Multi-Objective Optimization in Distillation Unit: A Case Study

604 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 84, OCTOBER 2006

INTRODUCTION

Various levels of ecological degradation have brought environmental issues into current social awareness. The chemical process industry, due to its high complex

nature, is facing major challenges in responding to the political and social imperatives of continuous improvements in its environmental performance while at the same time ensuring its economic and fi nancial validity. However, several attempts have been made to integrate environmental and health considerations with economics in early stages of process design (Chen and Shonnard, 2004; Kheawhom and Hirao, 2004; Palaniappan et al., 2002; Sharrat, 1999). A variety of environmental indicators have been used in the environmental assessment of chemical processes from simple mass balance indices to more complicated methods based on multiple media, multiple exposure pathways, and multiple categories of impacts. For example, Hoffman et al. (2001) have used an input-based indicator, Material Intensity Per Service unit (MIPS), as an environmental proxy measure for the evaluation of alternatives. This does not account for the release

Multi-Objective Optimization

in Distillation Unit: A Case Study

Naveed Ramzan* and Werner Witt

Lehrstuhl Anlagen und Sicherheitstechnik, Brandenburgische Technische Universität,Burger Chaussee 2 Lehrgebäude 4/5, Cottbus 03044, Germany

of substances to the environment and thus can produce mislead-ing results. Therefore, emission based indicators are more accurate in representing actual impacts.

Today, detailed process design tasks involve simulation, evaluation and optimization of the entire process. In fact, optimi-zation is one of the most important steps in any chemical process design. Over the past decade, optimization of environ-mental performance has started to incorporate alongside traditional economic criteria. Several systematic methodologies are available for detailed characterization of environmental impacts of chemicals, products and processes and have been incorporated into the design and optimization of chemical processes. The most commonly used methods are Life Cycle Assessment (LCA) (Azapagic and Clift, 1999a, b; Azapagic, 1999), Methodology of Environment Impact Minimization (MEIM) (Stefanis and Pistikopoulos, 1997), Waste Reduction

Increasing social pressure and strict legislations have resulted in changing the approach of traditional design practices to incorporate multiple objectives in the design of process plants. Distillation is one of the major operations in the chemical process industry that is widely used for purifying products or recovering solvents or separation of valuable reactants from waste stream. In this paper, a procedure for multi-objective optimization is discussed with the help of a distillation unit from hydrocarbon recovery plant of a distillate fraction process. The procedure developed here consists of four stages and is based on current design tools. The aim is to support decisions during design phase and optimize the process variables in order to generate a process with improved economics along with satisfaction of environmental objectives. Total potential environment impact and total annualized cost are used as indicator for environmental and economic objectives, respectively.

La pression sociale croissante et les législations strictes ont eu pour effet de modifi er la manière traditionnelle de concevoir les pratiques de façon à inclure des objectifs multiples dans la conception des installations de procédés. La distillation est une des opérations importantes de l’industrie des procédés chimiques et est largement utilisée pour purifi er des produits ou récupérer des solvants, ou encore pour séparer les réactifs intéressants dans les courants de résidus. On analyse dans cet article une méthode d’optimisation à objectifs multiples à l’aide d’une unité de distillation venant d’une installation de récupération d’hydrocarbures d’un procédé de fraction de distillat. La méthode mise au point ici consiste en quatre phases et utilise des outils de conception courants. Le but est d’appuyer les décisions lors de la phase de la conception et d’optimiser les variables de procédés afi n de fournir un procédé offrant de meilleures économies ainsi que la satisfaction de répondre à des objectifs environnementaux. L’impact environnemental potentiel total et le coût annualisé total sont utilisés comme indicateurs pour les objectifs environnementaux et économiques, respectivement.

Keywords: multi-objective optimization, total annualized cost, distillation unit

* Author to whom correspondence may be addressed.E-mail address: [email protected]

VOLUME 84, OCTOBER 2006 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING 605

Algorithm (WAR) (Cabezas et al., 1997, 1999; Young and Cabezas, 1999) and Environmental Fate and Risk Assessment (EFRAT) (Shonnard and Hiew, 2002).

