Optimization of the Design and Operation of an Extractive Distillation

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Optimization of the Design and Operation of an Extractive Distillation System for the Production of Fuel Grade Ethanol Using Glycerol as Entrainer Pablo García-Herreros and Jorge M. Gomez* Departamento de Ingeniería Química, Universidad de los Andes, Carrera 1 No. 18a-10, Bogota, Colombia

Ivan D. Gil and Gerardo Rodríguez Departamento de Ingeniería Química y Ambiental, Universidad Nacional de Colombia, Avenida Carrera 30 No. 45-03, Bogota, Colombia

bS Supporting Information ABSTRACT: The extractive distillation of ethanol using glycerol as entrainer is studied in order to find its optimal design and operating conditions. The optimization is formulated as a mixed integer nonlinear programming (MINLP) problem. The discrete variables determine the number of stages of the columns and their feed stage locations. The continuous variables include the variables of the equilibrium model and operating variables. The solution of the optimization problem is achieved through a two-level strategy that combines stochastic and deterministic algorithms. The result obtained establishes the process that maximizes an economic criterion for the industrial production of bioethanol satisfying the problem constraints.

1. INTRODUCTION In the past decade, worldwide concern about global warming and crude oil prices has produced an increase in the demand for bioethanol as a replacement for gasoline. The fuel obtained from renewable sources offers well-documented environmental advantages.1,2 However, its competitiveness against fossil fuels is still dependent on the international price of oil and government subventions. Designing highly efficient distillation processes is decisive in the competitiveness of bioethanol against fossil fuels. Among all operations involved in the production of fuel grade ethanol, the separation process takes up a large fraction of the total energy requirements.3 The application of optimization methods to the design of ethanol distillation allows exploring simultaneously the configurations and operating conditions that provide the best economic projections. Initially, the research made by Black and Ditsler4 on fuel grade ethanol production revealed high energy requirements for extractive distillation using ethylene glycol in comparison with azeotropic distillation using n-pentane. Later research explored extractive distillation using gasoline as entrainer for the production of gasohol;5-7 the research improved the economic projection for the mass consumption of bioethanol. Finally, the research made by Lynn and Hanson8 proved the energy advantages of the production of fuel grade ethanol by extractive distillation using ethylene glycol as entrainer. Many methodologies have been proposed for the design of homogeneous extractive distillation systems, most of them using graphical or simplified methods.9-11 The research made by Knight and Doherty12 introduced optimization elements on the design of extractive distillation for the production of fuel r 2011 American Chemical Society

grade ethanol using ethylene glycol as entrainer. Even though this procedure was based on a simplified model, they formulated an economic optimization that produced a favorable design for the production of fuel grade ethanol, unlike the design originally proposed by Black and Ditsler.4 A rigorous simulation of extractive distillation for the production of fuel grade ethanol using ethylene glycol as entrainer was developed by Meirelles13 based on experimental data. The results obtained confirmed the advantages of extractive distillation against azeotropic distillation, even though the design was based on univariate sensitivity analysis. Recently, the availability of glycerol as byproduct in the production of biodiesel has encouraged the search for new uses. Its capacity to alter the relative volatility of the ethanol-water mixture allows using it in the process of extractive distillation,14 substituting environmentally harmful entrainers as ethylene glycol. The use of glycerol as extractive distillation entrainer for the production of absolute ethanol was originally patented by Schneibel.15 Modern research made by Uyazan et al.16 and Dias et al.17,18 presented extractive distillation systems that used glycerol as entrainer and achieved favorable energy consumption in comparison to the former studies. However, the methodologies used for these designs were based on sensitivity analysis and factorial planning of the decision variables. These methodologies ignored the interaction among the multiple variables that influence the process. The effects of these interactions are especially important in nonlinear systems such as distillation models. Received: September 2, 2010 Accepted: February 1, 2011 Revised: January 21, 2011 Published: February 23, 2011 3977

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Industrial & Engineering Chemistry Research

