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A paper in the proceedings of a conference on fluidization 245 16–17 November 2011, Johannesburg, South Africa

IFSA 2011, Industrial Fluidization South Africa: 245–256. Edited by A. Luckos & P. den Hoed Johannesburg: Southern African Institute of Mining and Metallurgy, 2011

Neural network detection of the onset of slugging in a fluidized bed

M. Carsky and M.G. Ntunka School of Chemical Engineering, University of KwaZulu-Natal, Durban

Keywords: fluidization, bubbling bed, slugging, neural network

Abstract—Depending on the rate of coalescence above a gas distributor in gas fluidized beds, bubbles of diameter approaching the column diameter can be formed. This phenomenon often occurs in columns with a large bed height to bed diameter ratio. In this event, “slugging” is said to occur. The transition from a bubbling regime to a slugging regime is accompanied by a drop in bubble/slug rising velocity. Slug formation is in most cases an undesirable phenomenon: slugs lead to a drop in efficiency of mass transfer processes due to a poor gas-solid contact and in the case of laboratory and pilot plant operation may lead to serious scaling problems. Experiments were performed in a 150 mm diameter column, with three closely sized fractions of river sand particles (diameter of 0.6–0.8 mm, 0.8–1 mm, and 1–1.4 mm). All these experiments were initially conducted using air at ambient temperature and pressure. Air velocities were chosen such that a transition from a bubbling to slugging regime could take place. Different experiments were then performed using a mixture of sand particles (29% of a fraction 0.6–0.8 mm, 23% of a fraction 0.8–1.mm, and 48% of a fraction 1–1.4 mm) at higher fluidization velocities with fully developed slugging under ambient and increased temperatures of 25, 200, 300, and 400°C. The detection system consisted of two pressure-sensing probes spaced 5 cm vertically apart. The shape of the ΔP�time trace from such a pair of pressure probes not only gives a good indication of the presence of a bubble, but also can be used to determine its velocity and size. Initially, correlations taken from the literature for bubble and slug velocities were compared with the experimental data. In turn, the experimental data was then used to train a neural network. A feed-forward back-propagation neural network was employed to model the relations among particle size, temperature, air fluidization velocity, bubble/slug size and rising velocity. Results indicate the neural network model was capable of predicting the velocities of bubbles and/or slugs and identifying the transition from a bubbling fluidized bed to a slugging bed. An improvement was evident if compared with a previously used criterion for the onset of slugging.

INTRODUCTION Early research efforts in order to understand bubble phenomena associated with gas fluidized beds appear as early as 1950.1 Bubbles in gas fluidized beds give rise to rapid and extensive particle mixing that is usually required by the particular process. In most cases, slug formation, on the other hand, is an undesirable phenomenon: slugs lead to a drop in efficiency of mass transfer processes due to a poor gas-solid contact and in the case of laboratory and pilot plant operation may lead to serious scaling problems. Slugging often occurs because of relatively small column diameters and a high aspect ratio (bed height/bed diameter). Depending on the rate of coalescence above a gas distributor, bubbles of diameter approaching the column diameter can be formed. In this event, “slugging” is said to occur. The transition from a bubbling regime to a slugging regime is accompanied by a drop in rising velocity from Ub to Us. In the case of fine particles (Geldart group A powders) the formation of round topped slugs forces the particles to move in a downward direction within the annular span between the wall and slugs. In the present work, coarser particles are used (Geldart groups B and D materials). Here, slugs in the shape of flat-ended cylinders rise in the bed while the particles “rain”

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through the slugs. At higher gas velocities these slugs often split into the so-called “wall” or “asymmetrical” slugs.

THEORETICAL

Empirical models for a bubble and slug velocity A relation between the velocity of a rising bubble in a fluidized bed and its size was found empirically from an analogy with gas bubbles rising through liquids of low viscosity. For an isolated bubble (remote from the walls) it has been shown2 that

bb gDKU =∞ (1)

The bubble velocity in Eq. (1) depends slightly on the properties of bed material, nevertheless this variation is not very large and a mean value of 0.71 is usually used for K in Eq. (1)2, over a wide range of materials and particle sizes. For bubbles in swarm conditions, the commonly accepted equation is that of Davidson and Harrison3, namely

∞+−= bmfb UUUU )( (2) From Eqs. (1) and (2) it follows for the bubble velocity in a swarm that

bmfb gDUUU 71.0+−= (3)

