Artificial Neural Network and Neuro-Fuzzy Methodology for Phase

Article pubs.acs.org/IECR

Artificial Neural Network and Neuro-Fuzzy Methodology for Phase Distribution Modeling of a Liquid−Solid Circulating Fluidized Bed Riser Shaikh A. Razzak,*,† Syed M. Rahman,‡ Mohammad M. Hossain,† and Jesse Zhu§ †

Department of Chemical Engineering, and ‡Center for Environment & Water, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia § Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Ontario N6G 5B8, Canada ABSTRACT: Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) modeling techniques are applied to study the radial and axial solids holdup distributions in a liquid−solid circulating fluidized bed (LSCFB) system. The modeling process is based on the experiments that were conducted using 500 μm size glass beads as solid phase. The radial nonuniformity of the solids holdup is observed under different superficial liquid velocities at superficial solids velocity of 0.95 cm/ s and auxiliary liquid velocity of 1.4 cm/s at four axial locations (H = 1.0, 2.0, 3.0, and 3.8 m above the distributor). The effects of different operating parameters such as auxiliary and primary liquid velocities and superficial solids velocity on radial phase distribution in different axial positions of the riser are considered in the model development and analysis. The adequacy of the developed models is investigated by comparing the model predicted and experimental solids holdup data obtained from the pilot scale LSCFB reactor. Radial nonuniformity of the solids holdup is observed under different superficial liquid velocities at superficial solids velocity of 0.95 cm/s and auxiliary liquid velocities of 1.4 cm/s at four axial locations (H = 1, 2, 3, and 3.8 m above the distributor). The cross-sectional average solids holdup in axial directions is compared to the output of the two models. The model outputs show good agreements with the experimental data and reasonable trends of phase distributions. The correlation coefficient values of the predicted output and the experimental data are 0.95 and 0.96 for ANFIS and ANN models, respectively.

1. INTRODUCTION Over the years, the fluidized bed systems have found numerous applications in different areas of chemical and biochemical process industries due to their efficient operation. Recently, the liquid−solid circulating fluidized bed (LSCFB) reactors have received growing interest in wastewater treatment, desulfurization of petroleum products, and biochemical porcesses.1,2 One common characteristic of these systems is the use of lighter and smaller particles that entrain easily in the fluidized beds.3 Such characteristic allows the solid particles circulation between the riser and the downer columns at higher rates as compared to conventional fluidized beds. The circulation facilitates the regeneration of the solid particles (catalysts, adsorbents, etc). As a result, steady-state process operation with enhanced mass transfer between phases and high throughputs can be achieved. In a typical LSCFB, the solid particles move upward with the influence of upward liquid flow in the riser column. The entrained particles are then collected and separated at the top of the riser column (separator). Finally, the collected particles are recirculated back to the riser via the downer column.4,5 Generally, LSCFBs operate at high liquid velocities where particle entrainment is very common, especially for the processes that require continuous solid particles/catalysts regeneration to maintain steady-state process operations. In most of the cases, the deactivated catalysts, biomedia, ion exchange resins, or adsorbents are regenerated by circulating them between the main reactor/contactor (riser) and the regenerator (downer) using a closed and continuous loop.6−8 The reaction/adsorption processes are accomplished in the © 2012 American Chemical Society

riser, while the regeneration/desorption is carried out in the downer column. To ensure efficient process operation, better understanding of the hydrodynamics of both the riser and the downer columns is essential. The hydrodynamic analysis of a LSCFB offers information about the flow characteristics under the wide operating conditions and different parameter values. The present research group reported solids holdup distributions in both radial and four axial locations in the riser sections of LSCFBs.4,5 It was observed that relatively insignificant nonuniformity appears only for very heavy particles under a narrow range of operating conditions.9,10 Because of this reason, the axial flow structure in LSCFBs is considered completely different from the consistently nonuniform behavior of gas solid circulating fluidized bed. Some other research articles available in the open literature also reported solids holdup in various fluidized bed systems. In general, there are two common approaches in studying the hydrodynamics of LSCFBs: (i) experimental and (ii) modeling. Although the experimental studies are essential to establish the viability of a given technology, it requires relatively high capital investments. Moreover, the experimental approaches are time-consuming. To minimize the cost and time required in experimental studies, it is common practice of using suitable correlations/ models to predict the hydrodynamics of a fluidized bed system under given conditions. For example, Lahiri and Ghanta11 Received: November 29, 2011 Accepted: August 29, 2012 Published: August 29, 2012 12497