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Table 1. Research on Homogeneous Extractive Distillation for the Production of Fuel Grade Ethanol author

year

entrainer

distillation model

thermodynamic model

Black and Ditsler4

1972

ethylene glycol

rigorous

van Laar

energy consumption

Lynn and Hanson8

1986

ethylene glycol

graphical

pseudoequilibrium

energy consumption

graphical

Knight and Doherty12

1986

ethylene glycol

simplified

Margules

total annualized cost

systematic optimization procedure

Meirelles13

1992

ethylene glycol

rigorous

NRTL

energy consumption

sensitivity analysis

Uyazan et al.16

2006

glycerol

rigorous

NRTL

energy consumption

sensitivity analysis

Dias et al.17

2009

glycerol

rigorous

UNIQUAC UNIFAC

energy consumption

factorial planning

this research

2010

glycerol

rigorous

NRTL

profitability

MINLP optimization

Table 1 shows a summary of the research related to homogeneous extractive distillation for the production of fuel grade ethanol. In previous work, García-Herreros et al.19 have already reported successful economic optimization of the operation of an extractive distillation system without considering the design problem. The novelty of this work is supported by the combined optimization of the decision variables for the design and operation of the extractive distillation process. This methodology allows maximizing a profit objective function considering the nonlinearity of the model. The optimization of the design and operation of extractive distillation can be formulated as a mixed integer nonlinear programming (MINLP) problem. This methodology allows considering simultaneously the influence of design and operating variables on a profit objective function. The solution is achieved through the combination of a stochastic algorithm and a deterministic algorithm in a two-level strategy that is developed on a rigorous model of the distillation process; this strategy assures a comprehensive analysis of the feasible region. The results obtained show the convenience of using this methodology for the design of competitive processes.

2. EXTRACTIVE DISTILLATION PROCESS Extractive distillation is the partial vaporization process that occurs in the presence of a miscible entrainer that alters the relative volatilities of the components present in the mixture to be separated. The addition of a new substance to the mixture modifies the feasible compositions of the products obtained by distillation. The entrainer used for the extractive distillation must have low volatility, high boiling point, and complete miscibility in the mixture, and it cannot form new azeotropes.20 The extractive distillation system is made up by two distillation columns: the first one for the extraction process and the other for the entrainer regeneration. The mixture to be separated and an entrainer are fed into the first column to obtain a highly concentrated distillate. The second column regenerates the entrainer that can be reused in the extractive distillation column.21 The separation of the ethanol-water azeotropic mixture using glycerol as entrainer is carried out in the extractive distillation column that operates at atmospheric pressure (101 kPa); this column produces as distillate ethanol with purity over 99.5 mol %.22 The water-glycerol mixture that is obtained as bottom product from the extractive column is fed to the regeneration column; this column operates at an absolute pressure of 20 kPa in order to avoid the thermal decomposition of glycerol.23 The regeneration column produces as distillate a stream of water and as bottom product the regenerated glycerol. The diagram of the process is shown in Figure 1.

design criterion

design methodology sensitivity analysis

3. MODEL OF EXTRACTIVE DISTILLATION The extractive distillation process is modeled as a series of separation stages. At each stage, liquid and vapor flows get in contact in order to reach thermodynamic equilibrium. The stages are represented through equations for mass balances, energy balances, mole fraction summations, and phase equilibria, known as MESH equations.24 Each stage has the following as model variables: molar flow of liquid, mole fractions of liquid, molar flow of vapor, mole fractions of vapor, and temperature. Additionally, this model of distillation considers as a model variable the condenser heat duty. The model requires the calculation of enthalpies for the liquid and vapor phases, as well as the equilibrium constants. The nonideality of the liquid phase is considered through the nonrandom two liquid (NRTL) model; the vapor phase is considered an ideal gas because of the low operating pressures. In order to represent the degree of separation attained at each stage in a realistic manner, Murphree tray efficiencies25 can be used to adjust the model. According to the description rule,26 there are two degrees of freedom in the MESH model of a distillation column with total condenser, defined operating pressure, and specified feed streams. In order to specify the distillation model, the reflux ratio and the reboiler heat duty of the columns are considered as operating variables. 4. DESIGN AND OPERATION OF THE EXTRACTIVE DISTILLATION SYSTEM The rigorous design of the extractive distillation system implies establishing the following: exchange areas of condensers and reboilers, column diameters, column heights according to the number of stages, and feed stage locations. The structure of the system is constrained to the conventional configuration of the extractive distillation process in which the entrainer feed stage is always above the azeotropic mixture feed stage. This is achieved by dividing both distillation columns into sections separated by the feed stages: three sections for the extraction column (rectifying, extractive, and stripping sections) and two for the regeneration column (rectifying and stripping sections). The design variables of the extractive distillation system are the number of stages in each one of the five column sections. These variables can only take discrete values. Other design aspects such as column diameters and exchanger areas are calculated from the model variables through empirical relations27 that guarantee the feasibility of the design from geometric and hydraulic points of view. Defining the operating conditions of the extractive distillation system implies establishing the values of the operating variables of the columns as well as the conditions of the feed streams. 3978

