Neural network model for the on-line monitoring of a crystallization process

NEURAL NETWORK MODEL FOR THE ON-LINE MONITORING OF A CRYSTALLIZATION PROCESS

R.Guardani, R.S.Onimaru and F.C.A.Crespo

Department of Chemical Engineering, University of São Paulo USP,

Cx. P. 61548, CEP 05424-970 São Paulo - SP, Brazil

E-mail:[e-mail]

(Received: April 19, 2001 ; Accepted: July 26, 2001)

Abstract - This paper presents the results of the application of a recently developed technique, based on Neural Networks (NN), in the recognition of angular distribution patterns of light scattered by particles in suspension, for the purpose of estimating concentration and crystal size distribution (CSD) in a precipitation process based on the addition of antisolvent (a model system consisting of sodium chloride, water and ethanol). In the first step, in NN model was fitted, using particles with different size distributions and concentrations. Then the model was used to monitor the process, thus enabling a fast and reliable estimation of supersaturation and CSD. Such information, which is difficult to obtain by any other means, can be used in the study of fundamental aspects of crystallization and precipitation processes.

Keywords: Particle size distribution, Laser diffraction, crystallization, Neural Networks modeling.

INTRODUCTION

The problem of predicting and measuring crystal size distribution (CSD) in crystallizers has been the subject of both theoretical and experimental studies for nearly two decades. Particle size is commonly accepted as a major controlling parameter in a wide variety of important processes and systems. Therefore, the control of CSD in industrial precipitation has received considerable attention in recent years due to its important effects on solid-liquid separation characteristics and the quality of the final product ( Heffels et al., 1993).

The use of the light-scattering technique to measure particle size distributions of solid particles suspended in fluids has become increasingly popular in recent years as a consequence of its good reproducibility, the simplicity of the procedure and its ability to measure particles in the submicron range. The technique is based on the measurement of the angular distribution of light diffracted by particles situated in the path of a light beam. The image, formed on a perpendicular plane by the diffraction of a monochromatic beam by a particle, consists of a series of concentric rings. A rigorous theory describing the scattering of light by spherical particles was formulated by Mie in 1908 and is able to predict the electromagnetic field at any point in space (Van de Hulst, 1957). Methods of calculation based on Mie’s theory provide adequate results for particles with diameters of the same order of magnitude as that of the incident light wavelength. For particles with larger diameters, however, the computation algorithms provide less accurate results and other models must be employed. The most frequently used models are based on Fraunhofer diffraction, which provides accurate results for particles larger than about 20 mm (for a He-Ne laser).

However, at present there is a limitation on the application of the light-scattering technique based on forward diffraction in highly concentrated suspensions, due to the intensity of multiple light scattering. This phenomenon is caused by the presence of many particles in the light path, creating multiple deviations in the light beam before the detector is reached.

To compensate for the problem of multiple scattering, an alternative approach was proposed in a previous paper (Nascimento et al., 1997). The particle size distribution is obtained by a NN model, which uses as input variables not only the scattered light intensity, but also the concentration of particles in the suspension.

Neural networks have been arousing great interest as predictive models as well as models for pattern recognition, and a large number of papers can be found in the literature. The fitting algorithm developed at the LSCP (Process Control and Simulation Laboratory, Chemical Engineering Department at the University of São Paulo) has been successfully applied to a number of different problems involving complex systems, such as in modeling the kinetics of photochemical reactions (Nascimento et al., 1994) or predicting atmospheric ozone concentration (Guardani et al., 1999). Specifically in the case of industrial processes some examples of applications are in olefin polymerization (Chan and Nascimento, 1994) and the optimization of industrial processes (Nascimento et al., 2000). The fitting is based on the backpropagation algorithm, which is a generalization of the steepest descent method (Rumelhart and McClelland, 1986) applied to a "feedforward" neural network with the structure illustrated in Fig. 1 where the boxes represent the neurons. Each processing neuron first calculates the weighted sum of all interconnected signals from the previous layer, plus a bias term and then generates an output through an activation function (Eqs. 1 and 2), which can assume different forms but is most commonly expressed as a sigmoidal function.

