Simplified Mechanistic Model of the Multiple Hearth Furnace for Control Development

This paper presents the simplified mechanistic model of a Multiple Hearth Furnace (MHF), developed for process control implementation. The detailed mechanistic model of the MHF and its solving procedure are introduced. Based on the detailed model, the simplified model is developed in the nonlinear Hammerstein-Wiener form, which defines a specific type of nonlinear state space models suitable for example for Model Predictive Control (MPC) implementation. The simplified model aims to preserve the key physicalchemical phenomena taking place in the furnace and to reproduce the nonlinear dependencies between the input and output variables. Finally, the paper presents the simulation results to compare the mechanistic and the simplified models. The comparison confirms that the dynamics of the simplified model accurately follows the mechanistic model outputs. Introduction Furnaces, such as the rotary kilns and multiple hearth furnaces, are widely used in industry for the calcination of clay minerals, such as kaolin. However, these processes continue to provide challenges in maintaining efficient process operations. In particular, it is hard to control the final product quality, due to the difficulty in measuring the product characteristics, the solid temperature profile in the furnace, and the rates of the calcination reactions. Instead, the existing control systems mostly rely on the gas temperature measurements and traditional control implementations, such as PID. This strategy, however, does not allow achieving stable solid phase temperature profile and uniform product quality. In contrast, a Model Predictive Control (MPC), based on a model describing the physicalchemical phenomena in the furnace, would be able to stabilize the solid temperature and minimize the product quality variations. 1 Process Description This paper considers a multiple hearth furnace used for kaolin calcination, having the counter-current solid and gas flows. The furnace has eight hearths, and eight burners, combusting natural gas to provide the heat necessary for the calcination reactions, are located in hearths 4 and 6. The amount of air flow, supplied to the burners for the gas combustion, is calculated based on the stoichiometric ratio. The burners are placed with a tangential alignment. Kaolin is supplied to the first hearth located at the top of the furnace. In the calciner, the material is moved by the metal plates, called blades, which are attached to the rotating rabble arms, designed with the intention of transporting the material outwards on even-numbered hearths and inwards on odd-numbered hearths. The kaolin traversing the even numbered hearths moves outward to descend through the holes at the outside border of the hearth, while in the odd-numbered hearths kaolin falls to the next hearth through a single annulus located around the shaft carrying the rabble arms. The temperature of the solid increases as it travels down through the furnace and reaches its maximum in Hearth 6. Kaolinite transforms to metakaolin in the hearths 3, 4 and 5 at the temperature between 400-700 °C. The metakaolin is released from hearth 5 at a temperature approximately 800 °C, which continues elevating in the hearth 6, where the transformation of metakaolin to the Al–Si spinel phase occurs [1]. SNE 28(3), 2018, 97 100, DOI: 10.11128/sne.28.sn.10426 Received: Sept. 15, 2016 (Selected EUROSIM Congress 2016 Postconf. Publ.), Revised July 30, Accepted: August 25, 2018 SNE Simulation Notes Europe, ARGESIM Publisher Vienna, ISSN Print 2305-9974, Online 2306-0271, www.sne-journal.org Gomez Fuente et al. Mechanistic Model of the Multiple Hearth Furnace 98 SNE 28(3) – 9/2018 SN Thus, the main objective of the hearth 6 is to increase the temperature in order to facilitate the absorption of aluminum into the silica phase. The control of temperature in the hearth 6 is essential to avoid overheating, which may result in the undesired formation of a more crystalline material that may generate some abrasion problems. The temperature of the solids begins to decrease in the hearths 7 and 8, and the product leaves from the hearth 8 through two discharge holes at a temperature of 750 °C. 2 Dynamic Model of the MHF This section describes the mechanistic model of the MHF developed by Eskelinen et.al.[2]. The modeling equations are developed for the six parts of the MHF: the gas phase, solid bed, central shaft, walls, rabble arms, and the cooling air. The model comprises the calcination reaction kinetics, the mass and energy balances, the transport phenomena in the parts of the MHF, as well as additional equations describing the temperature dependent parameters, more details can be found in [3]. The following assumptions have been made to simplify the model development. The solid bed in the hearths is split into four or five homogenous annular volumes, depending on the rabble arm configuration. The volumes are assumed to be equal in mass content and radial direction. The mixing model, describing the solids movement in the hearths, assumes that one shaft rotation disseminates a part of the volume contents to the neighbor volumes. Thus, the solid mass distribution between the volumes of hearth can be calculated after one shaft rotation as follows: (1) Where and connote the feed and the mass loss in the solid phase in Hearth . The mixing matrix is used to transform the distribution of solids in Hearth after one central shaft rotation. Specifically, the column of the matrix denotes the distribution of volume contents between the volumes of the hearth. 3 Model Simplification This section describes the simplified model developed based on the mechanistic model presented in Section 2. A simplification of the mechanistic model is designed, describing the dynamics and the nonlinear behavior of the system separately. In more details, the simplified model is expressed as a Hammerstein-Wiener model (HWM), decomposing the model in blocks containing the nonlinearities in static form and the linear dynamics. The linear block, enclosing the dynamics of the process, is preceded and followed by a static non-linear blocks. The dynamics of the MHF includes the very fast component related to the gas phase, and the slower component representing the solid state. For MPC implementation, the temperature of the solid has to be described dynamically. Furthermore, as the temperature of the inner layer of the walls has a direct effect on the solid-walls heat exchange, it is also considered as a model state. The simplified model is implemented as following: (2) where is a vector containing the process inputs (kaolin feed rate, gas flows to the Hearths 4 and 6), is the state vector contains the temperature of the solids in each volume of the furnace and the internal wall temperature in the hearths, contains the gas phase temperature next to the walls in the hearths, is the time constant parameter of the linear dynamic part of the modeling equations. The time constant is obtained for each modeling equation by identification performed using the MATLAB® identification toolbox. is a static nonlinear function calculating the steady state of the furnace using the process input values. In order to implement the first function , a look up table has been created by running the mechanistic model simulations with different process inputs. The obtained values are interpolated as follows: