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| I P R E S S U R E MI T I G A T I N G S Y S T E MS T R A NS I E N T A NA L YS I S R E S U L T S Prepared by WESTINGHOUSE ELECTRIC CORPORATION for THE WESTINGHOUSE OWNERS GROUP ON REACTOR COOLANT SYSTEM OVERPRESSURIZATION JULY 1977
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| TABLE OF CONTENTS Section Title Abstract iv 1 Introduction 1-1
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| : 1. 1 Purpose of Study 1-1 1 .2 Review of Past Events 1-2 1.3 Selection of Parameters for Study 1-4 1.4 Summary of Parameters 1-8 2 Calculation Method 2-1 2.1 LOFTRAN Program and Special Modeling 2-1 2.2 Reference Relief Valve Model 2-5 2.3 Mass Input Model 2-13 2.4 Heat Input Model 2-19 3 Typical Results 3-1 3.1 Mass Input Mitigated by Relief Valve 3-1 3.2 Heat Input Mitigated by Relief Valve 3-9 4 Instructional Guide for Setpoint/Overshoot Determination 4-1 4.1 Introduction 4-1 4.2 Algorithms Used for Setpoint/Overshoot Determination 4-3 4.2.l Setpoint Determination for Mass Input 4-3 Transient i
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| Section Title Page 4.2.2 Setpoint Overshoot Determination for Heat 4-11 Input Transient 4.3 Development of Interpolating Mass Input Equation 4-23 4.3.l Analytical Basis 4-24 4.3.2 Development of Application Factors 4-25 5 Conservatisms in Study , 5-1 5.1 Relief Valve Stroke Time 5-1 5.2 Effect of Metal Expansion 5-4 5.3 Effect of Reactor Coolant and Injection Water 5-8 Temperatures - Mass Input Cases 5.4 Effect of Steam ~enerator Mass and Overall Heat 5-9 Transfer Coefficient - Heat Input Cases 5.5 Effect of Reactor Coolant Pump Startup Time - Heat 5-13 Input Cases 6 Other Considerations 6-1 6.1 Effect of Pressuri2er Water Temperature 6-1 6.2 Effect of Backpressure on Relief Valve 6-4 6.3 Capacity of Multiple Relief Valves 6-6 6.4 Relief Valve Cycling 6-11 6.5 Relief Valve Capacity Change with Flashing 6-17 Appendix A Summary Table A-1 Mass Input Results A-2 Heat Input Results A-6 ii
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| ;;;
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| - j
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| '
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| ABSTRACT The results of pressure transient analyses for the reactor coolant system of a pressurized water reactor during low-temperature, water solid operation are presented for particular cases of either mass or heat input to the system.
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| The analyses were performed using conservative bounding input parameters plus parameter sensitivity studies to provide for results applicable to plant
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| *specific parameters. For the cases presented, the use of a nominal, two-inch air-operated relief valve, such as the pressurizer power operated relief valve, is shown to mitigate the pressure transient without the need for imme-diate operator intervention. A procedure is presented for selection of the relief valve setpoint to avoid violation of the 10CFR50 Appendix G pressure limitation for the reactor vessel.
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| iv
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| SECTION l INTRODUCTION l .l PURPOSE OF STUDY During the past few years (1972 to 1976) a number of events have occurred at operating PWR plants in which the reactor coolant pressure exceeded the allowable limit for the particular temperature as prescribed by the requirements of 10CFR50 Appendix G, during low-temperature, low-pressure, water solid modes of operation. These overpressure events were caused by either equipment malfunction, incorrect operator action or a combination of the two. In the vast majority of the events, the unsched-uled pressure transient was recognized by the operator and terminated by manual action.
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| The purpose of this study was to evaluate the performance of a pressure mitigating system using pressurizer power operated relief valves for the causative events and plant parameters which bound the plants under consideration. The study included an evaluation of the overpressure events which have occurred and a review of the existing design features and operating practices to select for the analysis that group of causa-tive events and pertinent plant parameters which encompass the operating plants within the WOwners Group.
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| 1-1
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| 1.2 REVIEW OF PAST EVENTS Using the published records of Abnormal Occurrence Reports and informa-tion provided to the industry by the NRC in June 1976 (see Appendix C) an evaluation was made of the type of events which had occurred, their causative factors and the plant conditions at the time of the event.
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| This review led to the general conclusion that 24 of the 29 reported events could be divided into the two major categories of either mass input or heat input to an isolated constant volume of reactor coolant.
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| The other 5 events were either of unknown origin (3) or were caused by operators following inadequate procedures while controlling the reactor coolant pressure.
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| The review demonstrated that of the 18 events caused by mass input to the reactor coolant system, by far the greatest number (14) involved a mismatch between the charging and letdown flows. In all but one of the events, the mismatch was caused by a loss of letdown flow while the charging system remained in *operation with a relatively low rate of mass input.
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| The remaining 4 mass input events were the result of an abnormal actua-tion of portions of the safety injection system. In the one event involving pumps, a single safety injection pump was started by an*
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| operator and flow inadvertently entered the reactor coolant system. In the other 3 events, the accumulator isolation valves were deliberately opened by the operator or inadvertently opened by a spurious signal from the engineered safety features actuation circuits. (Of course, pres-surization caused by the accumulators is self limiting due to the relatively low gas pressure maintained in the accumulator.)
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| 1-2
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| For the majority of the mass input caused pressure transients, the abnor-mal condition was recognized by the operator and terminated by operator action. However, the limit of the magnitude of the pressure*transient in most cases was a direct result of the speed of the operator in recognizing the situation and taking remedial action.
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| Among the few (6) events attributed to the heat input case, five of the events reported were those in which a temperature asymmetry was allowed to develop in the reactor coolant system, generally due to insufficient mixing. Then, when a reactor coolant pump was started, the cooler vol-umes of reactor coolant would circulate around the system and be heated by warmer sections of the system, particularly the steam generators.
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| These heat input events are self limiting in that the temperatures eventually equalize and past experience has indicated that the magnitude of the pressure transient is not great. One event was the result of re-moving heat from the coolant such that the temperature was allowed to decrease to a temperature too low for the coolant pressure being control-led at the time.
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| 1-3
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| 1.3 SELECTION OF PARAMETERS FOR STUDY
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| : 1. 3.1 Relief Valve The pressurizer power operated relief valves were selected as the logical mechanism for mitigating reactor coolant pressure transients because the hardware already exists on the operating plants. The valves are typically 2 inch nominal body size globe valves each located in a 3 inch line. Their normal function is to relieve reactor coolant pressure at operating plant conditions so the extension of the function to provide relief at a lower pressure is a natural utilization of the function. Since the power relief valve is controlled by an instrumentation system using electrical signals, the implementation of the function to a lower pre~sure range can be easily accomplished by electrical circuitry independent of the existing logic circuits which need not be affected. The reference relief valve model described in Section 2.2 was developed based on the general characteristics of a typical power operated relief valve.
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| 1 .3.2 Reactor Coolant Volume The operating plants in the owners group to which this study is directed consist of 2, 3 and 4 loop plants with various designs of reactor vessels, steam generators and pressurizers such that reactor coolant volume enclosed varies widely. To bound all of the plants, the study considered the use of two extreme volumes; 6000 and 13,000 cu.ft. in all of the cases evaluated for both mass input and heat input.
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| 1-4
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| 1 .. 3.3 Reactor Coolant Pressure For the mass input cases, two initial reactor coolant pressures were considered but it was found that for the particular cases studied, the pressure transient was well defined at the time the relief valve setpoint was reached and there was a negligible effect on the relief valve performance due to the difference in starting pressure. Therefore for conservatism, the majority of the mass input cases were started from a coolant pressure of 50 psig to assure that the mass input mechanism was always at full performance before the mitigating relief valve came into opera-tion.
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| The heat input cases which involved the operation of a reactor coolant pump were restricted to a minimum initial pressure of 300 psig because of a pump shaft seal requirement. Again for conservatism, this minimum pressure was used in all the analyses to assure that the pressure transient was allowed to become well established before the mitigating relief valve was brought into operation.
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| 1.3.4 Reactor Coolant Temperature The initial reactor coolant temperature selected for use in the analyses was based on a review of the credible operating condi-tions which might be experienced in a plant when in a low-tempera-ture, low-pressure water solid condition. For all of the mass input cases, the reactor coolant was considered to be at a cold shutdown temperature of 100°F (see Section 5.3 for additional discussion of this parameter) and the pressurizer filled solid with water at 100°F (see Section 6. l for additional discussion).
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| 1-5
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| The heat input cases were studied with various values of initial reactor coolant temperature from 100°F to 250°F, the maximum range of temperature which might be expected for operation in a water solid condition. Over this range, as was expe~ted, the heat input transients became more severe with the higher tempera-tures but the allowable coolant pressure, according to the 10CFR50 Appendix G rules, also increases.
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| 1 .3.5 Mass Input Mechanisms The review of past experience indicated that the case of a loss of letdown while charging flow continued was the most likely cause of a pressure transient. Among the operating plants, there are charging system designs which consist of positive displace-ment pumps, centrifugal type pumps and combinations of the two.
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| The lowest normal flow rate occurs in those plants with small positive displacement pumps where a representative flow rate is about 40 gpm.
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| The maximum normal charging flow rate occurs in those plants with centrifugal type pumps where a representative flow rate is about 120 gpm. The design mass input cases due to loss of letdown flow were therefore considered to be between 40 and 120 gpm.
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| Although there has been only one occurrence of inadvertent mass injection due to the operation of a safety injection pump, and these pumps are normally made inoperative during low-temperature low-pressure plant operation, the potential does exist for this type of mass input transient. Therefore, the analyses was extend-ed to include the performance of the mitigating system for the case of a single safety injection pump being placed in operation (see Section 2.3).
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| 1-6
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| The safety injection accumulators were not considered as a credible mass input mechanism for this study because there are multiple administrative controls to ensure isolation including de-ener-gizing valve control circuits during plant shutdown operations.
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| 1 .3.6 Heat Input Mechanisms The pressure transient events selected for study involved the cases where a temperature asymmetry was formed in the reactor cool-ant system in which the steam generators were at a higher temperature than the remainder of the system. The magnitude of the temperature difference between the steam generators and the reactor coolant system is dependent on the previous plant opera-tions which allowed the asymmetry to develop. For the purpose of this study to bound the possible events, temper~ture differences between the steam generators and the reactor coolant system up to l00°F were evaluated. However, it is considered realistic to assume a maximum temperature difference of 50°F as the design case because much higher differences are difficult to develop and are easily recognized by the operator as abnormal conditions requiring special attention.
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| 1-7
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| 1.4
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| ==SUMMARY==
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| OF PARAMETERS 1 . 4. 1 Genera 1 The plants represented by the ~ Owners Group comprise a group of 2, 3 and 4 loop pressurized water reactor plants, each with one steam generator and one reactor coolant pump per loop. Typical total reactor coolant system volumes for the plants under con-sideration range between about 6000 cu.ft. and 13,000 cu.ft., and these two volumes were therefore used for this study.
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| 1 .4.2 Reference Relief Valve The relief valve selected for use in the study as described in Section 2.2 exhibits the following general characteristics:
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| : 1. Opening time; 3 seconds
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| : 2. Closing time; 5 or 20 seconds
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| : 3. Flow capacity; Cv = 50 gpm/ Jpsi per valve
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| : 4. Set pressures, various; 400, 500 and 600 psig 1 .4.3 Mass Input Cases The following two representative mass input cases as described in Section 2.3 were considered:
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| : 1. Charging flow with letdown isolated; 40 and 120 gpm
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| : 2. Inadvertent operation of one safety injection pump; 870 gpm at 500 psig The following parameters were considered for the mass input cases:
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| 1-8
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| : 1. Temperature of reactor coolant; 100°F
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| : 2. Temperature of injected water; 100°F
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| : 3. Initial pressure of coolant; 50 or 450 psig 1.4.4 Heat Input Cases The temperature asymmetry conditions selected for study as heat input cases are discussed in Section 2.4. The following are the cases considered for both a 6000 and 13,000 cu.ft. plant size:
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| RCS/SG llT r:o r---------------~~actor Coolant .
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| i I
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| I
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| *-*-.. _ Temperature i I
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| *-.._
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| I 100 140 180 250 Steam *'**-., ~
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| Genera tor Temp. -- *------- ..._____
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| 150 50 190 50 200 100 20 230 50 240 100 250 i
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| 280 j 100 I
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| 300 I 50 J
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| 1-9
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| SECTION 2 CALCULATION METHOD 2.1 LOFTRAN PROGRAM AND SPECIAL MODELING The one loop version of the LOFTRAN t program was utilized to perform the mass input analyses and the four loop version was utilized for the heat input analyses. No changes to either version of the program were necessary for the studies. However, some input modeling, input additions and initialization changes were required as described in the following paragraphs.
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| 2.1.1 Mass Input Analysis No special features of LOFTRAN were required for the mass input cases. However, some input adjustments were made to ensure that the mass input model was representative of the conditions specified for analysis.
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| One such adjustment was made to ensure that an isothermal condi-tion was maintained. Since LOFTRAN was not programmed to be initialized at zero power, a very small, constant power level was maintained and nominal, full reactor coolant flow was maintained.
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| This initialization condition does not alter the resultant pres-sure increase for actual mass input cases where the reactor coolant pumps may not be running.
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| To m1n1m1ze the pressure defect associated with the compressibility of a saturated (hot) water solid pressurizer (a representation required by LOFTRAN to maintain the specified reactor coolant pres-sure), the pressurizer water volume was reduced to 100 ft 3 . The t - WCAP-7907 2-1
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| volume difference between a nominal pressurizer and the 100 ft 3 was incorporated into the total system volume but at an initial temperature of 100°F.
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| 2.1.2 Heat Input Analysis Except for the decay heat (loss of RHRS) and pressurizer heater input cases, more extensive adjustments were necessary for model-ing the heat input cases.
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| The heat input cases analyzed involved the startup of a pump in one loop with the plant in a cold shutdown condition and with temperature asymmetries in the reactor coolant loops. Two possible asymmetries were assumed. One was the RCS/SG case, in which the steam generators, primary and secondary, were at a higher tempera-ture than the remainder of the reactor coolant. The second considered that the water in the loop seal ~iping from the steam generator outlet to the pump suction was at a lower temperature than the remainder of the coolant and steam generators. In both cas~s the temperature of the reactor coolant in the tubes was at a temperature equal to the saturated condition of the secondary water mass.
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| The multiloop version of the LOFTRAN program was used to obtain the capabilities for a reactor coolant pump startup in one loop and for the reverse flow simulation in the inactive loops. To circumvent a flow initialization problem, the LOFTRAN loop out of service option was used with a very small input power (LOFTRAN does not permit zero power initialization) to establish a very low 2-2
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| natural circulation flowrate following the pump coastdown. After initialization for the natural circulation flow conditions, the code was returned to the normal program sequence to initiate the remainder of the heat input transient.
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| Before the heat input transient was initiated, however, it was necessary to input the required temperature profile.
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| For the case of the RCS/SG temperature asymmetry, the coolant temperature was made uniform everywhere except in the steam gen-erator tubes. The steam generator secondary temperature and the coolant temperature in the steam generator tubes were input as equal but different than the reactor coolant temperature.
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| For the case of the loop seal temperature asymmetry, the tempera-ture of the coolant volume in the loop seal was input different from the temperature throughout the remainder of the reactor coolant system (including the steam generator tubes) as well as the steam generator secondary temperature.
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| Also in the loop seal case, steam generator outlet plenum volume was set to a very small value to minimize mixing in the reverse flow loops before the cold slug from the loop seal entered the steam generator tubes.
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| After temperature initialization, the input parameters of core heat flux, steam flow and feed flow were stepped from their respective initial (natural circulation mode) conditions to zero during the first time step. Reactor coolant pump startup is initiated at t = 0 seconds using the default homologous data asso-ciated with the 93A pump model.
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| 2-3
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| As in the mass input case, the pressurizer volume was minimized (set equal to 100 ft 3 ) and the difference in pressurizer volume (actual - 100 ft 3) was added to the inactive volume of the reac-tor coolant.
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| 2-4
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| 2.2 REFERENCE RELIEF VALVE MODEL The relief valve model selected as the reference for use in the transient analyses describes a nominal two inch air-operated open-close valve with a linear plug characteristic. The capacity of the valve is based on a standard geometry globe-type valve with a flow coefficient Cv equal to 50; where the flow coefficient is defined as the flow of water at 60°F, in gallons per minute, at a pressure drop of one pound per square inch across the valve while the valve is in the full open position: (i.e.,
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| Cv = QI lfTp)
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| Since the reference relief valve is considered to discharge into the pres-surizer relief tank, there will be a backpressure at the valve discharge depending on the conditions in the relief tank at the time of valve actuation. The gas blanket pressure in the relief tank normally will not exceed 10 psig but the pressure can increase, due .to repeated relief valve discharges, to. a maximum of 100 psig at which time a rupture disk on the tank will open to prevent a further increase in pressure.
