Modeling, analysis and multi-objective optimization of an industrial batch process for the production of tributyl citrate

Journal Pre-proof

Modeling, Analysis and Multi-objective Optimization of an Industrial Batch Process for the production of Tributyl Citrate Juan D. Fonseca , Abderrazak M. Latifi , Alvaro Orjuela , ´ D. Gil Gerardo Rodr´ıguez , Ivan PII: DOI: Reference:

S0098-1354(19)30527-7 https://doi.org/10.1016/j.compchemeng.2019.106603 CACE 106603

To appear in:

Computers and Chemical Engineering

Received date: Revised date: Accepted date:

20 May 2019 1 October 2019 14 October 2019

Please cite this article as: Juan D. Fonseca , Abderrazak M. Latifi , Alvaro Orjuela , ´ D. Gil , Modeling, Analysis and Multi-objective Optimization of an InGerardo Rodr´ıguez , Ivan dustrial Batch Process for the production of Tributyl Citrate, Computers and Chemical Engineering (2019), doi: https://doi.org/10.1016/j.compchemeng.2019.106603

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Highlights     

Tributyl citrate production process at industrial scale was studied Batch reactive distillation of citric acid esterification with butanol was modeled Model verification with two industrial scale experiments was done Optimization of batch time and total energy consumption was performed Decision-making aid tool for ranking Pareto front solutions was implemented

1

Modeling, Analysis and Multi-objective Optimization of an Industrial Batch Process for the production of Tributyl Citrate Juan D. Fonseca a, Abderrazak M. Latifi b , Alvaro Orjuela a*, Gerardo Rodríguez a , Iván D. Gil a a

Department of Chemical and Environmental Engineering, Universidad Nacional de Colombia – Sede Bogotá, Carrera 30 45-03, Bogotá, Colombia b

Laboratoire Réactions et Génie des Procédés LRGP-CNRS, ENSIC-Université de Lorraine, 1 rue Grandville, Nancy54001, France. *[email protected]

Abstract This work describes the modeling and optimization of a trybutil citrate (TBC) production process at the industrial scale. The process comprises a batch reactive distillation for the esterification of citric acid with butanol. The dynamic model of the process was constructed based upon validated kinetic and thermodynamic models, implemented in gPROMS® software, verified with industrial scale experiments, and used for further optimization to minimize batch time and energy consumption. Manipulated process variables were the molar ratio of butanol to citric acid, the alcohol loading policy, and the heat supply profile, and a Pareto front of optimal solutions was obtained. Depending on the main goal, the optimization process allowed to obtain energy savings up to 28%, and the corresponding processing times were reduced by 36%. Finally, multi-attribute utility theory (MAUT) approach was used as decision-making aid tool to select the preferred operating conditions for TBC production at the industrial scale. Keywords Citric acid, esterification, tributyl citrate, biobased plasticizer, batch reactive distillation, multiobjective optimization

2

1. Introduction Plasticizers are chemical compounds used as additives for polymeric materials during their transformation and processing. They cause a glass transition temperature decrease making the polymers more flexible, soft, and easy to process [1]. Besides, some specialized plasticizers can be used to modify properties such as fire response, rheological behavior, biological degradation, weather conditions resistance, and compatibility with other additives [1, 2]. Currently, the plasticizers market is strongly dominated by phthalates, particularly di-ethyl hexyl phthalate DEHP, which accounted for more than 65% of world consumption in 2017 [3]. Nevertheless, a shift in market distribution is expected due to the transition from petroleum-based to bioderived compounds in the chemical industry. Additionally, restrictions have been imposed for the use of DEPH in some niche applications such as toys, childcare articles, cosmetics, medical devices, and food packaging [4–6]. In this regard, a wide range of substances such as adipates, sebacates, citrates, benzoates and vegetable oil-based esters, have been identified as potential substitutes for the phthalates [3, 5, 7]. Among these, citric acid esters stands out as promising alternatives, because they are safe biobased compounds, and their plasticizing performance is similar to that of DEHP in a variety of applications [3, 8, 9]. Currently, the most common citrate plasticizers are the acetylated and nonacetylated esters derived from ethanol and butanol: triethyl (TEC) and tributyl citrate (TBC). Despite their potential, citrates competitiveness in the plasticizers market is limited due to their higher costs, so in general, they are mainly used in higher value added products or in sensible applications [9]. Industrially, citrates are produced via acid-catalyzed esterification of citric acid with large excess of the corresponding alcohol in batch operations. The thermal decomposition of citrate species and the bubble point of the reacting mixture limit the temperature of reaction, so normally long reaction times are required to ensure complete conversion. Also, water removal is needed to shift chemical equilibrium towards the esters; this is mainly done by distilling water off along reaction, requiring further separation and alcohol recycle. All these characteristics turn citrates production into a highly energy-and materials-intensive process. Additionally, many operative decisions at the industrial practice are made based upon heuristics and/or operator’s experience, which makes the process prone to unintended failures. This occurs because there is a lack of knowledge on the physicochemical phenomena taking place during the process, and because there are no available

3

models capable to describe and predict the process performance under different operating conditions. If all these issues are overcome, there might an opportunity to boost citrates in the plasticizers market. Recently, the technical difficulties during citrates processing have been addressed in different ways, mainly for TEC and TBC production. Process intensification for TEC synthesis has been evaluated by using reactive distillation systems [10, 11]. These studies focused on exploiting the synergies obtained from the integration of reaction-separation operations, achieving less ethanol consumption, higher yields, lower production costs, and reduced byproducts generation. In the same direction, a recent work described a systematic methodology for the design of intensified TEC production processes by using economic and controllability criteria [12]. Nevertheless, feasibility of reported reactive distillation schemes is still under study because very large columns are required due to the low reaction rates, and to overcome this, columns with side reactors have been proposed [13]. In contrast, TBC production has been seldom studied, and the literature reports have been mainly focused on the evaluation of the reaction kinetics, catalyst screening, and phase equilibria determination [14–19]; few have dealt with TBC production under intensified processes. Surprisingly, while some innovative solutions have been proposed for citrates production, few has been done on the optimization of the current production process [20], that corresponds to a batch reactive distillation (i.e. with reaction in the reboiler). In principle, the implementation of reactive distillation schemes seems suitable for citrates production, especially for TBC. In this case, the simultaneous water removal during reaction can lead to overcome equilibrium limitations of the esterification steps, enabling complete conversion of the acid groups. Also, as there is a butanol-water heterogeneous azeotrope, the distilled vapor can be condensed and decanted to allow butanol recycle and selective water removal. As the compositions of each liquid phase in the decanter is fixed disregarding the vapor composition (i.e. within the immiscible region at a given temperature), this adds flexibility and resilience to the operation. In addition to this, batch reactive distillation using a multi-product facility fits well with citrates production, taking into account the current demand, and the need for a portfolio of citrates for different applications. Besides, lower investment and operating costs compared with a decoupled production process (i.e. reaction followed by separation) are expected [21–23]. Considering the aforementioned, this work aims to model, validate, and improve a batch reactive distillation process for TBC production at the industrial scale. Initially, a typical industrial TBC process is described, identifying the main units, processing steps, and operating variables. Then, a mathematical model of the process was constructed and implemented within gPROMS® software. 4

