Fractionation of polyethylene wax by pilot-scale molecular distillation: new insights on process development

Journal Pre-proof Fractionation of polyethylene wax by pilot-scale molecular distillation: new insights on process development Eluize Vayne Maziero, Rafael Budel Salles, Laura Plazas Tovar, ˜ Bertuol Eduardo Hiromitsu Tanabe, Daniel Assumpc¸ao

PII:

S0263-8762(19)30458-7

DOI:

https://doi.org/10.1016/j.cherd.2019.09.041

Reference:

CHERD 3831

To appear in:

Chemical Engineering Research and Design

Received Date:

30 October 2018

Revised Date:

19 August 2019

Accepted Date:

28 September 2019

Please cite this article as: Maziero EV, Salles RB, Tovar LP, Tanabe EH, Bertuol DA, Fractionation of polyethylene wax by pilot-scale molecular distillation: new insights on process development, Chemical Engineering Research and Design (2019), doi: https://doi.org/10.1016/j.cherd.2019.09.041

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Fractionation of polyethylene wax by pilot-scale molecular distillation: new insights on process development Eluize Vayne Mazieroa, Rafael Budel Sallesa, Laura Plazas Tovarb, Eduardo Hiromitsu Tanabea, Daniel Assumpção Bertuola,* a

Environmental Processes Laboratory (LAPAM), Chemical Engineering Department, Federal University of Santa Maria, 97105-900, Santa Maria, RS, Brazil b

Catalysis and Green Chemistry Laboratory (LabCQV), Chemical Engineering Department, Federal University of São Paulo, 09913-030, Diadema, SP, Brazil *To whom correspondence should be addressed. Tel.: + 55 55 3220 8607; E-mail: [email protected] (Daniel Bertuol)

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Highlights

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Graphical abstract

Molecular distillation (MD) emerging in plastics industry for fractionation of

PE-Wax fractionated into light paraffin wax and super microcrystalline wax (SM-

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polyethylene wax (PE-Wax).

Wax).

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High-yield of distillate fraction (63.4%) with a n-paraffin distribution until n-C30.

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SM-Wax (from n-C22 to n-C90) as potential material for thermal energy storage.

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Highlight scale-up parameter of MD: Distillate flow rate/feed flow rate ratio (0.60).

ABSTRACT

A falling film molecular distillation (FFMD) process was used in a pilot plant to fractionate a polyethylene wax (PE-Wax) into light paraffin wax (LP-Wax) and super-microcrystalline wax (SM-Wax). The pseudoization technique was applied to represent the molecular distribution of the PE-Wax by pseudo-components (PS1 and PS2). Investigation was made of the influences of the evaporator temperature (EVT), feed flow rate (FF), and condenser temperature (CT) on the percent recovery of distillate (DP), the yield of PS1 in the distillate ( YD _ PS1 ), and the distillate flow rate/feed flow rate ratio (DF). The predictive models and the multi-response optimization

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provided decision criteria about the most suitable operating conditions for fractionating PEWax. The best experimental data for DP, YD _ PS1 , and DF (63.4%, 81.5%, and 0.60, respectively) were obtained with EVT of 184 °C, FF of 1.81 kg/h, and CT of 28 °C, at 0.1 Pa.

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The LP-Wax, recovered mainly in the distillate, exhibited a normal distribution throughout the

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carbon number range from n-C13 to n-C30. The SM-Wax, recovered in the residue, showed a higher latent heat of storage (>169 kJ/kg), according to the phase-change performance of the

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material. These results offer new insights into processing PE-Wax to obtain value-added

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products with narrower carbon number distributions.

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Keywords: Molecular distillation; polyethylene wax; multi-response optimization.

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Central composite rotatable design Confidence interval Carbon number distribution Simulated distillation GC Differential scanning calorimetry Distillate stream at the optimum condition Falling film molecular distillation Fisher distribution Latent heat storage Light paraffin wax Molecular distillation Phase-change materials Polyethylene wax Pseudo-components Determination coefficient Residue stream generated under the optimum conditions Super-microcrystalline wax Thermogravimetric analysis

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Nomenclature CCRD CI CND DGC DSC Dopt FFMD F-test LHS LP-Wax MD PCMs PE-Wax PS1 and PS2 R2 Ropt SM-Wax TGA Greek letters β0 β1, β2, and β3 β11, β22, and β33 β12, β13, and β23 ∆HSL ∆HSS Variables CT D DF DP DS di EVT

Coefficient of regression at the central point Coefficients of regression of the linear terms Coefficients of regression of the quadratic terms Coefficients of regression of the interaction terms Enthalpy of the solid-liquid (melting) transition (kJ/kg) Enthalpy of the solid-solid transition (kJ/kg) Condenser temperature (°C) Overall desirability Distillate flow rate/feed flow rate ratio Percent recovery of distillate Distillate flow rate (kg/h) Individual desirability functions Evaporator temperature (°C)

1.

Kn Lmin i MFP Ps RP RS TP TS Ti max

Feed flow rate (kg/h) Mass fractions of PS1 and PS2 in FF Knudsen number Minimum acceptable value for response Yi Mean free path (m) Pressure system (Pa) Percentage recovery of residue Residue flow rate (kg/h) Percentage recovery of trap Trap flow rate (kg/h) Maximum target value for response Yi

YD _ PS1

Yield of PS1 in the distillate

YD _ PS2 Yi

Yield of PS2 in the distillate Predicted response

Introduction

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FF f F _ PS1 , f F _ PS2

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The plastics industry has grown steadily during the last 50 years, with the worldwide production of plastics expected to exceed 500 million metric tons by 2050 (Thomas et al.,

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2019). In the plastic manufacturing process, the polymerization of ethylene using Ziegler-Natta

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catalysts in the slurry phase generates polyethylene wax (PE-Wax) as a byproduct, which has a low molecular weight, compared to that of the polyolefin (Missau et al., 2018). The presence

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of wax is due to dissolution of the low molecular weight polymer, as well as to the melting of polymer chains, for which the melting temperature is lower than the corresponding polymerization temperature (Cardoso and Fisch, 2016). Some polymerization processes

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include one or more additional phase separation steps in the recycling system, in order to

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remove the PE-Wax from the recycled monomer stream. Different techniques such as primary recycling (in-plant recycling), secondary recycling (mechanical recycling), tertiary recycling (chemical or feedstock recycling), and quaternary recycling (energy recovery) have been increasingly employed in the recycling, recovery and management of solid plastic waste (Okan et al., 2019).

The wax components vary in quantity and number, depending on the origin of the wax (Martini et al., 2015). Many natural waxes consist of complex mixtures of long-chain nonpolar compounds with carbon numbers ranging between n-C20 and n-C60 (Holloway and Jeffree, 2003), resulting in a microcrystalline wax containing a high percentage of iso-paraffinic (branched) and naphthenic hydrocarbons (Martini et al., 2015). Therefore, the wax has to be purified or fractionated to ensure that its properties are suitable for the intended application (Missau et al., 2018). Some of the current processes used to fractionate the wax include

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recrystallization, solvent percolation, wax sweating, supercritical fluids, and molecular distillation (MD). In the recrystallization technique, the wax is dissolved in a suitable amount of solvent in a heated vessel, followed by filtering and removal of the solvent by distillation

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(Zaky and Mohamed, 2010). In the solvent percolation technique, the solvent is percolated, under gravity, onto the wax in a column, after which the wax and oil phases are separated from

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the solvent by distillation (Zaky et al., 2007). The melt crystallization or sweating technique is

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used as a way of de-oiling the wax, but is not always successful, due to trapping of the oil in the crystalline wax matrix (Crause and Nieuwoudt, 2000). The supercritical fluid technique uses solvents such as ethane, hexadecane, or carbon dioxide, together with high pressure

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(Crause and Nieuwoudt, 2003). Supercritical solvent extraction for the fractionation of waxes is still not used in industry (Crause and Nieuwoudt, 2000). Compared to other processes, static

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crystallization easily leaves the product with no solvent residues, but is an expensive technique

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with the highest capital costs.