Distillation is one of the major operations in the chemical process industry carried out for the separation of liquid mixtures into their components. In particular it is used for purifying products or recovering solvents or valuable reactants from waste stream which otherwise results in pollution to the environment and loss of economic performance of the process. However, designing a distillation process does not guarantee a benefi t to the environment unless design process incorporated both economic and environmental benefi ts simultaneously. Kim and Smith (2004) discussed the design of waste solvent recovery process (Batch Distillation to recover acetic acid) for maximizing total profi t and minimizing potential environmental impacts. Mukhatri (2000) has described the economic optimization by sensitivity analysis using AspenPlus™ for a distillation (stripping column) unit for hydrocarbon recovery from a waste stream.

In the present paper, the selection of best alternative design, from both economic and environmental points of view, of the distillation (Stripping column) unit for recovering hydrocarbons and other solvents from the off gases of the distillate fraction plant, has been described. The remainder of the paper has been divided in seven sections. The second section explains the multi-objective optimization problem and the state of art techniques available for its solution. The third section describes the basic scheme of the systematic procedure adopted for this problem and the fourth section explains calculation loop of multi-objective optimization using AspenPlus™. In the fi fth section, the problem at hand is defi ned in detail and the solution approach described in the third section is applied to solve it. The results obtained are discussed with recommendations. The conclusions and future work are described in sixth and seventh sections, respectively.

MULTI-OBJECTIVE OPTIMIZATION PROBLEM AND SOLUTION APPROACHESMulti-objective optimization problem is also called multiple-criteria (multi-criteria) optimization problem or vector optimiza-tion problem. The task is to fi nd the optimum, which minimizes or maximizes multitude of objectives that are subjected to a number of constraints and bounds.

MinimizeX

F X∈ ℑ

( )

where

F X f X f X f Xm( ) ( ), ( )........ ( )= { }1 2

subject to:

h Xg Xlb x ub

ij

k

( )( )

=≤

< <

00

i = 1 ... qj = 1 ... pk = 1 ... n

(1)

The elements of the multi-objective optimization problem are design vector X, design variables (upper and lower boundary limits, lb and ub, respectively), equality constraints hi(X) = 0, inequality constraints gj(X) ≤ 0, and multiple confl icting objective functions F(X). In relationship to the case study (see Case Study section) these elements can be described as follows. The design vector X= [x1, x2… xn] has to be within the decision space ℑ with lb < xk < ub where k = 1, 2, … n and consists of all

design and process variables, e.g. column diameter (x1), steam rate (x2), etc. The mathematical basis of the problem e.g. mass and energy balance equations, thermodynamic equilibrium relations, etc. represent the equality constraints hi(X) = 0. All of the conditions, i.e., concentration of the bottom product in the distillation system such as xMethanol in B ≤ 0.02 represents inequality constraints gj(X) ≤ 0. The objective function vector F(X)={f1(X), f2(X)………fm(X)} takes the form F(X)={TAC(X), PEI(X)}where

TAC = Total Annualized Cost PEI = Potential Environmental Impact

Since the components of objective function vector are competing in general there is no unique solution to this problem, rather it is the non-dominated set, also known as the Pareto set after the French Italian economist and sociologist Vifredo Pareto. This set is the collection of alternatives that represent potential compro-mise solution among the objectives. Mathematically, the non-dominated solution can be defi ned as if X’ is a particular set of feasible values for the decision variable vector X. A solution X* is non-dominated if it is feasible and if there is no other feasible solution X’ such that:

F X F Xi i( ) ( )’ *≤ i=1, 2, 3 m …… (2)

where m is the number of objectives, and with at least one of these inequalities is a strict inequality (assuming all objectives are to be minimized). Each point along the non-dominated set in the objective space has an equivalent point in the decision space but the graphical interpretation of non-dominance applies only in the objective space. The corresponding decision variables can be found by using the objective values. All the solutions in the non-dominated set are candidates for selection and are selected depending on decision maker’s preferences. Thus, moving along the non-dominated set is essentially trading off one objective for another. In Figure 1, the curve AB represents the non-dominated solution set or Pareto optimal trade-off surface.

There is a large array of techniques for multi-objective optimi-zation problems (Diwekar, 2003). However, we can divide the solution approaches to multi-objective optimization problem into two groups (Kalyanmoy, 2001):• Ideal multi-objective optimization procedures;• Preference-based multi-objective optimization procedures.