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| The flow capacity of the reference relief valve versus upstream pressure (reactor coolant pressure) is shown for various values of backpressure on Figure 2.2.l. All of the short-term transient analyses (one relief valve cycle) presented in this study were based on the flow capacity of the reference relief valve subjected to a constant backpressure of 10 psig.
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| (See Section 6.2 for additional discussion.)
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| The reference relief valve was considered to have a linear flow character-istic; that is, the flow through the valve at a constant differential pressure is directly proportional to the lift of the stem. This selection is consistent with the type of valve used as the pressurizer power-operated relief valve in the operating nuclear plants. However, the effect of using a non-linear valve type (see Figure 2.2.2) was also investigated to see if the performance of the system would be improved by changing to a special 2-5
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| r plug-seat design. The opening and closing time characteristics of the non-linear valve were taken as the same as the reference linear va1ve.
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| The opening and closing characteristics of the reference relief valve used in the transient analyses were based on a particular but typical type of operator used to drive the valve stem. The reference operator was taken as an air diaphragm type with a stroke of 3/4 inch, a dia-phragm area of 220 sq.in. and a compressed spring to hold the valve closed.
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| The air pressure range required to stroke the valve was taken as 11 to 64 psig; that is, the valve stem starts to move with 11 psig pressure on the diaphragm and reaches the full stroke of 3/4 inch under a pressure of 64 psig.
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| When the relief valve is signalled to open, air is admitted into the pip-ing to the valve and into the diaphragm chamber. The air continues to flow into this volume for a period of time, depending on th~ controlling restriction in the line, and increas~s th~ pressure until the unit pres~
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| sure on the diaphragm reaches 11 psig. At this pressure, the force on the diaphragm equals the spring force holding the valve closed and a further increase in air pressure will cause the valve stem to begin to move and open the valve. For the reference valve model, this initial time delay, before the valve starts to move, is about 20% of the total time for the valve to act and is shown o.n Figure 2.2.3.
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| After the valve starts to move, the air flow into the diaphragm chamber continues to both increase the pressure to overcome the spring force and to fill the additional volume made available as the stem moves. When the v~lve reaches the full open position the air pressure in the diaphragm chamber is 64 psig, but since the supply pressure could be as high as 100 psig the air continues to flow into the diaphragm chamber after the valve movement has stopped until the chamber pressure equals the supply pressure. Figure 2.2.3 describes the valve stem movement (stroke) versus normalized time for the reference valve supplied from a normal 100 psig air system.
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| 2-6
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| The valve is considered to be held open by the excess air pressure in the diaphragm chamber until receipt of a signal to close. Until the excess air has vented down from 100 psig to 64 psig, the valve stem will not move. This time delay of about 16% of the total time for the valve to act is shown on Figure 2.2.4. As the air pressure decreases below 64 psig, the stem begins to move under the action of the compressed spring and air flows out of the diaphragm chamber to both decrease the pressure and to remove a volume of air necessary to allow the diaphragm to move. At an air pressure of 11 psig, the valve will be in the full closed position but air will continue to vent from the diaphragm chamber until the pressure is equalized with the atmosphere. Figure 2.2.4 des-cribes the valve stem movement (stroke) versus normalized time for the ,
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| reference valve.
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| In the analyses presented in this study, the relief valve characteristics used to mitigate the pressure transients are described by the use of the three Figures 2.2.l, 2.2.3 and 2.2.4. For instance, if a reactor coolant pressure of 500 psig is reached during an increasing pressure transient at a time equal to 1/2 the valve stroke time, then the flow rate of water at 100°F through the valve at that instant is:
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| 1107 gpm (Figure 2.2.1)
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| * v~~:f
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| * 0.395 (Figure 2.2.3) = 438.3 gpm or 60.5 lb/sec The total time for the reference relief valve to act in the opening direc-tion was taken as 3.0 seconds which is about 1 second longer than a typical power operated relief valve in an operating plant. This total time in-cludes a 0.6 second time delay (20% of total time) from the receipt of the signal until the relief valve starts to open. The time in the transient when the valve open signal was received was varied, to simulate different values 9f the valve setpoint between 400 and 600 psig, to obtain the effect of the setpoint on peak transient pressure.
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| 2-7
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| r After the reference relief valve has opened and turned the pressure transient from an increasing to a decreasing transient, the relief valve is assumed to receive a close signal when the pressur~ has decreased to
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| . a value 20 psi below the original setpoint. This value of the reset pressure was used in all of the analyses in which a full valve cycle was.evaluated. Upon receipt of the signal to close at the time in the transient when the pressure was 20 psi below the valve setpoint pressure, the valve was closed using the characteristic shown by Figure 2.2.4 where the total time was taken as either 5 or 20 seconds.
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| In the transients which did not result in full opening of the reference relief valve (e.g., letdown isolation with continued charging pump opera-tion) the stroke position in effect at the time the reset pressure was reached was ~he initial position used for the start of valve closure.
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| If other than fully open, the time delay in Figure 2.2.4, associated with depressurization of the diaphragm chamber from 100 psi to 64 psi, is not in effect. Further, the total closing time is accordingly reduced in relation to the stroke position at reset pressure.
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| 2-8
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| REFERENCE RELIEF VALVE c = 50
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| \)
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| 2-9
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| .......
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| 2-12
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| 2.3 MASS INPUT MODEL The two credible means of adding excess mass to the reactor coolant sys-tem while the plant is in a relatively cold (100°F) solid-water mode of operation are by creation of a mismatch between the charging and letdown flows or by inadvertently placing a safety injection pump in service.
| |
| The most likely event as evidenced by the experience of the operating plants is the charging/letdown mismatch case. However, the inadvertent start of a safety injection pump has the potential for greater rates of mass input and hence more rapidly increasing coolant pressure transients.
| |
| Therefore, the inadvertent start of a safety injection pump with the plant in a cold shutdown condition was selected as the limiting case.
| |
| Two particular cases of a mismatch between charging and letdown flows were evaluated; one considering the use of a positive displacement pump and the second a large centrifugal type pump. For both of these cases, the transient was initiated from the steady state condition of equal charging and letdown flows by terminating the letdown flow in a ramp fashion, as would occur if a valve in the letdown line was inadvertently closed. For the positive displacement pump case, the charging flow was considered to remain constant as the backpressure increased, while for the centrifugal pump case, the flow was considered to decrease with in-creasing backpressure as the flow was passed through a piping system with a constant resistance (Figure 2.3.1).
| |
| The flow from the positive displacement pump was taken as 40 gpm, a relatively typical low charging flow rate for a pl~nt shutdown condition, while for the *centrifugal pump case the charging flow was taken as 120 gpm, a relatively high value for normal charging service.
| |
| 2-13
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| In the operating nuclear plants, there are various designs of safety injection systems and several types of pumps in use. A survey of the various systems and pumps resulted in the selection of four typical system delivery characteristics and these are shown on Figure 2.3.2.
| |
| Each of the characteristics shown on Figure 2.3.2 represents the maxi-mum expected flows into the reactor coolant system against various backpressures for the case of a single, new, non-degraded pump deliver-ing through all the available injection flow paths.
| |
| . '
| |
| From an inspection of Figure 2.3.2, it is evident that the system represented by Curve C is the worst case in that the system delivery into the reactor coolant system is the greatest of all the systems shown over the reactor coolant pressure range of 400 to 600 psig, the range of most interest for the transient analyses. Therefore, the system delivery described by Curve C was used in the study and is referred to as the reference safety injection pump startup case.
| |
| From test data on typical safety injection pumps, it was determined that the motors under full voltage will bring the pumps to full speed in a little over 2 seconds. Therefore, in the study, the reference SI pump was considered to reach full speed in 2 seconds. The flow from the pump does not begin immediately because the pump first must be brought up to a speed sufficient to develop a discharge head greater than the backpressure to which it is attempting to deliver. This delayed flow initiation is shown graphically on Figure 2.3.3 for two values of reactor coolant backpressure. This figure shows the flow rate into the reactor coolant system increases from zero to its equilibrium value in less than one second for the particular case of a 450 psig reactor coolant back-pressure.
| |
| 2-14
| |
| | |
| Although the startup characteristics shown by Figure 2.3.3 were used in the analyses of the pressure transients for the reference SI pump start cases, it was determined that the volume of water injected during these short pump startup periods is relatively insignificant in the analyses.
| |
| Only for a specific case where the initial coolant pressure is very near the relief valve setpoint will the startup transient of the pump affect the pressure transient. For such a case, the relief valve would start to open as the pump came up to speed and the pressure transient would be mitigated earlier and more effectively.
| |
| In all mass input cases, reference SI pump startup and charging flow from either the positive displacement or centrifugal pumps, the temperature of the injected water was taken equal to the reactor coolant so that the resultant pressure transient is due to the addition of mass only and is not affected by the mixing of the injection water into the reactor cool-ant. (See Section 5.3 for additional discussion.)
| |
| 2-15
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| ----------------------------*--------~-r-*--:r-*-r-:-r*- *-----------. ---- -
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| ~i . FIGURE 2.3.i TYPICAL SAFETY INJECTION SYSTEM DELIVERY CHARACTERISTICS (SINGLE PUMP)
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| ____
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| 2.4 HEAT INPUT MODEL The investigation of the reported events of reactor coolant pressure transients and of current plant operating practices led to the conclu-sion that four credible heat addition mechanisms should be studied:
| |
| pressurizer heaters, core decay heat and two types of reactor coolant loop temperature asymmetry.
| |
| For the pressurizer heater case the reactor coolant system is consid-ered to be water solid and completely isolated so that any heat input to the water in the pressurizer results in an attempt to expand the system with a consequent increase in system pressure. The reference case considered the operation of 1800 KW of heaters, the design value for a large 4 loop plant, in a relatively small pressurizer of 1000 cu.ft. volume. t This large heat input to a small liquid volume results in a conservatively high rate of change of pressure but is not signifi-cant compared with other heat input cases studied as shown by Figure 2.4.1.
| |
| The case of heat input from core decay heat was investigated considering the decay heat from an 1882 MWt design core added to a small system volume of 6000 cu.ft. 12 hours after plant shutdown from an extended high power run. This is a conservatively large relative value of heat addition, but the magnitude of the unrelieved transient pressure response still is not significant compared to other cases of heat input studied as shown by Figure 2.4.1.
| |
| The first of the two types of temperature asymmetry considered in the study occurs when the reactor coolant is at a relatively uniform warm temperature with little or no natural circulation and the cold reactor coolant pump seal injection water continues to enter the system. The cooler injection water will settle as a pool in the loop seal below the t Typically there is l KW of pressurizer heaters for each l cu.ft. of pres-surizer volume.
| |
| 2-19
| |
| | |
| pump inlet formed by the p1p1ng from the steam generator outlet and the pump inlet (see Figure 2.4.2). The volume of cold water which can be trapped in the loop seal is determined by the piping layout and the typical volume used in the study was 140 cu.ft. in each loop. To fill this volume with cold water would require 3 to 4 hours of normal seal injection with the plant in a stagnant condition; i.e., no reactor cool-ant flow.
| |
| The coolant pressure transient is initiated *upon starting one reactor coolant pump. As the pump comes up to speed, the coolant flow rate slowly increases in the active loop and the pool of cold water will be drawn up into the pump and discharged out to the cold leg piping and reactor vessel where it mixes with the warmer coolant. Simultaneously the cold pool of water in the inactive loop(s) will flow backward through the steam generator(s) at a flow rate significantly less than in the active loop. As each of the cold pools of water flow through their steam generators, their temperatures will be increased by the heat transferred from the secondary side, and since the coolant cannot expand in the isolated reactor coolant system volume, the coolant pressure will increase. The coolant pressure will continue to increase until the temperatures of the reactor coolant and steam generator water are equal-ized (see Figure 2.4.1) or the excess coolant volume due to the* added heat is relieved through a ~elief valve.
| |
| The second type of temperature asymmetry occurs when the reactor coolant has been cooled down without sufficient circulation, for instance by use of the residual heat removal loop not augmented by the flow from a reactor coolant pump, and the steam generators remain at an average tem-perature higher than that of the reactor coolant. For this case, the steam generator shell, tubes, secondary water at the no-load level and reactor coolant enclosed in the tubes are assumed to be at a uniform 2-20
| |
| | |
| temperature (see Figure 2.4.3). When the pressure transient is ini-tiated by starting one reactor coolant pump, the reactor coolant flow rate increases, washing the warm water out of the tubes and replacing it with relatively cold water from the loops. The rate of flow in the active loop is significantly higher than that in the inactive loops which are subjected to reverse flow, but in all steam generators heat is transferred to the cooler reactor coolant causing an increase in pressure. The transient pressure increase will continue until the reactor coolant and steam generator water temperatures are equalized (see Figure 2.4.1) or the excess coolant is relieved through a relief valve.
| |
| For the cases with each type of temperature asymmetry, the reference steam generators were considered to have 58,000 sq.ft. of heat transfer area and a secondary water volume of 3580 cu.ft.; both parameters being significantly greater than those for any of the operating plants, so that the rate of heat transfer and total stored heat available for transfer were conservative in this study.
| |
| Heat transfer across the steam generator tubes was assumed to be con-trolled by free convection on the secondary side. The heat transfer coefficient associated with this mechanism was determined from the McAdams t correlation for turbulent boundary layers on a vertical sur-face, or:
| |
| I 2 l 1/3 1/3
| |
| = 0 13 Kl .e.__g_§_* p I 0
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| L_
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| I
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| µ 2 r
| |
| --
| |
| J t McAdams, W. H., "Heat Transmission", 3rd Edition, McGraw-Hill, New York, 1954 2-21
| |
| | |
| where:
| |
| hsec . = secondary film coefficient of heat transfer, BTU/hr ft 2 °F p = density of secondary water at film temperature, lbm/ft 3
| |
| µ = viscosity of secondary water at film temperature, lbm/ft hr t.T wa 11 = secondary to primary temperature difference, °F g = acceleration of gravity, ft/hr 2 f3 = temperature coefficient of volume expansion, (°F)-l k = conductivity of secondary water, BTU/hr ft °F p = Prandtl Number evaluated at secondary film temperature r
| |
| The reactor coolant pump characteristics used in the heat input studies were those representative of a controlled leakage sealed pump with a flow rate of about 95,000 gpm at normal plant conditions and a startup time of about 10 seconds.
| |
| From an inspection of Figure 2.4.1, it is evident that the heat input cases from pressurizer heaters and decay heat are not as significant as those for the cases with a loop temperature asymmetry. Therefore, these less significant cases were not studied further. Similarly, the loop seal asymmetry case is seen to give a relatively small pressure transient compared to the potential excursion possible from the RCS/SG temperature asymmetry cases and was not considered further in the study of heat input transients.
| |
| 2-22
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| 2-23
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| | |
| FIGURE 2.4.2 LOOP SEAL VOLUME STEAM GENERATOR RV NOZZLE 1*-'~
| |
| PUMP CENTERLINE t
| |
| LETD0\1N FLOW 2-24
| |
| | |
| FIGURE 2.4.3 SG SECONDARY NO-LOAD WATER LEVEL STEAM OUTLET t
| |
| -E---- NORMAL NO-LOAD FEEDWATER 4- WATER LEVEL INLET
| |
| ./
| |
| HOT LEG COLD LEG 2-25
| |
| | |
| SECTION 3 TYPICAL RESULTS 3.1 MASS INPUT MITIGATED BY RELIEF VALVE Based on the probability of occurrence and past experience, the most like-ly mass input case is considered to be the charging/letdown flow mis-match case in which the letdown is terminated within 2 seconds, presumably by a valve closure. Selecting an initial reactor coolant system pressure of 50 ps1g, the pressure response to the letdown isol~
| |
| tion will be as described by Figure 3. 1. l for a small plant with a reactor coolant volume of 6000 cu.ft. As would be expected, the pres-sure increases more rapidly for the case of the larger mass input from the centrifugal pump (about 16 lb/sec) than for the input from the positive displacement pump (about 6 lb/sec). For these particular examples, the reference relief valve was given a signal to open when the pressure rose above 615 psia, but since the reference valve operator has a time delay of 0.6 seconds, the pressure continued to rise until the valve started to open. Very soon after the valve started to open, the pressure was found to stop increasing and to begin to decrease as the capacity of the valve exceeded the relatively constant mass input rate. The valve continued to move open until the reactor coolant pres-sure had decreased 20 psi below the valve setpoint of 615 psia. At this reset pressure the valve was signalled to close but the pressure con-tinued to decrease as the valve began its closing cycle. Eventually the valve capacity decreased
| |
| - --
| |
| to less
| |
| -
| |
| than the continuing
| |
| -
| |
| mass input and the
| |
| --
| |
| reactor coolant pressure stopped decreasing and again began to increase toward the relief valve setpoint. It is interesting to note that for
| |
| .the relatively low values of mass input in these examples, the relief valve did not stroke to the full open position since the valve capacity 3-1
| |
| | |
| far exceeded that required to relieve the mass input. The valve floated on the motive air in the diaphragm chamber during the opening cycle and did not reach the full open position before the air was vented from the op~rator. However, due to the closing characteristics of the relief valve, the valve did close completely during each cycle.
