Designing an efficient artificial intelligent approach for estimation of

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Designing an efficient artificial intelligent approach for estimation of hydrodynamic characteristics of tapered fluidized bed from its design and operating parameters Mohsen Karimi, Behzad Vaferi, Seyyed Hossein Hosseini, and mojtaba rasteh Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02869 • Publication Date (Web): 15 Dec 2017 Downloaded from http://pubs.acs.org on December 26, 2017

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Industrial & Engineering Chemistry Research

Designing an efficient artificial intelligent approach for estimation of hydrodynamic characteristics of tapered fluidized bed from its design and operating parameters ∗

Mohsen Karimi a, Behzad Vaferi b , Seyyed Hossein Hosseini b, Mojtaba Rasteh d a

Laboratory of Separation and Reaction Engineering (LSRE), Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, S/N, 4099-002, Porto, Portugal b

Young Researchers and Elite Club, Shiraz Branch, Islamic Azad University, Shiraz, Iran c

d

Department of Chemical Engineering, Ilam University, Ilam, 69315-516, Iran

Department of Chemical Engineering, Hamedan University of Technology, Hamedan, P.O Box, 65155579, Iran

ABSTRACT Tapered fluidized bed with variable fluid velocity throughout the bed length is a special type of fluidized system. Accurate estimation of hydrodynamic characteristics of the tapered fluidized bed is required for adjusting the operational conditions, optimum design, and process control of this system. In this way, minimum fluidization velocity (Umf), minimum velocity of full fluidization (Umff), and maximum pressure drop (∆Pmax) are the main hydrodynamic characteristics of the tapered fluidized bed. In this study, an artificial neural network (ANN) paradigm was developed for prediction of these parameters. Parameters of the ANN model was

∗

Corresponding Author: Tel.:+98-9388419266; Fax: +98-7136410059 Email address: [email protected]; [email protected] (B. Vaferi)

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adjusted through minimization of absolute average relative deviation (AARD%) and mean square error (MSE) by back propagation algorithm. Finally, the proposed model predicted the experimental data of Umf, Umff and ∆Pmax with AARD of 1.1%, 1.36%, and 0.89%, respectively, while the best obtained results by five different empirical correlations were 4.12%, 9.4%, and 5.14% for Umf, Umff, and ∆Pmax.

Keywords: tapered fluidized beds; hydrodynamic characteristics; artificial neural networks; empirical correlations

1. Introduction Fluidization is a phenomenon that occurs when a mixture of solid particles in the fluid phase behaves as a normal fluid. This is often accomplished by passing of pressurized fluid through the particulate medium. Bubble formation takes place when the flow rate is more than the required value for fluidization. Thereafter, the bed expands and provides high surface contact between the solid particles and fluid phase.1 This property leads to several important applications for the fluidized systems including gas separation,2 catalytic reactions,2 oil removal from water,3 fiber suspension,4 hot gas desulfurization,5 crystallization,6 food processing,7 fluid-bed granulation,8 waste incineration,9 production of anhydrous borax,10 and wastewater treatment.11

1.1. Tapered fluidized beds Tapered fluidized bed is one of the most important types of fluidized systems. Schematic of this special apparatus is illustrated in Figure 1. The conical shape of this reactor can provide

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variable fluid velocity alongside the bed length. It can be clearly understood from Figure 1 that the fluid velocity declines from the bottom to the top of the bed. Figure 1 At first, a low amount of fluid (gas or liquid) flows upwards towards the stationary particles, and hardly passes through them. In the next step, by increasing the flow rate, particles move apart and some of them start to move and vibrate in the restricted regions which contribute to expanding the bed and enhancing its pressure drop. Pressure drop in the bed increases until it reaches the maximum possible value for the process. At this point, the particles are fully fluidized due to the high velocity of the fluid passing through. It should be mentioned that the weight of the fluid and particles in any section of the fluidized bed is equal to the pressure drop of that section.12,

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Knowing the hydrodynamic characteristics of the tapered fluidized bed is

important for defining proper operational conditions, optimum design, and control of the process. Minimum fluidization velocity ( U mf ), minimum velocity of full fluidization ( U mff ), and maximum pressure drop ( ∆Pmax ) are among the most important hydrodynamic characteristics of the tapered fluidized bed which have been studied by many researchers.14-16

1.2. Hydrodynamic characterization of tapered fluidized beds During the recent years, many empirical and analytical models have been proposed for estimation of the minimum fluidization velocity, minimum velocity of full fluidization, and maximum pressure drop.17-22 Peng and Fan22 proposed a theoretical model for prediction of minimum fluidization velocity and maximum pressure drop. They used the exerted dynamic forces on the spherical particles for development of their model. Jing et al.

19

and Shan et al.

