PHASE EQUILIBRIUM INVOLVING XYLITOL, WATER AND

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Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Phase Equilibrium Involving Xylitol, Water, and Ethylene Glycol or 1,2-Propylene Glycol: Experimental Data, Activity Coefficient Modeling, and Prediction with Artificial Neural Network-Molecular Descriptors Patrícia G. Machado,† Alessandro C. Galvão,*,† Weber S. Robazza,† Pedro F. Arce,‡ and Bruna E. Hochscheidt† Downloaded via KAOHSIUNG MEDICAL UNIV on July 19, 2018 at 20:15:30 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

Laboratory ApTher−Applied Thermophysics, Department of Food and Chemical Engineering, Santa Catarina State University−UDESC, Pinhalzinho, Santa Catarina 89870-000, Brazil ‡ Engineering School of Lorena, Department of Chemical Engineering, University of São Paulo (USP), Lorena, São Paulo 12600-970, Brazil S Supporting Information *

ABSTRACT: The xylitol molecule is an important building block that can be used in the production of such interesting chemicals as ethylene glycol and 1,2-propylene glycol. The development of productive processes that enable this transformation depends on various experimental and theoretical information. In order to supply part of this demand, this work sought to study the solubility of xylitol in binary liquid solutions formed by water, ethylene glycol, and 1,2-propylene glycol in the temperature range between 293.15 and 323.15 K, covering the entire molar composition range of the solution. The Jouyban−Acree, NRTL, and UNIQUAC models were used in the correlation of experimental data, and the mUNIFAC model was applied in the prediction of experimental data. In addition, an artificial neural network associated with molecular descriptors was developed to simulate the data. Xylitol showed solubility in the pure components with decreasing values in the following order: water, ethylene glycol, and 1,2-propylene glycol. The solubility in binary solutions had intermediate values according to the intermediate concentration values. The models used proved capable of correlating or predicting the experimental data. The artificial neural networks had a satisfactory performance in the data simulation, and the best observed architecture used four layers of the type 7-3-3-1.

1. INTRODUCTION 1.1. Role of Xylitol in the Biorefining Concept. The hemicelluloses present in the biomass are the second most abundant renewable organic material of vegetable origin on the planet. Made of different saccharides,1,2 this rich and available carbon source offers great potential from a sustainability perspective. Compared to petrochemical processing, the processing of biomass conducted in a biorefinery3 can lead to the production of chemical compounds with lower carbon emissions.4 One of the products that can be produced in a biorefinery gaining attention is xylose, a monosaccharide produced through the hydrolysis of xylan with the subsequent conversion to xylitol by a hydrogenation process. Both xylose and xylitol have many industrial applications, especially in the development of resins and polymers.5,6 In addition, xylitol is a potential source of glycol, which can be used as raw material in the production of ethylene glycol and propylene glycol.7 Ethylene glycol and propylene glycol are chemical substances of widespread commercial importance. They are involved in almost all aspects of daily life and are associated with energy, chemicals, automotive, textile, transportation, and manufacturing technologies. For this reason, they have attracted the interest of researchers in interdisciplinary fields.8 They are currently © XXXX American Chemical Society

produced in the petrochemical industry through processing of the oil derivatives ethylene and propylene.9 The development of reaction media and separation systems that enable the exploitation of xylitol as a building block is in need of information on a scientific nature. Many of the demands are answered by experimental studies. Phase equilibrium experiments generate information about the distribution of the components when phases coexist in equilibrium under the same temperature and pressure conditions. This information is crucial for the design of products, processes, and equipment.10 Despite the importance of the subject and the information that can be generated, studies on the solubility of xylitol are still scarce in the literature. Table 1 presents a review of the published studies in which the tested pure components and binary solutions, the temperature range, and the applied experimental method for the determination of the composition of the phases in equilibrium can be seen. To illustrate the solubility of xylitol, the studies indicate that at 293 K water is the solvent with the greatest solubilization Received: Revised: Accepted: Published: A