In ideal multi-objective optimization, multiple trade-off optimal solutions with a wide range of values for objectives are found fi rst and thereafter higher level information is used to

Figure 1. Pareto optimal trade-off surface


However, this method also has some weak points, which are: 1. Diffi culties in locating the extreme points;2. Many runs are necessary to fi nd the Pareto front.Goal Programming method gained much popularity for solving multi-objective optimization problems. In goal programming (GP) the objectives are formulated as goal criteria that the decision maker desires each objective to possess. The criteria could be formulated in the following ways. We want the objective to be:

Minimizaion:Maxmization: (5)Equality:Range:

Usually a point that satisfi es all goals is not a feasible solution. The goal programming problem is to fi nd the point in objective space whose criterion vector “best” compares with the utopian set, i.e., has the smallest deviation from the utopian solution. Different types of goal programming methods use different ways of determining which point in objective space compares best with the utopian solution set (Mistree and Hughes, 1993; Diwekar, 2003).

The Archimedean GP uses a weighted metric to determine the “best” solution. In lexicographic GP or pre-emptive GP, the goals are grouped according to priorities. In the fi rst stage a set of solutions which minimizes the deviation to the goal with highest priority is obtained. In the second stage this set of solutions is searched to fi nd a subset that minimizes the deviation from the second most important goal. The process continues until only one single point is left as the fi nal solution.

In this work, goal programming is used to carry out multi-objective optimization. The Pareto trade-off surface is obtained and then, considering the decision makers preferences, optimum solutions for different alternatives are compared using the Pareto approach.

SYSTEMATIC PROCEDUREThe aim of developing a systematic procedure is quantifi cation of all the environmental and economic effects during design phase in order to support decision-making process. The basic systematic procedure followed and the tools used to handle the problem are shown in the form of simplifi ed block diagram in Figure 2. The schematic procedure consists of four layers/stages:1. Generation of process alternatives and problem defi nition

stage;2. Analysis of alternative stage, i.e., generation of relevant data

for comparison of environmental and economic objectives;3. Multi-objective optimization stage;4. Design evaluation stage, i.e., decision making from the

Pareto-surface of non-inferior solution.

Stage 1: Generation of Process Alternatives and Problem Defi nition In stage 1, the following tasks are to be included for clear understanding of the process:• Defi nition of the scope of the study;• Statement of key assumptions and the performance targets;• Identifi cation of the key design, control, and manipulated

variables;

choose one of the trade-off solutions. Evolutionary Algorithms, i.e., Genetic Algorithms and Evolution Strategies fall in ideal multi-objective optimization procedures. Several authors (Coello, 2000; Shim et al., 2002; Van Veldhuizen and Lamont, 2000) have given a comprehensive survey of state of the art multi-objective evolutionary algorithm techniques. Bhasker et al. (2000) has discussed its applications in the fi eld of chemical engineering.

Although these methods have advantages which are less subjective, more practical, and methodical but at the same time have some problems e.g. these are often complex and the number of optimal solutions are often too large that make it diffi cult for decision makers to analyze and understand effectively. Also, the computational burden and cost of these methods are high.

The simplest method would be to scalarize an objective vector into a single component objective function, which converts the multi-objective optimization problem into single objective optimization problem. Based on higher level information, a preference vector is used to construct the composite function, which is then optimized to fi nd a single trade-off optimal solution. This procedure of handling multi-objective optimiza-tion problem is called preference based multi-objective optimiza-tion procedure. Classical optimization methods such as Weighted Sum Method, €-Constraint Method, and Goal Programming Method fall into this category and are widely used.

