Stirred-tank reactor, stability

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

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. 

This set of first-order ODEs is easier to solve than the algebraic equations where all the time derivatives are zero. The initial conditions are that a ut = no, bout = bo,... at t = 0. The long-time solution to these ODEs will satisfy Equations (4.1) provided that a steady-state solution exists and is accessible from the assumed initial conditions. There may be no steady state. Recall the chemical oscillators of Chapter 2. Stirred tank reactors can also exhibit oscillations or more complex behavior known as chaos. It is also possible that the reactor has multiple steady states, some of which are unstable. Multiple steady states are fairly common in stirred tank reactors when the reaction exotherm is large. The method of false transients will go to a steady state that is stable but may not be desirable. Stirred tank reactors sometimes have one steady state where there is no reaction and another steady state where the reaction runs away. Think of the reaction A B —> C. The stable steady states may give all A or all C, and a control system is needed to stabilize operation at a middle steady state that gives reasonable amounts of B. This situation arises mainly in nonisothermal systems and is discussed in Chapter 5. 

This conclusion is in agreement with observations of the performance of stirred tank reactors. Nonetheless, it is the situation where the intersection occurs at an intermediate value of the conversion (or of Qg) that is of greatest interest from a stability analysis viewpoint. 

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 solutions of the nonsteady-state expression, Eq. (164), both for single tanks and chains of tanks have been made by Acton and Lapidus (Al), Mason and Piret (M5, M6), and Standart (S22). Aris and Amundson (A15, A16), Bilous and Amundson (B7), Bilous et al. (B9), and Gilles and Hofmann (G3) have studied the stability, control, and response of a stirred tank reactor. 

Stability estimates for the stirred tank reactor (with W. Regenass). Chem. Eng. ScL 20, 60-66 (1964). 

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). 

In the production of 2, strains with entA - mutation have long-term stability and production rates are high. Typical cultivation of 2,3-trans-CHD 2 is performed at pH 6.8 and 37 °C in a stirred-tank reactor with glucose feeding in a fed-batch mode. Microbial production over a process time of 40 h affords 92 g 2 from 690 g glucose monohydrate in a 20-L cultivation experiment. This corresponds to a molar yield of 17% [13]. Advantageously, 2,3-trans-CHD 2 is the major product with no... 

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... 

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. 

Westbrook, G. 1960. The simulation, stabilization and optimization of stirred tank reactors on the digital computer, M.S. Thesis. Department of Chemical Engineering, University of Minnesota, Minneapolis, Minnesota. 

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. 

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