On-Line Crystallization Process Parameter Measurements Using

The sensitivity of particle sizing by ultrasonic attenuation spectroscopy to material ... process as attenuation changes with time because of crystal ...
0 downloads 0 Views 182KB Size
Download PDF
On-Line Crystallization Process Parameter Measurements Using Ultrasonic Attenuation Spectroscopy Mingzhong Li, Derek Wilkinson,* and Kumar Patchigolla

CRYSTAL GROWTH & DESIGN 2004 VOL. 4, NO. 5 955-963

Department of Chemical Engineering, School of Engineering & Physical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK

Patricia Mougin SSCI, Inc., 3065 Kent Avenue, West Lafayette, Indiana 47906

Kevin J. Roberts Institute for Particle Science and Engineering, Department of Chemical Engineering, University of Leeds, Leeds LS2 9JT, UK

Richard Tweedie Malvern Instruments Ltd., Enigma Business Park, Malvern, Worcestershire, WR14 1XZ, UK Received December 8, 2003

ABSTRACT: Batch crystallization is an important process in many industries, for example, fine chemicals, foods, and pharmaceuticals. On-line measurement of process parameters, such as crystal size distribution (CSD), crystal shape, solid concentration, nucleation, and growth rates, is important for process understanding and for product quality control. In this paper, L-glutamic acid crystallization process parameters (CSD, concentration, and the onset of crystallization) are monitored in-situ by ultrasonic attenuation spectroscopy, showing that ultrasonic attenuation spectroscopy has significant advantage over existing particle sizing methods such as laser diffraction when measuring concentrated suspensions. However, as currently implemented, the CSD and concentration analyses are conducted off-line because of the complexity of the analysis procedure, which requires lengthy calculation and a large set of physical parameters describing solid and liquid phases. A novel inversion method based on two neural networks working together is developed to determine CSD and concentration directly from ultrasonic attenuation measurements during crystallization. The neural network to recover CSD has 50 hidden neurons and the other with 20 hidden neurons approximates the reference intrinsic attenuation. This approach has been used to obtain parameters of the crystallization process in simulations and experiments. Compared to current analysis methods, neural networks supply solutions essentially instantaneously and without the need to know physical parameters of the solid and liquid phases. Introduction Crystallization is an important unit operation that is widely used in the chemical industry for the production of fine solids, especially in the fine chemical, food, and pharmaceutical industries. In-process measurement and control of solid properties, such as crystal size distribution (CSD), crystal shape, solid concentration, crystal nucleation and growth rates, are important to understand the process and for close control of high value-added product quality. Difficulties are experienced in measuring on-line particle size distribution using techniques such as light scattering, which requires low solid concentration for analysis. This in turn has required suspension dilution resulting in an unwieldy experimental arrangement for rapid, practical measurements. Ultrasonic attenuation spectroscopy is a comparatively new characterization technique offering the attractive possibility of on-line and in-situ particle size analysis. From measurements of ultrasound attenuation * To whom correspondence should be addressed. E-mail: [email protected], tel: +44 (0) 131 451 4717; fax: +44 (0) 131 451 3129.

by the dispersed system at different frequencies, the particle size distribution and concentration can be obtained. In principle, it is capable of examining optically opaque, concentrated systems at up to 70% volume fraction without the need for analyte dilution and so is attracting attention as a potentially useful technique for directly characterizing practical particulate suspensions. Ultrasonic attenuation spectroscopy has been shown to be suitable for on-line crystallization process parameter measurements,1-6 including CSD, concentration, metastable zone width, nucleation rate, and growth rate. However, the technique as currently implemented has a significant shortcoming. Deconvolution of ultrasonic attenuation spectra is based on the mathematical model of Epstein and Carhart (1953)7 and Allegra and Hawley (1972)8 (the ECAH model), which predicts the attenuation of a sound wave when passing through a suspension. A comprehensive description by this model requires a set of physical parameters describing solid and liquid phases including density, heat capacity, shear rigidity, etc. It is difficult to obtain all these parameters

10.1021/cg030041h CCC: $27.50 © 2004 American Chemical Society Published on Web 08/13/2004