Subsequently, validation of the model was done by comparison with data obtained from industrial scale batches. Afterwards, a dynamic multi-objective optimization problem was formulated and solved to enhance TBC production. Optimization was focused on minimizing batch time and energy consumption of the process. Finally, the multi-attribute utility theory (MAUT) was used to classify the Pareto front solutions according to decision-maker preferences. 2. Methods 2.1. Tributyl citrate process description and data collection TBC is produced by esterification of citric acid with butanol in the presence of an acid catalyst. The process involves three sequential-parallel reversible reactions, having the partially substituted citrates (mono and dibutyl citrate) as intermediate products, and water as byproduct in each esterification step (Figure 1). C

COOH

C

COOH + C4H9OH

C

COOH

C

COOC4H9

C

COOH

C

COOH

Cat.

OH

Citric Acid C

COOC4H9

C

COOH

C

COOH

OH

Butanol

+ H2O

Monobutyl Citrate C

COOC4H9

C

COOH

Cat.

OH

+ C4H9OH

OH

C

+ H2O

COOC4H9

Dibutyl Citrate C

COOC4H9

C

COOC4H9

C

COOC4H9 + H2O

C

COOC4H9

Cat.

OH

C C

COOH

+ C4H9OH

OH

COOC4H9

Tributyl Citrate

Figure 1. Reaction scheme for tributyl citrate synthesis. As the citric acid is solid, there is need to use an excess of alcohol to ensure its complete dissolution. This process takes time, and it can be done beforehand in a side tank, or within the stirred tank reactor by operating in a fed-batch mode during the initial loading time. The last option is preferred as dissolution is improved at higher temperatures, and because produced water enhance dissolution rate. However, solid loading needs to be carefully done to avoid vapor emissions, or wetting of the solids at the inlet port that can generate caking. At the industrial scale, the process typically requires between 18 to 24 hours to achieve the desired yield. The reactive system is composed of a stirred and jacketed reactor, coupled to a distillation column and a top decanter (Figure 2). The reaction in the stirred tank is carried out at the bubble point of the mixture under atmospheric pressure, with continuous heating, and with periodic 5

additions of fresh butanol. The reactor also works as reboiler for the distillation column that fractionates the vapors produced during reaction (i.e. mainly butanol and water). The heating utility of the reboiler is medium pressure steam. At the top of the column, a nearly butanol-water azeotropic mixture is generated, which after condensation splits into two liquid phases. The two liquids are separated in the decanter; while the organic phase is used as reflux to the column, the aqueous phase is removed for further treatment and recovery of the dissolved butanol. From the bottom of the fractionation column, a butanol-rich stream is obtained and sent back to the reactor. C-1 Azeotropic Mixture Organic Phase

D-1

Aqueous Phase Butanol

DC-1 DC-1 Butanol Butanol – Water Butanol

R-1

Figure 2. Process scheme for the tributyl citrate production.(R-1, reactor; DC-1, distillation column; C-1, condenser; D-1, decanter). Taking this into account, two industrial scale experiments on TBC production under batch operation were done. Variables that are typically monitored by process operators were recorded along the experiments. These corresponded to acid value and temperature profiles in the reboiler, mass of periodic butanol additions, and flow rates of the heating steam. Experimentally, acid value was determined by an acid-base titration of collected samples from the reactor, using a standardized sodium hydroxide solution. The reported acidity represents the concentration of acid species in the mixture, namely, citric acid, mono-butyl citrate, di-butyl citrate and catalyst. Thus, discounting the contribution of the catalyst, the acid value was reported as the equivalent mass of citric acid with respect to the sample volume (kgCA/L, % wt./v). According to operators, acid values and temperature are good indicators of process performance, and they are used as surrogates for

6

decision making and process control. The corresponding operating conditions used in the two evaluated batches are summarized in Table 1. Table 1. Operating conditions of industrial scale experiments for tributyl citrate production. Parameter

Run 1

Run 2

Acid:alcohol mol ratio(initial)

1:4.2

1:5

Acid:alcohol mol ratio (final)

1:5.4

1:5.9

Citric acid loading (kg)

8000

8000

Catalyst loading (kg)

40

40

Batch time (h)

22

20

Pressure (kPa)

93.2

93.2

Initial Temperature (°C)

60

60

2.2. Process Modeling and Simulation 2.2.1.

Reactor/reboiler model

As aforementioned, citric acid esterification is carried out using an acid catalyst. Recent kinetic studies have been reported for methane-sulfonic acid, sulfuric acid, ionic liquids and ion exchange resins as catalysts [16–19]. In this case, the industrial scale experiments were done using methanesulfonic acid as catalyst, and the corresponding kinetic expressions were obtained from literature and described in equations 1 to 3 [17]. These expressions involve two contributing effects, the selfcatalytic due to the presence of acid groups in citric species, and the catalytic effect of methanesulfonic acid.

[(

)

](

)

(1)

[(

)

](

)

(2)

[(

)

](

)

(3)

Here,

,

and

are the reaction rates of formation of mono-butyl citrate (MBC), di-butyl citrate

(DBC), and tri-butyl citrate (TBC), respectively.

represents the mole fraction, and the subscript

numbers indicate each one of the components involved in the process (1-citric acid, 2-MBC, 3DBC, 4-TBC, 5-butanol and 6-water). reactor loading,

and

is the weight percentage of catalyst with respect to total

are the reaction rate coefficients for the self-catalyzed and catalytic 7

reaction, respectively.

are the equilibrium constants for each reaction step. The temperature

dependence of the kinetic parameters is described by Arrhenius-type expressions as presented in Equations 4 and 5. The whole set of kinetic parameters are summarized in Table 2. (

)

(4)

(

)

(5)

Table 2. Kinetic parameters for the esterification of citric acid with butanol using methane-sulfonic acid as catalyst [17] Reaction

Parameter

Units

Value

1/s

3.207 x 106 8.873 x 106 1.166 x 107

Self-catalytic

71433 J/mol

77346 80894 2.678 x 105

1/(%cat*s)

3.103 x 105 4.247 x 105

Catalytic

57917 J/mol

60065 66406 8.68

Equilibrium constants

3.56 1.04

The conceptual model used to describe the reactor operation is depicted in Figure 3, assuming a complete stirred tank. The corresponding total and component molar balances along processing time are stated in Equations 6 and 7.

