ML18227B517
| ML18227B517 | |
| Person / Time | |
|---|---|
| Site: | Turkey Point  |
| Issue date: | 07/31/1977 |
| From: | Florida Power & Light Co, Westinghouse Electric Corp |
| To: | Office of Nuclear Reactor Regulation, Westinghouse Owners Group |
| References | |
| Download: ML18227B517 (234) | |
Text
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PRESSURE MITIGATING SYSTEMS TRANSIENT ANALYSI/S RESULTS t
Prepared by WESTINGHOUSE ELECTRIC CORPORATION for THE WESTINGHOUSE OWNERS GROUP ON REACTOR COOLANT SYSTEM OVERPRESSURIZATION JULY 1977
TABLE OF CONTENTS Section Title ~Pa e Abstract iv Introduction 1.1 Purpose of Study 1.2 Review of Past Events 1-2 1.3 Selection of Parameters for Study 1-4 1.4 Summary of Parameters 1-8 Calculation Method 2-1 2.1 LOFTRAN Program and Special Modeling 2-1 2.2 Reference Relief Valve Model 2.3 Mass Input Model 2-13 2.4 Heat Input Model 2-19 Typical Results 3-1 3.1 Mass Input Mitigated by Relief Valve 3-1 3.2 Heat Input Mitigated by Relief Valve 3-9 Instructional Guide for Setpoint/Overshoot Determination 4-1 4.1 Introduction 4-1 4.2 Algorithms Used for Setpoint/Overshoot Determination 4.2.1 Setpoint Determination for Mass Input Transient
Section Ti tl e ~Pa e 4.2.2 Setpoint Overshoot Determination for Heat 4-11 Input Transient 4.3 Development of Interpolating Aass Input Equation 4-23 4.3.1 Analytical Basis 4-24 4.3.2 Development of Application Factors 4-25 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 .Generator 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 Other Considerations 6-1 6.1 Effect of Pressurizer Water Teiopeerature 6-1 6.2 Effect of Backpressure on Relief Valve 6-4 6.3 Capacity of Multiple Relief Valves 6.4 Relief Valve Cycling 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
Section Title Pa(ac Appendix B Figures B-1 Mass Input B-2 Heat Input B-39 Appendix C Table 1 - Incidents of Pressure Transients Beyond Tech. C-1 Spec. Limits
ABSTRACT The resul ts 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.
The analyses were performed using conservative bounding input parameters plus parameter sensitivity studies to provide for results applicable to plant 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.
SECTION 1 INTRODUCTION 1.1 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.
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 W Owners Group.
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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.
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.
The other 5 events were either of unknown origin (3) or were caused by operators following inadequate procedures while controlling the reactor
, coolant pressure.
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'll but one of the events, the mismatch was caused by a loss of letdown flow while the charging system remained in operation wi'th a. relatively low rate of mass input.
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 operator and flow inadvertently entered the reactor coolant system. In the other 3 events, the accumulator isolation valves were delibera'tely opened by the operator or inadvertently opened by a spurious signa'1 from the engineered safety features actuation circuits. (Of cour se, pres-surization caused by the accumulators is self limiting due to the relatively low gas pressure maintaine'd in the accumulator.)
1-2
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 resu'lt of the speed of the operator in recognizing the situation and taking remedial action.
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
'y warmer sections of the system, particularly the steam generators.
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.
1.3 SELECTION OF PARANETERS FOR STUDY 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 pressur e 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'ssure 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.
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.
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 tions~mass input cases were started from a coolant pressure of 50 the psig to assure that the mass input mechanism was always at full performance before the mitigating relief valve came into opera-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 oper ation.
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. 1 for additional discussion).
1-5
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 expected, 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.
l 1.3.5 Nass 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.
The lowest normal flow rate occurs in those plants with small positive displacement pumps where a representative flow rate is about 40 gpm.
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.
Although there has been only one occurrence of inadver tent 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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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.
1.3.6 Heat Input t<echanisms 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, temperature differences between the steam generators and the reactor coolant system up to 100'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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1.4
SUMMARY
OF PARANETERS 1.4.1 General The plants represented by the W Owners Group comprise a group of 2, 3 and 4 loop pressurized water reactor plants, each with one s'team 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.
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:
Opening time; 3 seconds
- 2. Closing time; 5 or 20 seconds
- 3. Flow capacity; C = 50 gpm/ fps3 per valve
- 4. Set pressures, various; 400, 500 and 600 psig 1 4.3 Hass Input Cases The following two representative mass input cases as described in Section 2.3 were considered:
- l. Charging flow with letdown isolated; 40 and 120 gpm
- 2. Inadvertent operation of one safety injection pump; 870 gpm at 500 psig The following parameters were considered for the mass input cases:
1-8
- 1. Temperature of reactor coolant; 100'F
- 2. Temperature of injected water; 100'F
- 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:
~Geactor Coolant Temperature 100 140 180 250 Steam Generator Temp.
150 50 190 50 200 100 20 230 50 240 100 250 280 100 300 50 1-9
SECTION 2 CALCULATION METHOD 2.1 LOFTRAN PROGRAM AND SPECIAL MODELING The one loop version of the LOFTRAN 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.
Input Analysis
'.1.1 Mass 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.
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.
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.
To minimize 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-ft sure), the pressurizer water volume was reduced to 100 3 . The i - WCAP-7907 2-1
volume difference between a nominal pressurizer and the 100 ft3 was incorporated into the total system volume but at an initial temperature of 100'F.
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.
h 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 piping 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 cases the temperature of the reactor coolant in the tubes was at a temperature equal to the saturated condition of the secondary water mass.
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
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.
Before the heat input transient was initiated, however, it was necessary to input the required temperature profile.
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.
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.
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.
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.
2~3
As in the mass input case, the pressurizer volume was minimized (set equal to 100 ft ) and the difference in pressurizer volume (actual - 100 ft3 ) was added to the inactive volume of the reac-tor coolant.
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2.2 REFERENCE RELIEF YALVE 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 C 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.,
= Q/ ~hp)
Cv 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.
The flow capacity of the reference relief valve versus upstream pressure (reactor coolant pressure) is shown for various values of backpressure on Figure 2.2.1. 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.
(See Section 6.2 for additional discussion.)
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
plug-seat design. The opening and closing time characteristics of the non-linear valve were taken as the same as the reference linear valve.
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.
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 ll psig pressure on the diaphragm and reaches the full stroke of 3/4 inch under a pressure of 64 psig ~
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 the controlling restriction in the line, and increases the pressure until'he unit pres-sure on the diaphragm reaches ll 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 20K of the total time for the valve to act and is shown on Figure 2.2.3.
the valve starts to move, the air flow into the diaphragm chamber
'fter 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 valve 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 refer ence valve supplied from a normal 100 psig air system.
2-6
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 16K 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 reference. valve.
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 2.2.1, 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:
62.4 1107 gpm (Figure 2.2.1)
- 1 62 1
- 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 (20K 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 of the valve setpoint between 400 and 600 psig, to obtain the effect of the setpoint on peak transient pressure.
2-7
'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 pressure has decreased to 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
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'ransient 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.
II 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 the initial position used for the start of valve closure.
If other than fully open, the time delay in Figure 2.2.4, associate'd 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 rese't pressure.
2-8
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~ ' f4 f FIGURE 2.244 I' 4 Vtt I
4 REFERENCE RELIEF YALYE CLOSING CHARACTERISTIC
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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 star t 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 plant 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
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 fout 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 '.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, refer red 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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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 temper ature 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. 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 Typically there is 1 KW of pressurizer heaters for each 1 cu.ft. of pres-surizer volume. 2-19
pump inlet formed by the piping from the steam generato'r outlet and the pump inlet (see Figure 2.4.2). The volume of cold wa'ter which can be trapped in the loop seal is dete'rmined 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., n'o reactor cool-ant flow'. The coolant pressure transient is initiated u'pon star ting one reactor coolant pump. As the pump comes up to spe'ed, the coolant flow rate slowly in'creases in the active loop and the pool of cold wat'er 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. Simultan'eously 'he cold pool of water in the inactive loop(s) will flo'w backward through the steam generator(s) at a flow rate significantly less th'an in the active loop. As each of the cold pools of water flow th'rough their steam generators, th'eir temperatures will b'e increase'd by the'eat transferred from the secondary side, and since the coolant cannot expand in the isolated reactor coolant system volum'e, th'e coola'nt pressure will increase. The coolant pressure will continue to increas'e until the temperatures of the reactor coolant and steam generator wa'tei are e'qual-ized (see Figure 2.4.1) or the excess coolant'olume due to the'dd'e'd heat is relieved through a relief valve. The second type of temperature asymmetry occurs when the rea'ctor 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','he 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 correlation for turbulent boundary layers on a vertical sur-face, or: h 4
=0.13K ~8'*
2 p 1/3 1/3 2 wal 1 McAdams, W. H., "Heat Transmission", 3rd Edition, McGraw-'ill, New York, 1954 2-21
where: sec secondary film coefficient of heat transfer, BTU/hr ft 'F P density of secondary water at film temperature, ibm/ft3 viscosity of secondary water at fili temperature, ibm/ft hr wa1 1 secondary to primary temperature d'ifference, 'F 9 acceleration of gravity, ft/hr2 6 temperature coefficient of volume expansion, ('F) k conductivity of secondary water, BTU/hr ft 'F Pr Prandtl Number evaluated at secondary film temperature 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 in'spection 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, II these less significant cases w'ere 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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F IGURE 2.4. 2 LOOP SEAL VOLUME STEAM GENERA rOR RV NOZZLE PUMP CENTERLINE LETDOWN FLOW 2-24
FIGURE 2.4. 3 SG SECONDARY NO-LOAD WATER LEVEL STEAM OUTLET FEEDWATER~
~ NORMAL NO-LOAD 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 psig, the pressure response to the letdown isola-tion will be as described by Figure 3.1. 1 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 operator. However, due to the closing characteristics of the relief valve, the valve did close completely during each cycle. The reactor coolant pressure wi'Il 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-I 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 setpoinC 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 va'lve 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. Ther e 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 volume into which a given mass rate is injected. This relationship of the system volume is shown for the particular case of the refer ence SI pump mass input into two different system volumes of 6000 and 13,000 cu.ft. on Figure 3.1.4. The pressur e 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 press'ur e, the relief valve setpoint can be set at a lower value so that the valve be-gins to relieve at a lower 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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RCS PRESSURE OVERSHOOT FIGURE 3.1.5
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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 mixed with the 180'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 l transfer mechanism became predominant, the coolant pressure increased I'apidly. The reactor coolant pressure continued to increase until the pressure r eached 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 mi'tigated. Very soon afterwards, the valve had opened sufficiently to provide a capacity in excess of the expansion rate of the coolant and the coolant pressure decreased rapidly after reaching an over shoot of 100 psi above the setpoint. For comparison, a transient pressure response for the particular cape 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, versus the overshoot of 100 psi for the 50'F aT 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 temperatures; 100'F, 140'F and 180'F. For a given initial reactor coolant temperature (e.g., 180'F) the overshoot is seen to increase with increasing 4T, where the aT 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 aT, e.g., less than 10'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 severe'-"tem-perature difference of 100'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 will 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. 1 3-12
I ~ ~ ~ ~ ~
~
I ~ ~
~ ~ ~
f " 'IGURE 3.2.1
\~ ': ~ t
~
,"i I'
I ~ ~~ II
~ ~
~ ~ ~
~ ~ I t
~ ~
~ ~
~ ~ ~
i'
~ }
~ ~ ~
.RCS PRESSURE RESPONSE, TO ~ I~ ~ tt ~ I~
~ ~
,HEAT INPUT TRAIIS IENT WITH ti"' ji 'I' ~ t ~
.RE L E oI f VALVE OPEN I HG OO
~ ~
ttl ~ OO
- - RCS PUilP STAPTUP IH I. LOOP ~I t ~
t ~ t
!- RCS VOLUi'IE = 6000 CU.FT.