956 Crystal Growth & Design, Vol. 4, No. 5, 2004

accurately in practice over the range of conditions typically experienced in a crystallizer. In addition, analysis of measured attenuation spectra must be carried out off-line because of the long calculation time required for the iterative solution. In this paper, the application of ultrasonic attenuation spectroscopy for on-line process parameter measurements was further investigated during the batch crystallization of L-glutamic acid from an aqueous solution. A new inversion method based on neural networks was developed to determine the CSD and concentration directly from ultrasonic attenuation measurements during the crystallization process. This method uses two neural networks operating together to determine the CSD and concentration simultaneously. Training data were generated from the Ultrasizer (Malvern Instruments) software using the ECAH model. The neural networks, one with 50 hidden neurons to recover the CSD and the other with 20 hidden neurons to approximate the reference intrinsic attenuation, were trained by the Levenberg-Marquardt algorithm.9 The results retrieved by this new method have been extensively validated by experiments, showing that the developed method can rapidly recover CSD and concentration in suspensions without the need to know a comprehensive set of physical parameters for the solid and liquid phases. Ultrasonic Attenuation Spectroscopy. When a sound wave passes through a suspension, changes occur to the wave as well as to the two phases of the medium. A particle presents a discontinuity to sound propagation, and the wave scatters with a redistribution of its acoustic energy throughout the volume before being detected at the receiver (scattering and diffraction losses). In addition, absorption phenomena occur when particles move relative to the suspending medium and mechanical energy degrades to heat (viscous losses); temperature differences develop between phases with mechanical energy transferring into heat (thermal losses). There are a number of solutions to the modeling of acoustic propagation in dispersed systems.10,11 The ECAH theory developed by Epstein and Carhart7 and Allegra and Hawley8 is the one most commonly used to model the relationship between particle size distribution and ultrasound attenuation measurements. This theory is based on a mathematical treatment associated with the propagation of an ultrasonic wave through a liquid containing an ensemble of particles. The ultrasonic velocity and attenuation coefficients are related to the overall phase and magnitude of this wave. The ECAH model has shown that ultrasonic attenuation can be accurately characterized through fundamental equations based on the laws of conservation of mass, energy, and momentum, the thermodynamic equations of state, and stress-strain relations for isotropic elastic solids or viscous fluids. In this manner, the attenuation spectrum associated with any particle size distribution and particle concentration can be predicted for any suspension or emulsion provided a set of mechanical, thermodynamic, and transport properties is known for both the suspending and suspended media. These physical properties are velocity of the ultrasonic wave, density, thermal expansion coefficient, heat capacity,

Li et al.

thermal conductivity, attenuation of the ultrasonic wave, viscosity (for the liquid phase), and shear rigidity (for the solid phase). As the model does not account for multiple-particle effects, it should be applied with caution to high concentration suspensions.12,13 The mathematical model involves several physical properties of the suspension system. The values used for these properties obviously affect the particle size and concentration as determined from acoustic measurements, and a correct set of parameters is thus crucial for reliable results. However, in many instances not all mechanisms play a significant role and the number of significant model parameters that need to be determined with accuracy is fewer. The significant model parameters can be identified through a sensitivity analysis. The sensitivity of particle sizing by ultrasonic attenuation spectroscopy to material properties in two systems of organic crystals, glutamic acid crystals in aqueous solution of glutamic acid and monosodium glutamate crystals in aqueous solution of monosodium glutamate, has been investigated.14 It was found that the same properties are significant for both material systems generally: the densities of both phases, shear rigidity of the particles, and sound speed and attenuation of the continuous phase. For these material systems, the size and concentration returned by analysis of ultrasound attenuation are insensitive to several properties that are required for the ECAH model: thermal dilation, thermal conductivity, and heat capacity of both phases and sound attenuation of the particle phase. Experimental Methods Experimental Setup. Ultrasonic attenuation measurements were carried out using an Ultrasizer (Malvern Instruments), operating over frequencies from 1 to 150 MHz. The instrument uses two pairs of broadband transducers driven by a continuous-wave signal to ensure accurate attenuation measurements. Measurements of the attenuation of a sound beam passing through a suspension are obtained as a function of frequency. The attenuation coefficient measured at a particular sound frequency f is defined as

Rf )

()

