Operating conditions, stable/unstable

Either of the two stable operating conditions can be selected by adjusting the positions of the curves so that only one intersection is obtained. In a plant, long-time unstable operation is unlikely because of imprecise temperature control. 

It is worthwhile to note here that in Figs. 3 and 4 the current densities measured at a methanol and air flow rates of 2 ml/min and 2 L/min, respectively show the inconsistency even at the same operating conditions. The reason is expected to be due to the water produced at the cathode. Comparing Figs. 3 and 4, the measured current density response looks quite unstably scattered at low air flow rates in Fig. 3, while it seems to be stable even at the low methanol flow rates in Fig. 4. This instability of measured current density in Fig. 4 could have caused by the water formed at the cathode during the operation of the stack. In fact, it has been observed from the experiment that the water produced at the cathode looks accumulated in the cathode flow channels for a while and it bursts out intermittently to the cathode outlet. Based on the experimental observations, for the stable operation of the 5W... 

When Wa = substituted aminoacyl, that is, when Wa-Xaa is a peptide, there is a strong tendency to form an oxazolone. The 2-alkyl-5(4//)-oxazolone that is formed is chirally unstable. Isomerization of the 2-alkyl-5(4//)-oxazolone generates diaste-reomeric products. When Wa = R0C=0, there is a lesser tendency to form an oxazolone. The 2-alkoxy-5(4/7)-oxazolone that is formed is chirally stable. No isomerization occurs under normal operating conditions. Finally, when Wa = R0C=0, an additional productive intermediate, the symmetrical anhydride, can and often does form. 

What makes controller design challenging is that all real processes can be made closed loop unstable when a controller is implemented to steer the process to specified operating conditions. In other words, a process which is open loop stable and therefore will come to a new, although not the desired, steady state after a disturbance may become unstable when a controller is implemented to steer the process towards the desired steady state. Stability is therefore of vital concern in all control systems. 

The lamps may be operated on AC or DC, but for polymerisation studies and radical lifetime measurements DC must be used. For a low-pressure lamp the intensity falls to nearly zero 120 times per second for a 60 cycles AC source " the high-pressure lamp also tends to be unstable with AC . Circuits (Fig. 35) are shown for medium-pressure and high-pressure lamps operating procedures are given quite clearly in these last two references. The low-pressure lamp reaches stable operating conditions quite quickly, but the other two types require some time to do so (10-15 min). The high-pressure lamp also has a very short lifetime. 

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 conditions, whereas the curve intersection point B is unstable. On start up, the reaction conditions will proceed to an eventual steady state, at either point A or... 

The combustor is naturally unstable under certain operating conditions. Figure 16.7 shows combustor pressure oscillations and the Fast Fourier Transform (FFT) spectrum under atypical, unstable operating condition. The fundamental mode at 39 Hz and its higher harmonics were observed. The fundamental-mode frequency corresponds to the inlet quarter-wave mode of acoustic oscillations. During stable operation as shown in Fig. 16.8, the amplitude of pressure oscillations is much less. Also, no significant peak was observed in the pressure spectrum. 

It is important to note that the behaviour of these steady states is not identical with respect to inherent disturbances in operating conditions, as for example feed reactor temperature, composition or flow rate of the feed, or temperature and flow rate of the cooling agent, etc. Some are insensitive to such variations, in the sense that after the disturbance vanishes the system comes back naturally in the original state. These are stable stationary states, as the points A and C in Fig. 8.17. In the case of the point B the situation is essentially different. This is an unstable stationary state because in the absence of a control action small disturbances will move the system either to the high conversion state (reaction ignition), or to the low conversion state (reaction extinction). This type of behaviour is dangerous for operation and must be avoided. 

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. 

The transition from stable operating conditions at low temperatures to an unstable point and then stable high-temperature operation can be illustrated on an Arrhenius plot of ln(rate) versus reciprocal gas temperature,... 

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