Purification of naphthalene by zone refining: Mathematical modelling and optimization by swarm intelligence-based techniques

Separation and Purification Technology 234 (2020) 116089

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Purification of naphthalene by zone refining: Mathematical modelling and optimization by swarm intelligence-based techniques

T

C.H. Silva-Santosa, J.V.F. Moraisa, F. Bertellib, A. Garciac, N. Cheungc,

⁎

a

São Paulo Federal Institute for Education, Science and Technology, Itapetininga, Brazil Santa Cecília University, Post-Graduate Program of Mechanical Engineering, Santos, Brazil c University of Campinas, UNICAMP, Campinas, Brazil b

ARTICLE INFO

ABSTRACT

Keywords: Naphthalene Purification Zone refining Artificial intelligence Optimization

Naphthalene based ionic liquids have been recently reported in applications of photoluminescence at room temperature. Further usages of Naphthalene cover phosphorescence aspects and liquid-phase exfoliation of graphite for graphene sheets production. Naphthalene is also known for its use in resonance studies and scintillation counters. All the aforementioned applications are sensitive to trace contaminants. One of the purification routes consists of zone refining, a large family of techniques based on the solidification/segregation theory. Separation of solute (impurity) and solvent is gradually increased through subsequent passes of a molten zone travelling along a bar. The impurities accumulate at its ends resulting into a high purity material at the intermediate region. Zone refining is a time costly batch technique since subsequent passes are needed and the movement of the molten zone is inherently slow to avoid impurity entrapment when the liquid solidifies. Since the length of the molten zone influences the impurity distribution, the challenge to achieve refining efficiency consists on establishing the best set of these lengths with a view to minimizing the molten zone passes. This work aims to fulfill this challenge using a semi-analytical/numerical model combined with two swarm artificial intelligence approaches. Experimental impurity profiles of Rhodamine after a number of molten zone passes in a Naphthalene bar are compared with theoretical predictions of the mathematical model for validation purposes. The two swarm artificial intelligence approaches applied are bio-inspired algorithms: Particle Swarm Optimization, which mimics the bird flock flying behavior - velocity and coordinate for each bird; and the Cuckoo Search, which is based on the brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds. Each algorithm is shown to successfully interact with the mathematical model permitting the purification of Naphthalene by zone refining to be optimized. Both algorithms have demonstrated that better purification effect can be achieved by using larger zone lengths for the initial zone passes. It is shown that fewer iterations are needed by Cuckoo Search to achieve convergence as compared to Particle Swarm Optimization.

1. Introduction

important to use technologies to recover and recycle ILs, for example the ones related to separation and purification processes [4]. Naphthalene based ionic liquids have attracted attention recently in applications of photoluminescence at room temperature for the development of a new generation of photoluminescent inks [5]. Additional uses of Naphthalene concerns phosphorescence aspects [6,7], preparation of carbon-coated Si70Sn30 nanoparticles [8] and liquid-phase exfoliation of graphite for graphene sheets production [9]. Naphthalene is also known for its use in resonance studies, scintillation counters [10] and pharmacological compounds [11]. Removal of trace contaminants from Naphthalene is important for all the aforementioned applications since Naphthalene must be extremely pure. Different levels of purity are found in Naphthalene due to the diversity of techniques used for its

Ionic liquids (ILs) are also denominated room-temperature ionic liquids due to their melting points lower than 100 °C. These liquids are generally molten salts composed of ions. ILs have been seen as environmentally friendly solvents when considering their negligible vapor pressure, acting as alternative to traditional organic solvents [1]. On the other hand, soil and aquatic environments are susceptible to ILs contamination because of their solubility in water and terrestrial permeability [2,3]. Although the applications of ILs have increased on chemical processes owing to their capability to simultaneously dissolve organic and inorganic substances, ILs still face their high cost. Allying both issues, i.e. environmental impacts and economical concerns, it is ⁎

Corresponding author. E-mail address: [email protected] (N. Cheung).

https://doi.org/10.1016/j.seppur.2019.116089 Received 25 May 2019; Received in revised form 2 September 2019; Accepted 14 September 2019 Available online 14 September 2019 1383-5866/ © 2019 Elsevier B.V. All rights reserved.

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obtention such as, distillation of the middle fraction of the coal tar; catalytic hydrogenation and crystallization. One of the purification routes for Naphthalene consists of the zone refining technique [12,13]. Zone refining is a known group of similar methods generally used to purify crystals, either metals or semiconductors such as germanium and silicon, for high technology applications. In these methods, soluble impurities are distributed in the solid phase, based on the segregation phenomenon, by passing a molten zone of fixed length through a bar of a material. The objective is to achieve maximum solute transport, so that part of the bar becomes depleted in impurities and part enriched. This technique allows a high degree of separation of impurity and solvent based on the principle that the impurities are more soluble in the liquid than they are in the solid. Zone-refining has also been extensively used for purification of organic compounds since no contact takes place between the compound being purified and any other solvent or chemical [10,14–16]. Although considered as the ultimate purification technique for several substances, zone refining has low processing rates and high energy consumption due to the large temperature gradients during the process. In order to overcome these drawbacks, optimization techniques based on Artificial Intelligence (AI) have been used for designing the best sequence of liquid zone lengths for each pass. A few works can be found in the literature dealing with the optimization of the liquid zone length using AI techniques, such as Tree Exploration [17] and Genetic Algorithm techniques [12,18,19]. The aim of the present work is to determine the optimized sequence of liquid zone lengths along different passes of the molten zone, with a view to providing the lowest impurity profile and minimum number of zone passes. To achieve this objective, firstly, a mathematical model is validated against some experimental conditions of zone refining of Naphthalene containing 0.5 wt% Rhodamine as the impurity. Afterwards, two Particle Swarm Optimization techniques: (i) that mimics the flight of a flock of birds; and (ii) the Cuckoo Search, which is based on the brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds, are the AI swarm techniques used to interact with the validated mathematical model with a view to furnishing the best set of sequential liquid zone lengths that maximizes purification.