dx.doi.org/10.1021/ie301746y | Ind. Eng. Chem. Res. 2012, 51, 12497−12508

Industrial & Engineering Chemistry Research

Article

time delayed neural networks (TDNN) are typically designed on the basis of the RN topology. A typical feed-forward neural network consists of two inputs, one output, and one hidden layer, shown in Figure 1. The input

developed an Artificial Neural Network (ANN) model to predict the holdup in slurry pipelines by considering the solid concentration, particle diameter, slurry velocity, pressure drop, and solid and liquid properties as inputs. ANNs are biologically inspired systems consisting of massively connected processing elements organized in layers and tied together with weighted connections. Generally, the ANN is designed by numericallearning-based algorithms and can be “trained” to approximate virtually any nonlinear function to a required degree of accuracy.12 Because of this capability, the ANNs are considered as a class of universal approximators. The ANN as a representative of nonlinear modeling is also considered to design and scale-up fluidized beds rather than relying on the concept of uniform flow and one-dimensional steady-state modeling. Nakajima et al.13 investigated the performance of the ANN model to approximate the dynamic behavior of pressure fluctuation in a circulating fluidized bed. Otawara et al.14 proposed an ANN approach to model the nonlinear behavior of bubble motion in a three-phase fluidized bed. On the other hand, neuro-fuzzy systems represent a class of hybrid intelligent systems combining the main features of ANN with those of fuzzy logic systems. It aims to avoid difficulties encountered in applying fuzzy logic model for the systems represented by numerical knowledge, or conversely in applying ANN for the systems represented by linguistic information.15 The present study is focused on a detailed study of the hydrodynamic behavior of a LSCFB using a high density (2500 kg/m3) and large glass bead particles under a wide range of operating conditions. Toward this end, Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy System (ANFIS) models were developed using pilot scale LSCFB experimental data. The developed models were validated using a different set of experimental data of the same LSCFB. The solids holdup predicted by the developed ANN and ANFIS models was evaluated by various statistical indicators such as mean squared error (MSE), root mean square error (RMSE), mean absolute error (MAE), and R-square value. Finally, both the ANN and the ANFIS models were employed to predict solids holdups with the change of operating parameters such as primary, secondary liquid flow rates and superficial solids velocity of the riser of both reactors, and the results are verified with the experimental data.

Figure 1. Typical architecture of a simple feed-forward neural network having two inputs, one output, and one single hidden layer.

layer is not associated with any calculation and directly transfers the inputs to the first hidden layer. The other connections carry real valued weights, which modify the strength of signals carried from other nodes. The nodes of hidden layers and output layer receive the sum of the weighted inputs of the previous layer and the bias as inputs. The corresponding activation function transforms the incoming input and broadcasts the output to the nodes of the next layer or to the environment. The output of each node of the hidden layer can be given by: 1 zk = f (∑ wikxi + w0k) = f (q) = 1 + e −q (1) i where wik is the connection weight from the ith input node to the kth hidden node, and w0 is the bias. In the above-mentioned example, a logistic sigmoid function is considered as the activation function of the hidden node.

3. THE ANFIS APPROACH ANFIS is developed to serve as a basis for constructing Fuzzy Inference System (FIS) with suitable membership functions, and its architecture is obtained by embedding the FIS into a framework of ANN.16 A simple Takagi−Sugeno-type ANFIS model developed by Takagi and Sono17 for two inputs (x and y) and one output is given in Figure 2. The architecture and functions of each layer are described below.

