Elsevier

Powder Technology

Volume 387, July 2021, Pages 363-372
Powder Technology

Estimation of the minimum spouting velocity and pressure drop in open-sided draft tube spouted beds using genetic programming

https://doi.org/10.1016/j.powtec.2021.04.049Get rights and content

Highlights

  • New models developed for predicting minimum spouting velocity and pressure drops.

  • Genetic programming approach to develop the new models.

  • The average absolute deviations are below 16% in all models.

  • The previous models showed considerably lower precision than the present ones.

  • The novel correlations follow the experimental trends at the different operating conditions.

Abstract

Explicit dimensionless models are proposed for estimating the minimum spouting velocity, operating pressure drop and peak pressure drop in open-sided draft tubes spouted bed using the genetic programming (GP). The models are developed based on 664 experimental data for minimum spouting velocity, 660 for peak pressure drop and 652 for operating pressure drop. The parameters of significant influence are considered as GP input variables, and reliable semi-empirical correlations have been obtained. The models predict the hydrodynamic parameters analyzed with average absolute relative errors of 12.90%, 15.99% and 10.92% for the minimum spouting velocity, peak pressure drop and operating pressure drop, respectively. A comparison of literature correlations with the present ones shows that the latter lead to considerably lower errors from the experimental data. The prediction capability of the new models was evaluated in a range of operating and geometric conditions and a close agreement with the experimental data was observed.

Introduction

Studies on the application of spouted beds have been conducted in many fields, as are those involving coal gasification [1,2], combustion of fuels [3], drying of vegetables [4] and others [[5], [6], [7], [8]]. This contact technique is commonly used when fluidization cannot satisfy the mixing requirements, especially for particles bigger than 1 mm. The main advantages of spouted beds lie in their better gas-solid contact and higher heat and mass transfer rates with coarse particles [9]. Several modifications have been applied to the conventional spouted beds for improving their hydrodynamic behavior. Thus, use of conical spouted beds instead of the conventional cylindrical spouted beds leads to lower pressure drops and the capacity for handling particles with a wide size distribution in a wide range of gas velocities. Furthermore, use of draft tubes improves operation stability and flexibility with all beds. These types of spouted beds usually require lower gas flow rates and lead to lower pressure drops than the conventional ones, apart from the fact that they are suitable for the treatment of fine particles with a wide size distribution [[10], [11], [12], [13], [14], [15], [16], [17]]. However, the design and scale up of the spouted beds with draft tubes involves challenges, and further studies are essential to predict their hydrodynamic parameters, such as minimum spouting velocity and pressure drop.

Different configurations for the draft tubes have been suggested in the literature, with the most common being porous, nonporous and open-sided or slotted draft tubes. There are several experimental studies concerning hydrodynamics of spouted beds with draft tubes [[18], [19], [20], [21]]. Altizbar et al. [8] compared the performance of different types of draft tubes for the drying of fine particles. The results showed that the drying time required when a porous draft tube is used is about 50% lower than when a nonporous draft tube is used. However, the air velocity required when a porous draft tube is used is about two times higher than that when a nonporous draft tube is used. Nevertheless, the pressure drop for both porous and nonporous tubes is of the same order. They found that although the configuration with the open-sided draft tube needs a similar drying time as that with a porous one, the air flow rate required in the former is about 20% lower. Ishikura et al. [10] observed that increasing the diameter of the porous draft tube leads to higher solid circulation rate. Moreover, the porous draft tube boosts solid circulation compared to the nonporous one. Altzibar et al. [22] investigated the minimum spouting velocity for conical spouted beds equipped with different configurations of draft tubes. They found that although the open-sided draft tube spouted bed has many advantages, such as better gas-solid contact and higher solid circulation flow rate, the minimum spouting velocity for this type of draft tube is significantly higher than that for porous draft tubes. Luo et al. [14] studied the operating and peak pressure drops for spouted beds with and without draft tube. According to their results, draft tube spouted beds lead to lower operating and peak pressure drops than the conventional conical spouted beds. Similar results were also reported by Altzibar et al. [23].

