Oscillatory solution, stirred tank reactor

In this short initial communication we wish to describe a general purpose continuous-flow stirred-tank reactor (CSTR) system which incorporates a digital computer for supervisory control purposes and which has been constructed for use with radical and other polymerization processes. The performance of the system has been tested by attempting to control the MWD of the product from free-radically initiated solution polymerizations of methyl methacrylate (MMA) using oscillatory feed-forward control strategies for the reagent feeds. This reaction has been selected for study because of the ease of experimentation which it affords and because the theoretical aspects of the control of MWD in radical polymerizations has attracted much attention in the scientific literature. 

The classical problem of multiple solutions and undamped oscillations occurring in a continuous stirred-tank reactor, dealt with in the papers by Aris and Amundson (39), involved a single homogeneous exothermic reaction. Their theoretical analysis was extended in a number of subsequent theoretical papers (40, 41, 42). The present paragraph does not intend to report the theoretical work on multiplicity and oscillatory activity developed from analysis of governing equations, for a detailed review the reader is referred to the excellent text by Schmitz (3). To understand the problem of oscillations and multiplicity in a continuous stirred-tank reactor the necessary and sufficient conditions for existence of these phenomena will be presented. For a detailed development of these conditions the papers by Aris and Amundson (39) and others (40) should be consulted. 

Later Uppal et al. (1974) applied the bifurcation theory to find all the solutions including the oscillatory solutions of the Continuous Stirred Tank Reactor. The CSTR equations that they studied are simplied form of those studied by Gurel and Lapidus (1965) more specifially the exponents b2 and b3 are equal to one ... 

Doedel, E.J. R.F. Heinemann. 1983. Numerical computation of periodic solution branches and oscillatory dynamics of the stirred tank reactor with A —> B C reactions. Chem. Eng. Sci. 38 1493-9. 

Continuous stirred tank reactor polymerization reactors can also be subject to oscillatory behavior. A nonisothermal CSTR free radical solution polymerization can exhibit damped oscillatory approach to a steady state, unstable (growing) oscillations upon disturbance, and stable (limit cycle) oscillations in which the system never reaches steady state and never goes unstable, but continues to oscillate with a fixed period and amplitude. However, these phenomena are more commonly observed in emulsion polymerization. High-volume products such as styrene-butadiene rubber (SBR) often are produced by continuous emulsion polymerization. As noted earlier, this is... 

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