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CALCULATION TABLE OF CONTENTS CALCULATION NO. L-003445 Revision 001 PAGE NO. 2 SECTION: PAGE NO. SUB-PAGE NO. DESIGN ANALYSIS COVER SHEET 1 OWNERS ACCEPTANCE REVIEW CHECKLIST 1a TABLE OF CONTENTS 1 PURPOSE 4 2 INPUTS 4 3 ASSUMCPTIONS AND LIMITATIONS 6 4 REFERENCES 7 5 METHOD OF ANALYSIS 9 6 NUMERIC ANALYSIS 15 7 CONCLUSIONS 19 8 APPENDICES 19 Appendix A -RWCU Flow Loop Error Calculation 1-8 Appendix B - RWCU Temperature Loop Error Calculation 1-6 Appendix C - CRD Flow Loop Error Calculation 1-16 Appendix D - RR Pump Motor Power Loop Error Calculation 1-9
CALCULATION TABLE OF CONTENTS (CONT.) CALCULATION NO. L-003445 Revision 001 PAGE NO. 3 ATTACHMENTS A1-A4 ATTACHIVIENT A, RTP Corp . Card, Vendor Data ATTACHMENT B, Rosemount Transmitters (Selected Pages) B1-1310 ATTACHMENT C, Rosemount Nuclear Instruments Letter C1-C2 ATTACHMENT D, GE Control Rod Drive Spec . (Selected Pages) D1-D2 ATTACHMENT E, Weed Instrument Thermocouple Vendor Data E1-E2 ATTACHMENT F, Signal Resistor Unit Purchase Part F1 +2 ATTACHMENT G, Component(s) List G1-G1 ATTACHMENT H, Calibration Data Sheet for Loop 2C11-N004 H1-H1 ATTACHMENT I, Thermodynamic Properties of Fluid Systems 11-113 ATTACHMENT J, Calibration Data Sheet for 2B33-R653A J1-J1
CALCULATION PAGE F77 LATION NO. L-003445 Revision 001 PAGE NO. 4 of 20 1 PURPOSE 1 .1 The purpose of this calculation is to determine the uncertainty in the reactor core thermal power (heat balance) calculation performed by the POWERPLEX-III core monitoring software . This calculation will evaluate the contribution of the uncertainties of the different instrument channel loops, which provide signals used by the POWERPLEX-III software to calculate core thermal power (CTP), to the uncertainty of the CTP value at rated power as documented in Figure 1 .2-1 of the UFSAR. This calculation is being performed in support of the licensing amendment for Measurement Uncertainty Recovery (MUR) power uprate . 2 INPUT 2.1 The equation that the POWERPLEX-III core monitoring software uses to calculate core thermal power is (Reference 4.1 .2): CTP = QYw 'f' Qcr + Qcu + Qrad - Qp 2.2 The design basis numbers for operation of LaSalle Unit 2 at 100% rated power, 3489 MWth, are listed in Figure 1 .2-1, "Reactor System -- Rated Power Heat Balance", of the UFSAR (Reference 4.6.1). 2.3 The conversion factor for converting million BTUs/hr to MWt is (Reference 4.1 .2):
= C1 3.413 MBTU/MWh 2.4 The table below lists the parameters which provide input to the core thermal power calculation, their uncertainty values and the source of these values :
CALCULATION PAGE Description Units Nominal Value Uncertainty Uncertainty Basis 26 1020.0 Reactor Dome Pressure PSIA (Ref. 4 .6 .1) +/-19 .067 L-002513 W FW Feedwater Flow Rate 15.113 Mlbm/hr t 0 .0484 L-003444 (0 .32°/°*nom) Ref. 4.6.1) WCR CRD Flow Rate 0.0320 t 0.001602 Appendix C Mlbmlhr Ref. 4.6.1 WCU RWCU Flow Rate (352 0.1330 Appendix A MIbmlhr +/- 0 .005341
~ $ m @ 532.6 F (Ref. 4.6.1 426.5 Feedwater Temperature o F (Ref. 4.6.1) +/- 0.57 L-003444 Control Rod Drive 80 Temperature F (Ref. 4.6.1) t 10 Section 3 .3 RWCU Suction of 532.6 Temperature +/- 3.138 Appendix B (Ref. 4.6.1)
RWCU Discharge °F 436 .0 +/- 3 .138 Appendix B Temperature (Ref. 4.6 .1) RAD Radiated and Misc MBTU/hr 13.99 +/-10% Section 3.4 Thermal Losses Ref. 4.2 .3 Recirc Pump Motor MW 12.4 +/- 0.709 Appendix D Energy Input Ref . 4 .6.1 Recirc Pump Motor ETA
°l° 94.0 t 1 °l° Section 3.5 efficiency Ref . 4.2.3 HG Saturated Steam gTU/fbm 1191 .6 t 0.05 Ref . 4.6 .6 Enthalpy (~ 1020 psia}
(Ref. 4.6.1 ) Feedwater Enthalpy HFW BTU/Ibm 404 .7 +/- 0.005 Ref . 4.6 .6 (subcooled %1020 psia) Ref . 4.6.1 CRD Enthalpy HCR (subcooled @ 1020 psia) BTUllbm 48 .0 +/- 0.005 Ref . 4.6 .6 80 °F Ref . 4 .6.1 HCU1 RWCU Suction Enthalpy BTUllbm 527.3 +/- 0.005 Ref . 4.6.6 (subcooled @ 1020 psia) Ref. 4.6.1 RWCU Discharge HCU2 Enthalpy (subcooled @ BTUllbm 415.1 +/- 0.005 Ref . 4.6.6 1020 sia (Ref. 4.6.1
CALCULATION PAGE 3 ASSUMPTIONS AND L IMITATIONS 3.1 Calculation of M&TE errors is based on the assumption that the test equipment listed in each of the Appendices is used. The use of less accurate test equipment will require evaluation of the effect on the results of this calculation. 3 .2 It is assumed that the equipment utilized to calibrate the M&TE is more accurate than the M&TE equipment by a ratio of at least 4:1 such that calibration standard errors can be considered negligible with respect to the M&TE specifications. This is considered a reasonable assumption since M&TE equipment is typically certified to its required accuracy under laboratory conditions using instrument standards (Reference 4.1 .1, Appendix A, Section 5 .1 .4). 3 .3 A conservative assumption has been made that CRD temperature variations are bounded by t 10 °F of the design basis value based on engineering judgment. This is based on a 20 °F variation equaling 20% of the allowable range per Reference 4.5.4, and a review of other MUR submittals . 3.4 A conservative assumption has been made that the radiated and miscellaneous thermal loss value listed in Reference 4.2.3 is bounded by a +/- 10% variation based on examination of other MUR submittals . 3 .5 A conservative assumption has been made, based on Reference 4.4.1 .2, that the RR Pump motor efficiency when the Unit is operating at design basis conditions is bounded by a f 1 % variation. 3.6 It is assumed that RWCU blow down flow during steady-state operations is 0 gpm based on Reference 4.6.1 . 3.7 It is assumed that a 2 degree variation in steam temperature is sufficiently small such that the variation of enthalpy with pressure is linear for the calculation of steam enthalpy uncertainty. This is based on engineering judgment from review of the steam tables. 3.8 It is assumed that a t 5'Fvariation in temperature is sufficiently small such that the variation of enthalpy with temperature is linear for the calculation of liquid enthalpy uncertainty. This is based on engineering judgment from review of the steam tables . 3 .9 It is assumed that a f 30 psi variation in pressure is sufficiently small such that the variation of enthalpy with pressure is linear for the calculation of liquid enthalpy uncertainty. This is based on engineering judgment from review of the steam tables . 3.10 It is conservatively assumed that the moisture carryover fraction is 0 (Reference 4.1 .2). 3 .11 It is assumed that all variables used for calculation of the various enthalpies can be considered as independent based on engineering judgment, since enthalpies are relatively insentive to pressure and all flow and temperature measurements are provided by different instruments. 3.12 It is assumed that CRD and RWCU pressures are equal to Reactor Steam Dome Pressure for the calculation of CRD and RWCU enthalpy uncertainties based on the use of this pressure for calculation of these enthalpies in reference 4.1 .2. 3 .13 Since the vendor does not state a drift error for the PPC input cards, Reference 4.1 .1, Appendix A, Section 3 .1 provides a default value of 0.5% of span per refueling cycle for electronic devices.