June 2, 2018 July 8, 2018 July 9, 2018 July 9, 2018 DOI: 10.1021/acs.iecr.8b02480 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research Table 1. Published Studies on the Solubility of Xylitola T (K)

method

b, c, n

293−323

analytical

a a, l j

303−358 310 289−345

analytical analytical synthetic

j a, k j c, i, m a, c, l h, e, f, g, d, a, c, i j

294−384 293−328 373 293−323 278−323 293−343

synthetic synthetic synthetic synthetic synthetic synthetic

CNIBS/RK CNIBS/RK Apelblat equation

16 17 18 19 20 21

288−339

analytical

PC-SAFT

22

solvent

model Jouyban−Acree, NRTL, UNIQUAC

NRTL, eNRTL, UNIQUAC

the interaction parameters Δgij and Δgji, incorporates two dimensionless interaction parameters τij and τji adjusted to the experimental data. The dimensionless parameter can be considered as dependent on temperature. The nonrandomness existing in the solution is represented by the parameters αij and αji, in which αij is usually set as equal to αji and where for αij = 0, the model takes the form of the Margules function with one parameter, assuming a completely random system. Although it is also used as an adjustable parameter, αij can be used as a fixed value equal to 0.2, 0.3, or 0.47, where the last value can be used for solutions with an ordered structure caused by hydrogen bonds. In the correlative model UNIQUAC,26 the activity coefficient is described as the sum of a combinatorial contribution γCi with a residual contribution γRi . The combinatorial contribution does not have adjustable parameters, depending only on the composition, size, and shape of the molecules. Due to the existence of molecules of different shapes in solution, the combinatorial contribution describes the deviation from ideality through entropic effects. The residual contribution, with two adjustable parameters, is an enthalpic correction caused by interaction forces when different molecules interact in a mixture. Both contributions depend on the molecular structure of the pure components represented by the parameters r and q, illustrating, respectively, the volume and the external surface area of the molecule. In this study, the values of these two parameters were taken from the literature27 and are presented in Table S1 (Supporting Information). As in the NRTL model, the two adjustable binary interaction parameters τij and τji are associated with the characteristic interaction energy between molecules of type i and j. The UNIFAC model is a predictive model based on the group contribution concept in which the energy associated with the molecular interactions are independent of the nature of the molecule, depending only on groups or structural radicals. Since the number of functional groups is much smaller than the number of atoms in a molecule, the configurational energy is simplified as being the sum of the interaction energies between the groups. As in the UNIQUAC model, the expression for the activity coefficient is also calculated by taking the sum of a combinatorial contribution with a residual one. The modified model (mUNIFAC)28 is based on empirical modifications to the original model.29,30 The difference between the original and the modified model lies in the combinatorial contribution that uses the exponent 3/4 in the calculations of the volumetric fraction.31 All of the parameters of the UNIFAC model used in this study were taken from the literature.32 In addition to the use of Gibbs energy models to describe the nonideality of solubility data, the experimental results were evaluated through the thermodynamic simulation with artificial neural networks using critical properties and molecular descriptors as independent variables. 1.3. Artificial Neural Networks, Molecular Descriptors, and the SMILES Code. Artificial neural networks (ANNs) are robust and efficient computational tools that have been gaining attention from researchers in chemical engineering. These tools include learning, testing, and prediction stages that can be applied in the calculation of the properties of pure components and mixtures. In practice, artificial neural networks are a set of artificial neurons connected in layers (architectures), with their signals being transmitted from the first (input) to the last layer (output).

ref 12 13 14 15

a

(a) water, (b) methanol, (c) ethanol, (d) 2-propanol, (e) n-butanol, (f) n-pentanol, (g) toluene, (h) N,N-dimethylformamide, (i) acetone, (j) ionic liquids, (k) water + methanol, (l) water + ethanol, (m) ethanol + acetone, (n) methanol + ethanol.

capacity with approximately 62 wt % solubility and that toluene is the solvent with the lowest solubilization capacity with a solubility of around 0.007 wt %. As can be seen, the synthetic method, which uses an optical device to check the phase equilibrium, has been applied more frequently than the analytical method. In assays with sampling, one can see that the analyses were done by gravimetry, refractometry, or chromatography. Because of the nonexistence of experimental studies on the solubility of xylitol in glycols, this study sought to evaluate the solubility of xylitol in binary liquid solutions formed by water/ ethylene glycol and water/1,2-propylene glycol, covering the entire molar composition range at different temperatures. In the experiments, the composition of the samples taken from the liquid phase were quantified through refractometry tests. 1.2. Jouyban−Acree, NRTL, UNIQUAC, and UNIFAC Models. Despite the undeniable importance of experimental trials, mathematical models are applied to validate and develop solution theories and to simulate and optimize processes.11 An assessment of Table 1 also reveals that the modeling of the solid−liquid equilibrium involving xylitol is still not widespread. For this reason, the experimental results were correlated by the empirical model Jouyban−Acree, by the local composition models NRTL and UNIQUAC, and by the predictive group contribution model UNIFAC. The Jouyban−Acree model23,24 based on the Redlich−Kister equation is represented by eq 1, where xs represents the solubility expressed as molar fraction, x1 and x2 are the molar fractions of components 1 and 2 in the binary liquid solution, x01 and x02 correspond with the solubility in pure components, Ji are the adjustable coefficients, and T is the experimental temperature 2

ln xs = x1 ln x10 + x 2 ln x 20 + x1x 2 ∑ i=0

Ji T

(x1 − x 2)i

(1)