INITIAL PRESSURE = j00 PSIG TEHPERATURE ~ ISOOF
'CS t~ ~
- RELIEF VALVE SETPOINT ~ 500 PS IG
~
;::i t~
~ ~ ~ ~
~ '
~ ~
o ttt
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lA II ~ ~ I ~ ~ ~ O~~
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ID ~ I RCS SG AT = 50o,F ~ ~
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= ~ t'0
- = RC S/SG 2 F ..I
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3-13
t ~ ~ I ~ : ' 'I'"I FIGURE 3. 2. 2 RCS TEMPERATURE = lOOoF:J-t
~ ~
- I OOF lSO~F
~ I ~ ~ I tl
~ ~ ~ ~ ~ ~ ~
~ t
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I'tlat :.ii EFFECT OF RCS/SG TEMPERATURE ASYMMETRY"
~ ~
~ ~ '.-'. ON PRESSURE CVERSHOOT
- -'INITIAL RCS PRESSURE = 300 PSIG i'.i -RCS VOLUME = 6000 CtJ.FT.
-RCP STARTUP IN 1 LOOP
- .:I "RELIEF VALVE SETPO I NT = 500 PS IG
~ I
~ ~
~ ~
~ I
+
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-I I I
\~
, PSII
~
~ I I MAX SETPO I >IT
~ ~ 't
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I* I~ F IGURE 3. 2. 3 3 .;; .:;:3::: '.:::I
~ ~
~ ~ ~ ~ t i: l 0~ ~ I t ~ >>
~ ~
-i>>
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- t:tt t >>3-
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o ~ I>> lA ~ ~ 4
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3
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t:0 h ~ t ~ ~ ~ Lll 3 04 ~~ \~~ :.:!if~EFFECT OF RCS TEHPERATURE ON l-~ ~ ~ ~ ~ OQ ::ii,'.;tPRESSURE OVERSHOOT X~ o~ 0 ~
- ---.."-INITIAL RCS PRESSURE = 300 PSIG::=-
- ":""RCS VOLUHE = 6000 CU.FT.
- .:.'-.'.:.:.-RCP SU IN I LOOP ~
i-:i i"-,PEEL IEF VALVE SETPOINT ~ 500 PSIG '
~ ~
..., RCS/SG A - 50~F ~ 00 ~
~I
~ ~ ~ ~
>>:3 ~ I
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- .:.P - P ,PSI 1 ~
3
~g SETPOI flT
( I~ ~ I ~~ ~
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t
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3'II ~ ~
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FIGURE 3.2.4
.:,:..',....!,=::..:l::::I:.:!:::l.=
l I.,-.:.::...:..3:,:j:: .:.:;.,L I PRESSURE RESPONSE FOR 1 RELIEF VALVE CYCLE
~ ~
.I'""
t' "INITIAL RCS PRESSURE = 300 PS IG
."RCS VOLUIIE -- 6000 CU.FT.
' t "RELIEF VALVE SETPOINT = 600 PSIG 5
7 t
~
RCS/ SG AT 100 /200
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3-16
SECTION 4 INSTRUCTIONAL GUIDE FOR SETPOINT/OVERSMOOT DETERMINATION
4.1 INTRODUCTION
Determination of rel1ef valve setpoint for a specific plant requires knowledge of the expected overshoot which could occur under all possible mass input and heat input add1tions for that plant. Many mass input and heat input possibilit1es were considered 1n 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 W Owners Group on RCS, Overpressurizat1on. The bounding envelope of mass input and heat input generic results are not generally applicable to any spec1f1c plant. To determine a specific relief valve setpo1nt, a means of 1nterpolating the setpoint overshoot from the generic envelope has'een made available and algorithms have been developed to facil1tate 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 generjc setpoint overshoot envelope. This procedure is presented in Section 4.2.2, together with an example of its application for a specif1c RCS volume and steam generator design.
The mass input algorithm involves the use of a procedure for the deter-mination of a relief valve setpoint, which includes interpolation of. setpoint overshoot for plants with RCS volume, relief valve setpoint, relief valve opening time and mass input rate different from, but in-cluded within, the envelope of generic setpoint overshoot results. In-terpolation is expedited through the use of an equation, developed for this purpose. This equation is based on the adjustment of 'reference (generic envelope) setpoint overshoot results by linear application i factors, with one factor determined for each of the input parameters; RCS volume, relief valve setpoint, relief valve. opening time; and mass'nput rate for the specific plant under consideration. The equation and application factor development is presented in Section 4.2.1. 4-2
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: BP (V S~ Z x) hPREF (x)
- FV
- FS
- FZ The procedure for determining the relief valve setpoint is des-cribed below. To illustrate the application of the procedure, a set.of sample input parameters will be considered, and the results of the sequential application of each step of the procedure to these parameter s will be noted.
PARAMETERS FOR MASS INPUT EXAMPLE Relief Valve Setpoint = 500 psig Relief Valve Opening Time = 2.0 seconds Mass Input Rate = 60, lb/sec RCS Volume 10,000 cu.ft. Applying the mass input procedure: 4-3
ate Procedure Exam le 'A'icaHon Select relief valve setpoint Setpoint = 500 p'si'g operating range For limiting mass input rate, aP88F
= ~82 si for mass input obtain ~PREF from Figure rate (x) = 60 lb/sec 4.2:1 For total RCS volume, obtain F>
= 0.71 for tot~1 RCS volume F> factor from Figure 4.2.2 (V) = 10,000 cu.ft.
For the relief valve opening F2
= 0.733, for relief vaive time (total, including delay), opening time' = 2.0 seconds obtain Fz factor from Figure 4.2e3 For the relief valve setpoint FS
= 1.14 for relief valve selected, obtain FS factor setpoint = 500 psig.
from Fi gure 4.2. 4
~
6 Calculate the product of fac- AP (10,000 cu.ft., 500'si'g, tors b,PREF Fy FS and'z 2 seconds, 60 lb/sec) 49 determined in Steps 2 through psit 5 (application of Equation 1). This is the setpoint overshoot, aP. i Conservative - LOFTRAN analysis fon these conditions gives an overshoot
, equal to 25 psf.
4-4
r>> FIGURE 4.2.1 Mass In ut ~ hPREF
- Reference Overshoot '>> f
~ ~
U>>' I~X;Q Lt
~ ~ ~ ~ ~
~ $
~ ~
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>> ~'
1 ~ ~ ~ ~
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~
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o$ gO g Ãg e' tf ~
~ >> ~
t ~ I ' f ~ ~ 1 ~ f ~
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fr ~
>> $1
>>qW r~
Input Rate - lb/sec::."..
~
- . x, Mass
'>>W 1>>>>
tr ~
~ ~ $ ~
~ ~ r ~ r r f f 1' >>r>>
f >>
't ~ r'
~ f t r
I
~ ~ ~
f t
~
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M~ RCS Vol ume Factor
~ ~
FIGURE 4."2;2 Fy PM
~ ~ ~ 4
~ 4'<<l
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PM
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4~ ~ ~ ' 4 'I
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I Ml 4 ~ ~ 'Pl PM ~ fr
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t t' ~
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" V, Total RCS Volume - ft3 4 ~
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t<<4 ~~ f ~ I 7 ~ ~ ~
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P ~ I ~ ' ~4 I' ~ 44 ~ ~ ~ ~ tP ~ f ~ ~M 4-6
~ ~ ~
FIGURE 4.2.3
- Relief Valve
~ I FZ Opening Time Factor M: ~
I~
~ ~
~ 4 r ~ ~ y I 'y ~
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4 ~ ~ ~ ~ 1 ~ ~ llew
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Zi Relief Val ve Openi
~
r r
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I ng Time, seconds
~
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4-7
I ~
~ 4:2.'4
+
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I I ~ FIGURE
~ ~ I ~ ~ 4
\ ~ I ~
4
~
Mass In ut
!. N-.'
~ V ~
, .FS - Rel)ef Valve Setpofnt Factor'
~ 1<< t ~ ~ , ri *
~ ~ ~ ~ ~ ~ ~ ~ ~
~~
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N4g 4+ et I~ ~ I~ 4~ ~ ~ ~ 4 ~ I ~ ~ ~ ~
- 'z"
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~
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t Tt e i<< CA u f= 4
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h 4 4<< L,M izv . 4 4 11 I~ 1 t' vjZ 'I ~ 1 t<< ~ ~ <<4
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J ' ~ 4 ~ ~ th f
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r'tt VT ~ I ~ 144 I QI f 1le~ z.
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e
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ee
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S, Relief Valve Setpofnt - ps$ g I~
~ ~~ ~ ~ ~ ~ ~ ~ f
~ f
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~
~
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4>> ~
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'4-8
ate Procedure Exam le A lication Add a,P (Step 6) to the relief P+,X
= 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
'""" '~x " pex temperature = 100'F, Appendix G G limitation, se-
'ppendix pressure limit = 540 psig + 15, lected relief valve setpoint or 555 psia. Thus, PX >
is acceptable. If PX Appendix G limitation. Appendix G limitation, go to Step 8. If PX > Appendix G limita- Reducing setpoint by 10 psi tion, selected relief valve (564 psia - 555 psia) to 490 setpoint i~s too high. Reduce psig and repeating Steps 2 setpoint and repeat Steps 5 through 6 results in aP = 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 J -'.-- -'.-- = FIGURE 4.2 5
~ I I
~ ~ I i4 , ~
~ l-
= ~ =
I Example Plant Operation Pressure-Temperature Cur ve i, I I
'I Appendix G Limit I
~ L I Oy Vl CL
- il: 'ili 4 I4 .
~ I PLANT OPERATING RANGE I ~
I I RCP 81 Seal Limit RCP NPSH g Limit
- ~
RCS Temperature, oF I:l:::ll'lill ~ ~
~ '
4<<10
4.2.2 Setpoint Overshoot Determination for Heat Input Transient Correlations of RCS setpoint pressure overshoot variation with RCS volume, steam generator overall UA and initial RCS temperature are presented in Figures 4.2.6, 4.2.7 and 4.2.8 for the following conditions: Initial RCS Pressure = 300 psig RCS/SG aT = 50'F Relief Valve Setpoint = 500 psig SG Heat Transfer Area = 58,000 ft 6,000 ft < RCS Volume < 13,000 ft 4-11
I
- "I" - I i l~i~-.,::. FIGURE 4.2.6' EFFECT OF RCS VOLUME ~
ON PRESSURE OVERSHOOT :::.,I,, J.. -:
<< ~
~ ~
RCS PUMP STARTUP, IH, 1 LOOP
<< ~ ~
4~
~
INITIAL,PRESSURE = 300 PSIG ~ ~
<< ~
RCS/SG'T = 50'f << RELI'EF, VALVE* SETPOINT =- 500 PS'IG ~ ~
~ << << ~ ~
~ ~ ~ <<
<<" .1 <<
~ << ~ --"- l" << ~- <<
- Ii << <<
'oo
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1
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co.. !...'.::.1 : 1:I --.gua
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,~ RCS VOLUME, CU. F~T. " '<<
~ ~ <<
4'-12
FIGURE 4. 2. 7
~ I
~ ~
~ ~
*t"I ~ I I
~, I ~ " ~ ~ I I~
I
~
~
~ ~
~ I t
I ' EFFECT OF STEAM GENERATOR UA ON 4 PRESSURE ~ t
'I 4 OVERSHOOT
~ ~ ~
0, 44s 0 I ~
~ ~
~ ~ ~ ~
I ~'
~ 4 ~ ~ ~ ~ I 4
>>I I ~
~
hf rt 4 ~
~
sshl o~ I I~ I~
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t1 ~ 4
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I4 4 4 t~ ~ Wp 4 ~ I O'Ih I ~ 4~ ~ 4 O ~ ~ ~
~ s~ O.
psl ~ II Hk I *~ ~ I~ Ht ~
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1 ~
"O
LLI C);-: sshP Isr Ass ~h ~ IE4 ~ ~O V Lt 7'l ~ h ~
~4+ 4 4
- hrt ls. ~ 4~4 I t
~ rh
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~ ~ ~ ~ ~ ~ ~& ~ ~ ~ ~ ~ ~
SEg Iit, + 4 ls Csrr X 4
~ '
I ~ I
- RCS PUMP STARTUP IN 1 LOOP 44 1
4' ~
- RCS VOLUME = 6000 CU. FT.
's 4 - INITIAL PRESSURE = 300 PSI6 I
~
I~ ~' ::-: RCS/SG aT = 50't. 4 ~ ~
- RELIEF VALVE SETPOINT.= 500 PSIG 4
~ \ SG HEAT TRANSFER AREA = 58,000FT2 -.