2. THE ANN APPROACH The topology of ANN refers to the ordering and organizing of the nodes from the input layer to the output layer and the way the nodes and the interconnections are arranged within the layers of a given network.15 The selection of any particular topology depends on the type of concerned problems. Depending on the data processing nature, ANN topologies can be classified into feed-forward and recurrent architectures. A network with feed-forward architecture possesses nodes that are hierarchically arranged in layers starting with the input layer and ending with the output layer, and, between, a number of hidden layers provide most of the network computational power.15 The feed-forward topology is associated with the backpropagation learning (BPL) algorithm. The topology is used by the multilayer perceptron network and the radial basis function network. Yet the recurrent networks (RN) allow for feedback connections among their nodes and are structured in such a way as to permit storage of information in their output nodes through dynamic states, hence providing the network with some sort of memory.15 The Hopfield network and the

Figure 2. ANFIS architecture. 12498



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⎡ φ1 ⎤ ⎢ ⎥ ⎢ φ2 ⎥ ⎢⋮⎥ φ = ⎢ ⎥, ⎢⋮⎥ ⎢ ⎥ ⎢⋮⎥ ⎢⎣ φn ⎥⎦

First Layer. All nodes of this layer generate membership grades of input variables, which vary between 0 and 1. The node stores the parameters to define a bell-shaped membership function (μ). Its function can be written as follows:

Oi1 = μ Pi(x)

(2)

and Oi1+ 2 = μQ i(y)

(3)

⎧ 1 ⎛ x − c ⎞2 ⎫ ⎟ ⎬ μ(x) = exp⎨− ⎜ ⎩ 2⎝ σ ⎠ ⎭

(4)

⎡ w1̅ w1̅ x1 w1̅ y1 ⎢ ⎢ w1̅ w1̅ x 2 w1̅ y2 ⎢ ⋮ ⋮ ⋮ A=⎢ ⎢⋮ ⋮ ⋮ ⎢ ⋮ ⎢⋮ ⋮ ⎢w w x w y 1̅ n 1̅ n ⎣ 1̅

where i = 1, 2; x and y are the inputs; Pi or Qj are the linguistic labels; and c and σ are the mean and variance of the membership function, respectively, which are also known as premise parameters. Second Layer. The node of this layer performs connective operation “AND” and any other T-norm within the rule antecedent to determine the corresponding firing strength. The node function follows: O1,2 i = μ Pi(x)*μQ i(y) = w1, i

= μ Pi(x)*μQ i(y) = w2, i

(5)

for

i = 1, 2

∇δ = − η

wi = w̅ ∑ wi

for

i = 1, 2

(6)

(7)

(8)

where zm = ak + bkx + cky; a, b, and c are constants; and i = 1, 2. Fifth Layer. The final node represents an addition node, and the output is calculated as follows: 2

O5 =

∑ wi̅ (ai + bix + ciy) = φ i=1

(9)

where ϕ = model output. In ANFIS architecture, if the premise parameters are fixed, then the output of the whole system is a linear combination of the consequent parameters.18 Finally, the output can be expressed as the following matrix format for n number of training samples.

φ = AP

(11)

∑ni = 1(Ti

− φi) , T = target, and ϕ 2

4. EXPERIMENTAL SETUP AND METHODOLOGY For model training (development) and model validation (testing), a pilot scale LSCFB system is considered. The experimental data used for this investigation were developed by the leading author of this Article using the experimental facilities available at the Particle Technology Research Centre (PTRC), The University of Western Ontario, Canada. A schematic diagram of the experimental setup of the LSCFB is shown in Figure 3. The LSCFB consists of two main sections: a riser and a downer, both made of Plexiglas. The riser is 5.97 m tall and 0.0762 m (3”) in diameter, while the downer is 5.05 m tall and 0.2 m (8”) in diameter. A gas−liquid−solid separator is located at the top of the riser to separate out the solids from the liquid flow. A solid circulation rate measurement device is located near the top of the downer. There are two liquid distributors at the bottom of the riser, the main liquid distributor, made of seven stainless steel tubes occupying 19.5% of the total riser cross section and extending 0.2 m into the riser, and the auxiliary liquid distributor, a porous plate with 4.8% opening area at the base of the riser. Solids circulation is maintained in the LSCFB system by appropriate pressure balance between the riser and the downer. Solid particles are moved up in the riser mainly by the liquid flow assisted by the gas flow. Liquid pumped from the reservoir is divided into two streams with the main flow entering the pipe distributor and the other going to the auxiliary liquid distributor. The auxiliary liquid flow is employed to facilitate the flow of solid particles from the downer to the riser, with the main purpose of controlling the solids circulation rate and acting as a nonmechanical valve. The combined effects of both primary and auxiliary liquid flow produced the total liquid flow, which carries the solid particles up in the riser. When the

