve the same configuration ofthe rectification column (1 single stage).

The Pareto solutions obtained in the bi-criteria problems wereplotted in a parallel coordinates plot (see Fig. 11). Similar conclu-sions as in the Rankine cycle are obtained in this second case.

As observed, the environmental impacts are equivalent sincewhen one is minimized the others are also decreased. This isbecause all the damages are highly dependent on the steamconsumption. Further, they are all conflictive with the cost as theirminimization increases the cost of the cycle.

Table 5 summarizes the extreme points (i.e., minimum TAC andminimum environmental damage indicators). As in the previouscase, the minimum TAC design differs considerably from the

Table 4Extreme solutions. Case study I: Rankine cycle.

Objective function Min TAC Min HH Min EQ Min DR

TAC [V/yr] 3,491,584 3,619,084 3,625,842 3,646,903HH [Points] 342,931 334,887 334,952 334,987EQ [Points] 344,555 336,547 336,518 336,586DR [Points] 2,941,189 2,877,357 2,876,312 2,873,056

2.18 2.2 2.22 2.24 2.26 2.28 2.3 2.32 2.34 2.36x 104

2550

2600

2650

2700

2750

2800

2850

Total Annualized Cost (euro/yr)

Dam

age

to H

uman

Hea

lth (P

oint

s)D

amag

e to

Eco

syst

em Q

ualit

y (P

oint

s)

Dep

letio

n N

atur

al R

esou

rces

(Poi

nts)

EQHHDR

1.06

1.08

1.12

1.10

1.04

1.02

1.14x10 4

Fig. 10. Total annualized cost vs impact damage categories. Case study II: Absorptioncycle.

1 2 3 490

91

92

93

94

95

96

97

98

99

100

Objective functions

Perc

enta

ge w

ith re

spec

t to

the

max

imum

val

ue (%

)

DREQHHTAC

Fig. 11. Parallel coordinates plot. Case study II: Absorption Cycle. Objective functions:Total annualized cost (TAC), damage to human health (HH), damage to ecosystemquality (EQ), and depletion of natural resources (DR).

Table 6Extreme solutions. Case study II: Absorption cycle.

Objective function Min TAC Min HH Min EQ Min DR

TAC [V/yr] 21,917 22,940 22,951 22,954HH [points] 2734 2584 2593 2593EQ [points] 2740 2582 2565 2578DR [points] 11,228 10,568 10,552 10,497

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377 375

minimum environmental impact alternatives. The main differenceconcerns the duty provided to the system (140 kW vs. 131 kW).These results are consistent with the fact that the environmentalimpacts are highly dependent on the steam supplied to the reboiler.The extreme designs differ also in the reflux ratio of the

Table 5Details of the extreme solutions. Case study II: Absorption cycle.

Variable Min TAC Min HH Min EQ Min DR

Reboiler duty [kW] 140.39 131.79 131.05 131.11High pressure [bar] 13.28 12.95 12.96 12.95Low pressure [bar] 4.48 4.82 4.97 4.93Mass flow of stream

1 [kg/s]0.32 0.33 0.33 0.33

Ammonia fractionof stream 1

0.51 0.53 0.54 0.54

Temperature ofstream 5 [�C]

41.15 38.27 38.20 38.16

Temperature ofstream 9 [�C]

20.20 21.45 22.80 22.08

Reflux ratio (mass) 0.055 0.043 0.042 0.042Number of trays 1 1 1 1Feed tray 1 1 1 1COP 0.63 0.67 0.68 0.68Total exchange

Area [m2]89.13 119.77 120.26 120.34

Steam [kg] 904,972 838,389 837,074 836,897Electricity [MJ] 10,895 10,454 10,544 10,542

rectification column and the temperatures of stream 5 and 9. Withregard to the discrete variables, all of the designs lead to a rectifi-cation column with one single stage. In the minimum TAC, theenergy consumption rate in the reboiler and reflux ratio in therectification column are larger than in the minimum impact one.

As observed, solutions with minimum impact show larger COPvalues and greater exchanger areas. The exchange area in thesesolutions is approximately 31% greater than in the minimum TACdesign. This is due to the fact that the contribution of the mass ofsteel to the total impact is rather small. Regarding the use of energy,the minimum TAC solution consumes approximately 8% moresteam and 4% more electricity than the minimum environmentalimpact one. Hence, the impact caused during the operation phase ismore significant than that associated with the construction phase.Particularly, the construction of the equipment units contributesaround 4% to the total EI. As observed in Table 6, the TAC in theminimum cost solution is 4.67%, 4.71% and 4.73% lower than in theoptimal HH, EQ and DR solutions, respectively. Moreover, HH, EQand NR can be reduced by up to 5.80%, 6.82%, and 6.96%, respec-tively, compared to the minimum TAC solution.