control performed by an electronic circuit operating through feedback loop. Water cooled rings were used to delimitate the liquid zone length and also to impose an appropriate thermal gradient to maintain a flat solid-liquid interface avoiding impurity entrapment. In order to promote the controlled displacement of the solid-liquid interface along the sample, the heating and cooling sets are connected to feed screws and the rate of displacement of the liquid zone can be adjusted from 10−6 to 10−4 m/s by using a reduction system. Mechanical stirring, used for providing the homogenization of the liquid, was achieved by rotating the ampoule using an electric motor able to feed up to 500 rpm. A series of experiments were performed in order to determine the best set of operating parameters assuring the flat solid/liquid interface and liquid homogenization. These used experimental parameters were: thermal gradient of 1 × 104 °C/m, liquid zone rate of 7 × 10−6 m/s and ampoule rotation of 100 rpm. The Rhodamine dye plays the role of the impurity in Naphthalene and the Rhodamine profile along the bar is determined through measurements of the amount of light passing through the sample. At one side of the bar, a light emitted by a LED (Light Emitting Diode) undergoes the sample at its transverse section. When the light emerges on the opposite side of the sample, a light dependent resistor is responsible for measuring the light loss. The electric resistance of the photoresistor is at its minimum, known as offset value when Naphthalene is pure, i. e. Naphthalene devoid of Rhodamine, and increases according to the intensity of the red color, that is, according to the current quantity of Rhodamine in the Naphthalene sample. In this sense, using serial dilutions of Rhodamine, a calibration curve is generated and a predictable pattern between the Rhodamine concentration and the reading from the photoresistor is built, as shown by Fig. 2. At least triplicate resistance readings for each selected bar position have been performed but no variation has been detected. 3. Mathematical modeling of zone refining for multipass distribution of impurities The solute (impurity) distribution coefficient, also known as partition coefficient (k), is the ratio of the solid and liquid composition, i.e. k = CS/CL, generally determined considering equilibrium cooling conditions, that is, using phase diagrams. On the other hand, other influent parameters can be taken into account such as the partial mixture of impurities in the liquid, as originally treated by Burtom, Prim and Slichter [20], who considered the solute mixture occurring only within a diffusion layer (δ), impurity diffusivity in the melt (D) and also

2. Experimental procedure A device has been designed to allow the horizontal zone refining process of Naphtalene to be carried out. Samples of Naphthalene/ Rhodamine were placed into sealed pirex tubes, with 0.8 m in length, to be purified. Fig. 1 shows a single heater made of Nichrome wire resistance, in which heat is uniformly distributed along different lengths of copper rings involving a Pyrex glass tube, which is responsible to generate distinct liquid zone lengths. The heating system can furnish temperatures from 40 °C to 140 °C with ± 0.5% of variation due to a

Fig. 1. Schematic representation of the experimental device for horizontal zone-refining.

Fig. 2. Calibration Concentration. 2

curve

–

Electrical

Resistance

versus

Rhodamine

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uniform concentration of the impurities in the remaining liquid (CL) due to convection effects. The effective distribution coefficient can be defined as [21]:

kef =

k k + (1

k ) exp

( ) v D

(1)

Eq. (1) also allows to evaluate the influence of the rate of displacement of the solid/liquid interface (v) on the value of the distribution coefficient, kef → k as v → 0, and kef → 1 as v → ∞, i. e., k ≤ kef ≤ 1,0. The kef expression can be applied to the analysis of solute redistribution of a finite system, as long as its length is significantly larger than the diffusion boundary layer in the liquid. Concerning purification effects, the maximum degree of mixing is desirable, provided by kef → k, thus permitting the use of higher zone travel rates to be used, as can be realized from Eq. (1). It is worth noting that the ideal (v) consists in permitting most impurities to leave the solid towards the liquid without being trapped by the solidification front. In the zone refining process only a small liquid zone is generated and moved slowly through the bar, either by the movement of the bar itself or by the movement of the heating zone, as shown schematically in Fig. 3. The rejected impurity, or solvent, is accumulated in this liquid zone and after each zone pass, it is progressively concentrated at the extremities of the bar (k > 1 at the left extremity and k < 1 at the right extremity). This liquid zone can be passed repeatedly along the bar increasing the degree of purification. For example, considering an impurity having k = 0.1, the average concentration of this impurity in the first half of the bar is reduced by a factor close to 1000 after only five passes of the liquid zone along the bar [22]. The following dimensionless variables presented in Fig. 3 are defined as:

L = 1,

Z=

z < 1 and L

X=

x L

1

Fig. 4. Impurity concentrations profiles at the starting extremity of the sample in the nth pass and in the previous one (n − 1), for k < 1.

gradient ahead the solid front owing to liquid homogenization along the refining process; The resulting impurity profiles will be a function of the number of passes (n) and the relative position in the bar (X). The calculation sequence consists of four distinct regions along the bar: 1- for the formation of the first solid at the beginning of each pass (X = 0); 2- for the effective zone of advance of the liquid zone (0 < X 1 − Z); 3- for the last region where normal solidification occurs (1 − Z < X < 1) and 4for the extremity of the bar (X = 1). Region 1 (X = 0): The liquid zone Z is divided into m segments of length dx, according to the scheme of Fig. 4. The new uniform composition of the liquid zone, at a specific pass (n) and position (X), given by CLn(X ) , is the total impurity inside the control volume, of the previous pass n-1, equally distributed for each of the elements (m).