20

suggested other models to characterize the hydrodynamic behavior of gas–solid tapered fluidized

3



beds for coarse and fine particles, respectively. In these studies, the Ergun's equation is used for calculation of pressure drop in the process, and they neglected variations of the kinetic energy in the bed. Since some researchers incorporated the most influential parameters of the tapered fluidized system in their models, their proposed correlations are among the most popular models in the recent years.23-29 The model by Biswal et al.

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which was developed for a bed with variable velocity of inlet

gas and spherical glass particles, can predict the expansion ratio of the tapered fluidized bed. This model can only be used for a bed with 10° tapered angle filled by glass spheres. Moreover, Depypere et al. 7 proposed a correlation for prediction of the bed expansion ratio with spherical particles in a tapered bed with 8.13° tapered angle. The static pressure and wall temperature are incorporated in this model. Sau et al.

24

developed a dimensionless model to estimate the bed

expansion ratio of both spherical and non-spherical particles in the tapered fluidized beds with different geometries. Based on modified Ergun’s equation Liyan et al. 29 proposed an expression for pressure gradient across the bed and accordingly, developed a new drag coefficient to predict gas-particles interaction in tapered bubbling fluidized beds. During the recent years, many empirical and analytical models have been proposed for estimation of the minimum fluidization velocity, minimum velocity of full fluidization, and maximum pressure drop. In addition, other correlations were initiated from the modified Ergun equation, 22 while the others were developed by different sort of regression on experimental data. The summary of the most well-known empirical correlations that are often used for estimation of hydrodynamic characteristics for tapered fluidized beds are presented in the Appendix A in Supporting Information section.

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2. Artificial Neural Networks Artificial neural networks are categorized as the nonlinear mathematical approaches derived by simulation of the neurological activity of the human brain.30 Accuracy, simplicity, and flexibility of the ANN models lead to their application in function approximation, pattern recognition, process modeling, fault detection, process control and optimization.30-34 One of the benefits of ANN models is their ability to correlate independent and dependent variables, even for the most sophisticated phenomena. 32, 33, 35, 36 Multi-layer perception (MLP) neural network is the most well-known and widely used type of ANN model for function approximation. 36-38 These networks constitute several layers of interconnected processing units, namely neurons. The mathematical manipulation performed in the neurons, can be expressed by Eq. (1).

 N  n j = f ( x ) = f  ∑W jr X r + b j   r =1 

(1)

In this equation, b j , X r , W jr and f represent the biases, value of entry information to the neuron, weight coefficients, and transfer function, respectively. n j indicates the value of output signal from the neurons. In this study, the log-sigmoid is used as transfer function. This transfer function can be defined by Eq. (2). f (x) =

1 1 + exp( − x )

(2)

It is possible to create various types of ANN models by changing the way of interconnections among neurons in various layers. The MLP networks often consist of three different layers including input, hidden, and output layers. The input layer receives values of independent variables from external resources and sends them to the hidden layer. The hidden layer performs several mathematical manipulations on the received information and delivers them to the output

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layer. Numbers of neuron in the output layer are equal to the number of dependent variables. The values of exit signals from the output layer represent the values of dependent variables. 37, 38 As it can be observed from Eq. (1), an ANN model has several parameters, namely weights and biases that should be adjusted by using the experimental data of the considered process. 37, 38 There are several training algorithms such as genetic algorithm, scaled conjugate gradient, back propagation, cascade correlation, and quick propagation for evaluating the parameters of ANN models.39-42 Based on our previous experience,

30-32, 36-38

the Levenberg–Marquardt algorithm

43

usually provides a better performance for evaluating the ANN parameters, and has therefore been used in this study.

3. Development of the ANN Model For development of any ANN model, it is necessary to follow a systematic procedure as noted below: -

Defining the objective in terms of the dependent variables(s) that need to be estimated.

-

Selection of the most influential independent variables on the considered dependent variable(s).

-

Gathering relevant and enough experimental data for the considered system by either doing experiments or from literature.

-

Determination the degree of linear dependence between different pairs of independent and dependent variables using available theories such as a correlation matrix analysis.

-

Adjustment of the parameters of various topologies of the ANN models using appropriate training algorithms.

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-

Finding the best topology of the ANN model through minimization of different statistical accuracy indices.

-

Comparison between the predictive accuracy of the developed ANN model with other available correlations.

The detailed explanation of the above mentioned steps is presented in the subsequent sections.

3.1. Selection of independent variables The first step of development of any MLP model is finding the most significant independent variables on the considered dependent variables. Based on previous studies the hydrodynamic characteristics of tapered fluidized beds depend on particle properties (size, shape, density, voidage and inter particle forces), fluidizing gas properties (density and viscosity), bed geometry (tapered angle, inlet diameter) and bed loading (initial solid height in the bed).