| |
| The reactor coolant pressure will repeat the cycle through the relief valve setpoint pressure and reset pressure as shown on Figure 3.1~1 until the mass input is terminated. The figure clearly shows the pressure transient is quickly mitigated by the reference relief valve for the en-tire range of charging flow rates and that the peak pressure reached (less than 625 psia) is less than 10 psi above the valve setpoint.
| |
| The effect of a much larger mass input flow rate on the pressure response and relief valve performance is demonstrated by Figure 3.1.2 which shows the pressure response for the case of an abnormal operation of the refer-ence safety injection pump. For this example of a very high mass input (113 lb/sec) into a 6000 cu.ft. volume plant, the pressure rose rapidly
| |
| .to the setpoint of the relief valve. Due to the inherent time delay of the valve operator, the pressure continued to rise about 74 psi above the setpoint before the valve started to open. After the valve had started to open, it very quickly provided sufficient capacity to mitigate the pres-sure transient, but due to the rapid rate of change of system pressure during the early period of the valve stroke, the pressure rose to a peak of 770 psia before it began to decrease. The pressure overshoot above the valve 615 psia setpoint was 155 psi for this particular example of an extreme mass input into a small coolant volume.
| |
| 3-2
| |
| | |
| For the example SI pump startup case shown on Figure 3. 1.2, the relief valve did reach the full open position during its cycle and, therefore, when it received the close signal, there was a short time delay for the motive air to vent from the operator before the valve started to move.
| |
| This time delay plus the finite time for the valve to stroke resulted in a pressure decrease before the valve capacity became less than the mass input rate. When the capacity of the valve became less than the input flow rate, the reactor coolant pressure again began to increase toward the valve setpoint. The valve will continue to cycle open and closed with an 8-1/2 second cycle time while following the coolant pres-sure response until the mass input is terminated.
| |
| There is a direct relationship between the rate of change of reactor coolant pressure and the rate of mass input into a given system volume as indicated by Figure 3.1 .2 and Figure 3. 1.3, and, conversely, there is also an inverse relationship between the rate of pressure change and the size of the vblume into which a given mass rate is injected.
| |
| This relationship of the system volume is shown for the particular case of the reference SI pump mass input into two different system volumes of 6000 and 13,000 cu.ft. on Figure 3. 1.4.
| |
| The pressure overshoot above the 615 psia setpoint for the reference SI pump mass input case was shown to be about 155 psi on Figure 3.1.2, which gave a peak pressure of 770 psia. To reduce the peak pressure, the relief valve setpoint can be set at a lower value so that the valve be-gins to relieve at a 1ower pressure. However, the capacity of the valve is less and the mass input from the SI pump is greater at the lower pressure so the valve is not as effective in mitigating the pressure transient. These two effects of reduced capacity and higher mass input result in the pressure overshoot being increased from 155 to 192 psi as the setpoint is reduced from 600 to 400 psig for a net gain of 163 psi in the peak pressure reached. This effect is shown on Figure 3. 1.5.
| |
| 3-3
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| 3-5
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| FIGWRE 3. 1. 31
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| 3-8
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| 3.2 HEAT INPUT MITIGATED BY RELIEF VALVE As shown in Section 2.4, the heat input cases which have the potential for severe pressure transients are those in which the steam generators exhibit a higher temperature than the remainder of the reactor coolant system. The magnitude of the difference in temperature is dependent on the means by which the temperature asymmetry was achieved, but a typical difference is considered to be about 50°F because higher differentials are more difficult to achieve and are more easily recognized by the operator.
| |
| The transient pressure response for a typical heat input case in which the initial reactor coolant temperature was 180°F and the temperature differential to the steam generators was 50°F (secondary temperature 230°F; steam pressure 21 psia) is shown on Figure 3.2. 1. For this transient in a 6000 cu.ft. plant (2 loop), one of the two reactor cool-ant pumps was started to circulate the reactor coolant through the warmer steam generators. As the coolant flow began, the warm water (230°F) in the tubes of the steam generator in the active loop was forced out and into the reactor coolant pump where it was pumped into and mi~ed with the l80°F reactor coolant. In the inactive loop(s), the warmer water from the tubes of the steam generator was forced out in a reverse direction due to the backflow in the inactive loop, and also mixed with the cooler reactor coolant. This initial mixing of the warm water with the larger volume of cooler water caused an initial shrinkage effect and tended to decrease the initial coolant pressure.
| |
| 3-9
| |
| | |
| Simultaneously, the cooler reactor coolant which entered the steam generator began to be heated as it moved through the tube bundle. As heat was added to the coolant due to heat transfer from the secondary water in the steam generator, the coolant attempted to expand and caused a resultant pressure increase. The net effect of the expansion due to the heat transferred to the coolant and the shrinkage effect due to the mixing of the warm water into the cooler coolant was a relative-ly constant coolant pressure in the initial few seconds of the transient as seen on Figure 3.2.1. Then, as the flow rate increased and the heat transfer mechanism became predominant, the coolant pressure increased rapidly.
| |
| The reactor coolant pressure continued to increase until the pressure reached 500 psig, the setpoint of the relief valve. The relief valve was given a signal to open when the pressure reached 515 psia (at 9.2 seconds) but due to the inherent time delay of 0.6 seconds, the pres-sure continued to increase until about 9.8 seconds into the transient, at which time the relief valve began to open and the pressure began to be mitigated. Very soon afterwards, the valve had opened sufficiently to provide a capacity in excess of the expansion rate of th~ coolant and the coolant pressure decreased rapidly after reaching an overshoot of 100 psi above the setpoint.
| |
| For comparison, a transient pressure response for the particular case in which the temperature differential was only 20°F is also shown on Figure 3.2.1. With the lesser temperature difference, the transient is much slower and the resultant setpoint overshoot is. only 15 psi, vetsus the overshoot of 100 psi for the 50°F ~T case.
| |
| 3-10
| |
| | |
| Figure 3.2.2 is presented to show the relationship between the setpoint overshoot and the temperature difference between the steam generators and the reactor coolant for three initial RCS tempe~atures; 100°F, 140°F and l80°F. For a given initial reactor coolant temperature (e.g., 180°F) the overshoot is seen to increase with increasing ~T, where the ~T as high as 100°F has been plotted to show the effect. It can also be seen from Figure 3.2.2 that at low values of ~T, e.g., less than l0°F, no setpoint overshoot would be expected because the pressure would only rise from the initial value of 300 psig to some pressure less than 500 psig and the relief valve would not be actuated.
| |
| As already evidenced in Figure 3.2.2, the initial temperature of the reactor coolant also has a significant effect on the magnitude of the resultant pressure transient for the heat input cases. Figure 3.2.3 in-dicates the effect of the initial temperature on the setpoint overshoot for a 50°F differential temperature. By way of illustration, Figure 3.2.3 gives a pressure overshoot of 113 psi at a temperature of 200°F, whereas the overshoot is only 30 psi for an initial temperature of 100°F.
| |
| The heat input transients due to temperature asymmetry in the reactor cool-ant system are unique in that they are self limiting; 'i.e., when the temperatures are brought to equilibrium by the reactor coolant flow, the transient is ended. The use of a relief valve to mitigate the pressure transient will result in a valve cycling effect when the valve capacity is greater than the expansion rate of the coolant as it is heated, but the valve will only be required to cycle a few times until the temperatures in the system are brought to equilibrium and coolant expansion ceases.
| |
| The first cycle will result in the largest*setpoint overshoot. Subsequent valve cycles will result in diminishing overshoots as the coolant expan-sion rate diminishes until eventually the valve will close and remain closed.
| |
| 3-11
| |
| | |
| Figure 3.2.4 describes the first complete cycle for the reference relief valve as it mitigates a heat input transient with an initial sever~ tem-perature difference of l00°F. For this particular case, the valve is signalled to open at a pressure of 615 psia and the resultant setpoint overshoot is 145 psi. Then, as the pressure is caused to decrease by the valve action, the valve is signalled to close at 595 psia (20 psi below setpoint) and.the valve closes over a period of 5 seconds. The figure indicates the valve will close completely and the pressure will again begin to rise toward the setpoint. The open/close cycles wi11 be repeat-ed but subsequent cycles are expected to become of longer duration and of lesser magnitude, as the temperatures in the system approach equili-brium, until the valve will no longer be required to lift.
| |
| 3-12
| |
| | |
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| 3-15
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| 3-16
| |
| | |
| SECTION 4 INSTRUCTIONAL GUIDE FOR SETPOINT/OVERSHOOT DETERMINATION
| |
| | |
| ==4.1 INTRODUCTION==
| |
| | |
| Determination of relief valve setpoint for a specific plant requires knowledge of the expected overshoot which could occur under all possible mass input and heat input additions for that plant.
| |
| Many mass input and heat input possibilities were considered in LOFTRAN analyses which were performed to generate values of setpoint overshoot.
| |
| The analyses were performed for operating plant parameters selected to bracket or bound those of the plants in the WOwners Group on RCS Overpressurization. The bounding envelope of mass input and heat input generic results are not generally applicable to any specific plant. To determine a specific relief valve setpoint, a means of interpolating the setpoint overshoot from the generic envelope has been made available and algorithms have been developed to facilitate such interpolation.
| |
| The heat input algorithm involves the use of a procedure to interpolate the*setpoint overshoot for plants exhibiting a reactor coolant (RCS) volume and steam generator design different from those defined by the
| |
| ;
| |
| generic setpoint overshoot envelope. This procedure is presented in Section 4.2.2, together with an example of its application for a specific RCS volume and steam generator design.
| |
| 4-1
| |
| | |
| The mass input algorithm involves the use of* a'. procedure for the deter-mination of a relief va*lve setpoint, whic'h H1cludes ir{terpola'ffon of:
| |
| setpoint overs*hoot for pla:rifs with RCS volume, relier valve-' setpOirit, relief valve operii*ng time arid niass fnpl.it ra'te d'iffereht frbrri'1- but in-c 1uded w1th1 n, the enve fope of gener'it setpofnif o'vershodt restiffs'. -In-'
| |
| terpolation is expedited through the use o!f ari equatforf, de\ieloped for this purpose. Ttiis equation' fs based* o-11' the' adJus--tinefrit- bf. ref~rence
| |
| ( generk enve1 ope) setpofnt overshoot res'i.il t's by 1'i near-- a'ppl,1"catfon factors, with ohe factor d'etEfrmi ned for each Of the' fopuf pa*f'a:m*~lef*s; RCS vo 1ume, relief valve set~:foi nt, relief va*l ve openi n'g: fihie*j and;: mass input rate for the spekffic plant under corisfder'atfon,* the':: e}ql.iafia~*
| |
| and applicatibn factor developrifont is prese'ntea* fri s~cflorf'4>2. r.
| |
| ::.
| |
| | |
| 4.2 ALGORITHMS USED FOR SETPOINT/OVERSHOOT DETERMINATION 4.2.1 Setpoint Determination for Mass Input Transient Determination of a relief valve setpoint which will not result in a peak pressure in excess of the Appendix G limit, for the case of mass input as applied to a specific operating plant, is accom-plished with a procedure based on the following simplified interpolating equation:
| |
| AP (V, S, Z, x) = APREF (x)
| |
| * Fv
| |
| * Fs
| |
| * Fz ( 1)
| |
| The procedure for determining the relief valve setpoint is des-cribed below. To illustrate the application of the procedur~, a set of sample input parameters will be considered, and the results of the sequential application of each step of the procedure to these parameters will be noted.
| |
| ii
| |
| /!
| |
| . PARAMETERS FOR MASS INPUT EXAMPLE Relief Valve Setpoint = 500 psig Relief Valve Opening Time = 2.0 seconds Mass Input Rate = 60. 1b/sec RCS Volume = 10,000 cu.ft~
| |
| App~ying the mass input procedure:
| |
| 4-3
| |
| | |
| I*
| |
| Procedure Examp.1 e** AppJitation l Select relief valve setpotnt Set po int.*:.= 500* *ps.ig,_
| |
| operating range
| |
| * 2 For limtting ma~s input rate, 6.PREf: = 82 *psi. for* *mass input obtain 6PREF from~Figure: ra:te.: (x) * = 60*.:*lb/sec.:.
| |
| : 4. 2. 1 3 For to ta 1 RCS vo 1ume, obtain:* FV* =:= 0~7J for:. to.ta~. RCS'* vol:ume; Fv factor from: Figure 4~2.2 (VJ.=** 1O*~.ooo .. cu. ft'i 4 . F.or the relief valve open-fog. Fz = 0~*733~.:for relief valve.-
| |
| time (total, 1.ncluding delay), opening.: time: z, = 2: Q. secon.ds:
| |
| ._obt.ain: Fz factor from Figure**
| |
| 4.2.3 5 For the relief valve. setpotnt F5. =c L 14 fo.r reM.ef.* val;ve) selected, obtain F~ factoD setpoint = 500 ps*i;gi.
| |
| from Figure 4,2.4 6 Calculate the product of* fac~. 6P. (To:~',QOO*. cu. ft.,,, 50tkps i 9*.~*
| |
| tor.s tiPREF' Fv,* F5, and Fz 2:~ seconds;*. 60' *1 b/sec}. = 49><
| |
| de.termined in Steps 2- through psi-t i ~ l 5 (application of Equation l)j Thfs is the se.tpo.int overshoot, 6P.
| |
| ' I
| |
| ~ '
| |
| t Conservative - LOFTRAN analysis. for these. cond~tion-s .g.ives .an* ov.ershoot *
| |
| . equal to 25 psi.
| |
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| |
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| ~.~~ Z, Relief Valve Opening Time, seconds ;:;:!::;: -----.. -~ .... ---- :::-!:::-~ ::::;:-:::
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| 4-7
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| 1 1 I
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| :: \ FIGURE 4.2.4*
| |
| Mass Input
| |
| ;.::.:: .......