25

The concept of the NRTL model is established on the idea of local composition, in which the concentration around a molecule is different from the concentration in the bulk of the liquid. Due to the different interaction energies between equal molecules and different molecules, the model also applies the concept of nonrandomness. The energy difference, reflected by B

DOI: 10.1021/acs.iecr.8b02480 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Table 2. Comparison of Experimental Data and Literature Values: Refractive Index (nD) at 293.15 K and Specific Mass (ρ) at 298.15 K component water ethylene glycol 1,2-propylene glycol

nExp D 1.33299 1.43159 1.43262

nLit D a

e

1.3330; 1.33299 1.4319;a 1.4315b 1.43247;c 1.43297d

ρExp

ρLit

0.99705 1.10972 1.03274

0.99702;f 0.9982g 1.1084;h 1.1096i 1.03259;j 1.03286k

a

Reference 38. bReference 39. cReference 40. dReference 41. eReference 42. fReference 43. gReference 44. hReference 45. iReference 46. Reference 47. kReference 48.

j

benchtop refractometer, and by analyzing the specific mass at 298.15 K, performed in a 25 mL pycnometer previously calibrated with water. The results of the assays and the values available in the literature are presented in Table 2. The data confirms the quality of the purchased reagents. The study of the solid−liquid equilibrium was conducted in jacketed glass cells (useful volume of 50 mL) coupled to a thermostatic bath, so the experiment could be conducted between 293.15 and 323.15 K with intervals of 5 K. Inside the cells, known quantities of solid and liquid were added, filling the entire volume. The cells were closed with rubber stoppers, fixed with clamps, and placed on magnetic stirrers. After stabilization of the test temperature, the mixtures were severely agitated for a period of 3 h in order to achieve saturation of the solvent. The temperature inside the cells was monitored by a bulb thermometer with an uncertainty of ±0.5 K. After agitation, the cells remained without agitation for a period of 24 h so the phase equilibrium could occur, causing the excess solid to be deposited at the bottom of the cell with the solvent with the solubilized solid remaining in the upper part. After the phase separation period, the rubber stopper was removed and replaced by a glass dropper. The tip of the dropper was connected to a rubber hose (3 cm in length) sealed by a small metal clamp so that the inside of the submerged parts was not filled with the solution. These clamps were carefully removed to ensure that the solution filled the inner part of the dropper. In order to achieve greater experimental productivity, 3 equilibrium cells connected in series to the same thermostatic bath were used, allowing for the testing of 3 points of solubility. Three samples were removed for each cell in equilibrium. These samples were added to test tubes, which were placed in a thermostatic bath at 325.15 K. The aliquots were subsequently evaluated through refractometry in a model RX-5000i digital benchtop refractometer of the ATAGO brand with an uncertainty of ±0.00004 and adjustable temperature. The values were converted into solubility results using previously built calibration curves for the temperature of 325.15 K. The tests of the methodology were performed by evaluating the solubility of adipic acid in water and comparing the results obtained with the values available in the literature.

