Transient Reactor Period

With the introduction of microreactors, transient reactor operations became interesting due to their low internal reactor volume and, thus, fast dynamic behavior. In 1999, Liauw et al. presented a periodically changing flow to prevent coke development on the catalyst and to remove inhibitory reactants in an IMM microchan-nel reactor [58]. This work was preceded by Emig in 1997, of the same group, who presented a fixed-bed reactor with periodically reversed flow [59]. In 2001, Rouge et al. [14] presented the catalytic dehydration of isopropanol in an IMM microreactor. 

The problem is separable for a bare homogeneous reactor. However, only the case of a step input of reactivity, i.e., the case of a constant value of p, is easily solved. In this case, the kinetic equations are readily reduced to a second order (for the case of one delayed neutron group) homogeneous linear differential equation with constant coefficients. For an input of positive reactivity two solutions arise, of the form and where o>i > 0 and 0)2 < 0. The first solution controls the persisting exponential rise of the flux, where it is recalled that T = l/o>i is the reactor period, and the second solution which rapidly becomes small is called the transient solution. 

Stable and transient reciprocal reactor periods for a representative special case with large initial reactivity input... 

The long prompt neutron lifetime (about 1 ms) means that for reactivity transients even above prompt critical, the rate of rise in power is relatively slow. For example, the reactor period for an insertion of 5 mk is about 0.85 s L whereas for 7 mk it is about 2.4 s 1. The SDSs are, of course, designed to preclude prompt criticality. 

This model would have some application in the early stages of the flux rise after t = 0, and before the concentration of the delayed-neutron precursors has been built up significantly over its steady-state value. For example, Eq. (9.122) is a good approximation to (9.121) when the transient effects, represented by the second term, are significantly larger than those due to the stable reactor period, i.e., when... 

The reactor will be pulsed with reactivity insertions from 1% to 1.4%(or the maximum available) in 0.1% increments. Calculate the transient rod fired position to obtain the desired reactivity insertions. One pulse will be fired for each reactivity step. A second pulse will be fired for one of the steps to provide an indication of the reproducibility of the measurements. The signal from the gamma ion chamber is sampled at one millisecond intervals and stored in the TestLab. The TestLab internal program calculates the information needed for the reactor log and records two channels of power-level data derived from the gamma-ray dose from the reactor core. The first channel, labeled "pulsetrace", records the full pulse. The second, labeled "pulserise", uses a smaller range and thus records the early part of the pulse most useful for reactor period measurements. In both cases the raw data is normalized such that the output is in MW. 

For the same constant reactor period, which ONE of the following transients requires the SHORTEST time to occur A power increase of... 

Refer to the attached figure. Calculate the stable reactor period for the indicated transient. Show all of your work. 

The Inhour Equation relates reactivity insertion, p, to reactor period, T. Some positive reactivity is inserted into Reactor A, while the same amount of negative reactivity is inserted into Reactor B. After all transients have decayed away, the absolute value of the period will be ... 

Equation (4,16) has not been derived mathematically. It is a convenient physical representation of the effect of reactivity addition rate on reactor period. The period actually shortens, as explained, because X increases, However, for illustrating the transient period effect, equation (4,16) comes in handy,... 

The fastest potential positive reactivity transient postulated for SRS cores is the startup accident. In this transient, groups of control rods are unintentionally withdrawn from the reactor at no power, or very low power conditions. This results in the creation of very short reactor periods before any temperature changes occur. WSRC examined the consequences of the startup accident with all but the least restrictive safety feature disabled and found that even with the limiting value of the prompt coefficient given in DPST-88-956, the transient would be safely terminated by safety rod scram. 

The typical duration of thermohydraulic transients is given by the time which the coolant needs to pass the core. This time being about 0.7 sec in the core average, all core transients with periods of a few seconds or more pose no problem in this regard. In particular, the behavior of the reactor due to ship motion of a 7 sec period should be described reasonably well by this model. Also the load following characteristics can be determined properly. 

At an arbitrarily chosen time zero, mark the recorder chart and close the switch to fill the empty void holder. Shortly after the void holder is full ( 30 sec) the transient periods will disappear, and a steady asymptotic period will be established. From the power level versus time data given on the power level recorder chart, the reactor period can be determined in several ways perhaps the most instructive is to plot the power level versus time data on semilog paper. What does the straight-line portion of the graph indicate From this graph, measure the period, A calculated curve is available to convert the measured asymptotic period to reactivity. 

Analysis of CSTR Cascades under Nonsteady-State Conditions. In Section 8.3.1.4 the equations relevant to the analysis of the transient behavior of an individual CSTR were developed and discussed. It is relatively simple to extend the most general of these relations to the case of multiple CSTR s in series. For example, equations 8.3.15 to 8.3.21 may all be applied to any individual reactor in the cascade of stirred tank reactors, and these relations may be used to analyze the cascade in stepwise fashion. The difference in the analysis for the cascade, however, arises from the fact that more of the terms in the basic relations are likely to be time variant when applied to reactors beyond the first. For example, even though the feed to the first reactor may be time invariant during a period of nonsteady-state behavior in the cascade, the feed to the second reactor will vary with time as the first reactor strives to reach its steady-state condition. Similar considerations apply further downstream. However, since there is no effect of variations downstream on the performance of upstream CSTR s, one may start at the reactor where the disturbance is introduced and work downstream from that point. In our generalized notation, equation 8.3.20 becomes... 

Transients All processes must be started and shut down, and the transients in these periods must be considered. Feedstocks can vary in quahty and availabihty, and demand can vary in quantity and in required purities so the reactor system must be tunable to meet these variations. These aspects are frequently considered after the steady-state operation has been decided. 

When the production scale is large, the same reaction can be carried out continuously in the same type of reactor, or even with another type of reactor (Chapter 7). In this case, the supplies of the reactants A and B and the withdrawal of the solution containing product C are performed continuously, all at constant rates. The washout of the catalyst or enzyme particles can be prevented by installing a filter mesh at the exit of the product solution. Except for the transient start-up and finish-up periods, all the operating conditions such as temperature, stirrer speed, flow rates, and the concentrations of incoming and outgoing solutions remain constant - that is, in the steady state. 

Fig. 16.6 Transient temperature histories in a reactor whose volume oscillates as illustrated in Fig. 16.5. In addition to the no-oscillation case, three oscillation frequencies are shown. The lower panel is an enlargement of the period just around the ignition of the a> = 2500 Hz...

The coke profiles in the reactor bed can be predicted excellently by the model as shown by the solid lines in Figure 1. Figure 2 shows good consistency is also obtained for the average coke content over the reactor bed versus time on stream. Note that within the time period of reactor startup plus one hour of operation, the average coke content of the reactor bed is already at about 5 wt%. The model cannot be applied to this startup and initial period with the rapid transients of temperature, activity "spike" and concentration. However, compensation for this interval can be made by a time translation of the model a model time of 36 hours is fixed at an experimental time of zero. A temperature difference of more than 20C between the center of the bed and outer wall of the reactor in the startup stage has been observed in our laboratory for some experiments. About three-fourths of this difference is across the catalyst bed itself. Startup of the reactor at reasonably lower temperatures in order to control the coke formation and to better maintain the catalyst activity is important, if not critical. 

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