19-21, 23-27

It is

observed that these independent variables can be manipulated to establish five dimensionless groups. These dimensionless groups are: the Archimedes number ( Ar = gd p3 ρ g ( ρs − ρ g ) / µg2 ), the Bond number ( Bo = 6.IFP / Π .g .ρs .d p3 ), ε 0 / φ s , H 0 / D0 , and cos ( α ) [the definition all of these variables have been presented in the Nomenclature section]. Both the correlation matrix analyses (See section 3.3) and the previous empirical models,

27

confirm that these independent

variables are the most influential parameters on the hydrodynamic characteristics of the tapered fluidized beds. Schematic diagram of the developed MLP model for the simulation of hydrodynamic behavior of tapered fluidized bed is illustrated in Figure 2. It can be easily observed from Figure 2, that the minimum fluidization velocity, minimum velocity of full fluidization, and maximum pressure drop are estimated as a function of Ar, Bo, ε 0 / φ s , H 0 / D0 , and cos ( α ).

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Figure 2 It should be mentioned that the effects of various parameters including bed tapered angle, static bed height, inter-particle forces (IPF), and spherical and non-spherical particles with different sizes are included in these dimensionless groups.

3.2. Data gathering As previously discussed, weights and biases of the MLP model need to be adjusted using the experimental data of considered system. In this study 192 experimental data for tapered fluidized beds which covered the Archimedes number 372.5 – 6.1×104, Bond number of 2.87×10-6 – 2.74,

ε 0 / φ s of 0.46 – 0.57, H 0 / D0 of 0.455 – 1.429, and cos ( α ) of 0.957 – 0.991 were collected from literature.

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These experimental data have been obtained by changing material (4 cases),

particle diameter (4 cases), static bed height (4 cases) and tapered angle (3 cases) which create 192 (4×4×4×3) different experimental conditions. Physical properties of the materials in the various experiments and their ranges are presented in Table 1. Also the gas viscosity and density in the experiment are 18.27×10-5 (Pa.s) and 1.23 (kg/m3), respectively. In addition, the summary of the dimensions of the tapered fluidized beds in the various experiments and the ranges of their associated minimum fluidization velocity, minimum velocity of full fluidization, and maximum pressure drop is reported in Table 2. As it can be seen from these tables, four different materials with different sizes and geometries are used as solid particles in the tapered fluidized beds. Table 1 Table 2 These experimental data are utilized for both adjustment of the MLP parameters, and evaluation of its predictive accuracy. Our previous experience has suggested that by scaling

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(normalization) the independent and dependent variables it is possible to ease the training stage and obtain better results.36-40 Therefore, all of variables of the tapered fluidized bed have been normalized between [0 - 1].

3.3. Correlation matrix analysis Finding the variables that have strong effect on the system behavior is required for conducting all types of the modeling-based studies. Correlation matrix analysis is a statistical theory that measures the power of a linear dependence between any two different variables.

32, 38

In this

study the Pearson’s correlation matrix is used for doing such an analysis. Table 3 presents the values of linear dependence between different pairs of independent and dependent variables for the tapered fluidized bed. It can be observed from Table 3, that the Ar has the maximum amount of linear dependence with both Umf and Umff, while ε 0 / φ s has the highest degree of linear dependence with ∆Pmax. Table 3 3.4. Training Training of MLP network using a suitable learning algorithm is the most important step for correlating inputs and outputs of most nonlinear multi-variable systems. During this stage, the weights and biases of the MLP model are adjusted in a way that correlates the independent and dependent variables with enough accuracy. We also employed a training algorithm that corrects the parameters of the MLP model, by minimizing the error between the experimental data and MLP results. Although, there are several training algorithms which can be applied for adjusting the parameters of the MLP network,

37, 38

based on the author's previous experience,

36, 38, 41

the

Levenberg–Marquardt algorithm usually provides better performance.42 Absolute average

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relative deviation (AARD%), mean square error (MSE), and regression coefficient (R2) are among the most frequently used statistical accuracy indices, which have been widely utilized in the field of ANN methodology. The mathematical formulations of these indices are expressed by Eqs. (3) through (5).

(

1 N MSE = ∑ PVi Act. − PVi cal. N i =1

1 AARD % = N

∑ (PV N

i

R2 =

Act .

2

)

(3)

 PVi Act .. − PVi cal .  ∑  PVi Act . i =1  N

− ∆PV

i =1

) − ∑ (PV N

2

Act i

  × 100  

(4)

− ∆PVi cal )

2

i =1

∑ (PV N

Act . i

− ∆PV

(5)

)

2

i =1

here PV denotes the parameter value, and can be any dependent variables of this study i.e., Umf , Umff, and ∆Pmax.