The main objective of the artificial neural network is to solve problems the same way a human being does, although the neural network architectures are more abstract and simple than the human brain.33 In an ANN, the information made available (independent variables) forms the input layer. After the learning stage of the neurons, the network is tested and then predicts the dependent variables, making the results available in the most external layer. The configuration of the architecture of layers is the main decision for the success of the predictive stage of the neural network. For example, for a simple architecture in three layers, the first layer contains the input neurons and sends data through the connections to the second layer of neurons, which then pass them on through more connections to the third layer of output neurons. Complex architectures have a higher number of layers and may even have a greater number of layers of both input and output neurons. The learning stage of ANNs is fundamental for the simulation. The set of models that will be minimized in accordance with a certain criterion is therefore implemented in this stage. One approach is the gradient descent method using the Levenberg− Marquardt Backpropagation training algorithm. The connections between the layers take on the role of “weights” that manipulate the data in the calculations. When the number of independent variables is insufficient to obtain satisfactory results in the simulation, molecular descriptors (MD) have to be used. Molecular Descriptors are obtained from the chemical information on a molecule based on logical and mathematical procedures. In general, MDs can be classified as topological, geometric, thermodynamic, and constitutional indices.34 Dragon 7.035 is one of the types of special software used to calculate the numerical values of MDs and the fingerprints of complex molecules, offering more than 5000 molecular descriptors divided into 30 logical blocks. Each block contains sub-blocks to allow for the easy retrieval of MDs. The software reads molecular structure files with a special code that can be generated by such chemical drawing software as SMILES (.smi). The simplified molecular-input line-entry system (SMILES) is a code in the form of a line notation for describing the structure of chemical species using short ASCII strings. SMILES’ vocabulary and grammar allow for the definition of atoms, bonds, aromatic and nonaromatic rings, stereoisomers, isotopes, etc.36,37

3. MODELING OF THE SOLUBILITY RESULTS 3.1. Solid−Liquid Equilibrium. For a system in phase equilibrium at the same temperature T and pressure P, the isofugacity criterion for the existence of the equilibrium defines that the molar fraction of a solubilized solid in a liquid phase xs depends on the fugacity of the pure solid in the phase containing only solid fss, on the fugacity of the solid in an arbitrary standard state f0s , and the activity coefficient of the solubilized solid γs considering the same standard state as presented in eq 2.

2. EXPERIMENTAL SECTION In the experiments, the solvents were used without undergoing any additional treatment. The solids were previously dried in an oven for 1 h at a temperature of 353 K and then placed in a desiccator until the beginning of the experiments. Table S2 (Supporting Information) shows the origin and the purity of the reagents used. The quality of the solvents was attested by analyzing the refraction index at 293.15 K, performed in a digital C


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Industrial & Engineering Chemistry Research xs =

f ss (T , P) γs(T , P ,

xs)f s0 (T ,

P)

acentric factor, molecular descriptors, and water composition of the system as learning variables (independent variables). After establishing the independent variables that define the characteristics of the different ternary systems, SMILES codes were generated for the glycol and xylitol molecules and then the numerical value for the molecular descriptors was determined by the Dragon 7.0 software. For the prediction stage of the solid− liquid equilibrium, the xylitol and glycol compositions were considered as dependent variables. An MS-Excel file with six specific spreadsheets was created for the learning, testing, and prediction stages of the solid−liquid equilibrium. The file was built so that each dependent variable had its independent analog for each step. In the first, third, and fifth spreadsheets, developed for the three ANN stages, different data of the independent variables were allocated. In the second, fourth, and sixth spreadsheets, the data of the dependent variables were allocated, also for the learning, testing, and prediction stages. A routine was developed on the MATLAB platform for the mathematical treatment, interacting directly with each worksheet. In the learning stage, the computer program reads the input data (first and second spreadsheets), defines the ANN architecture applying the backpropagation algorithm containing the number of layers, and generates weights and biases that are stored for the next ANN stage. In the testing stage, the computer program reads the weights, the biases, and the data of the third worksheet for which the data on the solid−liquid equilibrium for the water + xylitol + glycol system must be learned, runs the calculations a number of times (defined by the user), and stores the results in the fourth spreadsheet. On the basis of the results, the average absolute deviation (eq 7) and the maximum absolute deviation are evaluated and the user chooses the best set of results that minimize the maximum absolute deviation for one or two dependent variables (compositions of xylitol and/or glycol).

(2)

Considering the standard state as the state of a hypothetical fluid, the ratio between the fugacities is determined by a thermodynamic cycle in which the solute undergoes a transformation from a solid state to the hypothetical liquid state so that the molar fraction of the solubilized solid takes the form expressed by eq 3. ΔFusHs jij 1 1 zy 1 jj − zzzz − j R j TmS T z RT k { C Δ T ps dT Tms T

ln xs = −ln γs + +

1 R

∫

∫T

T

ms

ΔC p dT s

(3)

In eq 3, ΔFusHs represents the enthalpy of fusion and Tms the melting temperature of the pure solid, ΔCps corresponds to the variation in the specific heat of the solid, and R is the universal gas constant. Disregarding the third and fourth terms on the right side of eq 3, one gets the simplified expression represented by eq 4, which describes the molar fraction of a solubilized solid in a liquid in phase equilibrium condition in which the solid phase is formed only by the unsolubilized component.27 ln xs =