The idea of weighting method (Diwekar, 2003) is to associate each objective function with a weighting coeffi cient and minimize the weighted sum of the objectives, i.e., turn the multi-objective problem into single objective optimization problem and then any traditional technique for solving the problem can be used. This is mathematically described as:

F X w f X f

w 0 w

i ii

mT

i ii

m

( ) ( )

,

= =

> =

=

=

∑

∑1

1

1

w (3)

Theory (Kuhn-Tucker conditions) predicts that as long as all weights are greater than zero, the optimal solution of the weighted problem is a Pareto optimal solution (Diwekar, 2003). Although the formulation of this method is simple it has disadvantages. The disadvantages of this method are (Kalyanmoy, 2001; Diwekar, 2003):1. Fails on non-convex Pareto fronts;2. An evenly distributed set of weighting factors does not

necessarily produce an evenly distributed representation of the Pareto set;

3. Many runs are necessary to fi nd the Pareto front.Many of these disadvantages can be overcome by the €-Constraint method. In the €-Constraint method one objective, i, is selected for optimization and the others are reformulated as constraints, i.e.:

MinimizeX

f X∈ ℑ

1( )

subject to:

F Xh Xg X

m mij

( )( )( )

≤ ≠=≤

ε m = 1 ... n but m li = 1 ... qj =

00 11 ... p

k = 1 ... n lb x ubk< <

(4)

f X gf X g

f X gf X g g

p p

p p

p p

p pl

pu

( )( )

( )( ) [ , ]

≤≥

=∈


WAR developed by US Environmental Protection Agency is used as environmental module for generation of environmental related data. Using information from process module and environmental module, process diagnostic summary tables are generated in the data manager. These tables consist of mass input/output table, energy input/output table, capital and utility annual expense summary, and environmental impact summary.

Stage 3: Multi-Objective OptimizationThe purpose of this stage is to set-up multi-objective optimiza-tion among these confl icting objectives. Total annualized cost as economic objective and potential environmental impact as

environmental objectives are used. The aim is to fi nd out the trade-off surface for each alterna-tive. From the trade-off surface, the best compromise design depending on the decision maker’s preferences is obtained. The way of strategy to carry out multi-objective optimization using AspenPlus™ and MatLab are described in Figure 3.

Stage 4: Design EvaluationIn the fi nal stage, the best compro-mise design obtained for each alternative are compared. The Pareto approach is very appropri-ate for this purpose and is used widely in academia as well as in governmental institutions such as the U.K. Environmental Agency and its methodology for the defi ni-tion of the Best Practicable Environmental Option (BPEO).

• Defi nition of the system boundary;• Identifi cation of constraints;• Choice of functional unit for all calculations, i.e., SI, or AES;• Collection of relevant information about the process and

chemicals to be handled;• Generation of different alternatives.

Stage 2: Analysis of AlternativesThis stage is composed of process module, environmental module, and data manager. In the process module, each alterna-tive is modelled using AspenPlus™ and various steady state simulation runs are performed to generate relevant data. The

Figure 2. Block diagram of systematic procedure

Figure 3. Calculation loop for multi-objective optimization


where acidity is the sum of the mass fraction of the acids i.e acetic acid, formic acid, and propionic acid in the base stream.

The aim is to optimize the control variables or operating conditions and select the best alternative, which minimizes the cost and environmental impact.

The base case D-I (Existing column unit) is a simple multi-component distillation unit. The primary source of ineffi ciency in multi-component, simple distillation is due to the irreversible mixing of non-identical streams (Shah, 2002). Simple columns are forced to sacrifi ce effi ciency to achieve product specifi cation in multi-component systems. The concentration of middle boiling components often reaches a maximum on intermediate trays and then decreases to satisfy the overall mass balance. This remixing (backmixing) inherently affects the effi ciency of separation. Another potential source of mixing is due to the differences between the composition of the feed stream and the liquid composition on the feed tray. The use of complex column confi gurations can minimize these mixing losses, as well as reduce energy consumption and decrease capital costs. Therefore, the main alternative proposed is to withdraw a side stream from the bottom section of the column. The further alternatives are generated by varying the number of trays. Thus, a total of six alternatives namely, D-I, D-II, D-III without side streams, and D-IV, D-V, D-VI with side streams are considered for study (Figure 4). The goal is to select the best alternative, which satisfi es both objectives.