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Figure 1. Extractive distillation process.

In the extractive distillation of the ethanol-water mixture using glycerol as entrainer, it is especially important to establish the proportion of entrainer that is reused, the makeup quantity, and its feed temperature. The column pressures and feed conditions of the azeotropic mixture are fixed as parameters; the feed conditions to the regeneration column are the same conditions of the bottom product of the extractive distillation.

5. FORMULATION OF THE OPTIMIZATION PROBLEM The mathematical formulation of the optimization problem includes discrete (y) and continuous (x) variables. This kind of optimization problem is known as mixed integer nonlinear programming (MINLP). It is made up by an objective function subject to model and operational constraints. The objective function depends on the discrete and continuous variables. The constraints depend only on the continuous variables, but the number of constraints depends on the value of discrete variables. The form of the MINLP problem for the economic optimization of the design and operation of the extractive distillation system is max Z ¼ f ðx, yÞ ð1Þ s:t: hðxÞ ¼ 0 gðxÞ e 0

ð2Þ

x ∈ X, y ∈ Y 5.1. Optimization Variables. The objective function and the constraints of the optimization problem are evaluated from the

Table 2. Decision Variables of the Optimization Problem description design variables

nomenclature

number of stages in section 1

N1


N2


N3


N4

number of stages in section 5 operating variables reflux ratio in the extraction column

N5 R1

reboiler duty in the extraction column

Qr1

reflux ratio in the regeneration column reboiler duty in the regeneration column

R2 Qr2

fraction of regenerated entrainer used

RR

feed temperature of entrainer

TS

entrainer to feed ratio

S/F

optimization variables. These variables can be classified as model variables, operating variables, and design variables. From the analysis of the degrees of freedom of the distillation model, it is possible to establish a group of variables that completely specifies the distillation model. These decision variables define the design and operating conditions of the distillation system. The group of decision variables of this problem is shown in Table 2; it can be seen that all design variables are discrete and all operating variables are continuous. 5.2. Constraints. The optimization problem is subject to two sets of constraints: model constraints and operational constraints. 5.2.1. Model Constraints. The model constraints, h(x), are the MESH equations. The number of equilibrium stages of the 3979


Industrial & Engineering Chemistry Research distillation columns is one of the design aspects to establish; therefore, the number of model constraints depends on the values of the design variables. This situation has no effect on the degrees of freedom of the problem or on the decision variables because adding intermediate stages contributes the same number of variables and equations. 5.2.2. Operational Constraints. The operational constraints, g(x), are formulated as inequalities. The production of fuel grade ethanol by extractive distillation using glycerol as entrainer has two operational constraints related to the purity of ethanol used for fuel blends22 and the decomposition temperature of glycerol:.23 • minimum purity of ethanol produced: g1(x) g 99.5 mol % • maximum operating temperature of the columns: g2(x) e 555 K 5.3. Objective Function. The criterion for the optimization of the design and operation of the extractive distillation system is the maximization of the annual profit in the production of fuel grade ethanol. The objective function is made up of five elements: • value of products: market value of the ethanol produced in 1 year of operation • raw materials cost: value of the azeotropic mixture and the entrainer makeup used in 1 year of operation • operating costs: value of the utilities required for the operation of the columns in 1 year • infrastructure cost: cost of the distillation columns, complementary equipment, and installation • annualizing factor: factor used to annualize the infrastructure cost in a 5 year depreciation period The mathematical expression of the objective function is max Zðx, yÞ ¼ CP ðxÞ - CRM ðxÞ - CO ðxÞ - AF CI ðx, yÞ ð3Þ It can be observed that the design variables have a direct effect on the infrastructure cost; however, their influence on the distillation model affects other elements of the objective function. The infrastructure cost is calculated from empirical relations28,29 (see Supporting Information) that consider the internal flows of the distillation columns in order to establish proper geometric and hydraulic conditions. 5.4. Parameters. The optimization of the extractive distillation system is formulated based on a specified feed of the azeotropic mixture. The pressure of the distillation columns and the efficiencies of the separation stages are considered constant. The cost parameters of the objective function are approximated to market values; their influence on the optimal structure is expected to be small according to Emhamed et al.30 The values of the parameters used for the optimization are shown in Table 3.