ΔFusHs ijj 1 1 yzzz jj − z − ln γs R jj TmS T zz k {

(4)

In this study, the calculation of the activity coefficient of the solubilized solid was developed with the excess Gibbs energy models NRTL, UNIQUAC, and UNIFAC. 3.2. Adjustable Parameters of the Models. The parameters Ji of the Jouyban−Acree model were calculated as a function of temperature so that the resolution of the linear system was done by least-squares minimization. The average relative deviation (ARD%) between the values calculated by the model xcal s and the experimental values xs was determined by eq 5, where Np is the number of experimental points. 100 ARD% = Np

Np

∑ i=1

xs − xscal xs

100 %Δxs = Np

Np

∑ |x2pred − x2exp|i i=1

(7)

In the prediction stage, in possession of the best results, the computer program predicts the values of the dependent variables for the data of the fifth worksheet. The predicted results are stored in the sixth worksheet, which is compared with the results generated by the ANN with the experimental data. With the comparison it is possible to assess the performance of the selected architecture, and in the case of success, it is possible to predict the phase equilibrium behavior of the ternary system using unknown values for the independent variables. The procedure described above was used to test different ANN architectures so that the architecture with the best performance was applied to the data of this work.

(5)

The binary interaction parameters of the NRTL and UNIQUAC models were considered dependent on temperature, and they were determined by minimizing the objective function represented by eq 6, where 1 represents the solubilized solute, 2 represents water, ethylene glycol, or 1,2-propylene glycol, and x is the molar fraction in the liquid phase. The maximum likelihood method was applied in the minimization, and the average relative deviation (ARD%) was also applied to check the ability of the NRTL, UNIQUAC, and UNIFAC models to correlate or predict the experimental data. Ä exp É Np Å exp calc Ñ ÅÅÅ |x1, i − x1,calc ÑÑÑ x x | | − | 100 i 2, i 2, i ÑÑ OF = + ∑ ÅÅÅÅ ÑÑ exp exp Np i = 1 ÅÅ x1, i x 2, i ÑÑ (6) ÅÇ ÑÖ

5. RESULTS AND DISCUSSION 5.1. Experimental Data. Figure 1 shows the solubility of adipic acid in water along with values published in the literature. As can be seen, in general the data is in alignment, indicating that the method applied in this work is satisfactory. In order to assess the existing deviations, the results were evaluated at temperatures of 293.15 and 323.15 K in comparison with some of the published data. For the respective temperatures, the values of this work expressed as molar fraction are 0.00226 and 0.01169. Apelblat and Manzurola49 obtained values of 0.00239 (5.9% higher) and 0.01080 (7.6% lower) at the same temperatures.

4. THERMODYNAMIC SIMULATION The capabilities of the artificial neural network (ANN) were used for learning, testing, and predicting the behavior of the liquid phase of the solid−liquid equilibrium of ternary solutions. The developed ANN used the temperature, critical properties, D


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214% in ethylene glycol, and 300% in 1,2-propylene glycol, showing that the solubility of xylitol is much more dependent on the temperature in the glycols under study than in water. The solubilization of a solid in a liquid follows the principle of affinity between solid and solvent, and this affinity is a reflection of the polarity of the involved components. The xylitol molecule, a polar molecule, has five hydroxyl groups that provide interactions with other polar molecules. The polarity of the liquids is best represented when their dielectric constant is evaluated. The dielectric constant of water is greater than that of ethylene glycol, which in turn is greater than 1,2-propylene glycol, indicating that the polarity of the evaluated components decreases following the order water > ethylene glycol > 1,2propylene glycol. As a consequence, the solubility of xylitol is greater in water followed by ethylene glycol and 1,2-propylene glycol. The solubility of xylitol in binary solutions had intermediate values in relation to the solubility in pure components. This behavior is associated with the reduction of the dielectric constant due to the addition of an antisolvent. The mixture of two components, water + ethylene glycol or water + 1,2propylene glycol, leads to the formation of a solution with a dielectric constant dependent on the composition of the solution, and this consequently leads to an intermediate solubility value of the solid. 5.2. Thermodynamic Modeling. The Jouyban−Acree model proved to be able to correlate the solubility data of the evaluated ternary solutions with the ARD% values ranging between 0.35 and 1.19. Tables S5 and S6 (Supporting Information), respectively, show the values of the adjustable parameters and the values of ARD% existing between the experimental data and the model results. As can be seen, despite the great ability of the model to correlate the experimental data, the adjustable parameters do not have a reliable behavior as a function of temperature. This characteristic of the model prevents its use to predict the solubility values at different temperatures than those under study. Regarding the behavior of the activity coefficient models (NRTL, UNIQUAC, and UNIFAC), the UNIQUAC model showed the best ability to correlate the experimental data with the ARD% values in the two ternary solutions under study and for all temperatures, as can be seen in Table S6 (Supporting Information), ranging between 0.86 and 5.45. The NRTL model had the second best performance with ARD% ranging between