4. Results and Discussions In this section, the optimum configuration of the MLP network is determined, and the respective results of the prediction of hydrodynamic characteristics for the tapered fluidized bed are benchmarked by both experimental data and available empirical correlations. Also, the effect of the variations of the system parameters on the Umf, Umff, and ∆Pmax is investigated. Finally, the stepwise procedure is given for appropriate usage of this methodology and facilitating the interested readers to regenerate the reported results in this study.

4.1. Proposed Model

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It has been found that a single hidden layer MLP network with a non-linear transfer function can accurately predict the behavior of the majority of multivariable phenomena.

44-46

Therefore,

in the present study, a MLP network with only one hidden layer is used for estimation of the hydrodynamic characteristics of tapered fluidized beds. Eighty percent of experimental data was used for training, while other twenty percent was utilized for testing the performance of the trained network. The fifth-fold cross validation is used for finding the best structures of the ANN models. Final results obtained in the Table 4. For more information about the details of the modeling procedure, the readers are referred to the author’s previous study. 38 Table 4

4.2. Model verification Evaluation of the performance of the developed model is necessary for assuring its application and assessing its reliability for prediction of behavior of the considered process. In this section, the results of the MLP model were validated using both experimental data and other available correlations for the tapered fluidized beds.

4.2.1. Evaluation using experimental data Figure 3 (A, B, and C) depict comparison between actual values of the hydrodynamic characteristics of tapered fluidized bed and their associated predicted results by the optimum MLP approach for both training and testing groups. These figures illustrate the actual and predicted values of the data of Umf, Umff, and ∆Pmax. The perfect estimations (prediction values equal to the actual values) are shown by the dashed 45° line. Small deviations from these 45°

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line confirm that the predicted values of training and testing subsets have been correctly mapped on their associated experimental data. The optimum MLP network presents the R2-values of 0.9997, 0.9994, and 0.9978 between the predictions and experimental data for Umf, Umff, and ∆Pmax, respectively. These results justify an excellent performance of the MLP model by simultaneous predicting three important hydrodynamic parameters of the tapered fluidized bed. Figure 3

4.2.2. Evaluation using other available correlations In this section, the predictive accuracy of our proposed model is compared with some available empirical correlations in literature.

17, 22, 23, 26, 27

Table 5 summarizes the performances

of these approaches for estimation of hydrodynamic properties of the tapered fluidized bed in terms of AARD%. Our proposed model shows the best performance for prediction of Umf, with an AARD of 1.1%. Rasteh et al.’s

27

model with an AARD%=4.12 is the next accurate model,

and Sau et al.’s 23 approach is shown to have the worst results with a AARD%=49.01. The results of comparing the predictive accuracies of various approaches for the estimation of ∆Pmax are also presented in Table 5. It can be seen that the performance of our proposed MLP

network is superior to other considered correlations. The optimum MLP network estimated the ∆Pmax with AARD=0.89%, while the AARD% of the best empirical correlation is 5.77 times

larger than this value. Table 5

4.3. Parametric studies

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Effect of variations of H 0 / D0 and cos ( α ) on the minimum fluidization velocity (Umf), minimum velocity of full fluidization (Umff), and maximum pressure drop (∆Pmax) are illustrated in Figures 4 through 6, respectively. These figures represent the experimental data, prediction results of both optimum MLP model and Rasteh et al.’s

27

model. It is obvious that all

hydrodynamic properties of the tapered fluidized bed are increased by increasing of H 0 / D0 and cos ( α ).In Figures 4-6, the excellent performance of the developed MLP network in tracking the

path of change of experimental data as well as estimating the individual data points is observed. The predictive accuracies of our MLP model is better than the Rasteh et al.’s 27 (2015) model which is the best model among the previous proposed correlations. Figure 4 Figure 5 Figure 6 In the previous three figures, the excellent performances of the proposed artificial intelligent model for calculating Umf for variations in H0/D0 are justified. More results with other four dimensionless groups and the output parameters are presented in Appendix B in Supporting Information section.

4.4. Required information for using the developed MLP model Complete information of the developed MLP networks is necessary for facilitating other researchers to use the proposed model and reproduce its results. This information is as follows: -

Topology of the MLP model is 5-10-3.

-

Converged values of weights and biases of the optimum MLP networks are presented in Table 6.

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Table 6 -

Log-sigmoid transfer function was used for all neurons.

-

All of independent and dependent variables were normalized between [0 1] by using the following equation:

Vnormal =

V − Vmin Vmax − Vmin

(6)

where, V can be replaced by any independent or dependent variable, Vmax and Vmin represent the maximum and minimum values of each variables, and Vnormal is the associated normal variable. -

The developed model can be employed for simultaneous estimation of the Umf , Umff, and ∆Pmax, when the ranges of the independent variables are 372.5

Designing an efficient artificial intelligent approach for estimation of

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