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 7 of 20 However, the vendor includes a 0.5% error which is over conservative for a 16 bit AID converter. Therefore, the 0.5% accuracy is considered to include drift . 3 .14 If specific M&TE cannot be identified for performing a calibration, a conservative assumption is made that the M&TE used is at least as accurate as the reference accuracy of the instruments being calibrated . 4 REFERENCES 4.1 METHODOLOGY 4.1 .1 NES-EIC-20 .04, "Analysis of Instrument Channel Setpoint Error and Instrument Loop Accuracy," Revision 5 4.1.2 EMF-2469, Revision 8, POWERPLEX-III CMSS Software Design Specification 4.1 .3 NUREGICR-3659, A Mathematical Model for Assessing the Uncertainties of Instrumentation Measurements for Power and Flow of PWR Reactors 4.2 PROCEDURES 4.2.1 LIS-RT-201, Unit 2 Reactor Water Cleanup High Differential Flow Isolation Calibration, Rev. 20 4.2.2 LIP-GM-927, Thermocouple Loop Check, Rev. 4 4 .2.3 LTP-1600-10, Calculating Core Thermal Power, Rev. 27 4.2.4 MA-LA-773-472, Unit 2 RR System/Meter Calibrations By OAD, Rev. 6 4.3 LASALLE STATION DRAWINGS 4.3.1 1E-2-4224AB, Schematic Diagram, Leak Detection System "LD" (E31) Part 2, Rev. I 4.3.2 1E-2-4707AQ, Wiring Diagram Analog Input Cabinet 2C91-P618 AITs 1,2,3,4 Right Side, Rev. E 4.3 .3 1E-2-4707AX sheet 3, Wiring Diagram Analog Input Cabinets 2C91-P607, P617, P618, P631, & P635, Rev. A 4.3.4 1E-2-4207AE, Schematic Diagram - Cont. Rod Drive Hyd. Sys. RD (Cl 1B) PT. 5, Rev. F 4.3.5 M-2097 sheet 2, P&ID/C&I Details Reactor Water Clean Up System - RT, Rev. J 4.3 .6 1E-2-4228AG, Schematic Diagram -- Reactor Water Cleanup System "RT" (G33) Part 7, Rev. P 4.3 .7 1E-2-4707AG, Wiring Diagram - Analog Input Cabinet 2091-P617 AIT'S 1,2,3,4 Left Side, Rev. M 4.3.8 1E-2-4707AK, Wiring Diagram -- Analog Input Cabinet 2C91-P617 AIT'S 5,6,7,8 Left Side, Rev. J 4 .3.9 1E-2-4000PC, Relaying & Metering Diagram Reactor Recirculation Pumps 2A & 2B, Rev. M 4.4 GENERAL ELECTRIC (GE) DRAWINGS 4.4.1 Reactor Recirculation System Drawings: 4.4.1.1 234A9302TD sheet 21, IDS Recirculation System LaSalle 1,2, Rev. 4 4.4.1 .2 421H151, Performance Specifications for Nuclear Reactor Recirculating Pump Motors -Induction Type, Rev. 4 4.4.2 234A9303 sheet 2, IDS CRD Hydraulic System, Rev. 8 4.4.3 158B7077A, Flow Nozzle, Rev. 4
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 8 of 20 4.5 VENDOR PRODUCT INFORMATION 4.5.1 RTP Corp . 8436/32 8-Channel Isolated Low-Level Analog Input Card, Vendor Data Sheet 08/2004 (Attachment A) 4.5.2 Rosemount@ 1153 Series B Pressure Transmitter Product Manual 00809-0100-4302, Rev BA (Attachment B) 4.5.3 Rosemount@ 1151 Pressure Transmitter Product Manual 00813-0100-4360, Rev HA March 2008 (Attachment B) 4 .5 .4 GE Control Rod Drive System Design Specification, #22A4260, revision 4 (Attachment D) 4 .5 .5 Weed Instrument Nuclear Qualified Thermocouple Assemblies Product Sheet 10/99 (Attachment E) 4 .5.6 RTP Corp . 8436/30 Isolated Thermocouple Card, Vendor Data Sheet 09/1998 (Attachment A) 4.6 OTHER REFERENCES 4.6.1 LaSalle UFSAR, Rev. 17, Figure 1 .2-1, Tables 3.11-15 and 3.11-24 4.6.2 PASSPORT data as of 8/10/2009 4.6 .3 Edwards, Jerry L. Rosemount Nuclear Instruments letter in reference to "Grand Gulf Nuclear Station message on INFO plant reports, subject Rosemount Instrument Setpoint Methodology, dated March 9, 2000". Letter dated 04/04/2000 . (Attachment C) 4.6.4 NED-I-EIC-0255, "Measurement and Test Equipment (M&TE) Accuracy Calculation For Use With Commonwealth Edison Company Boiling Water Reactors," Revision 0 4.6.5 ASME, "Fluid Meters Their Theory and Application" Sixth Edition, 1971 . 4.6.6 Lemmon, E.W., McLinden, M.O ., and Friend, D.G ., "Thermodynamic Properties of Fluid Systems", Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P.J. Linstrom and W.G. Mallard, National Institute of Standards Technology, Gaithersburg MD, 20899, http://webbook .nist.gov, (retrieved October 21, 2009) (Attachment I) 4.6.7 195B9537 Sheet 6 & Sheet 9, Signal Resistor Unit Purchase Part, Rev. 16 (Attachment F) 4.6.8 Evaluation No. 2009-03676, "LaSalle PEPSE MUR PU and EPU Heat Balances", Revision l. 4.6.9 Calibration Data Sheets for loop 2011-N004 (Attachment H) 4.6.10 DELETED 4.6.11 NED-I-EIC-0214, "Reactor Water Cleanup High Differential Flow Isolation", Revision OOOB 4.6.12 L-002513, Reactor Dome Narrow Range Pressure IndicationError at the Plant Computer 4.6.13 L-003444, Bounding Uncertainty Analysis for Thermal Power Determination at LaSalle Unit 2 using the LEFM4+ System 4.6.14 Calibration Data Sheet for 2B33-R653A (Attachment J)