These techniques involve several stages and can generate serious pollution, besides

having poor safety aspects, due to the quantities of organic liquids required, all of which restrict their potential applications (Chen et al., 2005). In contrast, physical fractionation (Ciesińska et al., 2016) and MD do not use any solvents to fractionate the waxes, resulting in the generation of much less waste, greater safety, and better economic potential, compared to supercritical

fluid methods (Crause and Nieuwoudt, 2003). The MD technology is considered one of the best methods for separating, purifying, and reducing the risk of decomposition of thermally unstable compounds (Laoretani and Iribarren, 2018). MD is characterized by a distance between the evaporation and condensation surfaces that is on the order of magnitude of the mean free path (MFP) of the molecules (Fregolente et al., 2007; Laoretani and Iribarren, 2018). Consequently, the maximum evaporation rate is reached and matches the rate of molecules escaping from the liquid surface of the film formed

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in the evaporator, so that the equipment operates in a non-equilibrium condition (Kapłon et al., 1986).

In the last seven years, the successful processing of different materials has supported

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increased development of MD as a reliable technique. MD has been shown to be a viable process for removal of phthalic acid esters from sea buckthorn pulp oil (Chen et al., 2019),

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separation of squalene from olive pomace oil (Ketenoglu et al., 2018), fractionation of heavy

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oil fractions (Zuñiga Liñan et al., 2012; Tovar et al., 2017), purification of organic acids (Komesu et al., 2017), concentration of monoacylglycerols rich in polyunsaturated fatty acids (Solaesa et al., 2016), and obtaining high purity dodecanedioic acid (Yu et al., 2015).

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Thermal energy storage systems are crucial for reducing the dependency on fossil fuels and have attracted growing interest for various indoor and outdoor applications (Abdelrazeq et

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al., 2019). Thermal energy storage can be accomplished by using components known as phase-

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change materials (PCMs), which can undergo phase changes (usually solid to liquid changes), while absorbing or releasing large amounts of energy (Sobolciak et al., 2016; Abdelrazeq et al., 2019). In addition, enhancement of the thermal properties of paraffin wax, in terms of faster absorption and release of thermal energy, is favorable for solar energy storage (Lin and AlKayiem, 2016). A suitable phase change temperature and a high melting enthalpy are two crucial requirements for PCMs (Sobolciak et al., 2016). For this purpose, paraffin wax can be

considered an ideal PCM, due to its advantageous characteristics including high heat of fusion, non-corrosive nature, stable chemical properties, and favorable compatibility with conventional materials (Tao et al., 2015). Therefore, in the present work, a PE-Wax was fractionated by falling film molecular distillation (FFMD), using a pilot plant, with a view to enhancing its potential for thermal energy storage. The PE-Wax was considered as a mixture of two lumped model compounds (PS1 and PS2). Investigation was made of the effects of FFMD operating parameters including

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the evaporator temperature (EVT), condenser temperature (CT), and feed flow rate (FF), in a system with pressure system (Ps) of 0.1 Pa, on the percent recovery of the distillate (DP), the yield of PS1 in the distillate stream ( YD _ PS1 ), and the distillate flow rate/feed flow rate ratio

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(DF). New insights concerning the optimum conditions enabled the fractionation of PE-Wax obtained from ethylene polymerization into a light paraffin wax (LP-Wax) and a super-

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microcrystalline wax (SM-Wax), with narrower carbon number distributions and with the

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possibility of acquiring very high added value as PCMs, representing one of the most efficient

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ways of storing thermal energy.

2. Materials and Methods

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2.1 Raw material

A PE-Wax sample with a moisture content of 10.5% was supplied by the company

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Alkaest Indústria Ltda. (São Sepé, Rio Grande do Sul, Brazil). The sample was homogenized and stored in a plastic bag, at room temperature, until used in the experiments. Determination of the acid value (in mg KOH/g), according to ASTM D1386 (1998), found no free acid present in the PE-Wax sample. The ash content, determined according to ASTM D2584 (2018), was less than 1.0 (±0.17)% and was mainly due to additives that were not fully combusted.

2.2 PE-Wax characterization The density of the PE-Wax was measured using automatic gas pycnometers (Ultrapyc 1200e). Thermogravimetric analyses (TGA) were performed using a Shimadzu TGA-50 analyzer. A known mass of the sample (15.0 mg) was heated from room temperature to 600 °C, in an alumina holder, at a constant rate of 20 °C/min, under a stream of nitrogen at a flow rate of 50 mL/min. The thermograms were used to identify the thermal degradation events. Differential scanning calorimetry (DSC) experiments were performed using a

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Shimadzu DSC-60 Plus calorimeter, with nitrogen as the purge gas (at 50 mL/min). Samples with a mass of 5.0 mg were sealed in aluminum pans and an empty pan was used as the reference. The pans were heated from 20 °C to 150 °C, at a heating rate of 10 °C/min, and the

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peak temperatures and enthalpies of the solid-solid and solid-liquid (melting) transitions (∆HSS and ∆HSL, respectively) were determined from the scans.

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The molecular distribution of the PE-Wax was determined by the simulated distillation

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GC (DGC) method, using an Agilent Technologies 7890A gas chromatograph. The DGC conditions were an initial oven temperature of 40 °C, heating rate of 10 °C/min, and final temperature of 430 °C. A GC-FID system set at 430 °C was used for detection, with H2, air,

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and N2 (make-up gas) flow rates of 35, 350, and 30 mL/min, respectively. The boiling point profile, up to about 720 °C (corresponding to the elution of n-C100), was determined using a

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silica capillary column (polydimethylsiloxane stationary phase, 6 m × 530 μm i.d., 0.15 μm,

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Wasson KC100). The temperature of the column was programmed from 50 °C to 430 °C, at 15 °C/min. For the DGC method, the retention times and detector signals were directly correlated by external calibration of the boiling points and the carbon number distribution (CND).

2.3 Molecular distillation (MD) 2.3.1 Determination of MD hydrodynamic parameters by the pseudoization technique

The computational pseudoization technique (Tovar et al., 2012b) was applied to estimate the molecular distribution of the PE-Wax. The method creates a group of dummy components, based on their boiling points, CND, and density. For mixtures with many components, Tovar et al. (2012b) suggested that the hydrocarbon components should be grouped into 25 pseudo-components, in order to reduce the dimensionality of the problem for calculation of the mixture properties, as well as to reduce the computational effort. However, in the present case, the estimated properties of the mixture were similar after the second pseudo-

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component. Hence, two main classes of pseudo-compounds represented the PE-Wax, which were denoted PS1 and PS2.

