Prediction of flooding and pressure drop in a spinning cone column using neural networks

Spinning cone column as a distillation tower has various applications in food industry. It has a complex geometric structure which makes the modeling of liquid and gas regimes in the column rather difficult.In the last decade, artificial neural networks havebeen used in various industries considerably. Unlike empirical correlation, neural network does not requirephysical mechanism which occurs in column. Therefore, in this research the effect of tray speed, pressure drop, cone spacing, and flooding for both small and large scales operation has been examined using artificial neural network. Furthermore, variation of gas and liquid flow rate in an industrial scale spinning cone column has also been evaluated. To obtain this objective, multilayer perceptron structure and Levenberg-Marquart training algorithm has been utilized. The findings of this study reveal that the predictions of this work are much accurate than those obtained from the existing empirical correlation. There also exists a good compatibility between the pressure drop values predicted from the present study and the experimental data in both dry and wet state (normalized bias = 0.00232, mean squared error = 0.0021, and root mean squared error = 0.0021). From the scheme adopted in this work, the spinning cone column capacity at different operating conditions could be estimated more accurately than the exiting correlations.

Spinning cone column (SCC) as a distillation tower has various applications in the food industry. The spinning cone column is a gas-liquid contacting device consisting of a vertical countercurrent flow system, which contains a succession of alternate rotating and stationary metal cones, whose upper surfaces are wetted with a thin film of liquid. Liquid flows down the upper surfaces of the stationary cones under the influence of gravity and moves up the upper surfaces of the rotating cones in a thin film by the action of the applied centrifugal force. Vapor flows up the column and traverses the successive fixed and rotating cones [1]. Figure 1 shows the liquid and gas flow regimes in a SCC. Flooding limit is an important criterion in the distillation tower, since it is an index of tower’s capacity. By knowing the geometric structure of the rotary conical tower, we could determine the effective parameters on the flooding such as gas flow rate, liquid flow rate, cone spacing, and rotation speed of the trays.

In the last decade, artificial neural networks have been used in various industries considerably [2]. Neural networks are nonlinear calculation algorithms for images, signals, and numerical data processing. Regarding some features of neural networks such as internal dynamic of neural networks in prediction, changing information error, unnecessary information in input data, employing neural networks in the engineering field as a tool to control and observe the process performance has been increased substantially. Multilayer perceptron is one of the most frequent structures which are utilized in neural networks [3].

Spinning cone column has a complex geometric structure which makes the modeling of liquid and gas regimes in the column rather difficult. Unlike empirical correlation, neural network does not require physical mechanism which occurs in column. Furthermore, multilayer perceptron structure could predict values outside the training limit. Therefore, in this research, the effect of tray speed, pressure drop, cone spacing, flooding for both small and large scales operation has been examined using artificial neural network. Furthermore, variation of gas and liquid flow rate in an industrial scale spinning cone column has also been evaluated.

Rotatory conical columns

The first research on SCC was carried out in 1937 by Pegram and co-workers which gave the details of the column [4]. Mir and Wilingham in 1939 conducted some experiments on distillation column on a laboratory scale (as cited in Makarytechev et al. [5]). Later on and in 1963, Ziolowski and co-workers performed pressure drop studies on the separation of benzene-tetra-chloride mixture for the first time (as cited in Makarytechev et al. [6]). Liquid film flow on rotatory conical tray was studied by Prince and co-workers in Sydney University, who examined the liquid flow regime in SCC in 1998 and showed that scale up causes a change in liquid flow regime. In a further work, they also examined the speed rate and liquid film thickness on the rotator in 2001 [7]. Macarif and Langrich exhibited a relationship between pressure drop and flooding limit in 2004 and 2005 (as cited in Riley and Sykes [8]).

From 2002, computational fluid dynamics was adopted by some researchers to study on SCC in the absence of liquid phase. Therefore, in this paper, the flooding limits in a rotatory conic distillation column in an industrial scale have been studied in order to improve SCC design and predict tower capacity using a neural network.