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 9 of 20 5 METHOD OF ANALYSIS n r .m 5.1 The reactor heat balance for a BWR reactor is provided by the formula stated in Section 2.1 and is repeated here for continuity in the development of the computation of the various uncertainty terms. Equation 1, CTP = Qhw + Qcr -F' QCU + Qred - Qp where CTP = Core Thermal Power
= net power transferred to feedwater (MWth)
= net power transferred to Control Rod Drive (CRD) cooling water (MWth)
QCU = net power transferred to the Reactor Water Clean Up (RWCU) system (MWth) Qred = net power radiated to the Drywell and other thermal losses (MWth) QP net power input to the reactor coolant by the Reactor Recirculation (RR) pumps (MWth) The POWERPLEX-III core monitoring software calculates the energy terms for feedwater, CRD and RWCU by multiplying the fluid mass flow by the enthalpy increase of the fluid added by the reactor. The energy loss due to radiated heat to the Drywell and other losses is a constant currently estimated at 13.99 MBTU/hr (Reference 4.2.3). The energy contribution to the feedwater from the RR Pumps is calculated by multiplying the electrical power consumed by the pump motors, as measured by the pump motor watt transducers, by an efficiency factor of 0.94 (References 4 .1 .2 and 4.2.3). Expressing the energy terms for Qf Qr, and QU from Equation 1 in terms of mass flow, W, and enthalpy, H, and adding the conversion factor for MBTU/MWth as documented in Reference 4.1 .2, results in the following equation: Equation 2, WFW * ((HG-- FM
- HFG) - HFW) +WCR * ((HG - FM
- HFG) - HCR) +(WCU
- HCU 1- (WCU -WCUbd)
- HCU 2)) + QRAD CTP= ---
C1 - V1-Where: WFW is FeedwaterMass Flow Rate (lbmlhr) HG is Saturated Steam Enthalpy (BTU17bm) FM is Moisture Carryover Fraction (%) HFG is Latent Heat of Vaporization (BTU17bm) HFW is Feedwater Enthalpy (BTU17bm) HCR is Control Rod Drive Water Enthalpy (BTU17bm) WCR is CRD Mass Flow Rate (lbm/hr)
CALCULATION PAGE WCU is RWCU Mass Flow Rate (lbm/hr) WCUbd is RWCU Blowdown Mass Flow Rate (lbmlhr) HCUI is RWCU Suction Enthalpy (BTUllbm) HCU2 is RWCU Discharge Enthalpy (BTUllbm) QRAD is Radiated and Other Heat Losses (BTUlhr) QP is RR Pump Power (MW) CI is BTUlhr to MWth Conversion Per Section 4 .6.1, RWCU blowdown flow is assumed to be zero during steady state operation . Per Section 3.10, a moisture carryover fraction of 0% is assumed to conservatively overestimate reactor power. Setting WCU and FM equal to 0 reduces Equation 2 to the following equation : bd Equation 3, WFW * (HG- HF'W) +WCR * (HG- HCR) +WCU * (HCUI -HCU2) +QRAD _ Qp CTp= C1 In equation 3 above, the energy input to the feedwater by the RR Pumps is not measured directly but is calculated by multiplying the measured electrical power consumption of the RR pump motors by their efficiency . As a result QP can be expressed as QP
- ETA where ETA is the RR pump motor efficiency .
e~k All mass flows and fluid temperatures are measured via independent instruments. As such, all input variables are modeled as independent. Only the calculated enthalpy pressure effects are dependent since the steam dome pressure measured from the same instrument is applied in each calculation. However, considering the very small dependence of enthalpy on pressure and small uncertainty in steam dome pressure, this dependency is not expected to significantly affect the results (Section 3 .11) . The mathematics of determining the uncertainty in CTP is developed in Reference 4.1 .3 . Equation 3 has been further evaluated using equation 16 of Reference 4 .1 .3 to determine uncertainty of core thermal power variables. Per Section 3.11 all variables are considered to be independent so all of the cross product terms from the squaring operation are zero . Performing the partial derivative and squaring operations on Equation 3 above with the RR pump power contribution expressed as QP
- ETA yields the following result .