44 T]
~
I I~ I I ~
~ ~ I ~ ~ ~ ~ 4 4 ~ I I ]
I'Zoo..- ." t" ~ ~ ~ ~
~ ~ '4 ~ I I ~
~ ~ I~ ~ 4 i
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t' t -t.s i tQX SETPOINT' ~ \
~
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'thtt
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4-13
t ~ I th ~ ~ 4 ~
.'4 3:
t ~
'f 4
"" 'FIGURE'4-;2.8
~ I~J
~ ~ ~ ~
~ II ~
~ ~
~ 0 01 C ~
~ ~
0 ~ I
'W ~
~ 00 I~ 4 ~ ~0
~ ~ ~
EFFECT OF STEAM GENERATOR UA ON I~ ~ ~
~ ~ PRESSURE OVERSHOOT >:~ ~ . ~ ~
h
~
~ '.
~ ~
4 ~ ~ ~ ~ ~ j 4 ~ I~ ~ 0
~ ff 4 I ~ I ~ ~ 0 ~ ~ ~ ~ ~
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01 4I 4 lP OI' . tT 'M
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~ ~ 4 44 ffe ffff'
<<+ r
~
- e. '0 tf
~ '
P4~ ff 0 0 ~ 00 he I ~ 0 0 ROS PUMP.'STARTUP IN 1 LOOP.'CS
~ ffh VOLUME " 13000,'CU'T'I INITIAL PRESSURE = 300 PSIG RCS/SG b,T = 50'P
~ ~
I 4, 4 4
~ 4 RELIEF VALVE SETPOINT = 500 - PS I G 0 ~
~ r r 4 ~ ~ ~
re SG HEAT TRANSFER AREA" = 58'OOOFT
~
~
~ << '
~4 ~ ~
0 ~ h
~ ~ 4 '
~h 0~ ~ ~
<< ~
~ I ~ ff ~
~ ~ lt 4
~ ~ II ~ 4 ~ ~ J
~ 4 ~ ~ 1~ ~ f I ~ ~ ~4 MrlrL I ~
M ~ 0 ~ ~ ~ 4 I~ ~ ~
\~ ~ 'I
~ ~ ~ 0
~ ~ I ~ ~
IM\ 0~ ~ ~0
~ ~
~ ~ 0 re ~ ~ ~ >>
~
~ ~ ~
'I ' 0
~ ~ ~
t
~ I
~ ~
~ ~ ~
II4
~
~
~ ~ ~
00 ~
~ ~
".j MAX'ETPOINT ~ ~~
I~
~ rl I tf
~ ~ 0 ~ ' \4 4~ t
~ 04
~ I+<<M44 f ~ ~'
~ ~
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44
~
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~ 0
~
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I t
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r
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~ 4 '.
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 linear ization factors and associated conservatisms as for the mass input case. I 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 RCS Volume 10,000 cu.ft. Initial RCS Temperature 180'F RCS/SG bT 50'F Relief Valve Setpoint 500 psig Applying the heat input procedure: 4-15
ate Procedure Exam le A 1 ication For both the 6000 ft and For T803 = 180'F, aPf6K = ~98 si 13,000 ft3 RCS volumes, obtain , and apfI13K< = ~68 si for RCS reference setpofnt overshoots .volumes .of 6K and 13K, respec-
~
6K a ~ 13K fr m Ffg tively. 4.2.9 for the initial RCS temperature, TRCS. 180'F and ~P = 98 Using both Figures 4.2.10 and TRCS 4.2.11, determine the refer- psi, UA6< = 0.115 {Figure ence normalized UA (UA6K and 4.2.10). For TA06 = 180'F and for both RCS volumes = 68 Psi, UA{3$ 0.184 UA13K) using TRCS'or DP6K and hP13K mined fn Step 1 and deter-for the aP{3< (Figure 4.2. 11). fsotherm, Determfne what fraction, f, 29,000 ft-/58,000,ft = 0.5, of 58,000 ft constitutes the actual steam generator heat transfer area. Multiply both UA and UA UA' 0. 115
- 0.5 = 0.05'75 and K 6K f
(from Step 2) by (from Step UA' 0.184
- 0.5 = 0.092
- 3) to obtain new normalized UA'6K and UA'13K values.
t Setpofnt Overshoot, aP = PMAX - PSETPOINT 4-16
i l~~~ 1
=I'Q EFFECT OF RCS VOI UNE . FIGURE 4. 2. 9 ON PRESSURE OYERSllOOT i:::::::::::::::::i::::::::::I:::::::::I::::::::- I::::I::::;.--t"::i::-:
,::::;; ';::I;.:.::::l::::::l::.:":i">>'..i:.: i"
- RCS PUMP STARTUP IN 1 LOOP :: II::::".I:..:I:;:;I".:I::.,I":;
- INITIAL PRESSURE = 300 PS
- RCS/SG AT = SO F
~
I RELIEF VALVE SETPOINT = 5 00
~ ~ I
~~
~~
t
~ ~ ~
~
- I I
~
PSIG:
- --.. .=:::
~ ~ r-.:-i
.I .:.-':::I:::.:
~
. ~: ~ ~ ~
. = ~
-.-.I'::::-:il:~:::-.::::
~ .--: ~
m MM-:--~~I~~
~
~~i:-::::.
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--:.: ~:i -::: ~:
o LA '-"-
~og LD ao~ ..I -.... ~
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~
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0 ~ ~ ~ ~ ~ t
~ t H~H)
~ ~ ~ ~ ~
LLL ~ ~ ~ ~
~ ~ ~ ~ ~
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I ' : >eoo'-, V Itl X ~ ~ ~ ~
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.LI ~
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~ ~~ ~ t ~
~ ~ 140'",
~ \~
~~ ~ ~ t t ~
t ~
"~ I~
~~ ~ ~ ~~
I:-:::" lOOoF
~ ~ ~ ~
~ ~~ ~
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~ ~
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~
aalu.4, oa l -: /gOOCF
~ ~ ~
~ 1~
RCS VOLUI'!E, CU. FT. ~ ~ ~ t
~ ~
~ ~
4-17
;! z.'I * ' I I
~
l I ~ ~
~ ~ :.::i FIGURE 4.2.10
< ~ ~ ~ ~ I~ ~ ~ ~ ~ ~ ~ . ~
I~
= t
'* t
~ ~
EFFECT OF STEAM GENERATOR UA ON -":'.;: '. PRESSURE OVERSHOOT
~
,II ~
~
33
~ ~
~ t<tj 0 ~ ~ ~ ~ I ~ ~ ~ I~ ~ ~ ~ 4 ~ ~ ~~ ~ ~ ~ ~ ~ ~
Z3:
~ ~
- I ) I
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I ~-
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- .:=- a".;:J
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ft a
~
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Q
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t 04 ~ ~
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t
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-. RCS PUMP STARTUP
~ ~4 ~ ~ lf lfl I'l i ~
1 ~
~
~
4 IN 1 LOOP. t ~ I -,. RCS VOLUME = 6000 CU. FT..
~ \
- INITIAL PRESSURE = 300. PSIG
~ ~ I t
-,'CS/SG AT = 50 f
~ 4
~
~ t ~ ~ - RELIEF VALVE SETPOINT.= 500 PSIG t~ .~ ~ I
- SG HEAT TRANSFER 'AREA = 58,000FT2
~ I~
- ."".i
- ::.:!:".::J:::-;t::::f::::.::':::!:.:a::::!::::f:::--::.
- loo l . ZOO E < ~ ~
I~ t j MAX SETPOINT' I ~ tt~
~ ~
~ ~ 4f t ~
~ ~ ~ ~ ~ ~ ~ 4 t ~ ~ ~ ~
t
~ ~ ~
4-18
~ s, ~
~ ~ /*
re 4.2.11
I'FIGURE
~ ~ ~ ~
~ I ~
~'
EFFECT OF STEAN GENERATOR UA ON
/ ~ I L~ PRESSURE OVERSHOOT -I
~ I ~
~ ~ ~
~ I ~
~ ~ ~
.C: IL 'I ~
~ ~ ~ \ ~ ~ ~
~ ~ ' '
' ~ ~ I ~
~ ~
~
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/ ~ ~ I ~ ~
l ~ ~ rrt ~
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t
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~ ~
/
l
~ ~ ~ ~ ~ ~
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' <<N
~ ~ ~ ~
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~ + :: 0E4.
- N O
LLI .0 ~ A I
~ /p
':: ~ .
1
/ ~ I
~ ~ L ~ ~ ~ ~
ON XII gd gU +1N XQ RCS PUMP STARTUP IN 1 LOOP g4
- RCS VOLUME = 13000 CU. FT.
/ ~
INITIAL PRESSURE = 300 PSIG RCS/SG 4T ='50'P RELIEF VALVE SETPOINT = 500 PSIG SG HEAT TRANSFER AREA = 58,000FT
~ I~ <<~
~ I --=t ~
~ ~
~ ~
t
\ ~
I~
~
t
' t~ ~ I ~ r ~
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~
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~ I MAX SETPOtNT'::QOO I
~'
'I I~ ~' ~ ~
~
I~~
~ ~ ~ ~
~
~ ~ ~ ~ ~ ~
4-19
ate Procedure Exam le A lication For the same 'isotherm, TRCS, From Figure 4.2.12, for'TRCS = and for UA'6K and UA'13K, 180'F and UA'6K = '0;0575, obtain new setpoint overshoots ., AP'<< = ~44 si. From Figure
~P'6K and ~P'13K for the 6000 4.2.13, for TRCS
= 180'F and ft and 13,000 ft volumes. UA'>3< = 0.092', 4P'i3K = ~35 si For the actual'olume, VRCS, For VRCS
= 10,000 cu.ft.,
linearly interpolate the set- aP'6K 44'psi and .~P 1-3K Point overshoot, hP yRCS for psi, the new steam generator UA from the relationship: P VRCS 10K RCS . 10,000 - 6000 6K 7000 6K 13K .7000
= ~39 si Thi s P yRCS i s the overshoot corresponding to the actual steam gener'a tor heat transfer area and=RCS volume.
s 4-20
~ ~
~ ~
~ ~
~ ~
~ ~
II ~ I
-.-: FIGURE 4.2.12
~ ~ ~ 1 ~
~ ~ ~ I~ ~
~ '
~ I
~ ff ~ ~ f EFFECT OF STEAM GENERATOR UA ON ". I ~ ~ ~ I PRESSUPE OVERSHOOT
~ >
I~I 4 ~ ~
~ I
. l~ I 0 ~ ~ I ~ I ~ ~
~ ~
~ ~
~ I f~
~ I
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'-J='J o.
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0
-0 ~ ~ ~ g J I
~ I
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ID 4 ~ La> ' h4 I ~ 5 4, W ~ X!t gd gC Xg f ~ g4 I+'f Ifwlr~frfrwrrl
~
f' . ' ~ ~ ~ ' t f fI I~ ~ ~ ~ xh . ~ TT T'ai ~ Ox
- RCS PUMP STARTUP IN 1 LOOP ON I ~ 1 ~
- RCS VOLUME = 6000 CU. FT.
~ I
- INITIAL PRESSURE = 300 PSIG f
~ ~
~
I f :".: RCS/SG ~T = 50't-f ~ ~ ::-' RELIEF VALVE SETPOINT.= 500 PSIG
~~
SG HEAT TRANSFER AREA = 58,000FT
~ I ~ I
~ ~ I~ ~
4-
~ ~ ~ ~ '. too Zoo
~ ~
~4
~ ~ ~
I' ~ ~ ~ ~
~ >>
TI' NX SETPOtNT' ~
<T
~ \'\ ~ ~ ~ ~ ~ ~ ~ ~ ~ I
~ ~
~
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~ ~
~ ~ ~ ~ ~ ~~~ ~ ~~ I ~ ~ r ~ I ~ ~ ~
~
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T
~
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~
+\\
~ ~ ~ r ~
4-21
gal W' '
~
~ ~
~ v
~ ~ ~ ~ ~ ~ ~ ~ I* '! ~
' ~
I~
" FIGURE'.2.13
~ ~ ~
I ~ ~ 4I i EFFECT OF STEAM GENERATOR UA ON
~ ~ ~ l ~
I~ ~ ~
-PRESSURE OVERSHOOT
~ ~ ~ ~ I ~ ~ ~
~ ~
~ l 8 ~ ~ r
~ i ~ I
~ rl. Wl ~ L\ J
~
~ 4 ~ ~
~ ~ ~ ~ II 60 Pt 3 it>} JQ=++
~
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0'.,"4. ~
~ t ~
~ y ~
l L' I
~ ~ I
~ P,, Ig
~ ~
-~.