6. SOLUTION STRATEGY The solution to the optimization of the design and operation of the extractive distillation system is achieved through a twolevel strategy. The discrete variables are considered in a master problem that uses a stochastic algorithm to evaluate different configurations of the system. The continuous variables are optimized in a nonlinear programming (NLP) subproblem that uses a deterministic algorithm in order to find the optimal operating conditions of the system. The interaction between both levels allows defining the optimal design and operating conditions of the columns under the quantitative criterion

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Table 3. Parameters of the Optimization Problem description

nomenclature

pressure in the extraction column

P1 = 101 kPa

pressure in the regeneration column

P2 = 20 kPa

feed flow of the azeotropic mixture

Faz = 100 kmol/h

molar percentage of water in the azeotropic mixture

Zaz,1 = 15

molar percentage of ethanol in the azeotropic mixture

Zaz,2 = 85

feed temperature of the azeotropic mixture

Taz = 293.15 K

Murphree tray efficiency

E = 1.0

operation time per year market value of fuel grade ethanol

t = 6000 h/year $30/kmol

cost of the azeotropic mixture

$15/kmol

cost of makeup glycerol

$75/kmol

cost of reboiler energy

$10-2/kJ

annualizing factor

AF = 0.2

established by the objective function. The two-level optimization strategy is shown in Figure 2. The implementation of the optimization is carried out using the software MatLab 7.8.0. on an Intel Core 2 Duo CPU 3.07 GHz processor with 3.21 GB RAM. The software allows creating in independent functions the specified model of the distillation system, the routine for the enthalpy calculations, the routine for the thermodynamic equilibrium calculations, the constraints of the optimization problem, the objective function, the routine for the initialization, and a simulated annealing algorithm. The main advantage of this strategy for solving MINLP problems is that a large state space can be evaluated by solving a limited number of the relatively simple NLP problems. Therefore, it increases the likelihood of finding the global optimum. The implementation on MatLab allows verifying the model and visualizing the results easily. This implementation has been developed considering the flexibility of the model as a key aspect. 6.1. Initialization. As starting points for the optimization, three different design and operating conditions are used. These conditions are normalized for an azeotropic feed flow of 100 kmol/h after the configurations originally proposed by Uyazan et al.,16 Dias et al.,17 and García-Herreros et al.;19 recirculation of the regenerated entrainer is considered in all initial conditions. The initial sets of decision variables for these design and operating conditions are shown in Table 4. Considering a set of initial decision variables, a global mass balance is made for each distillation column. Initial estimates of the model variables are obtained by linear interpolation of the global mass balance. The initial values of the decision variables and the estimates of the model variables are used to initialize the specified model (zero degrees of freedom) of the extractive distillation system; the model is solved using the LevenbergMarquardt31,32 algorithm of the fsolve function included in Matlab. The solution of the specified model comprises values of the variables that satisfy the equality constraints and therefore represent a feasible operating point. The optimization process is initialized from a feasible operating point in order to favor the achievement of the optimum. 6.2. Master Problem. At this level, the five design variables are optimized using the simulated annealing algorithm.33 The role of the master problem is to randomly propose design configurations that are evaluated in the NLP subproblem. This algorithm allows analyzing the different regions of feasible design moving in directions opposite to the local optima. This is achieved by 3980



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Figure 2. Two-level optimization strategy.