I0 1 ln ∆L I1

(1)

where Rf is the attenuation, I0 and I1 are the incident intensity and the intensity after passing through the sample respectively and ∆L is the acoustic path length. ∆L can be adjusted to suit the attenuation characteristics of the sample under investigation (between 0.03 and 4 in.). Crystallization studies were carried out inside the 2.8-L sample chamber of the Ultrasizer instrument by combining a computer-controlled crystallization apparatus with the ultrasonic spectrometer. Cooling coils were fitted in the chamber and connected to a thermostatic water-bath (Haake F3) with a fiber optic turbidity probe to determine the onset of crystallization and a platinum resistance thermometer (Pt100) to monitor the temperature in the chamber. A computer interface was used to control the temperature in the chamber. A schematic of the complete experimental setup is shown in Figure 1. Materials and Methods. Aqueous solution of L-glutamic acid (Aldrich, 99%) was prepared with distilled water. Experiments on the crystallization of L-glutamic acid were carried out by cooling an aqueous solution at 2% by mass from 50 to 15 °C. To obtain the R-form of L-glutamic acid, a linear cooling

Crystallization Process Parameter Measurements

Crystal Growth & Design, Vol. 4, No. 5, 2004 957

Figure 1. Schematic of experimental setup used for crystallization. Figure 3. Comparison of turbidity and ultrasound attenuation at 10 MHz in detecting onset of crystallization. Table 1. Physical Properties of L-Glutamic Acid and a Saturated Aqueous Solution of L-Glutamic Acid at 25 °Ca

glutamic acid property (kg m-3) sound speed (m s-1) thermal dilation (K-1) thermal conductivity (J m-1 s-1 K-1) heat capacity (J kg-1 K-1) viscosity (N s m-2) shear rigidity (N m-2) attenuation (dB m-1)

Figure 2. Evolution of ultrasonic attenuation spectra recorded during cooling crystallization of R-form L-glutamic acid.

Experimental Results and CSD Analysis Throughout the crystallization process, attenuation spectra were recorded (Figure 2), which clearly show the transient nature of the crystallization process as attenuation changes with time because of crystal growth. Turbidity data measured during the crystallization provided an indication of the onset of crystallization, which can be compared to attenuation measurements obtained at a single frequency. Figure 3 compares detection of the onset of crystallization by turbidity probe and ultrasound attenuation measurement at 10 MHz. It can be seen that there is a small difference between the two measurements, 27.5 °C for the turbidity measurement and 25 °C for the ultrasound attenuation measurement at 10 MHz. Inversion of measured attenuation spectra to CSD and concentration was carried out using the Ultrasizer software (Malvern Instruments) off-line because of the long calculation time. Liquid and solid system physical properties which are required to implement the ECAH model are listed in Table 1. A sensitivity analysis14 found that attenuation by the liquid medium was

1.54 × 103 4.07 × 103 2.0 × 10-5 4.22 × 10-1

1.00 × 103 1.48 × 103 2.6 × 10-4 5.9 × 10-1

1.24 × 103

4.2 × 103

8 × 109 4 × 10-4

1.0 × 10-3 (3.2 × 10-1 2.2 × 10-5 × T) × f (-2.9×10-3×T+2.0)b

aAnd bdB

rate of 0.4 °C/min was used to prevent formation of the β-form. The temperature was then kept constant at 15 °C until the acoustic attenuation spectrum became constant. Under these conditions, the L-glutamic acid crystallizes in its prismatic, isometric R-form.

saturated solution of glutamic acid at 25 °C

at T °C for the acoustic attenuation of the mother liquor. m-1, where T is in °C and f in MHz.

strongly dependent on temperature, so this temperature dependence of the acoustic attenuation of the mother liquid was allowed for over the temperature range of the crystallization. Temperature dependence of the physical properties of L-glutamic acid crystals was found to be negligible. Physical properties characterizing the liquid medium were taken to be equal to those of water because of the low working concentration. To confirm accurate inversion of CSD and concentration, model validation experiments have been done. A comparison of measured results and theoretical prediction by the ECAH model using the physical properties in Table 1 is shown in Figure 4 where the concentration of L-glutamic acid crystal of R-form (mean diameter 97.6 µm and standard deviation 1.59, determined by laser diffraction) is 0.5 vol % and chamber temperature is 25 °C. There are small prediction errors at some frequencies mainly due to the crystal size measurement; however, the overall prediction is generally reasonable. Figure 5 shows evolution of the CSD during crystallization of R-form L-glutamic acid from aqueous solution as a series of log-normal distributions obtained from the measured spectra in Figure 2. The evolutions of crystal mean size and concentration during the crystallization are given in Figure 6. Growth of the crystals can clearly be seen in both size and concentration.