Figure 1. Solubility expressed as molar fraction xs of adipic acid in water as a function of temperature T: (●) this work, (▲) ref 49, (⧫) ref 50, (+) ref 51, (◊) ref 52, (×) ref 53, (○) ref 54, (■) ref 55, (□) ref 56.

Gaivoronskii and Granzhan50 also found values of 0.00227 (0.5% higher) and 0.01105 (5.5% lower) at the same temperatures. For the temperature of 293.15 K, Deng et al.51 published the value of 0.00225 (0.3% lower); for the temperature of 323.15 K, Shen et al.52 obtained the value of 0.01058 (9.6% lower). The experimental results for the solubility of xylitol in a ternary solution, as a function of the molar fraction of the binary liquid solution for the temperatures under study, are presented in Figure 2. An increase in the solubility could be observed with increasing temperature for all concentrations of the binary solutions and for the temperature interval evaluated. This behavior has been previously discussed,57 and it can be explained by the endothermic fusion process of xylitol, so that the higher the temperature, the more solid is solubilized. Tables S3 and S4 (Supporting Information) show the solubility results expressed as molar fraction and mass fraction for all solutions and temperatures under study. Regarding the solubility of the solid in pure solvents, water was observed to have a great capacity to solubilize xylitol, followed by ethylene glycol and 1,2-propylene glycol. At a temperature of 293.15 K, the solubility in water is 0.61030 gs/ gsol, 0.12214 gs/gsol in ethylene glycol, and 0.04767 gs/gsol in 1,2propylene glycol. At a temperature of 323.15 K, the solubility in water is 0.80140 gs/gsol, 0.38327 gs/gsol in ethylene glycol, and 0.19088 gs/gsol in 1,2-propylene glycol. These figures show that with an increase of 30 K the solubility increases 31% in water,

Figure 2. Solubility expressed as molar fraction xs of xylitol as a function of molar fraction of water in the binary mixture (a) water + ethylene glycol and (b) water + 1,2-propylene glycol at different temperatures: (●) 293.15, (■) 298.15, (▲) 303.15, (⧫) 308.15, (○) 313.15, (□) 318.15, and (◊) 323.15 K; solid lines are the Jouyban−Acree model. E


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The ANN analysis consisted of three stages using 134 data points for learning, 10 data points for testing, and 10 data points for the prediction so that the data was different at each stage. The random distribution of data between the three groups is of fundamental importance for the development of a network with a satisfactory predictive capacity. For all of the tested architectures, the error between one iteration and the next was set as 1 × 10−4, the maximum number of iterations was set as 500, and the program was executed 50 times. Configurations with three layers (3-X-1, 5-X-1, 7-X-1, 10-X-1, and 15-X-1) and four layers (3-X-X-1, 5-X-X-1, 7-X-X-1, 10-XX-1, and 15-X-X-1) were tested for only one dependent variable, x2. The results obtained with two dependent variables, x2 and x3, were not good in terms of accuracy. The input layer with three and five neurons contains temperature, composition (x1), and critical properties as independent variables. The output layer always has one neuron corresponding with the dependent variable, which is the composition of xylitol in the ternary liquid solution. The optimized architecture for the artificial neural network was composed of four layers (7-3-3-1): an input layer with seven neurons, two hidden layers with three neurons each, and an output layer with one neuron. A sigmoid hyperbolic tangent activation function was used for the two hidden layers, and a linear activation function was used for the output layer. The weight matrices and diagonal vectors for the optimized ANN model are listed in Tables S12, S13, and S14 (Supporting Information) for the interaction between the input layer and the hidden layer, the first hidden layer and the second hidden layer, and the second hidden layer and the output layer, respectively. In these tables, wI represents the weight matrix (three lines × seven columns) for the connection between the input layer and the first hidden layer, wH1−H2 is the weight matrix (three lines × three columns) for the connection between the first and the second hidden layer, wH2 represents the weight matrix (one line × three columns) for the connection between the second hidden layer and the output layer, bH1 is the diagonal vector (three lines) to the first hidden neurons, bH1−H2 is the diagonal vector (three lines) to the second hidden neurons, and, finally, b0 represents the diagonal vector (one line) to the output neurons. The accuracy of the ANN was evaluated by absolute deviation calculations for the three dependent variables in the predictive stage. The best architecture for the neural network (7-3-3-1) was obtained with 18 executions of the program. Tables S15−S20 (Supporting Information) show the values of the average absolute deviation for all evaluated architectures. In the learning stage, the individual absolute deviations between the experimental and the correlated values in the prediction of the composition of xylitol in the liquid phase were lower than 1.0% for most data. Only 8 of the 134 data points had absolute deviations exceeding 5.0%, with 5.4% being the highest value found. An average absolute deviation for the composition of xylitol in the liquid phase of 1.07% was observed. This value is considered accurate enough to state that the ANN learned correctly.