(2)

where L is the length of the sample; z is the liquid zone length; Z is the normalized zone length; x is the distance from the bar extremity; X is the normalized distance from the bar extremity. The mathematical model considers the following hypotheses:

CLn(0) =

1 m

m 1

Csn (i1. dx ) )

i=0

(3)

The first solid formed will be related to the composition of the liquid according to the distribution coefficient of the impurity (k) and as m = Z/dx, Eq. (3) is expressed as:

– the impurity distribution coefficient is constant, when liquidus and solidus lines are straight; – the length of the liquid zone and the zone travel rate are constants along each nth pass, since the heating and speed control systems are calibrated to guarantee steady state regime; – the impurity concentration in the liquid zone, CL, is uniform, since rotating speed of the ampoule is able to promote liquid homogeneity; – the initial concentration C0 is uniform along the whole bar, since rotation of the ampoule, previous to the refining process start, is able to promote liquid homogeneity; – the densities of liquid and the solid Naphthalene are the same, remaining roughly constant for the working temperatures since precipitations during melting and solidification have not been realized; – diffusion of solute in the solid is negligible, due to inexistent solute

CSn(0) = k

dx Z

m 1 i=0

Csn ( i1)

(4)

Region 2 (0 < X ≤ 1 − Z): A solute (impurity) mass balance may be written, according to the scheme of Fig. 5:

Fig. 5. Modifications on impurity concentrations profiles due to a displacement dx of the liquid zone, for k < 1.

Fig. 3. Scheme of the zone refining process. 3

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These techniques have been applied to estimate thermodynamic properties of ionic liquids, including recent examples to data properties processing in pure and mixture ionic liquids [24], liquid equilibria estimation [25] and prediction of multiple and simultaneous physical properties (viscosity, density and electrical conductivity) [26]. In these cases, the natural based inspired algorithms were considered. This CI category mimetizes nature behaviors, concepts and populations, such the genetic representation associated with Darwin’s natural selection theory, the vertebrate immunological system dynamics to detect pathogens, particles swarm interrelation and others [27]. Henceforth, considering the necessity of purification of ionic liquids, the present work applies two different swarm intelligence algorithms approaches (Particle Swarm Optimization – PSO and Cuckoo Search Algorithm – CSA) in connection to the mathematical model presented in the previous Section 3, in order to optimize liquid zone lengths and the minimum number of liquid zone passes for the best purification effect on Naphthalene. Therefore, the metaheuristic mimetization starts on the matrix PnPart x nAttr initialization to store swarm population randomly generated, where nPart is the number of particles (candidate solution) in the population and nAttr the number of attributes necessary to describe each particle. Each attribute is randomly set under a predefined range from the minimal (vMin) until a maximum (vMax) value. Considering the swarm correctly created and distributed in the search space, an iterative procedure is initiated and performed until a stop criterion is satisfied, which is herein designated by the number of iterations predefined in 300. During the iterative process, the particles tends to be changed by some criteria, which are commonly associate with how fast (velocity) a particle moves in the search space. This mimetization occurs in the PSO and in CSA, and these adaptation values describe the cuckoos flight to identify best nest to lay their eggs [28,29]. When a particle is changed, the objective function is called to update its value in the search space. Although there are different swarm intelligence algorithms, including fish, bat, particles (PSO) and Cuckoo search algorithms (CSA) [30], the two last algorithms were chosen with a view to comparing their optimization results. The PSO is considered the steady state algorithm and CSA the alternative solution by the computational approaches that mimetize the cuckoo chaotic parasitic principia designed by the flight Lévy [31,32]. Thereby, in Section 4.1 the Particle Swarm Optimization (PSO) algorithm is summarized, followed by Section 4.2 that describes the main characteristics of the CSA with Lévy flight mimetization. These algorithms were developed for a Scilab 6.0.2 version.

Fig. 6. Impurity concentration profiles in last end of the sample in the nth pass and in the previous one (n − 1), for k < 1.

(5)

Z . dCL = CS . dx

The right side of Eq. (5), CS . dx , means the difference of impurity concentration inside an incremental volume element dx in the liquid region of the freezing interface, and the corresponding concentration after solidification of this element due to a displacement dx (Eq. (6)); while the left side, represents the increase in the equalized solute concentration of the liquid zone due to the mentioned displacement dx.

CS = CSn(X1+ Z

CSn(X

dx )

(6)

dx )

Thus, the concentration profile of the impurity after the passage of the liquid zone is given by the expression:

CSn (X ) = CSn (X

dx )

+

k. dx n 1 (CS (X + Z Z

dx )

CSn(X

dx ) )

(7)

Region 3 (1 − Z ≤ X < 1): When the liquid zone reaches the last extremity of the bar, the solute redistribution follows the normal solidification equation. Fig. 6 shows a schematic representation of the impurity profile in this region. It is worth noting that the amount of impurity incorporated into the liquid zone will correspond to the difference between the total amount of impurity initially present in the bar and the amount incorporated into the already solidified profile:

CLn(X ) =

C0 Z

dx Z

1 dx

CSn(i)1

i=1 z

(8)

Region 4 (X = 1): Using the condition of total mass conservation, it is assumed that the sum of the concentration at all points of the bar should always be equal to C0, that is: X =1 X =0