8

FR FV

FOH

Q R-1

Figure 3. Reactor scheme for the tributyl citrate production process. (FR) - (FV) are the interconnection fluxes with the distillation column, (F OH) represents the butanol inlet flow and (Q) the heat duty (6)

∑

Here,

(7)

is the total number of accumulated moles in the reactor at time t ,

coefficients according to the reaction scheme of Figure 1, the volume of liquid in the reactor,

and

are the stoichiometric

is the molar density of the liquid,

the inlet and outlet molar flowrates, and

represents the punctual butanol additions. The subscripts i and k indicate each one of the components and reaction steps, respectively. Taking into account the reaction scheme (Figure 1), the component mole balances along the reaction time can be expressed as described in Equations 8 to 13: (8) (9)

(10) (11) (12)

9

(13) It was assumed that the interconnection streams with the distillation column (

and

) contained

butanol and water only. This happens because the large difference of volatility between them and the citric species. According to reported data, CA and DBC decompose before boiling, and the normal boiling point of TBC is 325 °C (170 °C at 0.13 kPa) [8,15,24]. Comparatively, the normal boiling point of the butanol and water are 117°C and 100°C, respectively [25]. Thus, the model was built under the assumption that CA, MBC, DBC and TBC remained in the reactor during the whole process. The corresponding dynamic energy balance for the reactor is presented in Equation 14, where and

,

are the temperature-and composition-dependent specific enthalpies of each stream, and

represents the heat duty supplied to the reactor by steam condensation in the jacket. (14)

The composition of the vapor stream leaving the reactor and entering the fractionation column ( ) was defined according to the vapor-liquid equilibrium of the reactive system. The NRTL model was used to describe the interactions of the liquid phase in the reactor, and ideal vapor phase was assumed. As stated before, the vapor phase included butanol and water only, and the partial pressure of the citric species is neglected. Then, the corresponding equilibrium calculations are expressed in Equations 15 to 17. (15) (16) (17) As before, subscripts 5 and 6 correspond to butanol and water in the liquid phase.

represents the

vapor pressure of the pure components which are calculated with Antoine’s equation using the parameters presented in Table S1 of the supplementary material.

is the activity coefficient in the

liquid phase computed with the NRTL model. The corresponding binary parameters were estimated using UNIFAC predictions and reported in Table S2 of the supplementary material. A verification of the vapor-liquid equilibria prediction for butanol-water is also presented in Figure S1 of the

10

supplementary material. Thus, given a reactor pressure ( ) and temperature, water ( butanol ( 2.2.2.

) and

) compositions in the vapor phase can be obtained along reaction time

Distillation column model

In the TBC production process, the main objective of the fractionation column is to separate the mixture butanol-water coming from the reactor. This enables water removal and butanol recirculation to overcome equilibrium limitations. The model was constructed under the assumption of negligible vapor holdup, equilibrium stage separation, constant pressure drop along the column, negligible heat losses, and a total condenser. Again, the batch distillation was conceived for the separation of the binary butanol-water only assuming that no citrates reach the column. The separation trays are numbered from bottom to top, and the corresponding mole and energy balances for each stage were proposed following the scheme presented in Figure 4.

Lj+1 hL,j+1 Vj hV,j NT,j Stage j

Lj hL,j

Vj-1 hV,j-1

Figure 4. Schematic representation of a distillation stage. j is the stage number, N the molar liquid hold-up, L-(V) the liquid flow rate, V is the vapor flow rate, and h is the specific enthalpy of each stream. Therefore, the dynamic component mole balances for the tray j are described by means of Equation 15. (15) Here,

represent the molar hold up of component i at stage j along time, and

liquid flow rates, and

and

the vapor and

their corresponding compositions in mole fraction. To compute the

liquid flowrate that leaves each tray ( ), the Francis weir equation was employed [26]. This 11

expression considers the geometry of the industrial column (diameter of the column, length and high of the weir), and it is included within the available templates in gPROMS ®. The details of the calculation are presented in Equations 16 to 18.

|

|

(16)

|

|

(17) (18)

Where

is the height of liquid in the stage j,

respectively,

and

and W the height and length of the weir

are dimensionless flow coefficients (1.84 and 1.5 respectively),

density of the liquid in tray j, and

is the

is a minimum height (parameter) that allows evaluating the

liquid flow in accordance with the algorithm conditions. Similarly to the reactor model, ideal behavior was assumed in the vapor phase, and the vapor-liquid equilibrium was represented with the NRTL activity model, as described in Equations 19 to 21 (19)

(20)

(21)

Here

is the vapor pressure of the component i at temperature of tray j;

coefficient; and

represents the activity

the total pressure in stage j. From literature reports, it is well stablished that

partial miscibility occurs in the mixture butanol-water; this could lead to the formation of two liquid phases inside column [27–29]. However, as shows Figure S2 in the supplementary material, the heterogeneous zone corresponds to rich water compositions. Hence, considering the continuous water removal, and the large butanol excess employed in the TBC production process, it is not expected to obtain liquid concentrations into the partial miscibility region. Thus, a single liquid 12

phase model was assumed inside the column. Nevertheless, as verified later, there was no presence of two liquid phases in the column trays, but only in the decanter. Additionally, the dynamic energy balance for tray j was expressed by Equation 22, where represents the total energy hold up at the stage, and

and

are the temperature-and composition-

dependent specific enthalpies of vapor and liquid streams, respectively (22)

2.2.3.