Table 4. Initial Values of the Decision Variables description design variables

operating variables

initialization 1

initialization 2

initialization 3


N1 = 3

N1 = 3

N1 = 3

number of stages in section 2 number of stages in section 3

N2 = 7 N3 = 8

N2 = 23 N3 = 12

N2 = 8 N3 = 8


N4 = 4

N4 = 8

N4 = 3


N5 = 2

N5 = 3

N5 = 4

reflux ratio in the extraction column

R1 = 0.35

R1 = 0.94

R1 = 0.63 Qr1 = 7925.2

reboiler duty in the extraction column (MJ/h)

Qr1 = 4891.0

Qr1 = 2581.2

reflux ratio in the regeneration column

R2 = 0.05

R2 = 0.012

R2 = 3.81

reboiler duty in the regeneration column (MJ/h)

Qr2 = 877.2

Qr2 = 1529.7

Qr2 = 3277.8

fraction of regenerated entrainer used feed temperature of entrainer (K)

RR = 1 TS = 353.15

RR = 1 TS = 423.15

RR = 1 TS = 360


S/F = 0.4

S/F = 0.316

S/F = 1.20

following a probability of accepting changes that deteriorate the value of the objective function; the probability is determined through the Metropolis criterion.34 As the process moves forward, the probability of moving in directions opposite to the optimum is decreased, therefore focusing the search in the most promising region. Finally, the process stops when the probability of moving to suboptimal regions reaches a considerably low value. The simulated annealing is implemented through three cycles: the inner cycle, the outer cycle, and the temperature cycle. The inner cycle changes every design variable once, and the outer cycle allows evaluating a diverse variety of design candidates for each temperature level. At each annealing temperature, there

must be enough iterations for the system to attain steady state. This algorithm requires the use of random numbers for the evaluation of probabilities and the candidate generation. Random numbers are generated by using functions included in Matlab. The success of the stochastic algorithm depends on a comprehensive analysis of the feasible region and its capacity to focus the search on the regions with the best projection. The annealing schedule is a decisive element for the success of the optimization and its running time. This schedule is adjusted by the algorithm parameters: initial temperature of annealing, number of movements per variable, temperature decrement rate, and final temperature of annealing. The values of the parameters are determined by 3981



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Figure 3. Trajectory of the objective function.

Table 5. Solutions Obtained description design variables

operating variables

operational constraints objective

solution 1

solution 2

solution 3


N1 = 2

N1 = 12

N1 = 2


N2 = 9

N2 = 20

N2 = 9


N3 = 7

N3 = 5

N3 = 7


N4 = 2

N4 = 7

N4 = 2


N5 = 4

N5 = 3

N5 = 4


R1 = 0.04

R1 = 0.1479

R1 = 0.04


Qr1 = 5978.4

Qr1 = 6132.0

Qr1 = 5978.4

reflux ratio in the regeneration column reboiler duty in the regeneration column (MJ/h)

R2 = 0.1283 Qr2 = 1266.9

R2 = 0.1354 Qr2 = 1194.1

R2 = 0.1283 Qr2 = 1266.9


RR = 1.00

RR = 1.00

RR = 1.00

feed temperature of entrainer (K)

TS = 305

TS = 326

TS = 305


S/F = 0.52

S/F = 0. 52

S/F = 0.52

ethanol mole percentage

g1 = 99.5

g1 = 99.5

g1 = 99.5

temperature at reboiler (K)

g2 = 502

g2 = 446

g2 = 502

annual profit (MM $/year)

Z = 5.4311

Z = 5.3227

Z = 5.4311

experimentation after the criteria established by Cheng et al.35 in order to guarantee an appropriate cooling of the system. The initial temperature (TO) is fixed at a value of 5 for an initial acceptance rate of around 95%. The number of individual movements of the variables at each temperature level is set to 25. A geometric temperature decrement is used, fixing the decrement rate (R) at a value equal to 0.8. The final temperature of annealing is set to 0.5; at this temperature at least 25 different configurations are analyzed with no change in the optimal design. 6.3. NLP Subproblem. At this level, each design configuration proposed by the master problem is optimized in order to find the best operating conditions according to the objective function. The subproblem is solved by finding the values of the continuous variables that maximize the profit objective function and satisfy all constraints. This is achieved using the interior point algorithm of the fmincon function included in Matlab, which has proved to be successful for solving large-scale nonlinear programming problems.36 The application of this method allows optimizing