The neural network model adopted in this work is made up of three layers: input, hidden, and output. The system "learns" by making changes in its weights (Wi,j) while the input and output variables chosen for the network learning are presented to the model in a normalized form. In the fitting process, not only network parameters, such as the number of neurons in the hidden layer or the normalization limits, but also learning parameters, such as the rate of change of the dumping/accelerating factor, h, are varied. The mean quadratic deviation based on the data from the test set was adopted as the fitting criterion. The quality of the fitting is the result of a combination of the parameters above. As a rule, the number of neurons in the network should be as low as possible in order to avoid overfitting. The fitting process consists of minimizing the quadratic deviation (E), defined as

where y_k comes from the input-output pairs of data (x, y) available for training the network. Ok is the output obtained from Eq. 2 applied to the neurons of the output layer. Thus, O_k is equivalent to f(S_k). In the traditional gradient approach for minimizing the mean square error with respect to the weights, Wj,k, the derivatives, dE/dWj,k, are calculated and the set of weights moves in the direction of steepest descent of the derivative. This technique requires the use of all the input-output pairs to determine the gradient. The backpropagation algorithm also uses gradient information to change the weights, but they are calculated with respect to only one input-output pair at a time. For the output layer, the weights are changed according to Eq. 4:

where

and h represents a dumping or accelerating factor. For the hidden layer, the weights are updated by using the expression below for DW:

At each iteration, the weights between the hidden and output layers are adjusted first. Subsequently, the weights between the input and hidden layers are changed. After presentation of the first input-output pair, the second pair is processed, and so on.

The precipitation process considered in this work, known as "salting-out", or "drowning-out" precipitation, is based on the addition of a so-called antisolvent to a solution. The antisolvent is miscible with the original solvent, but its addition causes a decrease in the solubility of the solute. Supersaturation can thus be controlled by the rate of addition of the antisolvent, and this results in a more efficient control of the CSD. Such processes have been arousing increasing interest in a number of applications in the chemical and related industries (Nývlt, and Zacek, 1986).

In this work, the NN-based method for estimating CSD was used as a monitoring tool in an antisolvent precipitation process in order to obtain information on the time evolution of supersaturation and CSD. The ethanol-water-NaCl system was adopted in this study.

EXPERIMENTAL

The apparatus consists of a one-liter, jacketed, baffled crystallizer made of borosilicate glass. The temperature of the crystallizer is controlled by a thermostatic bath and kept constant at 30^oC. The starting solution consists of NaCl in water (X_NaCl=0.25). This solution is fed to the crystallizer before the experiment starts. In all experiments the starting solution contains 100g of NaCl and 300g of water.

The antisolvent consists of ethanol or a mixture of ethanol and water. During each experiment the antisolvent is continuously fed in to the crystallizer by means of a digitally controlled peristaltic pump. After 30 min of experiment, the pump is stopped and the suspension is immediately filtered in a vacuum system and left to dry at 100 ^oC for about 10 minutes. A summary of the operating conditions in the experiments is shown in Table 1.

To measure the CSD, a known mass of dry NaCl crystals was weighed and added to a known volume of dispersing fluid, which consisted of isopropyl alcohol. The solids concentration in the suspension varied from 7 to 210 g of particles per liter of suspension. The CSD measurements were carried out in a Malvern Mastesizer X laser diffractometer, which uses a He-Ne laser and a detector consisting of 31 concentric rings. A 300 mm Fourier lens was used in all the measurements.

RESULTS AND DISCUSSION

CSD Measurements

Figure 2 shows the dependence of the obscuration rate on particle concentration for particles with different size distributions. The obscuration rate tends asymptotically to wards 100% as the concentration increases. For smaller particles the obscuration rate increases in a more pronounced way, since for a given mass concentration, there are more particles per unit volume of suspension than there are for larger particles.

In order to illustrate the effect of multiple light scattering, Figures 3 and 4 show the variation in the Sauter average diameter (d_3,2 or surface-volume) and in the CSD based on the optical model (Fraunhofer), for sample FAP 4. The average diameter remains relatively constant for obscuration rates between 10 and 30%, which is exactly the range recommended by the equipment manufacturer. Beyond that limit, the average diameter decreases due to the effect of multiple light scattering. The CSD also presents a dislocation to the left and an increase in dispersion as the obscuration rate increases. The same behavior was observed for samples FAP 1, FAP 2, FAP 3 and FAP 5.