The hydrodynamic parameters of the molecular distillation (MFP and Knudsen number,

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Kn) were then estimated, based on the range used for the evaporator temperature (EVT, 120– 184 °C) and the system pressure (PS, 0.1–2.06 Pa). The modeling and simulation for PS1 and

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PS2 were based on kinetic theory (Hickman, 1944; Tovar et al., 2017).

2.3.2 Falling film molecular distillation (FFMD) experiments on a pilot scale Fractionation of the PE-Wax was performed using a FFMD pilot plant (Model KD 6,

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UIC GmbH, Alzenau, Germany), shown in Fig. 1. The equipment consisted of a vertical double-jacketed cylinder evaporator (1, in Fig. 1), together with a cooled and centered internal

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condenser and a rotating roller wiper basket. The evaporation surface area was 0.06 m2. The

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pilot plant was equipped with a vacuum system composed of pumps arranged in series (achieving 0.1 Pa), as well as an in-line cold trap (8-11, in Fig. 1). The feed and product lines were equipped with check valves to enable continuous feed/discharge of the streams of materials. All the operating conditions were displayed and monitored by the control system. The EVT, CT, and FF values varied according to the experimental design (Table 1). EVT was limited by the melting and degradation temperatures of the PE-Wax at 0.1 Pa.

Firstly, the PE-Wax was kept at an internal temperature of 120 oC in a storage tank (12, in Fig. 1) fitted with a heating system (5, in Fig. 1). The PE-Wax was fed by a rotating (380 rpm) roller wiper basket with a gear pump. Centrifugal gravity forced the distribution of the material onto the surface of the evaporator (at EVT), reaching the typical thickness of a thin film (Fregolente et al., 2007). The evaporated molecules then travelled through the distillation gap (0.02 m) onto the surface of the condenser (at CT), with the most volatile compounds, which were not condensed, being collected in the cold trap (8, in Fig. 1). For each experiment,

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the outlet liquid streams (distillate and residue) were collected in a gutter around the rotor, with a heating system (4, in Fig. 1) used to maintain the temperature at 120 °C, and then flowed down to the collector vessels (2 and 3, in Fig. 1), where they were stored in glass bottles prior

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to characterization using DGC, DSC, and TGA analyses.

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The heating duty of the KD 6 FFMD pilot plant unit consisted of three contributions:

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(i) heat energy requirements for heating the PE-Wax feed from ambient temperature to 120 °C (solid-liquid melting transition); (ii) heat energy requirements for evaporating the PE-Wax over the evaporator surface; and (iii) heat energy requirements for heating the outlet liquid streams

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(distillate and residue) in the gutter around the rotor. The cooling duty was assumed to be the same as the heating duty. The energy usage was 2 kW for heating circulators 4 and 5 (Fig. 1),

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4 kW for heating circulator 6, and 1.5 kW for the cooling water bath.

2.3.3 Calculations Equation 1 shows the mass balance equation, considering the total feed flow rate of the

PE-Wax (FF) and the outflows consisting of the residue flow rate (RS), distillate flow rate (DS), and trap flow rate (TS). Equations 2-4 were used to calculate the percentage recoveries for the distillate (DP), residue (RP), and trap (TP).

FF =DS  RS  TS

(1)

DP   DS

 DS  RS  TS  100

(2)

RP   RS

 DS  RS  TS  100

(3)

 DS  RS  TS  100

(4)

TP  TS

It was expected that PS1 and PS2 would be mainly associated with DS and RS, with a

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minor contribution from TS. The yields of PS1 and PS2 for DS were obtained using Equations 5-6.



  FF  f

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  FF  f

YD _ PS2   DS  f D _ PS2 

F _ PS1

F _ PS2

 100

(5)

 100

(6)

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YD _ PS1   DS  f D _ PS1 

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where YD _ PS1 , YD _ PS2 are the yields of PS1 and PS2 in DS, and f F _ PS1 , f F _ PS2 are the mass

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fractions of PS1 and PS2 in FF (based on the pseudoization technique and CND). The PS1 and PS2 yields in RS, and possibly in TS, could be estimated as 100 (expected theoretical yield) minus their yields in DS.

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In order to gain insight into the development of the process and its use for scaling-up, the distillate flow rate/feed flow rate ratio (DF) was estimated using Equation 7. (7)

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DF  DS FF

2.4 Experimental design and statistical analysis A central composite rotatable design (CCRD) was employed to investigate the effects

of the FFMD critical parameters including EVT, CT, and FF. The response variables selected were DP, YD _ PS1 , and DF. The base points of EVT for the design were selected from the simulation of the hydrodynamic parameters. Selection of the CT and FF ranges was based on

the equipment manufacturer’s recommendations and previous studies (Chen et al., 2007; Zuñiga Liñan et al., 2012; Tovar et al., 2017). Each parameter was investigated at five levels (Table 1). The experiments consisted of 2(3) trials plus a star configuration and three replicates at the center point. The significances of the factors and their interactions were determined using the p values at confidence levels of 97.5% (for the DP and DF responses) and 99.0% (for the

YD _ PS1 response). The analyses were performed using Statistica 8.0 software (StatSoft). The responses (DP, YD _ PS1 , and DF) were estimated using Equation 8: (8)

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Yi  0  1   EVT    2   CT   3   FF   11   EVT  EVT    22  CT  CT  

33  FF  FF   12  EVT  CT   13  EVT  FF    23  CT  FF 

where Yi is each predicted response, β0 is the coefficient of regression at the central point, β1,

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β2, and β3 are the coefficients of regression of the linear terms, β11, β22, and β33 are the coefficients of regression of the quadratic terms, and β12, β13, and β23 are the coefficients of

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regression of the interaction terms. Contour plots were constructed for the fitting of Equation

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8 for each response. The regression models were validated using the determination coefficient

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(R2), the Fisher distribution (F-test), and additional experiments.

2.5 Multi-response optimization

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The responses DP, YD _ PS1 , and DF were optimized simultaneously by means of the individual desirability functions (di) (Fleig et al., 2017). The di scale ranges from 0 to 1

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(completely undesirable response up to the fully desired response, at a confidence level of 97.5%). Based on di, the overall desirability (D), which is defined as the weighted geometric mean of di, could be obtained according to Equation 9: D  wi d1w1  d2w2  d3w3

(9)

Therefore, if the target value ( Ti max ) for response Yi is the maximum and Lmin is the i minimum acceptable value for response Yi, then di is described by Equation 10: 0    Yi  Lmin  di    max i min    Ti  Li   1

if Yi  Lmin i

(10)

if Lmin  Yi  Ti max i if Yi  Ti max

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3. Results and Discussion 3.1 DGC, TGA, and DSC analyses of the PE-Wax

The PE-Wax used in this work was a PE homopolymer wax with the appearance of

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white pearls and a density of 950 kg/m3, in agreement with the aspect and value reported in the literature (Bayat et al., 2013). As discussed by Missau et al. (2018), PE-Wax has many physical

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and chemical properties that make it suitable for a wide range of industrial applications, while

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improving its properties or defining a narrow CND can make it suitable for use in applications such as phase-change materials (PCMs).

The DSC heating curve (Fig. 2a) showed two endothermic peaks. The first, at 92.69 oC

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(∆HSS = 97.17 kJ/kg), represented a solid-solid transition, in agreement with Bacaud and Rouleau (1996). A second peak, which was distinctly visible at 115.15 oC (∆HSL = 6.13 kJ/kg),

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represented the solid-liquid melting transition. Hence, the overall latent heat storage (LHS) was

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about 103.3 kJ/kg.