6. Conclusions

This work has introduced a computational approach for theoptimal design of thermodynamic cycles considering economic andenvironmental concerns. Our approach combines simulationpackages with rigorous deterministic mathematical programmingtools and LCA analysis. The capabilities of this approach were testedin two thermodynamic cycles: a steam power cycle and anammonia-water absorption cooling cycle, for which we minimizedthe total annualized cost and a set of environmental impactsmeasured in three LCA damage categories.

Numerical results showed that the environmental performanceof thermodynamic cycles can be improved by compromising theireconomic performance. We also found that the main contributionto the total impact is the operation phase. The optimization of theindividual damage categories produces similar results, indicatingredundancies between them.

Acknowledgements

The authors wish to acknowledge support from the SpanishMinistry of Education and Science (projects ENE 2011-28269-CO3-03) and the Spanish Ministry of External Affairs (projects PHB2008-0090-PC).

Appendix A. Life cycle assessment of the thermodynamiccycles

The environmental impact is quantified following LCA princi-ples, in a similar manner as done before by the authors in otherworks [47e50]. The LCA comprises four phases [51]:

1. Goal and scope definition. This phase defines the systemboundaries, functional unit, assumptions made and type ofimpact assessed. The system boundaries correspond to the

R. Brunet et al. / Applied Thermal Engineering 48 (2012) 367e377376

limits of the energy system. The functional unit is defined asa given amount of power/cool generated. We quantify theimpact in three categories: damage to human health (HH),damage to ecosystem quality (EQ), and damage due to deple-tion of natural resources (DR).

2. Life cycle inventory analysis (LCI). This phase quantifies theinput and output flows associated with the operation andconstruction of the cycles. The damage during the operationphase is given by the natural gas and electricity consumptionrates, which are retrieved from the process simulation. Thisinformation is translated into the corresponding LCI usingenvironmental databases. The LCI of the construction phase isapproximated by the LCI of the mass of steel contained in theprocess units.

3. Life Cycle Impact Assessment. This phase translates the LCI intothe corresponding environmental damages (denoted by thecontinuous variable DAMd) using damage factors (dfb,d) avail-able in the literature [16].

DAMd ¼Xb˛B

dfb;d$LCIb (8)

4. Life cycle interpretation. In this phase, the LCA results areanalyzed and a set of conclusions and recommendations areformulated. In this work, this step is carried out in the postoptimal analysis of the optimal solutions found.

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Nomenclature

Sets/IndicesD: decision variablesE: equality constrainsI: inequality constraintsi: topologyj: external equality and inequality constraintsj˛ EQ: external (explicit) equality constraintj˛ IEQ: external (explicit) inequality constraintk: iterationo: objective functionsu˛HX: heat exchangersu˛U: equipment units

AbbreviationsA: AbsorberC: CondenserCOP: Coefficient of performanceDR: Depletion of natural resourcesE: EvaporatorEI: Environmental impactEQ: Damage to ecosystem qualityHH: Damage to human healthLCA: Life cycle assessmentLCI: Life cycle inventory analysisMILP: Mixed-integer linear programming

moMINLP: Multi-objective mixed-integer non-linear programmingmoNLP: Multi-objective non-linear programmingMOO: Multi-objective optimizationNLP: Non-linear programmingNPV: Net present valueP: PumpRC: Rectification columnSC: Refrigerant subcoolerSHX: Solution heat exchangerSQP: Successive quadratic programmingTAC: Total annualized costTPC: Total plant costVLV1: Refrigerant expansion valveVLV2: Solution expansion valve

VariablesAm: Heat exchanger area of unit m (m2)CF: Fixed cost (V)Cb: Exchange area (m2)Cu: Cost of the unit (V)CO: Operating cost (V/yr)DAMd: Environmental damages (Points)Diam: Diameter of the rectification column (m)H: Height of the rectification column (m)LCIb: Input and output flows (kg/yr)Qu: Heat transfer of unit u (kW)TAC: Total annualized cost (V/year)Wu: Mechanical power of unit u (kW)a: Auxiliary variableQ: Penalty value for the constraint violation

Parametersc1: Cost parameter (V/m2)c2: Cost parameter (V)c3: Cost parameter (V/kW)cq: Unitary cost of steam (V/MJ)cw: Unitary cost of electricity (V/MWh)crf: Capital recovery factordfbd: Damage factors (Points/kg)deuro: Conversion from dollars to euros (V/$)Fc: Cost factor that depends on the type of columnfd: Coefficient of the design typefp: Coefficient of the design typefm: Coefficient of the material constructionM & S: Cost factortop: Operational hours (h/yr)