~~A
- RCS PUMP STARTUP 'IN 1 LOOP
- RCS VOLUME = 13000 CU.'FT;
=LL - .INITIAL PRFSSURE = ~OO, PSIG
~ ~ l ~
~
I
~
- RCS/SG AT 50 P ".
= E - RELIEF VALVE SETPOINT = 500 PSIG
-'- SG HEAT TRANSFER AREA = 58,000FT
~ ~ ~ '
I ~ 1 ~ ~
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~
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tT
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PSt
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V
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MAX 'ETPO.~ NT ~ . '. I: <f
~ ~ ~ ~ ~ ~ I ~ ~ P 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 generic data. hP (V S Z x) hPREF (x)
- FV
- FS
- FZ where:
aP (V, S, Z, x) setpoint overshoot, psi V total RCS volume, cu.ft. relief valve setpoint, psig relief valve opening time, seconds x mass input rate, lb/seconds REF 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 aPREF,, and three application factors which account for variation in the aPREF 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
4.3.1 Analytical Basis Development'of Equation (1), and, more specifically, the develop-
"ment of the three application factors is based on an elementary, linear, algebraic equation involving one dependent and 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 constant .value c for a specific, reference value of x = xr, then
-f(xr) = c b=0 a =. c/x and Equation (2) becomes f(x) =( x )
x (3) Now consider two linear functions of x, f (x) and f (x), both passing through the, origin of the coordinate system, .with fl(x ) -= cl f2(x ) - c2 These functions may be written,as'-24
fl(x) cl (x ) x (6) and f2(x) ( c2
) x (7)
Both functions fl and f2 are graphical.ly 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(x ) r values for the two functions, or f,(x) = f,(x) *-c2 cl (s) 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) ft3 and relief valve setpoint = 600 psig. If this curve is linearized from the point (aP, 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 (x) described earlier, namely 4-25
~ ~4 I
~
~~
~ ~ MASS INPUT
- FIGURE 4.3;1
~ ~ ~ ~ aery Analytical Basis for ~ III Mass Input Equation >> ~
~ I ~ ~ I~
~ ~
I~ I I
~ ~ ~ 4 ~ ~
I~ I ~ 1 I
~ II
~ ~ I
~ 'I ~ ~ I ~
\~
rr ~ ~ I~ ~
~ ~ r~ ~
't
~
41 tv>> 4 4 ~ ~ ~ 4 ~
~
tI ~ ~ ~
>>~
fl(x ) cl
~ ~
I ~ 4
~ rt ~
4~
.f2(x) -c, 4 ~ ~
~.
fr2- ~
~ ~ ~
4
~
1 ~ 4
~ ~ >> ~ t >>'
I v t4>>
~
>>'~>>
t>>r ~ 4 144>> t >>t ~ + >> v ~ '\>>
~ 4
~ '1>>
~ ~
4 .~ >>>>
' t '
4
~' P t>>
>> ~ I ~.
tr 4 ~ ~ >>4 4 ~ I ~ ~ 14't ' 1'I v
~ 4 ~ ~
lt
'4>>1
~
~ ~ ~ ~ ~ ~
~ ~~ ~ ~ ~
tt 4 I' t ~ ~ ~ ~ 0
'I
>>4>>>>
i ~ ~ ~ 4
~'
~ >>> X.
4>>
>>Q ~ ~ 4 ~'
rrv
+4>>>>
~
~
~rrv ~4 g
4>> op >>
.404>>>>'I>> g I~ ~ 4 ~ 44 >>g 4 ~ ~'
1~
'\~ ~
4-,26
~ ttt << t 4.3.2 JJJ ~
tI t i
~
~ tt <<r<<4
~
I t t tte 4 FIGURE T ttJ tt' ttt t J~ it. EFFECT OF MASS INPUT RATE ON PRESSURE OVERSHOOT
~ ~.
<<'t Jr
~
t~ t ~ 4 J<<. ~ ~ I t t
~
~
tt
~ << t~ ~
~ ~
~ I t' ~
~ ~
~ ~
~ ~ ~
t
~ ~
I
~ ~ I ~
I~ I I I I
".,::RCS VOLUME ~ 6000 CU.FT.
~ ~ ~ ~ I
~ I~ "600 PSIG RELIEF VALVE OPENING SETPOINT ."
I~ I It I = ~ > ~ ~ ~ ~
~
~ ~ I I
~ ~
0 Ol CA
- .: C4 ~ ~
4
<<z -" ~ <<
No tJ ~ ~ ~ ~ Z Vg Za Og
~.
zO OO Z+ lh
~' ~ t 'Vl ~~
Itt Og
- 0tt4, Xg o~Y I~
'I
~ ~
I
~
~ 't t ~ ~ ~
~ ~ I I~ t ~ ~
~ ~
~
I I
~ I I~
~ II t~ ~
~ ~
MASS RATE, LB/SEC
~ ~
~ ~
I~ I~t
~ ~ ~ ~ ~ ~
~
~ t ~ t t t~t~ ~ t t 4-27
~ ~
~ ~ ~ ~ ~ ~ 4 ~ 1 ~ I~ ~
FIGURE 4.3 3 ~ I Mass In ut ~ I hPREF
- Reference Overshoot
~ 4 ~
4 ~ ~ r
~ I
<< ~ 4 ~ ~ ~ ~ ~ ~ ~ ~
~ ' I~
~ ~ I 4 ~ 1 I
~
~ ~ ~ ~
44 I ~ ~ 41 ~ 'I
~ t
~ ~ I ~ ~ ~ ~ ~ I ~ 4 ~ I ~
~
1 I ~ \~ I~
~ 'I
- I 4
~ ~ 1 ~ ~
- 1' I ~ I 1 ~
~ ~
~ ~ ~1 1 't
~ it ~
~ ~ ~ 4 ~
I ted
~ ~
3'" '
~ ~
~ I
~- cl ~PREF (x) 155 ps1 =":- "-::
~>> ~ 4J ~
I ~ ~ I~ I I 4 ~ ~ 4 ~ ~ ~
~ ~ ~ 4 ~
~ ~ ~ ~ I I ~
I \~ I 4 I
~
~ ~ I ~ ~ ~ I
~ ~
~ ~ ~ ~ ~
~' t. ~ ~ 44 f tf1 4 ~ ~
~ 1 ~ I 4
4
-- x'= ll3 lb/sec
~ 4 ~ ~
~ ~ 4 4 ~
~'
1
~
4 ~ ~ ~
~~
~'
I4 ~
~ ~
F 4 ' I j"
~
4t4
~ ~ ~
~ ~ ~
4 ~ 'I ~ ~
~ ~ 4 4 ~ ~
4 4 t<<t I I I ijV 'N t<<44' ~ ~ ~ ~ 'I 1 ~ I 'I ~ ~ ~ ~ ~1 ~ 44 1 ~ M I~ ~4 4 44 J.
<<f:i ~ 111
~
I 4
~ ~
~ 444
~ ~'
~ ~ '
'.+ )":!,'H ~ 4) ~ ~ ~ $ ftf ~
ffr1 4 Input Rate - lb/sec
<<g f jj >f.
x, Mass t4+ ~ M.
~
4<< ~ 1 J
~4 4 44.
A @M 4-28
fl(x) ~ aP K/600(x)
~ (
cl
) x (9) where:
6K/600 linearized reference setpoint overshoot, psi x mass input rate, lb/sec x- reference mass input rate, lb/sec cl 6K/600 r ft
'or 3
the reference conditions of 6000 RCS volume and 600 psig relief valve setpoint, Equation (9) may be written (10) Further, assume that the setpoint overshoot for the same 600 psig setpoint but for a 13,000 ft3 RCS volume, or hP13K/600 may also be represented by a second linear func-tion (Figure 4.3.4), namely, f2(x) = BP13K/600(x)
=
(
'2
) x (11) where:
hP13K/600 linearized setpoint overshoot for the second linear function, psi c2 13K/600 r ft3
'or Y = 13,000 (and S = 600 psig), Equation (11) may be written:
13K/600 113 lb/sec (>>) 4-29
~ I~
I~ ~ ~ FIGURE 4.3.4
~ I MASS INPUT t ~
~ I I Linearized Setpoint Overshoot Et I 1
~ I RCS Volume Variation It~ I ~
~ 1, I I ~ I
~ I ~ ~ ~
~ Ih ~ I
~ ~ ~
I~
~ ~ ~ t
\~
~ ~
~ I ~ I 'I I
I ~ ~ I Et I ~ I~ I~
~ 1
~ ~ ~ I I~
~ 'I I ~
~ ~
~ I
~ ~ ~
1 *
~ ~ ~ ~ ~
~ ~
1 ~ I
~ ~ ~ ~ ~
~ t I~~
.:"-'1 <<$ ~-
I
~ ~ ~
~ I ~
ttt
~
CL ~ ~ I 0 .~ ~ .
- I Vl S- -- ~ ~
~ II O "- ~ ~
- t ~
0Q. S ~ 1 Ch << t~
~ ~ ~ ~
~ CL ~ \
I t t
~
~ ~ ~
~ I I
~
~
J
~
- px> ~ ~ t ~ I I ~
1 1 ~ ~ ~ ~ I~
\~
~ I
- x ~ 1131 b/sec
'I
\
I I~ I ~ ~
~
tt
~ ~
I~ ~ I 1$ 1
~ ~ ~ ~
~ ~ I~ ~ I ~
~ I
.~
' ~ ~ ] ~ ~ I ~ ~
'lfi $$
~ ~
4::. I~ ~ ~ t 1
~ ~ If I~ ~ 1' I~ ~ I I' t I
' I
'<<f f ~
J~ ~ 't I
~ ~
~~
~ ~ ~ ~
J $$
~ J ~ ~. ~ ~ ~
~ ~
t
~ I
$ ~
t~
~ ~ ~ rft :-"
t+ Mass Input Rate - 1b/sec, ~' I ~ M t f J I I<< *~
~
~ t
~
~ 'Jt i T4>> 't
~ << ~
ff ff t ~ '
~
~
~
J II t ~ ~ t J ~J ~ 'I I' tt ~~ ~ I ~ 4<< ~
~ f I+w I' 4-3O
where: 2
~
13K/600 (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 RCS volume in terms of an overshoot determin'ed for the reference 6000 ft3 volume, and a ratio of overshoots (c2/cl) determined at the reference mass input rate, or x = 113 lb/sec. This relationship, for which setpoint remains unchanged at 600 psig, may be written
" (x
- c2 13K/600 6K/600
- 75 REF T55
= 0.484 aP (x) (13)
E For RCS volumes intermediate to 6000 ft3 and 13,000 ft, values of c2 will vary between 75 psi < c2 < 155 psi and the c2/cl ratio will vary between 0.484 < c2/cl < 1.00 If the c2/cl 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 relief valve setpoint for any 6000 ft3 < V < 13,000 ft would be obtained from the relationship 4-31
rl ~ ~ FIGURE 4.3.5 wtv I ~ll J 1+
~ JJ ~ 4
~ I FV
- RCS Volume Factor
~ jt ~
I
~ ~
h
~ r>>t vr 4 ' lw
~ ~ ~ I 4 4 ~ ~
- t. I 4 f~ ~
~
~ I ~ ~
w ~ \
~ ~ r I 1:
4 ~ m ~ 4
~ ~ 4 ~ I ~
~ ~ ~ ~
~ ~
II 4 f ~ ~ ~
~ ~
33/ f.~. t~ t
~
~ ~ ~ ~
~ I I
~
I ~ 4 I I I I 4~
~ ~
~
~ I ~ )44 ~ << ~
\
~
~ -~ 4 ~ ~ 4 ~ I~ ~
't f I' I Jr v
I ' 4~
~ 4
~
t ~'
* ~
4
~ ~
~ ~ ~
fl ~
~
11 I Iw
~
4 ~ f ~ ~ ~ ~ 4 ~ I ~ 1' ~ I 11 ~ w ~ ~' ~ I ~ 4 ~ ~ ~ 1 ~ ~
~ rf ~ r Jwr ~ itI ~
~
~
1
'I 4
~ ~ ~
\~
~ ~ 1 '
t
~ ~ ~ ~
~ <> 4
~ 4
~ '4
~ ~ ~ ~ lh 44 I ~ 4 4
~ ~ 4 I ~
~
'tW ~ If ~ ~
~ ~ 4
+
I
>>I<<
~ I~
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~
1'w ~ WI
~ I ~ ~
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~
~
i' wr ~ 4 ~
~ I~ 4 ~
I Tw w' tw t
~
'tr 'I
~ ~ ~ ~ ~ 4' 1+k ~
"T ~ ~'
gW + 4 ~ fw ~1 tr ~ 4 ~ 1 fw
<<IwJJ~
$ 444 rf r ~
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1 ~ ~ ~ f 4 Jw t ~ w>>t' 4 I ~ V, Total RCS Volume - ft 4-32
* (14)
V/600 REF .V wher e: A V/600 (x) setpoint overshoot at mass input rate' for RCS volume V and S = 600 psig, psi REF ) reference setpoint overshoot at x (GK/600) FV RCS volume factor
- 2. FS
- Relief Valve Setpoint Factor Just as the AP6K/600 (x) and AP13K/600 (x) functions were linearized in Figure 4.3.4 for a change in RCS volume from 6K ft3 ft to 13K 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 ft variation from 6K 3 to 13K 3 , ft it may also be applied to the situation where setpoint is varied. In this case, to obtain the setpoint overshoot AP at 400 psig for a 6000 ft 3 plant knowing AP at 600 psig, Equation (8) is utilized to obtain AP6K/400 (x) =
APREF (x) *- 2S
- 192 6K/600 ~55 6K/600 ( ) (15) 4-33
I~
~ I~ FIGURE 4.346
~ ~ ~ ~ ~
MASS INPUT I ~ ~ 3
~ ~ I Linearized Setpoint Overshoot
~ ~ ~ ~
Volume and Setpoint Variations
~ ~ ~ I
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t4 t't 4 ft 4 M x, Mass Input Rate lb/sec,,,'~f
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~ 4 4 4 i4 4-34
For a RCS volume of 13K ft, this relationship 3 (for a set-point change from 600 psig to 400 psig) would be
* (W)
AP]3K/400 (x) ~P13K/600 (x)
= 1.27 hP13K/600 (x) (16)
To ensure a conservative determination of setpoint overshoot for a setpoint variation at any RCS volume, the maximum co-efficient (1.27) 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'quation (15) is given by (x) ~ aPV/S aPV/600 (x) FS (17) where: FS
= relief valve setpoint factor as defined in Figure 4.3.7 S relief valve setpoint 400 psig < S < 600 psig Incorporating the volume variation effect from Equation (14),
(17) becomes 'quation PV/S (x) = aPV/600 (x)
- FS
* (18)
REF V S 4-35
~ J II ~ ~
.>>41 44<< 'I ~~
4 I I~ ~ ~ ~ ~ ==- FIGURE 4'.347
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J ~ r ~ O 4 t OJ. S, Rel)ef Valve Setpoknt - ps1g
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<<O J 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 Rel ief Yal ve Opening Time Factor Figure 4.3.8 describes the variation in setpoint overshoot AP with 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 equal to 6000 ft and 13,000 ft . To facilitate the determination of setpoint overshoot with var iation 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 bZ', then the co-ordinate system for the linear functions will have a new abscissa, Z, defined in terms of the original abscissa hZ'19) 0 seconds < Z' 3 seconds) and the displacement Z'where: hZ'g or Z = Z' 4-37
':I 4.3.8 FIGURE C R ~ MASS INPUT
~ I ~
I Reference Relief Valve Stroke Time R R Rj
',I ", 'i"i:: ::'!'=; 3: :! :
~ ~
R ,
".'I R
R 6000 cu.ft.