Several predictive methods have been proposed in the open literature for estimating the minimum spouting velocity and pressure drops in conventional spouted beds (those without draft tubes) [9,[24], [25], [26], [27], [28], [29], [30], [31], [32], [33]]. However, only a few models are available for draft tube spouted beds, especially for those with open-sided ones. Kmiec et al. [34] developed an empirical model based on their experimental data for non-porous draft tube spouted beds. They showed that an empirical correlation based on the Archimedes number and geometrical parameters of the draft tube spouted bed leads to the highest accuracy. Altzibar et al. [35] proposed three correlations for predicting the minimum spouting velocity, operating pressure drop and peak pressure drop in beds of fine solid particles using non-porous draft tubes. However, their analysis was performed based on date within a limited range. San José et al. [36] developed a model for the minimum spouting velocity in non-porous draft tube spouted beds by modifying the earlier model by Olazar et al. [26] for conventional spouted beds. The modification consisted in adding dimensionless factors related to the geometrical factors of the draft tubes. However, the model by San José et al. [36] does not predict satisfactory results for the experimental data by Altzibar et al. [23]. Hosseini et al. [37] evaluated five intelligent methods for estimating the minimum spouting velocity in non-porous draft tube conical spouted beds. The results obtained based on an algorithm using the Multi-Layer Perceptron with Bayesian Regularization learning rule (MLP-BR) combined with Self-Organizing Map (SOM), namely, MLP-BR-SOM, showed the best accuracy among all tested methods. Karimi et al. [38] used the Multi-Layer Perceptron Artificial Neuron Network (MLP-ANN) method for predicting the peak and operating pressure drops in open-sided draft tube spouted beds. They indicated that 3 hidden layers with 4–12-4 structure leads to the best results with the average absolute relative errors of 1.30% and 11.88% for operating and peak pressure drops, respectively. Hosseini et al. [39] proposed explicit correlations for the minimum spouting velocity and operating pressure drop in shallow spouted beds equipped with nonporous draft tubes using the smart method of genetic programming (GP). The new correlations showed fairly good results for estimating these parameters and confirmed the ability of the GP for estimating the hydrodynamic behavior of draft tube spouted beds. Altzibar et al. [22,23] developed correlations based on their experimental data for minimum spouting velocity and pressure drop in different configurations of draft tube spouted beds using the least square fitting method (LSFM), and obtained relatively good results.

Based on the above brief literature survey, most of the previous studies focused on the hydrodynamic characterization of non-porous draft tube spouted beds and predictive methods for open-sided draft tube spouted beds are indeed rare. In addition, there is a lack of accurate explicit correlations developed by smart methods for estimating the minimum spouting velocity and pressure drop in open-sided draft tube spouted beds applicable for the design and scale up of these systems. Therefore, the main goal of this study is to obtain highly accurate mathematical correlations for estimating the minimum spouting velocity, peak pressure drop and operating pressure drop in spouted beds with open-sided draft tubes using the smart method of genetic programming (GP). The results of the proposed models are evaluated under different conditions and compared with the available empirical models. In addition, the impact of each operating and geometric parameter on the minimum spouting velocity and pressure drop is also discussed using the new models.

Section snippets

Genetic programming (GP)

There are two approaches for solving optimization problems: classical and metaheuristic computation methods. The classical methods can be used for the problems with specific characteristics such as those with unimodal and two-times differential objective function. In contrast, the metaheuristic methods can solve an optimization problem with non-limitation in its objectives. One of the metaheuristic algorithms which is applied to find the best correlation by fitting a data set is GP so that this

New predictive methods

A procedure based on GP method is used to establish robust nonlinear correlations for estimating the minimum spouting velocity, operating pressure drop and peak pressure drop in open-sided draft tube spouted beds.

Conclusions

The minimum spouting velocity, operating pressure drop and peak pressure drop have been analyzed in open-sided draft tube spouted beds. Three databases containing 664 points for the minimum spouting velocity, 652 points for the operating pressure drop and 660 points for the peak pressure drop were gathered and the smart method of genetic programming was used for obtaining explicit models for theses hydrodynamic parameters.

The GP technique allowed attaining accurate correlations for all data

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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