Unstable conditions, operation

The type of initiator used affects the molecular weight and conversion limits in a reactor of fixed size and the molecular weight distribution of the material produced at a given conversion level. The initiator type also dictates the amount of initiator which is necessary to yield a given conversion to polymer, the operating temperature range of the reactor and the sensitivity of the reactor to an unstable condition. Clearly, the initiator is the most important reaction parameter in the polymer process. 

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. 

Still be very sensitive to a particular variable. On the other hand, an unstable condition is such that the least perturbation will lead to a finite change and such a condition may be regarded as infinitely sensitive to any operating variable. Sensitivity can be fully explored in terms of steady state solutions. A complete discussion of stability really requires the study of the transient equations. For the stirred tank this was possible since we had only to deal with ordinary differential equations for the tubular reactor the full treatment of the partial differential equations is beyond our scope here. Nevertheless, just as much could be learned about the stability of a stirred tank from the heat generation and removal diagram, so here something may be learned about stability from features of the steady state solution. 

Second, catalysis was a chapter of chemistry, well defined and limited to the chemistry of combinations unstable under operating conditions. 

Carbon is thermodynamically unstable at operating conditions of a PEMFC cathode because the equihbrium potential of its electrooxidation to carbon dioxide is ES/C02 = 0-207 V versus RHE at 298 K [8,247], In 1970s-1980s, corrosion... 

Equation (5.22) offers a quick way of estimating the reactor stability. If AT, is 20°C and the preliminary design calls for T = 80°C and 7 = 30°C with a moderate conversion, the reactor would probably be uncontrollable since [T — 7 ) >> AT,. With a greater value of UA and (T — 7 ) = 25°C, the reactor would be unstable according to Eq. (5.22). But if the reaction is first order, a more thorough analysis using Eq. (5.13) might indicate stable operation. However, it would be risky to operate close to unstable conditions unless controls are present to prevent a runaway reaction. 

It is clear from what happened that the operators at Chernobyl did not realise the significance of violating the operating rules and taking the reactor to an extremely unstable condition. They seem to have been determined to carry out the planned test to the exclusion of all other considerations. In the UK considerable emphasis is placed on operators being trained to appreciate the factors bearing on safe operation of the plant and to adhere strictly to them. 

In the consideration of mine shaft ventilation, the limit flow volume, or, the limit air velocity, is often a subject of study, such as the McPherson s maximum relative velocity proposal (McPherson 1993 de la Vergne 2003). This issue has mainly been related to the evaluation of the fan capacity and the energy consumption, whereas few reports are about the influence of increased flow volume beyond the conventional design guideline on conveyance motion or hoisting operation. For a ventilation network that utilizes a vertical production shaft as the intake or exhaust, it is necessary to investigate the conveyance motion under the increased flow volume to ensure the conveyance will not run under unstable conditions. 

The strong parametric sensitivity resulting from this coupling largely determines the start-up procedure, steady-state and transient operations (Ruiz et al., 1995). Moreover, even small variations in the input variables might lead to unstable conditions (Alejski and Duprat, 1996). This fact implies that a feasible operation of a RD column requires several control loops to mitigate the effects of disturbances. 

However, how does one design a column away from unstable conditions in the hrst place and then operate it within the operating window when process conditions vary ... 

A marginal flooding condition will, however, result in an unstable tower operation. Unexplained swings in bottoms product rate or bottoms level likely mean the trays are alternatively priming and dumping. A sudden drop in the temperature difference between the top and bottom of a tower, followed by a return to a normal temperature profile, indicates a marginal... 

It is known that controlled operation of chemical reactors at naturally unstable conditions should be of interest in the design of some commereial reactors because the unstable or so-called intermediate states may offer a desirable compromise between a state of very low activity or conversion on the one hand and a state of poor selectivity on the other l. In the present paper the model of a tubular reactor with negligible mass diffusivity and high diffusivity of heat is considered. 

Figure 1.31 shows the decay ratio contour map for coupled neutronic and thermal-hydraulic stability of the Super LWR. The decay ratio contour line of DR =1.0 indicates the stability boundary on the power versus flow rate map of the Super LWR. At the high power low flow rate region, the reactor becomes unstable. At low power operation and during startup, it is necessary to take care to satisfy the stability criteria. At the low power low flow rate region, the unstable conditions should be avoided by carefully adjusting the flow rate. 

Partial power operating conditions are also analyzed to investigate the stability during the power increase phase. The calculated decay ratios at 40% core power with various flow rates are shown in Fig. 5.51 and those at 50% core power are shown in Fig. 5.52. The decay ratio map is shown in Fig. 5.53. Unstable conditions arise when the power to flow rate ratio is high, especially at low power operation. Figure 5.54 shows the flow rate required to satisfy the criterion of coupled neutronic... 

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