Stage 2: Analysis of Alternatives

Process ModuleA base case process model is used to evaluate the current performance of the process and serves as a guide to analyze different alternatives. For this study, tray-by-tray model applying mass and energy balances and equilibrium relations at each tray in the column (MESH equations) is used for distillation unit with and without side stream. The independent variables are the product rates and compositions, internal vapour, liquid rates and compositions, and stage temperatures. Equilibrium constants, K values, and mixture enthalpies are dependent variables. Variables related to feed conditions are known or set. In this case study the feed and side stream fl ow rate are fi xed because of the capacity constraints of upstream and downstream units in the plant. Therefore, the refl ux ratio and steam rate are selected as two remaining degree of freedoms for optimization of each alterna-tive to meet two composition specifi cations in the top and bottom products.

A number of rigorous methods are available to solve such set of equations. However, the well supported Boston Method with a wide variety of features, options and power to solve a wide range of columns is in the RADFRAC and the MULTIFRAC methods of AspenPlus™. Therefore, the base case model is developed using RADFRAC (Kister, 1989). Once the model is confi gured in AspenPlus™, several simulation runs are carried out for each alternative for the study of the actual behaviour of the system and setting operational constraints.

Economic ModuleA variety of methods are available in the literature of chemical engineering economics for economical evaluation of chemical processes (Baasel, 1990; Doherty and Malone, 2001; Guthrei, 1969; Peters and Timmerhaus, 1991; Warren et al., 1999). Return on investment (ROI), net present value (NPV), pay back period

The Pareto-approach aims at eliminating alternatives that are clearly dominated, i.e., other feasible alternatives exist, which are better with regard to both or more objective functions. This strategy can easily be translated into a vectorial language if discrete data is considered.

CALCULATION LOOP FOR MOOP USING ASPENPLUS™The calculation loop used for multi-objective optimization problem (MOOP) is shown in Figure 3. First economic optimiza-tion of each alternative is carried out using SQP optimization algorithm build within AspenPlus™. The value of economic objective function obtained from this optimization act is an economic goal in multi-objective optimization. The lower and upper limits for environmental objective functions are calculated using WAR algorithm from the material and energy balance information from process model. The DataManager (Excel Spreadsheet) acts as working platform linked with environmental module (WAR), Proces module (AspenPlus™) and with MatLab 7.0 for multi-objective optimization. The ActiveX technology (also called OLE automation) enables external windows applica-tion to interact with AspenPlus™ through a programming interface using Microsoft Visual Basic 6.0. With this automation interface the inputs and the results of AspenPlus™ simulation is connected to the DataManger. HappLs (IHapp) and HappIP are objects exposed by AspenPlus™. Through one of these objects, the other objects and their properties and methods in AspenPlus™ are accessed within the DataManager. The input and result data in the AspenPlus™ simulation are exposed as a tree structure of IHNode node objects. The root node of the tree is obtained by the tree property of HappLS. Each IHNode object may have zero or more offspring IHNode objects. Each IHNode object has a dimension property, which determines how the offspring nodes are organized. The optimization toolbox of MatLab is accessed in the DataManager via Excel Link Tool box provided in MatLab 7.0. The fgoalattain() function is used for multi-objective optimization and fmincon() and SQP optimizer within AspenPlus™ is used for single objective optimization for setting the goals.

CASE STUDYThe systematic procedure is demonstrated with the help of a stripping column case study taken from a real chemical plant and is described here.

Stage 1: Problem Defi nition and Generation of AlternativesThe unit under discussion is part of a hydrocarbon recovery plant, which removes hydrocarbons and other solvents from the off-gases of the distillate fraction plants. Water, acetone, methanol and acetic acid are the main components of the feed stream. The product stream (acetone rich) is separated from the effl uent by using live steam injection. The column has a diameter of 0.728 m and consists of 35 trays. The live steam is entered at stage 35 (the stages are numbered from top to bottom) at a temperature of 141ºC and a pressure of 375 kPa. The feed, which is at its bubble point, is entered at stage 16 with a column head pressure of 100 kPa. The separation targets (mass %) are:

Distillate: water < 10%Base: acetone < 2000 ppm methanol < 2% acidity < 3%


(PBP), and total annualized cost (TAC) are commonly used as economic indicators. In this work total annualized cost is used as economic objective function.

