Multiobjective optimization and experimental validation for batch cooling crystallization of citric acid anhydrate

Accepted Manuscript

Multiobjective optimization and experimental validation for batch cooling crystallization of citric acid anhydrate K. Hemalatha , P. Nagveni , P. Naveen , K. Yamuna Rani PII: DOI: Reference:

S0098-1354(18)30086-3 10.1016/j.compchemeng.2018.02.019 CACE 6033

To appear in:

Computers and Chemical Engineering

Received date: Revised date: Accepted date:

21 December 2017 9 February 2018 19 February 2018

Please cite this article as: K. Hemalatha , P. Nagveni , P. Naveen , K. Yamuna Rani , Multiobjective optimization and experimental validation for batch cooling crystallization of citric acid anhydrate, Computers and Chemical Engineering (2018), doi: 10.1016/j.compchemeng.2018.02.019

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ACCEPTED MANUSCRIPT Highlights Multiobjective optimization of crystallization of citric acid anhydrate is carried out

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Solubility of citric acid anhydrate is validated experimentally

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Different polynomial cooling policies are compared through simulation

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Piecewise constant temperature control profile is determined through MOO

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Tracking optimal profile through experiment showed NMS & CV comparable to

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simulation results

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Multiobjective optimization and experimental validation for batch cooling crystallization of citric acid anhydrate K. Hemalatha1, 2, P. Nagveni1, 2, P. Naveen1, 2, K. Yamuna Rani1, 2* 1

Process Dynamics and Control group, Chemical Engineering Department& 2

Academy of Scientific and Innovative Research (AcSIR),

CSIR-Indian Institute of Chemical Technology, Hyderabad-500007, India.

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*E-mail: [email protected]

Abstract

Multiobjective optimization (MOO) of crystallization systems is gaining importance due to

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its ability to handle multiple conflicting objectives together for finding optimal operating policies. The present study focuses on batch cooling crystallization of citric acid. Among the two forms of citric acid, citric acid anhydride (CAA) is chosen for experimentation as no

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such study is available. MOO is carried out to seek optimal cooling policy for unseeded cooling crystallization of CAA to maximize mean crystal size while minimizing variance in

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size. In this procedure, temperature is discretized using piecewise constant-control vector

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parameterization which is simple and convenient for practical implementation. The model reported in literature is suitably modified for solubility parameters which are verified

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experimentally, and employed for optimization. One of the optimal solutions from the Pareto solution set is implemented through experimentation successfully and the measured product

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crystal properties are comparable to the predicted results obtained through optimization. Keywords

Multiobjective optimization; batch cooling crystallization; citric acid anhydrate; crystal size distribution; optimal cooling policy; experimental implementation.

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1. Introduction Crystallization processes have been widely used for production, purification or recovery of solid materials in almost all process industries. In particular, batch crystallization is primarily used in pharmaceutical, food, specialty and fine chemical industries. The solids obtained through crystallization are further processed to yield powders, pastes, dispersions,

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tablets, etc. Thus the control of crystal properties such as size, shape, morphology, and purity that decides the quality and solid characteristics of the final product is of major concern in batch crystallizationas it has significant effect on the ease of down-stream processing such as

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filtration and drying.

Considerable amount of research has focused on optimization and control of batch cooling crystallizers including online monitoring that are discussed in recent review papers (Nagy and Braatz, 2012; Nagy et al., 2013; Ulrich and Frohberg, 2013; Samad et al, 2013;

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Simon et al., 2015). Majority of the studies have focused on control of crystal size distribution (CSD) or shape, as these crystal properties strongly influence the product quality,

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functionality and processing (Doherty, 2007). The optimal control of batch crystallizers can

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be achieved through supersaturation control by manipulating the temperature throughout the batch. Thus, for batch cooling crystallization processes, it is necessary to determine an

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optimal temperature trajectory satisfying any of these performance objectives through which a desirable product quality is obtained.

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Determination of optimal model-based control policies has been widely investigated

in the literature. The concept of programmed cooling of batch crystallizers has been introduced by Mullin and Nyvlt, (1971) who proposed that a significant increase in the crystal size is obtained by implementing a cooling profile obtained for constant nucleation rate throughout the batch. This fact has been emphasized by several researchers who ascertained improvement in crystal size with controlled cooling compared to different 3

ACCEPTED MANUSCRIPT temperature profiles including natural and linear cooling curves (Mullin and Nyvlt, 1974; Jones, 1974; Mayrhofer and Nyvlt, 1988; Rohani and Bourne, 1990; Bohlin and Rasmuson, 1992; Xie et al, 2001). Several studies have focused on optimal seeding in a batch crystallizer (Chung, et al., 1999; Ma et al, 1999; Chung, et al., 2000; Zhang and Rohani, 2003;Hu et al., 2004; Costa et al., 2005; Shi et al, 2006; Choong and Smith, 2004; Patience et al., 2004;

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Aamir et al., 2010). Seed properties such as seed size and mass and seed loading (Kubota et al., 2002) are also proven to affect final crystal size distribution in addition to temperature and have also been optimized. Substantial research activity has been devoted to closed loop temperature/concentration control studies including classical control approach and predictive

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control approach for control of crystal size distribution (Miller and Rawlings, 1993; Miller and Rawlings, 1994; Matthews and Rawlings, 1998; Zhang and Rohani, 2003; Fujiwara et al, 2002;Lewiner et al, 2001;Fujiwara et al, 2004; Worlitschek and Mazzotti, 2004; Shi et al,

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2005; Shi et al, 2006; Christofides et al, 2007; Yu et al, 2007; Nagy et al, 2008;Nagy et al, 2009; Aamir et al, 2009; Hermanto et al, 2009; Mesbah et al, 2011; Kwon et al, 2014; Kwon

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et al, 2015). Few experimental studies have been reported for implementation of optimal

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temperature profilesfor some case studies. Jones and Mullin (1974) compared different cooling curves experimentally for potassium sulfate-water system and found that the

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programmed cooling with constant nucleation control and metastable control showed improvement in product crystal size compared to natural cooling. Similarly, Mohameed etal.

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(2002) have also implemented three different cooling curves and studied the effect of cooling rate on crystal size distribution for potassium chloride-water system to choose an optimal trajectory. Worlitschek and Mazzotti (2004) optimized the temperature trajectory for the batch cooling crystallization of paracetamol from ethanol with the final particle size distribution defined as the control objective. Aamir et al. (2012) proposed a novel targeted direct design approach to systematically design different cooling profiles and hence batch

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ACCEPTED MANUSCRIPT times, with the objective being the desired shape of product CSD and validated experimentally for potassium dichromate-water system. Significant research on batch cooling crystallizers focused on finding the optimal cooling profiles in order to improve the process performance using a single objective pertaining to the product size distribution (Chung et al, 1999; Chung et al, 2000; Choong and Smith, 2004; Costa et al, 2005; Ma et al, 1999;

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Mohameed et al, 2003; Ward et al, 2006; Hounslow and Reynolds, 2006; Hsu et al, 2013; Tseng, et al, 2017) while incorporating process model equations and temperature magnitude and rate limits, and optionally minimum yield, as constraints. However, there has been a lot of interest in seeded cooling crystallization processes compared to unseeded crystallization

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processes. The optimization or control objectives that are usually considered as measures of product characteristics in the above cited literature are large mean size, uniform distribution or minimum coefficient of variation, desired shape of product size distribution, seed

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properties, shorter batch times or high yield. Some of these studies are dedicated to choice and comparison of objective functions (Ward et al, 2006; Hsu et al, 2013; Tseng, et al, 2017)

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used in batch cooling crystallization processes.

