Continuous stirred reactor periodic states

Transitions Between Periodic and Chaotic States in a Continuous Stirred Reactor... 

Experimental Observation of Multiple Steady States and Periodic Activity for a Continuous Stirred-Tank Reactor... 

Example 4.8 Chemical reactions and reacting flows The extension of the theory of linear nonequilibrium thermodynamics to nonlinear systems can describe systems far from equilibrium, such as open chemical reactions. Some chemical reactions may include multiple stationary states, periodic and nonperiodic oscillations, chemical waves, and spatial patterns. The determination of entropy of stationary states in a continuously stirred tank reactor may provide insight into the thermodynamics of open nonlinear systems and the optimum operating conditions of multiphase combustion. These conditions may be achieved by minimizing entropy production and the lost available work, which may lead to the maximum net energy output per unit mass of the flow at the reactor exit. 

The principal advantage of continuous reaction vessels is that they operate (after an initial transient period) under steady-state conditions that are conducive to the formation of a highly uniform and well-regulated product. In this section, we shall confine the discussion to continuous stirred-tank reactors (CSTRs). These reactors are characterized by isothermal, spatially uniform operation. 

The term semibatch reactor has sometimes been used for the continual operation of a reactor in the transient state. Such would be the case if a stirred reactor were started up and shut down on a repeated cycle, with a significant proportion of the production contributed from periods during... 

The U-sequence has been found in experiments on the Belousov—Zhabotinsky chemical reaction. Simoyi et al. (1982) studied the reaction in a continuously stirred flow reactor and found a regime in which periodic and chaotic states alternate as the flow rate is increased. Within the experimental resolution, the periodic states occurred in the exact order predicted by the U-sequence. See Section 12.4 for more details of these experiments. 

These are systems that exchange both energy and matter with the environment through their boundaries. The simplest chemical reaction engineering example is the continuous stirred tank reactor. These systems do not tend toward their thermodynamic equilibrium, but rather towards a state called stationary non-equilibrium state and is characterized by minimum entropy production. Open systems near equilibrium have unique stationary non-equilibrium state, regardless of the initial conditions. However far from equilibrium these systems may exhibit multiplicity of stationary states and may also exhibit periodic states. 

Polymerizations. Polymerizations were performed in solution with a 0.5-L continuous stirred tank reactor this apparatus provided polymers of constant composition. After steady-state operation was obtained (approximately three residence times, see Figure 1), 10-mL samples were periodically taken from the effluent, added to 200 xL of a hydroquinone solution, and stored at 10 °C. These samples were subsequently analyzed by HPLC to estimate the mean and variance of the residual monomer concentration and copolymer composition. The polymerization temperatures were 45 and 60 °C for the dimethylamines and 50 °C for DADMAC. The initial monomer concentration was 0.5 mol L" and the monomer feed ratio was varied between 0.3 and 0.7. Azocyanovaleric acid (ACV, Wako Chemical Co.) and potassium persulfate (KPS, BDH Chemicals) were used to initiate the reaction. The solution was agitated at 300 1 rpm for the duration of the polymerization. 

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. 

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... 

The reactor vessel is usually a stirred tank. The monomer phase is subjected either to turbulent pressure fluctuations or to viscous shear forces, which break it into small droplets that assume a spherical shape under the influence of interfacial tension. These droplets undergo constant collisions (collision rate >1 s ), with some of the collisions resulting in coalescence. Eventually, a dynamic equilibrium is established, leading to a stationary mean particle size. Individual drops do not retain their unique identity, but undergo continuous breakup and coalescence instead. In some cases, an appropriate dispersant can be used to induce the formation of a protective Aim on the droplet surface. As a result, pairs of clusters of drops that tend to coalesce are broken up by the action of the stirrer before the critical coalescence period elapses. A stable state is ultimately reached in which individual drops maintain their identities over prolonged periods of time [247]. 

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