CSn(X ) dx = C0

4.1. Particle swarm optimization (PSO) algorithm The PSO algorithm emerged in the 90′s to simulate social behavior, followed by some benchmarks with Genetic Algorithms in some engineering problems. It is a metaheuristic inspired type, which is based on birds’flights and fish shoal movements, correlating how each individual interact with the group to conquer its space and to reach its destiny [33,34]. It mimetizes a candidate solution set (called particle) designated by swarm. Each particle is associated with the swarm by few parameters used to identify its position and travel velocity, which is associated with the optimization parameters and how their score (fitness) is converging to the expected results, respectively. The first step of the PSO algorithm is the random swarm initialization and identification of local best candidate (Pbest) and global (Gbest) solution in this group. The Pbest is the best candidate solution achieved in each iteration and Gbest, the global best solution resulted until the current evaluation. These parameters are necessary to calculate the velocity of each j-attribute and of each i-particle by Eq. (11), where LC and LS are constant parameters, cognition and social learning rates, respectively, to correlate the Pbest and Gbest particles by random uniform absolute value defined by the vectors R1 and R2, whose length is similar to the number of the input unknowns denoted by nAttr.

(9)

The concentration of the last solid formed will be given by:

CSn(1) = C0

1 m

m dx

CSn(i)

i=0

(10)

4. Swarm intelligence algorithms Artificial Intelligence (AI), also called computational intelligence (CI), aims including the real world representation (mimetization) and techniques to support engineering and science problems optimizations. There are a large number of CI approaches grouped into categories such as, natural inspired algorithms, Fuzzy Logic, Knowledge-Based Agents and the most recent coined group of machine learning based techniques. This last group usually integrates other CI group algorithms by some sophisticated data storing, processing and analysis in large scale database with a wide number of different information, converging to Big Data applications [23]. 4

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C.H. Silva-Santos, et al.

vi, j = vi, j + LC x R1j x (Pbest (j )

vi, j ) + LS x R2j x (Gbest (j )

vi, j )

(11)

Levy

Herein, the velocity (vi,j) is added to the Pi,j particle attribute when its value is greater than or equal to vMinj; and lower than or equal to vMaxj, and they represent the acceptable range of values for each input j-attribute of the i-particle. This particle moving procedure by a certain velocity is repeated until a certain condition is satisfied. In this work, this stop criteria condition is determined by a total of 1000 for both PSO and CSA algorithms.

Levy )·

sin(0.5· ·

Levy )

0.5· Levy

Levy (0.5· Levy )· Levy

0.5·(1

Levy )

nAttr l=1

(

)

rand ()· Levy 1/ Levy rand ()

nAttr

·(nest

Pbest )

(15)

The general dataflow linking the metaheuristics (PSO and CSA) to the mathematical model in order to optimize the purification of Naphthalene is presented in Fig. 8. The metaheuristics randomly generate four different parameters (npasses, Amax, minx and opt) in a certain acceptable range, shown in Table 1. The objective function is herein the integration between the zone refining mathematical model and some constraints to penalty or reward this value according to some pre-requirements further detailed. Therefore, this objective function calculates the particle location in the search space, being necessary to be recalculated when any change in the particle is performed, as shown in Fig. 8 after the random generation of each particle and swarm operators. The parameter npasses, represents the number of allowed liquid zone passes through the bar and it is limited to 20, to avoid large number of passes since the purification process is slow (v = 7.10−6 m/s). As a constraint, when the number of npasses is greater than 10, the objective function applies a penalty to motivate the algorithm to search lower number of passes. The penalty is the multiplication of the impurity concentration (Cs (x)) by 1/dx, being dx the incremental space (Fig. 4). In the case of the present problem, dx = 0.001. The second parameter is Amax, which is a value to support smooth descendent curves from Eqs. (16a)–(16d), creating a vector A by the function linspace (1, Amax, n) with n elements linearity distributed from

The Lévy_Flight function returns the cuckoo step size to search the next nest. At first, a σLevy is calculated by Eq. (13) taking into account a ΓLevy function that represents a factorial random number distribution, as shown in Fig. 7, and being described by Eq. (14), where the parameter t is associated with a factorial number to be calculated from the respective input x value. The βLevy represents a Brownian random walk that is usually limited in the interval of 1 ≤ βLevy ≤ 2, being designated here as 1.5 [30]. The constant α is a parameter used to localize the Lévy Flight in the search space, herein α = 1.

+

(14)

4.3. Computational procedure to optimize the purification of naphthalene

(12)

Levy ·(1

e t t x 1dt|x > 0

StepSizeLevy = 0.01·

The Lévy flight is a nonlinear numerical solution used to describe the chaotic vortices chains behavior in certain unbounded jet flows, where the trajectories have infinite mean square displacement per flight [35]. It is a Markovian stochastic process described by a probability density function (PDF) [36] which is adopted by CSA to support the determination of cuckoos' lengths motion with a view to searching best nest to lay their eggs. The Cuckoo Lévy Flight algorithm considered in this work follows the Yang and Deb [28] implementation, ith cuckoo (Pi) updated by Eq. (12), where the nest is the number of nests considered in the optimization procedure and is a multiplicative operator for each ith cuckoo attribute.

=

0

As aforementioned, σLevy is a normalized random distribution function used to determine the step size of each cuckoo. The Levy step size (Eq. (15)) is associated with a normalized uniform random distribution function rand() to improve the Brownian particle walk in the search space by a normalized velocity.

4.2. Cuckoo search algorithm (CSA)

Levy

=

(13)

Fig. 7. The ΓLevy function distribution. 5

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Fig. 8. General dataflow integration of metaheuristics (PSO and CSA) with the numerical mathematical model. Table 1 Parameters limits range.

