Continuous stirred tank reactor steady-state multiplicity

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

Emulsion Polymerization in a CSTR. Emulsion polymerization is usually carried out isothermally in batch or continuous stirred tank reactors. Temperature control is much easier than for bulk or solution polymerization because the small (. 5 Jim) polymer particles, which are the locus of reaction, are suspended in a continuous aqueous medium as shown in Figure 5. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. Gerrens and coworkers at BASF seem to be the first to report these phenomena both computationally and experimentally. Figure 6 (taken from ref. (253)) plots the autocatalytic behavior of the reaction rate for styrene polymerization vs. monomer conversion in the reactor. The intersection... 

Some specific aspects in the modeling of gas-liquid continuous-stirred tank reactors are considered. The influence of volatility of the liquid reactant on the enhancement of gas absorption is analyzed for irreversible second-order reactions. The impact of liquid evaporation on the behavior of a nonadiabatic gas-liquid CSTR where steady-state multiplicity occurs is also examined. 

Steady State Multiplicity, Stability, and Complex Transients. This subject is too large to do any real justice here. Ever since the pioneering works of Liljenroth (41), van Heerden (42), and Amundson (43) with continuous-flow stirred tank reactors, showing that multiple steady states — among them, some stable to perturbations, while others unstable — can arise, this topic has... 

Membrane reactor stability. Multiple steady states have been found in continuous stirred tank reactors (perfect-mixing reactors) or other reactors where mixing of process streams take place. This phenomenon is also evident in membrane reactors. The thermal management of a membrane reactor should be such that the reactor temperatures provide a stable range of operation. 

The classical problem of steady-state multiplicity in a continuous stirred tank reactor (CSTR) was brought to popular attention in 1953 in the theoretical article by Van Heerden. " Large amounts of experimental work which measured these steady states were performed by the group of Schmitz beginning in 1970. Schmitz also wrote two excellent reviews on multiplicity, stability, and sensitivity of steady states in chemical reactors and the application of bifurcation theory to determine the presence of steady-state multiplicity in chemical reactors.Even these reviews are not inclusive and it is our intention in this subsection to only provide a background to the novice in reactor design. 

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. 

Example 14. /. Multiple steady states and hysteresis in a nonisothermal continuous stirred-tank reactor (CSTR) [1,2]. In a CSTR, the curve for the temperature dependence of heat loss to the cooling coil is linear (loss proportional to temperature difference) while that for heat generation by the reaction is S-shaped (Arrhenius ex-... 

In continuous stirred-tank reactors (CSTRs), complex kinetics may give rise to multiple steady states even in isothermal operation, especially in heterogeneous catalysis. However, to unravel the causes may be difficult. Here, Feinberg s network theory can help [3]. It operates with a deficiency index that is a readily calculated zero or positive integer. The most useful result of the theory is ... 

While constructed to encompass all types of reactors, the theory is mainly oriented toward continuous stirred-tank reactors and steady-state multiplicity. [For batch reactions, the TOOLBOX returns the not very enlightening information that no steady state can be sustained for the hydrogen-oxygen reaction network 9-50 (deficiency zero in batch) it gives no warning that the system is explosive.]... 

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. 

Multiple steady-state behavior is a classic chemical engineering phenomenon in the analysis of nonisothermal continuous-stirred tank reactors. Inlet temperatures and flow rates of the reactive and cooling fluids represent key design parameters that determine the number of operating points allowed when coupled heat and mass transfer are addressed, and the chemical reaction is exothermic. One steady-state operating point is most common in CSTRs, and two steady states occur most infrequently. Three stationary states are also possible, and their analysis is most interesting because two of them are stable whereas the other operating point is unstable. 

Vasquez-Bahena J, Montes-Horcasitas MC, Ortega-Lopez J et al. (2004) Multiple steady-states in a continuous stirred tank reactor an experimental case study for hydrolysis of sucrose by invertase. Proc Biochem 39(12) 2179-2182... 

One unique but normally undesirable feature of continuous emulsion polymerization carried out in a stirred tank reactor is reactor dynamics. For example, sustained oscillations (limit cycles) in the number of latex particles per unit volume of water, monomer conversion, and concentration of free surfactant have been observed in continuous emulsion polymerization systems operated at isothermal conditions [52-55], as illustrated in Figure 7.4a. Particle nucleation phenomena and gel effect are primarily responsible for the observed reactor instabilities. Several mathematical models that quantitatively predict the reaction kinetics (including the reactor dynamics) involved in continuous emulsion polymerization can be found in references 56-58. Tauer and Muller [59] developed a kinetic model for the emulsion polymerization of vinyl chloride in a continuous stirred tank reactor. The results show that the sustained oscillations depend on the rates of particle growth and coalescence. Furthermore, multiple steady states have been experienced in continuous emulsion polymerization carried out in a stirred tank reactor, and this phenomenon is attributed to the gel effect [60,61]. All these factors inevitably result in severe problems of process control and product quality. 

Control of industrial polymerization reactors is a challenging task because, in general, control engineers lack rigorous polymerization process knowledge, process model, and rapid online or inline sensors to measure polymer properties. Exothermic polymerization processes often exhibit strongly nonlinear dynamic behaviors (e.g., multiple steady states, autonomous oscillations, limit cycles, parametric sensitivity, and thermal runaway), particularly when continuous stirred tank... 

The exciting issue of steady-state multiplicity has attracted the attention of many researchers. First the focus was on exothermic reactions in continuous stirred tanks, and later on catalyst pellets and dispersed flow reactors as well as on multiplicity originating from complex isothermal kinetics. Nonisothermal catalyst pellets can exhibit steady-state multiplicity for exothermic reactions, as was demonstrated by P.B. Weitz and J.S. Hicks in a classical paper in the Chemical Engineering Science in 1962. The topic of multiplicity and oscillations has been put forward by many researchers such as D. Luss, V. Balakotaiah, V. Hlavacek, M. Marek, M. Kubicek, and R. Schmitz. Bifurcation theory has proved to be very useful in the search for parametric domains where multiple steady states might appear. Moreover, steady-state multiplicity has been confirmed experimentally, one of the classical papers being that of A. Vejtassa and R.A. Schmitz in the AIChE Journal in 1970, where the multiple steady states of a CSTR with an exothermic reaction were elegantly illustrated. 

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