958

Crystal Growth & Design, Vol. 4, No. 5, 2004

Li et al.

The output of the hidden units can be represented as

hj ) F(sj) ) F(VTj I), j ) 1,2, ‚‚‚,nh

(2)

where I ) [1,x1, ‚‚‚,xn]T is the network input vector, Vj ) [vj,0,vj,1, ‚‚‚,vj,n]T is the weight vector connecting the network inputs to the jth hidden unit, and F(x) is the sigmoid function. The output of the output layer neurons can be represented as

yi ) g(WTi H), i ) 1,2, ‚‚‚,m

Figure 4. Validation of ECAH model for suspension of 0.5% volume L-glutamic acid crystal of R-form at 25 °C.

Figure 5. Evolution of CSD during crystallization of R-form L-glutamic acid.

On-line CSD and Concentration Monitoring using Neural Networks Ultrasonic attenuation spectroscopy can be used for on-line monitoring of batch crystallization processes. On-line acoustic attenuation measurements can be used to analyze dynamic parameters such as CSD, crystal concentration, and onset of crystallization. However, these parameter analyses must be carried out off-line because of the long calculation time required by the conventional method of analysis. In the following, a novel method to determine CSD and concentration rapidly from ultrasound attenuation measurements based on neural networks has been investigated. Neural Networks. Neural networks have been attracting great interest as predictive models for complex nonlinear processes because of their outstanding ability to approximate an arbitrary nonlinear function. Success in applying neural networks depends strongly on the choice of the neural network’s structure, the available set of data, and training algorithms. The most common neural network for modeling is the feedforward network. Figure 7 represents an n-input, m-output feedforward neural network with one hidden layer having nh hidden units.

(3)

where H ) [1,h1, ‚‚‚,hnh]T is the network hidden layer output vector, Wi ) [wi,0,wi,1, ‚‚‚,wi,nh]T is the weight vector connecting network hidden layer units to the ith output neuron, and g(x) may be either a line function or a sigmoid function depending on the problem. In this work, g(x) ) F(x) ) 1/(1 + e-x), the sigmoid function, was selected. The neural network defines a mapping G:X f Y where X ∈Rn is an input vector and Y ∈Rm is an output vector. Any nonlinear function can be approximated by the network through appropriately determined weight matrices V ) [V1,V2, ‚‚‚,Vnh] and W ) [W1,W2, ‚‚‚,Wm]. The training of a neural network may be classified into either batch learning or pattern learning. In batch learning, the weights of the neural network are adjusted after a complete sweep of the entire training data, while in pattern learning the weights are updated during the course of the process using data gained in the process. Batch learning has greater mathematical validity as the gradient-descent method can be implemented exactly. Pattern learning, usually applied as batch learning approximations, can be used to modify network weights on-line so that a model can track the dynamics of a timevarying process. In this work, batch learning was selected as appropriate to train the network off-line. CSD Determination using Neural Networks. Problems to be addressed to use neural networks to determine CSD on-line are the selection of appropriate network inputs and outputs, the number of hidden units and the training algorithm. The network outputs are required to represent the characteristics of the CSD. For this particular application, it can be seen (Figure 5) that the CSD can be well represented by a log-normal distribution characterized by two parameters: the crystal mean diameter D and the geometric standard deviation σ. Thus, the two parameters crystal mean diameter and standard deviation are selected as the network outputs. From the evolution of the crystal concentration shown in Figure 6 during crystallization, it is seen that the solid concentration is low to moderate, less than 1% volume fraction. The ECAH model is thus suitable for the prediction of ultrasonic attenuation passing through the suspension, as has been validated (Figure 4). For a crystallization process, attenuation measurements depend not only on the CSD and concentration but also on the process temperature. So the network inputs must include the temperature and attenuation measurements at different frequencies. Attenuation measurements could be used directly as the network inputs, but this would lead to difficulty in training the network because of the effects of concentration and background attenuation. For a low concentration sus-

Crystallization Process Parameter Measurements

Crystal Growth & Design, Vol. 4, No. 5, 2004 959

Figure 6. Evolutions of CSD and concentration during crystallization of R-form L-glutamic acid.

