Stability, reactor

The complete design of any reactor must also take into account questions concerning the stability of operation, particularly in relation to heating effects. 

In an endothermic reaction, the reactant temperature will fall as reaction proceeds unless heat is supplied from an external source. With a highly endothermic reaction, it may be necessary to supply a considerable amount of heat to maintain a temperature high enough to provide a rate of reaction and equilibrium conversion which are large enough for the process to be operated economically. Under these circumstances, the rate of heat transfer may effectively determine the rate of reaction and so dominate the problems involved in the reactor design. 

With an exothermic reaction, on the other hand, it may be necessary to remove heat to control the reaction and, if the reaction is reversible, to ensure a reasonable equilibrium conversion. The possibility of thermal runaway is always present with an exothermic process and this, with its implications for safety, must always be examined in any full reactor design. 

The additional problems which arise in heterogeneous reactors, where hot spots may cause permanent damage to the catalyst by sintering, will be examined in Chap. 4. 

Consider a simple first-order exothermie reaction, A — B, carried out in a single, constant-volume, continuous stirred-tank reactor (Fig. 3.12), with constant jacket coolant temperature, where r = - k Ca,. 

At steady state, the temperature and concentration in the reactor are constant with respect to time and 

From the steady-state heat balance the heat losses can be equated to the heat gained by reaction, giving 

The above equation then represents the balanced conditions for steady-state reactor operation. The rate of heat loss, Hl, and the rate of heat gain, Hq, terms may be calculated as functions of the reactor temperature. The rate of heat loss, Hl, plots as a linear function of temperature and the rate of heat gain, Hq, owing to the exponential dependence of the rate coefficient on temperature, plots as a sigmoidal curve, as shown in Fig. 3.14. The points of intersection of the rate of heat lost and the rate of heat gain curves thus represent potential steady-state operating conditions that satisfy the above steady-state heat balance criterion. 

The cooling conditions given by curve II, however, indicate three potential steady-state solutions at the curve intersections. A, B and C. By considering the effect of small temperature variations, about the three steady-state conditions, it can be shown that points A and C represent stable, steady-state operating 

Rate of heat generation by chemical reaction in the reactor 

Suppose that the temperature fluctuation, Sr, was in the opposite stability of the operating point U to this diange. What direction, such that the reactor temperature dropped. Analyze the operating point is reached eventually  

Because of this behavior, we say that the point U is intrinsically unstable. A very small fluctuation in temperature (or composition) will cause the reactor to wander away from an intrinsically unstable operating point until it reaches some other steady-state operating point. 

Suppose that the temperature fluctuation, ST, was in the opposite direction, such that the reactor tenqteratuie dropped. 

The question of whether the reactor operates at SI or S2 depends on how it is started up. In order to determine the effect of startup conditions, the unsteady-state energy and material balances must be solved simultaneously. This task is beyond the scope of this chapter. 

The type of stability analysis carried out above is not mathematically rigorous. However, it is a very useful way to understand the concept of stable and unstable operating points. In mathematical terms, the above analysis has shown that a steady-state operating point will be unstable if 

The water-to-fuel volume ratio is determined from consideration of the reactivity coefficient for safe and stable operation. This ratio is selected to provide cold lattice coefficients. 

---

Heat Release and Reactor Stability. Highly exothermic reactions, such as with phthaHc anhydride manufacture or Fischer-Tropsch synthesis, compounded with the low thermal conductivity of catalyst peUets, make fixed-bed reactors vulnerable to temperature excursions and mnaways. The larger fixed-bed reactors are more difficult to control and thus may limit the reactions to jacketed bundles of tubes with diameters under - 5 cm. The concerns may even be sufficiently large to favor the more complex but back-mixed slurry reactors. 

Plug flow characteristics of aging reactor Stabilization (hydrolysis)... 