Multilayer perceptron structure

The base of multilayer perceptron (MLP) is made up of artificial neurons, which a simple mathematical operation is performed on its inputs, which is shown in Figure 2. The input neuron of the first layer includes P₁P₂, and P_R, variables and threshold or bias expression. Each of the input variables is multiplied by weight coefficient, and then the grand total is added to bias. Finally, a defined activated function performs a mathematical operation on inputs and results the outputs. MLP structure is a standard combination of inputs, hidden units, and outputs. The outputs of all processing units of each layer are correlated to all units of the next layer. All processing units of the input layer are linear, but in the hidden layer, nonlinear neurons are used. In this structure, sigmoid function in hidden layer and pure line function in output layer have been utilized. The neural networks adopted for training algorithms utilize real data of input and output in order to define a hidden relation between input and output using weight coefficients, bias, and performance functions [9].

Levenberg Marquarts training algorithms

Although back propagation (BP) algorithm is frequently utilized, however, it has two disadvantages:

· Low speed of convergence

· Static and stoppage of network parameters due to falling in local minimum

Therefore, Levenberg Marquart algorithm which is faster than BP was adopted in the present study [10]. For training purposes, it was necessary to optimize the standard function based upon the networks parameters. Based on the Newton method, variation of parameters in each training step is as follows:

where is a Hessian matrix, and is a function gradient of J with respect to the neural parameters vector (i.e., ). As the standard network function is defined as mean sum square errors, therefore we would have:

Where and p is the number of training model and S_L is number of network output.

Levenberg Marquart method is as follows:

where μ_m is the Levenberg Marquart learning coefficient and is a nonnegative number [10].

Empirical model

In this paper, experimental data of Langrich and Macariof for industrial scale (i.e., 0.801 m in diameter) and small scale (i.e., 0.148 m in diameter) have been utilized (as cited in Makarytechev et al. [6]). The number of data for industrial and small scale was 40 and 230, respectively. In this research, 40% of data have been used for the network training and the rest for testing. Mean percentage error of the results was about 10%. Table 1 exhibits the details of neural network features adopted in this work.

The statistical parameters, i.e., normalized bias (NB), mean squared error (MSE), root mean squared error (RMSE), and squared correlation coefficient (R²), which are described in the following equations, are used for the fitness investigation and error determination of the model. Normalize bias is a parameter which it defines whether the output values has been predicted less or higher than the actual amount.

Simulation results revealed that neural networks for both cases of industrial and small scale operation must be run separately. This is caused owing to the fact that there would be a change in the liquid flow regime. In this work, effective parameters such as rotation speed, cone spacing in the beginning of flooding for small scale column, and pressure drop have been examined. Furthermore, the work has been extended to an industrial scale column. Finally, a generalized correlation has been obtained for the flooding limit in industrial scale. These cases have been elucidated in more depth below.

Effect of tray speed in SCC

As the rotation speed increases, it is expected that at low gas flow rate, the flooding in SCC occurs instantaneously. This was verified by the prediction of this work as shown in Figure 3. However, the decline trend has two slopes as shown in Figure 4, and in fact, there exists a point of inflection. Therefore, for an increase in the rotation speed of about 9% (500 rpm) and a reduction of 18%, the gas flow rate decreases accordingly.

Effect of cone spacing in SCC

Space between rotary and fixed trays is one of the most important geometric parameters in SCC which is an effective way for flooding to initiate. Figure 5 reveals that as the cone spacing increases (i.e., B), the gas flow rate increases for the formation of flooding which means the column capacity enhances. Figure 5 reveals that a reduction on cone spacing increases the column capacity. On the other hand, as cone spacing increases, the column capacity decreases accordingly. Furthermore, for an increase of about 10% of cone spacing, the capacity of column increases about 8%. However, this reduces to about 2% at the end.