Fourth Layer. In this layer, the output is obtained by multiplying the normalized firing strength of the rule by the rule output of Takagi−Sugeno type. The output of the node follows: Oi4 = wz i̅ i

∂E ∂δ

where η = learning rate, E = = model output.

Third Layer. The node of this layer performs normalization to determine the relative strength of each rule. The output follows: Oi3 =

w2̅ w2̅ x1 w2̅ y1 ⎤ ⎥ w2̅ w2̅ w2̅ y2 ⎥ ⎥ ⋮ ⋮ ⋮ ⎥ ⋮ ⋮ ⋮ ⎥ ⎥ ⋮ ⋮ ⋮ ⎥ w2̅ w2̅ xn w2̅ yn ⎥⎦

The unknown matrix P can be estimated with the help of the least-squares method. The gradient descent technique is usually considered for tuning the architecture.16 It indicates that the premise and consequent parameters are learned with the help of gradient descent and least-squares method, respectively. The overall error (E) can be expressed in terms of δ for a premise parameter (δ):

and O2,2 i

⎡ a1 ⎤ ⎢ ⎥ ⎢ b1 ⎥ ⎢ c1 ⎥ P = ⎢ ⎥, ⎢a2 ⎥ ⎢ ⎥ ⎢ b2 ⎥ ⎣⎢ c 2 ⎦⎥

(10)

where 12499



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The solids circulation and liquid flow rate can be controlled independently by adjusting the ratio of auxiliary and primary liquid flow. The solid particles entrained in the solid−liquid separator at the top of the riser are returned to the downer by gravity. During the settling, solids particle passes through the solids circulation rate measuring device, which is a special section of the downer located near the top of the downer and just below the solid returning pipe connecting to the riser (Figure 3). A vertical plate divided this section into two parts, and two half butterfly valves were installed at each end of this section. During the measurement, the butterfly valve needs properly flipping from one side to the other so solids particles can be accumulated on one side of the measuring section for a given time period. The solids circulation rate is measured using the following equation: A

Gs =

d hρε s s 2

tA r

(12)

where Gs is the solid circulation rate, h is the height of the accumulated particle (m), t is the accumulation time (s), ρs (kg/m3) is the solids density, εs is solids holdup, Ad is crosssectional area of the downer, and Ar is cross-sectional area of the riser of the accumulated solid particles. Superficial solids velocity was estimated by dividing Gs by the density of the particles: Figure 3. Schematic diagram of the LSCFB system.