TAC = 0.20 (TCI) + Operating Cost (6)

where

TAC = Total Annualized CostTCI = Total Fixed Capital Investment

The total capital investment for most of the distillation units includes the column cost, tray cost, condenser cost, and reboiler cost. The column and tray cost is sensitive to factors such as tray spacing, number of stages, column diameter, etc. Condenser and reboiler cost depends on heat transfer areas required. Signifi cant operating cost with distillation units are associated with the cooling (water) and heating (steam) utilities cost. Although cost of these utilities vary according to local conditions but guidelines are available in literature to calculate these costs. So the total annualized cost of the distillation system is:

TAC f N D A A C Q C Qt col con r w con steam r= ( ) + +, , , (7)

A total annualized cost model in this case is:

Column cost (Warren et al., 1999):

C L D F pcol col M c= + −1780 2 86 1 694 10 01 7 4080 87 1 23 . . [ . . ( . . ln ool

colp)

. (ln ) ]+1 395 2 (8)

Tray cost (Warren et al., 1999):

C D D F N Ftray col col MB t q= + +⎛

⎝⎜⎜

⎞

⎠⎟⎟( . . . )193 04 22 72 60 38 2

(9)

Condenser cost (Warren et al., 1999):

C A F pcon con M con= +450 1 65 1 220 7 0 09 . .( . . ) (10)

Reboiler cost (Guthrei, 1969):

C C F F F Ireboiler ob d p M= +( ) (11)

where Cob is obtained from Guthrie’s cost charts and Fd depends on the reboiler type. For kettle type reboiler Fd = 1.35

Operating Cost

C C F C Qop steam steam w con= + (12)

so

TAC C C C Ccol tray con op= + + +0 20. ( ) (13)

where L = Lmin + HtNtMaterial Factor FM = 4; FMB=2; Fq=1Steam cost = $ 8/1000 kg at p = 1206 kPaCooling water cost = $0.0246/1000 kgTray spacing Ht = 0.3 m; Lmin= 3 Ht

Figure 4. Column alternatives generated


Since live steam is injected into the column from plant and no reboiler is used C reboiler = 0 for this case study.

Environmental ModuleThe total potential environmental impact (PEI) is used as the environmental objective function. The total potential environ-mental impact is expressed in terms of different potential impact indexes such as human toxicity potential by ingestion (HTPI), human toxicity potential by inhalation or dermal exposure (HTPE), ozone depletion potential (ODP), global warming potential (GWP), acidifi cation potential (AP), photooxidation chemical potential (POCP), aquatic toxicity potential (ATP), and terrestrial toxicity potential (TTP), which are combined together using weighting factors, ∞n. The generalized formulation for PEI based on WAR algorithm is:

Minimize PEI where

PEI I

I M Q

n ncp

n

EnvCat

ncp

j njnj

r jE

j

= ∞

= +

=∑

∑∑ ∑

.1

Ψ Ψ (14)

The impact Icpn has two contributions. First contribution is due to the waste stream (base stream) after distillation and second due to energy consumption during distillation. The values of normal-ized impact scores of chemicals for different categories of environmental impact and normalized impact score of coal energy (as coal is being used as fuel for steam production in the plant) used in the calculation of PEI are given in Tables 1 and 2, respectively. The total mass fl ow rate of each stream is multiplied by the sum of normalized impact scores of the chemical in that

stream for each category to calculate potential impact of that category due to fi rst contribution and heat duty is multiplied with the normalized impact scores of energy of each category to calculate the second contribution. The weight given to each category (Table 3) based on the methods described in eco-indica-tor99 (framework for life cycle assessment) is multiplied with the potential impact of that category and then summed together to give the total potential environmental impact of the stream. The potential environmental impacts of the product streams (distillate and side stream) are considered as zero.

Sensitivity AnalysisTo make better decisions, it is of value to carry out a sensitivity analysis. The aim of the sensitivity study is to identify the value of potential variables that result in preference for different alterna-tives. Thus, a number of simulations for different conditions are performed using the process model developed for each alternative. For each simulation run, economic and environmental perform-ance objectives are calculated using economic and environmental models. The relevant data for each alternative are transferred into the data manager. Diagnostic summary tables are set-up in the data manager and sensitivity of performance objectives with respect to key operating variables is studied so that good initial guess is made for optimization calculation loop. A sample result of sensitivity analysis performed is shown in Figure 5.