TGA was applied to investigate degradation of the PE-Wax in different temperature

ranges (Fig. 2b-c).

The TGA curve showed that degradation of the PE-Wax started at 200 oC and was completed at 464 oC, using a heating rate of 20 oC/min, demonstrating that the PE-Wax was

heat-stable, which is a characteristic of shape-stabilized phase-change materials (Abdelrazeq et al., 2019). The DGC analysis enabled determination of the CNDs of the different types of molecules in the PE-Wax, as a function of their boiling points. It can be seen that the DGC chromatograms (Fig. 3a) essentially reflected the elution of compounds with relatively high boiling points, corresponding to saturated n-hydrocarbons including branched-chain paraffins, cycloparaffins, heavier cycloparaffins, and naphthenic hydrocarbons (Bacaud and Rouleau,

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1996; Arabiourrutia et al., 2012).

The DGC chromatogram defined a microcrystalline wax with CND from n-C12 to n-

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C100. The peaks in Fig. 3a corresponded to a range of boiling points from 218.4 to 719.6 oC. The fractions between 218.4 and 388.5 oC (CND from n-C12 to n-C24) and between 388.5 and

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719.6 oC (CND from n-C24 to n-C100) represented the two main pseudo-compounds, PS1 and

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PS2, accounting for 20.68 and 79.32 wt.% of the PE-Wax, respectively. The CND and thermal characteristics enabled computational simulation of the

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hydrodynamic parameters of PE-Wax fractionation by FFMD in a pilot plant.

3.2 Understanding the MD hydrodynamic parameters

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Fig. 4 shows the behavior of the MFPs for PS1 and PS2, using different combinations

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of EVT and Ps. The MFP depended more on Ps than on EVT. The behavior of the MFP of the pseudo-composition of PE-Wax was similar to that found in a previous study by Tovar et al. (2017). There were three operating ranges for the fractionation of PE-Wax. The first was with moderate vacuum, where the PS was above 2.06 Pa and the MFP of PS1 only reached 0.001 m at the highest EVT value (Fig. 4a). For the second range, when the Ps value was reduced from 2.06 Pa to 1.33 Pa, the MFP of PS1 doubled as the EVT increased from 120 oC to 152 oC. This

indicated that it corresponded to unobstructed path distillation, where there was free transportation of the molecules at a pressure of 1.33 Pa (Fig. 4b). For the third range, the MFP values of PS1 were from 0.02 m to 0.023 m, suggesting that this behavior corresponded to the MD (Lutišan and Cvengroš, 1995), where the transfer distance (0.02 m) was comparable to the average free path of molecules evaporating at a PS value below 0.1 Pa (Fig. 4c). Accordingly, it would be expected that as EVT increased, the vapor pressure would also increase rapidly, while at the same time, the MFP of the molecule would become larger, in a high vacuum regime

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(or even under ultra-high vacuum). Furthermore, when the MFP of the molecules was larger than the size of the chamber in the MD device, the fluid dynamics of the vapor would be described by free molecular flow. This is the opposite of the viscous flow encountered at higher

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pressures (PS > 1.33 Pa).

It is well known that the vapor phase will exhibit different physical properties in MD

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devices, since vapor behaves as a collection of independent particles, so Kn determines the

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dynamic regime of the appropriate vapor phase. In the present study, numerical simulation of Kn confirmed that the fractionation of PE-Wax at 0.1 Pa and 120 oC < EVT < 184 oC would correspond to MD. The simulation estimated Kn values between 1.00 and 1.15 for PS1, while

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the dimensionless number for PS2 ranged from 0.80 to 0.90. A Knudsen flow enables the processing to be characterized and the anisotropic status to be obtained (Kawala and

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Dakiniewicz, 2002; Tovar et al., 2017). The vacuum (at 0.1 Pa) also controls heat transfer rates

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in thin film molecular distillers.

3.3 PE-Wax fractionation by FFMD: analysis of EVT, CT, and FF In FFMD, evaporation occurs at different rates and the vapor phase has different physical properties, since the vapor behaves as a collection of independent particles. The nonequilibrium character of the process is shown by the irreversible transfer of the substance from

the surface of the evaporator and its total condensation on the condenser surface (Hickman, 1944; Laoretani and Iribarren, 2018). Considering these behaviors, the fractionation of the PEWax was analyzed considering the main operating parameters (EVT, CT, and FF), Table 1 shows the FFMD results for different combinations of EVT, CT, and FF. The mass balance showed a higher percentage of losses (∼51%) as the FF increased, due to the high resistance to transfer of heat and mass in the liquid. Hence, the transfer resistance increased and the distillation rate decreased, since molecules from the liquid phase within the

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thin liquid film surface were not transported to the vapor phase during the vaporization process. Consequently, the movement of molecules from the vapor phase to the liquid phase was not probable during the condensation process, as analyzed using the MD hydrodynamic parameters

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(Section 3.2). Similarly, insights concerning the limitations of EVT and CT are related to diffusion and heat transfer efficiency. Figure 5 shows the significance of the linear and

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quadratic process variables, together with the interaction factors, where smaller p-values for

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the variables indicate greater significance in terms of the response.

3.3.1 Effects of EVT, CT, and FF on DP

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The results of the statistical analyses are summarized in Fig. 5. EVT was highly significant, with p =1.94×10-3. All the two-way interactions were significant, suggesting that

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DP was directly related to EVT. The main quadratic effect was significant, with p = 9.78×10-3.

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The main first order effects of CT and FF were also significant, with p = 9.42×10-3 and 7.73×102

, respectively. In addition, there was a significant interaction between every pair of variables

(Fig. 5). Two-dimensional response contour plots (graphical representations of Equation 8) were constructed, in order to illustrate the main interactive effects on DP, YD _ PS1 , and DF. The effects of the interactions between EVT, CT, and FF on DP (Fig. 6a-c) suggested that higher CT and FF values would not enhance DP, under the experimental conditions. Fig. 6a shows two

zones of relatively high DP, with the best values for DP (>37.2%) obtained by the FFMD process being achieved at low or high values for CT and FF. However, lower FF values may not ensure a thin film over the surface of the evaporator, so the process would be limited by mass transfer. At low feed rates, there is insufficient wetting of the evaporator surface, known as the “dry-wall” effect, resulting in low evaporation rates. The efficacy of FFMD is generally related to the efficiencies of diffusion and heat transfer. As FF is increased, the evaporation rate increases and reaches a maximum value at optimal FF. When FF is increased beyond this

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optimum, the film thickness increases, and the evaporation rate consequently decreases. Significant EVT×CT interactions were illustrated by the semi-elliptical or saddle nature of the contour plots in Fig. 6b. The DP value increased up to 35.7% with increase of EVT and

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decrease of CT, suggesting that the efficiency of FFMD could be described by the ratio between the molecules definitively captured in the cooling system and those evaporated from the

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evaporator. Therefore, increase of CT led to decreased efficiency, due to significant re-

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evaporation of the condensate. However, depending on the process, it may be necessary to operate with higher CT (Batistella et al., 2002). In addition, the saddle nature of the DP contour plot indicated significant EVT×FF interaction, as shown in Fig. 6c, where the lines confined to

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the right-hand corner (39.6%) show the highest predicted values for DP. Therefore, FF was one of the most important operational parameters influencing the evaporation rate and product yield

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in the fractionation of PE-Wax by FFMD, especially considering the effects of EVT and film

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thickness. Therefore, for EVT up to 184 °C and FF between 1.0 and 2.5 kg/h, the film thickness should decrease, resulting in a higher evaporation rate and improved product yield. Hence, the surface temperature of the liquid film, representing the operating

temperature of the evaporator, was a crucial factor for the evaporation rate. An increase in the supply of heat to the evaporating liquid caused the temperature to rise, consequently increasing the saturated vapor pressure, as well as DP. Therefore, the condition required was a sufficiently

low CT to ensure that all the molecules reaching it were captured, in which case the transfer resistance was reduced and the distillation rate increased, as reported previously (Tovar et al., 2012a; Komesu et al., 2017).