Z n = maxx

Parameter

Minimal Value

Maximum Value

npasses Amax minx (%) opt

1 1 3 1

20 20 7 4

exp(A) ·(maxx max(exp(A))

Z n = maxx

A ·(maxx max( A )

Z n = gsort

exp(A) ·(maxx max(exp(A))

minx )

minx )

minx ) + minx

minx )

(16d)

The parameter maxx represents the maximum length of the liquid zone. In this study, initial maximum lengths are established in 80, 60, 40 and 20% in order to evaluate the influence of the different initial lengths on the resulting impurity distribution along the bar. The first value of the vector A is maxx (A1 = maxx) and the last A value is minx (An = minx). However, the values in the middle elements of the vector are determined by the linspace instruction. In Eq. (16c), the function gsort is used to sort the data by descendant values. The Zn in Eq. (16a) is an exponential descendent curve while Eq. (16b) considers a descendent curve in terms of square root, and finally Eq. (16d) is a linear descendent curve. Each of the four different types of decreasing Z profiles are randomly generated based on the predefined range of the four parameters previously described in Table 1. Therefore, the metaheuristic sends to the objective function these random values as input parameters, which are used to generate a Zn profile vector given by one of the four Eqs. (16a)–(16d), according to the random option (opt). After the definition of the Zn profile vector, the mathematical model calculates the impurity profile. When the absolute value of Rd is greater than 0.01, a constraint penalization is applied, returning Rdex = Rd × 100. Otherwise, if Rd is lower than 0.001 and nPasses is also lower than 10, a bonification is applied to Rdex, which tends towards −1, where Rdex = −1/nPasses + Rd.

1 to the Amax value, being Amax the maximum value of the A vector. These equations were initially specified to support a smoothing descendent initially unknown profile of the Zn zone length. The Amax interval presents similar n values to search for descendent smooth curves associated with n values [37,38]. The parameter minx represents the minimum length of the liquid zone (3–7%) achieved by the zone refining device. The last parameter, opt, represents the association of the numbers 1, 2, 3 and 4 with Eqs. (16a)–(16d), respectively. These equations were implemented to provide different random smooth descendent normalized curves (ratio between values of vector A and the maximum value of vector A) to fit these curves in the predefined interval from minx to maxx [39]. It is reported that better purification efficiency is associated with longer zone lengths for early passes followed by shorter zone lengths for later passes [12]. In this sense, Eqs. (16a)–(16d) represent different ways to decrease the zone length (Zn) from one pass to the subsequent (Zn+1), which will be evaluated. Fig. 9 presents a general objective dataflow informing the routes options (opt) according with randomly selected values. The black ellipse (N.M.) in Fig. 9 indicates where the numerical method takes place for the impurity profile predictions necessary to calculate Rd, which is the difference between the impurity concentration along the bar in the nth pass (Csn(x ) ) and in the previous one (n − 1)th pass (Csn(x )1).

Z n = maxx

A ·(maxx max(A)

5. Results and discussions 5.1. Mathematical model validation Since the distribution coefficient of impurity (k) is the main constant dictating how the impurity is segregated to the liquid during solidification, it is important to determine its value for the Rhodamine/ Naphthalene system. Cooling curves of samples containing 0.25, 0.5, 1, 2.5 wt% Rhodamine were obtained through low cooling from the melt until solidification completion in order to construct a partial phase diagram, as shown in Fig. 10. For low Rhodamine concentrations, it can be realized that the phase diagram exhibits a linear behavior, permitting to assume a constant coefficient k = 0.5. It has been reported that a variable k approach in simulations is important to be considered to predict correctly the impurity profiles when liquidus and/or solidus

(16a) (16b) (16c) 6

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Fig. 9. General objective function dataflow detaching the four different descendent type of functions. 1

10

Rhodamine profile Liquid zone length: 10%

0

Cs/Co

10

-1

10

10

Experimental 1 pass Experimental 7 passes Simulated 1 pass Simulated 7 passes

-2

0.0

0.2

0.4

0.6

0.8

1.0

x/L

Fig. 10. Experimental partial phase diagram of Rhodamine/Naphthalene obtained through cooling curves.

(a)

lines are far from linearity [40]. It can be seen in Fig. 11 that the simulated profiles, for initial concentration C0 = 0.5%, and for the cases of small (Z = 10%) and large (Z = 60%) liquid zone lengths, are in good agreement with the experimental profiles. This validation of the mathematical model permits its usage as a tool to preview the influence of operational zone refining parameters, such as the length and the number of passes of the liquid zone. 5.2. Optimization results The adopted number of particles in the swarm algorithms was 100 (nPart = 100). Furthermore, considering the benchmarking between PSO and CSA, a stop criterion based on the iteration number was designated by 300 (nIter = 300), considering some previous efforts where this number of iterations was shown to be enough to achieve the best solution in this application. These optimizations were performed in a computer with Linux Mint 16.04 X86_64, 8 GB of RAM memory and Intel I5 3.2 GHz based processor. Each optimization algorithm runtime machine turned around 1 h.

(b) Fig. 11. Concentration distribution of Rhodamine (impurity) along the length of the Naphthalene sample after zone refining: (a) liquid zone length: 10%; (b) liquid zone length: 60%.