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| Relief Valve Setpoint Factor
| |
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| | |
| Step Procedure Example Application*
| |
| 7 Add 6P (Step 6) to the relief PMAX = 515 psia (relief valve valve setpoint (Step 1) to setpoint) plus 49 psi, or 564 obtain maximum transient pres- psia. From Figure 4.2.5 at RCS sure, PMAX" If PMAX < temperature = 100°F, Appendix G Appendix G limitation, se- pressure limit= 540 psig + 15, lected relief valve setpoint or 555 psia. Thus, PMAX >
| |
| is acceptable. If PMAX > Appendix G limitation.
| |
| Appendix G limitation, go to Step 8.
| |
| 8 If PMAX >Appendix G limita- Reducing setpoint by 10 psi tion, selected relief valve (564 psia - 555 psia} to 490 setpoint ii too high. Reduce psig and repeating Steps 2 setpoint and repeat Steps 5 through 6 results in 6P = 49.4.
| |
| through 7 until an acceptable psi and PMAX = 505 psia +
| |
| setpoint is determined. 49.4 = 554.4 psia. Since 554.5 psia <Appendix G limit, 490 psig is an acceptable setpoint.
| |
| * 4-9
| |
| | |
| I
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| |
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| .. _**,_:*_,::,__**._,* 1--*:_,::_____,---..._ .. - + - ; - - - t..----t.-!i__,_j: , RCS Temperature, "F l_.. * ,:. : :: :: ::*:k: :I : ; -* i :--
| |
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| |
| 4-10
| |
| | |
| 4.2.2 Setpoint Overshoot Determination for Heat Input Transient Correlations of RCS setpo1nt pressure overshoot variation with RCS volume, steam generator overall UA and initial RCS temperature are presented 1n Figures 4.2.6, 4.2.7 and 4.2.8 for the following conditions:
| |
| Initial RCS Pressure = 300 psig RCS/SG ~T = 50°F Relief Valve Setpoint = 500 psig SG Heat Transfer Area = 58,000 ft 2 6,000 ft 3 ~RCS Volume ~ 13,000 ft 3 4-11
| |
| | |
| *,
| |
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| |
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| |
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| 4-12
| |
| | |
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| |
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| |
| *t :_i_; :. , ... :J FIGURE 4. 2. 7
| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
| * 1
| |
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| |
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| |
| t::I ------+---+--+-~----
| |
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| |
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| |
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| |
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| |
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| |
| -- o--
| |
| -- z :.:...:.. __..__
| |
| RCS PUMP STARTUP IN l LOOP RCS VOLUME = 6000 CU. FT.
| |
| INITIAL PRESSURE = 300 PSIG RCS/SG ll.T = 50°f RELIEF VALVE SETPOINT.= 500 PSIG SG HEAT TRANSFER AREA = 58,000FT2
| |
| .
| |
| * 1*
| |
| . I: : . : : :.: .!::'. :I::~: I:~!: I:'.:~ l ~::: t= :-~::1:::: ':: :*T::: I: :::J ::~:I::: J ~::
| |
| ~-~~-~~::l::~ ~:::!:100 :i:::: .~ .. i :zoo*
| |
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| |
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| |
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| |
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| |
| . ... .. .
| |
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| : : : :1::::
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| +. PHAX
| |
| ;,. I PSETPOINT' PS'
| |
| \
| |
| 4-13
| |
| | |
| -~
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| |
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| |
| EFFECT OF STEAM GENERATOR UA ON
| |
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| |
| .:: : J PRESSURE OVERSHOOT
| |
| -...-+-. - .*. .. l"''
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| :-: : ..1~-: :*:.
| |
| ::*.: !: ::.:
| |
| ~~*:J:i~
| |
| *- RCS VOLUME = 13000 CU. -FT.
| |
| INITIAL PRESSURE = 300 PSIG RCS/SG AT = 50°f RELIEF VALVE SETPOINT -
| |
| SG HEAT TRANSFER AREA =
| |
| -~r:::- *.::== .::-:.:
| |
| 1* .......
| |
| oo: ::~
| |
| *: :::r :-~:
| |
| I.,. ~ ..
| |
| .:..t.!:
| |
| ., ... ....,.
| |
| t ....
| |
| ...
| |
| ** - ~ ill"
| |
| ....
| |
| .,. *. ,_1-.
| |
| *
| |
| * 1-
| |
| -r---
| |
| ...
| |
| +-'
| |
| *:..:;_
| |
| :; t:.
| |
| -.;*~:.:.:
| |
| 4-14
| |
| | |
| To determine the setpoint overshoot for a smaller steam generator heat transfer area and for an intermediate RCS volume, the fol-lowing interpolation procedure is used. This procedure utilizes Figures 4.2.6, 4.2.7 and 4.2.8 directly without the introduction of linearization factors and associated conservatisms as for the mass input case.
| |
| The use of the procedure is described for the following example heat input parameters and the results of the sequential applica-tion of each step in the procedure to these parameters will be noted.
| |
| PARAMETERS FOR HEAT INPUT EXAMPLE SG Heat Transfer Area = 29,000 ft 2 RCS Volume = 10,000 cu.ft.
| |
| Initial RCS Temperature = 180°F RCS/SG AT = 50°F Relief Valve Setpoint = 500 psig Applying the heat input procedure:
| |
| 4-15
| |
| | |
| */
| |
| Procedure Example Applic,tion .
| |
| 1 For both the 6000 ft 3 and For TRCS = 18Q°F, 6Pt6K = 98. psi 13,000 ft 3 RCS volumes~btain *and 6Pt 13 K = 6~ .ps 1 *for RC~
| |
| reference setpoint overshoots volumes of 6K and 13K' resP.~c 6P 6K and b.PlJK from Figure tive.ly.
| |
| 4.2.9 for the initial RCS temperature~ TRCS' 2 Using both Figures 4.2. 10 and For TRCS = 180°-F and b.P ;:: 9f3 4.2.11, determine the refer- psi, UA 6K = 0.115 {F.igur.e ence normalized UA (UA6K and 4. 2.10). F.or TRCS = l80°F ~nd UA 13 K) for both RCS vofumes b.Pl.JK = .68 .psi, UA 1JK = 0. H34 using 6P 6K and 6P 13 K deter- (Fi~ure 4.2.11).
| |
| mined in Step 1. and for the isotherm, TRCS' 3 . Determine what fraction, f, :29,000 ft 2/58,000
| |
| ... ft 2 -
| |
| = 0.5 of 58,000 ft 2 .constitutes the actual steam generator he~t transfer area.
| |
| " .
| |
| : ~
| |
| 4 Multiply both UA 6K and UAlJK UA *6K = O. 115
| |
| * a..5 .:: ,0.:0~~5 and (from Step 2) by f (from Step I :
| |
| * * '** .0 **"5 *= '0.-~.=1 UA l3K o* * *104 ~n2
| |
| : 3) 'to obtain new no rrna l 1zed 1 1 UA £K and UA lJK values.
| |
| t Setpoint Overshoot, b.P = PMAX - PSETPOINT
| |
| * 4-16
| |
| | |
| ~ ;;;; ~~~[:.;:_ ; ;.;.1;~:- ;;f~~ ;;~~~:~;; ;~~;i~ ~;i~:: :;~h:~ ;;~[~~ ~;;g~ ~~;+/-~ ~;:r_~;:*~*d::::::~~~~+:':i;~: :.::-:!-~::.{=+:~
| |
| ~iL. :~J~~ ~~~= :~F- =.:~ ~~'-:::?.:= 3~~:~ ~~f~ :?Ji== ~~~f=-:: ::~j~:..::~-= ~:::;::=~N::::: ~~~~.=:~!~~~~,- ::~
| |
| I~ ~ m~*~ :;t~t~~~;~~;i~ i~~mt ~;~ r~1~~ -~~1~i;~f~ ::~fi~~:~1;~1~I~~~~-Jl~-!::~;:!
| |
| ~i'. ~ ~:l~~ -~t~~~ ~~~0~~ ~~ :~~~~~~~~1~0-~:::!~~~~ ~~~:~~
| |
| ll.~:f:t:_~~r~ :m~ L~~~~ ~~;~~ ~~ ~t~;~ r~~~ ~mms~~~~ :81~-~]Z;r~~1~~~~r+/-~~~
| |
| 1
| |
| !!!~:~~ *~~* 5!SEE~ at~~ ~~~~~t~~=~~~~~ f~i E= ~~~ ~~~~~~~~ ~~~~t~~;:
| |
| 1
| |
| :~~t:~~ ~-~~~t~~~ :~~1.~~::*~~i:~~ ~~~t:~:: ~~!~~ ~~~b~~: ~-~~~~~~ ~=-~-i~::.> *::~~-:~:f~~::*-::~:~,:~;:~~:~ ::*~~E;~
| |
| 11
| |
| ~~:~Tu; ;~J;I:: '.ti~~i=~~~ ~~~~3ill~i ;t~~~1!f: ~~~1:~~~.r~~;~~;; ~~7i~i ~~;:
| |
| ~:~~~~ ::~~ ~~ ::T;v__ ::*.i~~1~:::::~=~ ::-:*~;~:. :~~.f~:; i-~T~:- :~l~ :~[~:-: ::.:i;~~ :.::;>:f.::L:::I~:.::!~ :~-i=:~.: ~~L~ :~~~::i*: =~~
| |
| ~~ ~~~ ~~~ :::= :::=r=~: :~T< ~=~f:d::::*~:::: ~~?t::=: ::~~=.if~: :::=-,::::r:::t:::r::r:*~:;* 100°F l>:::: ~~T-::~::::::: ~~~t~
| |
| ,:.:;iL; ~~~T~~~ ~;_L:: ~:J::;: ::;1~:~ :~x;:~ :~~]~~~:::]~::~I~:: :~~-i:.:: ::::!::.::.::.:: ... ;.*.*: .. :~~~;::*~.:::;;~;
| |
| ~~ ~?~ ~: ~~~~ ~~~~::- :~:f~~= ~=-~f:=~: :-~:-~*-*:.:~*::~r~~~ :.:::~~; ~~t:~: ~::~~~~ :~=:f:~~ ::~~n~;~ :~~~r:~~: ~~::~:~:: ~::r:~~-~ ~~~~+:~~~ =~~~~~~~ =~~-~r~~~~
| |
| ::=:: ~: :~:
| |
| -'""*----
| |
| ~:.::: ~i"::. :':::. :.=.~ ~:;_i1> :::~;::: :~~:r..::.~: ~~~~>::
| |
| *** -*-* * * *
| |
| * t ** -1
| |
| ~~~~=~:.: ~~~~:: ::;:t.;;:; ~~~~~:~ ~~;f~< ~~~T=-:'~ ~:~~~~: :~::h~~ ::~:::: ~~~i~~~
| |
| *r
| |
| | |
| RCS VOLUME = 6000 CU. FT.
| |
| INITIAL PRESSURE = 300 PSIG RCS/SG AT = 50°f RELIEF VALVE SETPOINT.= 500 PSIG
| |
| .::~_*j~:. :*.=.:.- -:~~ =:r~.=-: :::::i:.:~:. :::_:_1::.: . *.:. --+--
| |
| :::: !..*.: SG HEAT TRANSFER AREA = 58,000Fi 2 ::
| |
| t--~f-----1 *---- ---- ***--* **--* - - *-*- *****I**--
| |
| :.*r:::-: ::.._:.::_1_:_**.-~.: -::~_:___ :_*:-:-~~:.:-_-:_1_:=-~~ :-~~~t:::* : '1***, ... l'--:1:*::1'**-l~---1:::.1.:*:
| |
| - *1:-***.***-~*:** ***-~**:* .. -~~-
| |
| :-::1::;i:-~-:-:r~~--:1:::*:j.:::.:
| |
| .. :***,**-*~*--*, .. -~-
| |
| .
| |
| ..*--------------t---
| |
| . I . ZOO i
| |
| ' ....
| |
| .... ,... .... ,I .....
| |
| . : ~:
| |
| .. 'l'.*-*--..---*
| |
| -.. -*--
| |
| -- ..
| |
| . - . . t .* - -
| |
| ....
| |
| _*::: ~=-=*: .:-::= : :::
| |
| -* _......, -. --- , .... _
| |
| *---t*--*-
| |
| :r:: -**-
| |
| .--.-,
| |
| -- -* ::::-:
| |
| -... - ~:~:i::::
| |
| . *- - . ***.
| |
| 4-18
| |
| | |
| RCS VOLUME = 13000 CU. FT.
| |
| INITIAL PRESSURE = 300 PSiG RCS/SG aT = 50°f . !
| |
| RELIEF VALVE SETPOINT =
| |
| 4-19
| |
| | |
| Step Procedure Example Application 5 For the same 1sotherm, TRCS' From Figure 4.2.12, tor TRCS =
| |
| and for UA 1 6K and UA 1 13 K, 180°F and UA 1 6K = _0.-0575, obtain new setpoint ovarshoots !:IP' 6K = 44 .psi. From Figure l:IP 1 6K and l:IP 1 13 K for the 6000 4.2.13, for TRCS = 180°F and ft 3 and 13,000 ft 3 volumes. UA 1 13 K = 0.092, ~P 13 K = 35 psi 1
| |
| 6 For the actual volume, VRCS' For VRCS = 10,000 cu.ft.,
| |
| linearly interpolate the set- l:IP 1 6K = 44 psi and *l:IP 1 13 K = 35 point overshoot, l:IP 1 VRCS' for psi, the new steam generator LIA from the relationship:
| |
| 1
| |
| ~p lOK =
| |
| 1 l:IP VRCS =
| |
| 44 - l0,00~0006000 ('44 - 35)
| |
| = 39 .psi This P'vRCS is the overshoot corresponding to the actual steam *generator heat transfer area and RCS volume.
| |
| 4-20
| |
| | |
| *.
| |
| RCS PUMP STARTUP IN l LOOP RCS VOLUME = 6000 CU. FT.
| |
| INITIAL PRESSURE = 300 PSIG RCS/SG AT = 50°f RELIEF VALVE SETPOINT.= 500 P~IG SG HEAT TRANSFER AREA = 58,000FT 2
| |
| --**E*--
| |
| . -- --*4 PKAX pSETPO INT'
| |
| -*-
| |
| --- - .....
| |
| -~-
| |
| : : : . I.: : : :r:.:
| |
| . ......,....,.
| |
| ,,. ~ ......
| |
| 4-21
| |
| | |
| .*
| |
| FIGURE 4.2.13 EFFECT OF STEAM GENERATOR UA ON PRESSURE OVERSHOOT
| |
| --- :1-::::..: ::!....! ::.::
| |
| .,. ' .
| |
| lll l *
| |
| - ~ I "'
| |
| -Ll7 '
| |
| ;+H ~;:r iill ~-, -*
| |
| RCS VOLUME = 13000 CU. FT.
| |
| INITIAL PRESSURE = 300 PSIG RCS/SG 6.T :; 50°f .!
| |
| RELIEF VALVE SETPOINT = 500 PSIG
| |
| = 58,000FT 2
| |
| ***-- -** -*-* ---*-* +--~-+~~;--~...+-~--<--<~
| |
| *~*
| |
| ~ r * *
| |
| '- ....
| |
| 4-22
| |
| | |
| 4.3 DEVELOPMENT OF INTERPOLATING MASS INPUT EQUATION The following, simplified equation is utilized for determining mass input setpoint overshoot for a specific set of plant input parameters from the gener,ic data.
| |
| 6P (V, s, Z, x) = 6PREF (x)
| |
| * Fv
| |
| * Fs
| |
| * Fz (1) where:
| |
| 6P (V, S, Z, x) = setpoint overshoot, psi v = total RCS volume, cu.ft.
| |
| s = relief valve setpoint, psig z = relief valve opening time, seconds x = mass input rate, lb/seconds 6PREF (x) = reference overshoot at mass input rate x, psi FV = RCS volume factor FS = relief valve setpoint factor Fz = relief valve opening time factor Equation (1) involves obtaining a product of a reference overshoot 6PREF' and three application factors which account for variation in the 6PREF from reference values of RCS volume, relief valve setpoint and relief valve opening time. Linearizations involved in the development of Equa-tion (1) will necessarily introduce some degree of conservatism in the pressure overshoot and in the determination of relief valve setpoint.
| |
| 4-23
| |
| | |
| 4.3.l Analytical Basis Development of Equation (1), and, more specifically, the deve}op-ment of the three application factors is based on an elementary, linear, algebraic equation involving one depend~nt ~nd one inde-pendent variable, or f(x) = ax + b (2)
| |
| If this linear function is defined to pass through the origin of the coordinate system, and if f(x) takes on the con*st'ant value* c for a specific, reference value of ~ = xr' then f(xr) = c b =0 a = c/xr and Equation (2) becomes f(x) = (L) x (3) xr Now consider two linear fLmctions 'of x,
| |
| * f 1(x) and f 2:Cx), ooth passing through the origin of the: coord.in'a*te system*, with (4)
| |
| (5)
| |
| These functions may be writterr as 4-24
| |
| | |
| (6) and (7)
| |
| Both functions f 1 and f 2 are graphically depicted in Figure 4.3.1.
| |
| In solving Equations (6) and (7) simultaneously, the equation for one linear equation may be obtained in terms of the second equa-tion by multiplying the second equation by _the ratio of c(xr) values for the two functions, or (8)
| |
| This analytic technique for the determination of one linear func-tion from a known second linear function through the use of a multiplication factor is extended to the development of interpola-tive factors for the generic mass input study.
| |
| 4.3.2 Development of Application Factors
| |
| : 1. FV - RCS Volume Factor Consider the setpoint overshoot-mass input rate correlation shown in Figure 4.3.2 for VRCS = 6000 (6K) ft 3 and relief valve setpoint = 600 psig. If this curve is linearized from the point (6P, mass rate)= (155 psi; 113 lb/sec) through
| |
| *the origin (0 psi, 0 lb/sec), the resultant linear function as shown in Figure 4.3.3 exhibits the same characteristics as the linear analytic function f 1(x) de~cr_ibed earlier, namely 4-25
| |
| | |
| ....... ~
| |
| MASS INPUT FIGURE 4.3.l Analytical Basis for ::::i::::
| |
| Mass Input Equation ... ....
| |
| ............
| |
| t-<--+--* *-* - ....I....
| |
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| _.,. __ _ -**-- -*---- -*-- - -- ****1****
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| \I
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| ,
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| .... **------* *-*-**- ---- .... .......... ; ... . .
| |
| _, ____ .-...-- .......... -- . -....... ---- '---
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| *- *-***
| |
| _ __ _ , _ _ ......., _ __ _ , _ . _ , . . _ __ , _ _ _ 1-----**-~ - -- **---- ----- .,. ------
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| |
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| |
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| |
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| ==-= :-_:-:: :_::.::- -::_:.:
| |
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| |
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| |
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| |
| *::.:*:~
| |
| ---- *--...4-
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| |
| ----= -:---
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| |
| ----- ----- ----- ----*I-~
| |
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| |
| *-**- - I . --- .
