Continuous stirred tank reactor stability

Chapter 1 reviews the concepts necessary for treating the problems associated with the design of industrial reactions. These include the essentials of kinetics, thermodynamics, and basic mass, heat and momentum transfer. Ideal reactor types are treated in Chapter 2 and the most important of these are the batch reactor, the tubular reactor and the continuous stirred tank. Reactor stability is considered. Chapter 3 describes the effect of complex homogeneous kinetics on reactor performance. The special case of gas—solid reactions is discussed in Chapter 4 and Chapter 5 deals with other heterogeneous systems namely those involving gas—liquid, liquid—solid and liquid—liquid interfaces. Finally, Chapter 6 considers how real reactors may differ from the ideal reactors considered in earlier chapters. 

The main features of the copper catalyzed autoxidation of ascorbic acid were summarized in detail in Section III. Recently, Strizhak and coworkers demonstrated that in a continuously stirred tank reactor (CSTR) as well as in a batch reactor, the reaction shows various non-linear phenomena, such as bi-stability, oscillations and stochastic resonance (161). The results from the batch experiments can be suitably illustrated with a two-dimensional parameter diagram shown in Pig. 5. 

J. Alvarez-Ramirez, J. Snarez, and R. Femat. Robust stabilization of temperature in continuous-stirred tank reactors. Chem. Eng. Sci., 52(14) 2223-2230, 1997. 

There are several control problems in chemical reactors. One of the most commonly studied is the temperature stabilization in exothermic monomolec-ular irreversible reaction A B in a cooled continuous-stirred tank reactor, CSTR. Main theoretical questions in control of chemical reactors address the design of control functions such that, for instance (i) feedback compensates the nonlinear nature of the chemical process to induce linear stable behavior (ii) stabilization is attained in spite of constrains in input control (e.g., bounded control or anti-reset windup) (iii) temperature is regulated in spite of uncertain kinetic model (parametric or kinetics type) or (iv) stabilization is achieved in presence of recycle streams. In addition, reactor stabilization should be achieved for set of physically realizable initial conditions, (i.e., global... 

The relevant parameter for studies of operating stability of enzymes is the product of active enzyme concentration [E]active and residence time T, [E]active T. In a continuously stirred tank reactor (CSTR) the quantities [E]active and T are linked by Eq. (2.28), where [S0] denotes the initial substrate concentration, x the degree of conversion and r(x) the conversion-dependent reaction rate (Wandrey, 1977 Bommarius, 1992). 

Example 5—Stability dependence on the set of inputs. Consider a continuous stirred-tank reactor modeled by the following equations, in continuous time ... 

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. 

Low-temperature solution processes are state-of-the-art for the production of ethylene/propylene or ethylene/propylene/diene elastomers (EPDR or EPDM). A continuous stirred-tank reactor (CSTR) or a series of two or even more such reactors is used [2]. n-Hexane, n-heptane, or Ce, C7 fractions are the solvents. Catalyst, co-catalyst and other compounds are introduced with the solvent into the reactor. The monomers (ethylene, propylene) are injected as gases other olefins are introduced in liquid form. The polymerization process runs around 50 °C and at pressures up to 2 MPa. Downstream the catalyst/co-catalyst system is deactivated and their residues are dissolved in dilute acid or aqueous NaOH. The copolymer is stabilized with an antioxidant. Steam treatment removes the rest of the solvent and monomers, and agglomerates the product to crumbs. These crumbs are then dried and finished to bales or pellets. 

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. 

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. 

However, a commercially feasible process for bulk polymerization in a continuous stirred tank reactor has been developed by Montedison Fibre [103,104]. The heat of reaction is controlled by operating at relatively low-conversion levels and supplementing the normal jacket cooling with reflux condensation of unreacted monomer. Operational problems with thermal stability are controlled by using a free radical redox initiator with an extremely high decomposition rate constant. Since the initiator decomposes almost completely in the reactor. 

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. 

The work-up of batch processes, run in stirred vessels, had often faced the challenge to efficiently separate and recover the enzyme used. Meanwhile, there is abundant know-how available to immobilise enzymes on different carriers, though some issues need always to be considered maintained activity of the enzyme, its stability towards solvents and the operating temperature used in a reaction. Enzyme immobilisation allows for continuous reactions carried out in columns or in a sequence of continuous stirred-tank reactors. Certain advantages are offered by Degussa s enzyme-membrane-reactor (EMR), where the enzyme is surrounded by a hoUow-fibre membrane, that is permeable to substrate and product. 

A large number of case studies is reported in scientific literature dealing with physical equilibria, design purposes for unit operations, reactor stability, and so on. We have included some below to highlight their individual peculiarities. These include heat exchange in a thermal furnace, vapor-liquid equilibrium calculation, multiple solutions in a continuously stirred tank reactor (CSTR) reactor, and critical nuclear reactor size. Certain special cases are also discussed in Section 7.22. 

Rastogi, R. P. Das, I. Singh, A. R. 1984. A New lodate Driven Nonperiodic Oscillatory Reaction in a Continuously Stirred Tank Reactor, J. Phys. Chem. 88, 5132-5134. Rawlings, J. B. Ray, W. H. 1987. Stability of Continuous Emulsion Polymerization Reactors A Detailed Model Analysis, Chem. Eng. Sci. 42, 2767-2777. 

For slower reactions a different kind of constant power reactor is used, known as the agitated cell reactor. The agitated cell reactor (ACR) shown in Figure 5.42 is a form of constant power reactor where the product flows through a series of agitated cells. The concept adapts a well-rooted meso-scaled technique of the continuously stirred tank reactor to the constant power notion for greater increase in process control and stability. 

Other suggestions have been made concerning the measurement of relative stability. One such suggestion [3] was based on the connections of two continuous stirred tank reactors, CSTRs, each filled with one or the other stable stationary state the final state of both CSTR is predicted to be the more stable stationary state. However, the final state has been shown theoretically [4] and experimentally [5,6] to depend also on the strength and manner of mixing of the CSTRs, and therefore is not a useful, direct measure of relative stability. 

Another continuous operation that is very popular in industry, but is not used very much in the chemical laboratory, is the continuous stirred tank reactor (CSTR) (it is silently assumed that the CSTR is operated in the steady state). The reactants are fed continuously into a well stirred vessel, and a constant product flow leaves the reactor through an exit port that can be located anywhere in the reactor wall. If the reactor contents are indeed well mixed, the reactants entering the vessel are diluted immediately, and the reaction proceeeds at relatively low reactant concentrations. The pr uct flow leaving the reactor must then have the same composition as the reaction mixture. This may appear to be an illogical way of carrying out a chemical reaction, but it has several distinct advantages, at least for reactions that are intrinsically rapid. The most important advantage is the thermal stability, especially in the case of exothermic reactions. Since the reaction proceeds at low reactant concentrations, the reaction rate per unit volume is relatively low, and so is the heat evolution. These are both constant in time. 

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