1.30 and 9.66, and the UNIFAC model had the worst performance with ARD% values ranging between 1.85 and 14.75. Considering the average value of the ARD% (2.36% for UNIQUAC, 4.24% for NRTL, and 5.45% for UNIFAC), it is important to consider that both the UNIQUAC and the NRTL models are correlated to experimental data, generating a set of adjustable parameters, while the UNIFAC model is a predictive model that uses no experimental data in the generation of results. Table S7 (Supporting Information) shows the temperature dependence of the binary energy interaction parameter of the NRTL model, while Table S8 (Supporting Information) shows the temperature dependence of the nonrandomness parameter for the ternary solutions under study. The temperature dependence of the binary interaction parameter of the UNIQUAC model is presented in Table S9 (Supporting Information). The composition of the liquid phase determined by the NRTL, UNIQUAC, and UNIFAC models is presented in Table S10 (Supporting Information). 5.3. Simulation by Artificial Neural Networks and Molecular Descriptors. The SMILES codes generated for the xylitol and glycol molecules are presented in Table S11 (Supporting Information), the eight molecular descriptors used are presented in Table 3, and the numerical value of the MDs determined using the SMILES code and the Dragon 7.0 software are presented in Table 4. Table 3. Molecular Descriptors (MD) Used in This Work MD

name

sub-block

nH

no. of hydrogen atoms

nC nO Pol

no. of carbon atoms no. of oxygen atoms polarity number

RDCHI

reciprocal distance sum Randic-like index

nROH

no. of hydroxyl groups

nHDon

no. of donor atoms for H bonds van der Waals volume for McGowan volume

VvdwMG

block

basic descriptors

constitutional indexes

distance-based indexes Randic-like connectivity indexes basic descriptors

topological indexes connectivity indexes

basic descriptors

molecular properties

functional group counts

The network used in this study was of the Feed-Forward Backpropagation type (newff Matlab function). A Levenberg− Marquardt-backpropagation-type algorithm was used in the training stage (trainlm MatLab function). Several architectures were tested with and without the use of molecular descriptors in order to choose the most accurate configuration. Without the prior knowledge of the optimal number of layers and neurons for the prediction of the solid−liquid equilibrium, a scan through trial and error was made in the simulation. The architecture of the network should be simple, and the accuracy of the results is imposed in order to find the optimal setting. Table 4. Numeric Values for the MD Described in Table 3 MD

nH

nC

nO

Pol

RDCHI

nROH

nHDon

VvdwMG

xylitol ethylene glycol 1,2-propylene glycol

12 6 8

5 2 3

5 2 2

12 1 2

1.966 1.334 1.401

5 2 2

5 2 2

78.713 37.948 47.540

F


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tion for the development of mathematical models and theories of solutions. The solubility of xylitol in the solutions under study was found to be dependent on the temperature and the molar composition of the binary liquid solution. The dependence of the solubility on the molar fraction of the binary solution is related to the dielectric constant of the mixture. The solubilization capacity of pure components is higher in water followed by ethylene glycol and 1,2-propylene glycol. Binary liquid solutions have an intermediate solubilization capacity regarding the solubility in pure components. The Jouyban−Acree model with adjustable parameters as a function of temperature is an excellent option for the correlation of the solubility data. The approach does not seem reliable in the generation of results at different temperatures than those under study, however. The NRTL and UNIQUAC models were able to provide excellent results in the correlation of experimental data. The UNIQUAC model had a better performance than the NRTL model, and in the temperature range under study, the parameters of both models show a linear dependence as a function of the inverse of the temperature. This observation enables the generation of data for temperatures that are intermediate to those under study. The UNIFAC model had the worst performance among the models evaluated, but it was able to predict the solubility behavior. The thermodynamic simulation based on artificial neural networks using critical properties and molecular descriptors as independent variables was performed on several architectures for one and two dependent variables with configurations of 3 and 4 layers. The results showed that one dependent variable is sufficient to thermodynamically simulate the solid−liquid equilibrium of systems containing xylitol, water, and glycols. The optimal architecture found had 4 layers of the type 7-3-3-1. The results of the prediction step proved to be as accurate as those obtained with the activity models.