It may be well anticipated that aspect ratio H/D, particle size and density, bed height and bed diameter all affect the transition from bubbling to slugging regimes. Unfortunately, there is no reliable criterion for the onset of slugging in the literature taking into account all these factors. Steward5 showed that the change from bubbling to slugging regime for gas fluidized beds with H/D > 1 occurs for

2.035.0

>−

gD

UU mf (4)

Only the bed diameter appears in Eq. (4) explicitly (particle size and density are implicit because of Umf). This criterion may be taken as a rough estimate of the onset of slugging only. The velocity of symmetrical slugs (typical for Geldart group A powders) is given by12

0.35s mfU U U gD= − + (5)

For coarser particles (Geldart groups B and D materials) and higher air velocities (as in our present work) asymmetrical slugs can be expected in the slugging bed. In this case, the work of Birkhoff and Carter4 is applicable; the rising velocity of asymmetrical slugs in beds with continuous slug formation and (U - Umf ) > 0.1 m/s being then given by

0.35 2s mfU U U gD= − +

(6)

In this present work, the results of Eqs. (3), (4), (5), and (6) are compared both with experimental data and the neural model predictions.

EXPERIMENTAL All the experiments were carried out in a 150 mm diameter column.6,7 In the cold work used to develop the probe and software, three closely sized fractions of river sand particles (0.6–0.8 mm, 0.8–1 mm, and 1–1.4 mm, with the minimum fluidization velocity Umf = 0.321, 0.431, and 0.511 m/s, respectively) were fluidized using air. Air velocities were chosen such that a transition from a bubbling to slugging regime could take place. Further input for the neural network training over a sufficiently wide interval was obtained from experiments performed at higher fluidization velocities with fully developed slugging. These experiments used a mixture of sand (29% of a fraction 0.6–0.8 mm, 23% of a fraction 0.8–1.mm, and 48% of a fraction 1–1.4 mm) at temperatures of 25, 200, 300, and 400°C. The corresponding values of the minimum air

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fluidization velocity Umf were 0.427, 0.379, 0.352, and 0.329 m/s, respectively. The bed height H was fixed at 0.5 m. In the warm experiments, the bed was heated to various temperatures with hot flue gases from an LPG burner. The detection system, shown in Figure 1, consisted of two pressure-sensing probes immersed in the bed and spaced 5 cm vertically apart. As previously shown8,9 the shape of the ΔP�time trace from such a pair of pressure probes, not only gives a good indication of the presence of a bubble, but also can be used to compute its velocity and size. The signals from the pressure probes were processed in real time using a data acquisition system. Further details of the experimental set-up, including the bubble detection system and the logic/computing algorithms are given elsewhere.6,7

Figure 1. Bubble detection system

NEURAL NETWORK FOR BUBBLE PHENOMENA The development of the first artificial neural networks was motivated by biological nerve systems which consist of densely connected networks of real neurons. An individual biological neuron has only limited computation ability but interesting computational properties emerge when several neurons are combined together in various ways. This concept is used in artificial neural nets. An artificial neural network is typically a massively parallel interconnected network of “artificial neurons” (also called processing elements, nodes or units). The way in which these processing elements are mutually interconnected determines the network architecture. In this work we have used the most common type of neural network architecture, the feedforward network (often called backpropagation network or Multi-Layer Perceptron). In a feedforward network each processing element has several inputs and one output. The inputs are combined and then modified by the activation function and passed to the output of the processing element. A feedforward neural network is made up of layers of processing elements (see Figure 2). The input layer acts as an input data holder which distributes inputs into the network. The data from the input layer are propagated through the network via the interconnections to processing elements in the first hidden layer where they are combined and modified by activation functions. The signals keep proceeding in this way from layer to layer until they reach the output layer. An example of the structure of a feedforward neural network with one input layer, one hidden and one output layer is illustrated in Figure 3. This network would be sometimes called a (3-5-1) feedforward network, referring to the numbers of neurons in the input, hidden, and output layers, respectively.

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x1

x2

x3

x0 (Bias)

Output

ySummation

Tran

sfor

mat

ion

Figure 2. A processing element in the hidden layer of a neural network.

Output Layer

HiddenLayer

Input Layer

Figure 3. An example of a 3-5-1 feedforward neural network.