Equation 4, UCTP = [(W W 2)
- UWFW) + ((HGP ) Fw 2
- 6HG ) + (( HG CR CR 2
- a'HG) + (
( aWCR } 2 * °rWCR)
+
(( aCTP ) 2 * ~2 ) + (( aCTP ) 2 * ~2 ) + ((- aCTP ) 2
- o ,2 aCTP 2 ,~ 2 Wcu
+
wcu allCUI Hcui aH'CU2 HCU2) ((- allFW) ~HFW ) _ aCTP 2
- 2 aCTP 2 ,~ 2 aCTP 2 ,~ 2 aCTP 2
- 2
+ (( allCR) 6HCR) + (( aQRAD) 6QRAD) + (( aETA) QETA) + << aQp ~QP )J where the (~ terms are the variances (square of the standard deviation) of the different
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 11 of 20 variables. 5.2 The partial derivative terms in Equation 4 can then be determined by taking the partial derivative of Equation 3 with respect to each of the variables with the following result : aCTP = HG - HFW aWFW aCTP = WFW allG FW aCTP = WCR DHGc, DCTP = HG - HCR aWCR aCTP = HCU I - HCU2 awcu aCTP = WCU DHCU FW aCTP = - WCU aHCUCR acTP = _ WFW allFW aCTP = - MICR aCTP allCR aQRAD aCTP - _ We. aETA aCTP w _ETA aQP 5.3 To complete the CTP uncertainty calculation, the enthalpy uncertainties must be computed. Since enthalpy varies with pressure and temperature, the partial differential of each enthalpy term will be taken with respect to temperature, pressure and the uncertainty, lo, inherent in the steam tables . The results will be squared to provide a statistical average and the square root of the result taken to provide the standard deviation of the enthalpy. Per section 3.11 the enthalpy variables are considered independent so all of the cross product terms can be set to zero. The result of these mathematical operations is Equation 5 below and is used as the basis for determining the enthalpy uncertainties: Equation 5, o"h ( a )2(Crt)2+(a)2(a,)2+(a h )2 o 0 )2 Per sections 3.3, 3 .4, 3.5, 3 .7, 3 .8 and 3 .9, the variation of enthalpy with T, P and to is considered to be linear. Therefore Equation 5 can be expressed as: Equation 6,
CALCULATION PACE CALCULATION NO. L-003445 Revision 001 PAGE NO. 12 of 20 cry = (o )2(a,T )2 +( 1)z(a .p )2 +( 0
) 2 (a." )
The calculation of uncertainty for saturated steam enthalpy, aHC , uses a modified form of Equation 5 above since temperature input is not required to determine saturation enthalpy for vapor. Thus 6H is set to 0 and the uncertainty associated with the saturated steam enthalpy is expressed as: G 2 . 2 +( ~ r cr HC = ( ) (a p) r)2(lSlo )z AP 0 Where: HG is the enthalpy of saturated steam (BTU/Ibm). P is the steam dome pressure (psia) . Io is the accuracy of the steam table information. The uncertainty associated with the control rod system water enthalpy is expressed as: 6HCR = ( dHCR ) 2 (a
,TCrr ) 2 + ( AHCR ) 2 (a, p ) 2 + ( AHCR ) 2 (a,,o) 2 ATCR AP A1 0 Where: HCR is the enthalpy of CRD system water (BTU/lbm).
P is the steam dome pressure (psia) . Io is the accuracy of the steam table information. TCR is the CRD water temperature (° F) . The uncertainty associated with the feedwater enthalpy is expressed as: ( AHFW ) 2 (a, + ( AHFW ) 2 (a. HFW ) 2 (Cr,, ) 2 CTHFW = p) 2 + (
~ ATFW 0 Where: HFV is the feedwater enthalpy (BTU/lbm).
TFW is the feedwater temperature (° F). P is the steam dome pressure (psia) . Io is the accuracy of the steam table information. The uncertainty associated with the RWCU suction enthalpy is expressed as: AHCUI 2 AHCUI 2 . 2 AHCU 1 2 2 aHCUI -" ( ATCU1 )2 (°rrcUr ) +( ) (a p ) +( ) AP NO Where: HCUI is the RWCU suction enthalpy (BTU/lbm). TCUI is the RWCU suction temperature (° F).
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 13 of 20 P is the steam dome pressure (psia) . to is the accuracy of the steam table information . The uncertainty associated with the RWCU discharge enthalpy is expressed as: AHCU2 +( ~1H~U2 )2(Qp)2 CU2 )2(Q,lo 0"U'
~
V ( aTCU2 ) 2(a~ua) 2
+( )z n
Where : HCU2 is the RWCU discharge enthalpy (BTU/lbm). TCU2 is the RWCU discharge temperature (° F) . P is the steam dome pressure (psia) . Io is the accuracy of the steam table information. 5.4 The rated Reactor Dome Pressure value is used to calculate the different enthalpies (Section 3.12). 5.5 For calculation of the loop uncertainties in the Appendices, temperature, humidity and pressure errors, when available from the manufacturer, are evaluated with respect to the conditions specified in the station EQ Zones. If not provided, an evaluation is made to ensure that the environmental conditions are bounded by the manufacturer's specified operational limits . If the environmental conditions are bounded, these error effects are considered to be included in the manufacturer's reference accuracy (Reference 4 .1 .1, Appendix I). 5.6 For calculation of the loop uncertainties in the Appendices, published instrument vendor specifications are considered to be based on sufficiently large samples so that the probability and confidence level meets the 2rs criteria, unless stated otherwise by the vendor (Reference 4.1 .1, Appendix A, Section 8.0). 5 .7 For calculation of the loop uncertainties in the Appendices, seismic effects are considered negligible or capable of being calibrated out (Reference 4.1 .1, Appendix I, Section 2.5). Since there is no difference between normal operating and calibration conditions with respect to vibration effects, these are considered to be calibrated out (Ref. 4.1 .1, Appendix I, Section 2 .5) 5.8 For calculation of the loop uncertainties in the Appendices, the calibration standard error is considered negligible (Section 3.2).( 5 .9 For calculation of the loop uncertainties in the Appendices, the insulation resistance error is considered negligible because operation of the instrumentation in an abnormal or harsh environment is not considered by this calculation. (Reference 4.1 .1, Appendix A, Section 7.0) . 5.10 It is expected that regulated instrument power supplies are designed to function within supply voltage limits . Therefore, the power supply error is considered negligible with respect to other error terms unless the vendor specifically specifies a power supply effect (Reference 4.1 .1, Appendix I, Section 2.3).
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 1 4 of 20 5.11 The methodology used to calculate the loop uncertainties for RWCU flow and temperature, CRD flow and RR Pump motor power in the Appendices is based on NES-EIC-20.04 "Analysis of Instrument Channel Setpoint Error and Instrument Loop Accuracy" (Reference 4.1 .1). These are non-safety-related indication loops, but the indication is used to calculate Core Thermal Power, which is a licensing limit. Per Reference 4.1 .1, the Level 2 methodology is appropriate for a licensing limit. The Level 2 methodology specifies combining the random errors via square-root-sum-of-the squares (SRSS) . However, because this parameters are used as inputs to significant plant evaluations such as determination of Core Thermal Power, this analysis will use the Level 1 methodology of Reference 4.1 .1 and express the results as 26 numbers. The random errors are combined via Square Root Sum of the Squares (SRSS) and taken to a 26 value, and then the non-random errors are added to the result . This is expressed as: TE = 2cs + Ye 5.12 The enthalpy uncertainty is determined by equating it to one half of the least significant digit with the number expressed to five significant digits . This is equal to +/-0.05 BTU/lbm for steam and t 0.005 BTU/lbm for liquid . For steam, HG = 1191 .6. Therefore, one half of 0.1 equals 0.05 . For feedwater, HFW = 404. 70. Therefore, one half of 0.01 equals 0.005.
