Analysis of a Semi-batch Reactor for Control Purposes

The paper presents a control system design oriented analysis of a semi-batch reactor used for tanning waste recovery. The analysis is performed with the help of modelling and simulation means and provides useful information for optimal control design of the process. INTRODUCTION The tannery is an essential industry process today. Its product is a natural hide. Some of the leather properties (such as softness, plasticity, stability, absorption) cannot be replaced by any artificial material. There are a lot of technological operations during the leather-to-hide conversion, starting with washing, continuing by tanning etc. These are usually connected with huge water, energy and chemicals consumption resulting in negative impact on the environment. Recently, one of the very fundamental operations is chromium salt tanning. It is possible to obtain only 200 [kg] of hide from 1000 [kg] of leather, but over 600 [kg] of solid waste originates from this process; the rest is drained away in the form of liquid waste during the chromium salt tanning process. The USA produces almost 60 000 tons of this solid waste and the worldwide production is approximately 10 times bigger (Cabeza et al. 1998). Currently, majority of this solid waste is land filled. It can result in leakage of Cr3+ into groundwater. After oxidation, for example in sewage treatment plants during purification from unhealthy bacteria, the Cr3+ to Cr6+ conversion can occur. The Cr6+ compounds belong to cancerous substances so they are dangerous to health. As a consequence, at present, alternative methods of dealing with the chromium waste are sought and investigated (Aloy and Vulliermet 1998; Tiravanti et al. 1996, 1997). The enzymatic hydrolysis is one of the considered alternatives (Kolomazník et al. 1996). This technique separates the chrome from protein in the form of the chromium filter cake. All products of this process are usable – it is a waste-free technology. This paper deals with an analysis of a chemical reactor for chromium sludge (chromium filter cake) recovery. The reactor is used for the enzymatic hydrolysis and the analysis is performed from the control theory point of view by simulation means mainly to obtain useful information for subsequent optimal control design. The contribution is structured as follows: after the introduction, a detailed description of the reactor follows. In the next sections, a mathematical model of the system is derived and all variables are defined together with their physical values and limits. Further, steady-state and dynamical behaviour is studied by simulation means. A detailed analysis of the reactor from the systems theory point of view follows in next sections, giving useful information for optimal control design. Possible control strategies are discussed at the end of the contribution together with areas for possible future research. A SEMI-BATCH REACTOR The chromium sludge is processed in a chemical reactor sketched in Fig.1. by an exothermic chemical reaction with chrome sulphate acid. During this reaction a considerable quantity of heat is developing so that control of the reaction is necessary. Figure 1: Chemical Reactor Proceedings 22nd European Conference on Modelling and Simulation ©ECMS Loucas S. Louca, Yiorgos Chrysanthou, Zuzana Oplatková, Khalid Al-Begain (Editors) ISBN: 978-0-9553018-5-8 / ISBN: 978-0-9553018-6-5 (CD) System description In order to investigate main properties of the real process, a mathematical model of the chemical reactor was derived based on Fig.2. Figure 2: Chemical Reactor Scheme The scheme above shows a chemical semi-batch reactor with initial filling mP[kg] given by the solution of chemicals without the chromium sludge (filter cake). This is fed into the reactor by [kg/s] to control the developing heat since the temperature has to stay under a certain critical level ( FK m ( ) o 100 C T t ≺ ), otherwise the reactor could be destroyed. On the other hand it is desirable to utilise the maximum capacity of the reactor to process the maximum amount of waste in the shortest possible time (higher temperature is desirable). Therefore an optimal control strategy has to find a trade-off between these opposite requirements. Mathematical model Under usual simplifications, based on the mass and heat balance, the following 4 nonlinear ordinary differential equations can be derived (Macků 2005, 2004): ( ) FK d m m dt = t (1) ( ) ( ) ( ) ( ) FK FK FK d m k m t a t m t a t dt = + ⎡ ⎤ ⎣ ⎦