| |
| : :..:..:L:.:::.
| |
| ::::L:::=
| |
| _____ _J - - - -
| |
| --- -+-*-
| |
| ,.----
| |
| *-- -*--* :~~-=:;:: _,: ~-
| |
| I t---- --~~- ------* --- -- - - .., ___ -- - ****--- -- ----== - -- :*: ---1.:: .-:-
| |
| t- - t -
| |
| t--- - - * - - - - f - - - - ---:----~
| |
| *---..:._-= =--*-- r::::.. -- '------ ----- :=:-
| |
| - - - - - -*---- ~-~* *---- -...- -- ----
| |
| *---., --- -
| |
| - .. --
| |
| * t------+----+-----*..,~_* --<f----+*-~*---"*------*-_._. __ --_,__-::-= .::..:::. ~-- -- -*---- ----
| |
| - - ---- -
| |
| ---
| |
| _J_ ,-l--
| |
| :J...1-4-26
| |
| | |
| FIGURE 4.3.2
| |
| ,.. __ _ ~ - ... t .
| |
| ....
| |
| .I-'*
| |
| * r.:--!-t-r; ~F~rh+t*+tt~H-;T;-H+~'->-:-+;...-
| |
| _:_:: .: __:_ .;._:__:_:: i.:.::.:.:_ :::.::- ::-r. . --- r---.-- -f-+-r-l- J::.~:tt+j r+::~ +f-t+ _;+"ft ::::-: ~::+.;:* J::---~ f-t;;:+~~~
| |
| __:.-:-:: - - - -- -,---~f-+---i- .+~ -n-*--~H--!...~ EFFECT Of MASS INPUT RATE µ,---- . ' I- t-:-+ ~~r--
| |
| --- --* -- ~-*-:....._ ... LL..
| |
| ~ -r------++-+ ON PRESSURE.OVERSHOOT
| |
| ----"'---~~--*-- ----~-+~-~
| |
| ~- ------ ::t::l ._,_
| |
| ,..-. --- -___ --__ -----
| |
| ..., - .
| |
| i::: , .. ,
| |
| ...
| |
| ~ .. . ~
| |
| * ...... 1--
| |
| :;:.RCS VOLUME* 6000 CU.FT.:: *'** '.'.:l ,;j,
| |
| :: 600 PSl.G RELIEF VALVE OPENING S-E--TP_0_...1-NT_.._-+--..-- ...- - - - .
| |
| -***;* _______ .._ __ _
| |
| --------r----* -- --1-------
| |
| .*. --
| |
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| r- - - - - - - ~~--
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| -*-** -
| |
| ~---* .......... .,....---~--** f--* -- ----- - - - -
| |
| ---- --*--
| |
| - - - - ---... - -
| |
| --- *--
| |
| -----*>--*-- --**-- - -
| |
| _. . . :--=z::: ==::: :=:::
| |
| _____ ,_. ___ ;.,.___ _ _ ... - - - - **... *-
| |
| * f--* - *- -
| |
| 0 ----1---- t--*-
| |
| N ~- =~:-= ==~~=~~ _:__*,~==-:: ~ *-'-~-'-~-C~--+-*-_:__.-1-"'-:__:_.,:_~+***: :-.::~~ - - - - - - ...:.==:_ .::_::..=:_=
| |
| ("() ----* - - r - - . - - . - ~* . . --- --*-- - -** --- - * - - -- * - - * ---- ---- --- * - - - - **
| |
| ..... -
| |
| ---..:-..:;;.o.: ~------
| |
| ---- -- ~ ---
| |
| - I---- r---: - ,___._;
| |
| ---*- - -- - ---t---* r----- - ------- --------.:...i----- --
| |
| =- -- --=--;:.----- -
| |
| 1---* -- - * *;-
| |
| ----- - 1-----r.....* --*
| |
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| |
| +-----+---*----+
| |
| f- - ...
| |
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| |
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| - ----:= *====
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| |
| -- =:.:__ - * -- -*::
| |
| ~=~=-==-====--=-=*t-==-:+/-==-:1>--==:I::=:::!:-=-=--=-~~~ -~-----=~
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| ~-=--=-t=-=....:.--:::_L.---- --i------- -----* ----- ----- ***h**-
| |
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| |
| - --------------
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| ------r----- - - - - - - - - - * - * - - - . *-* -- ---- . ---*
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| ----
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| -_:_-=._-i-_~_-----_:-1-~-::.-::._____
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| --::.-j~-::_-::_-::_t._::--
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| ____-_~r~-==*-:__-=-+-~-=--=---=+>---*--_--::_--._:*+---+-/--1~'-+--+---+----*-*--+-----_-_-_-+-=----~:-:1-~-.:-.:-:,_----~-=-:+--=-------r--**--*---+----t.-._-_-_r_-_-_._--11--+-_-_-
| |
| ----- - *-- -- ---- ----t-----1-------* ----- - - -
| |
| - :z:: ___-_:_:__r->-:____-=._-_.-__;-,_
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| __ ___-i_
| |
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| *:-: ~1 : L:~::- :*:: ~
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| --*-..:.... .. -*- **:* FIGURE 4.3.3
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| 4-28
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| c
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| = (-1) x (9) xr where:
| |
| AP 6K1600 (x) = linearized reference setpoint overshoot, psi x = mass input rate, lb/sec
| |
| = reference mass input rate, lb/sec
| |
| = AP6K/600(xr), psi For the reference conditions of 6000 ft 3 RCS volume and 600 psig relief valve setpoint, Equation (9) may be written
| |
| _ ( 155 psi ) _ ( )
| |
| AP6K/600 ( x ) - 113 lb/sec x - APREF x (10)
| |
| Further, assume that the setpoint overshoot for the same 600 psig setpoint but for a 13,000 ft 3 RCS volume, or AP 13 K1600 , may also be represented by a second linear func-tion (Figure 4.3.4), namely, (11) where:
| |
| AP 13 K1600 = linearized setpoint overshoot for the second linear function, psi c2 = AP13K/600 (xr)' psi For V = 13,000 ft 3 (and S = 600 psig), Equation (11) may be written:
| |
| (12) 4-29
| |
| | |
| FIGURE _4. 3. 4 MASS INPUT
| |
| .:\
| |
| Linearized Setpoint Oversho_ot I
| |
| .:
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
| ----~ -*-- 0 c...
| |
| <J f---+--+--+--+-+-*-*........ -+.>,_I::+:_*-"111""-.7::_:*+-~-::-+:-+---+--+-::: xr
| |
| * 113 1b/sec \
| |
| ::::t::v :I: *::.\: :1 r---*!~**-..-+---t--+---+~-t--1--*~*~"+-*~*~~"-+-*-*-*_*+---+---+~-+---+---'f--+---+--r1~--t--+---+~-t--+---+---t~-+----+---r--~
| |
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| |
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| |
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| |
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| |
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| |
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| |
| "-+--* .........-r----!- * -+t f-, ~+++ ~++
| |
| -+-r-4-30
| |
| | |
| where:
| |
| c2 = ~P 13 K 1600 (113 lb/sec} = 75 psi From Equation (8}, Equations (10} and (12} may be combined to give the setpoint overshoot for a 13,000 ft 3 RCS volume ih terms of an overshoot determin*ed for the reference 6000 3 . .
| |
| ft volume, and a ratio of overshoots (c 2/c } determined at 1
| |
| the reference mass input rate, or xr = 113 lb/sec. This relationship, for which setpoint remains unchanged at 600 psig, may be written c2
| |
| = ~P6K/600 (x}
| |
| * c 1
| |
| -- ~ pREF ( x }
| |
| * 155 75
| |
| = 0.484 ~PREF (x} (13) 3 . 3 For RCS volumes intermediate to 6000 ft and 13,000 ft
| |
| * values of c2 will vary between 75 psi~ c2 ~ 155 psi and the c2/c 1 ratio will vary between If the c2;c 1 ratio is set equal to Fv, the RCS volume appli-cation factor, its variation with RCS volume would be as
| |
| - - - -
| |
| shown in Figure 4.3.5, and the setpoint overshoot at 600 psig
| |
| . 3 3 .
| |
| relief valve setpoint for any 6000 ft ~ V ~ 13,000 ft would be obtained from the relationship 4-31
| |
| | |
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| ( 14}
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| where:
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| l\PV/600 (x} = setpoint overshoot at mass input rate ~ for RCS vblume V and S = 600 psig, psi l\PREF (x) = reference setpoint overshoot at x (6K/600)
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| Fv = RCS volume factor
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| , 2. Fs - Relief Valve Setpoint Factor Just as the 6P 6K1600 (x) and 6P 13 K1600 (x) functions were linearized in Figure 4.3.4 for a change in RCS volume from 3
| |
| 6K ft to 13K ft 3, linear correlations for setpoint varia-tions from 600 psig to 400 psig can be drawn as shown in Figure 4.3.6. Further, just as Equation (8) was utilized to relate one linear function to another for RCS volume variation from 6K ft 3 to 13K ft 3, it may also be applied to the situation where setpoint is varied. In this case, to obtain the setpoint overshoot l\P at 400 psig for a 6000 3
| |
| ft plant knowing l\P at 600 psig, Equation (8) is ~tilized to obtain
| |
| * c2S l\P 6K/400 (x) = l\PREF (x) * -c1- .
| |
| = l\P 6K/600 (x) * (~ ~~)
| |
| = 1.25 6P6K/600 (x) (15) 4-33
| |
| | |
| .. , ... ,...
| |
| :::~-: :**:: 1*. FIGURE 4.3 .. 6 MASS INPUT
| |
| ::j::::
| |
| .:1.
| |
| Linearized Setpoint Overshoot
| |
| *;*** Volume and Setpoint Variations : : : : f:: : :
| |
| ::::1::::
| |
| : :J~ .: : : :. ..:...: :.:. ..::..::.
| |
| - *-*- ::::i-
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| ::::1::::
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| ::::j*:::
| |
| - * *
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| * 1* - * *
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| : : : : I - ~: : **-*1****
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| :::_:.::.:..:.:.
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| ' i - .
| |
| ***:i:::: :: ~ :i: :::
| |
| -* .. *, ....
| |
| i::: .****. '1 ***
| |
| ~--
| |
| 1---'-~ :.:*_:_; :::::. =::= ::::!.: :-rt:.
| |
| - -* - .... - -* .;._ .. **- *.* J.J_, -
| |
| -;-**t
| |
| 'i-*
| |
| ****l-**-
| |
| ::::1::::
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| * - *- ***-* *- - - - - ** _....;._. __.!_ * -
| |
| **-**1*** , *- -
| |
| :::: :::: :::.\::::
| |
| I*-*-
| |
| *-** **-* ---** **--
| |
| : :...: : :.:-:*.:*~...:.:; l.::*: --***1**** :::t:
| |
| -*-* -***
| |
| . . . . I * . .
| |
| :_:::i::::
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| ..
| |
| - - *.* 1-- - -*- ---***
| |
| 1----- ---- ---- ----- ---- **-*1***-
| |
| '
| |
| *-
| |
| =----=~
| |
| ____ ~~::-:- *-**1 :-:.-=:t::=-
| |
| - **t*--***
| |
| i-:-**-* ---- ..
| |
| - **t- ....... *--~- ... _...
| |
| ::.::. :~:*1_
| |
| **-1-* ----** ***-*-*
| |
| ***-* ...... :::.'.. *~;-~.;. ::J!
| |
| ---- *---- ------
| |
| ........ --*-
| |
| --** ::-:*:1:-_--_-_' ----'1---- ****'****-
| |
| ~~i~~ Czs = l92t-:-::-:::-t-=-*=*-:-:i---:-::::--~---:-:::::-*t-~-=-~...r.--:*:::*-*:r.___==-=-*+*--*---=-*=-*1-...::..::--:..:_;.:::;-i-=*=*..:-:::.:+'-=-*=*=**=*11:1F:...**:::.:=-F=:.:-=--::.*:.::::i-..:.:.:.:.t=.:.:::+:.:..::.:ii.::..::::.:+:-_.:_.:_.:.*-~:::.=:.--::-j1-=::.:::.:::.:::-J_..::::*.:-=.::.;.l.:..:::.*:.*-::i*
| |
| r---- . --- --- ~::.::L::: :::~*::~::_~~ T: ::~~i:::_ :_:/t: ~~~~ :::: :~~J:::-
| |
| t - .. - -~- --- - - -- ..
| |
| -!***-
| |
| t--* ..
| |
| ..., :::::_ill>i).7.~i~j;[; .. ,. -~; xr
| |
| * 113 lb/sec f""
| |
| :a" ..
| |
| ;;::* f"'
| |
| i' ..
| |
| ~- +~:i ~ttt :ft!j ~~~~ H
| |
| ~-4 -~- ~~-',*+/-- +-~~;- ~::~~--- j*J_ + -*-1-i i-~ t--i-tti- *rd-i t
| |
| --H-t 4-34
| |
| | |
| For a RCS volume of 13K ft 3, this relationship (for a set-point change from. 600 - psig to 400 psig)
| |
| I would be AP13K/400 (x) = AP13K/600 (x) * (~)
| |
| = 1.27 AP13K/600 (x) (16)
| |
| To ensure a conservative determination of setpoint overshoot for a setpoint variation at any RCS volume, the maximum co-efficient (l.27) in Equations (15) and (16) is utilized in the development of the application factor for the *generalized correlation for setpoint variation. In this correlation, for any relief valve setpoint between 400 psig and 600 psig, the setpoint overshoot for RCS volume V from Equation (15) is given by (17) '
| |
| where:
| |
| F5 = relief valve setpoint factor as defined in Figure 4.3.7 S = relief valve setpoint 400 psig ~ S ~ 600 psig Incorporating the v6lume variation effect from Equation (14), '
| |
| Equation {17) becomes (18) 4-35
| |
| | |
| ~--
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| Mass Input
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| ... ::+:~ __ :_:-_*::-: :: .. -----
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| +++.
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| .:;-+r-'~--=- .. ~ ~ ----+
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| - ....,
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| -t-' -"+ ~ ,m ~i2 ~ ~~:t-t-,"H _,, t4::t *~ :ti:;.t ;t::: _;:r:1 ~~~ =~::::: [:§ £[+::* 1~3=-~~~ ~~~ =-:~::_ ~-= :~
| |
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| ' ... ~ 1~ h-' -+. .......... - - ...... ......., ~ ........ -.+-
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| I '-1--H .*!=t:: +-t * ~ :.;.:i-t .Ltii -i.H:t J:-__ .~_ ~--:~ : :1! .::-:=.µ=-~~ :.~::-:_ :-:r:::-~,----,r-__~__-<-t",__-_,.__ .~_ ... -
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| ... ...J..-...-,. -- 1""T r - - -- .: :_:*_:_
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| ' ~: ... ~. :.:-:-:: ----.
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| __ ......,._ __
| |
| **-*
| |
| *---
| |
| -~~-J.
| |
| **---1-----o--
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| - *---"'--
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| S, Relief Valve Setpo1nt ps1g .-~- - **-f---i-:--
| |
| - ' ' ' *r ! 1111
| |
| :.
| |
| ~ :.~=:: :::=!:~
| |
| ---1----*-~
| |
| 4-36
| |
| | |
| To this point in the development, the effects of relief valve setpoint and RCS volume variations on setpoint over-shoot have been accounted for in Equation (18}. The effect of relief valve opening time remains to be considered.
| |
| : 3. Fz - Relief Valve Opening Time Factor Figure 4.3.8 describes the variation in setpoint overshoot
| |
| ~p wit~ relief valve opening time, which includes a time delay (for air accumulation prior to valve stem motion) equal to 20% of the total opening time. Correlations are presented for 400 psig and 600 psig relief valve setpoints at RCS volumes eq~al to 6000 ft 3 a~d 13,000 ft 3
| |
| * To facilitate the determination of setpoint overshoot with variation in valve opening time, each correlation in Figure 4.3.8 was linearized by drawing a line, tangent to each curve at the reference condition (relief valve opening time =
| |
| 3 seconds), and intersecting the abscissa at a point to the lift of the origin.
| |
| Figure *4.3.9 illustrates this procedure for the reference case (600 psig setpoint, 6000 ft 3 RCS volume). If the new origin defined by the linear approximation is designated as
| |
| '
| |
| 0 and the displacement of the origin as ~z*. then the co=
| |
| 1
| |
| ,
| |
| ordinate system for the linear functions will have a new abscissa, Z, defined in terms of the original abscissa Z' (where: 0 seconds < Z' ~ 3 s~conds) and the displacement
| |
| ~z*, or Z = Z' + ~z* (19) 4-37
| |
| | |
| _,
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| 4-38
| |
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| I j. :! 'jt** . :* i 6000 cu. ft.