Figure 9. Background attenuation at different temperatures.

Figure 8 shows the attenuation curve at different concentrations for L-glutamic acid crystals having a size distribution with a mean of 25 µm and deviation 1.4 at 10 MHz when the suspension’s temperature is 25 °C. From the figure, we can see that ultrasound attenuation varies linearly with crystal concentration and Rf_intrinsic and Rf_b are 1.8107 and 0.5415 dB/in., respectively. Figure 9 shows the relationship between background attenuation Rf_b and frequency f at different temperatures calculated by the software. This can also be measured using the Ultrasizer instrument. Background attenuation varies strongly with the operating frequency but is also dependent on suspension temperature. To eliminate the effects of concentration and background attenuation on network training, the ratios of attenuation to a reference Rf R were selected as inputs to the neural network, defined as

Figure 7. Structure of a feedforward neural network.

Rf,fR(D,σ) )

Rf(D,σ) - Rf,b Rf R(D,σ) - RfR,b

)

C × Rf_intrinsic(D,σ) C × RfR_intrinsic(D,σ)

Figure 8. Ultrasound attenuation at different concentrations for a suspension of L-glutamic acid crystals with mean 25 µm and deviation 1.4 at a frequency of 10 MHz and at 25 °C.

pension, attenuation at a frequency f can be represented by

Rf (D,σ) ) CRf_intrinsic(D,σ) + Rf_b

(4)

where Rf (D,σ) is the measured attenuation at the frequency f; C is the crystal concentration; Rf_intrinsic is the intrinsic attenuation at a reference concentration (arbitrarily chosen to be 1% volume fraction) at the frequency f; and Rf_b is the background attenuation at the frequency f, which is a function of the measurement frequency but is independent of the CSD. Intrinsic attenuation is dependent only on the CSD.

)

Rf_intrinsic(D,σ) RfR_intrinsic(D,σ)

(5)

where fR is a selected reference frequency. In this paper, 40 MHz was selected as the reference frequency. For the given reference frequency fR and the measurement frequency f, the ratio Rf,fR is determined only by the parameters of the CSD and is independent of the suspension concentration. This approach is justified provided the concentration is below the maximum limit of the ECAH model. The suspension’s temperature has already been selected as one of the neural network inputs. The number of attenuation ratios to use as network inputs is another problem to be considered; too few inputs will result in the loss of significant information, while too many will make the network unnecessarily complex and difficult to train. Figure 10 shows attenuation ratios based on a reference frequency of 40 MHz for different CSDs at 25 °C over a range of frequencies. It is seen that the curves are significantly different for different CSDs. From inspection of the shape of these curves, it was concluded that four attenuation ratios at different wavelengths are

960

Crystal Growth & Design, Vol. 4, No. 5, 2004

Figure 10. (a, b) Attenuation ratio for different crystal size distributions at 25 °C.

sufficient to represent the differences between the distributions. It is important to maximize the information content of data input to the neural network without requiring an excessive number of input nodes. Thus, the number of network inputs was set at five: one is temperature and the other four are attenuation ratios at different frequencies. The frequencies were selected at 20, 30, 50, and 55 MHz, within the operating range of the Ultrasizer instrument used in these experiments. Log-normal crystal size distributions with geometric mean diameters of 0.1-150 µm and standard deviations of 1.2-1.6, enough to cover the range of CSDs in the experiment, were considered for recovery by the neural network. A total of 1020 sets of training data at 1% volume fraction at different temperatures: 15, 18, 21, 24, 25, and 27 °C were generated to train the neural network using the Ultrasizer software and a further 12 sets of data were used to validate the effectiveness of the trained neural network. There were two important steps in the training procedure: determination of an adequate number of neurons in the hidden layer and the selection of a training algorithm. There are several training algorithms, such as adaptive back-propagation (ABP) algorithm,15 conjugate gradient (CG) algorithm16 and Levenberg-Marquardt (LM) algorithm.9 The LM algorithm was used to train the neural network, as it has been shown that the LM algorithm is the most effective