Table 6. Elements of the Objective Function under Optimal Design and Operating Conditions element of the objective function

value

value of products

$15,373,000/year

raw material cost operating cost

$9,001,000/year $543,400/year

infrastructure cost

$1,987,500

annual profit

$5,431,100/year

both distillation columns simultaneously; the convergence of the algorithm to a feasible operating point is favored since the interactions among both columns equations are considered.

7. RESULTS The optimization trajectory presented in Figure 3 shows the tendency of the simulated annealing to maximize the objective 3982



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Table 7. Results of the Postoptimality Analysis variable design variables

value



constraint violation

1

$5,361,100/year

none

2

$5,431,100/year

none

3

$5,424,100/year

none

8

$5,414,900/year

none

9

$5,431,100/year

none

10

$5,398,100/year

none

6

$5,422,300/year

none

7 8

$5,431,100/year $5,419,500/year

none none

1

$5,325,600/year

none

2

$5,431,100/year

none

3

$5,430,100/year

none

3

$5,400,500/year

none

4

$5,431,100/year

none

5

$5,393,900/year

none


0.036 0.04

$5,433,800/year $5,431,100/year

ethanol purity none

0.044

$5,427,000/year

none


5380.6

$5,230,500/year

none

5978.4

$5,431,100/year

none

6576.2

$3,597,900/year

ethanol purity

0.1155

$5,428,700/year

none

0.1283

$5,431,100/year

none

0.1411 1140.2

$5,433,100/year $5,492,200/year

ethanol purity ethanol purity

1266.9

$5,431,100/year

none

1393.6

$5,172,400/year

none

0.9

$3,867,000/year

none

1.00

$5,431,100/year

none

-

-

none

274.5

$5,331,100/year

ethanol purity

305 335.5

$5,431,100/year $4,917,000/year

none none

0.47

$5,032,200/year

none

0.52

$5,431,100/year

none

0.57

$5,38,700/year

ethanol purity




operating variables

objective function

reflux ratio in the regeneration column

reboiler duty in the regeneration column (MJ/h)


feed temperature of entrainer (K)


function as the process moves forward. It can be observed that the first iterations frequently accept undesirable changes in the configuration; as the optimization moves forward and the annealing temperature decreases, the acceptance of configurations becomes stricter, and the search focuses on the most promising regions. When the initial configurations are compared to the optimum found, it can be observed that the optimization makes all processes around 60% more profitable. The results of the optimization establish the values of the design and operating variables that maximize the objective function satisfying the constraints of the problem. From the three initial sets of decision variables two different configurations are obtained; the solutions found from the first and third initial sets of decision variables are equal. The solutions obtained from each initialization are shown in Table 5. Every solution establishes a feasible operating point that satisfies the operating constraints; however, the maximum value of the objective function is obtained from the first and third

initializations. The solution obtained from the second initialization cannot be a global maximum. The behaviors of the different elements of the objective function under the optimal design and operating conditions are shown in Table 6.

8. ANALYSIS AND DISCUSSION Both configurations obtained through the optimization process represent designs that are economically attractive for the industrial production of bioethanol. The annual profits of those configurations are very similar, but their design and operating conditions are different. This situation is a consequence of the nonconvexity of the problem that traps solutions into local maxima. A slower annealing schedule could be used in order to increase the probability of achieving the global maximum from any initial set of variables; however, the computation time could become impractical. A postoptimality analysis is carried out in order to test the sensitivity of the objective function to variations on the decision 3983



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Table 8. Comparison of Energy Consumptiona

a

extraction column

regeneration column

author

(MJ/kg AE)

(MJ/kg AE)

Uyazan et al.16

1249

224

Dias et al.17

664

393

this research

1524

323

AE, anhydrous ethanol.