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| |
| :** ! *i 50 *1 :':I./ I'/** :*: :/, :! :*;.~ 600 ps1g **4 --***+**--:!--***+**--***..;............ 1
| |
| ___ !---+------1 1
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| ***1 :* .. i:. , .
| |
| . I 4-39
| |
| | |
| For anY relief va'lve opening dme*~ i* ~* ther-efC>r*e, th'Ei _1 setpoint overshoot ~p may be obtained from the' 1 i nea*r rel 9..:''
| |
| tionship
| |
| ( 21 ) .
| |
| The Fz factor was optimized f*ram a i ihea*ri z:a:tidn of afr the*
| |
| correlaticins in Figufe* 4. 3.9'~ rt was deb~frmfriecf tti*a-t 6oth setpofot parametrics for 6606 .ft3 Rts vofume* proffucecf £Her largest abscfssa arsplacement (~i* = 6. is se*ca*ncfr). fhiS~
| |
| di spl ~cement maximi ies the Fz facfo'r tO eris:ure a* cons*ervatfve
| |
| 'setpoirit overshoot. A plot of the F''z factor wfth* valv~
| |
| opening tiiTie, z*, fs shown in Figure 4'.3. l"o. lt sfi'oulH &e
| |
| * not'ed- t*hat conserva*t1 sm in overshoot Cietermi ri~ft1cfo incF~as~s as the rel 1ef valve!' open i ilg t iilier is reduced frorii th~ j* sticond*
| |
| refer'ehce value.
| |
| B~ way of 111 ust'ratfo-n of the us'e of the Fz fa''tti>-r ,* "c&nsi~a~f' a.re n. ef va 1ve opening. time cff 2. a s*eccl'rids. fhe *reT'-er'Eihde .
| |
| ' .
| |
| se.tpoint ove*rshoot llPREF (= _t;PfiK/s'6o) w~uld B~- d-e~ermiff~:cil a*s.
| |
| follows. From Figure 4.3*.10*, for z* = 2.0 se*cond*s*;*
| |
| Fz. = 0.73
| |
| .:.
| |
| from Equa tfori ( 21 ) ,
| |
| 4-46
| |
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| * 6PREF (x) (22)
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| = 0.73
| |
| * 155 psi
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| = 113 psi This compares almost exactly with the setpoint overs.~opt given in Figure 4.3.8. For smaller valv.e op~nil)g ti.1)1~_§,
| |
| use of Equation (21) will give progressively. more
| |
| , '' .. . .conserva-
| |
| ** * ' : ',.
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| tive values of overshoot.
| |
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| |
| . .*.,
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| ,,:tim.e ,. as
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| _-'
| |
| given by Equation (21) .into the expressic;>n
| |
| . .
| |
| (Eqµattqn 18)
| |
| '' '* *'*, '
| |
| which reflects the effect of relief valve setpotnt and RCS volume inte~polation, the following expresst~n is -~~rtyed:
| |
| ( 2,3) or
| |
| .which is the simplified
| |
| .
| |
| interP,olatirig _equation.
| |
| ' . .
| |
| (E,qµ~tiqn
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| 1) used in the alm)rithm for setpoint determinaticm far*.~~e.mC:sS input transient.
| |
| 4-42
| |
| | |
| SECTION 5 CONSERVATISMS IN STUDY The analyses presented in this report were conducted such that certain para-.
| |
| meters provided a degree of conservatism in the peak pressure reached during a transient .. By selecting more realistic values of the parameters, the peak pressure would be reduced. This section describes the use of five particular items, each of which resulted in a conservatively high calculated value of the peak transient pressure.
| |
| 5.1 RELIEF VALVE STROKE TIME The reference relief valve selected for use in this study was considered to have a total opening time of 3.0 seconds from the instant the signal to open is received until the valve reaches the full open position. Many of the pressurizer power operated relief valves have been found by experi-.
| |
| ence to act in less than 3 seconds.
| |
| To evaluate the effect of a decrease in the stroke time, a calculation was made for the particular case of mass input from the reference SI pump into a* small 6000 cu.ft. volume system, for two values of valve stroke time. The first time was the reference stroke time of 2.4 seconds (that is, no delay time to fill the air system) in which the overshoot above the setpoint was found to be 80 psi. When the stroke time was reduced from 2.4 to 1.5 seconds, the overshoot was reduced to about 62 psi. Ex-trapolating the data to a value of zero overshoot, corresponding to a valve that opens 1nstantane6usly, the relationship shown on Figure 5.1 i~-ob tained. This figure indicates the sensitivity of the setpoint overshoot to the time to stroke the valve and the advantage provided by the faster valves.
| |
| 5-1
| |
| | |
| The effect of the stroke time on pressure overshoot for two valves is also shown on Figure 5.1.
| |
| | |
| ._., .... .
| |
| l- ******
| |
| ...... ..... .
| |
| LINEAR RELIEF VALVE NO TIME DELAY RELIEF VALVE SETPOINT = 600 PSIG
| |
| ~ :.:.1 1:: ; INITIAL RCS PRESSURE= 50 PSIG
| |
| .ii!~ ~~-~~ ~:~ ....'..
| |
| ..____,;._...___,__,_
| |
| RCS VOLUME = 6000 CU.FT . - ........................... . ........
| |
| . .
| |
| ..:~..:... :.:.:.:c.:.: :.:::: ~ ~.:.;..:.........:..:..: *-1-----1
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| |
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| |
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| |
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| |
| ~:!.::::*:::::::
| |
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| |
| : : : : : : ~{ :.: : .
| |
| 5-3
| |
| | |
| 5.2 EFFECT OF METAL EXPANSION The coolant pressure transients for all ,cases presented in this stu;d~
| |
| * were computed assuming that the coolant,was enclosed by a rigid, nop~
| |
| yielding boundary and that the pressure change was a direct result !o.f th_e inability of the coolant to expand jnt.o a larger volurne. In re,ality, the pressure boundary is elastic, and for each increas.e i'l;
| |
| ' '
| |
| co.olant pressure, there is a finite increase in system volume which will tend*to mitigate the coolant pressure response.
| |
| To evaluate the significance of the pressure boundary elasticity effect,,
| |
| an estimate was made of the unit change in system volume for. a particu.,.
| |
| lar change in internal system pressure. Only the simple geometric shapes of cylinders 'and hemispheres were utilized in: the delt~ voJum.e calculatio*n and the other portions of the pressure boundary; reactor:;*
| |
| ves'sel upper head and nozzle course, pump casing, steam g,enerator in;let and outlet plenums and miscellaneous connecting piping were assumed to be inelastic.
| |
| Table 5.2 summarizes the results of the calculation to determ.ine the, change in volume, for a coolant pressure change of 1000 psi, of eaGh.
| |
| major portion of the reactor coolant system. The first two columns indicate the total coolant volume enclosed in the elastic section Jnder cohs i dera t ion and the second two co 1umns indicate the change in vo:l'u.me (c~.ft.) of each of the sections under a 1000 psi internal pressµre~
| |
| 1 The last two columns are listed to show' which sections contribute th,e gr'ea test percentage of the total vo.l ume; change.
| |
| 5-4
| |
| | |
| Table 5.2 indicates that for a volume typical of a 2 loop plant, the total volume will increase about 3 cu.ft. for a 1000 psi pressure change. To evaluate the effect of this increased volume, the mass in-put case with the reference SI pump was recomputed by considering that a portion of the mass input supplied by the pump is used to fill and pressurize the additional volume made available by the metal expansion.
| |
| For the particular case evaluated, i.e., the reference SI pump and 6000 cu.ft. volume plant, it was determined that only about 83% of the pump flow was effective in increasing the coolant pressure and the remaining flow would be used to fill and pressurize the expansion volume.
| |
| Figure 5.2 describes the reduction in the peak pressure reached in the cycle when the pressure boundary expansion is taken into consideration.
| |
| The figure shows the pressure overshoot above the setpoint calculated for the inelastic case is at least 35% higher than the realistic pres-sure overshoot for the actual elastic system. A similar significant degree of conservatism is inherent in all analyses presented in this study.
| |
| The pressure boundary would also change dimensions if the temperature of the metal were changed during the transients. For the mass input cases, the system was assumed to be isothermal at 100°F so for these cases there would be no dimensional change. However, in the heat input cases the reactor coolant did increase in temperature due to the heat trans-ferred from the steam generators but at such a rapid rate that the massive metal parts of the reactor coolant system could not be changed in temperature during the short term transients considered. Therefore, the temperature effect on metal expansion was not included in this study.
| |
| 5-5
| |
| | |
| TABLE 5.2 RCS VOLUME
| |
| | |
| ==SUMMARY==
| |
| | |
| Total 2 ft 3 i1V/1000 psi %
| |
| 4 Loop 2 Loop 4 Loop 2 Loop 4 Loop 2 Loop RE'.ACTOR VESSEL 3775 2089 2.37 1.32 42.0 43.9 (lower shell and head)
| |
| II
| |
| 'PRESSURIZER 1800 1000 1.34 0.73 23.8 24.2 I
| |
| U1 I
| |
| O'I STEAM GENERATOR 3065 1532 1.44 0.72 25.6 23.9 (tubes only}
| |
| PIPING 1225 '612 0.:48 0 .2'4 8.5 8.0 (equivalent 29 11 ID')
| |
| *~ 5.63 :J .'01
| |
| | |
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| |
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| |
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| |
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| |
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| |
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| |
| =:::::::: ::::::~
| |
| '"!::::: *:::: : ::: :
| |
| -.:-!...: :-::: ::*:: ;_:_.:_::_*~_;_:_;_.:_;:_~~.::_*.~*;:-:_.~-_.-._.-_~:_'~::--_:~
| |
| 1 *.. ~t~--t-S~E-T~P-O-l~N~T~:=!,.=:~~;;b;~;;~:~;;~;;F+:~::~:~=~:~~-3*~~~~~~~-~+:~:~~-~~~:~===~=-~-~=~~--~-~
| |
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| |
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| |
| ...
| |
| ~=
| |
| ,::::~
| |
| :::;:....: : **--
| |
| ::~:
| |
| ....
| |
| ... -*
| |
| ...............
| |
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| |
| ~~-.:~_-+:_:_::-+---1~~----*4*-*_*--*~------+--+-~-+--~----*~*~*-**-*1---t-~+--+~-+-*--*~-~-----*~*-**-*1---t--~+*-*-**-+---1~--+-=:~~~~:-:-:*~+:~*:-::+-:~~:~=-'---+'-'-'-l-"--'-+:..;..;:.;+'-'..:.:.i~~
| |
| ~::*: :::: ....
| |
| .... .... .. . .. *:::1:::: ...... .
| |
| t---
| |
| ~..:-;.:
| |
| ....
| |
| :::: .. :::+::
| |
| ::: ;:: : : : :: : ::
| |
| : ~ :.! ***'
| |
| *** 1
| |
| ............
| |
| ...........
| |
| :::*1 ....
| |
| :-:.: + --*.
| |
| ..1.
| |
| ... :::1 ...
| |
| ..... ,., : : : : : ; :: : ; : .. . ........... :1::
| |
| :::: :::: :::1 :1:* :::: :;:: :::: ::
| |
| 5-7
| |
| | |
| 5.3 EFFECT OF REACTOR COOLANT AND INJECTION WATER TEMPERATURES - MASS INPUT CASES All of the mass input transients evaluated considered the reactor cppl-ant to be isothermal at a temperature of 100°F (except the pressuri~er, see Section 6.1) during the period of injection. At this_ low tempera-ture, the bulk modulus of the water is at its maximum value (least compressible), which results in the greatest unit pressure change for any given unit volume change and hence the most severe transient. If the injection water temperature is equal to the coolant temperature and the uniform temperature of the coolant is about 210°F at the time of the mass injection, the bulk modulus would be about 8% lower and conse-quently the unit pressure change for a given volume addition would be 8%
| |
| less. At higher coolant temperatures the compressibility increases markedly, and, hence, the mass input transients become less severe as the temperature is increased.
| |
| A second effect of a higher initial coolant temperature which also was not included in the mass input cases is a shrinkage effect, whkh occurs when cold injection water mixes with the warmer reactor coolant. The effect of mixing a volume of cold water with a volume of hot water is a net shrinkage of the total fluid volume, and if the mixture is compressed in a fixed volume, the result will be a reduction in the compression pressure. No credit was taken in any of the mass input analyses for this shrinkage effect.
| |
| 5-8
| |
| | |
| 5.4 EFFECT OF STEAM GENERATOR MASS AND OVERALL HEAT TRANSFER COEFFICIENT -
| |
| HEAT INPUT CASES Two parameters which directly influence the transfer of heat from the hotter steam generator secondary to the colder reactor coolant are the heat source provided by the water mass contained in the steam generator secondary side, and the rate of heat transfer across the steam genera-tor tubes as determined by the overall heat transfer coefficient.
| |
| The quantity of heat available for heat transfer to the reactor coolant is dependent on the mass of water in the steam generator secondary and its temperature. In the LOFTRAN program, the entire steam generator secondary water mass is considered to be active in the heat transfer process. Since it is unlikely that free convection circulation will occur between the steam generator secondary mass in the tube bundle and the warmer mass above it or with the water in the downcomer region, the use of the steam generator secondary tube bundle mass alone would con-stitute _a reasonable representation of the heat source in LOFTRAN. In all of the heat input analyses, however, the entire steam generator secondary water mass of 215,000 lb. was input for the heat input study. _,
| |
| '"
| |
| This large mass provided a degree of conservatism in the setpoint over-shoot data obtained.
| |
| The free convective secondary side heat transfer coefficient, hsec* can be shown to control the primary to secondary heat transfer. Depending on the magnftude of the reactor coolant flow rate (which determines the primary side heat transfer coefficient, hpri) at any time following the pump startup, the heat transfer resistance due to hsec can c~nstitute u~
| |
| to 90 percent of the total -resistan!'.=e.- For-this reason, the overall heat transfer coefficient, U, used in the heat input LOFTRAN model was 5-9
| |
| | |
| assumed to be equal to hsec' This assumption also provides conservatism in the heat input analyses since it ignores the added resistance to heat transfer of the primary side film and the tube wall.
| |
| An* assessment was made of the effect of the steam generator mass and overall heat transfer coefficient conservatisms on the calculated set-point overshoot. The conservative and more realistic (less-conservative)
| |
| LOFTRAN heat input models used for the assessment utilized the following assumptions in their input development.
| |
| LOFTRAN Model Parameter Conservative Realistic Steam Generator Secondary Entire mass cor- Mass correspond-Water Mass, 1b responding to ing to tube bundle no-load steam coverage on-ly generator water level U, Overall Heat Transfer Equal to hsec Includes hpri' Coefficient, BTU/hr ft2 °F only hsec and tube wa 11 conduc-tivity Results obtained with these two models are shown in Figure 5.4 in the form of setpoint overshoot versus time after the relief valve starts to open. These results demonstrate that removal of the secondary wat~r mass and heat transfer conservatisms used in the heat input analysis co~ld result in a reduction in setpoint overshoot of as much as 48% (335 psi to 175 psi) for the particular case of a pump startup in one loop of a t~o loop, 6000 ft 3 plant with a RCS/SG temperature difference equal to 100°F and initial RCS temperature equal to 180°F.
| |
| 5-10
| |
| | |
| It should be noted that this dramatic reduction in overshoot is based partly on consideration of a heat transfer model for which only a very low flow of reactor coolant through the steam generator tubes was as-sumed, resulting in a significant hpri contribution. The magnitude of coolant flow, which will be in effect to influence hpri and heat trans-fer at any time fol1owing pump startup, is a function of the pump startup transient. If a flow startup transient 1s very slow, the as-sumption of low flow during the pressure transient would be valid and the setpoint overshoot response shown for the less conservative model in Figure 5.4 would be realistic.
| |
| 5-11
| |
| | |
| ;;:: ~:::
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| |
| 5-12
| |
| | |
| 5.5 EFFECT OF REACTOR COOLANT PUMP STARTUP TIME - HEAT INPUT CASES The rate of heat transferred from the steam generator to the reactor coolant, and consequently, the rate of coolant pressure change and set-point overshoot obtained for the heat input analyses, is dependent on the quantity of colder reactor coolant exposed to the hotter steam generator secondary heat source at any particular moment. The rate at which the colder coolant displaces the hot coolant in the steam genera-tor tubes is directly related to the rate at which the coolant flow rate increases with pump startup.