Decanter model

Once the top column product is condensed, it is directed to a decanter with the purpose of separating and removing water of the system. This is done by taking advantage of the partial miscibility of the mixture butanol and water, which allows discarding the rich-water phase and recycling the organic one (i.e. mainly butanol) as reflux for the column. Figure S2 of the supplementary material shows the corresponding liquid-liquid equilibrium of the butanol-water mixture at different temperatures. Equations 23 and 24 represent the dynamic mole balance of each component, where

denotes the molar flow rate coming from the condenser, and

and

the

output flow rates of light (organic) and heavy (aqueous) phases, respectively. (23) (24)

Additionally, the liquid-liquid equilibrium for the binary system is stated as presented in Equations 25 and 26. (25) (26)

2.3. Process Optimization 2.3.1.

Problem formulation

The main goal of a dynamic optimization problem is to find the time-dependent profiles of a set of variables that minimize/maximize a specified performance index. In general, an optimization

13

problem is composed of a performance index, the optimization variables (to be manipulated), the process model, and the equality and/or inequality constraints. In this work, according to process simulations and the current operation procedure, two objectives (

and

) were used during

optimization. These correspond to the energy consumption (E) and the batch time ( ), respectively. Then, the optimization problem for the TBC production process can be formulated as follows (Eq. 27-34).

Subject to

∫

(27)

∫

(28)

̇

(29) (30) (31) (32) (33)

(34)

Here, the final reaction yield ( ) is an end-point constraint that represents the molar ratio of produced TBC with respect to converted citric acid.

is an imposed path-constraint in order to

avoid the thermal degradation of citric species above 130°C [24, 30]. On the other hand, denotes the optimization variables, namely, heat input profile ( ), and punctual butanol additions (FOH) to the reactor. The corresponding limits of these variables were defined according to guidelines from a historical plant database. Regarding the initial conditions, the minimum butanol loading was defined to ensure citric acid dissolution (~3:1 butanol:acid mole ratio at 60 °C [14, 31]). However, as there is no upper limit for butanol loading in the reactor, three different alcohol:acid molar ratios (3.5:1 – 4:1 and 4.5:1) covering the commonly used ranges were evaluated. Other initial conditions required for integration corresponded to the catalyst loading (40

14

kg), citric acid loading (8000 kg), and initial temperature (60°C). The initial hold-up in trays is 10%, and decanter is empty at the beginning of operation. Regarding the batch time ( ), it is important to state that in accordance with the industrial operation, the process can be divided into two main steps. The first one is the pre-heating step, where only the reactor is under operation. Then, in the second one, a vapor stream (

) is being

continuously generated in the reactor, and hence the whole system (reactor – column – decanter) operates. Typically, and depending on the reactor loading and heating rate, the pre-heating entails 12 hours of around 20-26 hours of the whole esterification process. For this reason, the optimization was done for a time-horizon where

indicates the moment when the vapor generation begins, until

the end of the reaction ( ). 2.3.2.

Optimization approach

As aforementioned, the proposed optimization problem involves two simultaneous objectives: the energy consumption and the batch time. This means that rather than a unique value, there is a set of solutions (Pareto front) that are equally optimal, and represents the trade-off between the two objectives. Besides offering the possibility to obtain a wide range of operational conditions, this enables the inclusion of decision-makers for choosing the most appropriate solution based on their experience and on the process needs. A diversity of approaches has been reported in literature to address the multicriteria optimization of chemical processes. On one hand, the focus has been on dealing with some issues as the computing time and the classification of the Pareto front. In this regard, tools coupled to commercial simulators that can deal with arbitrary number of objectives allowing graphical exploration of the Pareto sets, have been developed [32]. This interactive method, which is based upon the approximation of the Pareto front and the real time visualization of the trade-offs of the objectives, provides the decision maker a complete insight of all optimal solutions. Concerning to computational effort, and specifically for dynamic reactive distillation processes, reduced order models have been proposed by using algebraic functions to approximate the process dynamics, and hence reduce the model complexity [33]. On the other hand, research accounting for the inherent uncertainty of the process parameters in multi-objective optimization can be found. For example, extensions of the average criterion method, the worst-case strategy, and the epsilon-constraint method, have been developed for multicriteria optimization at the design stage [34]. In the same way, the uncertainties in the process parameters and in the operator choices have been threated using chance constrained fuzzy simulation approach [35]. Using another approach, the operational risk associated with the 15

uncertainty of process parameters was addressed as an objective function in the interactive tool called Pareto Browser; this was developed to be used in multi-objective dynamic optimization problems under uncertainty [36]. In this work, the multi-objective optimization problem was solved using the weighting method, which consists in the transformation of the original problem in a single-objective optimization. Hence, the objective function can be expressed as stated in Equation 35, for the simultaneous optimization of the energy consumption and batch time in the TBC process. This is solved for different

values in order to obtain the set of points that form the Pareto front [37]. (35)

Here,

is the weighting factor,

cases (i.e.

and

and

are the values of the first objective for the two extreme

respectively), which also generate the corresponding values for

and

. This approach is employed to normalize the two objectives, avoiding inconsistencies due to their dissimilar order of magnitude. The optimization problem stated in Equations 27 to 35 was solved by using the control vector parameterization (CVP) method within gPROMS®. The problem was solved employing the standard solver for mixed sets of differential and algebraic equations (DASOLV), in a laptop computer with a Core i7® processor. Dynamic simulations lasted around 9 s and the optimization problem was solved within 5400 s for each weighting factors ( ). The classification of optimal solutions was done by means of a multi-criteria decision procedure. This consists of a model based upon a set of preference-related parameters (from decision-maker inputs) and the optimization results (from the Pareto front). In this work, the multi-attribute utility theory (MAUT) approach was used to stablish the preferred operating conditions during TBC production at the industrial scale. The MAUT method is based on the performance aggregation of the single utility functions that compose the global optimization problem [38, 39]. The solution strategy, described in Equations 36 to 38, requires the identification of the individual functions, and the determination of weighting ( ) and relative tolerance ( ) factors [39]. In this specific case, the utility functions correspond to the energy consumption ( ) and the batch time ( ). The weighting and tolerance parameters reflect the decision-maker desires, and in general, they are systematically obtained by doing surveys among experts to collect process information. Then, the global utility function ( ) is computed for each one of the Pareto front points for their subsequent classification. In this approach, the highest values of the function

represent the preferred solutions. 16

(

)

(

)

(36) (37) (38)

3. Results and Discussion 3.1. Industrial process characterization and model validation According to the operating procedure, citric acid and butanol were initially charged to the reactor with the catalyst. At the same time, steam heating started to reach the operating temperature that corresponded to the bubble point of the reactive mixture. Punctual additions of alcohol during the operation were used as make-up for the butanol losses during evaporation. Figure 5a and 5b depict the heating profiles and the times for butanol addition to the reactor, as recorded during the industrial experiments reported in the Table 1.