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Majority of the literature cited above on cooling crystallization has concentrated on solving single objective optimization problems for different crystallization systems.

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However, crystallization processes have multiple objectives that are conflicting in nature and there exists a tradeoff between these objectives which makes it necessary to consider multi

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objective optimization to obtain optimal operating policies for better CSD. Thus, it is necessary to study multi objective optimization (MOO) of batch cooling crystallization processes. Sarkar et al. (2006) carried out MOO for the first time for simulation of seeded cooling crystallization of potassium sulfate from water. Since then, the application of MOO to crystallization processes has received focus not only in cooling crystallization but also in reactive or antisolvent crystallization processes. Sarkar et al. (2007) have carried out MOO

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ACCEPTED MANUSCRIPT for reactive crystallization processes through simulation to find optimal feeding policies for maximum weight mean size and minimum coefficient of variation for barium sulfate-water system. Sheikhzadeh et al. (2008) and Trifkovic et al. (2009) have proposed novel real-time dynamic optimal control methodology for seeded, anti-solvent crystallization of paracetamol from isopropanol and water in an offline and online manner. The optimal antisovent (water)

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addition profile has been sought with respect to maximum mean size and high yield through simulation and also validated experimentally. They even compared the results of MOO with single objective optimization and suggested that better crystal growth and yield are achieved through MOO. Acevedo et al. (2015) have implemented a multiobjective optimization

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framework for size and shape optimization of two systems, potassium dihydrogenphosphate and paracetamol. The optimal cooling policies have been determined with mean size and target aspect ratio as objectives for unseeded cooling crystallization. Hemalatha and Rani

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(2017) have studied MOO of batch cooling crystallization of unseeded paracetamol crystallization and seeded potassium nitrate crystallization using maximization of mean size

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and minimization of CV as the objectives in the unseeded case and, additionally,

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minimization of nucleated mass in the seeded case. Yet, research studies considering multiple objectives in the context of batch cooling crystallization are less explored compared to

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traditional single objective optimization studies. Further, though several simulation studies are reported on batch crystallization of citric acid anhydrate(CAA) (which has applications in

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food, beverage and pharmaceutical industries), the process has not been studied in the context of MOO and the experimental validation for such process has also not been explored. Thus, crystallization of citric acid anhydrate is chosen as the topic of interest in the present work. In the present study, unseeded batch cooling crystallization of citric acid anhydrate is considered for multi objective optimization and experimental implementation. In this work, maximizing average crystal size and minimizing coefficient of variation are considered as

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ACCEPTED MANUSCRIPT objectives. Average crystal size, expressed in terms of number mean size, and coefficient of variation are considered based on the suitability for measurement according to our recent work (Hemalatha and Rani, 2017). In this recent work, MOO of unseeded and seeded batch cooling crystallization are studied through simulation only for Paracetamol and Potassium nitrate systems respectively, whereas in the present study, first attempt is made to implement

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the optimal cooling policy that is determined through MOO through experimentation for citric acid anhydrate, and the results obtained are compared with simulation studies. 2. Experimental system

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This section discusses details regarding the system chosen i.e. CAA including specific literature reported on its crystallization, solubility characteristics of CAA, experimental setup, the procedure used to carry out cooling crystallization in a batch crystallizer, and

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measurement and product characterization techniques used. 2.1. System Overview

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Citric acid is widely used in the food, beverage and pharmaceutical industries to

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impact a clean, refreshing tartness. Its prime use is as an acidulant, but it is also used as sequestrant of metal ions to give protection from the development of off-flavors and off-

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odors in certain food stuffs (Teixeira et al., 2012). Citric acid is also used in cosmetics and toiletries as buffer, and in a wide variety of industrial applications as a buffering and

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chelating agent. Citric acid is also a reactive intermediate in chemical synthesis. In addition, its carboxyl and hydroxyl groups permit the formation of a variety of complex molecules and reactive products of commercial interest (Soccol et al., 2006). Citric acid crystallizes in anhydrous and monohydrate forms. The transition temperature of CAA to monohydrate is first reported by Bennet and Yuill (1935) to be below 36.3 oC. Caillet et al. (2008) studied monitoring of solvent-mediated phase transition of citric

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ACCEPTED MANUSCRIPT acid anhydrate (CAM) to monohydrate using in situ Raman spectroscopy and reported the transition temperature to be below 34oC. According to several studies reporting the transition temperature of citric acid, it can be considered to be between 34 °C and 36.5 °C (Nemdili et al, 2016). There has been an increased interest in the study of crystallization of citric acid monohydrate (CAM) compared to CAA through experimentation (Sikdar and Randolph,

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1976; Berglund and Larson, 1984; Bravi and Mazzarotta, 1998(a), 1998(b); Caillet et al., 2007(a), 2007(b)).However, several simulation studies have been reported for crystallization of citric CAA where crystallization kinetics for CAM has been utilized to simulate crystallization of CAA (Bohlin and Rasmuson, 1992; Choong and Smith, 2004). Recent

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literature on crystallization of CAA includes experimental investigation of a seeded crystallization process on a vibrated bed bath crystallizer by Teixeira et al. (2012) andmeasurement of primary nucleation and growth parameters in a batch crystallizer by

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Nemdili et al. (2016).

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2.2. Solubility Studies

Solubility of a solute in a specific solvent is a key step in the study of the

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crystallization processes. Solubility of CAA in water and other solvents has been discussed in literature. However, in this study, the solubility of CAA in water has been verified

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experimentally first, to choose solubility data for crystallization experiment in comparison

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with the reported literature. The solubility of citric acid anhydrate in aqueous solution is determined by gravimetry and is also confirmed through titrimetry. Gravimetry is the oldest and simplest analytical method used for determination of solubility in any solvent. The basic steps involved in gravimetric analysis are dissolution, filtration, drying and weighing. To prepare CAA solution, solid citric acid anhydrate is purchased from Alfa Aesar (purity≥99.5), distilled water with PH of 6.5 serves as a solvent. Distilled water is filtered through vacuum filtration setup through 0.22µm membrane filter. Saturated solutions are prepared in100ml 8

ACCEPTED MANUSCRIPT beakers. Solubility is measured at temperatures ranging from 40°C to 60 °C in 10 °C increments. The temperature is controlled and maintained by thermostat baths, and the actual temperature is validated by a digital calibration thermometer (Wika, Germany, uncertainty of ±0.05°C). Syringes (25 mL) fitted with 0.44 µm membrane filters are used to sample 10 mL of solution into pre-weighed crucibles or conical flasks. Syringes are preheated when

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necessary to prevent nucleation inside the syringes during sampling. The filters are also preheated to exceed the solution temperature.