Table 1. Normalized impact scores for different categories of potential environmental impact of chemicals involved in the case study

Normalized Impact Score (Ψ)

Chemical HTPI HTPE TTP ATP GWP ODP PCOP AP

Methanol 0.0626 0.0011 0.0626 0 0 0 0.2462 0

Acetaldehyde 0.5332 0.0008 0.5332 0.0265 0 0 1.0547 0

Methyl formate 0.1696 0.0012 0.1696 0.0061 0 0 0 0

Ethanol 0.0499 0.0002 0.0499 0.0001 0 0 0.5364 0

Acetone 0.0608 0.0001 0.0608 0.0001 0 0 0.3562 0

Methyl acetate 0.1375 0.0005 0.1375 0.0023 0 0 0.05 0

Methyl ethyl ketone 0.1288 0.0005 0.1288 0.0003 0 0 0.9466 0

Ethyl acetate 0.0627 0.0002 0.0627 0.0039 0 0 0.4363 0

Water 0 0 0 0 0 0 0 0

Acetic acid 0.1065 0.0117 0.1065 0.0107 0 0 0 0

Formic acid 0.3204 0.0326 0.3204 0.022 0 0 0 0

Propoinic acid 0.1007 0.0098 0.1007 0.0141 0 0 0 0

Table 3. Weighting factors used in case study for different categories of potential environmental impact

Weighting factors (∞)

HTPI HTPE TTP ATP GWP ODP PCOP AP

5 5 10 10 2.5 10 2.5 10

Table 2. Normalized impact score of coal energy for different categories of potential environmental impact

Normalized Impact Score of Energy (ΨE)

HTPI HTPE TTP ATP GWP ODP PCOP AP

7.83 x 10–5 1.22 x 10–6 7.83 x 10–5 2.65 x 10–4 2.03 x 10–9 1.93 x 10–4 7.07 x 10–8 5.98 x 10–3


Figure 5. Sensitivity analysis results for alternative D-I

Stage 3: Multi-Objective OptimizationIn this stage, multi-objective optimization is set-up for each alternative to fi nd the best compromise solution, which is compared to select the best alternative. The multi-objective optimization problem for each alternative is:

Min F(X) → Min {TAC, PEI}

subjected to constraints, such as:

h X

g X

i

j

( )

( )

= → {

≤ →

0

0

MESH Equations x in B = 0

x

Acetone

H2O iin D 0.1 x in B 0.02 Acidity in B 0.03Constra

Methanol

≤≤

≤iint on feed

Feed 4000 kg/hEnvironmental impactPEI/h 3.

≥

≤ 0047E03

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

(15)

where X = [refl ux ratio, steam rate]

Though the constraint on acetone mass fraction in the base stream in the plant is:

xAcetone in B < 2000 ppm ~ 0.0022

However, in the case study xAcetone in B = 0 is introduced to the optimizer even though acetone is always present in real time scenarios in the base stream in traces but well below the limit (2000 ppm).

The optimization is carried out according to the calculation loop described in Systematic Procedures section and the Pareto trade-off surface for each alternative is obtained. Figure 6 shows Pareto trade-off surface for alternative D-I. The point P (TACmin, PEImin) represents the ideal solution where both objectives are at their minimum value and practically impossible to achieve. From the Pareto trade-off surface, a solution close to this ideal solution or a solution considering the preferences of the decision maker is selected for comparison of alternatives. Here, consider-ing the solution giving minimum total annualized cost along with satisfying the environmental objective constraint for alternative D-I is selected for comparison using Pareto approach. The summary of solution results selected for each alternative for comparison is given in Table 4 which clearly shows that withdrawal of side stream has a considerable effect on potential environmental impact. In effect, this reduces the potential environmental impact per kg from 0.796 to 0.560 but does not have considerable effect on total annualized cost. In the case of design alternatives with side stream (D-IV, D-V, D-VI) the variables refl ux ratio, steam rate, feed rate, and value of objective function PEI remains approximately same and total annualized

(a)

(b)

Figure 6. Pareto trade-off surface for D-I

(c)


cost reduces from D-IV to D-VI due to reduction in number of trays. In the case of design alternatives D-I, D-II, D-III without side stream, D-II has the minimum value of steam rate which results in minimum operating cost but have highest potential environmental impact. The D-III alternative gives the lowest value of PEI among alternatives without side stream but very high steam rate that makes its operating cost high. The refl ux ratio does not remain same in these alternatives because of different steam rate requirements to meet the purity. The next stage is to compare these alternatives for fi nal selection.