17

14

a

13

Heating Steam (kg/min)

Heating Steam (kg/min)

15

11

9 7

b 12

10

8

6

5

0

2

4

6

8

10

12

14

16

18

20

0

22

2

4

6

8

10

12

14

16

18

20

Time (h)

Time (h) 18

c

d

16

20

Acidity (% kg/L)

Acidity (% kg/L)

24

16 12 8 4

14 12

10 8 6 4

2 0

0

0

2

4

6

8

10

12

14

16

18

20

0

22

2

4

6

10

12

14

16

18

20

130

130

120

Temperature ( C)

120

Temperature ( C)

8

Time (h)

Time (h)

e

110

100

f

110

100

90 80 70

90 80

60

50

70 0

2

4

6

8

10

12

Time (h)

14

16

18

20

22

0

2

4

6

8

10

12

14

16

Time (h)

Figure 5. Results from the industrial scale experiments during batch production of tributyl citrate, at conditions reported in Table 1. Run 1 (a, c, e). Run 2 (b, d, f). (─) Heating steam flow rate. (--) Time for butanol additions. (●) Experimental data. (─) Model prediction. As observed, there is a continuous and variable heat input, and the corresponding butanol additions occurred at different time during the two batches. These variables were manipulated according to the operator’s expertise following two main guidelines: avoiding that the reactor temperature exceeded 130°C, and to reach the target acidity (0.3 % kg/L) as soon as possible. As the operating conditions were different in the experiments, the total processing times in both were also different. 18

18

20

As observed in Figures 5c and 5d, the acidity at the beginning of the operation shows a slight increase with respect to the initial loading. This was caused by the heterogeneity of the initial samples withdrawn from the reactor because there was some solid citric acid remaining in the liquid phase. However, as the whole acid loading got dissolved, the acidity profile along time decreased as expected. Also, as seen in Figures 5e and 5f, the operators successfully kept the process temperature below 130 °C to avoid thermal degradation of citric species. Regarding the proposed model, it is observed that it adequately predicts the time-dependent acidity and the temperature profile. Despite the stated assumptions involved in the model construction (e.g. completely mixed, no citric species in the vapor phase, negligible heat losses, etc.), predictions fitted well both experiments. This also constitutes an indicative for the accuracy of the employed physicochemical, thermodynamic, and kinetic models. The observed deviations of acidity between experiments and model predictions at the beginning of the operation (< 3 hours) indicate that the assumption of complete dissolution is not entirely correct. Currently, this is calculated according to the solid-liquid equilibrium, however the model could be further improved by incorporating a dissolution kinetics in the reactive media. In spite of the slight differences observed, the model predicts well the process performance and it can be used for further optimization. Aiming to verify the effect of butanol additions on the process performance, simulations of the studied batches were done, with and without butanol additions. The obtained reaction rates of the different citrate species and the reactor temperature profiles are depicted in Figure 6. Interestingly, as verified when comparing Figures 6a and 6c for Run 1, and Figures 6b and 6d for Run 2, butanol additions have no positive effect on the reaction rates. While this is counter intuitive taking into account the chemical equilibrium principles, there is need to consider the simultaneous interaction of phase equilibria and reaction kinetics. The reactor is already working under an excess of butanol and with water removal, so the chemical equilibrium is already shifted to the products. However, as the reaction media is operating at the bubble point of the mixture, this temperature is low because of the large excess of butanol. If the reactive mixture becomes richer in citric species, higher operating temperatures could be achieved, enhancing TBC production. This can be verified in the modeled temperature profiles of the Run 1 and Run 2 assuming no butanol addition (Figure 6e and 6f, respectively), and the corresponding TBC production rates (Figures 6c and 6d, respectively). This occurs because the last esterification step has the lowest equilibrium constant and the highest energy of activation for both, the self-catalyzed and the catalytic reaction.

19

4

Reaction rate x 104 (min-1)

Reaction rate x 104 (min-1)

6

a

5 4 3 2 1 0

b 3

2

1

0 0

2

4

6

8

10

12

14

16

18

20

22

0

2

4

6

8

Time (h)

12

14

16

18

20

Time (h)

6

4

Reaction rate x 104 (min-1)

Reaction rate x 104 (min-1)

10

c

5 4 3 2 1 0

d 3

2

1

0 0

2

4

6

8

10

12

14

16

18

20

22

0

2

4

6

8

Time (h)

10

12

14

16

18

20

Time (h)

140

130

120

110

Temperature ( C)

Temperature ( C)

130

e

100 90 80 70

120

f

110 100 90 80

60 50

70

0

2

4

6

8

10

12

Time (h)

14

16

18

20

22

0

2

4

6

8

10

12

14

16

Time (h)

Figure 6. Simulated reaction rates and temperature profiles in the industrial scale batch reactor during TBC production according to operating conditions of Table 1. (a, b) Reaction rates for Run 1 and Run 2 with butanol addition. (c, d) Reaction rates for Run 1 and Run 2 without butanol addition. (e, f) Temperature profiles for run 1 and 2, with and without butanol addition. (―) MBC production rate, (─) DBC production rate, (─) TBC production rate, (--) Time of butanol addition. (―) Temperature profile with butanol addition, (―) Temperature profile without butanol addition. The composition profiles in the reactor and the column during the experiments, and the corresponding output water flow rate from decanter, are presented in Figures S3 to S5 of the supplementary material. Additionally, the composition and temperature at every tray of the 20

18

20

distillation column is depicted in Figure S6, along with the reported liquid-liquid equilibrium data for the butanol-water system. This indicates that the column operates outside of the partial miscibility region, and the liquid at every stage was completely homogeneous. Moreover, Figure S7 allows to verify that the simplified VLE model predict almost the same results that the complete VLLE model in the operating region of the column. Main simulation results of Runs 1 and 2 are summarized in Table 3, including the hypothetical cases without supplying extra-butanol during reaction. The final reaction yield ( ) was computed in a molar basis, as the ratio of produced TBC to converted citric acid. In general, results suggest that yield to TBC, product purity, and raw material consumption can be improved using only a single initial alcohol loading. Additionally, decreasing the alcohol loading can have a positive impact in the subsequent TBC purification because of the reduced energy requirement. Clearly, this reduction is limited by the required amount for citric acid dissolution. Table 3. Simulation results of two TBC production batches Parameter

Run 1

Run 2

Base

Without +ButOH

Base

Without +ButOH

Yf to TBC (%)

96.2

97.4

93.9

95.3

TBC (% w/w)

66.0

81.0

60.3

68.8

ButOH (% w/w)

31.7

17.0

36.3

28.3

ButOH consumption (L)

20562

15830

22337

19187

T. max. (°C)

124.3

133.4

123.6

126.6

Energy consumption(kg steam)

13333

13333

11961

11961

TBC produced (kg)

14417

14557

14076

14271

3.2. Process optimization Once the reliability of the developed model was verified, process optimization was accomplished with respect to the controlled variables (

and FOH), and using different initial acid:alcohol feed

molar ratios. Figure 7 depicts the profiles of the optimization variables for three different cases: when only the energy consumption was optimized (ɛ = 1); when the energy consumption and batch time are minimized using the same weight factor (ɛ = 0.5); and when only the batch time is minimized (ɛ = 0).