Li et al.

training algorithm.17-19 A maximum of 500 iterations and a desired minimum mean square error (MSE) 5.0 × 10-4 were specified for the training procedure. Training experiments using between 45 and 60 hidden neurons were carried out to determine the appropriate number of hidden units according to a criterion of MSE between the desired outputs and the calculated outputs from the network. The training and validation results for neural networks with different numbers of hidden neurons are shown in Figure 11. It is clear that the neural networks with 50 and 55 hidden neurons trained by the LM algorithm gave the best approximating results. In this paper, neural networks with 50 hidden neurons were selected to predict the CSD. The recovered results obtained by the neural network compared with the true values of the crystal size distribution are given in Table 2. It is seen that the recovered results generally agree well with the true values. Concentration Determination using Neural Networks. There are several possible approaches to determining the crystal concentration. A common one is that the solid concentration is determined by monitoring solution supersaturation. Crystal concentration can be calculated based on the mass balance of the suspension using supersaturation measurements. In the following, a novel method using a neural network to determine crystal concentration is proposed. From eq 4, it is known that the intrinsic attenuation is determined only by the suspension temperature and the CSD characteristics, crystal mean diameter and standard deviation. A second neural network can be trained to approximate the relation of the CSD and the intrinsic attenuation at a reference frequency. The crystal concentration can then be determined by rearranging eq 4

C)

Rfr(D,σ) - Rfr_b Rfr_intrinsic

(6)

where Rfr(D,σ) is the measured attenuation at the reference fr, Rfr_b is the background attenuation at the reference frequency fr and Rfr_intrinsic is the intrinsic attenuation at the reference frequency fr, which is the output of the neural network. The above analysis establishes that the second neural network’s inputs should be temperature and the CSD characteristics, mean diameter, and standard deviation, while the network output is Rfr(D,σ), the intrinsic attenuation of the CSD at the reference frequency. The reference frequency fr is set at 40 MHz, as for the neural network to determine CSD. The training data used are the same as above. The training procedure is also the same: the LM algorithm was used to train the neural network with a maximum of 500 iterations and the desired MSE of 5.0 × 10-4. Training experiments using from 15 to 30 hidden neurons were carried out to determine the appropriate number of hidden units for this simpler network structure compared to that for the CSD determination. The training results are shown in Figure 12. The neural networks were readily trained and it took fewer than 100 iterations to reach the desired MSE. The results show that the neural network with 20 hidden neurons gave the best approximating

Crystallization Process Parameter Measurements

Crystal Growth & Design, Vol. 4, No. 5, 2004 961

Figure 11. Neural network training and validation results for CSD determination (a) 45 hidden neurons; (b) 50 hidden neurons; (c) 55 hidden neurons; (d) 60 hidden neurons. Table 2. CSD Results Recovered by the Neural Network with 50 Hidden Neurons mean (micron)

standard deviation

temp (°C)

true value

NN result

true value

NN result

15 15 15 17.5 17.5 17.5 22.5 22.5 22.5 25 25 25

1.72E+00 3.30E+01 4.90E+00 5.50E-01 3.50E+00 1.20E+02 1.35E+01 1.96E+01 5.67E+01 1.38E+02 1.11E+02 8.70E+01

1.00E-01 3.16E+01 4.96E+01 1.00E-01 1.89E+00 1.37E+02 8.49E+00 1.21E+01 5.65E+01 1.26E+02 9.56E+01 9.69E+01

1.52E+00 1.20E+00 1.36E+00 1.45E+00 1.60E+00 1.44E+00 1.29E+00 1.56E+00 1.49E+00 1.59E+00 1.21E+00 1.38E+00

1.52E+00 1.20E+00 1.36E+00 1.20E+00 1.60E+00 1.60E+00 1.29E+00 1.56E+00 1.49E+00 1.60E+00 1.20E+00 1.20E+00

results. The recovered results obtained by the neural network compared with the true values of the intrinsic