Stage 4: Design Evaluation The Pareto approach is used to fi nd the best alternative in the fi nal stage. The optimum solution of each alternative is located in the objective space for fi nding non-dominated solution or edegeworth Pareto optimal design (Figure 7). A solution that is not dominated by any other individual solution is said to be non-dominated solution. The non-dominated alternative in the current set of design alternatives is identifi ed. This alternative is considered the best and assigned as rank 1 in Figure 7. The alternative D-VI comes at rank 1. Considering this alternative as being virtually removed from the set of alternatives, the next set of non-dominated solutions are identifi ed and assigned rank 2. As shown in Figure 7, D-IV and D-III fall in this rank. This process is continued until all alternatives have been ranked.

CONCLUSIONSThe aim of this paper is to present a procedure for multi-objective optimization for incorpo-rating environmental objectives, along with economics, into design of chemical process units. The procedure is particularly suitable for screening alternatives on the basis of both economic and environmental considerations. Total potential environmental impact based on WAR algorithm and total annualized cost are used as environmental and economic performance indicators. The procedure was implemented by integrating in-house software with commercial simulation tools. The procedure is demonstrated with the help of

the distillation (stripping column) unit for recovering hydrocar-bons and other solvents from the off-gases of the distillate fraction plant.

FUTURE WORKIncreasing social pressure and strict legislations have resulted in changing the approach of traditional design practices to incorpo-rate multiple objectives in the design of process plant. Accordingly, we will extend the method in order to integrate other objectives like safety, for example, as well.

NOMENCLATUREAcon heat transfer area of condenserAr heat transfer area of reboilerB base stream fl ow rateCcol distillation column costCcon condenser costCob base cost of reboilerCop operating costCsteam steam cost per unitCtray tray costCw cooling water cost per unitD distillate fl ow rateDcol diameter of the columnEFRAT environmental fate and risk assessmentFd heat exchanger type factorFM material factorFMB bare module factorFp pressure factorFq quantity factorFsteam steam fl ow rateF(X) vector of objective functionsGP goal programmingg p vectors of goalsg(X) vector of inequality constraints, gj(X)Ht tray spacingh(X) vector of equality constraints, hj(X)I cost indexIcpn potential environmental impact due to

each category L height of columnlb lower boundLCA life cycle assessmentLmin minimum height of columnMEIM methodology of environment impact minimization

Table 4. Optimization results for each alternative

D-I D-II D-III D-IV D-V D-VI

Number of trays 35 32 30 35 32 30

Diameter m 0.728 0.728 0.728 0.728 0.728 0.728

TAC $/a 345884 319451 311847 343788 321698 306869

PEI / kg 0.796 0.988 0.742 0.560 0.509 0.510

PEI / h 7.81E02 8.89E02 7.75E02 7.06E02 7.09E02 7.10E02

Feed rate kg/h 4000 4000 4000 4000 4000 4000

Steam rate kg/h 589 540 630 572 570 569.5

Refl ux ratio 0.7 0.628 0.6370 0.7 0.7 0.7

Figure 7. Non-dominated set analysis


MIPS material intensity per unitMj mass fl ow rate of stream jNt total number of stagesPEI potential environmental impactpcol column design pressurepcon condenser design pressureQcon condenser loadQr reboiler loadSQP sequential quadratic programmingTAC total annualized costTCI total fi xed capital investmentub upper boundWAR waste reduction algorithmw vector of weighting factors, wiX vector of design variablesxk design variables

Greek Symbols∞n weighting factors for environmental impact categories of chemical nεm constant for objective functions m used in €-constraint methodΨnj normalized chemical impact score of chemical n in stream jΨE normalized impact score of energyℑ decision space

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Manuscript received January 26, 2006; revised manuscript received May 18, 2006; accepted for publication June 14, 2006.

Multi-Objective Optimization in Distillation Unit: A Case Study

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