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 15 of 20 6 NUMERIC ANALYSIS 6.1 Evaluation of the Enthalpy Uncertainties using Equation 6 (See Section 2.4 for referenced values). These values will be calculated at a 1 a level: The rated dome pressure for the heat balance calculation is 1020 .0 psia. At this pressure the saturation temperature is 547.06 °F (Ref. 4 .6 .6). Per section 3 .7, a +/- 1 °F variation will be used to determine the variation in steam enthalpy with pressure. The temperatures that bound this value (546.06 °F and 548.06 °F) will be used to determine the corresponding pressures at saturation, and to establish the change in saturation steam enthalpy, HG, relative to the change in temperature. Steam Enthal BTU/Ibm P 1028.4 1020.0 1011 .7 548.06 OF 1192 .3 - - 547.06 °F - 1192 .6 - 546.06 °F - - 1193 .0 BTU BTU 0.05 BTU 1193 -1192.3 ( 1bm Ibm )2 * ( 19.067psc )2 +( lbm )2 - 0.400 BTU Qrrc 1411 .7 psia -1028.4psia 2 2 lbm The conditions used in the heat balance to describe the RWCU suction enthalpy, HCU] , are a nominal pressure of 1020 psia and a rated temperature of 532.6 °F. Per Sections 3.8 and 3 .9, a +/- 5'F variation and a
+/- 30 psi pressure variation will be used to determine the variation of liquid enthalpy with temperature and pressure. Reference 4.6.6 will be used to develop the entries in the following table to calculate the uncertainty in the enthalpy for the RWCU suction.
RWCU Suction Enthalpy BTU/Ibm T P 990 1020 1050 537.6 °F 534.04 533 .99 533 .94 532 .6 °F 527 .75 527.70 527.66 527 .6 ° F 521.52 521 .48 521 .44 BTU BTU- B U TU 53399-----~ BTU-52148 527.75- 5276 BTT . 00 Ibm lbm )a * (3.139F ) 2 + ( lbm lbm )2 ,~ ( 19067Psi) 2 + ( 0 BTU lbm )2 =1963-' 537.6°F-52766'F 2 105(psia-990psia 2 2 1bm The conditions used in the heat balance to describe the RWCU discharge enthalpy, HCU2, are a nominal pressure of 1020 psia and a rated temperature of 436.0 °F. Per Sections 3.8 and 3.9, a +/- 5 °F variation and a t 30 psi pressure variation will be used to determine the variation of liquid enthalpy with temperature and
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 16 of 20 pressure. Reference 4.6 .6 will be used to develop the entries in the following table to calculate the uncertainty in the enthalpy for the RWCU discharge . RWCU Discharge Enthal BTUllbm T P 990 1020 1050 431 .0 °F 409.77 409.80 409 .82 436.0 °F 415.27 415.29 415 .32 441 .0 °F 420.79 420 .81 420.84 BTU BTU BTU BTU BTU 420181 - 409 80 3,13 g ~, 41532 - 41527 0.005
= (
Ibm lbm )2 *( )2 + ( Ibm Ibm )2 * (, 19.067Psi~ )2 + ( Ibm )a =1 .727 BTU 44 r F - 43 r F 2 1050psia- 990psia 2 2 Ibm The conditions used in the heat balance to describe the feedwater enthalpy, HFW, are a nominal pressure of 1020 psia and a rated temperature of 426 .5 °F. Per Sections 3.8 and 3.9, a t 5 °F variation and a t 30 psi pressure variation will be used to determine the variation of liquid enthalpy with temperature and pressure . Reference 4.6 .6 will be used to develop the entries in the following table to calculate the uncertainty in the enthalpy for Feedwater, HFW . Feedwater Enthalpy BTUAbm T P 990 1020 1050 431 .5 °F 410.32 410.35 410.37 426.5 °F 404.84 404.87 404.90 421 .5 °F 399.39 399.42 399.44 ( 41035 BTU - Ibm 431.5 F- 421.5° F BTU 39942 Ib m 2 0.57° F)2
) *(
2
+(
404.9 B BTU
-404.84 BTU lbm z
) *( 19.067 Psi 2
) +(
0.005-- BTU Ibm )'=0
.312 BTU 1050psia- 990psia 2 2 Ibm The conditions used in the heat balance to describe the CRD system water enthalpy, HCR, are a nominal pressure of 1020 psia and a temperature of 80 °F. Per Sections 3 .8 and 3 .9, a t 5 °F variation and a t 30 psi pressure variation will be used to determine the variation of liquid enthalpy with temperature and pressure .
Reference 4.6.6 will be used to develop the entries in the following table to calculate the uncertainty in the enthalpy for the CRD water.
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 17 of 20 CRD System Water Enthalpy (BTU/Ibm) T P 990 1020 1050 i 85 °F 55 .768 55 .848 55 .929 80 °F 50.794 50.875 50.957 75 °F 45 .820 45 .902 45 .984 BTU BTU BTU BTU BTU 55 .848 -45.902 F 50 .957 - 50 .794 .005
." Ibm )a *( 10. ) 2 +( Ibm Ibm )a * ( 19 .067p~
st )z + (0 Ibm BTU axcR ( 85 F - 75. F I'm 2 )x = 4 .973 1050psia - 990 psia 2 2 Ibm 6.2 Calculation of the variation in CTP with the different variables from Equation 4 and Section 5.2: acTP = HG - HFW = 1191 .6 BTU/Ibm - 404.7 BTU/Ibm = 786.9 BTUllbm aWFW acTP = WFW =15.113 M1bmlhr allGFW acTP - WCR = 0.0320 Mlbm/hr allGCR DCTP = HG - HCR = 1191 .6 BTU/Ibm - 48 .0 BTU/Ibm = 1143.6 BTU/Ibm aWCR acTP = HCUI-HCU2 = 527.3 BTU/Ibm - 415.1 BTU/Ibm
