Periodic regimes of continuous stirred tank reactors

Continuously stirred decanting reactor: Operability and stability considerations

“…Uppal et al (1974Uppal et al ( , 1976 and Vaganov et al (1978) were the first to apply this technique to map the dynamic features of a CSTR. A steady state becomes unstable and periodic solutions appear at a Hopf bifurcation (Hopf, 1942;Hassard et al, 1981;Iooss and Joseph, 1981;Chow and Hale, 1982;Golubitsky and Schaeffer, 1985), which is of codimension 1, since only the bifurcation parameter is fixed.…”

When do chemical reactions promote mixing?

“…(20) for a CSTR are possible. Such solutions have been found before [51,52] and analyzed in detail by Vaganov et al [11]. The threshold for an "oscillatory" instability is determined by the condition that  is zero at T = T min , where dT/d = 0 and T min is the stationary temperature corresponding to a minimum in V. Furthermore, this condition for the onset of oscillations may pass through the cuspidal point, when parameters are changed in magnitude.…”

“…This often holds true, in which case the dimensionless group  disappears from Eqs (1) and (2), leaving only three dimensionless numbers (Se, Da and Ze) to characterize the dependence of both  and  on . In fact, in this situation, the above two equations have the important significance that the dynamics of the approach to a steady state for the reactor and also the stability of each steady state of a CSTR can be characterized on a plot of Se versus Da for the appropriate value of Ze [5,11]. It is well known that there is a domain on the (Da, Se) plane, corresponding to the CSTR having two steady states: one is at a high temperature, the other at a lower temperature.…”

Increasing the reactant conversion through induced oscillations in a continuous stirred tank reactor by using PI control

“…The continuous stirred tank reactors (CSTR) in which a simple irreversible reaction A → B occurs has been widely used for investigating nonlinear phenomena [1][2][3][4]. The study of oscillating behaviors in a CSTR, with and without control, has shown that steady states, limit cycles and even chaotic behaviors can be obtained [5][6][7].…”

“…In prior works [1][2][3][4][5][6], [15][16][17][18][19][20], simple models considering only two independent variables of a controlled CSTR (such as concentration and temperature) have been analyzed to exploit the oscillating behavior. In this paper, a more general model is considered taking into account the mass balance of inert components (water with sulfur acid and methanol), the energy balances in the reactor and the coolant jacket and the equations of the control system.…”