A continuous multivariable function F(x) is approximated in neural network by a selected function f(x,w) for a fixed number of input variables

x = (x0; x1,...,xl) (7)

where w is an array of weights, x0 = 1 is a constant input called “bias” used to simulate thresholding effects in the neuron, xi, i = 1,...,l are neural network inputs, and l is the number of input nodes.

The output from the hidden layer is

y = (y0; y1,...,ym) (8)

where y0 = 1 is a constant output from the bias neuron, m is the number of processing elements in the hidden layer, and yj is an output from the jth processing element of the hidden layer expressed by Eq. 9:

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y f w xj ji ii

l= ∑

=( ),0

0 j = 1,...,m (9)

where w0ji is a weight associated with a connection between the ith processing element in the input layer and the jth processing element in the hidden layer. For the bias the weight w0j0 is equal to 1.

The expression for the output layer of the neural network is similar to that of eq. 8, only the signal from the bias neuron does not exist:

z = (z1, z2,...,zn) (10)

where

z f w yk kj jj

m= ∑

=( ),1

0 k = 1,...,n (11)

n is the number of output neurons, and w1kj is the weight associated with a connection between the jth processing element in the hidden layer and the kth processing element in the output layer. For the bias the weight w1k0 is again equal to 1.

The activation function f(.) is mostly chosen to be a sigmoidal function f(x) = 1/(l+e-x) or a symmetric sigmoidal function f(x) = tanh(x).

The purpose of developing a neural model is to devise a network (set of formulae) that captures the essential relationships in the data. These formulae are then applied to new sets of inputs to produce corresponding outputs. This is called generalisation, but before generalisation is possible a training set of data is needed in order to fit the model parameters. The problem of neural network learning, in effect, reduces to determining the set of weights in Eqs 9 and 11

w = (w0ij, w1kj) , (12)

that provides the best approximation to multivariable function F, when trained on an “example” data set.13 Neural network training leads to finding values of connection weights that minimise differences between network outputs z = (z1,...,zn) and the target values d = (d1,...,dn) specified by a teacher. An objective function is specified which is a measure of how closely the outputs of the network match the target values from the training set of data. The global error E is minimised by modifying the weights w by propagating the gradient of the objective function with a momentum term back through the network to improve the objective function:

( ) | ( )Δ ΔwEw

m wji tjit ji t

00 1

01= − +− −λ

∂∂

(13a)

for a hidden layer, and

( ) | ( )Δ ΔwEw

m wkj tkjt kj t

11 1

11= − +− −λ

∂∂

(13b)

for output layer. In Eq. 13 λ is a learning coefficient, m is a momentum coefficient, and t is an iteration

counter. The partial derivatives ∂E/∂wji0 and ∂E/∂wkj1 are evaluated locally by back propagating the global error E backwards from the output to the input layer. A network is said to generalise well when the input-output relationship, found by the network, is correct for input/output patterns of data not used in training the network.

A feed-forward back-propagation neural network10,11 was used to model the relation between inputs (particle size, air velocity, and temperature) and outputs (bubble velocity and size). As neither particle sizes nor temperatures were distributed uniformly in their domains a fuzzy encoding was employed to facilitate the neural network to develop the necessary generalisations.

Particle size was represented by three input neurons A, B, and C for fractions 0.6–0.8mm, 0.8–1 mm, and 1–1.4 mm, respectively. Each neuron was thus carrying information about a relative proportion of the corresponding particle size in the fluidized bed.

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Temperature was represented by fuzzy values 25°C, 200°C, 300°C, and 400°C defined on overlapping intervals as illustrated in Figure 4. Each fuzzy value had its own neural network input. For example, temperature 200°C was encoded as a quadruple (0, 1, 0, 0) and 250°C as (0, 0.5, 0.5, 0). This fuzzy encoding provided a smooth transition from one temperature to another on the input side of the neural network thus helping the network to generalise and find meaningful output even for temperatures that were not used for training.

100 200 300 400 500T

0.5

1T25 T200 T300 T400

Figure 4. Membership functions of fuzzy temperature.

The neural network consists of 8 inputs, the first seven of which are summarised in Table 1. The eighth input, the air excess velocity U – Umf, was scaled linearly into the interval [-1, 1]. Neural network outputs Ub and Db were subject first to a hyperbolic transformation and then scaled into the interval [-0.8, 0.8]. This transformation had the desired effect of spreading the data more evenly over the working interval and thus facilitated the training of the neural network.