Equilibrium is established by dissolution to saturation of solid material. Three dissolution experiments at the same temperature are conducted by adding an excess amount

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of commercial citric acid anhydrate in 20ml water taken in 100ml glass beakers. The beakers are placed on a hot plate provided with a magnetic stirring for three hours. The temperature is monitored and kept constant throughout the dissolution process. The samples are allowed to

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settle down by keeping them in a hot water bath maintained at constant temperature for 24 hours without disturbing them. For gravimetric analysis, a sample of 5ml each is withdrawn

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from the clear supernatant solution into pre-weighed crucibles through a syringe provided

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with filter. The mass of the crucible with saturated solution is recorded. Drying of samples is conducted by keeping the crucible in a hot air oven at the constant solubility temperature for

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two days. The mass of the samples is recorded repeatedly throughout the drying process to establish the point at which no water remains. Complete drying occurs when the mass of the

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sample remains constant over time. The samples are weighed at this final time when all the solvent is evaporated. The weight of the solid is recorded for all the three samples. The average is taken as solubility (kg. acid/kg. water) at that particular temperature. The results of this gravimetric analysis are confirmed through titrimetry also. A 5 ml sample of clear supernatant liquid is withdrawn and is diluted 10 times with distilled water. A sample of

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ACCEPTED MANUSCRIPT which is titrated against standard sodium hydroxide (1N) solution standardized with oxalic acid dihydrate (1N), using phenolphthalein (8-12 pH) as indicator in all the cases. 2.3.

Cooling crystallization of citric acid anhydrate The experimental unit consists of a jacketed glass vessel of capacity 250ml that serves i pr vi

ui

pit

45angle agitator rotating

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as a batch crystallizer. Stirri

at a constant speed of 300 rpm. The crystallizer is connected to a heating-cooling system or a bath circulator with temperature controller as shown in Fig.1. Pt 100 resistance temperature detectors (RTD’ ) are used for online temperature measurement of the crystallizer and the

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jacket. Also all the temperatures are recorded in a computer connected through data acquisition interface using LABVIEW. The crystallizer is fed with water and solid CAA according to a chosen initial concentration which is more than the saturation concentration. The initial conditions are chosen after rigorous simulation as explained in Section 4. The

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dissolution of CAA in water is carried out at a temperature higher than 70°C and held

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constant and stirred at a speed of 300 rpm for 60 min to ensure complete dissolution. The contents are quickly cooled to 62°C and held constant for 30 min. The crystallization

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experiment is carried out by implementing a cooling profile from 62°C to 41°C obtained through MOO. The total batch time is fixed at 2.5 hours. As there is no provision for

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automatic implementation of crystallizer cooling profile in the experimental setup, the

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temperature profile is tracked by adjusting the jacket (coolant) temperature set point in accordance with the crystallizer temperature profile and the actual procedure is explained in section 5.2. At the end of the batch time, the slurry is filtered for product crystals that are later analyzed to determine crystal size distribution. The results obtained from this experiment are then compared with the predicted simulation data obtained using multiobjective optimization. 2.4.

Measurement of crystal size distribution 10

ACCEPTED MANUSCRIPT The contents of the crystallizer are filtered using vacuum filtration. The crystals are then washed with acetonitrile solution in which citric acid is poorly soluble and are dried overnight at 40°Cin the oven. Following this, a solid sample is taken on a glass slide using a small spatula and the size is measured with an image analysis system, which consists of a table microscope, a digital camera and a computer equipped with Image analysis software.

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Images of crystals are taken and properties of final product crystals are measured using offline Image Pro Premier 9.1 software.

The parameter chosen for the crystal size characterization is the diameter of the

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crystal along its major axis as observed by microscopy. The experimental results are presented in terms of number average of crystal size and coefficient of variation as obtained from the image analysis process. The number mean size ̅ is given as: 1 N



n L i 1 i

(1)

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L

where

is the individual crystal size and N is the number of crystals.

(2)

Simulation system

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3.

L

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CV= 

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Coefficient of variation (CV) is determined from standard deviation (  ) and mean size as

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Determination of optimal cooling policy for unseeded batch cooling crystallization of citric acid anhydrate for implementation to achieve better product CSD is of interest in this work. For this purpose, the dynamic model with crystallization kinetics reported in the literature (Bohlin and Rasmuson, 1992) is chosen for simulation. The model assumptions are: uniform mixing, size independent growth with no growth rate dispersion, no agglomeration or breakage. The crystals formed initially in the process due to primary nucleation act as seeds for the remaining process and thus secondary nucleation also plays a role. The 11

ACCEPTED MANUSCRIPT population balance equation (PBE) is solved using method of moments, which has been used historically by many researchers (Chung et al, 1999; Choong and Smith, 2004; Shi et al, 2005; Shi et al, 2006), as itis simple and consumes less time during optimization, and is represented as follows:

n n  G(t )  0 t L

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(3)

This PBE is reduced to moment equations as

d0 B dt

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(4)

di  iGi 1 dt Boundary conditions:  j =0 at t=0

(5)

j=0, 1, 2, 3, 4, 5

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where n represents the number density of crystals with length L at time t. The total nucleation

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rate B is the sum of primary (BP) and secondary nucleation (BS). Primary, secondary nucleation and growth rate (G) are expressed in the form of power laws as follows.









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P

(6)

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BP  kP C  C*

S

(7)

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BS  kS C  C*

B  BP  BS



G  k g C  C*

(8)



g

(9)

The concentration C is a function of the third moment µ3, due to the crystal mass balance.

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ACCEPTED MANUSCRIPT dC d    c kv 3 dt dt

(10)

Where C is the solute concentration,  c is the density of the crystal, k v is the volumetric shape factor for a sphere crystal model and it is assumed to be constant throughout the

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crystallization process.The solubility is a function of temperature which is expressed in the form of second order polynomial equation. *

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C  C0  C1T  C2T  C3T

3

(11)

To obtain larger and fewer crystals it is desirable to suppress nucleation and enhance growth.

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This can be achieved by controlling the super saturation, which is the actual driving potential for both the nucleation and growth rates and is represented as a concentration difference C . C  C  C *

(12)

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C  is solubility in g. of solute/g. of solvent and is a function of temperature (T in K) as shown

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in Table1.

Assuming constant volume, the amount of solute leaving the solution must be accounted for

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by crystal growth and nucleation and the mass balance of solute concentration is given as

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dC  3 c k v G 2 dt

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(13)

where  c is the density of the crystal and the solute concentration C, Kg acid/Kg. solvent. The crystallization kinetic parameters used by Bohlin and Rasmuson (1992) are used

for simulation of the CAA-water system. The properties of CAA and parameters used for simulation of the model are reported in Table 1. The temperature of the system is decreased from 62°Cto 41°C in a batch time of 2.5 hours or 9000 sec following any chosen cooling trajectory (to be discussed in section 5). The system of equations from Eq.1 to Eq.13 is 13

ACCEPTED MANUSCRIPT simulated where at first, the super saturation is calculated from Eq. (12), and Eqs. (6) to (9) are employed to calculate nucleation and growth rates. Subsequently, moment equations, Eq. (4) and Eq. (5) are integrated in order to find the final product crystal properties. The concentration for the next time instant is calculated through the mass balance equation Eq. (13). During optimization (discussed in section 4), it is assumed that the crystallizer

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temperature is perfectly implemented (perfect control). For the purpose of control calculations, Tj is used as manipulated input which is utilized for implementation of optimal temperature trajectory and the energy balance equation is

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dT  UA T  TJ    H 3kvG2 M sol  dt M sluC p Cp M slu

(14)

where M sol is the mass of the solvent and M slu is mass of the slurry.

