A Multigene Genetic Programming approach for modeling effect of particle size in a liquid–solid circulating fluidized bed reactor

Highlights

• Model validated by comparing model predicted and a pilot scale LSCFB data.

• GP model predicted and experimental data are in agreement.

• Statistical performance measures the GP model is quite competitive.

• The solids holdup higher for GB-500 particles.

• MAPE of the predicted for GB-1200 found higher.

Abstract

This communication presents the application of Multigene Genetic Programming, a new soft computing technique to investigate the effects of particle size on hydrodynamics behavior of a liquid–solid circulating fluidized bed (LSCFB) riser. The Multigene Genetic Programming based model is developed/trained based on experimental data collected from a pilot scale LSCFB reactor using two different size glass beads (500 & 1200 μm) as solid phase and water as liquid phase. The trained Genetic Programming model successfully predicted experimental phase holdups of the LSCFB riser under different operating parameters. It is observed that the model predicted cross-sectional average of solids holdups in the axial directions and radial flow structure are well agreement with the experimental values. The statistical performance indicators including the mean absolute error (∼5.89%) and the correlation coefficient (∼0.982) also show favorable indications of the suitability of Genetic Programming modeling approach in predicting the solids holdup of the LSCFB system.

Introduction

Liquid–solid circulating fluidized bed (LSCFB) systems have found a wide range of applications including chemical, biochemical, environmental, and pharmaceutical processes (Atta et al., 2009, Razzak et al., 2008, Patel et al., 2005, Zhu et al., 2000, Liang et al., 1997). There are studies in the open literature also demonstrated the efficient operation of wastewater treatment using LSCFB (Patel et al., 2005, Liang et al., 1997). The operational suppleness of solid phase catalysts/adsorbents, superior mass and heat transfer between phases, and flexibility of solid particle regeneration facilities makes LSCFB processes attractive in various applications. In biochemical reactions, the solid particles of an LSCFB system can maintain a biofilm, which helps to control the reactions (Patel et al., 2005). Due to their potential applications in wide ranges of processes, the study of LSCFBs has become an interesting research topic. Especially, the investigation of phase distributions and hydrodynamic behaviors of LSCFB are essential in order to design efficient LSCFB systems.

In the open literature, there are only a few experimental studies available on hydrodynamics studies of LSCFB and other liquid–solid flow systems. The major reason for this limited research is associated with the cost of design and scale-up of the LSCFB systems. One way to minimize costs of LSCFB study is by developing correlations and/or suitable mathematical models based on small scale LSCFBs. The developed model/correlation can be used for scale-up the system and to predict the hydrodynamic behaviour of the LSCFB system. In this regard, the application of neural network models such as Abductive Network, Support Vector Machine, Artificial Neural Network (ANN), Neuro–Fuzzy Model (ANFIS) approach could be effective tools to model and study the hydrodynamic behaviour of LSCFB systems (Razzak et al., 2015, Razzak et al., 2012a, Razzak et al., 2012b, Razzak, 2013, Razzak, 2012, Razzak and Hossain, 2014). Lahiri and Ghanta (2008) proposed an Artificial Neural Network (ANN) model, considering holdups as a function of the solid holdup, velocity, and particle diameter, the pressure drop along with different solid and liquid properties. The neural network models for hydrodynamic studies of LSCFB provides relatively better predictions than the conventional statistical models. However, the problem with the neural networks models is their working characteristics, which cannot relate inputs with outputs by an analytical equation form. This problem can be overcome by applying soft computing approaches known as Genetic Programming. These soft computing techniques are very effective for solving highly complex non-linear problems (Lahiri and Ghanta, 2008). Genetic Programming is successfully used in a wide range of applications in other fields, such as rock mass modulus deformation estimation, rainfall estimation etc. (Ravandi et al., 2013). To the best of our knowledge, the Genetic Programming based approaches have not been applied to phase distribution modelling in LSCFB.

Therefore, the present study is aimed at investigating Genetic Programming modelling approach to predict the effects of particle size on hydrodynamics behaviour of an LSCFB system. In the model development and validation, the experimental data used are collected from a pilot scale LSCFB reactor with two different size glass beads (500 & 1200 μm) as solid phase and water as the liquid phase. The effects of major experimental parameters such as superficial liquid velocity (U_l), auxiliary liquid velocity (U_a), superficial solids velocity (U_s), normalized superficial liquid velocity (U_l/U_t) and net superficial liquid velocity (U_l − U_t) are considered as inputs in model development. It is relevant to highlight that the use of normalized superficial liquid velocity (U_l/U_t) is advantageous for the characterization of radial distributions of solids holdups. The net superficial liquid velocity (U_l − U_t) is an alternative to the slip velocity investigating the flow characterization.