Dynamic model chemical stirred tank reactor

In this chapter, the dynamics of ideally stirred tank reactors will be analyzed. First, the assumptions, required to limit model complexity, will be discussed. Next, various types of reaction will be considered such as simple first-order reactions, equilibrium reactions, parallel reactions, etc. Subsequently, the analysis will be expanded to include non-isothermal reactors. Numerical examples of chemical reactors are given and the non-linear model descriptions are compared with the linearized model descriptions. 

P. Albertos and M. Perez Polo. Selected Topics in Dynamics and Control of Chemical and Biochemical Processes, chapter Nonisothermal stirred-tank reactor with irreversible exothermic reaction A B. 1.Modelling and local control. LNCIS. Springer-Verlag, 2005 (in this volume). 

This section contains several models whose spatiotemporal behavior we analyze later. Nontrivial dynamical behavior requires nonequilibrium conditions. Such conditions can only be sustained in open systems. Experimental studies of nonequilibrium chemical reactions typically use so-called continuous-flow stirred tank reactors (CSTRs). As the name implies, a CSTR consists of a vessel into which fresh reactants are pumped at a constant rate and material is removed at the same rate to maintain a constant volume. The reactor is stirred to achieve a spatially homogeneous system. Most chemical models account for the flow in a simplified way, using the so-called pool chemical assumption. This idealization assumes that the concentrations of the reactants do not change. Strict time independence of the reactant concentrations cannot be achieved in practice, but the pool chemical assumption is a convenient modeling tool. It captures the essential fact that the system is open and maintained at a fixed distance from equilibrium. We will discuss one model that uses CSTR equations. All other models rely on the pool chemical assumption. We will denote pool chemicals using capital letters from the start of the alphabet. A, B, etc. Species whose concentration is allowed to vary are denoted by capital letters... 

The kinetic simulations of the pulse combustor ignition can be carried out under conditions which closely approximate those in a continuously stirred tank reactor (cstr). In those calculations, hot product gases are steadily mixed with cold, unbumed reactants until the mixtures ignite. The reaction mechanisms used are valid for high temperatures, and the most important, sensitive reaction is reaction (3), and the combined influences of chemical kinetics, acoustics, and fluid dynamics can all be incorporated into a coherent practical design model [20]. 

Chapter 3 concerns the dynamic characteristics of stagewise types of equipment, based on the concept of the well-stirred tank. In this, the various types of stirred-tank chemical reactor operation are considered, together with allowance for heat effects, non-ideal flow, control and safety. Also included is the modelling of stagewise mass transfer applications, based on liquid-liquid extraction, gas absorption and distillation. 

As discussed in Sect. 2.1, physical and mathematical models of ideal chemical reactors are based on two very simplified fluid dynamic assumptions, namely perfect mixing (BR and CSTR) and perfect immiscibility (PFR). On the contrary, in real tank reactors the stirring system produces a complex motion field made out of vortices of different dimensions interacting with the reactor walls and the internal baffles, as schematically shown in Fig. 7.2(a). As a consequence, a complex field of composition and temperature is established inside the reactor. 

Ramirez, W. F, and Turner, B. A., The Dynamic Modeling, Stability, and Control of a Continuous Stirred Tank Chemical Reactor, AIChE Journal 15, No. 6, 853 (1969). 

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