7

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Initial liquid zone length: 20%

Initial liquid zone length: 40%

-0.1110

-0.1160

-0.1115 -0.1120 -0.1125

-0.1165

Lc=1, Ls=1 Lc=1, Ls=3 Lc=2, Ls=2 Lc=3, Ls=1 Lc=2, Ls=1

-0.1135

Fitness

-0.1140 -0.1145 -0.1150

Lc=1, Ls=2 Lc=2, Ls=1 Lc=2, Ls=3 Lc=3, Ls=2

-0.1170

Fitness

-0.1130

-0.1155

-0.1175

-0.1160

Lc=1, Ls=1 Lc=1, Ls=3 Lc=2, Ls=2 Lc=3, Ls=1 Lc=3, Ls=3

-0.1165 -0.1170

-0.1180

-0.1175 -0.1180 -0.1185 0

30

60

90

120

150

180

210

240

270

-0.1185

300

0

30

60

90

Interactions

120

210

240

270

300

270

300

Initial liquid zone length: 80%

Lc=1, Ls=1 Lc=1, Ls=3 Lc=2, Ls=2 Lc=3, Ls=1 Lc=3, Ls=3

-0.1160

Lc=1, Ls=2 Lc=2, Ls=1 Lc=2, Ls=3 Lc=3, Ls=2

Lc=1, Ls=1 Lc=1, Ls=3 Lc=2, Ls=2 Lc=3, Ls=1 Lc=3, Ls=3

-0.1165

-0.1170

Lc=1, Ls=2 Lc=2, Ls=1 Lc=2, Ls=3 Lc=3, Ls=2

-0.1170

Fitness

Fitness

180

(b)

Initial liquid zone length: 60%

-0.1165

150

Interactions

(a)

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In addition, considering the nonlinearity in this problem, it was necessary to carry out an initial procedure to establish best PSO velocity parameters to balance its performance, calibrating the velocity LC and LS parameters in Eq. (11), considering 1, 2 or 3 as accepting values [41]. These initial PSO calibration procedures are presented in Fig. 12(a)–(d), for 20%, 40%, 60% and 80% of initial liquid zone length, respectively, where LC = 2 and LS = 1 are the best parameters for an overall balance of fitness considering all the four analyzed cases. The results presented in these figures are the average convergence results from three trials. Considering the previous PSO best results for LC = 2 and LS = 1, they were taken into account in order to compare PSO performance to the Cuckoo (CSA) one, such as presented in Fig. 13(a–d). It can be seen that in the four cases of initial liquid zone lengths, the CSA is better than the PSO [LC = 2, LS = 1]. Furthermore, it can be realized from Fig. 13(a–d), an abrupt convergence of the PSO algorithm in the initial iterations, maintaining constant values until the end of the iterations. It seems that the PSO has entered a stationary regime due to local minima values, provoked by the nonlinearity and chaotic behavior of the problem induced by the mathematical model. This is coincident with the concepts and theories of this PSO version unprovided from any computational approach to

evade from local minima under these conditions [42]. The Cuckoo algorithm continuously presents some descendent values along the iterations, reinforcing the PSO local minima search value, against a more efficient search space executed by the CSA algorithm. Cuckoo and PSO searches results are presented in Table 2, for each starting liquid zone lengths. This table presents the sequence of liquid zone lengths that provide the maximum purification with the minimum number of passes which was determined to be 8 passes for all cases. Although the liquid zone lengths results have centesimal precision, care should be exercised when purifying small bar lengths, considering the capable precision of liquid zone length furnished by the zone refining device. A better visualization on the evolution of descendent values of the liquid zone lengths along the passes can be observed in Fig. 14. It is possible to conclude that the higher difference in the liquid zone lengths, for a same pass, between Cuckoo and PSO procedures concerns the second and third passes. For the remaining passes, the difference mostly concentrates on the decimal scale. Table 3 presents the parameters npasses, Amax, minx and opt, responsible for the definition of Z values at each pass. Independently of the initial liquid zone length, it was found, for both algorithms, that the minimum number of passes is 08 to achieve an impurity distribution profile in which Rd < 0.01. Also, opt was always stated as 3, i. e., the 8

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Fig. 13. Benchmarking PSO and CSA algorithms convergence considering different initial liquid zone lengths (a) 20%, (b) 40%, (c) 60 and (d) 80%.

best way how Z decreases, for the zone refining of Naphthalene (k = 0.5), is ruled by Eq. (16c). More investigations deserve to be performed with other systems (different k) in order to verify if Eq. (16c) can be generalized as the best equation to describe de descendent way of Z values for any k. Different values of Amax and minx resulted from both AI techniques, which could be attributed to the distinct swarm approaches: PSO are linked to cognition and social learning rates (LC and LS) and Cuckoo, to step size σLev.

The simulated Rhodamine profiles predicted by Cuckoo and PSO techniques are in Fig. 15a and b. Since the discrepancy between the zone lengths sequence are not so large for Cuckoo and PSO, it is expected that the distribution of Rhodamine would not be so different among the profiles shown by both techniques, which can be realized comparing Fig. 15a and b. It can be seen that the adoption of larger zone lengths for the initial zone passes is more appropriate in terms of impurity transport efficiency, although there is practically no difference

Table 2 Sets of best liquid zone lengths [%] that provide the maximum purification efficiency for starting liquid zone lengths of 20, 40, 60 and 80%. Passes and Liquid zone length