attenuation are given in Table 3. It is seen that the recovered results agree well with the true values. Using eq 6, the crystal concentration can thus be calculated. Figure 13 shows how the two neural networks were combined to determine CSD and concentration simultaneously. Neural network 1 is used to recover the CSD. It has five inputs, the temperature and four attenuation ratios, and two outputs, the crystal mean diameter and standard deviation. Neural network 2 is used to predict the intrinsic attenuation at the reference frequency 40 MHz from three inputs, temperature with the outputs of neural network 1, crystal mean size and standard deviation. It has one output, the intrinsic attenuation at the reference frequency. Finally, the crystal concentration can be calculated from the measured attenuation, predicted intrinsic attenuation and the background attenuation using eq 6.

962

Crystal Growth & Design, Vol. 4, No. 5, 2004

Li et al.

Figure 13. Illustration of CSD and concentration determination using neural networks. Table 4. Evolution of the CSD and the Concentration Measured by Ultrasizer Software and Neural Networks during the Crystallization of a Solution of L-Glutamic Acid mean (µm)

deviation

conc (V%)

temp Ultasizer neural Ultasizer neural ultasizer neural (°C) software network software network software network 25.1 24.1 21.8 20.8 15

0.19 0.33 9.2 12.7 117

0.1 0.1 4.6 11.1 131

1.23 1.56 1.59 1.54 1.50

1.23 1.56 1.59 1.54 1.50

0.17 0.16 0.25 0.45 0.79

0.19 0.32 0.64 0.29 0.95

Discussion and Conclusion

Figure 12. Neural network training results for concentration determination (a) 15 hidden neurons; (b) 20 hidden neurons; (c) 25 hidden neurons; (d) 30 hidden neurons. Table 3. Intrinsic Attenuation Results Recovered by the Neural Network with 20 Hidden Neurons temp (°C)

true value (dB/in.)

NN result (dB/in.)

15 15 15 17.5 17.5 17.5 22.5 22.5 22.5 25 25 25

5.63E+00 4.17E+00 3.63E+01 2.76E+00 1.25E+02 1.06E+02 3.09E+01 6.55E+01 9.02E+01 3.38E+01 3.36E+01 3.44E+01

4.81E+00 6.99E+00 3.80E+01 7.13E+00 1.13E+02 1.02E+02 3.26E+01 6.41E+01 8.88E+01 3.40E+01 3.44E+01 5.65E+01

Crystallization Process Parameter Analysis using Neural Networks. To illustrate the effectiveness of the proposed method, crystallization process parameters have been analyzed using neural networks based on attenuation spectra recorded during L-glutamic acid crystallization. Table 4 shows the evolutions of the CSD and concentration determined by the neural networks and by Ultrasizer software. It is seen that the results recovered by the two methods are quite close, demonstrating that the proposed neural network method can be used to monitor crystallization process parameters, CSD and concentration.

In this paper, ultrasonic attenuation spectroscopy has been used successfully to monitor the evolutions of CSD and concentration during the L-glutamic acid crystallization process, showing that it has a huge potential advantage to measure the CSD and concentration in concentrated suspensions compared to other traditional particle sizing methods such as laser diffraction. However, using the conventional data reduction technique, the CSD and concentration analyses must be carried out off-line because of the complexity of the analysis procedure. For industrial applications in particular, rapid data acquisition on-line is much more valuable than off-line analysis. Obviously, incorporation of online analysis methods with ultrasonic attenuation measurements for crystallization processes merits further research. A novel method has been proposed to analyze on-line CSD and concentration during crystallization processes using neural networks with ultrasonic attenuation measurements. Two neural networks working together determine CSD and concentration simultaneously. Training data were generated using the Ultrasizer software. One neural network with 50 hidden neurons to recover the CSD and the second with 20 hidden neurons to approximate the reference intrinsic attenuation were trained by the Levenberg-Marquardt algorithm. Simulations and experiments have illustrated that it is feasible to use neural networks to obtain the parameters of the crystallization process. Compared to the Ultrasizer’s conventional analysis method, neural networks supply solutions essentially instantaneously and without requiring comprehensive physical parameters of the solid and liquid phases. For this particular application monitoring L-glutamic acid crystallization, the ECAH model is appropriate to