Table 1. Neural network inputs representing particle fractions and temperature.

# Particle size Temperature

A B C 25°C 200°C 300°C 400°C

1 1 0 0 1 0 0 0

2 0 1 0 1 0 0 0

3 0 0 1 1 0 0 0

4 0.29 0.23 0.48 1 0 0 0

5 0.29 0.23 0.48 0 1 0 0

6 0.29 0.23 0.48 0 0 1 0

7 0.29 0.23 0.48 0 0 0 1

Both hidden and output neurons used a tanh(.) activation functions. Several neural networks

with differing numbers of hidden neurons were mutually compared; and the network with 5 hidden neurons was eventually chosen because it exhibited the best generalisation capability. This network was trained 20 more times and after each run the training was stopped when a root mean square (RMS) error, evaluated from 10% of randomly selected testing samples, reached its minimum. In this way, a group of 20 networks trained to the best generalisation capabilities was generated. The neural network with the smallest RMS error consisting of 8 inputs, 5 hidden neurons, and 2 outputs (NN{8-5-2}) proved to be the most accurate for our purposes and was eventually chosen as the final one.

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RESULTS For a bed of given particle size (with corresponding Umf) approximately 50 readings of bubble size and velocity were taken for each value of excess velocity. The mean values of Ub and Db were determined and used for further calculations.

In Figures 5–11, experimentally determined values of bubble/slug rising velocities, predictions by the neural network (thick solid line), calculated bubble velocities of Eq. (3) (thin solid line), symmetrical slug velocities of Eq. (5) (thin dashed line), and asymmetrical slug velocities of Eq. (6) (thick dashed line) are plotted against the value of (gDb)0.5.

Figure 5. Bubble (slug) velocity for sand particles 0.6–0.8 mm at 25°C: measured velocity, bubble velocity (Eq. 3), asymmetrical slug velocity (Eq. 6),

symmetrical slug velocity (Eq. 5), neural network prediction, criterion for the onset of slugging (Eq. 4).

The detection system is not able to distinguish between slugs and bubbles. This is clear from

the measurement results where slugs are present having sizes (vertical cut length) greater than the bed diameter of 150 mm. The results of Figures 5–11 show a fairly good correlation between the experimental data and that provided by the neural network, in both the bubbling and slugging regimes. Of particular note is the indication of the transition between the two regimes of a fluidized bed – from bubbling to (asymmetrical) slugging bed. In terms of (gDb)0.5, overestimation is maximally 7.2%. As expected for the particles used symmetrical slugs do not appear in the bed (compare experimental data with equations 5 and 6). When considering the scatter of the experimentally measured bubble parameters and the limited number of data points available for training the neural network, this appears very promising. For purposes of comparison, Eq. (4) (as a criterion for the onset of slugging5) is included in Figures 5–7 (dashed vertical line). It is noted that this criterion constantly underestimates the onset of slugging.

Figures 8–11 show the effects associated with a bed consisting of a mixture of sand particles (0.6–1.4 mm) at higher fluidization velocities and at temperatures ranging from 25°C to 400°C. For these experimental conditions, the bed is in a fully developed slugging regime, far from the transition to the bubbling regime. Equation (6) here does not fit the measured slugging data as closely as in cases of individual size fractions. This is due perhaps to the uncertainty in the determination of Umf for a bed having a wide particle size distribution. Taking into account the accuracy of measuring the bubbling/slugging phenomena in a fluidized bed in general, the agreement nevertheless remains satisfactory. The neural network model, on the other hand, predicted the slug velocities fairly well in all instances (RMS = 0.221).

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253

Figure 8. Bubble (slug) velocity for sand mixture 0.6–1.4 mm at 25°C: measured velocity, bubble velocity (Eq. 3), asymmetrical slug velocity (Eq. 6), symmetrical slug velocity (Eq. 5), neural network prediction.


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As a neural network does not contain any information about the mechanism that governs the simulated process it cannot provide any reasonable extrapolation beyond the range of the training data (i.e. the bed material used, the bed height, the column diameter, and the range of temperatures). Moreover, a sigmoidal-shaped activation function limits the outputs of processing elements, thus keeping the output variables within the bounds of scaling.

