Walter H. Esselman, Robert L. Ramp, and Garold L. Hobmann

7- 1 INTRODUCTION

7- 1.1 Reactor Kinetics*

A nuclear reactor that is generating heat at a constant rate is a chain-reacting system in which the number of neutrons being produced in nuclear fission processes ex­actly balances the number of neutrons being absorbed m or escaping from the system. If it is desired to change the rate of heat generation (number of fissions per second), means must be provided to increase or decrease the absorption and escape of neutrons Once the heat-generation rate has reached the desired new level, means must be provided to restore the neutron balance so the system will once again generate heat at a constant rate The specific means used in present-day power reactors to alter the heat-generation rate upward or downward or to keep it constant are discussed in this chapter.

In the steady state (constant rate of generating heat), the reactor is critical when the effective multiplication constant к (sometimes written as keff) is just equal to 1 To increase or decrease the power level of the reactor requires that к be increased or decreased above or below unity during the interval when the power level is changing. Once the desired power level has been reached, к must be restored to unity so the reactor can again operate in a steady state, albeit at a new power level. The fractional deviation of the effective multiplication constant from unity is defined as the reactivity1

к — 1 1

Reactivity = p = ———— = 1 — j^-

or

5k

Reactivity = -— (with 5 k = к — 1)

К

The fundamentals of reactor kinetics are summarized in Chap. 1.

CHAPTER CONTENTS

7 1 Introduction……………………………………………………………………………………………….. 167

7-1.1 Reactor Kinetics…………………………………………………………………………… 167

7-1.2 Reactivity Variations During Operation…. 168

7-1.3 Methods of Reactivity Control…………………………………………………… 168

7-2 Reactor Control System……………………………………………………………………………….. 168

7-2.1 Approach to Criticality…. 168

7-2.2 Power-Increase Phase………………………………………………………………… 169

7-2.3 Power Operation Phase………………………………………………………………. 169

7-2.4 Shutdown Phase. . 170

7-3 Selection of Reactivity-Control Method………………………………………… 170

7-3.1 System Requirements. … . . 170

7-3.2 Means of Control… .. … . 173

7-3.3 Materials……………………………………………………………………………………….. 174

7-3.4 Rod Shape……………………………………………… . . . . 174

7-3.5 Rod Configuration. . . …………………………. 174

7-3.6 Types of Drives…………………………………………………………………………… 176

7-3.7 Rod-Position Indicators…………………………………………………………….. 178

7-4 Examples of Reactivity-Control Systems……………………………………… 180

7-4.1 PWR Power Plant at Shippingport…………………………………………….. 180

7-4.2 San Onofre Atomic Power Plant… … 183

7-4.3 Dresden Nuclear Power Plant…………………………………………………….. 185

7-4.4 Gas-Cooled Reactors………………………………………………………………….. 186

7-4.5 Fast Reactors……………………………………………………………………………….. 191

References………………………………………………………………………………………………………………… 191

Bibliography………………………………………………….. . . . … 191

Because к is very close to 1 at all times in an operating power reactor, the reactivity p or 5k/k is often abbreviated to Sk or “excess k” if 5k > 0. In terms of reactivity, the basic types of reactor performance are

p = 5k/k= 0 constant power level p = 5k/k > 0 power level increases p = 5k/k < 0 power level decreases

When the reactivity is not zero, the reactor power level increases or decreases with a characteristic time constant (reactor period) that is primarily dependent on the value of the reactivity, the prior operating history of the reactor, and the reactor configuration (arrangement and composi­tion of fuel, moderator, coolant, etc ) Period is the time required for the neutron level to increase (or decrease) by a factor of “e” (2.718) (see Chap. 1). The reactor period becomes too short for practical control if the reactivity is increased above zero by an amount equal to the delayed — neutron fraction, /3. For most presently operating power reactors, /3 ^0.007. This means that a positive p or 5k/k is always between zero and about 0 06% During operation at power, reactor control systems normally make adjustments at rates in the general range from 10 3/sec to 10 5/sec m 5k/k per second. Although the control adjustments during operation involve relatively small changes in reactivity, this is not necessarily true during reactor start-up and shut­down. The control system must be capable of “adding negative reactivity” to balance out the reactivity excess built into the reactor, and, if an emergency exists, it must do so rapidly. Under certain conditions reactivity changes

of—— 0 1/sec in Sk/k per second may be required The

excess reactivity built into a power reactor depends on many factors, it can be more than 10% in 5k/k For this reason control (and safety) systems must be capable of accomplishing large changes in reactivity during reactor start-up and shutdown. In addition, they must be capable of compensating for the effects of changing concentrations of the fission products 13sXe and 149Sm These can involve reactivity changes of several percent (see Sec 1-3.6 of Chap 1)