Crystallization Process Parameter Measurements

predict the attenuation spectrum because of the low crystal concentration. Thus, training data can be generated from the theoretical model and the CSD parameters and concentration can be approximated separately using two neural networks, simplifying the structure of each network compared to using a single neural network with the three outputs crystal mean, standard deviation and concentration. The single neural network approach would also need substantially more training data. For applications in which the ECAH model cannot be used to predict the attenuation spectra due to high solid concentrations, training data would have to be generated from experimental measurements of suspensions of known crystal size distributions and concentrations. For such cases, one neural network with three outputs including CSD characteristics and concentration would be adopted because the concentration is not in a linear relation with attenuation in concentrated suspensions. This would require a substantial increase in the quantity of training data and in training time. To implement on-line the CSD and concentration analysis, modification of the Ultrasizer software is required to enable the neural networks to access attenuation data on-line. Work is ongoing to realize online analysis of crystallization processes. Acknowledgment. The financial support of EPSRC (Grant GR/R93353/01) is gratefully acknowledged. The cooperation of colleagues on the project “Chemicals Behaving Badly” is also gratefully acknowledged. References (1) Mougin, P. In situ and On-Line Ultrasonic Attenuation Spectroscopy for Particle Sizing during the Crystallisation of Organic Fine Chemicals, Ph.D. Thesis, Heriot-Watt University, Edinburgh, U.K., 2001.

Crystal Growth & Design, Vol. 4, No. 5, 2004 963 (2) Mougin, P.; Roberts, K. J.; Tweedie, R.; Wilkinson, D.J. Acoust. Soc. Am. 2001, 109, 274-282. (3) Mougin, P.; Wilkinson, D.; Roberts, K. J.Cryst. Growth Des. 2002, 2, 227-234. (4) Mougin, P.; Thomas, A.; Wilkinson, D.; White, G.; Roberts, K. J.; Herrmann, N.; Jack, R.; Tweedie, R.AIChE J. 2003, 49, 373-378. (5) Roberts, K. J. Application of Process Analytical Techniques to Monitoring the Crystallisation of Organic Fine Chemical Products, Proceedings of the 15th International Symposium on Industrial Crystallization, Volume III, 1105-1117, 1518th September, 2002, Sorrento, Italy. (6) Hipp, A. K.; Walker, B.; Mazzotti, M.; Morbidelli, M.Ind. Eng. Chem. Res. 2000, 39, 783-789. (7) Epstein, P. S.; Carhart, R. R.J. Acoust. Soc. Am. 1953, 25, 553-565. (8) Allegra, J. R.; Hawley, S. A.J. Acoust. Soc. Am. 1971, 51, 1545-1564. (9) Hagan, M. T.; Menhaj, M. B.IEEE Trans. Neural Networks 1994, 5, 989-993. (10) Harker, A. H.; Temple, J. A.J. Phys. D 1988, 21, 1576-1588. (11) Tebbutt, J. S.; Challis, R. E.Ultrasonics 1996, 34, 363-368. (12) Hipp, A. K.; Storti, G.; Morbidelli, M.J. Phys. D: Appl. Phys. 1999, 32, 568-576. (13) Alba, F.; Crawley, G. M.; Fatkin, J.; Higgs, D. M. J.; Kippax, P. G. Colloids Surfaces 1999, 153, 495-502. (14) Mougin, P.; Wilkinson, D.; Roberts, K. J.; Jack, R.; Kippax, P.Powder Technol. 2003, 134, 243-248. (15) Weir, M. K.Neural Networks 1991, 4, 371-379. (16) Xu, X. P.; Burton, R. T.; Sargent, C. M.J. Dyn. Syst. Meas. Control - Trans. ASME 1996, 118, 272-277. (17) Li, M.; Wilkinson, D.; Schrodl, M.AIChE J. 2002, 48, 24922498. (18) Li, M.; Frette, T.; Wilkinson, D.Ind. Eng. Chem. Res. 2001, 40, 4615-4622. (19) Gordon, S.; Hammond, R.; Roberts, K.; Savelli, N.; Wilkinson, D. Trans IChemE, 78, Part A 2000, 1147-1152.

CG030041H