3.3.2 Effects of EVT, CT, and FF on YD _ PS1 The values of YD _ PS1 were influenced by the MFP of the molecules that determined the condition for the FFMD process to occur. The results of the statistical analysis (Fig. 5) showed

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that EVT was most significant, with p = 7.98×10-4. The two-way interaction (EVT×CT) was also significant, while the main quadratic EVT effect was not significant, suggesting greater linear influence of EVT on YD _ PS1 . The main first order effects of CT and FF were significant,

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while the main quadratic FF effect was not significant.

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Response contour plots (Fig. 6d-f) providing graphical representations of Equation 8 were constructed to illustrate the main and interactive effects of EVT, CT, and FF on YD _ PS1 .

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The plots showed that higher FF did not increase YD _ PS1 , under the experimental conditions, since increase of FF was accompanied by decrease of the residence time of the liquid on the

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evaporation surface, which affected the distribution quality of the liquid (Cvengroš et al., 1995). Falling film molecular distillation systems generally exhibit high heat transfer

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efficiency, which in the KD 6 pilot plant was achieved with a rotating roller basket and a gear

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pump that provided optimum FF that ensured rapid transfer and movement of the molecules over the evaporator surface, depending on the viscosity. In this system, it was essential to consider the time-EVT-FF relationships. Fig. 6d shows a fairly high YD _ PS1 zone (75.1%), with higher values for YD _ PS1 mainly being achieved with lower CT and FF values. Fig. 6e also shows higher values for YD _ PS1 with relatively higher CT values. However, the higher the CT value, the lower the separation

efficiency, due to re-evaporation of the condensate (Batistella et al., 2002). Moreover, the difference between EVT and CT must ensure an adequate temperature gradient, since there are fewer free paths for molecules that travel against the flow (Whitman et al., 2010). The EVT×CT interaction showed a maximum region (>60.0%) at EVT higher than 165 °C and CT ranging between 30 °C and 90 °C. Nevertheless, a minimum response for YD _ PS1 was found for EVT below 133 °C and CT above 75 °C. This corresponded to the minimum technical condition for PE-Wax fractionation by FFMD, corresponding to null recovery of PS1 in the distillate stream,

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as shown in Fig. 6e.

This confirmed that the vapor generated during the process of vaporization of the liquid mixture of PE-Wax was removed from the evaporator surface with minimum (or without any)

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contact with the liquid phase flowing down the tube, with the distance between the evaporator surface and the condenser surface being smaller than the MFP, as discussed in Section 3.2.

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It was observed that YD _ PS1 could exceed 68% with an increase of EVT and decrease of

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FF (Fig. 6f). However, the EVT×FF interaction was not significant (p = 2.03×10-2, Fig. 5). Based on these results, it was essential to determine an appropriate FF value in order to mix

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the liquid in the film and increase the heat transfer. With such mixing, the temperature and concentration gradients were equalized as a result of intense evaporation at the surface

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(Cvengroš et al., 1995). After evaporation, the molecules moved continuously from the surface of the liquid towards the pressure gradient. When the condenser was located at a distance from

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the liquid surface comparable to the MFP, a greater proportion of the molecules reached it without loss of direction (Whitman et al., 2010).

3.3.3 Effects of EVT, CT, and FF on DF In a processing system, scale-up is a highly important stage in the development of high added value products (Batistella et al., 2006). Furthermore, scale-up enables comparison with

competing technologies on a commercial scale, while also significantly improving environmental assessments (Piccinno et al., 2016). Scaling-up trials were outside the scope of this study, but the KD 6 pilot plant could be expected to provide scalable process parameters. Hence, DF could be designated as a design parameter, since it denoted the efficiency of the FFMD and could be of great relevance to industrial processes involving polymer recycling, including coupled processes such as pyrolysis (as a promising method for the recycling of plastic wastes ranging from polyolefins to wax) and the use of FFMD for the corresponding

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fractionation. In the present case, the regression model aimed to achieve the highest DF and maintain

YD _ PS1 as high as possible. Fig. 5 shows a summary of the results of the statistical analyses,

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where EVT was highly significant (p = 2.42×10-3) and the main quadratic effect was insignificant. The major first order effects of CT and FF were significant, as shown by the p

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values (8.36×10-3 and 3.22×10-3, respectively). The effects of the interactions CT×FF,

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EVT×CT, and EVT×FF on DF are illustrated in Fig. 6g-i, with the configurations showing that higher CT and FF values were unable to increase DF, under the experimental conditions. Fig.

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6g also shows two zones with relatively high DF. Using the FFMD process, higher DF values were mainly achieved with simultaneously low CT and FF values. However, lower FF values

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may not favor the formation of a uniform film on the evaporator surface, where transport of the evaporated compounds from the liquid mixture to the film surface must occur. As FF

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increases, the size of the uniform film increases and the transfers of heat and mass within the liquid increase (Cvengroš et al., 1995). However, the higher the value of FF, the lower the separation efficiency, since the re-evaporation of condensate accounts for appreciable values (Batistella et al., 2002). Therefore, it is important to ensure distillation of the mixture from the film surface and simultaneous transport of the evaporated molecules through the distillation gap, meaning that

the FFMD is governed by high diffusivity and is not mass transfer limited. Fig. 6h illustrates the EVT×CT interactions, where it can be observed that DF increased to 0.40 with increasing EVT and decreasing CT, confirming the need for a sufficiently low CT to ensure that all the evaporated molecules were captured by the condenser (Lutišan and Cvengroš, 1995; Tovar et al., 2017), which was previously observed for the DP response. The saddle nature of the contour plots can also be observed for EVT×CT (Fig. 6h) and EVT×FF (Fig. 6i). For these interactions, the highest DF values (between 0.29 and 0.40) occurred in the same region with the highest

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EVT values and the lowest CT and FF values. It can therefore be seen that CT was a crucial factor for the evaporation rate and for a higher DF value. Hence, the film thickness decreased with increase of CT, due to the low viscosity that led to a decrease of the amount of liquid on

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3.4 Statistical model for the responses

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the condenser, consequently decreasing DF (Shao et al., 2007).

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Multiple regression analysis was applied to the second order polynomial from Equation 8 to determine the best models for fitting each response (DP, YD _ PS1 , and DF). The results of

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ANOVA, regression coefficient, and determination coefficient (R2) calculations are shown in Table 2. Application of Fisher’s test resulted in F-values for DP, YD _ PS1 , and DF of 7.04, 8.30,

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and 10.57, respectively, indicating the significance of each model. The model equations showed high R2 values (0.90, 0.88, and 0.93 for DP, YD _ PS1 , and DF, respectively), suggesting

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that the models could not explain 9.1%, 11.1%, and 6.1% of the total variation, respectively.