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CONCLUSIONS A feed-forward back-propagation neural network with 8 inputs, 5 hidden and 2 output neurons (NN{8-5-2}) was employed to account for the relations among particle size, temperature, air fluidization velocity, bubble size and rising velocity in a fluidized bed. In addition to confirming a relatively good correlation between experimental data taken from both bubbling and slugging regimes (RMS=0.221 for all the data) the neural network model also identified the transition between the two regimes. An improvement of the previous criterion used in establishing the onset of slugging5 was also evident (a deviation of 1.56% versus 9.4% for particles 0.6–0.8 mm, 3.2% versus 7.2% for particles 1–1.4 mm, and unchanged deviation of 7.2% for particles 0.8–1 mm). Confirmation of the reliability of the experimental data used was based on the observation that slugs should occur when the diameter of rising bubbles approaches the column diameter. This was the case for ratios Db/D above 0.99. At higher fluidization velocities and temperatures, the bed was fully in slugging regime.

Previous models (Eqs. (3), (5) and (6)) are based on empirical relations and as such cannot be used to predict the onset of slugging. The neural network model adopted here addresses this problem with the result that the transition from bubbling to slugging regimes has been identified. As a neural network is insensitive to the exact mechanism that governs the simulation model, extrapolation beyond the domain of the training data is not practically nor theoretically feasible.

The present work shows that neural network modelling can be used for a prediction of the onset of slugging, and for the determination of bubble/slug velocities and sizes. Slugging is rather typical for laboratory-scale units; nevertheless an expert system for slug/bubble phenomena in a fluidized bed can be useful in the design of such units. The present model is limited by a single bed material (sand), range of particle sizes 0.6–1.4 mm, temperatures 25–400°C, and constant bed height and diameter. To develop an expert system for slug/bubble phenomena in a fluidized bed the future work should include effects of other materials, column diameters and bed heights.

ACKNOWLEDGMENT The financial support of this work from ESKOM through the TESP grant is gratefully acknowledged.

NOTATION d array of target values D column diameter, m Db bubble diameter, m E mean root square error g gravitational acceleration, m/s2 H bed height, m m momentum coefficient in Eqs 13a and 13b ΔP pressure drop, kPa T temperature, °C U air velocity, m/s Ub bubble velocity in a bubbling bed, m/s Ub ∞ velocity of an isolated bubble, m/s Umf minimum fluidization velocity, m/s Us slug velocity, m/s w array of weights of neural network interconnections x array of inputs to neural network x0 ,y0 bias y array of hidden layer outputs z array of neural network outputs Greek Letters λ learning coefficient in Eq. 13a and 13b

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REFERENCES 1. Davidson J.F. & Harrison D. Fluidisation. Academic Press, 1971. 2. Davis R.M. & Taylor G.I. Proc. Royal Soc. Ser., A200, 1950, 375. 3. Davidson J.F. & Harrison D. Fluidised Particles. C.U.P. 1963, Cambridge. 4. Birkhoff G. & Carter D. J. Rat. Mech. Anal., 6, 1957, 769. 5. Steward P.S.B. Fluidisation: some hydrodynamic studies. PhD Dissertation, Cambridge 1965. 6. Narsingh U. The Development of a Method for Monitoring and sampling from Gas Bubbles in a

Fluidised Bed Coal Combustor. MSc Thesis , University of Durban-Westville, Durban, South Africa, 1994.

7. Judd M.R., Carsky M. & Narsingh U. The Fuzzy pooling of some experimentally determined knowledge about bubble size and rise velocity and also the CO2/CO content of bubbles during fluidised air gasification. Fluidisation VIII, Tours, France, 1995.

8. Atkinson C.M. & Clark N.N. Powder Technology, 54, 1988, 59. 9. Sitnai O. Chem. Eng. Sci., 37, 1982, 1059. 10. Haykin S. Neural Networks – A Comprehensive Foundation. McMillan, New York, 1994. 11. Carsky M. & Hajek M. Neural network simulation of the transition from a bubbling to slugging

fluidised bed. CHISA, 23-28 August 1998, Prague, Czech Republic. 12. Hovmand S. & Davidson J.F. Trans. Inst. Chem. Eng., 46, 1968, T190. 13. Morris A.J., Montague G.A. & Willis M.J. Trans. Inst. Chem. Eng., 72, Part A, 1994, 3-19.

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