Since learning was successfully performed and the optimal network architecture was determined, 20 different data points (independent variables) of liquid solutions in equilibrium, not used in the learning process, were included in the third and fifth worksheet (10 different data points in each one) and were read by the routine developed in MatLab. The results of the composition of xylitol in the liquid phase in the testing and prediction steps are shown in Tables 5 and 6, respectively. Table 5. Absolute Deviation (%xs) for Xylitol Composition (xs) in the Ternary System (TS) for the Testing Step of the Configuration 7-3-3-1a TS

T (K)

x2

xs

xANN s

%Δxs

1 2 3 4 5 6 7 8 9 10

323.15 323.15 323.15 303.15 308.15 298.15 298.15 303.15 293.15 293.15

0.37111 0.67668 0.32690 0.28350 0.44473 0.46511 0.28715 0.61039 0.19468 0.84357

0.26112 0.32333 0.18556 0.06100 0.11252 0.07184 0.04888 0.12766 0.03286 0.15643

0.25262 0.31883 0.17966 0.05440 0.10522 0.06834 0.04118 0.12286 0.02706 0.15102

0.85 0.45 0.59 0.66 0.73 0.35 0.77 0.48 0.58 0.54

a

System temperature (T) and water composition in liquid phase (x2).

Table 6. Absolute Deviation (%xs) for Xylitol Composition (xs) in the Ternary System (TS) for the Prediction Step of the Configuration 7-3-3-1a TS

T (K)

x2

xs

xANN s

%Δxs

1 2 3 4 5 6 7 8 9 10

298.15 293.15 313.15 323.15 323.15 308.15 293.15 293.15 313.15 293.15

0.27760 0.55730 0.69211 0.43808 0.39367 0.77681 0.45866 0.77354 0.74351 0.84357

0.08059 0.07088 0.23057 0.27470 0.21441 0.22319 0.08682 0.14032 0.25649 0.15643

0.08271 0.07107 0.22633 0.27277 0.21697 0.22806 0.08544 0.13965 0.24779 0.15202

0.21 0.02 0.42 0.19 0.26 0.49 0.14 0.07 0.87 0.44

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b02480.

a

System temperature (T) and water composition in liquid phase (x2).

Table 5 shows the absolute deviations for the composition of xylitol in the liquid phase tested by the proposed ANN architecture for a different data selection than the one used during the learning stage. The results of the tests were obtained under the same conditions used during the learning process. In most cases, the configuration reproduces the composition of xylitol with absolute deviations below 0.60%. Table 6 shows the absolute deviations for the composition of xylitol in the liquid phase predicted by the proposed ANN architecture (optimal numeric method obtained) using different data than during the learning and testing stages. As can be seen, the ANN model reproduces the composition of xylitol in the liquid phase for the 10 experimental data points with an average absolute deviation of 0.31%.

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Source and purity of the chemicals, solubility data, parameters of the models, average relative deviation for the modeling, liquid-phase composition calculated by the models, SMILES code, weights and biases of the optimized ANN, results for the prediction step of different ANN architectures (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Alessandro C. Galvão: 0000-0002-8255-4511 Pedro F. Arce: 0000-0002-4687-5297 Notes

The authors declare no competing financial interest.

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6. CONCLUSION The results presented are fundamental for the research, development, and optimization of separation processes. In addition, phase equilibrium studies gather important informa-

ACKNOWLEDGMENTS FAPESC (Fundaçaõ de Amparo à Pesquisa e Inovaçaõ do Estado de Santa Catarina, grant no. 2017TR727) and FAPESP G


Article

Industrial & Engineering Chemistry Research (Fundaçaõ de Amparo à Pesquisa do Estado de São Paulo, grant no. 2015/05155-8) for financial support.

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PHASE EQUILIBRIUM INVOLVING XYLITOL, WATER AND

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