The models were also evaluated using the lack of fit test to compare the residual error

with the pure error from replicated points of the design. The lack of fit F-values of 33.05, 63.47,

and 22.32 for DP, YD _ PS1 , and DF, respectively, were not significant, for the specified confidence intervals (Table 2). Therefore, the F-tests generated valuable information about the suitability of the model. The results (Table 2) showed that the models provided satisfactory performance, which was supported by the experimental and predicted values (Table 1).

3.5 Multi-response optimization using Derringer’s desirability function

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Predictive models were used in order to optimize the fractionation of PE-Wax by FFMD, where DP, YD _ PS1 , and DF were the main parameters to be maximized. These objectives are usually conflicting. For example, the results listed in Table 1 revealed that the second

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highest DP values (trial 5) were not associated with the highest YD _ PS1 values, for the same CT

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value. Hence, the desirability function approach could be used to simultaneously obtain the maximum DP, YD _ PS1 , and DF values. Individual values for the desirability (di) of DP, YD _ PS1 ,

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and DF were calculated using Equation 8. For DP, the acceptable minimum and maximum values were considered as the experimental values in trials 1 and 2, respectively (Table 1),

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while for YD _ PS1 , the minimum value was 9.7% (trial 14) and the maximum experimental value was 77.6% (trial 2). Similarly, for DF, the minimum value was 0.08 (trial 3) and the maximum

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experimental value was 0.53 (trial 2).

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Fig. 7 shows the optimization of EVT, CT, and FF for the simultaneous response variables DP, YD _ PS1 , and DF. Each response (continuous line) was predicted as one of the variables was changed, while the others were maintained constant at selected values. The responses were submitted to t tests with a probability criterion of p < 0.025 (solid lines around the dashed line), with the region between the horizontal solid lines around the dashed line indicating statistically significant prediction profiles. The desirability function of each outcome

(far right column) was combined with the prediction profiles, in order to determine the optimal set of parameters based on the D function from Equation 9 (bottom row).

The results indicated that the optimum predicted values were 61.5% for DP, 84.9% for

YD _ PS1 , and 0.64 for DF, under the selected conditions of 184 oC for EVT, 28 oC for CT, and 1.81 kg/h for FF. Based on these results, verification experiments were carried out for the selected cases described in Table 1. The experimental responses were in good agreement with

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the predicted values, confirming that the operation optimized both the separation efficiency and the separation rate. There were no significant differences between the experimental and calculated values for DP, YD _ PS1 , and DF, under the optimal conditions (percent errors below

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3.0, 4.1, and 6.3% between the estimated and experimental values for DP, YD _ PS1 , and DF,

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respectively).

It should be noted that the predictive models for DP, YD _ PS1 , and DF (from Equation 8

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and the regression coefficients reported in Table 2) indicated possibly better results above the optimal EVT of 184 °C (at 0.1 Pa), but PE-Wax cannot be processed at temperatures above 184

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°C. The results showed that in a vacuum (at 0.1 Pa) and at elevated EVT values (>184 °C), the PE-Wax would probably degrade, resulting in a yellowish appearance, probably due to the

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formation of carbon oxides (Al-Sammerrai and Selim, 1986). These qualitative results were in

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agreement with the TGA curve (Fig. 2b-c) showing that the degradation of PE-Wax was completed at 464 °C at atmospheric pressure, corresponding to about 204 °C at 0.1 Pa (Maxwell and Bonnell, 1957). An understanding of PE-Wax degradation may also provide opportunities for extending the process to reactive molecular distillation.

3.6 Insights with respect to the FFMD streams

Two streams were generated under the optimum conditions: the distillate (Dopt) was collected at the bottom of the condenser tube, while the residue (Ropt) was obtained at the bottom of the evaporator tube. To further confirm the success of the PE-Wax fractionation under optimum conditions, the distributions of the boiling points of Dopt and Ropt were evaluated. Fig. 3b-c shows the DGC chromatograms for Dopt and Ropt. The derived DGC contained several main peaks, with the boiling points tending to be slightly lower for Dopt, compared to Ropt. For Dopt, the majority of the peaks eluted between 4 and 25 min,

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corresponding to a boiling point range of 242-529.2 oC. This showed that it was possible to define a specific region of major peaks and that these peaks corresponded to very low boiling points in the range from 242 oC to 444.9 oC. The DGC chromatogram defined a CND for Dopt

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corresponding to molecules from n-C13 to n-C30 (Fig. 3b). These results showed that Dopt contained a significant amount of lighter materials, denoted LP-Wax, while this elutable LP-

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Wax practically disappeared in Ropt. In analysis of the LP-Wax, a similar CND could be

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obtained by a single-stage crystallization (or static crystallization) at about 31 °C. Crause and Nieuwoudt (2003) simulated the wax product CND for single stage crystallization, obtaining a material lighter than n-C20. However, the recovery yield in a single-stage crystallizer was lower

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than 10%, compared to >80% in the case of PE-Wax fractionation into a narrow CND (n-C13 to n-C30) (see trial 20 in Table 1).

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Ciesińska et al. (2016) reported that a physical modification of PE-Wax by removal of

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the lowest molecular weight fractions led to an increase of the crystal phase content. As a result, the authors reported lower molecular weight products containing up to 14 carbon atoms in the molecule, hence defining a narrower CND than for the LP-Wax reported in this work. However, it was not possible to compare the initial CND with that for the PE-Wax, since it was not reported in the paper.

Adopting a different technology, Zamudio et al. (2015) performed supercritical fluid extraction (using CO2 as the supercritical solvent) of a mixture of n-C10 alkane and alcohol isomers. The experiments in a pilot plant were performed at relatively low temperature (36-75 °C) and higher pressure (6.43-13.02 MPa). The results showed n-C10 recovery >99% in the extract stream. Therefore, supercritical fluid technology could be well suited for the extraction of narrower carbon chain fractions from PE-Wax. The DGC chromatogram of Ropt displayed several GC peaks, with a boiling point range

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of 363-699.8 oC (Fig. 3c), indicating that n-C22 to n-C90 molecules and naphthenic hydrocarbons contributed to the peaks of the whole Ropt, denoted SM-Wax. Ropt showed a cumulative yield (from the DGC method) of only approximately 64.4% (by mass) at 699.8 °C,

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while nearly 40% of the mass of the sample did not boil above 699.8 °C.

The possibilities of using LP-Wax, recovered in the Dopt, and SM-Wax, recovered in

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the Ropt, were determined by both their CND values and their thermal properties, as well as

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according to other characteristics. Knowledge of these properties opens up new possibilities for their use.