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4. Multiobjective optimization

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In the face of the importance of the final CSD in the downstream processes and in product applications, the objectives of the optimization problems in crystallization are

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normally chosen according to specific features related to product quality and market demands. The most common objective functions in crystallization optimization problems are

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maximization of the mean crystal size at the end of the batch, minimization of the standard

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deviation of the final CSD or minimization of its coefficient of variation (CV), and sometimes minimization of the batch time (Hemalatha and Rani, 2017). A desirable change in one objective produces an undesirable change in another objective. This necessitates the application of MOO for crystallization processes. Many MOO studies have dealt with multiple objectives by combining them into one objective function composed of the weighted sum of individual objectives, or by transforming one objective into a single response function while using others as constraints. Such an approach requires prior knowledge of weights, 14

ACCEPTED MANUSCRIPT which makes it difficult to properly interrelate the properties and has the disadvantage of masking the physical significance of individual objectives. Using proper MOO solution strategies, it is possible to consider multiple objectives all at a time and solve simultaneously (Sarkar et al., 2006; Hemalatha and Rani, 2017). No studies are reported on MOO of cooling crystallization of CAA. In the present work, number mean size (NMS) and number

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coefficient variation (CV) are the two objectives considered for MOO of unseeded batch cooling crystallization of CAA and the optimization problem is formulated as follows. 4.1. MOO problem formulation and solution methodology

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As the focus of the present problem is on the practical implementation of the optimal cooling profile and to compare results of experimentation and simulation, maximization of average crystal size and minimization of coefficient of variation are chosen as objective

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functions as these are popularly studied and can be measured through experiment. Also, average crystal size is represented interms of number mean size and corresponding

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representation of coefficient of variation is considered. The chosen objective functions are NMS and CV and they are represented by moments

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of CSD to simultaneously optimize with respect to the temperature/cooling profile as a

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function of time. The appropriate constraints are also incorporated. These individual objectives are optimized simultaneously (J1=[J11,J12]) and the optimization problem is

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represented as follows with the objective function J11,representing maximization of NMS and minimization of CV is represented by the objective function J12.

1 0

(15)

   min J12   2 2 0  1 T (t )  1 

(16)

max J11  T (t )

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Subject to:

c1 : Tmin  T (t )  Tmax c2 :

(17)

dT 0 dt

c3 : t  t f

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where Tmax is the initial temperature and Tmin is the final temperature.

The temperature should always be a decreasing function of time for cooling crystallization throughout the batch. The inequality constraints ensure that the temperature

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profile can be implemented. Temperature is the manipulated variable and it is usually parameterized as a piecewise linear function with respect to time in earlier works related to MOO (Hemalatha and Rani, 2017; Acevedo et al., 2015; Sarkar et al., 2006). Experimental validation of such kind of an optimal temperature profile sought through MOO has been

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reported by Acevedo et al. (2015) where the temperature is controlled through automated

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environment. Such kind of automated environment is unavailable for experimental implementation for the present work. Hence, the temperature is chosen to be parameterized as

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a piecewise constant function which is simple and convenient for practical implementation in

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the present situation.

The solution methodology using Non-dominated sorting genetic algorithm (NSGA-II)

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as explained in an earlier work by Hemalatha and Rani, (2017) is chosen for MOO problem to obtain Pareto optimal set in the present study. In order to parameterize the input temperature trajectories T(t), the time interval (0, tf) is divided into P time stages of unequal length and piecewise constant control policy is sought in each time interval (tk, tk+1). T (t )  T (k )

for

t (k )  t  t (k  1)

(18)

where T(k) is the temperature at the beginning of kth interval. 16

ACCEPTED MANUSCRIPT The optimal control problem then is to find T(k), k=1,2…P. In the present study, P is considered as 11 between the temperatures Tmax and Tmin. The number of decision variables to the algorithm which are temperature variables is taken as 9, excluding Tmax and Tmin which are fixed initial and final temperatures. This temperature profile is used as the input for MOO through NSGA-II. The time stages are considered according to time instants represented by

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t(k). The explanation for considering unequal time intervals for optimization is given in Subsection 5.2. Results and Discussion

5.1.

Solubility study

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5.

Solubility of CAA in water is determined at temperatures of 40 C, 50 C and 60 C respectively. The experimental solubility data is compared to those reported by several

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sources (Dalman et al., 1937; Bohlin and Rasmuson, 1992; Teixeira et al., 2012; Apelblat, 2014; Nemdili et al., 2016). Fig. 2 shows comparison of the experimental results with the

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available literature. The solubility units reported in the literature by different studies is converted to weight fraction for the purpose of comparison. The experimental results

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obtained are comparable to most of those reported in the literature. The present experimental

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solubility results are closer to the data reported by Taxeiraet al., 2012.Hence, the solubility curve reported in their work as shown in Table 1, is chosen for simulation studies. Optimization of batch cooling crystallization of CAA

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5.2.

Different polynomial cooling profiles reported in the literature that are commonly

employed for simulations or implementation are compared through simulations using the dynamic model for citric acid anhydrate detailed in Section 3. The cooling profile is given by the following equation.



T (t )  Tmax  (Tmin  Tmax )t t f 

a



(19)

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ACCEPTED MANUSCRIPT where exponent a=1results in a linear profile, a=3 results in a convex profile suggested for controlled cooling of seeded process, and a=4 results in a convex profile suggested for controlled cooling for unseeded process. The profiles for a=3 and 4 are popularly known as Mullin-Nyvlt profiles for constant rate of nucleation. For unseeded cooling crystallization of citric acid anhydrate, Bohlin and Rasmuson

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(1992) reported that irrespective of cooling profile followed, larger mean size is achieved at an initial super saturation of 0.1 kg/ kg. This has been confirmed in our simulations and thus for the present work, initial super saturation is considered to be 0.1 kg/ kg and initial concentration of CAA is chosen accordingly. With C=2.9403 kg/kg as the initial

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concentration of CAA, the simulations are carried out to study the effect of three different cooling profiles on final achievable mean size and coefficient of variation. The results are as shown in Fig. 3. It is evident from Fig. 3 that the number mean size and CV obtained through

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Mullin-Nyvlt trajectory with power 4 denoted by P4 is inferior to those obtained by other two profiles. The Mullin-Nyvlt profile with power 3, also known as a cubic cooling profile

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denoted by P3gives better mean size(418.46 µm) compared to the other two profiles but r pr i

t

y ‘L’. T i typ

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inferior value of CV (41.6%) compared to the i

behaviour is concurrent with the results reported by Bohlin and Rasmuson (1992). For the

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linear profile, for an improvement of approximately 10% of CV, there is a decrease in mean size by approximately 150 µm which is not desirable. Among the three polynomial cooling

AC

profiles, for practical implementation, cubic profile can be considered as the best operating profile with respect to mean size and coefficient of variation. However, according to the optimization study reported by Choong and Smith (2004), slight deviation from the cubic profile is obtained as the optimal profile through single objective optimization studies. They have reported various single objective optimization studies with maximization of mean size, maximization of yield, minimization of coefficient of variation and minimization of batch 18

ACCEPTED MANUSCRIPT time as different objectives that yielded different optimal cooling curves for each case. It is concluded from their study that the objectives are conflicting in nature and a desirable change favouring one objective results in an unfavourable change in the other objectives. Hence, multiobjective optimization is necessary for determination of an optimal cooling profile with respect to specific objectives as it has the potential to consider tradeoff between multiple

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objectives.