Flooding in SCC

Flooding limit and column capacity in an industrial scale are important criteria in spinning cone column. Operating conditions of the column could be divided into three regions, they are preloading, loading, and flooding and are defined as follows [6]:

These limits could be distinguished with Fr_LG. Once 0.1 > Fr_LG, it is defined as preloading, and when 0.1 < Fr_LG < 1, the regime is called loading, and if Fr_LG >1, the regime is termed flooding. Furthermore, flooding condition could be predicted from the following correlation with a relative error of 20% [6]:

Therefore, with the above equation and by knowing the geometric parameter of the column (A_min, A_throath, P_c, and R_SO), we could estimate the gas flow rate at flooding condition for a specified liquid flow rate and rotation speed. A comparative study has been conducted between the predicted results of this study, the experimental data, and the existing correlation as shown in Figure 6.

Pressure drop in SCC

A comparative study between the pressure drop predicted from the present study and the experimental values in both dry and wet state are exhibited in Figures 7 and 8. The results demonstrate a good agreement between them. The mean square errors for predicting pressure drop for this work was 0.0021, and the mean absolute error for all data was about 5%.

Gas and liquid flow rate in industrial scale SCC

Figure 9 shows variations of gas with liquid flow rate for industrial scale spinning cone column at 500 rpm. The results reveal that there is a good agreement between the predicted results of the present study and experimental values. If the rotation rate is different (i.e., different from 500 rpm), the column capacity could be estimated from Figure 4 by increasing the column capacity by 18% for W = 250 rpm and decreasing by 9% for W = 750 rpm.

Flooding limit and column capacity are important criteria in spinning cone column. In this research and in order to improve spinning cone column design and predict tower capacity, the flooding limits, pressure drop, the effect of tray speed, cone spacing, flooding for both industrial and small scale operation have been assessed using artificial neural network. Furthermore, variation of gas and liquid flow rate in an industrial scale spinning cone column has also been studied. From the findings of this study and from the flooding graph obtained from this work, the spinning cone column capacity in different operating conditions could be estimated. The findings of this study reveal that the predictions of this work are much accurate than those obtained from the existing empirical correlation (about 10%). There also exists a good compatibility between the predicted pressure drop values of the present study and the experimental data in both dry and wet state (MSE = 0.0021, MAE = 5%, and NB = ;0.00232). Therefore, the findings of this study shows that the artificial neural nets technique with multilayer perceptron structure and Levenberg-Marquart training algorithm could be applied as a powerful tool and a cost and time effective way in predicting the spinning cone column capacity and the pressure drop.

Amin: minimum flow area (m2); Athroat: area of the outer throat of the column (m2); QL: liquid flow rate (lit/min); Qg: gas flow rate (lit/min); W: rotor speed (rpm); B: cone spacing (m); Fr: Froude number; g: acceleration due to gravity (ms22); kLL: empirical coefficient in the pressure drop correlation; Lmodel, i: model output value in the test i; Lexp,i: actual output value in the test i; n: number of test samples; PC: vertical distance between two fixed trays (m); RSO: outer radius of the spinning cone (m); μm: Levenberg Marquart learning coefficient; Pg: gas density (kg/m3); Pl: liquid density (kg/m3); 3;P: dimensional pressure drop (Pa) subscripts; LG: liquid–gas mixture.

The authors declare that they have no competing interests.

Hereby, Nasser Saghatoleslami, Mohammad Amiri, Jamal Rohi Golkhatmi certify that they carried out the work “Prediction of Flooding and Pressure Drop in a Spinning Cone Column Using Neural Networks” and approve the final manuscript.

Nasser Saghatoeslami: Associate of Prof. of Chemical Engineering

Mohammad Amiri and Jamal Rohi Golkhatmi: M.Sc. Research Student

Authors wishes to gratefully acknowledge the helpful comments of Dr. Morteza Zivdar and the facilities provided by the Ferdowsi University of Mashhad.

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