Fig. 2 shows the DSC curves for the PE-Wax, LP-Wax, and SM-Wax. The DSC results

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showed changes in the peak temperatures, as well as in the peak widths, when the LP-Wax and SM-Wax exhibited specific CND values, as shown in Fig. 3b-c. It can be seen that the DSC

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curve for the LP-Wax showed an endothermic peak at about 34.18 oC, indicating that it was

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the melting peak (∆HSL = 86.65 kJ/kg). However, the SM-Wax showed two thermal events and the material melted over a broad range of temperatures. The first endothermic peak appeared at 97.46 °C, with an enthalpy of 162.49 kJ/kg, presumably due to the solid-solid phase change of the SM-Wax. The later peak involving the solid-liquid phase change of the SM-Wax was the melting peak, at a temperature of 118.70 °C. The areas of these two peaks were summed, resulting in LHS of 169.04 kJ/kg for phase change of the SM-Wax. Comparing the thermal

events of the SM-Wax with those of the PE-Wax, it can be seen that ∆HSS and ∆HSL increased, indicating increased crystallinity (Ciesińska et al., 2016). In previous work, Ciesińska et al. (2016) chemically modified PE-Wax by oxidation, which resulted in changes of the properties of the material. The crystallization and melting temperatures were lower, compared to the initial PE-Wax, and decreased with increase of the state of oxidation. It was shown that the introduction of oxygen functional groups decreased the crystallinity of the PE-Wax, which was different to the PE-wax fractionated into SM-Wax

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in the present work, under optimum conditions, where FFMD was performed in the absence of an oxidizing agent.

The development of environment-protecting and energy-saving phase-change materials

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is currently an active research area in the science of materials (Tao et al., 2015; Abdelrazeq et al., 2019). The high LHS value of the SM-Wax indicated that it could be useful for energy

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storage, with the ability to absorb/release heat energy from/to the environment.

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Fig. 2 shows that the thermal stability of the PE-Wax was intermediate between the stabilities of the LP-Wax and the SM-Wax, with no specific trends for any of the materials. This behavior was expected, since the materials recovered in Dopt and Ropt exhibited decreases

et al. (2016).

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and increases of crystallinity, respectively, in agreement with the results reported by Ciesińska

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Of the three materials, the LP-Wax showed the lowest peak temperature of degradation

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(261 oC) with almost 200 °C and 215 °C differences, compared to the temperatures for the PEWax and SM-Wax, respectively. A possible reason for the lower resistance of the LP-Wax to thermal degradation was the low carbon numbers, associated with lower molar masses. There are increasing new possibilities for the use of PE-Wax in various applications (Abdelrazeq et al., 2019), making its fractionation or refining an essential requirement. The refining of waxes by static crystallization is a robust industrial process and is environmentally

safe, due to the absence of solvents (Sulzer, 2014). New applications for waxes are a strategic goal of commercial companies (an example is Polwax S.A.), especially considering refined paraffin waxes. During the last year, the use of supercritical fluids for the extraction and fractionation of wax has emerged as an alternative to static crystallization and MD (Manjare and Dhingra, 2019). Supercritical CO2 is widely employed as a solvent in extraction and purification processes, because it enables separation without any contamination or degradation, while no

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residual solvent remains in the product (Manjare and Dhingra, 2019). In comparison of the different technologies, supercritical fluid and MD techniques for the extraction and refining of PE-Wax can be considered complex, due to moving parts, the

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high vacuum generally required for MD, and the high pressure associated with supercritical fluid methods. The Sulzer process (static crystallization) has few moving parts, with the

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exception of pumps and valves (Sulzer, 2014).

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In the case of MD, it is evident that the mechanical design is a limiting factor that requires attention. However, the high heat transfer efficiency (under optimal conditions) of thin film molecular distillers makes them ideal for processing PE-Wax, achieving higher relative

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recovery yields of lower molecular weight products, compared to static crystallization. Supercritical fluid technology appears to be able to provide the best fractionation results

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or extraction yields. However, further studies are required in order to develop sustainable

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approaches for its use.

MD, as an innovative technology, enabled the PE-Wax obtained from ethylene

polymerization to be fractionated under mild solvent-free conditions for its possible use in commodities manufactured from plastic waste, as well as in energy storage. MD can be considered to represent a new generation of methodologies for industries manufacturing plastic products. A growing segment of the global PE market is concerned with the production of SM-

Wax from PE, with an extensive range of applications. Examples are improvements in lubricity, flow behavior, molding, and anti-block properties during the processing of plastics, as well as provision of resistance to slippage and friction in printing inks. However, in terms of applications, progress continues to be driven by new innovations.

4. Conclusions Falling film molecular distillation (FFMD) in a pilot plant for the fractionation of PE-

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Wax was proven to be feasible and effective at 0.1 Pa. The pseudo-composition of the PE-Wax (corresponding to CND from n-C12 to n-C100) revealed the potential of the use of plastic wastes to obtain value-added products from PE. Progress in the development of high-throughput

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process requires understanding and investigation of the influences of various FFMD parameters. The optimal process conditions for fractionation by FFMD under mild, solvent-

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free conditions, obtained by statistical optimization, were EVT of 184 °C, CT of 28 °C, and FF

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of 1.81 kg/h. Optimal experimental values for DP of 63.4% and YD _ PS1 of 81.5% confirmed the effective processing of the PE-Wax by means of its fractionation into LP-Wax and SM-Wax.

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A DF value of 0.60 showed that the process was governed by high diffusivity and would not be limited by mass transfer. The CND values and thermal energy properties of the materials

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produced were the most relevant characteristics that could be employed to choose the correct type of wax for a specific end use. Future applications still remain a challenge, while new

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insights into process development are strongly dependent on scale-up.

Acknowledgements The authors are grateful for financial support provided by the Brazilian agencies SDECT-RS, CNPq, and CAPES.

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Zuñiga Liñan, L., Lima, N.M.N., Manenti, F., Wolf Maciel, M.R., Maciel Filho, R., Medina, L.C., 2012. Experimental campaign, modeling, and sensitivity analysis for the molecular distillation of petroleum residues 673.15K+. Chemical Engineering Research and Design 90, 243-258.

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Figure 1. Falling film molecular distillation equipment (KD 6 pilot plant, UIC GmbH, Germany). Adapted from the UIC manual. (1) Evaporator-condenser; (2) residue flask; (3) distillate flask; (4-6) heating circulators; (7) cooling water bath; (8) cold trap; (9) rotary vane pump; (10) diffusion pump; (11) vacuum gauge; (12) feed vessel.

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Figure 2. (a) DSC heating curves, (b) TGA curves, and (c) derivative weight loss curves for PE-Wax (▬), LP-Wax (▬), and SM-Wax (▬).

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Figure 3. Simulated distillation gas chromatograms and CNDs of (a) PE-Wax, (b) LP-Wax, and (c) SM-Wax, obtained from FFMD under the optimum conditions: EVT of 184 °C, FF of 1.81 kg/h, and CT of 28 °C, at 0.1 Pa.

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Figure 4. Mean free path (MFP) for each pseudo-compound class of the PE-Wax (PS1 and PS2), at a distance of 0.02 m between the evaporator and condenser surfaces (▬), under different combinations of EVT (120, 152, and 184 oC) and Ps: (a) 2.06 Pa, (b) 1.33 Pa, and (c) 0.1 Pa.

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Figure 5. Standardized effect estimates and p-values (in front of the bars) for DP, YD _ PS1 , and DF. X1: Coded factor for EVT; X2: coded factor for CT; X3: coded factor for FF. Confidence intervals (CI) at 97.5% (for the DP and DF responses) and 99.0% (for the YD _ PS1 response).

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Figure 6. Contour plots for the effects of (a) CT×FF, (b) EVT×CT, and (c) EVT×FF on DP; (d) CT×FF, (e) EVT×CT, and (f) EVT×FF on YD _ PS1 ; and (g) CT×FF, (h) EVT×CT, and (i) EVT×FF on DF.