To carry out MOO of citric acid, mean size and coefficient of variation are considered as objectives as these two objectives exhibited a tradeoff between each other in

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our simulation studies. A multiobjective optimization problem for unseeded cooling crystallization is formulated with two objectives as discussed in Section 4. Usually, the manipulated variable, temperature is parameterized as a piecewise linear policy with respect to time. Due to limitations in practical implementation of such a cooling profile in terms of a

M

variable set point at every sampling instant, piecewise constant policy is chosen where the

ED

total batch time is discretized into 11 unequal time stages corresponding to various temperatures which can be read from the cubic profile.

PT

i.e. t(k)= {0, 1400, 2300, 3900, 5300, 6200, 6600, 7400, 8000, 8300, 8700, 9000};

CE

A controlled cooling profile can be constructed with these time stages, without any optimization and compared with the other polynomial profiles as shown in Fig. 3. When the

AC

unseeded process is simulated with the newly constructed profile CP, the obtained NMS and CV are 364.45 µ and 48.01% respectively and it is found that this is comparatively inferior to the terminal mean size and CV obtained for profile P3. Hence, an optimization is considered to be necessary with chosen objectives NMS and CV, to seek an optimal cooling profile for practical implementation. The popular Non-dominated sorting genetic algorithm (NSGA-II) is used for solving MOO problem. The solution methodology using NSGA-II and genetic

19

ACCEPTED MANUSCRIPT algorithm parameters reported by Hemalatha and Rani (2017) are used for the present MOO problem. 9 temperature variables (excluding initial and final temperature values) are considered as decision variables for NSGA corresponding to the 11 time stages. Unlike single objective optimization that results in a unique solution, MOO results in

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a set of optimal solutions known as Pareto optimal set or Pareto front. The tradeoff between the objectives NMS and CV can be observed from the Pareto optimal set of MOO as shown in Fig. 4.

In order to explore an alternative method of arriving at the solutions using weighted

AN US

sum approach and to compare with the solutions of MOO, the single objective optimization (SOO) is considered with weighted functions of the two chosen objectives. The following expression is used for SOO where the problem is to minimize the objective function J.

i

t

v u

t

w i

i

t r ‘x’ (r

i

(20)

r m 0.0 t 1.0), 25 ptimiz ti

ED

By c

M

J  x  ( J11)  (1  x)  J12 

runs are carried out and the solutions from these results are used to construct a Pareto set as

PT

shown in the Pareto plot between the two objectives J11(NMS) and J12(CV) in Fig.5. Whereas

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a single run of Multi objective optimization results in a Pareto solution set which consists of 100 optimal solutions (as the population size in NSGA is chosen as 100) that show tradeoff

AC

between the two objectives. SOO solutions are obtained in the region between A and Din Fig.5, whereas the MOO solutions are obtained between the region B and C. In the region of overlap (region BC), the solutions of SOO are slightly inferior to solutions of MOO. In the region BA, for a small drop in CV value, NMS is drastically reduced. On the other hand, in the region CD, for a small rise in WMS, CV is increasing drastically. Therefore, these regions cannot be considered to provide necessary tradeoff between the objectives. Thus choosing

20

ACCEPTED MANUSCRIPT MOO methodology over SOO using weighted sum approach provides tradeoff solutions with minimal effort. From the Pareto set of MOO, three representative solutions of Pareto set from Fig.4, i.e. end point of the upper Pareto front (UP), end point of the lower Pareto front (LP) and the

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middle point (MP) are chosen for comparison in terms of objectives in Table. 3., the corresponding optimal cooling profiles are shown in Fig. 6. It is observed that the range of NMS pertaining to the Pareto set is 310-363µ and CV is 42-33%, and thus the constructed profile CP is not a part of Pareto solution set and is considered suboptimal. MP is chosen to

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be the optimal Pareto point and the corresponding optimal cooling profile is considered for practical implementation. 5.3.

Tracking of optimal cooling profile for cooling crystallization of CAA

M

Unseeded cooling crystallization of citric acid anhydrate from aqueous solution is carried out in a batch crystallizer set up explained in section 2. The optimal cooling profile

ED

obtained through MOO is considered as a set point trajectory for experimental validation.

PT

Here, the controlled variable is the crystallizer temperature. The contents of the crystallizer are maintained at an initial temperature of 62°C. The heating-cooling system used for the

CE

present work does not have a provision for direct control of the crystallizer temperature (Tc). The heating-cooling system has provision to implement a given set point as the input jacket

AC

temperature or bath temperature. Trial experiments indicated a difference of 1°C between crystallizer temperature and bath temperature. Therefore, the set point temperature profile for jacket inlet bath temperature has been calculated from the determined optimal cooling profile. This trajectory so obtained has been used for tracking. For the purpose of comparison of experimental results with simulations, Eq. (14) has also been included in the set of equations employed for simulations. The crystallizer 21

ACCEPTED MANUSCRIPT temperature is considered as the set point and its optimal set point trajectory is tracked using the inlet jacket temperature (Tj) as the manipulated input using a PI controller. The controller parameters are chosen through trial and error method and are found to be: control gain Kc=0.15 and time constant =10 sec. During the experiment, the temperature data of the crystallizer, jacket inlet and outlet are recorded for every 20sec throughout the batch. The

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bath temperature set point profile is changed manually by giving step changes at specified intervals. The crystallizer temperature obtained through experiment is plotted along with the optimal cooling profile generated through offline optimization as shown in Fig. 7. The actual bath temperature is calculated as the average of jacket inlet and outlet temperatures

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represented by T j . The manipulated input temperature profile obtained through simulation and experiment are reasonably comparable as shown in Fig. 8. The experiment is continued for 2.5 hours and is terminated when the final temperature is reached at the end of the batch

M

time. The final crystals are analyzed to measure mean size and variance. Fig. 9 shows an

ED

image of few of the experimentally obtained final citric acid crystals taken using an optical microscope. The number mean size is measured to be 334.99µm and coefficient of variation

PT

to be 35.01 %. From Table 4, it can be concluded that the experimentally obtained results are

6.