.': I.,: I R R
R I I R ~ R ~ R I
! R R
[ R
- l. 400 psig I R
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=
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CL 13000 cu.ft.
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.".:: Valve Opening Time, Seconds '..
~ ~
~ I RE ~ ~ R R ~ R ~ ~ 4-38 R
FIGURE 4.3.9 MASS INPUT Reference Relief Valve 1 Stroke T1me 200
~ ~
I
....I
*I 6000 cu.ft.
j I I
~
400 pslg ;
~
I I '., I 150 600 ps$ g ' I
" *'i
'-100 i.,: 13000 cu.ft. Ii C/l ~ ~
Q CL,
. ~
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~ ~ 600 ps1g
~ ~ -~
a,ZI,: I~ ~ 0
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- 0I- Z 3. 75 ii., i
~
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I~
\
- - -,'alve Open)ng T)me, Seconds",,
~~ ~ '1 4-39
For any relief valve, opening time, Z', ther'efore, 'th' setpoint overshoot i P may be ob'ta'ined from the linear 'relq-tionship Z' lZ'
- V/S ' + a,Z' V/S
(.20) FZ
* 'PV/S (x) (21)
The FZ factor was optimized 'from a 'linearization of a'll the correla'tions in Figure 4.'3.9. It'was determined 'that, both ft setpoint parametrics for'6000 3. RCS'volume produced th' largest abscissa displacement (aZ' 0.'75:s'econds). 'This displacement maximizes the FZ factor to ensure a conservative setpoint overshoot. 'A,plot of 'the'FZ factor with'valve opening time, Z', is -shown in Figure 4.3. 10. It should be " noted that conservatism 'in 'overshoot determination'"increases as the 'relief valve opening time is're'duced 'from 'the:3:secon'd reference value. By way of illustration'of the use of the FZ 'factor, c'onsider a relief valve opening 'time'of 2;0 'seconds. The referenc'e setpoint overshoot aPREF ( 'hP6</600) wo'uld 'be determined 'as follows. From Figure 4.3. 10, P'or -Z'= 2.'0 ':seconds, FZ 0'73 'from Equation (21), 4-40
Li M~I :: FIGURE 4.3.10 44+ X ~ ~
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4
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- Relief Valve 'f ~ ~
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'I Opening Time Factor 441 4
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Zj Rel ref Va lve Opening T)m e, sec ond 4-41
Z-' 2.0) = 0.73 * (x) (22)' gP6K/600'(x; aPREF
='-
0;73'~'.155 psi
. ="113 psi' This corn'pa're's almos't'xactly w'i'th'he s'etpoi'nt oVershoot given in Figur'e 4.3.8; For smaller" v'alve op'eiii'ng'im'es',
us'e of Equatio'n'('21)'ill giv'e'r'og'ressiv'ely'orons/rva-'iv'e values of o'v'e'r'shoot'. Incorporating'he- effe'ct'f r'elie'f v'a'lve" openiiig'= time as given by Equation (21) in'to th'" expr'ession (Equation'8) Which refle'c'ts th'e effect of r'elie'f ValV'e" setpoint" and':RCS" volume i'nterpola'tion; the followii'ig'x'pr'es'sib'n'is dei ived:
~PV(S (x 'Z ) = ~PV'j S,'(x')
'".Z'r REF ( ) V FS Z hP (V' Z') 'PREF" (x) 'V
- FS,* 'FZ which is the simplified iiiterp'olating equation (E'quati'on')
used in the algorithm for setpoi'nt dete'rmination for the ma'ss'nput transien't; 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'mall 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 over shoot, corresponding to a valve that opens instantaneously, the relationship shown on Figure 5.1 is 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 oversho'ot for two valves 3's al'so shown on Figure 5.1. 5-2
FIGURE 5.1 EFFECT OF RELIEF VALVE OPENING TIME ON RC S PRESSURE OVERSHOOT LINEAR REL IEF VALVE
~ ~ ~ ~
" NO TIME DELAY
~ ~
- RELIEF VALVE SETPOINT ~ 600 PSIG N ~
. INITIAL RCS PRESSURE ~ 50 PSIG
" RCS VOLUME ~ 6000 CU.FT.
~-
~ ~
1 ~ ~
~ ~~ ~ ~ ~
RELIE F VALVE
-.~ ~
' ~ I~ ~ ~
2 RELIEF VALVES
~ ~ ~
~ ~
- .: SI PUMP STAR
~~ ~
~ ~
I.. LINEAR VALVE OPENING TIME, SECONDS 5-3
5.2 EFFECT OF METAL EXPANSION The coolant pressure transients for all,cases presented 1n this study were computed assuming that the coolant,was enclosed by a rig1d, noj-yi,elding boundary and that the pressure, change was a direct result ~of the inability of the coolant to expand into a larger volume. In reality, the pressure boundary 1s elastic, and for each increase in coolant pressure, there is a fin1.te increase 1n system volume which w111 tend 'to m1tigate the coolant pressure response. To evaluate the significance of the pressure boundary elasticity effect, an estimate was made of the un1t change 1n system volume for a,particu-lar change in internal system pressure. Only the simple geometric shapes of cylinders 'and hemispheres were utilized in the delta volume calculation and the other portions of the pressure boundary; reactor,'" vessel upp'er head and nozzle course, pump casing, steam generator inlet and outlet,'lenums and miscellaneous connecting piping were assumed to be inelastic. Table 5.2 'summarizes the results of the calculation to determine the change 1n Volume, for a coolant pr essur e change of 1000 ps1, of each major port'1on of the reactor coolant system. The f1rst two columns in'dicate the total coolant volume enclosed in the elastic section under co'nsideration and the second two columns indicate the change in,volume (c'u.ft.) of each of the sections under a 1000 psi internal pressure; Th'e last two columns are.listed to showi which sections contr1bute the gr'eatest percentage of the total volume'hange. 5-4 f
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 1nput supplied by the pump 1s used to fill and pressurize the additional volume made available by the metal expans1on. For the particular case evaluated, i.e., the reference SI pump and 6000 cu.ft. volume plant, it was determ1ned that only about 83K of the pump flow was effect1ve 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 35K higher than the realistic pres-sure overshoot for the actual elasti'c system. A similar sign1ficant degree of conservatism is 1nherent in all analyses presented in this study. The pressure boundary would also change dimensions if the temperature of ferredd the metal were changed during the transients. For the mass input cases, the system was assumed to be 1sothermal 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-from the steam generators but at such a rapid rate that the massive metal parts of the reactor coolant system could not be changed 1n temperature dur1ng the shor t term transients cons1dered. Therefore, the temperature effect on metal expansion was not included in this study. 5-5
TABLE 5.2 RCS VOLUME
SUMMARY
Total ft hV 1000
~4Loo ~2Loo ~4Loo '2Loo s$
~4Loo ~2Loo REACTOR VESSEL 3775 2089 2.37 1.32 42.0 43.9 (lower shell and head)
PRESSURIZER 1800 1000 1.34 0.73 23.8 24.2 STEAM GENERATOR ~-- 4065 -1 532 1.44 0.72 25.6. 23.9 (tubes only) PIPING 1225 612 0.48 0.24 8.5 8.0 (equivalent 29" ID) 5.63 3.01
~
5.2
~ ~ ~ ~ 4 ~
's::ij ii ."I FIGURE i y ~
~ I
~ >
~ ~ e
~ ~ ~ ~ ~ ~
- .::I:.:.
~ ~ ~
I' EFFECT OF MATERIAL EXPANSION ON :I
.:.:i PRESSURE OVERSHOOT
'i:: -REFERENCE Sl PUMP STARTUP "RCS VOLUME ~ 6000 CU.FT.