= 112.2 BTU/Ibm awcv acTP = WCU = 0.1330 Mlbm/hr 5HCU1 acTP = _wCU = -0.1330 Mlbm/hr aHCU2 acTP = -WFW = _ 15.113 Mlbm/hr allFW acTP - -WCR = -0.0320 Mlbm/hr allCR aCTP = (--QP
- 3 .413("" / I MWTH )) =-42.321"v MWTH )) = (--12.4MW
- 3 .413( "TU aETA HR HR HR
Q~ae z(n )LS6't= z(01'0)
- z (n" 66'£1)= z ( dLDe )
z(, )1'LI'S= z ((H.thUYl )£Itr'£* HTAN60L'0)* z076-0-)= da9z(dl.7e) z(n-is,w)6LI'0= z (10'0)* z (nmcwTZ£'Zfi-)= v.~.oz(d,Loe) z(nxayv)I0F0 = z (,7,A £L6'V* Z)
- z("OZ£0'0-) --- "oZ.0z(doHe) diDe z (~)It~L'88 = ('ZI £'0
- Z) * (' n"N~ ( dL~e) z(nM)IIZ -0= z(=LZL'I*Z)* z(W0££V0-)= zn~Z.0z(Zd.Lae~)
z( )£LZ'0 = z( ne £96'1
- Z)
- z( OUT -0) = tn~Z~p z(Ijj~e~)
z( )69£'0= z(DDAle grwit~£SDO'0)* z( -Z'ZII)= niiDZ( Zee z(ni,w)gS£'£= z(grwz09I00'0)* z(n.i8 9'£t1I)= a3iQZ(dZ~e ) z( nnign)T00'0= z(-,~OOt0
- Z)
- z (_OZ£0'0) = z z( d.L ee) z(,wW)Z9tT9#lI= z(~~t0*Z)* z(~£II'SI)= z z( doee) n+-"zDz(
z ( n.teW)OfiS'05t'I = z(qW t8t0'0)
- z ( nis 6'98L) = ie~)
- t-Z uopooS ui ajgvj m0 tuoij sanIVA Aluiullaoun aqj put Z'9 uopooS ui paaulnolLa sonlLIA aqj 2uisn t, uorjunbg uxojj sanlLA AIuTUVaaun jUnplAIpul auj jo uoixlnolUD £'9 Ji/(l,L9W 66'£I = Qyma = QNd oe djoe doe b6'0" = V.LT =
di'De OZ 10 8l 'ON 33vd LQQ uoIsinekj 9trvcoo-"l 'ON NOllbinowo 3ovd Noiivinmv3
CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 19 of 20 6.4 Total CTP Uncertainty is calculated using Equation 4 as follows: 2 UC, 1450.540(Mhr U ) 2 +146.462(h~)M 2 + 0.001() 2 + 3.356( MhrU ) 2 +0.359(-T) 2 + 0.273() 2
+0.211(M-- )2 +88 .741( M"~T MBrv ) 2 +0.179( MB~u )2 hr v ) 2 +0.101( hr hr U) 2 +5.174(
U c2rP =1697 .355( hTU ) z U C7r = 41 .199 MBTU/hr
= (41 .197 MBTU )/(3 .413 MBTU / MWTH) _ 12.071 MWTH UGTP hr hr LaSalle Licensed Thermal Megawatts (CTP) = 3489 MWTH (Section 2.2)
Therefore the uncertainty in the CTP calculated by the POWERPLEX-III core monitoring software as a percentage of rated thermal power is: U2d =+/-- 12.071 MWTH / 3489MWTH
- 100% = 0.346 %
CONCLUSIONS The total uncertainty associated with reactor thermal power (heat balance) calculation performed by the POWERPLEX-III core monitoring software is 12.071 MWTH or 0.346 % of the current LaSalle licensed thermal power limit of 3489 megawatts. This is a 2a number. 8 APPENDICIES 8.1 Appendix A - RWCU Flow Loop Error Calculation 8.2 Appendix B - RWCU Temperature Loop Error Calculation 8.3 Appendix C - CRD Flow Loop Error Calculation 8.4 Appendix D RR Pump Motor Power Loop Error Calculation
CALCULATION PAGE ATTACHMENTS i rr,~ Attachment A - RTP Corp. Card, Vendor Data Attachment B - Rosemount Transmitters (Selected Pages) Attachment C - Rosemount Nuclear Instruments Customer Letter Attachment D - GE Control Rod Drive Spec . (Selected Pages) Attachment E - Weed Instrument Thermocouple Vendor Data Attachment F - Signal Resistor Unit Purchase Part Attachment G - Component(s) List Attachment H -- Calibration Data Sheet for Loop 2C 11-N004 Attachment I - Thermodynamic Properties of Fluid Systems Attachment J, Calibration Data Sheet for 2B33-R653A
APPENDIX A -- RWCU FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision Oat PAGE NO. 1 of 8 The purpose of this Appendix is to calculate the uncertainty in RWCU mass flow rate at rated conditions of 3489 MWth for insertion into the table in Section 2.4 of the calculation. 1 .0 Reactor Water Clean-up (RWCU) Flow Loop Configuration 1 .1 RWCU flow is measured by a venturi tube flow meter located on the suction side of the RWCU Recirculation Pumps, which provides a dp signal to a Rosemount transmitter. The transmitter supplies a 4-20 milliamp signal to a signal resistor unit (SRU) which converts the signal to 32 160 millivolts for input to the PPC for display in the Control Room. The analyzed instrument loop consists of the following : flow element, flow transmitter, SRU, and a PPC input/output (1/O) module . The loop configuration is shown below (Ref. 4.3.1): MODULE 3 Loop components 2G33-N504 (Module 1) and 2E31-N503 (Module 2) are evaluated by Reference 4 .6.11. The applicable flow and dP values from Reference 4.6.11, Section 11 .1 .2.6.1 .4, are as follows: Full Scale Inlet Flow 440 gpm dP C Full Scale Inlet Flow 73 .3 "W.C. Required (Nominal) Inlet Flow 352 gpm Required (Nominal) Inlet dP 56.76 "W.C. The error values determined by Reference 4.6.11 are as follows: Transmitter Total Random Error (Reference 4.6.11, Section 11 .2.2.12.1) a2nc2 = +/- 0.426 mA Transmitter Total Non-Random Error (Reference 4.6.11, Section 11 .2.4 .4) Ee2nc = 0 mA.