21

25

a

b

20

15

FButanol (L/min)

Heating Steam (kg/min)

20

15

10

10

5

5

0

0 0

4

8

12

16

20

24

0

4

8

12

Time (h)

Time (h)

c

24

d

10

15

FButanol (L/min)

Heating Steam (kg/min)

20

12

20

10

5

8

6 4 2

0

0 0

4

8

12

16

20

24

0

Time (h)

4

8

12

Time (h)

16

20

24

3

20

e

f

2,5

15

FButanol (L/min)

Heating Steam (kg/min)

16

10

5

2 1,5 1 0,5 0

0 0

4

8

12

Time (h)

16

20

24

0

4

8

12

16

20

Time (h)

Figure 7. Optimal profiles of heat supply and butanol addition during the batch production of TBC using three different alcohol:acid feed molar ratios.(a, b) 3.5:1.(c, d) 4:1. (e, f) 4.5:1. Weight factors (--) ɛ = 0, (--) ɛ = 0.5, (─) ɛ = 1. In general, results indicate that the best operating policy is to use as large heat input as possible during the first processing hours. This happens because in the optimization, the reactor tends to rise to the highest allowed temperature as soon as possible to enhance reaction yield. Additionally, the obtained profiles indicate a direct relation between the optimization variables; this is, when a large heat duty is used, it is also necessary to add higher amounts of butanol. The reason for this is that the butanol injections represent the system response to two fundamental process demands: keeping 22

24

excess of alcohol in the reactor, and regulating the temperature to avoid decomposition of citric species. In consequence, at large heat loadings, there is higher water and butanol evaporation, and thus larger make-up butanol is required in the reactor. Regarding the multi-objective optimization, it can be seen that the optimal operating policy changes with the ponderation factor. For example, when the optimization is done with respect to the batch time minimization (ɛ = 0), the heat supply must be as higher as possible during the whole operation. This occurs because, once achieved the bubble temperature of the reactive mixture, the vapor flow rate that leaves the reactor (

) is proportional to the heat duty. Hence, in this case the optimization

is focused in achieving high water removal rates and high temperatures, without considering the energy consumption that this involves. The corresponding optimal profiles of temperature and acidity for each one of the cases shown in Figure 7, are presented in Figure 8. The corresponding set of optimal solutions that constitute the Pareto front for the evaluated feed ratios are presented in Figure 9. These results show the conflicting character of the two objectives and the trade-offs between them. Therefore, large energy consumption would reduce processing time but also increase additional butanol consumption. Meanwhile, long processing time would require less energy but at the cost of a reduced reactor productivity. It is noted the great potential improvement that can be obtained in the process with respect to the typical operating conditions (i.e. average between the two studied batches) at the industrial practice. Indeed, energy saving up to 28% and processing time reductions up to 10 hours can be achieved according to the optimization results. Once the points of the Pareto front are obtained, the remaining challenge consists in the selection of the most suitable conditions to be implemented at the industrial scale. This implies involving decision-maker inputs within the optimization procedure. Thus, based upon experience and knowledge of the process, decision-makers help establishing the preferences between the competitive objectives, in order to rank all the possible solutions. In this study, the MAUT approach was used as decision-making aid tool, considering a hypothetical scenario of preferences, and taken as example the feed ratio 3.5:1 butanol:acid.

23

135

20

Acidity (% kg/L)

Temperature ( C)

130

125

a

120

115 110 105

b

16 12 8 4

0

100 0

4

8

12

16

20

0

24

4

8

135

Acidity (% kg/L)

Temperature ( C)

16

20

24

20

130

125 120

c

115 110 105

d

16 12 8 4

0

100 0

4

8

12

16

20

0

24

4

8

12

16

20

24

Time (h)

Time (h) 135

20

Acidity (% kg/L)

130

Temperature ( C)

12

Time (h)

Time (h)

125 120

e

115 110 105 100

16

f

12 8 4

0 0

4

8

12

Time (h)

16

20

24

0

4

8

12

16

20

Time (h)

Figure 8. Optimal profiles of temperature and acidity in the reactor during the batch production of TBC using three different alcohol:acid feed molar ratios. (a, b) 3.5:1. (c, d) 4:1. (e, f) 4.5:1. Weight factors (--) ɛ = 0, (--) ɛ = 0.5,(─) ɛ = 1.

24

24

Energy (kg steam)

17000

14000

Typical industrial operating point

11000

8000 13

14

15

16

17

18

19

20

21

22

23

24

Time (h) Figure 9. Pareto fronts of the optimal solutions during the batch production of TBC for three different alcohol: acid feed molar ratios (○) 3.5:1. (□) 4:1. (∆) 4.5:1. The influence of tolerance parameter ( ) on the individual utility performance functions is shown in Figure 10. Here, it is observed that at high values of the relative tolerance parameter (e.g.

),

the single utility function decrease slowly from its optimal value ( =1). From the operating point of view, this represents a case when the price and/or impact of energy is not a big concern for the manufacturer. Thus, even solutions with elevated energy consumption could be ranked in high positions according to MAUT method. In contrast, when the relative tolerance is low (e.g.

),

the utility function is very sensible to changes in the operating condition, and a slight modification can imply significant impacts on the process performance (i.e. high energy costs). In the evaluated scenario, it was considered that the manufacturer uses residual streams for steam generation. Hence, energy is available at a relatively low cost and high energy consumption could be tolerated during TBC production. Regarding batch time ( ), an approximately lineal relation was assumed between the optimal points and the individual utility function. Table 4 summarizes the relative tolerance and weight factors used to rank the optimal solutions of the TBC production process.