| |
| For the Westinghouse Model 93A pump startup, the LOFTRAN program cal-culates that full loop flow occurs in approximately 9 to 10 seconds, based on internal calculations performed using default homologous pump data provided in the program. This rate is faster than the startup rate normally considered as representative of the 93A pump.
| |
| All of the pressure transients* and corresponding setpoint overshoots ob-tained with the LOFTRAN program for the heat tnput studies reflect this ..
| |
| .,
| |
| flow startup conservatism.
| |
| 5-13
| |
| | |
| SECTION 6 OTHER CONSIDERATIONS 6.1 EFFECT OF PRESSURIZER WATER TEMPERATURE In a water solid reactor coolant system, the compressibility of the coolant is related to its temperature. For the mass input studies, the analyses were to be performed for an isothermal coolant temperature equal to 100°F. However, for LOFTRAN to maintain a prescribed initial coolant.pressure, P0 , the pressurizer must be maintained at the satura-tion temperature, Tsat' corresponding to P0
| |
| * In the analyses, Tsat for the range of P0 considered (50 psig to 450 psig) varies between approximately 300°F and 460°F, which is several times higher than the isothermal (100°F) temperature required. Thus, the pressurizer water volume at Tsat > 100°F introduces into the model additional compressi-bility, which would reduce the setpoint pressure overshoot for the mass input transient.
| |
| The amount of overshoot defect is dependent on the volume of the warm-er compressible mass, i.e., pressurizer water volume. Figure 6.1 illustrates this effect. From this figure, a reduction in hot (approxi-mately 300°F) pressurizer water volume from 1021 ft 3 (pressurizer volume plus surge line volume for the 6000 ft 3 volume, 2 loop LOFTRAN model) to 3
| |
| l 00 ft produces a corresponding inc.rease in setpoint overshoot of 22 psi (133 psi to 155 pJi), or about 15 percent. Further reduction in pressurizer volume from 100 ft 3 to 10 ft 3 produces an increase in over-shoot* of only 3 psi (155 psi to 158 psi), or less than 2 percent.
| |
| 6-1
| |
| | |
| To avoid problems with internal LOFTRAN computations a*ssoci*a.ted wfth 3
| |
| the use of a very sma 11 pressur1 zer, and since the lOO ft . model .pro-3 duces only a negl 1g1*ble .compres*sib111ty effect, :the JOO ft :pres*su*rlzer water volume was selected for use .throughout the mass input and heat input analyses.
| |
| 6-2
| |
| | |
| 46 1320
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| 6.2 EFFECT OF BACKPRESSURE ON RELIEF VALVE The reference relief valve was considered to discharge into the pre:s-su.rizer relief tank against a small backpressure caused by the nitro~en pressure in the tank. Normally this gas pressure will be less than 5 psig, but for this study the backpressure was considered to be 10 ps~g, which is above the typical high pressure alarm.
| |
| As the relief valve discharges into the relief tank, the nitrogen g~s and vapor enclosed in the tank wi 11 be compressed as the water 1eve'l in the tank rises. A continuous discharge into the tank will ultimate-ly increase the gas pressure to.100 psig at which time the safety head (rupture disk) will open and the gas will be released to the.contain-ment. Therefore, the maximum static backpressure on the relief valve will be 100 psig.
| |
| The expected discharge flow rate ~rom the reference relief valve is
| |
| *relatively small for the size of the discharge lines .and relief tank when compared to the design fl ow rate from the pressurizer sa*fety valves.. There-fore, the dynamic backpressure on the reference relief valve is neg~igible.
| |
| To eval ua.te the effect *of the change in static *backpressure on the *
| |
| * vai ve, a comparison was made between th'e setpoint pressure overshocftl 'for
| |
| ' i the case of an extremely high mass input into a -small system volume*
| |
| (limiting mass input case) with both a 10 psig and 100-psig backpre~s.sure.
| |
| For the first relief valve lift cycle, the peak *pressure due -to an overshoot of 154 psi above the 600 psig setpoint was found to be .z54:
| |
| psig. Then if the injection into :the reactor coolant system :conUnues, the backpressure will increase with each subsequent relief valve lift 6-4
| |
| | |
| cycle, reaching a maximum of 100 psig. With the 100 psig backpressure, the flow rate through the valve will be slightly decreased (see Figure 2.2.1) and the consequent pressure overshoot will -intrease to 159 psi above the setpoint, resulting in a peak pressure of 759 psig. Subse-quent relief valve cycles after the relief tank has vented through the rupture disk will result in lower peak pressures.
| |
| If the reference case described above is considered to be typical of a 2 loop plant with a relief tank having a nominal volume of 800 cu.ft.
| |
| and an initial gas volume of 172 cu.ft., the reference SI pump would cause the tank to fill and pressurize in about 1-1/2 minutes. Therefore, it is concluded that, for this example limiting mass input case, the relief valve first will cycle 8 to 10 times with the peak pressure for each subsequent cycle being perhaps 0.5 psi greater than for the previous cycle. Then, after the rupture disk opens, the backpressure will be removed and the subsequent pressure cycles will be similar to the first valve lift cycle.
| |
| 6-5
| |
| | |
| 6.3 CAPACITY OF MULTIPLE RELIEF VALVES The analyses presented in this study considered the use of a single 1 air-operated relief valve, i.e., the reference relief valve, to limit the pressure transients. In all cases, the single reference valve was capable of mitigating the transient, since its capacity when full open was greater than any of the mass input rates.
| |
| To evaluate the effect of a change in relief valve capacity, a few cases were studied in which the relieving capacity was doubled by considering two reference relief valves in service. The results are shown in Figure 6.3.l for two particular cases of mass input. With the*expected rates of mass input from the charging/letdown flow mis~
| |
| match case, the effect of the increased capacity on setpoint over-shoot is insign~ficant; but there is a substantial effect on the rate of pressure decrease while the valves are relieving, which is primarily due to the slow closing time used in the analysis. It can be conclµded that the capacity of two valves is much greater than required, .and, coupled with the slow closing times, could be undesirable under certain circum-stances.
| |
| For the case of a large mass input into a small reactor coolant volume, as described by the reference SI pump c~se shown in Figures 6.3.1 ana 6.'3.2, the doubled capacity provided by the second relief valve d.oes cause the pressure transient to be mitigated earlier and results in a 23% decrease in the pressure overshoot,* i.e., from about 155 to 119 psi.
| |
| However, since the pressure increase is terminated by one valve, it c~n be concluded that one reference relief 'Valve has ample capacity to miti-gate this severe transient and, hence, the additional capacity, such as provided by a second valve, is not required.
| |
| 6-6
| |
| | |
| The results of a typical study of the effects of multiple valves for a severe heat input case are shown in Figure 6.3.3. This figure also shows that, as a result of doubling the relief capacity, the pressure transient is mitigated earlier and that the pressure overshoot is re-duced, e.g., for the 600 psig setpo1nt case the overshoot is decreased 21% from 140 to 111 psi. However, as in the case of the severe mass input case, the capacity of one reference relief valve was shown to be sufficient and additional capacity is not required.
| |
| 6-7
| |
| | |
| TTT
| |
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| :RCS VOLUME = 6000 cu. ;T.
| |
| -REL I EF VALVE SET PO I NT = 600 PS I G u :~~~ j0tfrt ~~tr~~~
| |
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| 6-10
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| | |
| 6.4 RELIEF VALVE CYCLING The reference relief valve has a unique characteristic of operation in that its position is determined by an air pressure under a spring load-ed diaphragm in the operator. When air is admitted or vented, the spring will be compressed or relaxed as the diaphragm moves. Air is controlled through a small solenoid valve which is positioned by an electric signal to either admit air into the valve operator or to vent the air from the operator to the atmosphere. If the solenoid is quick-ly signalled to change position {cycled), the air may not be capable of moving the diaphragm through a full valve stroke, i.e., the valve could theoretically float on a cushion of air.
| |
| In some of the analyses of this study it was found that the relief valve had excess capacity such that the relief valve did not reach the full open position before it was si~nalled to close. For these cases, the valve actually floated on the motive air as it stroked partly open and then returned to the closed position in preparation for another stroke.
| |
| The reference relief valve was considered to have a 3 second opening time, when stroked fully openi and either a 5 or 20 second closing time when stroked from fully open position. With the use of relatively short closing times, the valve will always return to the fuJl closed position and all the air will be vented with each cycle; hence, the opening characteristic for each subsequent cycle will include the conservative time delay of 0.6 seconds before the valve starts to open again.
| |
| 6-11
| |
| | |
| For the mass input cases, the relief valve was found to cycle open and closed to intermittently discharge the excess mass injected. The greater the rate of mass input the more rapid ~he valve cycling. As 1 seen from Figure 6.4.1. for a typical case of a charging/letdown flow mismatch in the range of mass input of 40 to 120 gpm the valve will 1
| |
| cycle about every 17 seconds if the injection flow is about 120 gpm and every 42 seconds if the flow is 40 gpm. This valve cycling will continue until the operator intervenes to restate letdown or to stop the mass input. For an extreme case of a high mass input rate, as for example the reference SI pump injection at about 830 gpm the relief 1
| |
| valve would cycle open and closed every 8-1/2 se.conds until the operator terminated the input.
| |
| The cycle time for the valve can be lengthened by slowing the rates at which the valve opens and closes but this would result in a larger pressure cycle. Figure 6.4.2 shows the effect of a longer closing time on* a typical large mass input transient. For this example, the cycle time is almost doubled. However, since there is a minimum coolant ,pres-sure required to protect the reactor coolant pump seals from possible damage, it would not be acceptable to allow the pressure to decrease j below about 300 psig. This is an economic consideration which must be in~1ua~~ in the overall system design.* Some plants, however, have clos-ing ttmes equivalent to the opening times (less than 3 seconds) and 11 undershoot 11 is not a problem.
| |
| Another consideration regarding relief valve cycling is the e~fect of two valves relieving simultaneously, which is a likely event. When the two valves are signalled to open, the effective capacity is double and neither valve has to lift as far for the pressure transient to be miti-gated and the valves signalled to close. Figure 6.4.3 illustrates the 6-12
| |
| | |
| characteristics of the pressure response for both the credible charging/
| |
| letdown flow mismatch case and the extreme mass injection case represent-ed by the reference SI pump injection. As would be expected, the setpoint overshoot is reduced, but due to the high relief capacity during the valve closing period, the coolant pressure decreases markedly for the 2 valve case. For the charging flow case with these particular plant parameters, there would be a concern for the reactor coolant pump seals for relief valves with slow closure times and capacities greater than the reference valve. For those plants with valve closing times equal to opening times, the undershoot would be expected to be similar to the overshoot. Thus, the consideration of the pump seals would not be applicable.
| |
| 6-13
| |
| | |
| **-** ... ' ** ** ::z; '"' ,. - *. **1* **: t*** '. r*. '"!" *:j * *:.:J ***;I'*** 1* '* *1* .. *1* ... ,.. '*1*' .. ,.. :;j * *. :j; ;; :)* .. '.j" .**. **:1 *****-**I**** I*.'* I* ***l * * *
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| * 1-:--::~::-:::+:-f--"~4:.:.;._*:.+.:.:**.:.:.i.**~;.;..:+:.:.;:.:.:+;;=;;;~:;;:: ::::.i::::,::.:.: :.::;,;:::-1::::,:::; ::;; :::; :;;; ::;: :::: ::::.i:::.:0 :,;:::i:tf' .. FIGURE 6.4.1 ~
| |
| ~~~~~~ ~~E~G~E I ~~~~o~~E ON b:::: **- .... ~::+:: .~
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| *:-:::.:
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| *- ............ .
| |
| -INITrAL RCS PRESSURE = 50 PSIG
| |
| ~****
| |
| r-~-::. - *-.
| |
| -RCS VOLUME = 6000 CU .. FT. :J::;: :::~[:: ::::k: ::::,:
| |
| -RELIEF VALVE SETPOINT*c 600 PSIG
| |
| -::-: ~~::u: :::r::
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| ~- ---- --
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| t:=:;:-:_~ ;;y... :A
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| *::;I ;~~:~~~:~~~~ 2 SEC. LETDOWN ISOLATION WITH CHARGING . -::~*~:~~~~~~~~~
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| 6-14
| |
| | |
| 1--'fu'"'-"'"~++-i-'l__.-t_-~+---:J ~j :-rr~:':i:i i [ - ~ ~-~--;\-_:_~'_:~--+-_*_*--,--+-_:_::
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| . . . .r_,1,_r_tr-+:
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| . -~:--~-+;_::_-'.:1+--_i~_~f~-*_*_*!-t-:__;;__:t---r-*--*1 EFFECT OF RELIEF VALVE CLOSURE Tl ME 1
| |
| . . ;~.-:-:- ~-:-:-:-nrn : ; : 1- Ij d
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| +/-i{i ::;-~ - -* * :,:_, .... l ,,
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| * j r+i fr~-"l.-tf-!- iW H-h nlLlf'." ~~~-~-j:f;-ff~f<'.-~!-::-:~ :::*r INITl*AL RCS PRESSURE= 450 PSIG -~jj~1Jt"*~f+/-ll~:[Etgg
| |
| _t;_: '.~~; ~if ~?: ::::i RCS VOLUME = 6000 CU. FT. -~;~)~~-8-ifufg~~~
| |
| -:::~~::;_:_:: _L:-+/- ~ .* , :::::1* REFERENCt:: SI PUMP* STARTUP _ ~:b:::*~~g~~?S:t:
| |
| : ~:~ I REFERENCE RELi EF VALVE
| |
| ..
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| * 1- *-* .. :_:_:_:: ;:::_:;; ----- --- *- :_:-:_:_ .:::_: ~ ;-_:- - ... .::.:-:: -: .. :::: +/-!J_:-
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| -T~ ---.!...._._,_!.._:..___ ----- -- - :=--= --=:~= ---::--:::...~- r...:...-::,-== :.:::..: :.i : :::: I:-::~:::-=:::-:>-::.::: -* .... ~. --- -:-:-:-:. .::-:.:- -: ::: _:-: :.::
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| --- -*-t--- -*- --- -- -*****I
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| :-:::__:::_:_ _ I~
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| ~==-:: *:::::~..:.:::: :~: ~-=-~=-S~-:~_::_,:::-
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| l-<-----+-~~----1---- **-------:--- ---* - ----1---- ----- -*-* - - - -
| |
| ___:=~ 600 PSIG RELIEF' VALVE OPENING. SETFOINT 1 :~~
| |
| ma~J~~ *--* - * **-::F-_~:~~-~~~ ~~~~:~~~:::;_ ::,--: -~~: TIME, SEC. JT[~ :~:~~t~-E ~~l:::~ ~~~-~-~;= ~~::f:-~
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| µc~:~-~-~-=~~-:J------+------j~. -._._4*.*.--.--.-.4*.-----*4*-__-_4 __ ~:_=_--:_-4:!-::_-:_:~
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| _
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| :_,:~r- ---+*-*-_:_.~_-_~_____::_-.'.~_-~,- '-: - ~_:---~- :-~,:_+- ,
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| __-____+--:_::~+-=-_~: :----+---J_:
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| _ + -:
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| * f- **-*-- --* ---*"!""" **71*-
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| 6-15
| |
| | |
| 54 3
| |
| ~: 0t-;JG-*.:l~~*** =TI;~o~] ,t~~.tlfi* *~~~E01RE{IEF*~1xt1 m~ *.Fi!JU_R;_ .* .l
| |
| * v '.<:::::: k: <:'~::: :::t:: :::: j -INITIAL RCS PRESSURE = 50 PS I G . -:ii;~<>< <i~:~: :~:f~:
| |
| '.:;- .:.:c:
| |
| p /. . .~~!.
| |
| !
| |
| *:::!::::!:* *:~
| |
| ;;:: ~::: ........ <J~~:~ <:1:::: /!/ ::::1~:~
| |
| '
| |
| *-RCS VOLUME = 6000 CU. FT.
| |
| .. * ** **** -RELi EF VALVE SETPO I NT = 600 PS I G ... 1 ....... 1...... , ....... \.--
| |
| ::..,.;..,,:.~ :*::: : :: : : . :. :
| |
| .****:-
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| . . . :..... .........
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| |
| I ... *--~ :.-' ~:*: :::: :::: ::.:: :::: ::::; ::: ~:: 2 SEC LETDOWN I SO LAT I ON WITH CHARGING
| |
| --
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| ......
