Dynamics of Chemical Stirred Tank Reactors

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. 

Chemical reactors are usually the most important part of a chemical plant. They form the heart of the process where raw materials are corrverted into products. ModeUng chemical reactors, in particirlar the kinetics, is generally not simple, however it depends very much on the goals we woitld like to achieve. In rrrarty cases, not all raw material is converted and it may be important to monitor the concentration of rrrrreacted components as to get an idea of the conversion that has been achieved. The reactor outlet concentration of rmreacted component is often the most important variable in which we are interested. 

To simplify the description of the reactor, the following assrrmptions have been made  

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Many chemical and biological processes are multistage. Multistage processes include absorption towers, distillation columns, and batteries of continuous stirred tank reactors (CSTRs). These processes may be either cocurrent or countercurrent. The steady state of a multistage process is usually described by a set of linear equations that can be treated via matrices. On the other hand, the unsteady-state dynamic behavior of a multistage process is usually described by a set of ordinary differential equations that gives rise to a matrix differential equation. 

Vejtasa, S.A. Schmitz, R.A. An experimental study of steady state multiplicity and stability in an adiabatic stirred reactor. AIChE J. 1970,16, 410 19. Schmitz, R.A. Multiplicity, stability, and sensitivity of states in chemically reacting systems - a review. Adv. Chem. Ser. 1975, 148, 156-211. Razon, L.F. Schmitz, R.-A. Multiplicities and instabilities in chemically reacting systems - a review. Chem. Eng. Sci. 1987, 42, 1005-1047. Uppal, A. Ray, W.H. Poore, A.B. On the dynamic behavior of continuous stirred tank reactors. Chem. Eng. Sci. 1974, 29, 967-985. 

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). 

Yet who would have thought the old man to have had so much hlood in him This title, given by Prof. Rutherford Aris and his collaborator W.W. Farr to their recent paper [Chem. Eng. Sci., 41 (1986) 1385], is a phrase used by Lady Macbeth (Macbeth, V, 1, 42-44). Fierce, isn t it Apparently, they mean it to imply that traditional theoretical problems in the dynamics of chemical reactions, in particular the known problem of the dynamics of the continuous stirred tank reactor (CSTR), are far from being exhausted. Novel mathematical approaches provide new results oriented to physico-chemical comprehension. This current trend is confirmed by the present volume. 

The nonlinearity of chemical processes received considerable attention in the chemical engineering literature. A large number of articles deal with stand-alone chemical reactors, as for example continuously stirred tank reactor (CSTR), tubular reactor with axial dispersion, and packed-bed reactor. The steady state and dynamic behaviour of these systems includes state multiplicity, isolated solutions, instability, sustained oscillations, and exotic phenomena as strange attractors and chaos. In all cases, the main source of nonlinearity is the positive feedback due to the recycle of heat, coupled with the dependence of the reaction rate versus temperature. 

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 reaction-diffusion dynamics of the acid autocatalytic Chlorite-Tetra-thionate (CT) reaction was thoroughly investigated (2). Like other autocatalytic reactions, the CT reaction exhibits a more or less long induction period followed by a rapid switch to thermodynamic equilibrium. In a continuous stirred tank reactor (CSTR), this reaction can exhibit bistability. One state is obtained at high flow rates or at highly alkaline feed flows, when the induction time of the reaction is much longer than the residence time of the reactor. The reaction mixture then remains at a very low extent of reaction and this state is often named the Flow (F) or the Unreacted state. In our experimental conditions, the F state is akaline (pH 10). The other state is obtained for low flow rates or for weakly alkaline feed flows, when the induction time of the chemical mixture is shorter than the residence time of the reactor. It is often called a Thermodynamic (T) or Reacted state because the reaction is almost completed in the CSTR. In our experimental conditions, the T state is acidic (pH 2). The domains of stability of these two states overlap over a finite range of parameter. 

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]. 

Introduction of membranes may, in some cases, lead to more flexibility in the design and study of chemical oscillators. The continuous-stirred tank reactor (CSTR) configuration, which is often used to study chemical oscillators because it maintains reaction and product concentrations away from equilibrium [1, 2], controls the transport of reactants, intermediates, and products by fluid flow, and does not discriminate among species. Membrane selectivity between chemical species can provide a basis for selection of dynamical behaviors that are unavailable with a CSTR. 

The dynamics of temperature and conversion within a cooled continuous-flow stirred tank reactor (CSTR) can be obtained from the material and energy balances. For a simple first order chemical reaction they are in a dimensionless form... 

Most chemical processes involve two important operations (reaction and separalion) that are typically carried out in different sections of the plant and use different equipment. The reaction section of the process can use several types of reactors [continuous stirred-tank reactor (CSTR), tubular, or batch] and operate under a wide variety of conditions (catalyzed, adiabatic, cooled or heated, single phase, multiple phases, etc.). The separation section can have several types of operations (distillation, extraction, crystallization, adsorption, etc.), with distillation being by far the most commonly used method. Recycle streams between the two sections of these conventional multiunit flowsheets are often incorporated in the process for a variety of reasons to improve conversion and yield, to minimize the production of undesirable byproducts, to improve energy efficiency, and to improve dynamic controllability. 

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. 

Computational fluid dynamics (CFD) is rapidly becoming a standard tool for the analysis of chemically reacting flows. For single-phase reactors, such as stirred tanks and empty tubes, it is already well-established. For multiphase reactors such as fixed beds, bubble columns, trickle beds and fluidized beds, its use is relatively new, and methods are still under development. The aim of this chapter is to present the application of CFD to the simulation of three-dimensional interstitial flow in packed tubes, with and without catalytic reaction. Although the use of... 

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. 

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