1 2 3 4 5 6 7 8

Initial liquid zone length: 20%

Initial liquid zone length: 40%

Initial liquid zone length: 60%

Initial liquid zone length: 80%

Cuckoo

PSO Lc = 1, Ls = 2

Cuckoo

PSO Lc = 1, Ls = 2

Cuckoo

PSO Lc = 1, Ls = 2

Cuckoo

PSO Lc = 1, Ls = 2

20 9.99 5.87 4.18 3.48 3.20 3.08 3.00

20 10.01 6.00 4.39 3.74 3.48 3.38 3.31

40 16.72 8.09 4.89 3.70 3.26 3.10 3.00

40 12.78 5.60 3.71 3.22 3.08 3.05 3.04

60 22.54 9.70 5.30 3.79 3.27 3.09 3.00

60 21.57 9.28 5.35 4.10 3.70 3.57 3.51

80 28.20 11.25 5.70 3.88 3.29 3.09 3.00

80 26.49 10.26 5.34 3.85 3.40 3.26 3.20

9

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Fig. 14. PSO and Cuckoo proposed liquid zone lengths sequence for each pass considering different initial liquid zone lengths of (a) 20% (b) 40% (c) 60% (d) 80%.

between the Rhodamine distribution profile concerning 60% and 80% starting zone lengths.

in good agreement with the experimental data. The interaction between the numerical model and the two swarm algorithms, Particle Swarm Optimization and Cuckoo, has provided optimized sets of liquid zone lengths with a view to maximizing purification efficiency and minimizing the number of liquid zone passes. Cuckoo search algorithm has proven to be more effective since convergence is achieved with fewer required iterations than Particle Swarm Optimization.

6. Conclusion Zone refining has proven to be an effective process for purifying ionic liquids to attend reusing or recycling needs. The mathematical model applied to simulate the impurity distribution along the length of Naphthalene samples during the zone refining process was found to be

Table 3 Sets of best parameters necessary to define liquid zone lengths that provide the maximum purification efficiency for starting liquid zone lengths of 20, 40, 60 and 80%. Parameters

