# NUKEFACT #11

#### MORE REACTOR RATE RATE EXAMPLES ... USING THE REACTOR RATE DIAGRAM

###### last update April 3, 1997

The rate example presented in NUKEFACT #8 was for a nuclear state of rho = +10x10-4 and rho-dot = +2x10-4 delta-rho/sec, such that the delayed neutron component representing source strength change was +0.5 DPM and the prompt neutron component representing source multiplication change was +0.9 DPM. The total reactor rate, the sum of the two contributors, was +1.4 DPM. Note that in order to identify components of reactor rate one must use the Startup Rate formulation (rather than Reactor Period). Examination of the rate Equation shows this to be the only form in which the components of reactor rate are separable (NUKEFACT #5 and #6).

The rate example presented in NUKEFACT #9 was for a nuclear state where rho = +10x10-4 and rho-dot = 0 delta-rho/sec, such that the delayed neutron component was again +0.5 DPM, but the prompt neutron component was 0 DPM. The total reactor rate, due solely to the increasing delayed neutron source strength, was +0.5 DPM. Now, consider a third situation, as follows:

Example 11.1: given rho = +10x10-4 and rho-dot = -2x10-4 delta-rho/sec, find the reactor rate ..... Enter the Reactor Rate Diagram (below) on the reactivity scale at rho = +10x10-4 and move upward to the ramp-in curve for rho-dot = -2x10-4 delta-rho/sec. Move horizontally to the Startup Rate scale and read SUR = -0.4 DPM. The reactor period is T = -26/0.4 = -65 seconds.

................................................. THE REACTOR RATE DIAGRAM

Here, the reactor is supercritical with an ongoing decrease in reactivity, i.e. rho-dot = -2x10-4 delta-rho/sec. As in the previous examples the delayed neutron component, associated with reactivity, acts to cause power to rise at a SUR of +0.5 DPM. Subtracting this delayed component from the total rate, the prompt neutron component is -0.4-(+0.5) = -0.9 DPM. This contribution is visible on the Rate Diagram as the vertical displacement between the stable rate curve and the ramp-in curve at rho = +10x10-4. Also observe that the ramp-in component has the same magnitude as the ramp-out component, but is of the opposite algebraic sign.

Of course, the significant feature of Example 11.1 is that even though the reactor is supercritical, the reactor rate is negative. Power is decreasing in a supercritical reactor. In the two previous examples, involving identical supercriticality, namely rho = +10x10-4, reactor rate was positive; power was increasing. In the first example both rate components were acting to increase power. In the second example the delayed neutron component was acting to increase power, while the prompt neutron component was zero (rho was constant). In Example 11.1 the two contributors to reactor rate are in opposition. The delayed neutron component acts to increase power, while the prompt neutron component acts to reduce power. In such a situation, it is the contributor of largest magnitude that determines the direction of ongoing power change, i.e. whether power is increasing or decreasing with time. Thus, the prompt neutron component of -0.9 DPM predominates, with the delayed neutron component only +0.5 DPM, and the net reactor rate is -0.4 DPM. Operationally, this example could represent ongoing insertion of one or more control rods, which causes power to decrease even though the reactor is supercritical. This behavior is an important aspect of power reversal, which will be discussed in a future NUKEFACT. Now consider a comparable case for the subcritical condition.

Example 11.2: given rho = -10x10-4 and rho-dot = +2x10-4 delta-rho/sec, find the reactor rate ..... Enter the Reactor Rate Diagram on the reactivity scale at rho = -10x10-4 and move upward to the ramp-out curve for rho-dot = +2x10-4 delta-rho/sec. Move horizontally to the Startup Rate scale and read SUR = +0.5 DPM. The reactor period is T = 26/0.5 = +52 seconds.

Here, the reactor is subcritical with an ongoing increase in reactivity, i.e. rho-dot = +2x10-4 delta-rho/sec. From the stable rate curve, the delayed neutron component acts to cause power to decrease at a SUR of -0.2 DPM. Subtracting this delayed component from the total rate, the prompt neutron component is +0.5-(-0.2) = +0.7 DPM. This contribution is visible on the Rate Diagram as the vertical displacement between the stable rate curve and the ramp-out curve at rho = -10x10-4.

Even though the reactor is subcritical, the reactor rate is positive. Power is increasing in a subcritical reactor. In Example 11.2 the two contributors to reactor rate are in opposition. The delayed neutron component acts to decrease power, while the prompt neutron component acts to increase power. In such a situation, it is the contributor of largest magnitude that determines the direction of ongoing power change, i.e. whether power is increasing or decreasing with time. Thus, the prompt neutron component of +0.7 DPM predominates, with the delayed neutron component only -0.2 DPM, and the net reactor rate is +0.5 DPM. Operationally, this example could represent ongoing withdrawal of one or more control rods, which causes power to increase even though the reactor is subcritical.

In the next NUKEFACT we discuss how reactor rate behaves with time during ramp reactivity change.