Several NUKEFACTs have addressed the Reactor Rate Diagram, namely #6, #8, #9, #11, and #12. It has been said, and rightly so, that a picture is worth a thousand words. The Reactor Rate Diagram is a picture of the equation that defines reactor behavior, namely the reactor rate equation. Specifically, the rate we've dealt with is that which occurs around criticality, i.e. in the region of operation where the non-fission neutron source is negligible. This is commonly identified as the "Delayed-Critical Region", because delayed neutrons are the only source neutrons. The two forms of the rate equations for the D-C Region are:
where:
SUR = startup rate, decades per minute
T = reactor period, seconds
The reference rate curves shown on the rate diagrams are calculated from these equations. The PWR Diagram uses Start-Up Rate, while the BWR Diagram uses Reactor Period. For reference purposes, both Diagrams open by displaying a family of three curves, namely (1) the stable rate curve (the locus of rates for constant reactivity conditions, i.e. where rho-dot is zero), (2) the ramp-out (transient rate) curve for a constant positive rho-dot of +2x10-4 delta-rho/second, and (3) the ramp-in (transient rate) curve for a constant negative rho-dot of -2x10-4 delta-rho/second. During ramp-out, the positive rho-dot moves the rate to the right along the ramp-out curve. During ramp-in, the negative rho-dot moves the rate to the left along the ramp-in curve. On termination of ramping, reactivity is constant and the rate moves vertically to the stable rate curve.
The PWR diagram appears as follows:
The equivalent reactor rate diagram scaled for reactor period displays the same three curves.Then, starting from the initial condition of criticality, a sequence of ramp-out and ramp-in actions using two of the three optional reactivity rates produces the following graphics:
The equivalent reactor rate diagram scaled for reactor period displays the same ramp sequence. First, let it be said that each point on the two dashed ramp curves of Figure 17.1 is calculated from the rate equation based on the rate at the instant the ramp is initiated, i.e. with a precursor mix associated with exponential power change. As the actual ramp continues, the precursor mix deviates from that of the stable rate, i.e. of the exponential, and the actual rate of the ramp deviates from the dash ramp curves.
The ramp sequence on Figure 17.2 is as follows:
The actual ramp curve for ±2x10-4 delta-rho/sec is the solid curve that is furthest removed from the stable rate curve. Note that in general, the actual ramp curve lies outside the dash ramp lines. Also note that the actual ramp curve for ±1x10-4 delta-rho/sec lies generally inside the dashed ramp curves. The proximity of the actual transient rate curves for rho-dot = ±2x10-4 delta-rho/sec to the dashed reference curves, as calculated from the rate equation using the stable rate lambdaeff value, is a measure of how well the rate equations represent the actual transient.
As enlightening as Figure 17.2 may be concerning the nature of reactor behavior, it is deficient. It is the evolving picture, the ordered sequence of the intermediate pictures, that transmits the real learning impact. It is the variable of time that makes the difference. Reactor behavior is about power change with time. Energize your ClassRoom learning process. The most important dimension of reactor behavior is time, which is never captured in a single still-life picture of the completed transient.