npasses Amax mix opt

Initial liquid zone length: 20%

Initial liquid zone length: 40%

Initial liquid zone length: 60%

Initial liquid zone length: 80%

Cuckoo

PSO Lc = 1, Ls = 2

Cuckoo

PSO Lc = 1, Ls = 2

Cuckoo

PSO Lc = 1, Ls = 2

Cuckoo

PSO Lc = 1, Ls = 2

8 6.22 3 3

8 7.92 4.31 3

8 6.94 3 3

8 4.98 5.25 3

8 7.49 3 3

8 6.97 3.02 3

8 7.82 3 3

8 5.89 5.32 3

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Environ. Saf. 99 (2014) 1–12. [4] N.L. Mai, K. Ahn, Y.M. Koo, Methods for recovery of ionic liquids – a review, Process. Biochem. 49 (2014) 872–881. [5] H. Zhu, G. Zhang, M. Chen, S. Zhou, G. Li, X. Wang, Q. Zhu, H. Li, J. Hao, Naphthalene-functionalized, photoluminescent room temperature ionic liquids bearing small counterions, Chem. Eur. J. 22 (2016) 6286–6293. [6] M. Era, K. Maeda, T. Tsutsui, Enhanced phosphorescence from naphthalene-chromophore incorporated into lead bromide-based layered perovskite having organic–inorganic superlattice structure, Chem. Phys. Lett. 296 (1998) 417–420. [7] O. Rinco, M.C. Nolet, R.O.C. Bohne, Probing the binding dynamics to sodium cholate aggregates using naphthalene derivatives as guests, Photochem. Photobiol. Sci. 2 (2003) 1140–1151. [8] Y.J. Kwon, J. Cho, High capacity carbon-coated Si70Sn30 nanoalloys for lithium battery anode material, Chem. Commun. 9 (2008) 1109–1111. [9] J. Xu, D.K. Dang, V.T. Tran, X. Liu, J.S. Chung, S.H. Hur, W.M. Choi, E.J. Kim, P.A. Kohl, Liquid-phase exfoliation of graphene in organic solvents with addition of naphthalene, J. Colloid Interf. Sci. 418 (2014) 37–42. [10] W.R. Wilcox, R. Friedenberg, N. Back, Zone melting of organic compounds, Chem. Rev. 64 (1964) 187–220. [11] C.S. Wang, Y.M. Sun, Studies on the formation of PEN. I. Kinetic aspects of catalysed reaction in transesterification of dimethylnaphthalate with ethylene glycol, J. Polym. Sci. Part A: Polym. Chem. 32 (1994) 1295–1304. [12] T. Cheung, N. Cheung, C.M.T. Tobar, R. Caram, A. Garcia, Application of a genetic algorithm to optimize purification in the zone refining process, Mater. Manuf. Process. 26 (2011) 493–500. [13] M. Suk, K. Leonartz, Halo Growth during unidirectional solidification of camphornaphthalene eutectic system, J. Cryst. Growth 213 (2000) 141–149. [14] H. Nojima, Studies of zone melting IV. The equilibrium distribution coefficient of the bibenzyl-stilbene system, Bull. Chem. Soc. Jpn. 51 (1978) 2513–2517. [15] H. Nojima, S. Akehi, Studies of zone melting V. The solid-liquid equilibrium and zone melting of the bibenzyl-diphenylacetylene system Bull, Chem. Soc. Jpn. 53 (1980) 2067–2073. [16] I.H. Hong, K.J. Tan, M. Toh, H. Jiang, K. Zhang, C. Kloc, Impurities in zone-refining anthracene crystals, J. Cryst. Growth 363 (2013) 61–68. [17] T. Cheung, N. Cheung, A. Garcia, Application of an artificial intelligence technique to improve purification in the zone refining process, J. Electronic. Mat. 39 (2010) 49–55. [18] T. Cheung, N. Cheung, C.M.T. Tobar, P.R. Mei, A. Garcia, Zone refining of tin: optimization of zone length by a genetic algorithm, Mater. Manuf. Process. 28 (2013) 746–752. [19] H. Jun, R. Qingbo, H. Zuqi, L. Xun, M. Daqiao, Application of a genetic algorithm to optimize redistribution process in zone refining of cerium, Rare Met. Mater. Eng. 46 (2017) 3633–3638. [20] J.A. Burton, R.C. Prim, W.P. Slichter, The distribution of solute in crystals grown from the melt. Part I: theoretical, J. Chem. Phys. 21 (1953) 1987–1991. [21] W.G. Pfann, Principles of zone-melting, Trans. Am. Inst. Min. Metall. Eng. 194 (1952) 747–753. [22] J.A. Spim Jr., M.J.S. Bernadou, A. Garcia, Numerical modeling and optimization of zone refining, J. Alloy Compd. 298 (2000) 299–305. [23] S.J. Russell, P. Norvig, Artificial Intelligence: A Modern Approach, Pearson Education Limited, Malaysia, 2016. [24] F. Yousefi, Z. Amoozandeh, Statistical mechanics and artificial intelligence to model the thermodynamic properties of pure and mixture of ionic liquids, Chin. J. Chem. Eng. 24 (2016) 1761–1771. [25] F. Shaahmadi, M.A. Anbaz, B. Bazooyar, The analysis of liquid–liquid equilibria (LLE) of toluene+ heptane+ ionic liquid ternary mixture using intelligent models, Chem. Eng. Res. Des. 130 (2018) 184–198. [26] E. Kianfar, M. Shirshahi, F. Kianfar, F. Kianfar, Simultaneous prediction of the density, viscosity and electrical conductivity of pyridinium-based hydrophobic ionic liquids using artificial neural network, Silicon 10 (2018) 2617–2625. [27] A.K. Kar, Bio inspired computing–a review of algorithms and scope of applications, Expert Syst. Appl. 59 (2016) 20–32. [28] X.-S. Yang, S. Deb. Cuckoo search via Lévy flights, World Congress on Nature & Biologically Inspired Computing (NaBIC), 2009. [29] W. Deng, R. Yao, H. Zhao, X. Yang, G. Li, A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm, Soft Comput. 23 (2019) 2445–2462. [30] M. Mavrovouniotis, C. Li, S. Yang, A survey of swarm intelligence for dynamic optimization: algorithms and applications, Swarm Evol. Comput. 33 (2017) 1–17. [31] X.-S. Yang, Nature-Inspired Metaheuristic Algorithms, Luniver press, 2010. [32] G.G. Wang, A.H. Gandomi, X. Zhao, H.C.E. Chu, Hybridizing harmony search algorithm with cuckoo search for global numerical optimization, Soft Comput. 20 (2016) 273–285. [33] Y. Shi, R.C. Eberhart, Empirical study of particle swarm optimization, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406) IEEE 3 (1999). [34] D. Wang, D. Tan, L. Liu, Particle swarm optimization algorithm: an overview, Soft Comput. 22 (2018) 387–408. [35] M.A. El Aziz, A.E. Hassanien, Modified cuckoo search algorithm with rough sets for feature selection, Neural Comput. Appl. 29 (2018) 925–934. [36] A.V. Chechkin, R. Metzler, J. Klafter, V.Y. Gonchar, Introduction to the theory of Lévy flights, Anomalous transport: Foundations and applications 49 (2008) 431451. [37] O. Fercoq, P. Richtárik, Smooth minimization of nonsmooth functions with parallel coordinate descent methods, Modeling and Optimization: Theory and Applications, Springer, Cham, 2017. [38] S. Ruder, An overview of gradient descent optimization algorithms. arXiv preprint

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(b) Fig. 15. Concentration distribution of Rhodamine along the length of the Naphthalene sample for zone refining with different initial liquid zone lengths (20%, 40%, 60%, 80%). (a) Cuckoo and (b) PSO predictions.

Acknowledgements The authors are grateful to FAPESP-São Paulo Research Foundation grant: 06/60117-5 and CNPq - National Council for Scientific and Technological Development and IFSP - Federal Institute of Education, Science and Technology of São Paulo (call PRP-226/2016) for their financial support. The authors are also grateful to Prof. Rubens Caram Jr., from University of Campinas, for permitting the use of his thesis experimental data necessary to validate the mathematical model. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.seppur.2019.116089. References [1] K.N. Marsh, J.A. Boxall, R. Lichtenthaler, Room temperature ionic liquids and their mixtures—a review, Fluid Phase Equilib. 219 (2004) 93–98. [2] T.P.T. Pham, C.W. Cho, Y.S. Yun, Environmental fate and toxicity of ionic liquids: a review, Water Res. 44 (2010) 352–372. [3] M.C. Bubalo, K. Radošević, I.R. Redovniković, J. Halambek, V.G. Srček, A brief overview of the potential environmental hazards of ionic liquids, Ecotoxicol.

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C.H. Silva-Santos, et al. arXiv:1609.04747(2016). [39] T. Heister, L.G. Rebholz, Scientific Computing: For Scientists and Engineers, Walter de Gruyter GmbH & Co KG, 2015. [40] N. Cheung, R. Bertazzoli, A. Garcia, Numerical and experimental analysis of an approach based on variable solute distribution coefficients during purification by zone refining, Sep. Purif. Technol. 52 (2007) 504–511.

[41] M. Jiang, Y.P. Ming, S.Y. Yang Luo, Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm, Inform. Process. Lett. 102 (2007) 8–16. [42] R. Jensi, G. Wiselin Jiji, An enhanced particle swarm optimization with levy flight for global optimization, Appl. Soft Comput. 43 (2016) 248–261.

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