Comprehensive discussions on reactor stability theories and safe engineering problems were presented by Eigenberger and Schuler (1986, 1989), Zaldivar (1991), Barton and Rogers (1993), and Grewer (1994). The very basic theory developed by Semenov (1928) for zero-order reactions is very illustrative for a physical explanation of explosion phenomena. The theory enables evaluation of conditions at which thermal explosion will occur. 

Figure 3.17. Phase-plane representations of reactor stability. In the above diagrams the point -I- represents a possible steady-state solution, which (a) may be stable, (b) may be unstable or (c) about which the reactor produces sustained oscillations in temperature and concentration.

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. 

In the operation of BWRs, especially when operating near the threshold of instability, the stability margin of the stable system and the amplitude of the limit cycle under unstable condition become of importance. A number of nonlinear dynamic studies of BWRs have been reported, notably in an International Workshop on Boiling Water Reactor Stability (1990). The following references are mentioned for further study. 

It is well known, and it has been seen in the previous example, that to scale-up the size of a CSTR affects the reactor stability, because the ratio of heat transfer area to reactor volume decreases as far as the size of the reactor is increased (they are proportional to the square and power of three, respectively). 

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... 

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 first step is relevant to the start-up phase, which in this particular case we chose to extend for up to 1 h in order to verify the reactor stability also in these conditions, where water is not present and while there is a higher oxygen concentration in the feed gas with respect to the ATR conditions. By lowering the 02 CH4 ratio, the H2 concentration at the reactor outlet increases, approaching the value expected by thermodynamic evaluation and CH4 conversion is still complete. A further decrease in the 02 CH4 feed ratio to values lower than 1.16 corresponds to an abrupt decrease in temperature in the lower section and a simultaneous temperature increase in the catalytic reforming section. 

With single reactions we are concerned with conversion level and reactor stability. Questions of product distribution do not occur. 

In the wet oxidation process, materials partially or completely dissolve into a homogeneous, condensed-phase mixture of oxygen and water, and chemical reactions between the material and oxygen take place in the bulk water phase. This condensed-phase makes wet oxidation an ideal process to transform materials which would otherwise be non-soluble in water to a harmless mixture of carbon dioxide and water. Since oxidation reactions are also exothermic, the high thermal mass of supercritical water makes this reaction medium better suited for thermal control, reactor stability, and heat dissipation. The purpose of this research was to establish a new method for selectively oxidizing waste hydrocarbons into new and reusable products. 

Catalytic test. The catalytic behavior was evaluated for the gas phase isobutene trimerization reaction using a fixed bed reactor, with dimensions of 2 cm of diameter and 55 cm of length respectively. The operation conditions and evaluation procedure were as follows the catalyst was activated at 400°C in flowing air (1 ml/s) during 8 hours. After the activation treatment, temperature was lowered to 40°C and a mixture of isobutane/isobutene 72 28 w/w was feed. The GHSV value was varied to 8, 16, 32 and 64 h respectively. The average time of reaction was 11 h. The time of reactor stabilization after the beginning of the catalytic evaluation was 2 h. 

The autocatalytic reaction scheme A + 2B —> 3B, B —> C was introduced in 1983s and has proved itself to be fecund of useful applications in the study of reactor stability and chemical oscillations.6 We shall depart from their notation for we wish to be able to generalize to several species, Au and it is not desirable to use the concentration of A as a reference concentration when it is going to be varied. Similarly, the several species will have different rate constants for the several autocatalytic steps and therefore the first-order rate constant of B — C is most apt for the time scale. 

The interest in periodically forced systems extends beyond performance considerations for a single reactor. Stability of structures and control characteristics of chemical plants are determined by their responses to oscillating loads. Epidemics and harvests are governed by the cycle of seasons. Bifurcation and stability analysis of periodically forced systems is especially important in the... 

Amundson, N. R. and Aris, R., 1958, An analysis of chemical reactor stability and control—I. Chem. Engng Sci 7,121-131. 

An analysis of chemical reactor stability and control-IV Mixed derivative and proportional control. (with D.J. Nemanic, J.W. Tierney, and N. R. Amundson). Chem. Eng. Sci. 11, 199-206 (1959). 

---