~ '.I -INITIAL RCS PRESSURE ~ 50 PSIG
- .:,. -RELIEF VALVE SETPOINT ~ 60 0 PSIG ";...-
~ ~
~ t
'I A
Qe
..L ~ ~ ~
~~
1 ~ ~ i I
~ ~ + ~
~
.i. RE FEREN CE S I PUM
~ ~
~ ~ I' $
I
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" SI I~
PUM P WITH MTL EXPANSIO t~ ~ A ~ ~ I ~
~~ I-
~ ~
~ 0
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~ - ~
SETPOINT ~ ~
~ ~
~ ~ ~ ~ ~
~ ~
5-7
II 5.3 EFFECT OF REACTOR COOLANT AND INJECTION WATER TEMPERATURES - MASS INPUT CASES All of the mass input transients evaluated considered the reactor cool-ant to be isothermal at a temperature of> 100'F (except the pressurizer, 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> injection, the bulk modulus
'he mass would be about 8X lower and conse-quently the unit pressure change for a given volume addition would be 85 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, which 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 f~s a net shrinkage of the total fluid volume, and if the mixture is compressed inl a fixed volume, the result will be a'eduction in the compression pressure. No credit was taken in any of the mass input analyses fo', this shrinkage effect. Cg 5-8
5.4 .EFFECT OF STEAN GENERATOR NSS AND OVERALL HEAT TRANSFER COEFFICIENT-HEAT INPUT CASES Two parameters which directly influence the tr ansfer 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 depen'dent 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 consider ed 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, h , can sec'e shown to control the primary to secondary heat transfer. Depending on the magnitude of the reactor coolant flow rate (which determines the primary side heat transfer coefficient, h ) at any time following the pump startup, the heat transfer resistance due to h can constitute up to 90 percent of the total resistance. For this reason, the overall heat transfer coefficient, U, used in the heat input LOFTRAN model was 5-9
assumed to be equal to h . 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. I An assessment was made of the effect of'he steam generator mass and overall heat transfer coefficient conservatisms on the calculated set-po'int overshoot. The conservative and more realistic (less-conservative) LOFTRAN heat input models used for the assessment utilized the following assumptions in their input development.'OFTRAN Model Parameter Conservat ve Rea st c Steam Generator Secondary Entire mass cor- Mass correspond-Water Mass, lb responding to ing to tube bundle no-load steam coverage only generator water level U, Overall Heat Transfer Equal to h Includes h ri, Coefficient, BTU/hr 'F only fthm hsec .and tube wall, 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 water mass j and heat transfer conservatisms used in the heat input analysis could result in a reduction in setpoint overshoot of as much as 48K (335 psi to 175 psi) for the particular case of a pump startup in one loop of a two 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 h ri contribution. The magnitude of pri coolant flow, which will be in effect to influence h prii and heat trans-fer at any time following pump startup, is a function of the pump startup transient. If a flow startup transient is 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
- FIGURE 5t4
~ '. '. ~
I (
~
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t~ t~t I
~ t ~ ~
I
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"'.EFFECT OF HEAT INPUT LOFTRAN MODEL ON PRESSURE ,'!.CONSERVATISMS OVERSHOOT'NITIAL PRESSURE ~ 300 PSIG RCS'VOLUME ~ 6000 CU.FT.
~ RELIEF VALVE SETPOINT ~ 600 PSIG
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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'nd corresponding setpoint overshoots ob-with the LOFTRAN program for the heat input studies reflect this 'ained flow startup conservatism.'-13
2 I I I
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, P , the pressurizer must be maintained at the satura-tion temperature, T , corresponding to P 0 . In the analyses, T sat for the range of P 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 T t > 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 ft3,'(pressurizer volume plus surge line volume for the 6000 ft3 volume, 2 loop LOFTRAN model) to 100 ft3 produces a corresponding increase in setpoint overshoot of 22 psi (133 psi to 155 psi), or about 15 percent. Further reduction in ft ft pressurizer volume from 100 3 to 10 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 computa'tions associated, with the use of a very small. pressurizer, and since 'the l00 ft3, model:.pro-3 duces only a.negligible coppressibil1ty effect,;the I100'ft pressurizer water volume was selected for use throughout;the mass ~input and;heat input analyses. 6-2
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6.2 EFFECT OF BACKPRESSURE ON RELIEF VALVE The reference relief: valve'as considered to discharge into the tank against a small backpressure caused by the nitrogen pres-'urizer,relief 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 psig, which is above the typical high pressure alarm. As the relief valve discharges into the, relief tank, the nitrogen gas and vapor enclosed in the tank will be compressed as the water level 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 from the reference relief valve is relatively small for the size of the discharge lines and relief tank when compared to the design flow rate from the pressurizer safety valves. The} e-fore, the dynamic backpressure on the reference relief valve is negligible. N To evaluate the effect of the change in static backpressure on the valve, a .comparison was made between th'e setpoint pressure overshoot> for the case of an extremely high mass inpu't into a small system volume " (limiting mass input case) with both a 10 psig and 100 psig backpres'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 Then if the injection into the r'eactor coolant system continues, 754'sig. the backpressure will increase with each subsequent relief valve lift
'-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 increase 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 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 fullj, 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 refer ence relief valves in service. The results are. shown'n Figure 6.3.1 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 insignificant; but there is a substantial effect on the rate'f pressure decrease while the valves are relieving, which is primarily due to the slow closing time used in the analysis. It can be concluded 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. I For the case of a large mass input into' small reactor coolant volume, as described by the reference SI pump case shown in Figures 6.3.1 and 6.3.2, the doubled capacity provided by the second reliefvalve does, cause the pressure transient to be mitigated earlier and results in a 23% decrease in the pressure overshoot,'.e., from about 155 to ll9 psi. However, since the pressur e increase is terminated by one valve, it can be concluded that one reference relief 'valve has ample capacity to miti-H 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 setpoint case the overshoot is decreased 215 from 140 to ill 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
R, FIGURF 6.3.1,
~ . ". CONPARISON OF I VERSUS 2 RELIEF VALVES INITIAL RCS PRESSURE = 50 PS I G
-RCS VOLUHE = 6000 CU.FT.
-REI.IEF VALVE SETPOINT = 600 PSIG
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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 signalled to 'close. For these cases, the valve actually floated on the motive air as it stroked partly open h 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 open, 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 full 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 the valve cycling. As 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 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 wilIl continue until the operator intervenes to restore 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'alve would cycle open and closed every 8-1/2 seconds 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 pr es-sure required to protect the reactor coolant pump seals from possible damage, it would not be acceptable to allow the pressure to decrease'elow about 300 psig. This is an economic consideration which must b' included in the overall system design. Some plants, however, have clos-ing times equivalent to the opening times (less than 3 seconds) and "undershoot" is not a problem. Another consideration regarding relief valve cycling is the effect 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 over shoot 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 gr eater 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
FIGURE 6 4 1
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CYCLIC PRESSURE RESPONSE "INIT/AL RCS PRESSURE' 50 PSIG "RCS VOLUME = 6000 CU.FT.
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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 pressur e 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 100'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 flow's of fluid through the relief valve for the s'atu'rated water flow cases Here based on homogeneous, th'ermal-equilibrium, isentropic, expansion flow evaluated as follows: where h is the enthalpy at the G= 1 v 2g c J(h 0 -h)c .. upstream (saturated) condition and v and h are evaluated for the
= lb/sec - ft2 conditions 'at the exit plan'e.
The conditions of pressure and quality at the exit plane are fouhd im-plicitly for each particul'ar upstream condition and Figure 6.5.1 describes the mass flow thr'ough the valve at various upstream pr'essui es for both th'e subcooled and satur'ated flow modes. As can be seen from the figure, the capacity of the valve for discharge of saturated flow is reduced to about 715 of the subcooled flow rate 'for the 'rahge of 'pressu'res between 350 and 450 psig. From other parts of this study, the effect of changes in val've capacity can be estimated from the comparison between the transient pressure responses for a particular mass inpUt case with either one (100K capacity) or two (200K capacity) reference reli'ef valves. For this reference case, the pressure increases at about 125-135 psi/sec just prioi 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 tim'e delay to fill the lines and valve operator with motive air. i'NS 1 proposed standard N-661, Evaluation of Anticipated Transients With'out 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 setpoint of 415 psia. By extrapolating the capacity of the valve at 200K and 100K to a value of 715 (for saturated flow), it is found the overshoot during the stroke is 140 psi, giving a peak pressure of 415 + 81 + 140 = 636 psia. 'ime 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 with a hot pres-surizer is unrealistically conservative because it is based on tPe entire reactor coolant volume including the pressurizer being at a uniform cold temperature. A more realistic model would include a substantial volume sorbb of coolant (pressurizer volume) at a high temperature an), this less dense fluid being more compressible, consequently would be able to ab-some of the effect of the mass input similar to the action of an accumulator in a hydraulic system. (See Section 6.1 for additional dis-cussion.) The result of the higher temperature pressurizer would be to slow the rate of the pressure transient and hence result in a lesser pres-sure overshoot. 6-20
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~ ~ ~ er t4f '
1 RELIEF VALVE ~" Tt-
~
- SUBCOOLED ff t t t e
FLOW 2 RELIEF VALVES et e ffe ~ t
'PoiNTf e e I Ch ~ A ~ e CJ te CL
\~
I ~ " ta . ~ ' a
= ~
~ I e
RCS PRESSURE TRANSIENT
--t ~
I = w ~ WITH RELIEF VALVE OPENING
- INITIAL RCS PRESSURE = 50 PSIG
- RCS VOLUME = 6000 CU.FT.
~=
-i ~ - REFERENCE SI PUMP
'- RELIEF VALVE SETPOINT = 400 PSIG
- ~
~- +
~ ~
f ~ k
~ ~ t .)
f
~ >>
4 e ,f ~ a TIME, SEC.
~ ' I
~ ~
lett ~
~ ~
ea te
"~ ~
~ t \ et M - +I ~
j 6-22 l
FIGURE 6.5.3
"~ 'I
~ %-
~ '
~ ~
1 RELIEF VALVE I
+ ~ '.: ESTIMATED SATURATED MATER IA FW EO CAPACITY AT 615 PSIA
% ~
S ETPO I NT -.:+~
~ ~
. 1 RELIEF VALVE
"~
-~
SUBCOOLED FLOW
~ ~
- 2 RELIEF VALVES x'
C/l CZ'. 4l ~ I
~ I << ~ I z
~O 'U ~C Z Vl ~ I/I Og RCS PRESSURE TRANSIENT O4I I I j
- "-' " '- '""a
~
WITH RELIEF VALVE OPENING Xg o~
- INITIAL RCS PRESSURE = 50 PSIG I ~ e
- RCS VOLUME = 6000 CU.FT.
=~ I '. - REFERENCE SI PUMP
~ '
- RELIEF VALVE SETPOINT = 600 PSIG I
I e I~ ~ '...I I i 1 ME, SEC. I I
'.i
'= ~
6-23
I APPENDIX A
SUMMARY
TABLES
APPENDIX A
SUMMARY
TABLE - MASS INPUT RESULTS RCS VOLUME = 6000 CU.FT. RELIEF VALVE MASS INPUT MECHANISM : RESULTS S-0 0. E S
~0 A 0 Ol I OZ P~ tg
,INITIAL RCS Cb
~ DN CD C/l CP CD tO
.0 c5 C/l Appendix B
~a s- C)
C/l O. PRESSURE (psig) ~ r 0 C S-Cll Figure Number(s) Ch g5 Cll QJ CJ C/l Cll C/l Cl. CJ C/l 0l 0 0
~g A C O.~ M
~0 ~rOl S-Ol
> S-a$ ~r M C)
Cll r Ch 0 Ol CC$ 0 Ch CJ I o CU F > CD W S e O 0
'0
~
rial ~ Q 0 CO r X 'I Ql C/l
~ C=
0 ns I- O cj w CD m C/l CD Cll C/l CD OC CL 50 600 1 L 3.0 0 SI 755 155 M18, M22, M26, M34, M4 50 600 1 L 3.0 0/C S.I 755 155 M9, M12, 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 0/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 450 450 450 600 600 600 1 1 2 L L L 3.0 3.0 3.0 0 0/C 0
'ISI SI 751 751 151 151 M20, M24 M29 717 117
. 450 500 1 L 3.0 0 SI 667 167 M20, M25 450 500 2 L 3.0 0 SI 626 126
APPENDIX A
SUMMARY
TABLE - MASS INPUT RESULTS RCS VOLUME = 6000 CU.FT. RELIEF VALVE MASS INPUT MECHANISM .RESULTS S-Vl
~M 0 I
a S- M U I OK MO ~ W'l INITIAL RCS Zh Vl ~ Ql c
.O cd O c I Appendix B PRESSURE (psig) 0
~
M S cd
~c O QJ Ql Vl a
DW Cil Ol 0 C S-0 Vl Ql Vl G I
. Figure Number{s) r0 'rUl Vl QJ S-QJ a~
Ql Vl O Ql VI 0 acthcdr S A LLl
~ S-a vla E) cd Ql
~l Al Ql Ql
>O ~
Q S- rO a0 Cc I CA Ql ~ ep U0 C X ~r cd I- cd CL cd lA Vl O
~ M QJ Cl
~ g~ I 50 400 1 L 3.0 0 SI 592 192 M18, M23, M27, M4 50 400 2 L 3.0 0 SI 544 144 M27 50 400 1 NL 3.0 0/C SI 566 166 M31 50 400 2 NL 3.0 0/C SI 543 143 M33 50 400 1 L 1.5 0 SI 485 85 M27 50 400 2 L 1.5 0 SI 449 49 M27 50 600 1 L 3.0 0/C C/LI CCP 2 610 10 M6, M9, M10 50 600 2 L 3.0 0/C C/Li CCP 2 610 10 M6, M10 50 600 1 L 3.0 0 C/LI CCP -10 610 10 M8 50 600 1 L 3.0 0/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 1 L 3.0 0/C C/LI PDP 2 505 5 M7 50 400 1 L 3.0 0/C C/LI CCP 2 405 5 M6 50 400 1 L -8;0 0 C/LI CCP 10 410 10 M8
APPENDIX A
SUMMARY
TABLE - MASS INPUT RESULTS RCS VOLUME = 13,000 CU.FT. RELIEF VALYE MASS INPUT MECHANISM, RESULTS S-g s-s 0 S 02 0 C/l M 0 N ~ f I-Cl INITIAL RCS PRESSURE (psig) ~ S- ~ Ch r 0 Vl ~ CD S-
.O s
sCS O Ql CD Appendix B Figure Number(s) Vl sCS QJ S QJ CD Vl Ql Vl CL Ql C/l Ul 0 0 M I j r LU
~ r- Ol 00 r S-r Ql S rCS 'rM C
C) Vl 0 0. r Ul rCS S-s-rs 0-C/l
'a0 Ql Ql Vl CD Cl r0 S- I ~
QJ p >V s W I C/l Ql ~ CL, EO ~ S X 's sCS Sl C/l sCS O Vl ~ M Ql OC 50 600 1 L 3.0 0 SI 675 75 M19, M22, M4 50 600 2 L 3.0 0 SI 657 57 50 600 1. 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 28 628'16 50 600 2 L 1.5 0 SI 16 450 600 1 L 3.0 0 SI 673 73 M21, M24 450 600 2 L 3.0'.0 0 SI- 656 56 450 500 1 L' 0 SI 583 83 M21, M25 450 500 2 3.0 0 SI 562 62 50 400 1 L '.0 0 SI 495 95 M19, 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-. RELIEF VALVE MASS INPUT MECHANISM RESULTS S 0 M Ch 0 O. OK S HM UN". I-INITIAL RCS ~I/l QI~ CD rCI
.0Vl OVI a
Cl Appendix B PRESSURE {psig) VI
~
M S-CCS
~ r 0Ql Ql Vl Ql VI 0
DW C/l Ol 0 C S-0 Ql O I M Figure Number(s) il Ol QJ S Ql C
'I O~ O Ql VI 0
S O. r eg
'LI/I 00 ~rVl S- rcS C) 0I E S-M
)O CCI Ql r Ql Ql QI r r 0 I I
X~~ E O 0
~ EM I: CL CCS CCI OC O.