Us =

superficial liquid velocity is above a critical velocity, liquid and particles move concurrently upward to the top of the riser. Entrained particles in the riser, collected in the liquid−solid separator shown in Figure 3 at the top of the riser, are returned back to the downer after passing through the solids circulation rate measuring device, which is located near the top of the downer. Particles are separated by the large conical shape cylindrical liquid−solid separator due to gravity settling and returned to the downer by maintaining appropriate pressure balance. Liquid then returned from the top of the liquid−solid separator and the downer to the liquid storage tank. Solid particles are transported out from the top of the riser to the downer during the operation. It is necessary to continuously feed solid at the inlet of the riser to maintain appropriate pressure balance and optimum solid circulation rate. Auxiliary liquid flow is responsible for mobilizing solid particles from the base of the riser to ensure the continuous solid feed from the downer to the riser and serve as a control device, also called a nonmechanical valve. Usually depending on the geometry when the auxiliary liquid flow rate is zero, no solid particles can circulate no matter how high the primary liquid velocity, because no solids from the downer can flow down to the bottom of the riser. This is due to the hydrostatic pressure on those particles and also the wedging effect (for irregular shape particle only), which hold the particles in a compact form. These particles are loosened and pushed up to the tip of the pipes of the primary liquid distributor by auxiliary liquid flow. The combined effect of both primary and auxiliary liquids flow makes solids particles move and be carried up to the top of the riser. With a higher auxiliary liquid flow rate, more solids are fed to the riser, and, as a result, the solids circulation rate is increased. The solids circulation rate is mainly controlled by auxiliary and primary liquid flow.

hρ (Ad /2)εs Gs h(Ad /2)εs = s = ρs tρs A r tA r

(13)

An electrical resistance tomography (ERT) system used to do the experiments was manufactured by En’ Urga Inc., U.S. The ERT system consists of a sensor and PC-based data acquisition system. The inner diameter of the sensor is built in 16 equally spaced electrodes. These electrodes simultaneously send current and receive voltage signals. AC currents were applied to the electrodes. For each driving current, the ERT measures the electrical potential distribution through the electrodes flush mounted on the wall. During each operating frame, multiple driving currents are sequentially fed into a pair of neighboring electrodes. The voltages are measured on all other electrodes except the current injecting electrodes pair. The way in which the driving pair is switched and the voltage measurements are collected varies. With the applied current source, electrical potential distributions are generated within the fluids and the wall. Electronic circuits capture voltages between the electrodes and send them to a PC-based data acquisition system. The saved data are processed with an image reconstruction algorithm, which provides the phase distributions occurred in the experiments. The ERT system can provide phase distributions of a multiphase flow by measuring the peripheral resistance combinations, and reconstructing cross-sectional conductivity distributions for a given time. For a dispersed multiphase flow, ERT is able to convert the conductivity distributions to local phase holdups of the phases: electrically conductive phase and electrically nonconductive phase or phases. In this study, the former corresponds to water, that is, the liquid phase, while the latter to air and/or particles, that is, the gas and/or solid phase. Proper calibration is required to reduce the measurement error in converting the conductivity data to phase concentrations. Calibration was done for each 12500



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the standard deviation is small as compared to the mean value. The ranges are 5.6−35.0 cm/s for superficial liquid velocity Ul and 0.2−0.1346 for solids holdup, respectively. Skewness is a measure of the asymmetry of the data around the sample mean, and its negative value indicates that the data are spread out more to the left of the mean than to the right. On the other hand, the positive value of skewness means that the data are spread out more to the right. If the value of skewness is zero, it can be concluded that the distribution is normal distribution or any perfectly symmetric distribution. The skewness values of Ul and solids holdup found in this study revealed that these are spread out more to the left of the mean, and there is no clear indication that the data are generated from any perfectly symmetric distribution process. Kurtosis reveals the outlier-prone characteristics of a distribution, and the kurtosis of the normal distribution is 3. The kurtosis values of the data indicate that Ul and solids holdup are less outlier-prone than the normal distribution processes.

experiment by changing the conductivity of the liquid adding sodium chloride. Before the conversion, the local conductivity is first nondimensionalized using the equation: σ − σ1 σ= m σ0 − σ1 (14) where σm denotes the estimated local conductivity, σ1 denotes the local conductivity when the pipe is full of single liquid phase, and σ0 denotes the local conductivity when the pipe is full of gas or solid or both phases. The conductivity of the first phase (σ1) can be found easily with available commercial conductivity meters, while the local estimated mixture conductivity (σm) is determined from the pixel conductivity of ERT image data. The Maxwell relation is employed to convert the local conductivity to the local solid holdup: ε=1−

3σ * 2 + σ*

(15)