25

1

1

μ = 0.7 μ=3 μ = 0.3 μ=6

0,8

μ=2 μ = 0.8 μ = 0.2 μ=4

0,8

0,6

z2

z1

0,6

0,4 0,2

0,4

0,2

a

0 9000

11000

13000

b

0 13,0

15000

15,0

J1(kg steam)

17,0

19,0

21,0

23,0

J2 (h)

Figure 10. Representation of the effect of relative tolerance factor ( ) on the individual utility functions. (a) Energy consumption, (b) Batch time. Table 4. Parameters of the individual utility functions for MAUT method implementation. Function J1 J2

Weight 0.4 0.6

0.3 0.8

A classification of the Pareto points by using the MAUT approach is presented in Table 5 and Figure 11. The results were divided in 6 groups according to their position in the obtained ranking. Each group comprises two optimal solutions, except the first category, which corresponds only to the preferred one. The ranking clearly reflects the proposed decision-maker preferences, since the best point is relatively closer to the minimal processing time. Comparatively, those solutions located in the minimal energy consumption side are classified as the least preferable alternatives Table 5. Pareto front classification according to the MAUT method for TBC process using 3,5:1 butanol:acid feed molar ratio. ɛ

Energy ( kg vapor)

Time (h)

Utility Function

1

9117.6

23.3

0.400

0.9

9357.8

23.2

0.412

0.8

9686.3

19.2

0.681

0.7

9857.8

17.3

0.782

0.6

10318.6

16.4

0.821

0.5

10612.7

15.5

0.859

0.4

11274.5

14.9

0.875

0.3

11813.7

14.4

0.887 26

0.2

12867.6

13.9

0.880

0.1

14661.8

13.4

0.817

0

15593.1

13.3

0.600

Energy (kg steam)

17000

Typical industrial operating point

14000 Preferred solution

11000

8000 13

14

15

16

17

18

19

20

21

22

23

24

Time (h) Figure 11. Ranking of Pareto solutions according to the MAUT method in the TBC production process using 3.5:1 butanol:acid feed molar ratio. Rank of solutions (●) 2, (●) 3, (●) 4, (●) 5, (●) 6. Conclusions A dynamic model of an industrial scale batch process for tributyl citrate productions was developed. The process consisted of a stirred tank reactor coupled to a distillation column with top decanter for water removal. Based upon industrial scale experiments it was verified that the model was able to reproduce main process characteristics, so this can be used for process analysis and further optimization. The multi-objective optimization problem consisted in the simultaneous minimization of the total energy consumption and batch time. The butanol addition and heat supply policies were used as control variables, since these were identified as the major variables to ensure high reactions yields, low energy consumption and short batch times. The dynamic optimization was solved for three different alcohol-to-acid feed molar ratios, and it was found that the batch time can be reduced up to 36% by employing an optimal heat flow and butanol loading policy. Finally, the multiattribute utility theory (MAUT) approach was used to rank the Pareto front solutions assuming that low cost energy is available at the industrial facility. From this classification, it was found that the

27

batch time can be reduced up to 32% by employing an optimal heat flow and butanol loading policy.

Conflict of interests Declarations of interest: none

Acknowledgement This work was supported by “Departamento Administrativo de Ciencia Tecnología e Innovación – Colciencias”, under the Project Code: 1101-569-33201, and by the DIB projects code 42982.

References [1]

G. Wypych, Handbook of Plasticizers, 3rd ed., ChemTec Publishing, Toronto - Canada, 2017.

[2]

M.G.A. Vieira, M.A. da Silva, L.O. dos Santos, M.M. Beppu, Natural-based plasticizers and biopolymer films: A review, Eur. Polym. J. 47 (2011) 254–263. doi:10.1016/j.eurpolymj.2010.12.011.

[3]

IHS Markit, Plasticizers, (2018). https://ihsmarkit.com/products/plasticizers-chemicaleconomics-handbook.html (accessed December 5, 2018).

[4]

Plasticisers - Information Center, Regulation, (2018). https://www.plasticisers.org/regulation/ (accessed December 7, 2018).

[5]

A.D. Godwin, Plasticizers, in: M. Kutz (Ed.), Appl. Plast. Eng. Handb., 1st ed., William Andrew - Elsevier, Oxford, 2011: pp. 487–501. doi:10.1016/B978-1-4377-3514-7.10028-5.

[6]

M. Rahman, C.S. Brazel, The plasticizer market: An assessment of traditional plasticizers and research trends to meet new challenges, Prog. Polym. Sci. 29 (2004) 1223–1248. doi:10.1016/j.progpolymsci.2004.10.001.

[7]

F. Chiellini, M. Ferri, A. Morelli, L. Dipaola, G. Latini, Perspectives on alternatives to phthalate plasticized poly(vinyl chloride) in medical devices applications, Prog. Polym. Sci. 28

38 (2013) 1067–1088. doi:10.1016/j.progpolymsci.2013.03.001. [8]

A. Wypych, Citrates, in: Datab. Plast., 2nd ed., ChemTec Publishing, Toronto - Canada, 2017: pp. 182–204.

[9]

G. Wypych, Plasticizer Types, in: Handb. Plast., 3rd ed., Toronto - Canada, 2017: pp. 7–84.

[10]

D.J. Miller, N. Asthana, A. Kolah, D.T. Vu, C.T. Lira, Process for Reactive Esterification Distillation, US 7,667,068 B2, 2010.

[11]

A.K. Kolah, N.S. Asthana, D.T. Vu, C.T. Lira, D.J. Miller, Triethyl citrate synthesis by reactive distillation, Ind. Eng. Chem. Res. 47 (2008) 1017–1025. doi:10.1021/ie070279t.

[12]

M.A. Santaella, L.E. Jiménez, A. Orjuela, J.G. Segovia-Hernández, Design of thermally coupled reactive distillation schemes for triethyl citrate production using economic and controllability criteria, Chem. Eng. J. 328 (2017) 368–381. doi:10.1016/j.cej.2017.07.015.

[13]

C.B. Panchal, J.C. Prindle, A. Kolah, D.J. Miller, C.T. Lira, Integrated process of distillation with side reactors for synthesis of organic acid esters, US 9,174.920 B1, 2015.

[14]

M.A. Santaella, A. Suaza, C.E. Berdugo, J.L. Rivera, A. Orjuela, Phase Equilibrium Behavior in Mixtures Containing Tributyl Citrate, Citric Acid, Butan-1-ol, and Water, J. Chem. Eng. Data. 63 (2018) 3252–3262. doi:10.1021/acs.jced.8b00064.

[15]

A. Suaza, M.A. Santaella, L.A. Rincón, Á.L. Alarcón, A. Orjuela, Dibutyl Citrate Synthesis, Physicochemical Characterization, and Px Data in Mixtures with Butanol, J. Chem. Eng. Data. 63 (2018) 1946–1954. doi:10.1021/acs.jced.7b01064.