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| "'
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| . *-*
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| I 1
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| * * ** ~*- --:-\*--:- :-:- .:-: TIME
| |
| .: i SEC . : - r-,* -*--~I**--*-*----*--- *------1----***-t *--*--
| |
| ... : : . : I : : *I : " : <I : : . . .. : :*,. : . , . *. : . . i :. :.. : ' :! . : : . :
| |
| 6-16
| |
| | |
| 6.5 RELIEF VALVE CAPACITY CHANGE WITH FLASHING The reference relief valve for this study is assumed to be located on the pressurizer (i.e., the power operated relief valve) and therefore the properties of the fluid released are those associated with the pres-surizer. The analyses presented in this study are primarily based on past experience with operating PWR plants and an evaluation of the most likely conditions under which a relief valve actuation might be required.
| |
| It was concluded that the cold shutdown, solid water mode of operation was the predominate one to study. However, during plant heatup and cool-down operations when the plant is being continuously monitored and carefully controlled manually by the several trained operators, there is a short period of time when the pressurizer is filled solid and its water temperature is at or near saturation for the particular reactor coolant pressure being maintained (350 to 450 psig). If the relief valve should lift at this time, there would be flashing of the fluid as it passed through the valve, with a consequent decrease in mass relief capacity.
| |
| To evaluate the effect of the reduced mass flow on a typical pressure transient, a reference SI pump mass input case was evaluated both with a cold pressurizer and with a relatively hot pressurizer. The cold pres~
| |
| surizer case is presented in other parts of the report and involves a pressurizer with a water temperature of l00°F (equal to reactor coolant temperature). For the hot pressurizer cases, the temperature of the water is considered to be at saturation for a pressure of either 415 psia (448°F) or 615 psia (489°F).
| |
| 6-17
| |
| | |
| The mass flows of fluid through the relief valve for the saturated water flow cases Were based on homogeneous, thermal-equilibrium, isentropic, expansion flow evaluated as follows: t where h0 is the enthalpy at the G = _l \~-~~-) upstream (saturated) condition and VC v~~C v '"o C vc and he are evaluated for the
| |
| = 1b/sec - ft 2 conditions at the exit plane.
| |
| The conditions of pressure and quality at the exit plane are found im-plicitly for each particular upstream condition and Figure 6.5. 1 describes the mass flow through the valve at various upstream pressures' for both the subcooled and saturated flow modes. As can be seen from the figure, the capacity of the valve for discharge of saturated flow is reduced to about 71% of the ~ubcooled flow rate for the range of pressures
| |
| *between 350 and 450 psig.
| |
| From other parts of this study, the effect of changes in valve c~pacity can be estimated from the comparison between the transient pressure responses for a particular mass input case with either one (100% capacity) or two (200% capacity) reference relief valves. For this reference case,*
| |
| the pressure increases at about 125-135 psi/sec just prior to and for a short period after the relief valve reaches the setpoint. Therefore, there will be an overshoot of the setpoint of between 75 and 81 psi
| |
| *before the valve starts to relieve due to a 0.6 second time delay to fill the lines and valve operator with motive air.
| |
| f ANS proposed standard N-661, Evaluation *of Anticipated Transients Without Trip for Pressurized Water Reactors 6-18
| |
| | |
| From an inspection of the results of the pressure transients for the cases of one and two relief valves, it can be determined that the pres-sure overshoot during the time_ the valve(s) are relieving is 110 psi for one valve and 62 psi for two valves, both for a ~etpoint of 415 psia.
| |
| By extrapolating the capacity of the valve at 200% and 100% to a value of 71% (for saturated flow), it is found the overshoot during the stroke time is 140 psi, giving a peak pressure of 415 + 81 + 140 = 636 psia.
| |
| This peak pressure is about 30 psi higher than that pressure reached with one relief valve relieving subcooled water flow. Figure 6.5.2 shows graphically the difference in overshoot for the case of flashing flow versus subcooled flow.
| |
| A similar comparison was made considering the pressurizer water was ini-tially at a 615 psia saturated condition and again the difference between the flashing flow and the subcooled flow cases resulted in a difference in pressure overshoot of about 30 psi for the limiting mass input case and a relief valve setpoint of 615 psia (see Figure 6.5.3).
| |
| At lesser mass input rates relative to the system* volume, the difference in pressure overshoot between a subcooled and a flashing flow case would be expected to be less than calculated for the above example. This con-clusion can be reached because, at lesser*mass input rates, the rate of change* of coolant pressure is lower, and, hence, for any.given valve stroke time, the pressure change during the stroke interval will be smaller. In the extreme, a zero rate of coolant pressure increase at the setpoint or an instantaneous opening time would theoretically result in a zero over-shoot for all cases where the relief valve capacity exceeds the input flow.rate.
| |
| 6-19
| |
| | |
| The pressure transient versus time in the example case *wHh a ho't pres*;..
| |
| surizer is unrealistically conservative because it is based on the entire reactor coolant volume frtcluding the pressurizer being at a uni'f'orm cold temperature. A more realistic model would include a *substantial volume of coolant (press*urizer volume) at a high temperature *and, this *less dense fluid being more compressible, c*onSequently would be able ~to ab-sorb.some 6f the effect of the mass inpu~ similar to the action bf an accumulator in a hydraulic system. (See Sectibn 6.i fbr addftici'nal dis-cussion.) The result of the higher temperature pressu*riier .woul;d be to slow the rate of the pressure transient and hence result ii1 a Te*s*sefr* pres-sure overshoot.
| |
| 6-20
| |
| | |
| ~IU *v**~-
| |
| l~;;;E 1....- '-Ill c.1c.1" KEUFFEL & ESSER CO MADE IN U.S A. -rv J.. iJ .L V
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| ~I RATIO SATURATED/SUBCOOLED FLOW
| |
| ~~
| |
| | |
| RCS PRESSURE TRANSIENT WITH RELIEF VALVE OPENING INITIAL RCS PRESSURE = 50 PSIG
| |
| - RCS VOLUME = 6000 CU.FT.
| |
| - REFERENCE SI PUMP RELIEF VALVE SETPOINT = 400 PSIG
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| ~--~--t--~-1--~-+--/i+!:-.-+--_-_~1:-*+--~: _!-:-+---+---+-_4i-.-+--
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| |
| * i: RCS VOLUME = 6000 CU.FT.
| |
| ~---:*---*----~:----- .j ; . 'I.*.
| |
| REFERENCE SI PUMP
| |
| ! I,., ! I" RELIEF VALVE SETPOINT = 600 PSIG
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| I:
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| 1 : 1 .: 1
| |
| * 1 : .. *1: I, 6-23
| |
| | |
| APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TABLES A-1
| |
| * APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TABLE - MASS INPUT RESULTS RCS VOLUME = 6000 CU.FT.
| |
| I.,,
| |
| I RELIEF VALVE MASS INPUT MECHANISM :RESULTS
| |
| ........
| |
| fj S-0 i::....-..
| |
| : 0. *r-VI
| |
| ....... 3: .....
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| E i::
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| |
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| |
| .......
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| S- _J C> ...... -0 ........ .µ O'l I-*
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| oz -........-.. z
| |
| ........ V>.fJU' *r-Appendix B INITIAL RCS ........ O'l i:: ........ VI.._.
| |
| u .......... w-
| |
| _J C'I
| |
| *O..
| |
| cti
| |
| ..-- u VI 0.
| |
| " 0....
| |
| PRESSURE (psig) _J S- *r- u i:: ::> ....... i:: S-
| |
| .0 VI en QJ
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| ....... a.. Figure Number(s)
| |
| .µ i:: ........
| |
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| |
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| |
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| |
| (/') :E: > (/) u _J 0:: a..
| |
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| |
| *f*.
| |
| N I
| |
| 50 600 - l L 3,0 0 SI --- --- 755 155 Ml8~ M22, M26, M34, M4 5P 600 1 L 3.0 0/C S.I --- --- 755 155 M9, Ml2, M28, M30, M32 50 600. 2 L 3.0 0 SI --- --- 720 120 M26 50 600 2 L 3.0 0/C SI --- --- 720 120 M12, M28 50 600 1 NL 3.0 O/C SI --- --- 741 141 M30, M31, M32, M33 50 600 2 NL 3.0 0/C SI --- --- 720 120 M32, M33 50 600 1 L 1.5 0 SI --- --- 662 62 M26"'
| |
| 50 600 2 L 1. 5 0 SI --- --- 635 35 M26 450 600 1 L 3.0 0 SI ---
| |
| . --- 751 151 M20, M24 450 600 1 L 3.0 0/C SI --- --- 751 151 M29 450 600 2 L 3.0 0 SI --- --- 717 117 ---
| |
| 450 500 l L 3.0 0 SI --- --- 667 167 M20, M25
| |
| * I 450 500 2 L 3.0 0 S.I --- --- 626 126 ---
| |
| | |
| APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TABLE - MASS INPUT RESULTS J
| |
| '---*
| |
| RCS VOLUME= 6000:CU.FT.
| |
| (. ..
| |
| j*
| |
| ' .
| |
| RELIEF VALVE MASS INPUT MECHANISM . RESULTS I ~
| |
| !
| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
| .... u C/l ...... Appendix B
| |
| _J C>
| |
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| |
| c:
| |
| c: ::::> ........ c: s..
| |
| .0 <lJ C/l C/l 0.
| |
| ......... o... Figure Number(s)
| |
| +>
| |
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| |
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| |
| 50 . 400 l L 3.0 0 SI --- --- 592 192 Ml8, M23, M27, M4 50 400 2 L 3.0 0 SI --- --- 544 144 M27 50 400 l NL 3.0._ O/C SI --- --- 566 166 M31 50 400 2 NL 3.0 0/C SI --- --- 543 143 M33 50 400 l L 1. 5 0 SI --- 485 85 M27 50 499' 2 L 1.5 0 SI --- --- 449 49 M27 50 600 1 L 3.0 O/C C/LI CCP 2 610 10 M6, M9, MlO 50 600 2 L 3.0 0/C C/L.I CCP 2 610 10 M6, MlO
| |
| , ~
| |
| 50 690 l* L 3.0 0 C/LI CCP 10 610 10 M8
| |
| -*
| |
| 50 600. .
| |
| ~
| |
| l L 3.0 O/C C/LI PDP 2 605 5 M7 ,_ M9 450 600 1 L 3.0 0/C C/LI CCP 2 610 10 M6 50 500 l L f 3. 0 O/C C/LI PDP 2 505 5 M7
| |
| :
| |
| 50 400 1 L 3.0 0/C C/LI CCP 2 405 5 M6 i
| |
| I 50 400 1 L -3*.o 0 C/LI CCP 10 410 10 MB
| |
| | |
| APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TABLE - MASS INPUT RESULTS RCS VOLUME = 13.000 CU.FT.
| |
| r I
| |
| f l'
| |
| I RELIEF VALVE MASS INPUT MECHANISM s... 0.
| |
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| |
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| |
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| |
| .µ c: .......
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| 0 Ill Q) s.. c QJ c: (]J QJ o.-
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| 50 600 l L 3.0 0 SI --- --- 675 75 Ml9, M22, M4 50 600 2 L 3.0 0 SI --- --- 657 57 ---
| |
| 50 600 l NL 3.0 0 SI --- --- 667 67 ---
| |
| 50 600 2. NL 3.0 0 SI --- --- 658 58 ---
| |
| 50 600 1 L 1. 5 0 SI --- --- 628 28 ---
| |
| 50 600 2 L 1.5 0 SI --- --- 616 16 ---
| |
| 450 600 1 L 3.0 0 SI --- --- 673 73 M21, M24 450 600 2 L 3.0 0 SI --- --- 656 56 ---
| |
| 450 500 1 L' 3.0 0 SI ---
| |
| . --- 583 83 M21, M25 450
| |
| --
| |
| 500 2 L 3.0 0 SI --- --- 562 62 ---
| |
| 50 400 1 L . 3.0 0 SI --- --- 495 95 Ml9, M23, M4 50 400 2 L 3.0 0 SI --- --- 470 70 ---
| |
| 50 400 1 NL 3.0 0 SI --- --- 480 80 ---
| |
| | |
| APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TABLE - MASS INPUT RESULTS RCS VOLUME = 13,000.CU;Ft
| |
| -
| |
| Jt*
| |
| I RELIEF VALVE MASS INPUT MECHANISM . . RESULTS
| |
| :
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| <.Tl 50 400 2 NL 3.0 0 SI --- --- 469 69 ---
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| 50 400 l L 1.5 0 SI --- / --- \ 440 40 ---
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| 50 400 2 L 1.5 0 SI --- --- 422 22 ---
| |
| 50 600 l L 3.0 0 CL/I CCP 2 605 5 Mll 50 600 1 L 3.0 0/C CL/l CCP 2 605 5 Ml3 50 600 1 L. 3.0 o CL/I CCP 10 605 5 M12 50 400 1 L 3.0 0 CL/I CCP 10 605 5 Ml2 50 400... 1 L 3.0 o CL/I CCP 2 605 5 Mll 50 400 1 L' 3.0 0/C SI . --- --- 495 95 M36 I
| |
| '
| |
| ~~,.-
| |
| | |
| APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TAaLE - HEAT INPUT RESULTS RCS VOLUME = 6000 CU.FT.
| |
| . " ~ ~- ..
| |
| INITIAL SYSTEM REFERENCE SG MODEL TEMPERATURES (°F) RELIEF_ VALVE RESULTS
| |
| - -. ..,
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| .........
| |
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| I O"I ..20 180 200 500 1 C* 515 15 Hl9 50 ., 100 150 500 1 c 531 31 H1' H4, H6 50 140 190 500 1 c 562 62 Hl, H4, H6 50 180 230 500 1 c 598 98 Hl , H4, H6, Hl9 50 250 300 500 1 c 657 157 Hl , H6 100 100 200 600 1 c 745 145 H20, H22, H25 100 100 200 600 2 c 710 110 H~O 100 100 200 600 1 LC 650 50 H22 100 140 240 600 1 c - 845 245 H23 100 140 240 600 2* c 775 i-175 H23 100 180 280 600 1 c 935 335 H24, H25, H27, H28, H36, H37 100 180 280 600 2 c 825 225 H24 100 180 280 600 l ,
| |
| LC 775 175 H27
| |
| ..
| |
| | |
| APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TABLE - HEAT INPUT RESULTS RCS VOLUME = 6000 CU.FT.
| |
| INITIAL SYSTEM REFERENCE TEMPERATURES (°F) RELIEf. VALVE SG MODEL RESULTS
| |
| '
| |
| -*
| |
| -
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| 100 100 200 500 1 c* 640 140 H4, H20 100 100 200 500 2 c 610 110 H20 100 140 240 500 1 c 730 230 H4, H23 l 00 140 240 500 2 c 655 155 H23 100 180 280 500 1 c 780 280 H4, H24, H37 100 180 280 500 2 c 665 165 H24 100 100 200 400 1 c 540 140 H20, H21 100 100 200 400 2 c 510 110 H20 l 00 100 200 400 1 LC 460 60 H21 l 00 140 240 400 l c 545 145 H23 l 00 140 240 400 2 c 485 85 H23 100 180 280 400 l c 665 265 H24, H26, H37 100 180 280 400 2 c 515 115 H24 100 180 2.80 400 1 LC 547 147 H26
| |
| | |
| APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TABLE - HEAT INPUT RESULTS RCS VOLUME = 13,000 CU.FT.
| |
| INITIAL SYSTEM REFERENCE SG MODEL TEMPERATURES (°F) RELIEf _VALVE RESULTS
| |
| .,...
| |
| ..........
| |
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| |
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| 100 150 500 1 c- 527 27 H5 50 140 190 500 1 c 550 50 HS 50 180 230 . 500 1 c 569 69 H5
| |
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| |
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| |
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| |
| 2 c 680 80 H29 100 100 200 . . 600 1 LC 650 50 H31 100 140 240 600 1 c 775 175 H32 100 140 240 600 2 c 725 125 H32 100 180 280 600 1 c, 908 308 H33, H36, . H37 100 180 280 600 2 c 765 165 H33 100 180 280 600 1 LC 725 125 H34 100 100 200 500 1 c 608 108 HS, H29 100 100 200 500 2 c 575 75 H29
| |
| . t-' ',
| |
| | |
| APPENDIX A
| |
| | |
| ==SUMMARY==
| |
| TABLE - HEAT INPUT RESULTS RCS VOLUME = 13,000 CU.FT.
| |
| INITIAL SYSTEM REFER.ENCE ,
| |
| TEMPERATURES (°F) RELIEF .. VALVE SG MODEL RESULTS
| |
| ..-....
| |
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| |
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| |
| --
| |
| | |
| APPENDIX B FIGURES B-1
| |
| | |
| MASS INPUT B-2
| |
| | |
| f-------.f---* -~
| |
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| ,, R_CS VOLUME, cu. FT * .:....+~1--1 ....j.-1-~-.:...+-..L
| |
| = 6000 i '
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