Ql C/l
~ r 0 nS l- CCS Vl ~ M Ql CL C/I 50 400 NL 3.0 0 SI 469 69 50 400 L 1.5 0 SI 440 40 50 400 L 1.5 0 SI 422 22 50 600 L 3.0 0 CL/I CCP 605 5 M11 50 600 L 3.0 0/C CL/I CCP 605 5 M13 50 600 L 3.0 0 CL/I CCP 10 605 5 M12 50 400 L 3.0 0 CL/I CCP 10 605 5 M12 50 400 L 3.0 0 CL/I CCP 605 5 M11 50 400 L 3.0 0/C SI 495 95 M36
APPENDIX'
SUMMARY
TABLE - HEAT INPUT RESULTS RCS VOLUME = 6000 CU.FT. INITIAL SYSTEM REFERENCE TEMPERATURES ('F) RELIEF, VALVE SG MODEL RESULTS
~g
~ Ol Vl CL Conservative,(C) or" C) Appendix B Less Conservative (LC) I Figure Number(s)
Lal
~ f Cl) 0CL Q I
0C CO. 20 180, 200 500 1 C. 515 15 H19 50 100 150 500 1 C 531 31 Hl, H4, H6 50 140 190 500 1 C 562 62 Hl, H4, HG 50 -1 80 230 500 1 C 598 98 Hl, H4, H6, H19 50 250 300 500 1 C 657 157 Hl, H6 100 100 200. 600 1 C 745 145 H20, H22, K25 100 100 200 600 2 C 710 110 H20 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 l75 H23 100 180 280 600 C 335 H24, H25, H27, H28, H36, H37 935'25 100 180 280 600 2 C 225 H24 100 180 280 600 1 LC ~ 775 175 H27
APPENDIX A
SUMMARY
TABLE - HEAT INPUT RESULTS RCS VOLUME = 6000 CU.FT. INITIAL SYSTEM REFERENCE SG MODEL TEMPERATURES ('F) RELIEF VALVE RESULTS VI CL
- <<h
~g I
Ul CL Conservative (C) or CD Cl B Less Conservative (LC) I Figure Number(s) LrJ C/1
~g CL CI I CL QJ I/I.
100 100 200 500 C. 640 140 H4, H20 100 100 200 500 C 610 110 H20 100 140 240 500 C 730 147'ppendix 230 H4, H23 100 140 240 500 C '655 155 H23 100 180 280 500 C 780 280 H4, H24, H37 100 180 280 500 C 665 165 H24 100 100 200 400 C 540 140 H20, H21 100 100 200 400 C 510 110 H20 100 100 200 400 LC 460 60 H21 100 140 240 400 C 545 145 H23 100 140 240 400 C 485 85 H23 100 180 280 400 C 665 265 H24, H26, H37 100 180 280 400 C 515 115 H24 100 180 280 '00 LC 547 H26
APPENDIX A SUNMARY TABLE .- HEAT 'INPUT RESULTS = RCS VOLUME = 13,,000 CU.FT. INITIAL SYSTEM REFERENCE TEMPERATURES ('F) 'RELIEF VALVE SG MODEL RESULTS Ol CA
, rg Ul
~ p CL Conservative (C) or- Eh CL Appendix B I
Less Conservative (LC): Figure Number(s) S-O CL C Cl I 00 50 100 150 500 C. 527 27 H5 50 140 190 500 C 550 50 H5 50 180 230 500 C 569 69 H5 100 100 200 600 C 710 110 H29, H31 100 .1 00 200 -600 2 C .680 80 H29 100 100 200 600 1 LC 650 50 H31 100 140 240 600 C 775 175 H32 100 140 240 600 C 725 125 H32 100 180 280 600 C 908 308 H33, H36, H37 100 180 280 600 2 C 765 165 H33 100 180 280 600 '1 725. LC 125 H34 100 100 200 500 C 608 108 H5, H29 100 100 200 500 2 C 575 75 H29
APPENDIX A
SUMMARY
TABLE - HEAT INPUT RESULTS RCS VOLUME = 13,000 CU.FT. INITIAL SYSTEM REFERENCE SG MODEL TEMPERATURES ('F) RELIEF VALVE RESULTS Vl CL
! cn
~g P Ol ' I g
Vl Conservative (C) or" Eh CL CL C) Q Appendix B. Less Conservative (LC). I Figure Number(s) M tA eg O S-Ql ~ 5 CL I D E QJ CD CA. 4X 100 140 240 500 1 C. 667 167 H5, H32 100 '40 240 500 2 C- '15 == 115 H32 100 180 280 500 1 C 855 355 H5, H33, H37 100 180 280 500 2 C 650 150 H33 100 100 200 400 1 C 495 95 H29, H30
'00 100 200 400 2 C 465 65 H29 100 100 200 400 1 LC 435 35 H30 100 140 240 400 l. C 577 177 H32 100 140 240 400 2 C 490 90 H32 100 180 280 400 1' C 793 393 H33, H37 100 180 280 400 C 500 100 H33 100 180 280 400 1 LC 505 105 H35
I C <l APPENDIX B FIGURES
MASS INPUT B-2
Il t
<< ~ tt
~
~="'IGURE Ml
~
~ ~
='t ~
~
- EFFECT OF HASS INPUT RATE ~
ON PRESSURE OVERSHOOT-I
-~
+
=-=-" 600 PSIG RELIEF VALVE OPENING SETPOINT
~ ~
~ <<
rl<<+ RCS VOLUHE, CU. FT.
~
6OOO gl ~CL 3OOO =
+
t t 1'rl 1
+
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'IGURE'3 Reference Relief Y lve j
Stroke Time
" ..Ch
~ ':,"..'I .:.'I"..:I".:::: .:I:.;;"..:
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cu.ft.
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- Y alve Opening Time, Seconds
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4 I 4
+
\ ~
4 I ~ ~ *. ~ B-5
I ~ .t
~ ~
~ ~ ~ ~ :.", FIGURE M4
~
*~ EFFECT OF RELIEF VALVE SETPOINT:t:.- '
t, .t.". ON PRESSURE OVERSHOOT
-INITIAL RCS PRESSURE = 50 PSIG 4.
~ ~
~ ~ ~
1 REFERENCE RELIEF VALVE
~ *
~ '
~
~
t~~
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- .13 RCS VOLUME, CU. FT.
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te w W 4 WI4 4 W I 4 4 Q e I
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- R EFERE NCE SI PU ST ARTUP
~ t 4
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~ t tet 'IW.:9t tt .'ETPOINT, PSIG
<<44 H 4 4~ t -~ 4 - ~ I ~
FIGURE M5
~ I I I' I" I HASS INPUT TRANS IENTS
~ - ~ I~
- I
-'ll INITIAL RCS PRESSURE = 450 PSIG
--,I
'r-'j
- RCS,VOLUME = 6000 CU. FT.
i
- ~ ~ ~
i*=
, ~ ~ =I ~
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LET00W I S OLAT I ON.
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TIHE; SEC. H" >> Ht - 4 4te 4 Jg ~ >> -~
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~ t 48 )
B-7
TRANSIENTS ,; FIGURE M6 RCS PRESSURE FOR ONE CYCLE OF RELIEF
'H VALVE OPENING AND CLOSING ~ ~
FOR R, SEC. LETDOWN iSOLATION
- ~-
- RCS VOLUME ~ '6000 CU . FT.
I
~ ~
4
~
"600 PSIG RELIEF VALVE OPENING SETPOINT .
~ ~
t ~ IL 4 ' tt PH ~ 4 Wt ttt 4 ~ 4
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4 WH 00 PS IG RELIEF VALVE OPEN ING SETPOINT PH ~ ~ ~- 4 P t H I
~ 14 Ht " ~ 4
~ 50 PSIG 4 * .: INITIAL RCS
- ', '.,-t~~1-.-'..t.
PRESSURE 4'
-- INITIAL RCS PRESSURE ~ 450 PSIG I. ~ I N ~ W 4
4 ' ~
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I 4 H
-4 TIME e SEC ~
'"', .. '=: ~
i 4
~ '
4
- 4 4 tt - ~ ~ .
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FIGURE M7 IRCS PRESSURE TRANSIENT FOR ONE CYCLE OF RELIEF VALVE OPENING AND CLOSING
~ ~
~ ~
". . I'0 CONSTANT MASS INPUT RATE OF 40 GPM
~ ~ ~ - 2 SEC. LETDOWN ISOLATION 0
~ . I'.
t INITIAL RCS PRESSURE ~ 50 PSIG 4 4
" RCS VOLUME = 6000 CU. FT.
Io
~-
~ ~ I "I
~-
4 o 4 ~ ~ I I I' ='I ~I IA .-: 600 P SIG R EL IEF VALVE OPENING SETPOINT ":.. 44 44 ~ I~ ~ ~ cl' -"te:I
~ IW !
w'I 0 W I ~0 t40 I I ~ ~
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to ~ W ~
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~ - t FIGURE M8
~ ' ~ ~ J ~ ~ e e 'I e RCS P RESS URE TRANS I ENT ~ et WITH RELIEF VALVE OPENING e INITIAL RCS PRESSURE ~ 50 PS IG
- RCS VOLUNE = 6000 CU. FT.
'e e
- LETDOWN ISOLATION (/o SE'cP ~
~ y . t - ~ ~ J...=t e ~ e..
e
~ ~ t - e " ~ ~ ~ ~ e e" ~ t 600 PSIG RELIEF VALVE OPENING SETPOINT
~ -e t "400 PSI G RELI EF VAI VE OPE NING S ETP OINT"-
~ e Je J ~
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= = TIHEt
~ .. SEC
~
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i
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'et J e e
B-10
4 \ I
~
( I I I 4 P
.'IGURE M9 EFFECT OF NASS INPUT RATE ON
~ ~
- t CYCLIC PRESSURE RESPONSE Cae I;' I
- INITIAL RCS PRESSURE = 50 PS IG ~
I =
-RCS VOLUi'IE = 6000 CU.FT.