variables at the optimum. The simulation of the optimal design and operating conditions using the specified model allows evaluating the influence of the decision variables on the process annual profit. Each variable is changed individually in a range close to its optimal value. The results of the analysis are shown in Table 7. From the postoptimality analysis it can be observed that the proposed design and operating conditions maximize the objective function satisfying the equality and inequality constraints. It also shows that deviations of the decision variables from their optimum values either decrease the annual profit of the process or violate an operational constraint. This confirms that the maximum found is a local optimum; there is no certainty that this maximum is a global optimum; however, the implementation of the simulated annealing algorithm assures a comprehensive analysis of the feasibility region. When comparing the optimal design and operating conditions found in this research with the processes proposed by Uyazan et al.16 and Dias et al.,17 it is important to highlight the difference in the design criterion. Even though every research proposes an extractive distillation process for the production of fuel grade ethanol using glycerol as entrainer, the design criterion of the preceding works is the minimization of energy consumption in the columns’ reboilers. A comparison of the normalized energy consumption is shown in Table 8. From Table 8 can be observed that the process proposed in this research has the highest overall energy consumption. However, this study presents a criterion for design and operation that leads to greater economical profits. This kind of optimization is more suitable for the industrial application.

9. CONCLUSIONS The optimization strategy proposed considers the elements of design in combination with the operation of the extractive distillation for the production of fuel grade ethanol using glycerol as solvent. This approach allows analyzing the feasible processes in order to find the most suitable according to a quantitative criterion. This case, in particular, has found a design and operating conditions that offer greater profit in the process of producing fuel grade ethanol. This is achieved through a systematic process. The optimization tools allow solving this kind of problem based on rigorous models. The combination of stochastic and deterministic algorithms achieves the solution of the problem by separating the continuous and discrete variables. This two-level strategy makes easier analyzing a broad region of feasible solutions. The trajectory of the objective function through the progress of the simulated annealing algorithm keeps an ascending tendency that stands still at the optimal configuration. This optimization problem presents multiple local maxima; however, in most of the cases the algorithm works to move away from them in order to find better processes. Every optimization that was

carried out obtained similar values for the objective function, proving the effectiveness of the algorithm in designing processes that adjust to the quantitative criterion. The result obtained proposes a process that offers a very good economic projection for the industrial production of fuel grade ethanol using glycerol as solvent. Using a profit objective function centers the problem on the point of most interest for the industrial sector. From these results, it has to be highlighted that there is still much space for the application of optimization methods in the design of economically attractive processes, in particular those willing to increase the competitiveness of biofuels.

’ ASSOCIATED CONTENT

bS

Supporting Information. Empirical relations used for the infrastructure cost and details on the simulated annealing parameters. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors acknowledge the collaboration of COLCIENCIAS (Departamento Administrativo de Ciencia, Tecnologia e Innovacion), Colombia. Research Project Code 1101-45221113. ’ NOMENCLATURE X = continuous variables Y = discrete variables h = equality constraints g = inequality constraints Z = objective function CP = value of products CRM = raw materials cost CO = operating cost AF = annualizing factor CI = infrastructure cost k = index of the inner cycle in the simulated annealing i = index of the outer cycle in the simulated annealing T = annealing temperature R = temperature decrement rate N1 = number of stages in section 1 N2 = number of stages in section 2 N3 = number of stages in section 3 N4 = number of stages in section 4 N5 = number of stages in section 5 R1 = reflux ratio in the extraction column Qr1 = reboiler duty in the extraction column R2 = reflux ratio in the regeneration column Qr2 = reboiler duty in the regeneration column RR = fraction of regenerated entrainer used TS = feed temperature of entrainer S/F = entrainer to feed ratio P1 = pressure in the extraction column P2 = pressure in the regeneration column Faz = feed flow of the azeotropic mixture 3984


Industrial & Engineering Chemistry Research Zaz,1 = molar percentage of water in the azeotropic mixture Zaz,2 = molar percentage of ethanol in the azeotropic mixture Taz = feed temperature of the azeotropic mixture E = Murphree tray efficiency t = operation time per year

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