6. DEVELOPMENT OF THE ANN MODEL Identifying an appropriate topology is very important for developing an ANN model with reasonable generalization capability. To select the appropriate topology, the network, different number of hidden layers and neurons in each layer, transfer functions, numbers of iterations, and training algorithms were systematically considered. Finally, the desired model is developed using three neurons in two hidden layers. The transfer function for both the hidden layers was logsigmoid that squashes the input into 0 to 1. The values of the weight and bias of the considered network were updated with the help of an algorithm based on the Levenberg−Marquardt optimization technique.21,22 In this optimization method, mean squared error (MSE) of the network was used as performance measure. The considered learning rate and initial number of epochs were 0.001 and 100, respectively. The best performing model was obtained at epoch number 61. The mean prediction using ANN model is found to be within an error margin of 0.0016.

The cross-sectional area of the riser is divided equally into six sections (distributed radially, centered at r/R = 0.2034, 0.492, 0.6396, 0.7615, 0.8641, 0.9518) to measure the zone-based average solids holdup. Cross-sectional average solids holdup was also measured using an optical fiber probe. A good agreement was observed between all three measurement techniques.4,9

5. ANALYSIS OF EXPERIMENTAL DATA For reliable and effective modeling, it is essential to assemble experimental data for a wide range of operating parameters. In this investigation, the height (H), auxiliary liquid velocity (Ua) and primary liquid velocity (Up), and the solids holdup in different radial positions data are considered as inputs to predict the solid-phase holdups at the desired height for different operating auxiliary and primary liquid velocities.20 Tables 1 and 2 describe the characteristics of the input and Table 1. Values of Experimental Operating Parameters of the Pilot Scale LSCFB Ua (cm/s)

Ul (cm/s)

H (m)

r/R

1.4 2.8 4.2 5.6

5.6 8.4 11.2 22.4 35.0

1 2 3 3.82

0 0.204 0.49 0.64 0.76 0.86 0.95

7. DEVELOPMENT OF THE ANFIS MODEL To maintain the simplicity of the underlying models and reduce the complexity of computation needed for building model, the selection procedure is important to determine the appropriate inputs among all of the available candidate inputs. In this modeling work, all of the mentioned inputs in section 3 were considered for building the ANFIS model to predict solid-phase holdups because those inputs are the fundamental influential factors to describe the solid-phase holdups. In ANFIS, the leastsquares method leads to fast training, and the gradient descent method slowly changes the underlying membership function that generates the basis functions for the least-squares methods.23 Therefore, it can be expected that ANFIS is likely to produce satisfactory results even after a few epochs of training. The ANFIS model shows good performance, but sometimes produces spurious rules, which makes little sense.24 A fuzzy model with a large number of rules can reduce generalization capability.25 This problem can be solved by using an initial FIS generated by clustering techniques such as fuzzy C-means (FCM). Dunn26 developed FCM, and Bezdek27improved it. The clustering technique determines only the important rules and increases generalization capability of FIS. It reduces

Table 2. Description of Ul and Solids Holdup statistical parameters

Ul (cm/s)

solids holdup

max min standard deviation average kurtosis skewness

35.0 5.6 5.6 17.9 −1.41 0.22

0.1346 0.0212 0.0212 0.1 −1.18 0.22

output data. Table 1 shows the values of Up, Ua, H, and r/R for which measurements were taken. Table 2 reports statistical parameters. It shows that the data are narrowly distributed as 12501



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computational needs and ensures speedy model development. The next few paragraphs will briefly elaborate the concept of FCM. FCM clustering algorithm is the soft extension of the traditional C-means, which considers each cluster as a fuzzy set, while a membership function measures the degree to which each training vector belongs to a cluster.28 As a result, each training vector may be assigned to multiple clusters, which can partly overcome the drawback of dependence on initial partitioning cluster values in hard C-means.29 In this method, the following objective function is minimized: n

Jm =

K

∑ ∑ Uijmx || xi − kj ||

for

1≤m

Artificial Neural Network and Neuro-Fuzzy Methodology for Phase

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