CE

in good agreement with the predicted results. Conclusions

AC

In the present study, it is attempted to carry out multiobjective optimization for

cooling crystallization of citric acid anhydrate. Firstly, the solubility of citric acid in aqueous solution for different temperatures is determined through experiments and is found to be comparable with the data reported in the literature. Different polynomial cooling temperature profiles have been evaluated through simulation and it has been observed that cubic profile P3is found to be optimal with respect to larger mean size only. In order to find a cooling

22

ACCEPTED MANUSCRIPT profile for experimental implementation, the cubic temperature profile is approximated as piecewise constant profile with unequal time intervals. Further, MOO optimization problem is considered with NMS and CV as two objectives to find the piecewise constant crystallizer temperature profile. The obtained temperature profile is implemented in an experimental crystallizer unit equipped with a heating cooling system. The simulation results indicate that

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NMS and CV obtained by implementing cubic profile is found to be closer to the end point of lower Pareto front, LP in MOO. Whereas, the middle Pareto point, MP is chosen for experimental implementation. The experimental results (334.99µm, 35.01%) are found to be

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in good agreement with the optimal solution (341.02µm, 37.21 %) in terms of NMS and CV respectively. This study illustrates the usefulness of MOO for cooling crystallization process in giving a tradeoff solution between two objectives.

M

Acknowledgement

The first author acknowledges the financial support from Department of Science and r W m

ED

Technology (DST), India, u

AC

CE

PT

A/ET-40/2013.

i ti t’ pr r m WOS-A, ref. no. SR/WOS-

References Aamir, E., Nagy, Z.K., Rielly, C.D., Kleinert, T. and Judat, B., 2009. Combined quadrature method of moments and method of characteristics approach for efficient solution of population balance models for dynamic modeling and crystal size distribution control of crystallization processes.Ind.& Eng. Chem. Res., 48(18), 8575-8584. 23

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Aamir, E., Z. K. Nagy, and C. D. Rielly., 2010. Evaluation of the effect of seed preparation method on the product crystal size distribution for batch cooling crystallization processes. Cryst. Growth & Des., 10.11, 4728-4740. Aamir, E., Rielly, C.D., Nagy, Z.K., 2012. Experimental evaluation of the targeted direct design of temperature trajectories for growth-dominated crystallization processes using an analytical crystal size distribution estimator.Ind.& Eng. Chem. Res., 51, 1667716687.

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Acevedo, D., Tandy, Y., Nagy, Z. K., 2015. Multiobjective optimization of an unseeded batch cooling crystallizer for shape and size manipulation.Ind. &Eng. Chem. Res., 54, 2156–2166. Apelblat, A., 2014. Properties of citric acid and its solutions. In Citric acid. Sprin. Int. Pub. 13-141.

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Bennett, G.M., Yuill, J.L., 1935. The crystal form of anhydrous citric acid. Journal of the Chem. Soci. (Resumed)., 29,130-130. Berglund, K.A., Larson, M.A., 1984. Modeling of growth rate dispersion of citric acid monohydrate in continuous crystallizers. AIChE J., 30, 280-287. Bohlin, M., Rasmuson, A.C., 1992. Application of controlled cooling and seeding in batch crystallization. The Can. J. Chem. Eng., 70, 120-126.

M

Bravi, M., Mazzarotta, B., 1998(a). Size dependency of citric acid monohydrate growth kinetics. Chem. Eng. J., 70, 203-207.

ED

Bravi, M., Mazzarotta, B., 1998(b). Primary nucleation of citric acid monohydrate: influence of selected impurities. Chem. Eng. J., 70, 197-202.

PT

Caillet, A., Rivoire, A., Galvan, J.M., Puel, F., Fevotte, G., 2007(a). Crystallization of monohydrate citric acid. 1. In situ monitoring through the joint use of Raman spectroscopy and image analysis. Cryst.Growth& Des., 7,2080-2087.

CE

Caillet, A., Sheibat-Othman, N., Fevotte, G., 2007(b). Crystallization of monohydrate citric acid. 2. Modeling through population balance equations. Cryst.Growth& Des., 7, 20882095.

AC

Caillet, A., Puel, F., Fevotte, G., 2008. Quantitative in situ monitoring of citric acid phase transition in water using Raman spectroscopy. Chem. Eng. &Proc.: Proc. Intensif., 47, 377-382. Choong, K. L., Smith, R.,2004. Optimization of batch cooling crystallization. Chem. Eng. Sci., 59, 313–327. Christofides, P. D., Li, M., & Mädler, L., 2007. Control of particulate processes: Recent results and future challenges. Powder Tech., 175(1), 1-7. Christofides, P.D., El-Farra, N., Li, M. and Mhaskar, P., 2008. Model-based control of particulate processes. Chem. Eng. Sci., 63(5), 1156-1172. Chung, S. H., Ma, D. L., Braatz, R. D., 1999. Optimal seeding in batch crystallization. Can. J. Chem. Eng., 77, 590–596. 24

ACCEPTED MANUSCRIPT Chung, S. H., Ma, D. L., & Braatz, R. D., 2000. Optimal model-based experimental design in batch crystallization. Chemom. & Intell. Lab. Syst., 50(1), 83-90. Costa, C. B. B., Filho, R.M., 2005. Evaluation of optimization techniques and control variable formulations for a batch cooling crystallization process. Chem. Eng. Sci., 60, 5312−5322. Dalman, L.H., 1937. The solubility of citric and tartaric acids in water. Journal of the American Chem. Soci., 59,2547-2549.

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Fujiwara, M., Chow, P. S., Ma, D. L., Braatz, R. D.,2002. Paracetamol crystallization using laser backscattering and ATR-FTIR spectroscopy: metastability, agglomeration, and control. Cryst. Growth & Des., 2, 363-370. Fujiwara, M., Nagy, Z. K., Chew, J. W., & Braatz, R. D., 2005. First-principles and direct design approaches for the control of pharmaceutical crystallization. J. Proc. Cont., 15(5), 493-504.

AN US

Hemalatha K., Rani, K. Y., 2016. Sensitivity analysis of Pareto solution sets of multiobjective optimization for a batch cooling crystallization process. Proc. Of Indian Control Conference (ICC) IEEE., 493-498. Hemalatha, K., Rani, K.Y., 2017. Multiobjective Optimization of Unseeded and Seeded Batch Cooling Crystallization Processes. Ind. &Eng. Chem. Res., 56, 6012−6021

M

Hermanto, M.W., Chiu, M.S. and Braatz, R.D., 2009. Nonlinear model predictive control for the polymorphic transformation of L‐ glutamic acid crystals. AIChE J., 55(10), 26312645. Hounslow, M.J. and Reynolds, G.K., 2006. Product engineering for crystal size distribution. AIChE J., 52(7), 2507-2517.

ED

Hsu, C.W. and Ward, J.D., 2013. The best objective function for seeded batch crystallization. AIChE J., 59(2), 390-398.

PT

Hu, Q., Rohani, S. and Jutan, A., 2005. Modelling and optimization of seeded batch crystallizers. Comput.& chem.Eng., 29, 911-918.