EVT (°C)

CT (°C)

FF (kg/h)

Desirability

1. .5

30.0

0.

0.0

DP (%)

60.0

12.132.252.3

90.0

1. .5 0.

0.30 0.00

DF (-)

0.60

0.08 0.3 0.5

0.90

0.0 1.0

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0.75 0.50

0.00 100

12 28 44 60 76 92 108

184 150

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0.25

200

CT (°C)

4.58

FF (kg/h)

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EVT (°C)

0.89 1.81

Desirability, D

0.

25.0

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Figure 7. Profiles of predicted values and the desirability function for the optimization of DP, YD _ PS1 , and DF. The vertical dashed lines indicate the optimum condition values for EVT, CT, and FF. The prediction profiles were submitted to t tests against the true values (horizontal dashed lines), using a probability criterion of p < 0.025.

YD_Ps1 (%)

1.

.5

50.0

43.6 77.6

75.0

9.7

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100.0

Statistical level -1 0 152

171

41

60

79

1.64

2.74

e3.83 4.58

Mass balance (kg/h)

Percent recovery (%)

EVT ( C)

CT ( C)

FF (kg/h)

RS

DS

TS

% Loss

DP

RP

TP

133 171 120 152 152 152 184 152 171 133 171 133 171 133 152 152 152 140 184 184 184

79 41 60 92 60 60 60 60 41 41 79 41 79 79 60 60 28 50 90 28 28

1.64 1.64 2.74 2.74 0.89 2.74 2.74 2.74 3.83 1.64 3.83 3.83 1.64 3.83 4.58 2.74 2.74 1.00 1.00 1.81 1.81

1.39 0.70 1.37 1.33 0.21 1.41 1.39 1.19 1.43 1.33 1.38 1.47 1.29 1.48 1.33 1.32 1.39 0.73 0.50 0.60

0.19 0.86 0.23 0.53 0.24 0.59 0.67 0.54 0.47 0.25 0.62 0.36 0.30 0.63 0.71 0.54 0.75 0.25 0.18 1.09

0.00 0.09 0.18 0.24 0.20 0.20 0.18 0.20 0.09 0.00 0.23 0.10 0.00 0.30 0.19 0.19 0.24 0.02 0.30 0.03

3.83 -0.56c 35.06 23.34 27.30 19.61 17.94 29.34 47.82 3.91 41.73 49.62 3.02 37.01 51.34 25.10 12.90 0.10 2.00 4.97

12.1 (11.9) 52.3 (50.1) 13.1 (9.7) 25.4 (22.0) 37.1 (33.9) 26.8 (27.3) 30.1 (29.1) 28.1 (27.3) 23.7 (27.0) 15.7 (20.9) 27.6 (25.5) 18.5 (16.3) 19.1 (24.3) 26.2 (31.6) 32.0 (31.0) 26.3 (27.3) 31.6 (30.7) 25.0 (28.7) 18.4 (15.9) 63.4 (61.5)

87.9 42.1 76.8 63.2 32.1 63.9 61.9 61.7 71.7 84.3 61.9 76.3 80.9 61.5 59.6 64.3 58.4 73.1 51.0 34.9

0.0 5.5 10.1 11.4 30.8 9.3 8.0 10.1 4.6 0.0 10.4 5.2 0.0 12.3 8.4 9.3 10.0 1.9 30.6 1.7

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18a 19a 20a,b Derringer's desirability function

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184 92

Pr

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1.68

133

True parameter Trial

1

pr

Operability range and levels Real parameter [Coded parameter] -1.68 EVT (oC) 120 [X1] o CT ( C) 28 [X2] FF (kg/h) 0.89 [X3] Process variables of the CCRD experiments

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Table 1. FFMD parameters, levels, and mass balances for the CCRD experimental design (trials 1-17) and the experimental validation (trials 1820), with the experimental responses (in bold) and the predicted responses (in parentheses).

Recovery yield (%) DF (-)

YD _ PS1

YD _ PS2

0.12 (0.09) 0.53 (0.48) 0.08 (0.07) 0.19 (0.18) 0.27 (0.29) 0.22 (0.20) 0.25 (0.25) 0.20 (0.20) 0.12 (0.16) 0.16 (0.19) 0.16 (0.14) 0.09 (0.08) 0.19 (0.22) 0.17 (0.22) 0.16 (0.13) 0.20 (0.20) 0.27 (0.28) 0.25 (0.24) 0.18 (0.18) 0.60 (0.64)

13.4 (9.1) 77.6 (79.1) 19.6 (20.5) 15.1 (22.0) 43.0 (56.9) 43.1 (42.1) 70.1 (70.2) 43.0 (42.1) 33.3 (36.9) 65.6 (57.5) 37.6 (44.9) 17.9 (30.3) 74.8 (61.7) 9.7 (7.5) 32.9 (20.0) 40.3 (42.1) 61.8 (55.9) 59.2 (60.1) 73.1 (73.5) 81.5 (84.9)

11.2 46.1 5.6 20.6 22.8 15.9 12.8 13.9 6.9 1.9 10.5 7.1 3.9 18.3 11.1 14.4 18.6 16.1 3.6 54.7

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experiments for validation of the regression models; b Optimal condition; c Accumulation of mass in the line.

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Table 2. Regression coefficients and analysis of variance (ANOVA) for the quadratic models of DP, YD _ PS1 , and DF. Response DP

df Mean square F-value F-testa 9 7 5 2 16

148.468 21.088 29.170 8.825×10-1

9 7 5 2 16

1.690×10-2 1.599×10-3 2.199×10-3 9.850×10-5

7.04

4.82

33.05

39.30

10.57

4.82

22.32

39.30

8.30

5.61

63.47

99.36

7 9 7 2 16

980.449 118.120 151.189 2.382

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DF

Regression coefficient p-value R2 Source Sum of squares (Eq. 8) β0 -329.973 0.004 0.90 Regression 1336.209 β1 3.961 0.004 Residual 147.616 β11 -7.746×10-3 0.010 Lack of fit 145.851 β2 9.464×10-1 0.032 Pure error 1.765 β22 -9.940×10-4 0.328 Total 1483.825 β3 7.273 0.130 β33 1.493 0.023 β12 -1.160×10-2 0.006 β13 -2.219×10-1 0.005 β23 2.918×10-1 0.003 β0 -2.56428 0.008 0.93 Regression 1.521×10-1 -2 β1 3.007×10 0.007 Residual 1.119×10-2 -5 β11 -4.460×10 0.032 Lack of fit 1.099×10-2 -3 β2 4.865×10 0.118 Pure error 1.970×10-4 -5 β22 2.281×10 0.108 Total 1.633×10-1 -1 β3 1.643×10 0.033 β33 3.716×10-4 0.894 β12 -1.123×10-4 0.007 β13 -2.522×10-3 0.004 β23 2.901×10-3 0.003 β0 316.359 0.010 0.88 Regression 6863.142 β1 -1.760 0.044 Residual 1063.084 β11 4.120×10-3 0.077 Lack of fit 1058.320 β2 -4.621 0.003 Pure error 4.764 β3 -23.972 0.011 Total 7926.226 β33 -8.036×10-1 0.159 β12 2.141×10-2 0.005 β23 3.059×10-1 0.007

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df: Degrees of freedom. a Confidence intervals (CI) set at 97.5% (for the D and DF responses) and 99.0% (for the Y P D _ PS1 response).

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