APPENDIX A - RWCU FLOW` LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 2 of 8 The loop components evaluated in this document (and the applicable performance specifications and process parameter data) are as follows: 1 .2 Signal Resistor Unit (SRU) (Ref. 4.6.7) Resistance : 8 ohms Tolerance: +/- 0.5% 1 .3 PPC UO (low level analog input) cards for computer point IA1718 (Ref. 4.3.2 & 4 .3 .3): RTP 8436-32 8 Channel Isolated Low Level Analog Input Card performance specifications (Ref. 4.5.1) Accuracy: +/- 0.50% of full scale (32°F to 131 °F) Full Scale Voltage: +/- 160 mV 1 .4 Local Service Environment (Ref.4.6.1): Plant Process Computer E Zone A Location Control m o er Room Tem ture 50°F to 104°F Normal: 65 to 85°F Pressure 0. 125 to 3.0- *Wc Humidity 2 .6 to 90% RH (Normal expected : 20-50%) 1 .5 Calibration Instrument Data Per references 4.2.1, the loop is calibrated using a pressure source to simulate pressure input to the transmitter (measured by a pressure gauge for MTE1 1N). The calibration error due to MTE1,N is accounted for in the uncertainty value calculated in Reference 4.6.11 . The PPC UO card is not adjusted as part of this calibration. The output at the computer point is verified to read within +/- 4000 lbm/hr of the desired value (Reference 4.2 .1). This is converted to a gpm value for setting tolerance at rated conditions of 532.6 °F (Reference 4.6.1) as follows: ST = +/- (40001bm/hr) / ((8.3445 lb/gal @ sp gr = 1) *(0.7547 sp gr @ 532.6 °F)
- 60 min/hr))
ST = +/- 10.6 gpm 2.0 Reactor Water Clean-up (RWCU) Flow Loop Uncertainty 2.1 PPC I/O Module Errors (Module 3) Random Error, Normal Conditions a3
APPENDIX A --r RWCU FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 3 of 8 2.1 .1 Reference Accuracy RA3 Reference Accuracy is specified as +/- 0.50% of full scale voltage (FSV) (paragraph 1 .3) and considered to be a 2a value (Section 5.6) - RA32Q . f 0 .50%
- FSV
- RA32Q t 0.50% * (160 mV/100%) - RA32Q +/- 0.80 mV Converting to a 1 is value RA3 1, = t0.80mV/2
-- +/- 0.40 mV Converting to a in of WC value RA31,, -- +/- [73 .3 "W.C. / (160 mV - 32 mV)]
- 0.40 mV
= RA31a +/- 0.229 inWC Converting to % dp span RA31 a = +/- [0.229 inWC / 73 .3 inWC]* 100 RA31, = t 0 .313 % dp span 2.1 .2 Calibration Error CAL3 The 1/O module is not individually calibrated . Therefore CAL3 -- t0
APPENDIX A - RWCU FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 4 of S 2 .1 .3 Setting Tolerance ST3 Per paragraph 1 .5, the RWCU flow is read with a tolerance of t 10.6 gpm . Per reference 4 .1 .1 this is considered to be a acs value. Converting to a 1(y value ST3 - +/-10.6 gpm/3 ST3 -- +/- 3 .533 gpm Expressed as percent of nominal flow, ST3 .. _ +/- 3 .533 gpm / 352 gpm
- 100 ST3no. _ +/- 1 .004%
Converting error to % dP span using equation G10 from Reference 4.1 .1 :
% full span dp error t (2 * % nominal flow error) / (F,,.,, / Fnam)2 where F.ex and F am are in % of Frio..
= (400/352)
- 100
= 113.64%
% dp span error = +/- (2
- 1 .004) / (113 .64% / 100%)2
- ST3~m +/- 1.555 % dp span 2.1 .4 Drift Error D3 The vendor does not specify a drift error for the 1/0 module . Per Section 3.13, it is considered to be included in the Reference Accuracy. D3 t0 2.1 .5 Input error due to Signal Resistor a3r A +/- 0.5 % tolerance 8 fl resistor is connected across the input to the U4 card to develop the voltage signal read by the card (Ref. 4.3.1 and 4.6.7). The t 0 .5 % tolerance is considered to be a 2cs value (Section 5.6). The transmitter is scaled to provide a 4 -- 20 mA output for 0 - 73 .3 "W.C. dP input. At nominal flow (352 gpm), the dP presented to the transmitter is 56 .76 "W.C. (paragraph 1 .1) . The transmitter output at this dP input is: Flow Signal Out = (56.76 " W.C./ 73 .3 " W.C.)
- 16 mA + 4 mA 16.390 mA
APPENDIX A - RWCU FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 5 of 8 Therefore, the maximum error due to the resistor at nominal flow (352 gpm) with the I/O card scaled for 32 -160 mV equal to 0 - 73 .3 "W.C. (paragraph 1 .1) is a3r2Q = +/- [(0.005)
- 80 ]
o3r2Q = t 0.040 Q Converting to voltage error at the input to the UO card : a3r2Q = +/- [0.040 0
- 16.390 mA]
- +/- 0.656 mV Converting to "W.C.:
+/- o3r2a [(0.656 mV / (160 - 32 mV))
- 73 .3 "W .C.]
= t 0.376 "W.C.
Converting to a l6 value; a3rt,, = t 0.376 "W.C./2
= t 0.188 "W.C.
Converting to % of dP span; a3r = t (0.188/73.3)* 100 air = t 0.256 % of dP span 2 .1 .6 Random Input Error a3in From paragraph 1 .1; = a3in = cs2n C2 t 0.426 mA From Reference 4 .6.11, the transmitter output is 4 - 20 mA for 0 - 73 .3 "W.C. dP Therefore, converting to % of dP span; a3 in = t (0.426/16)
- 100 Win = t 2.663 % dp span 2.1 .7 Total Random Error a3 a3 +/- [(RA3) 2 + (CAL3 )2+ (ST3)2 +(aD3)2 + ((y3r) + (ar3in)2]'rz a3 t [(0.313)2 + (0)2 + (1 .555) 2 + (0)2 + (0.256)2 + (2.663)2]'12 a3 t 3.110 % dp span
APPENDIX A - RWCU FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 2.2 PPC I/O Module Errors (Module 3) Non-Random Error, Ee3 2.2.1 Humidity Error e3H No humidity effect errors are provided in the manufacturer's specifications . However, the I/O module is located in EQ Zone C 1 A, where humidity is maintained between 20 and 50% RH (Section 2.2.6). Therefore, humidity errors are considered to be negligible (Section 5.5). e3H = 0 2.2.2 Radiation Error e3R No radiation errors are provided in the manufacturer's specifications . However, the instrument is located in the Control Room, EQ Zone C1 A, a controlled environment (paragraph 1 .4). Therefore, it is reasonable to consider any radiation effect as negligible and capable of being calibrated out in accordance with Appendix I of Reference 4.1 .1 . Therefore, e3R = 0 2.2.3 Seismic Error e3S No seismic effect errors are provided in the manufacturer's specifications. A seismic event defines a particular type of accident condition. Therefore, there is no seismic error for normal operating conditions (Section 5.7). e3S = 0 2.2.4 Static Pressure Offset Error e3SP The UO module is an electrical device and therefore not affected by static pressure. e3SP = 0 2.2.5 Ambient Pressure Error e3P The UO module is an electrical device and therefore not affected by ambient pressure. e3P = 0 2.2.6 Process Error e3Pr The UO module/signal resistor combination receive an analog current input from the flow transmitter proportional to the dP pressure sensed . Any process errors associated with the conversion of volume flow to pressure, and pressure to a current signal, have been accounted for as errors associated with modules 1 and 2. Therefore,
APPENDIX A - RWCU FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 7 of 8 e3Pr = 0 2.2.7 Non-Random Input Error e3in From paragraph 1 .1 ; e31n = Fe2ne = 0 2.2.8 Total Non-Random Error Ee3 Ee3 = e3H + e3R + e3S + e3SP + e3P + ear + e3in 0+0+0+0+0+0+0 Ee3 = t0 3 .0 Reactor Water Clean-up (RWCU) Flow Loop Uncertainty Total Error TEd p = a3 + Tea (in % dP span) [la] TEdP = +/- 3 .110+0 Converting dP span errors to % nominal flow, TE %f,o ,, (using Equation G10 in Ref. 4.1 .1): TE%flow (% dp error / 2) * (FmaX/F.
