Stirred dynamic stability

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

Our understanding of the development of oscillations, multi-stability and chaos in well stirred chemical systems and pattern fonnation in spatially distributed systems has increased significantly since the early observations of these phenomena. Most of this development has taken place relatively recently, largely driven by development of experimental probes of the dynamics of such systems. In spite of this progress our knowledge of these systems is still rather limited, especially for spatially distributed systems. 

A reaction mass is to be concentrated by vacuum distillation in a 1600 hter stirred tank. Before distillation, the contents of the vessel are 1500 kg, containing 500 kg of product. The solvent should be totally removed from the solution at 120 °C, with a maximum wall temperature of 145 °C (5 bar steam). In order to evaluate the thermal stability of the concentrated product, a dynamic DSC experiment was performed (Figure 12.12). 

Viscosity (dynamic) a wide range of viscosity types are commercially available see Table V. Solutions should be prepared by gradually adding the hydroxypropyl cellulose to a vigorously stirred solvent. Increasing concentration produces solutions of increased viscosity. See also Section 11 for information on solution stability. 

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. 

Van Elk et al. [27] used a similar mathematical model, based on the penetration model for three reactants in an ideally stirred reactor, to study the dynamic behavior of the gas-liquid homogeneous hydroformylation process. The influence of mass and heat transfer on the reactor stability in the Idnetically controlled regime was analyzed and it brought to mind the existence of a dynamically unstable (limit circle) state under certain operating conditions. This model needs to be extended to account for the presence of a second liquid phase in biphasic hydroformylation. 

Multiple Steady States and Local Stability in CSTR.—In the two decades since the seminal work of van Heerden and Amimdson, there has been vast output of papers conoemed with the dynamic behaviour of stirred-tank reactors. Bilous and Amundson put the van He den analysis of local stability of the equilibrium state on a rigorous basis by use of linear stability theory. Their method is similar to the phase-plane treatments of thermokinetic ignitions and oscillations discussed here in Sections 4 and 3 (and preceded them dironologically). The mass and energy balance for the CSTR having a single reactant as feedstock may be expressed as ... 

As a consequence of their smaller drop size, the emulsions made through both dynamic processes will certainly exhibit a higher viscosity and probably a higher stability. Nevertheless, these two dynamically prepared emulsions will not be necessarily identical, since the actual drop size distribution depends upon the dynamic process character-isties, particularly the stirring efficiency. 

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. 

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). 

We shall turn now to the stirred tank reactor, which has been already studied in Section 1.8 relative to the existence of steady states. In this section we shall show that the steady states are odd in number, 2 m 4-1, among which m at least are unstable. Moreover, for values of the parameter 6 outside a certain range, the steady state is unique and stable. This will be the extent of our occupation with the stability problem. For standard work on the dynamics and stability of stirred tank reactors, including detailed phase space analyses, see the textbook of Aris [3], the work of Aris and Amundson [6,7], and Luus and Lapidus [32]. 

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