Neural Network Fitting

Application of the model has as its first step fitting, in which experimental data are used in the training and validation of a model based on a neural network. Then, the model can be used as a software sensor in the on-line monitoring of crystal concentration and CSD.

The model is composed of two feedforward neural networks (shown in Figure 5), each of which has a total of 32 inputs: the obscuration rate plus the light intensity measured at the 31 rings of the diffractometer. Both models have 8 neurons in the intermediate layer. This number was defined in preliminary fitting runs. Model 1 has one output: particle concentration. Model 2 has CSD as its output (in this case, 32 outputs, one for each size class). The reference values for the CSD of each sample used in fitting Model 2 were measured by laser diffraction at obscuration rates of about 20%.

Figures 6 and 7 illustrate the results of the model fitting in terms of particle concentration and CSD for data from the test set, which were not included in the neural network fitting. It can be seen that, after being adequately trained, the neural network model is able to compensate for the effect of multiple scattering, providing realistic results even at high obscuration rate values.

Use of the Model to Monitor a Crystallization Process

After fitting, the neural network model was used to monitor a drowning-out precipitation experiment.

This was done by conducting a "drowning-out" experiment under the following conditions:

1) temperature: 23 ^oC;

2) initial mass of aqueous solution in the tank (Mo): 357.0 g (X_NACI = 0.25);

3) antisolvent (absolute ethanol) mass flowrate (m): 0.348 g/s.

Throughout the experiment, the diffractometer operated automatically, performing measurements every 30 seconds. The light intensity distribution and obscuration rate data collected during this time were fed in to the NN model to compute crystal concentration and CSD.

From the model-computed values for crystal concentration, the mass of crystals per unit volume of suspension during this time could be calculated and the mass fraction of NaCl in the solution could be estimated, based on the following mass balance equations:

with

Thus, supersaturation during this time can be estimated from the difference between X_NaCl and the equilibrium mass fraction.

Figures 8 and 9 show the values for crystal concentration, supersaturation and CSD, during this time. In Figure 8 it can be observed that crystal concentration increases abruptly at the beginning of

the experiment, while the values for supersaturation negative remain. This is probably due to the local supersaturation caused by antisolvent mixing problems in the tank.

Figure 9

CONCLUSION

This study has shown that the measurement of CSD by laser diffraction, based on an optical model, is affected by the phenomenon of multiple scattering in high particle concentrations. The NN-based model was able to compensate multiple scattering, providing realistic estimations of the CSD, even for obscuration rates close to 100%.

These results indicate that the neural network model can be used as a software sensor for obtaining fundamental information about the crystallization process, enabling the improvement of process control and product quality as well as the further development of models for crystal formation and growth.

ACKNOWLEDGEMENTS

Sincere thanks are offered to FAPES and CNPq for the financial support.

NOMENCLATURE

CSD crystal size distribution E quadratic deviation f Sigmoidal function in Eq. 2 I light intensity [-] M mass [g] m liquid precipitation mass flowrate [g/s] N number of input variables in the neural network model NH number of neurons in the hidden layer NN neural networks Oj output from neuron j Ok output from neuron k in the output layer P index of output variables in the neural network model Q index of input variables in the network R² coefficient of correlation r index of input-output pairs in the learning set Sj weighted sum of inputs into a neuron Wi,j weight of variable i, in neuron j W matrix of weights set in the network xi normalized input variable i in the neural network model yk normalized output variable k in the neural network model X mass fraction [-]; Y mass fraction in solid t time [s] Greek Symbols h acceleration/dumping factor Superscripts 0 initial condition cr of crystals f final condition m point in learning set n number of detectors of scattered light ' first derivative

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Publication Dates

• Publication in this collection
  11 Oct 2001
• Date of issue
  Sept 2001

History

• Received
  19 Apr 2001
• Accepted
  26 July 2001