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Instable operating point

Figure 2.4 Semenov diagram the intersections S and I between the heat release rate of a reaction and the heat removal by a cooling system represent an equilibrated heat balance. Intersection S is a stable operating point, whereas I represent an instable operating point. Point C corresponds to the critical heat balance. Figure 2.4 Semenov diagram the intersections S and I between the heat release rate of a reaction and the heat removal by a cooling system represent an equilibrated heat balance. Intersection S is a stable operating point, whereas I represent an instable operating point. Point C corresponds to the critical heat balance.
A cold branch operating point. B instable operating point. [Pg.563]

The parameters used in the program give a steady-state solution, representing, however, a non-stable operating point at which the reactor tends to produce natural, sustained oscillations in both reactor temperature and concentration. Proportional feedback control of the reactor temperature to regulate the coolant flow can, however, be used to stabilise the reactor. With positive feedback control, the controller action reinforces the natural oscillations and can cause complete instability of operation. [Pg.351]

Chemical reactors are inherently nonlinear in character. This is primarily due to the exponential relationship between reaction rate and temperature but can also stem from nonlinear rate expressions such as Eqs. (4.10) and (4.11). One implication of this nonlinearity for control is the change in process gain with operating conditions. A control loop tuned for one set of conditions can easily go unstable at another operating point. Related to this phenomenon is the possibility of open-loop instability and multiple steady states that can exist when there is material and/or thermal recycle in the reactor. It is essential for the control engineer to understand the implications of nonlinearities and what can be done about them from a control standpoint as well as from a process design standpoint. [Pg.85]

In Section V, we have formally provided simple expressions [Eqs. (5.14), (5.15), and (5.16)] that allow passing from the moments to the parameters of the continued fractions. From a purely algebraic point of view the situation is satisfactory, but not from an operative point of view, an aspect which has often been overlooked in the literatiu e. Indeed, formulas bt ed on Hankel determinants could hardly be used for steps up to it == 10, because of numerical instabilities inherent in the moment problem. On the other hand, in a variety of physical problems (typical are those encountered in solid state physics ), the number of moments practically accessible may be several tens up to 100 or so the same happens in a number of simulated models of remarkable interest in determining the asymptotic behavior of continued fractions. In these cases, more convenient algorithms for the economical evaluation of Hankel determinants must be considered. But the point to be stressed is that in any case one must know the moments with a... [Pg.104]

Before performing a controllability analysis, ensure the stability of the plant. The first step is to close all inventory control loops, by means of level and pressure controllers. Then, check the stability, by dynamic simulation. If the plant is unstable, it will drift away from the nominal operating point. Eventually, the dynamic simulator will report variables exceeding bounds, or will fail due to numerical errors. Try to Identify the reasons and add stabilizing control loops. Often a simple explanation can be found in uncontrolled inventories. In other situations the origin is subtler. Some units are inherently unstable, as with CSTR s or the heat-integrated reactors. The special case when the instability has a plantwide origin will be discussed in Chapter 13. [Pg.493]

Figure 4-15, however indicates that an exclusion of static instability is not automatically sufficient for the safety assessment of the process under normal operating conditions. In this example operating points with high sensitivity values still exist. They are in the range of medium conversion values. Figure 4-17 shows the corre-spondii sensitivity values in addition to the previous information. [Pg.117]

Now it becomes obvious that the operating points with high sensitivity are dynamically unstable. This, as mentioned before, is not tolerable from a safety technical point of view. It can further be deduced that the exclusion of dynamic instability is the more stringent of the two stability requirements. [Pg.124]

This demonstrates the advantage of the graphical over the pure calculation method, which compares the values of two thermal reaction number values only. If the graphical presentation shows no operating point in the relevant range to be enveloped by the limiting curve of dynamic instability, it may also be concluded that all these points are statically stable. [Pg.124]

This article considers processes involving two reactants and two reactions. It is demonstrated that plantwide control relying on self-regulation results in regions of state multiplicity or unfeasibility, even if the stand-alone reactor has a unique, stable operating point. Moreover, when selectivity reasons require low per-pass conversion, instability is very likely. [Pg.431]

Figure 5. Instability of low conversion operating point in one-recycle systems. Figure 5. Instability of low conversion operating point in one-recycle systems.
Figure 9. Da-X bifurcation diagram for Figure 10. Instability of low conversion different kinetics (a=k2/ki). operating point in two-recycle systems. Figure 9. Da-X bifurcation diagram for Figure 10. Instability of low conversion different kinetics (a=k2/ki). operating point in two-recycle systems.
In multi-reaction systems, economical optimality implies high selectivity. This can be achieved at low per-pass conversion operating points that might be unfeasible due to the low-conversion instability. [Pg.436]

For multi-reactant / multi-reaction systems, state multiplicity occurs. The instability of the low-conversion branch restricts the selection of the operating point. [Pg.427]

A more rigorous analysis would show that the first inequality is a sufficient criterion for instability. If this inequality is satisfied, the operating point will be intrinsically unstable. The rigorous analysis also shows that the second criterion is a sufficient criterion for stability, provided that the CSTR is adiabatic. If the reactor is not adiabatic, the second condition is necessary, but not sufficient. [Pg.279]

Consider this eompressor operating in steady state at point A, with the reeyele valve elosed. If the resistanee in the eompressor diseharge system were to rise to point B, the eompressor would eneounter the surge region—essentially a region of flow instability. Catastrophie surge ineidents ean result in eomplete destruetion of the rotor. [Pg.391]

This first step makes necessary a correction of the atmosphere aberrations by means of an adaptive optics or at the minimum a tip tilt device. If the turbulence induces high aberrations the coupling efficiency is decreased by a factor VN where N is the number of spatial modes of the input beam. Note that tilt correction is also mandatory in a space mission as long as instabilities of the mission platform may induce pointing errors. Figure 10 (left) illustrates the spatial filtering operation. This function allows a very good calibration of... [Pg.298]

The lumped parameter model of Example 13.9 takes no account of hydrodynamics and predicts stable operation in regions where the velocity profile is elongated to the point of instability. It also overestimates conversion in the stable regions. The next example illustrates the computations that are needed... [Pg.499]

Stability or instability of a scheme from the primary family depends only on selection rules for the operator R. From the point of view of stability theory the arbitrariness in the choice of the operator R is restricted by the following requirements ... [Pg.455]

After the four ranks for levels of risk for fire, instability, toxicity and reactivity are established, other ranks will appear - dedicated to the operators involved (are they able to cope with potential dangers ), the peculiarities involved in setting up the apparatus (detecting weak points eg), effect of environmental conditions (lighting, supervision etc), and any rank likely to be involved in the globai security of the process. [Pg.33]


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See also in sourсe #XX -- [ Pg.51 ]




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