[16]

Z. Zheng, J. Xu, J. Jiang, Y. Lu, Y. Huang, Synthesis of tributyl citrate using SO 42-/ZrMCM-41 as catalyst, Process Saf. Environ. Prot. 25 (2011) 147–150. doi:10.1016/j.psep.2009.11.002.

[17]

O.M. Osorio-Pascuas, M.A. Santaella, G. Rodriguez, A. Orjuela, Esterification Kinetics of Tributyl Citrate Production Using Homogeneous and Heterogeneous Catalysts, Ind. Eng. Chem. Res. 54 (2015) 12534–12542. doi:10.1021/acs.iecr.5b03608.

[18]

H. Yang, H. Song, H. Zhang, P. Chen, Z. Zhao, Esterification of citric acid with n-butanol over zirconium sulfate supported on molecular sieves, J. Mol. Catal. A Chem. 381 (2014) 54–60. doi:10.1016/j.molcata.2013.10.001. 29

[19]

K.Y. Nandiwale, P. Gogoi, V. V. Bokade, Catalytic upgrading of citric acid to environmental friendly tri-butyl citrate plasticizer over ultra stable phosphonated Y zeolite, Chem. Eng. Res. Des. 98 (2015) 212–219. doi:10.1016/j.cherd.2015.04.037.

[20]

J.D. Fonseca, A.M. Latifi, A. Orjuela, I.D. Gil, G. Rodríguez, Dynamic Simulation and Optimisation of an Industrial Process for Tributyl Citrate Production, in: Comput. Aided Chem. Eng., 2016: pp. 1135–1140. doi:10.1016/B978-0-444-63428-3.50194-6.

[21]

A. Marquez-Ruiz, C.S. Méndez-Blanco, L. Özkan, Modeling of reactive batch distillation processes for control, Comput. Chem. Eng. 121 (2019) 86–98. doi:10.1016/j.compchemeng.2018.10.010.

[22]

D.Y. Aqar, N. Rahmanian, I.M. Mujtaba, Feasibility of integrated batch reactive distillation columns for the optimal synthesis of ethyl benzoate, Chem. Eng. Process. Process Intensif. 122 (2017) 10–20. doi:10.1016/j.cep.2017.08.012.

[23]

G. Fernholz, S. Engell, A. Gorak, Optimal operation of a semi-batch reactive distillation column, Comput. Chem. Eng. 24 (2000) 1569–1575.

[24]

M.M. Barbooti, D. Al-Sammerrai, Thermal decomposition of citric acid, Thermochim. Acta. 98 (1986) 119–126. doi:10.1016/0040-6031(86)87081-2.

[25]

B.E. Poling, G.H. Thomson, D.G. Friend, R.L. Rowley, W.V. Wilding, Physical and Chemical Data, in: Perry’s Chem. Eng. Handb., 8th ed., McGRAW-HILL, 2007: pp. 153– 155. doi:10.1036/0071511253.

[26]

Process Systems Enterprise (PSE), gPROMS ModelBuilder, (2014). www.psenterprise.com.

[27]

H. Kosuge, K. Iwakabe, Estimation of isobaric vapor-liquid-liquid equilibria for partially miscible mixture of ternary system, Fluid Phase Equilib. 233 (2005) 47–55. doi:10.1016/j.fluid.2005.04.010.

[28]

R. Stephenson, J. Stuart, Mutual Binary Solubilities: Water-Alcohols and Water-Esters, J. Chem. Eng. Data. 31 (1986) 56–70. doi:10.1021/je00043a019.

[29]

R. Peschla, B.C. Garćía, M. Albert, C. Kreiter, G. Maurer, Chemical equilibrium and liquidliquid equilibrium in aqueous solutions of formaldehyde and 1-butanol, Ind. Eng. Chem. Res. 42 (2003) 1508–1516. doi:10.1021/ie020743o.

30

[30]

D. Wyrzykowski, E. Hebanowska, G. Nowak-Wiczk, M. Makowski, L. Chmurzyński, Thermal behaviour of citric acid and isomeric aconitic acids, J. Therm. Anal. Calorim. 104 (2011) 731–735. doi:10.1007/s10973-010-1015-2.

[31]

H. Yang, J.H. Wang, Solubilities of 3-carboxy-3-hydroxypentanedioic acid in ethanol, butan-1-ol, water, acetone, and methylbenzene, J. Chem. Eng. Data. 56 (2011) 1449–1451. doi:10.1021/je101167z.

[32]

M. Bortz, J. Burger, N. Asprion, S. Blagov, R. Böttcher, U. Nowak, A. Scheithauer, R. Welke, K.H. Küfer, H. Hasse, Multi-criteria optimization in chemical process design and decision support by navigation on Pareto sets, Comput. Chem. Eng. 60 (2014) 354–363. doi:10.1016/j.compchemeng.2013.09.015.

[33]

P.S. Reddy, K.Y. Rani, S.C. Patwardhan, Multi-objective optimization of a reactive batch distillation process using reduced order model, Comput. Chem. Eng. 106 (2017) 40–56. doi:10.1016/j.compchemeng.2017.05.017.

[34]

I. V. Datskov, G.M. Ostrovsky, L.E.K. Achenie, Y.M. Volin, An approach to multicriteria optimization under uncertainty, Chem. Eng. Sci. 61 (2006) 2379–2393. doi:10.1016/j.ces.2005.11.005.

[35]

K. Mitra, Multiobjective optimization of an industrial grinding operation under uncertainty, Chem. Eng. Sci. 64 (2009) 5043–5056. doi:10.1016/j.ces.2009.08.012.

[36]

M. Vallerio, J. Hufkens, J. Van Impe, F. Logist, An interactive decision-support system for multi-objective optimization of nonlinear dynamic processes with uncertainty, Expert Syst. Appl. 42 (2015) 7710–7731. doi:10.1016/j.eswa.2015.05.038.

[37]

G. Pandu Rangaiah, Multi-objective Optimization: Techniques and Applications in Chemical Engineering, World Scientific Publishing, Singapore, 2009. doi:10.1007/978-184800-382-8_2.

[38]

M. Bystrzanowska, M. Tobiszewski, How can analysts use multicriteria decision analysis?, TrAC - Trends Anal. Chem. 105 (2018) 98–105. doi:10.1016/j.trac.2018.05.003.

[39]

B. Benyahia, M. a. Latifi, C. Fonteix, F. Pla, Multicriteria dynamic optimization of an emulsion copolymerization reactor, Comput. Chem. Eng. 35 (2011) 2886–2895. doi:10.1016/j.compchemeng.2011.05.014. 31

Graphical Abstract

32