~
P I "RELIEF VALVE SETPOINT = 600 PSIG t
'I
~ '
=
I -.: ~ - I';
~
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li I LL S I PUNP STARTUP 4
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tte I ~ 1 ~ Pt I~ ~ Ht
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4
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It I
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*~ I~
FIGURE I ' N10::
': I"* ' '
I
~"
COMPARISON OF I VERSUS 2 RELIEF VALVES
-~ I
-INITIAI RCS PRESSURE = 50 PSIG
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FIGURE Nl 1 RCS PRESSURE TRANSIENT
~ ~
WITH REL I EF VALVE OPENING INITIAL RCS PRESSURE ~ 50 PSIG
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~ ~ I
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'-.-: RCS PRESSURE TRANSIENT ~ ~
MITH RELIEF VALVE OPENING >>\
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INITIAL RCS PRESSURE = 50 PSIG ~ ~
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RCS P RESS URE TRAN S I ENT '-.: FIGURE M13:: FOR ONE CYCLE OF RELIEF VALVE OPENING AND CLOSING INITIAL RCS PRESSURE = 50 PSIG: ~ I ~ RCS VOLUHE ~ I3,000 CU. FT.
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FIGURE M14:.
~
".t RCS PRESSURE RESPONSE INITIAL RCS PRESSURE ~ 450 PSIG
" RCS VOLUME 6000 CU ~ FT.
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- ~
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FIGURE M19:; RCS PRESSURE TRANSIENT WITH RELIEF VALVE OPENING INITIAL RCS PRESSURE = 50 PSIG ' - ~
-4 I= RCS VOLUNE = 13>000 CU. FT. '
I
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RCS PRESSURE TRANS I ENT ~ << WITH RELIEF VALVE OPENING tW:I ++ I=I
' INITIAL RCS PRESSURE = 450 PSIG
- RCS VOLUNE = 6>000 CU. FT. = ~
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=-, FIGURE M21 *,:
RCS PRESSURE TRANSIENT WITH RELIEF VALVE OPENING INITIAL RCS PRESSURE = 450 PSIG
- RCS VOLUME = 13,000 CU. FT.
I~
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I EFFECT OF RCS VOLUHE ENVELOPE ON ... FIGURE M22 PRESSURE OVERSHOOT
\ ~
~* + "INITIAL RCS
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-RELIEF VALVE SETPOINT ~ 600 PSIG
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; :,.:. FIGURE M23
-~ RCS PRESSURE TRANSIENT ~
WITH RELIEF VALVE
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- =' ~
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f INITIAL RCS PRESSURE = 50 PSIG
- REFERENCE SI PUMP STARTUP
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RCS PRESSURE TRANSIENT
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REFERENCE SI PUMP STARTUP f':::"frr.:: RCS VOLUME, CU. FT. -~ I~ - ~
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EFFECT OF RELIEF VALVE, PARAMETERS FIGURE M26 -. ON RCS PRESSURE TRANSIENT f ..!l: INITIAL RCS PRESSURE = 50 PSIG ~ ~ & I
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1 FIGURE M27
~ I EFFECT OF RELIEF VALVE PARAMETERS ON RCS PRESSURE TRANSIENT INITIAL RCS PRESSURE = 50 PSI'G RCS VOLUME = 6,000 CU. FT..
- REFERENCE S I PUMP STARTUP
'I I'
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- ~ *e 4 I~
8-29
'I 'I
.I:"
, .I i FIGURE M28 RCS PRESSURE TRANSIENT FOR ONE CYCLE OF RELIEF
, VALVE OPENING AND CLOSING RCS PRESSURE = 50 l'SIG
.'NITIAL RCS VOLUNE M 6000 CU. FT.
-~ ~ * ~ ~ - REFERENCE SI PUHP
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RELIEF VALVE SETPOINT = 600 psIg -, i: It:). I,
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1 RELIEF VALVE I
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~ =
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" RCS VOLUME ~ 6000 CU. FT.
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REI'ERENCE Sl I'VMP STARTUP
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--; FIGURE" M31 RCS PRESSURE TRANSIENT FOR ONE CYCLE OF RELIEF -.'"
VALVE OPENING AND CLOSING INITIAL RCS PRESSURE ~ 50 PS I G
" RCS VOLUME 6000 CU. FT.
- REFERENCE Sl PUMP STARTUP
- NON-LINEAR (OUICK OPENING) RELIEF VALVE
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8-35
FULGUR,F. N34:
<< Wl EFFECT OF MATERIAL EXPANSION ON PRESSURE OVERSHOOT -'
- REFERENCE S I PUHP STARTU P l- >>
~
-RCS VO LUHE = 6000 CU . FT .
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tV
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V~ RCS PRESSURE TRANSIENT FOR ONE CYCLE OF RELIEF VALVE OPENING AND CLOSING ' INITIAL RCS PRESSURE = 50 PSIG
" RCS VOLUME = 131000 CU. FT,
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I B-38 I
HEAT INPUT B-39
EFFECT OF RCS VOLUME :.-.-'ÃURE H1 ON PRESSURE OVERSHOOT
~-
L ~ RCS PUMP STARTUP IN l LOOP 4
-'INITIAL PRESSURE = 300 PSIG 4
RCS/SG AT =" 50'I
- RELIEF VAI VE SETPOINT = 500 PSIG
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~ 1
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= 50'f 4
- RELIEF VALVE SETPOINT.= 500 PSIG
~ I-SG HEAT TRANSFER AREA = 58,000FT2
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<<Je
'I f'~ INT'e>>>>l t y>> WJ>>
8-41
1~ ~ Jr ~ I 4
't ~ '
- I
"-,;=:;=-" F IGURE H3
~ '=EP EFFECT OF STEAM GENERATOR UA ON PRESSURE
+-'
OVERSHOOT e t.'. ~ *
~
e
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4
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>>e +\ RCS PUMP STARTUP IN 1 LOOP I RCS VOLUME = 13000 CU. FT. I>> INITIAL PRESSURE = 300 PSIG RCS/SG hT " 50'P re RELIEF VALVE SETPOINT = 500 PSIG
~= SG HEAT TRANSFER AREA = 58,000FT 4
e t e
- e e ~
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e MAX SETPOINT' I 'I 1 'I f
~ I FIGURE H4
~ ~
~ ~ I 5 RCS TEMPERATURE = )OOOF .- 1 ODF 180oF =-,:-.
I
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4 ~ ~ XO ~ tt ~' O~ EFFECT OF RCS/SG TEMPERATURE ASYHMETRY-'N
~ <<I ~
~
~ HI PRESSURE OVERSHOOT
~ ~
W
- INITIAL RCS PRESSURE = 300 PSIG
~~ ~ ~ "RCS VOLUME' 6000 CU.FT.
w "RCP STARTUP IN 1 LOOP
~ ~~
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~ I ~ ~
=~
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S TENPE RATURE = 100 oF 140oF ~ I gO ~ <<
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I IIt W Vl I ~ I~ If 4 4 ~ EFFECT OF RCS/SG TEHPERATURE ASYHMETRY Y ON PRESSURE OVERSHOOT I 04 ~ I t ~ \<<
~ ---f "INITIAL RCS PRESSURE ~ 300 PSIG
-RCS VOLUNE ~ 13000 CU. FT.
"RCP STARTUP IN 1 LOOP "RELIEF VALVE SETPOINT = 500 PSIG
-*-I ~ .
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-"!:"PRESSURE OVERSHOOT
~~
X~ -=-"":-lNlTlAL RCS PRESSURE = 300 PSlG
~~
o~Y H ~"
- .::-:.::-RCS, VOLUIlE = 6000 CU.FT.
~ ~
I-;:! -.-'"RCP SU IN 1 LOOP
;.=:j-'-:PELIEF VALVE SETPOINT ~ 500 PSIG
~ ~ . RCS/SG AT 50 0 F
= ~
W
~ . .StÃ
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4
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HI
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I I<< I~ OF SYSTEM 4
<<2
'FFECT VOLUME ON PRESSURE RESPONSE 2"<<I 2 I
r ~ I
~
42!
~
<<l
.; '-INITIAL".RCS PRESSURE = 300 PSIG
'-".i-RCS SU IN 1 LOOP WITH RCS/SG hT - 180'/280'-: -.':-'-
~ ~ ~ ~4
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- I,.-;,-.,'
~
EQUI VALENT,MASS INPUT RATE FOR HEAT INPUT TRANS.IENT. :,. FIGURE H8
-INITIAL RCS PRESSURE ~ 300 PSIG
-RCS SU IN I LOOP WITH RCS/SG 6T ~ I80 /280 '
~ ~
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2 t *
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!i
- FIGURE H9
~ ~
~ I
*t EFFECT OF HEAT INPUT RATE
.;-. -INITIAL RCS PRESSURE ~ 300 PSIG
.; "RCS VOLUHE 6000 CU.FT.
t
~ ~ -"'-RCP SU IN 1 LOOP
~
-'-':-'NO RELIEF VALVE ACTUATION'"l ~4 4' 4 ~ 14 ~ 14 0 4 ~ ~ - ~ ~ ~ l
~ ~
\ H
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't '<< 4>>
t frf' i~t Wti ~ ~ W
~~
0 050 4 4 I'H
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~
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XKK 44' ~ 01 RC S/SG 18 000 300!: g.
/2 rstf '.:
W tg f <<
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1 5& t'ft g ~ 4 ~ 5'i CC ~=" ~ wt 4>>0 tWtt <<0 4 tt tt W 40 0>> 0 Wt 4W H 0 Wt 0@@ 04 ~ t 4t ~ W ~1 04<< W 00 41 I ~ 0 5 5 r..t wt-
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~ I~
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CORE DECAY HEAT DD I
~ ~
4 RESSURIZER HEATER ACTUAT 10 ~ 4
~ ~
IHE, SEC. 4 ~ ~
~ ~
- Wwf
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<<5 I ~ 40 0 ~~
WW tw
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HI
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f ~0
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41 ~ ~ I~ k.f
.-: FIGURE H10 H
HI
- ~
EFFECT OF HEAT INPUT RATE
~ <<i " INITIAL RCS PRESSURE = 450 PSIG
)
"~ -RCS VOLUME = 6000 CU.FT. ~
~-
~ =
I~ ~ *" ~ ~
.~
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4 1
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t tt
--'. .A " RCP SU WITH RCS'/SG bT ~ 180 /280
-- B -
RCP SU WITH RCS/SG 6T = 100 /200
- .DC'-"
~
+I
~ I CORE DECAY HEAT ADDITION PRESSURIZER HEATER ACTUATION
+~
I I
~ ~ ~
<<tl ~
~
I~
~ 4 H ff ~ 4 ~ ~
4
~ ~
H ~ ~ ii<< TINE, SEC.; 4
+II 4
- ~ .f 4 :
~
't 4 t ~ ~ ~ f 4~
~ tt0 t"<< t<<' IWt ~ <<0 ~ : FIGURE H11
~ I
~ 4
':-'A:-
RCS/SG T = I80 /280 ~*" ! ':.:-:.-'t='ll!
=~
I :.::;-.:: -:I ~
~ ~ 4 I 4 ~ ~
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+
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~
CS/SG
~ - l Wl 4444
~ ~
T ~ 200 40>>/2 5014ll ~ ~ 4
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4
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g 4 0 ~ 1 I Pf 0 IJT4
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~ ~
im deaf 0+40 W COMPARISON OF LOOP SEAL/RCS VERSUS RCS/SG
~ >> TEMPERATURE ASYMMETRIES
~ ' I 440>> t I 4>>0 >>1 "INITIAL RCS PRESSURE = 300 PSIG 0<<0 ~ tt 0 4 00 ~ 4 ~
~
~ << ~ 1 'I 0 "RCS VOLUME 6000 CU.FT.
+1!!
"RCP SU IN 1 LOOP
~ \
~ ~ ~ I 4 + "~
tt tt 4 4 4
~~
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t I 01>> ~ 4 I~ ~ ~ I ~
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i
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-~
I ~ t ~ >> t
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00
"" "" iil ilt>> i" ii; ~ ii+ 1>> ~
TIMEB SEC ~
~ ~
~ \
i-4 It ~
i FIGURE H12
~
I ~ iT 'CS/SG
~ 180o/280o
~ ~
S/SG ij ~ 140o/2 40o *I 4 I
~~
I " '
~~
I~
~
iT
~
~
=. -!RCS SG
~~ ~
100o/200o WW JL 4>> 41
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JJtJ Wt JW 0 0 tt \ ~ ~~ te ~4 ~ = W tt- W ~ W
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