Multiplicity, continuous stirred tank reactor

ILLUSTRATION 10.2 DETERMINATION OF HEAT TRANSFER AND VOLUME REQUIREMENTS FOR SINGLE AND MULTIPLE CONTINUOUS STIRRED TANK REACTORS... 

A cascade of three continuous stirred-tank reactors arranged in series, is used to carry out an exothermic, first-order chemical reaction. The reactors are jacketed for cooling water, and the flow of water through the cooling jackets is countercurrent to that of the reaction. A variety of control schemes can be employed and are of great importance, since the reactor scheme shows a multiplicity of possible stable operating points. This example is taken from the paper of Mukesh and Rao (1977). 

P. Gray and S. K. Scott. Autocatalytic reactions in the isothermal continuous stirred tank reactor Isolas and other forms of multiplicity. Chem. Eng. ScL 38, 29-43 (1983) Autocatalytic reactions in the isothermal continuous stirred tank reactor Oscillations and instabilities in the system A + 2B —> 3B, B —> C. Chem Eng. ScL 34, 1087-1097 (1984). 

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. 

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. 

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. 

Ignore the size of a process unit and multiple process units of the same type in series, such as the number of evaporators for multi-effect evaporation or the number of Continuously Stirred Tank Reactors (CSTRs). 

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. 

Features - continuous stirred tank reactors with agitators are used - multiple reactor zones typically used - polymerization takes place in "solution" - organic peroxides typically used as initiators - polymer has fewer branches but of somewhat longer length relative to tubular process... 

Ideal continuously stirred tank reactor (CSTR), including single and multiple stages... 

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.]... 

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. 

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. 

Cohen, D.S. J.P. Keener. 1976. Multiplicity and stability of oscillatory states in a continuous stirred tank reactor with exothermic consecutive reactions A B C. Chem. Eng. Sci. 31 115-22. 

Both to ascertain the role of the catalyst and to demonstrate the efiFects of pH, experiments have been performed at controlled levels of conversion of formaldehyde in a continuously stirred tank-reactor. Figure 2 shows such a simple reactor, in which the feed streams are segregated and the slurry of calcium hydroxide is kept agitated. Commercial, 37-percent formaldehyde solution is fed in from a separate reservoir, and a multiple-channel, peristaltic pump permits independent variation of the feed rates. 

MULTIPLE STATIONARY STATES IN CONTINUOUS STIRRED TANK REACTORS... 

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... 

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