CE

Jones, A. G., Mullin, J.W., 1974. Programmed cooling crystallization of potassium sulphate solutions. Chem. Eng. Sci., 29, 105–118. Kubota, N., Doki, N., Yokota, M. and Jagadesh, D., 2002. Seeding effect on product crystal size in batch crystallization. Journal of chem. Eng. of Japan., 35(11), 1063-1071.

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Kwon, J.S.I., Nayhouse, M., Christofides, P.D. and Orkoulas, G., 2014. Protein crystal shape and size control in batch crystallization: Comparing model predictive control with conventional operating policies. Ind. &Eng. Chem. Res., 53(13), 5002-5014. Kwon, J.S.I., Nayhouse, M., Orkoulas, G., Ni, D. and Christofides, P.D., 2015. Run-to-runbased model predictive control of protein crystal shape in batch crystallization. Ind. &Eng. Chem. Res., 54(16), 4293-4302. Lewiner, F., Févotte, G., Klein, J.P., Puel, F., 2002. An online strategy to increase the average crystal size during organic batch cooling crystallization. Ind. &Eng. Chem. Res.,41, 1321–1328. Ma, D.L., Chung, S.H., Braatz, R.D., 1999. Worst-case performance analysis of optimal batch control trajectories. AIChE J., 45, 1469–1476. 25

ACCEPTED MANUSCRIPT Matthews, H. B., & Rawlings, J. B., 1998. Batch crystallization of a photochemical: Modeling, control, and filtration. AIChE J., 44(5), 1119-1127. Mayrhofer, B., & Nývlt, J., 1988. Programmed cooling of batch crystallizers. Chem. Eng.&Proc. Proc. Inten., 24(4), 217-220. Mesbah, A., Huesman, A.E.M., Kramer, H.J.M., Van den Hof, P.M.J., 2011. A comparison of nonlinear observers for output feedback model-based control of seeded batch crystallization processes. J. Process Control, 21, 652–666.

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Miller, S.M., Rawlings, J.B.,1994. Model Identification and Control Strategies for Batch Cooling Crystallizers. AIChE J., 40, 1312–1327. Mohameed, H.A., Abu-Jdayil, B. and Al Khateeb, M., 2002. Effect of cooling rate on unseeded batch crystallization of KCl. Chem. Eng.&Proc. Proc. Inten., 41, 297-302. Mohameed, H.A., Abdel-Jabbar, N., Takrouri, K. and Nasr, A., 2003. Model-based optimal cooling strategy for batch crystallization processes. Chem. Eng. Res. & Des., 81, 578584.

AN US

Mullin, J. W., and J. Nývlt., 1971. Programmed cooling of batch crystallizers. Chem. Eng. Sci., 26.3: 369-377. Nagy, Z.K., Chew, J.W., Fujiwara, M., Braatz, R.D. 2008. Comparative performance of concentration and temperature controlled batch crystallizations. J. Proc. Cont., 18, 399−407.

M

Nagy, Z.K., 2009. Model based robust control approach for batch crystallization product design. Comput. & chem. Eng.,33(10), 1685-1691.

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Nagy, Z.K., Braatz, R.D., 2012. Advances and new directions in crystallization control. Annu. Rev. Chem. Biomol. Eng., 3, 55–75.

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Nagy, Z.K., Fevotte, G., Kramer, H., Simon, L.L., 2013. Recent advances in the monitoring, modelling and control of crystallization systems. Front. Chem. Eng. Res. & Des., 91, 1903–1922. Nemdili, L., Koutchoukali, O., Bouhelassa, M., Seidel, J., Mameri, F., Ulrich, J., 2016. Crystallization kinetics of citric acid anhydrate. J.Cryst.Growth., 451, 88-94.

CE

Patience, D.B., Dell'Orco, P.C., Rawlings, J.B., 2004. Optimal operation of a seeded pharmaceutical crystallization with growth-dependent dispersion. Org. Proc. Res. Dev., 8, 609-615.

AC

Rawlings, J.B., Miller, S.M. and Witkowski, W.R., 1993. Model identification and control of solution crystallization processes: a review.Ind. Eng. Chem. Res., 32(7), 1275-1296. Rohani, S. and Bourne, J.R., 1990. A simplified approach to the operation of a batch crystallizer. The Canadian Journal of Chemical Engineering, 68(5), 799-806. Samad, N.A.F.A., Sin, G., Gernaey, K.V. and Gani, R., 2013. A systematic framework for design of process monitoring and control (PAT) systems for crystallization processes. Comput. Chem. Eng., 54, 8-23. Sarkar, D., Rohani, S., Jutan, A.,2006. Multiobjective optimization of seededbatch crystallization processes. Chem. Eng. Sci., 61, 5282–5295.

26

ACCEPTED MANUSCRIPT Sarkar, D., Rohani, S., Jutan, A.,2007. Multiobjective optimization of semibatch reactive crystallization processes. AIChE J., 53, 1164−1177. Sheikholeslamzadeh, E., Rohani, S., 2013. Modeling and optimal control of solution mediated polymorphic transformation of L-glutamic acid. Ind. &Eng. Chem. Res., 52, 2633-2641. Sheikhzadeh, M., Trifkovic, M., Rohani, S., 2008. Real-time optimal control of an antisolvent isothermal semi-batch crystallization process. Chem. Eng. Sci., 63, 829-839.

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Shi, D., Mhaskar, P., El-Farra, N. H., & Christofides, P. D., 2005. Predictive control of crystal size distribution in protein crystallization. Nanotechnology, 16(7), S562. Shi, D., El-Farra, N. H., Li, M., Mhaskar, P., & Christofides, P. D., 2006. Predictive control of particle size distribution in particulate processes. Chem. Eng. Sci., 61(1), 268-281. Sikdar, S.K., Randolph, A.D., 1976. Secondary nucleation of two fast growth systems in a mixed suspension crystallizer: Magnesium sulfate and citric acid water systems. AIChE J., 22, 110-117.

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AN US

Simon, L.L., Pataki, H., Marosi, G., Meemken, F., Hungerbühler, K., Baiker, A., Tummala, S., Glennon, B., Kuentz, M., Steele, G., Kramer, H.J.M., Rydzak, J.W., Chen, Z., Morris, J., Kjell, F., Singh, R., Gani, R., Gernaey, K.V., Louhi-Kultanen, M., O'Reilly, J., Sandler, N., Antikainen, O., Yliruusi, J., Frohberg, P., Ulrich, J., Braatz, R.D., Leyssens, T., Stosch, M.V., Oliveira, R., Tan, R.B.H., Wu, H., Khan, M., O'Grady, D., Pandey, A., Westra, R., Delle-Case, E., Pape, D., Angelosante, D., Maret, Y., Steiger, O., Lenner, M., Abbou-Oucherif, K., Nagy, Z.K., Litster, J.D., Kamaraju, V.K., Chiu, M.S.,2015. Assessment of recent process analytical technology (PAT) trends: A multi author review. Org. Proc. Res. Dev., 19, 3–62.

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Soccol, C.R., Vandenberghe, L.P., Rodrigues, C., Pandey, A., 2006. New perspectives for citric acid production and application. Food Tech.& Biotech., 44, 2, 141-149.

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Teixeira, G.A., Vieira, W.F., Finzer, J.R.D., Malagoni, R.A., 2012. Operational optimization of anhydrous citric acid crystallization using large number of seed crystals. Powder Tech., 217, 634-640.

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Trifkovic, M., Sheikhzadeh, M. and Rohani, S., 2009. Multivariable real‐ time optimal control of a cooling and antisolvent semibatch crystallization process. AIChE J., 55(10), 2591-2602.

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Tseng, Y. T.; Ward, J. D., 2017. Comparison of objective functions for batch crystallization ui imp pr m P try i ’ mi imum pri ip . C mp. C m. E ., 99, 271-279. Ulrich, J., Frohberg, P., 2013. Problems, potentials and future of industrial crystallization. Front. Chem. Sci. Eng., 7, 1–8. Ward, J. D., Mellichamp, D. A., Doherty, M. F.,2006. Choosing an operating policy for seeded batch crystallization. AIChE J., 52, 2046–2054. Worlitschek, J., Mazzotti, M.,2004. Model-Based Optimization of Particle Size Distribution in Batch-Cooling Crystallization of Paracetamol. Cryst. Growth & Des., 4, 891–903. Xie, W., Rohani, S., &Phoenlx, A., 2001. Dynamic modeling and operation of a seeded batch cooling crystallizer. Chem. Eng. Comm., 187(1), 229-249. 27

ACCEPTED MANUSCRIPT Yu, Z.Q., Chew, J.W., Chow, P.S. and Tan, R.B.H., 2007. Recent advances in crystallization control: an industrial perspective. Chem. Eng. Res. and Des., 85(7), 893-905.

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Zhang, G.P., Rohani, S., 2003. On-line optimal control of a seeded batch cooling crystallizer. Chem. Eng. Sci., 58, 1887-1896.

List of Table Captions:

Table 1. Values of Parameters/Variables used for simulation of the model

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Table 2. Comparison of mean size and coefficient of variation of different cooling profiles Table 3. Comparison of objective function values for selected optimal solutions from Pareto solution set

List of Figure Captions:

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Table 4. Comparison of results obtained through experiment and simulation

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Fig. 1. Schematic diagram of experimental setup for cooling crystallization of CAA Fig. 2. Comparison of solubility data with literature

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Fig. 3. Comparison of different cooling profiles

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Fig. 4. Pareto solution set obtained through MOO

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Fig. 5. Comparison of optimization through weighted sum approach and MOO Fig. 6. Comparison of cooling profiles for selected solutions from the Pareto set of MOO Fig. 7. Comparison of crystallizer temperature profiles through simulation and experiment Fig. 8. Comparision of jacket temperature profiles through simulation and experiment Fig. 9. Image of Citric acid anhydriate crystals taken using optical microscope with 40X magnification

28

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Table 1. Values of Parameters/Variables used for simulation of the model Parameters/Variables

Value

Units

Total batch time tf

9000

sec

Final temparatureTmin

41

C

Initial temparatureTmax

62

C

Solubility C *

0.08412  0.09393T

Density of crystals ρ

1665

Volume shape factor kv

0.52

kg CAA/kg H2O

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 0.00148T  0.00001100T 2

3

where T i i C kg/m3 -

7

no kgkg kg

p

1.0×10

Primary nucleation rate exponent p

3.54

-

Growth rate exponent g

0.65

-

Secondary nucleation rate constant ks

0.88774×exp(4781/T)

no kgkg kg

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Primary nucleation rate constant kp

 p 1

no

where T is in K

0.543

-

Empirical exponent b

0.84

-

0.02652×exp(-3584/T)

kg/kg, where T is in K

206.09

kJ/kg

1.2538

kJ/(kg.K)

Enthalpy of system H

PT

Heat capacity C P

ED

Growth rate constant kg

M

Secondary nucleation rate exponent s

0.0216

AC

CE

Heat transfer coefficient UA

29

C)

kg

b

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Table 2. Comparison of mean size and coefficient of variation of different cooling profiles NMS, µm

CV, %

L

274.20

30.47

P3

418.46

41.67

P4

391.72

51.77

CP

364.45

48.02

AC

CE

PT

ED

M

AN US

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Profile

30

ACCEPTED MANUSCRIPT

Table 3. Comparison of objective function values for selective optimal solutions from Pareto solution set NMS, µm

CV, %

UP

363.18

42.98

MP

341.02

37.21

LP

310.96

33.22

AC

CE

PT

ED

M

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Profile

31

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Table 4. Comparison of results obtained through experiment and simulation NMS, µm

CV, %

Chosen optimal cooling policy (MP) simulation

341.02

37.21

Experiment

334.99

35.01

AC

CE

PT

ED

M

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Profile

32

M

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ACCEPTED MANUSCRIPT

AC

CE

PT

ED

Fig.1. Schematic diagram of experimental setup for cooling crystallization of CAA.

33

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0.8

0.6 0.5

0.4 Dalman et al. (1937) Bohlin and Rasmuson (1992)

0.3

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Solubility (weight fraction)

0.7

Teixeira et al. (2012) 0.2

Apelblat (2014)

Nemdili et al. (2016)

0.1

Experiment 0 35

40

45 50 Temperature (°C)

55

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30

AC

CE

PT

ED

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Fig.2.Comparison of solubility data with literature

34

60

65

ACCEPTED MANUSCRIPT

L

61

P₃ P₄ CP

51

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Temperature (°C)

56

41 0

1000

2000

3000

AN US

46

4000 5000 Time (sec)

6000

AC

CE

PT

ED

M

Fig. 3. Comparison of different cooling profiles

35

7000

8000

9000

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ACCEPTED MANUSCRIPT

AC

CE

PT

ED

M

Fig. 4. Pareto solution set obtained through MOO

36

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0.55 Solution set of SOO using weighted functions Pareto set obtained through MOO

0.5

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CV, %

0.45 0.4 0.35

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0.3

0.25 200

250

300

350

400

NMS, μm

AC

CE

PT

ED

M

Fig. 5. Comparison of optimization through weighted sum approach and MOO

37

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Lower end point (LP)

61

Middle point (MP) Upper end point (UP)

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Temperature (°C)

56

51

41 0

1000

2000

3000

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46

4000 5000 Time (sec)

6000

7000

8000

9000

AC

CE

PT

ED

M

Fig.6. Comparison of cooling profiles for selected solutions from the Pareto set of MOO

38

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61 Tc exp

56

51

46

41 1000

2000

3000

4000 5000 Time (sec)

6000

7000

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0

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Temperature (°C)

Tc optimal

8000

9000

AC

CE

PT

ED

M

Fig.7. Comparison of crystallizer temperature profiles through simulation and experiment

39

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T̅j exp

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Tj sim

56

51

46

41 1000

2000

3000

4000 5000 Time (sec)

6000

7000

8000

9000

M

0

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Temperature (°C)

61

AC

CE

PT

ED

Fig. 8. Comparision of jacket temperature profiles through simulation and experiment

40

PT

ED

M

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ACCEPTED MANUSCRIPT

Fig. 9. Image of citric acid anhydrate crystals taken using optical microscope with 40X

AC

CE

magnification

41