.m)2 + (% dp error / 2) * (FmaX/Fn0m)2 TE%tjow - (3 .110 / 2) * (113.64 % / 100) 2 + (0 / 2) * (113 .64 % / 1()() ) 2 TE%fj.a = +/- 2.008 % flow + 0 [la]
Converting to a 2a value, TE = t (2*2 .008 % flow) + 0% flow TE = t 4.016 % flow [2a] Expressed in gpm:
APPENDIX A - RWCU FLOWLOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 8 of 8
+/- [4.016 % flow
- 352 gpm] / 100 TE = t 14.136 gpm 4.0 The total error due in the RWCU flow indication at the PPC at rated flow conditions is :t 4.016 %
of flow or t 14.136 gpm. Converting this to a mass flow number at the specific gravity of 0.7547 at rated conditions (Reference 4.6.2) : Weight of 1 gallon of water at a specific gravity of 1 is 8.3445 lbs (Reference 4.6.6) Therefore : TE,bm = t 14.136 gpm
- 8.34451b/gal* 0.7547
- 60 min/hr TE[bm = t 5341 .4881bm/hr This value is entered into the table in Section 2.4 for RWCU Flow Rate under Uncertainty.
APPENDIX B - RWCU TEMPERATURE LOOP CALCULATION PAGE The purpose of this Appendix is to calculate the uncertainty in the RWCU Suction and Discharge temperature loops for insertion into the table in Section 2.4 of the calculation . 1 .0 RWCU Inlet & Outlet Temperature Loop Configuration 1 .1 The analyzed instrument loops consist of the following: thermocouples and PPC input/output (1/O) modules. The loop configuration is shown below (Ref. 4.3.6): MODULE 1 Thermocouples: 2G33-N004, 2G33-N015 MODULE 2 Computer Points - 2741, 2742 1 .2 Weed Instruments Model 1J40Dl-305-EG-A-2-C-008 (Reference 4.5.5 & 4.6.2) performance specifications : Temperature Range: 32°F - 600OF Limit of error (Reference Accuracy): t3°F Thermocouple Type: E 1.3 PPC UO (low level analog input) cards for computer points 2741 and 2742. (Refs. 4.3 .3
& 4.3.7):
RTP 8436-30 8 Channel Isolated Thermocouple Input Card performance specifications (Ref. 4.5 .6) Accuracy : +/-0.9°F (+/-0.5°C) Resolution : -}0.18°F (+/-0.1°C)
APPENDIX R -" RWCU TEMPERATURE LOOP CALC ULATION PACE CALCULATION NO. L-003445 Revision 001 PAGE NO. 2 of 6 1 .4 Local Service Environments (Ref. 4.6.1): Thermocouple Plant Process ComLyl& EQ Zone H4 A Location -Reactor NO- . Control Room C uter R Tem rature 94°F to 118°F 50°F to 104°F Normal: 65 to 85°F Pressure 0.2 "wc .12 3.0 "w Humidity 23 to 35% RH 12 .6 to 90% RH (Normal expected : 20-50%) 1.5 Calibration Per Reference 4.2.2, this loop is only checked for operability and is not calibrated . Therefore, the setting tolerance will be set to 0. 2.0 RWCU Temperature Loop Uncertainty 2.1 Thermocouple Errors (Module 1) Random Error, al 2.1 .1 Reference Accuracy RA1 Reference Accuracy is :t 3°F (Paragraph 1 .2). This is considered a 2a number per Section 5.6. RA12ff .= t3°F [26] Converting to a 16 value RAI is - +/-3°F 12 RA11Q = t1 .5°F 2 .1 .2 Calibration Error CALI, Calibration Standard Error STD1, Setting Tolerance ST1 (paragraph 1 .5): The thermocouple has no adjustment, therefore CAL1=STD1=ST1= 0 2.1 .3 Drift Error D1 The thermocouple is not an electronic device, therefore, D11Q = 0 2.1 .4 Power Supply Effects a1PS The thermocouple does not require a power supply, therefore,
APPENDIX B - RWCU TEMPERATURE LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 3 of 6 QIPS = 0 2.1 .5 Ambient Temperature Error d1T All thermocouple extension wire junctions are on adjacent terminals and are assumed to be at the same temperature. Therefore, (NIT 0 2.1 .6 Random Input Error Qlin Module 1 is the first instrument in the loop, so cylin = 0 2.1 .7 Total Random Error tsl 61 -- +/- [(RA 1)2 + (CAL 1)2 + (ST 1)2 + (DI )2 + ((Y 1 PS)2 + ((Y 1 T) 2 + ((s l in)2] 112 61 - +/- [(1 .5)2 + (0)2 + (0)2 + (0)2 + (0)2 + (0 )2 + (0)2] 1/2
+/- 1 .5°F 2.2 Thermocouple Errors (Module 1) Non-Random Error, Fel The thermocouple is not an electronic device and its output is only affected by temperature at the thermocouple junction . Therefore, elH=elR=elS=eIV=elSP=elP=0 2.2.1 Temperature Error e1T The temperature error is assumed to be random and included in the reference accuracy . Therefore, elT = 0 2.2.2 Non-Random Input Error elin The thermocouple is the first module in the loop . Therefore, elfin = 0 2 .2.3 Total Non-Random Error Fel ZeI = e1H + eIR + elS + e1SP + eIV + e1P + e1T + elfin
APPENDIX B - RWCU TEMPERATURE LOOP CALCULATION PAGE 0+0+0+0+0+0+0+0 2.3 PPC 1/O Module Errors (Module 2) Random Error, 02 2.3 .1 Reference Accuracy RA2 Reference Accuracy is specified as t 0 .9°F (paragraph 1 .3) and considered to be a 2rs value (Section 5.6) RA22Q = t0.9°F Converting to 16, RA21, = t0.9°F /2 RA2ra = t 0.45°F 2.3.2 Resolution error A/D2 A/D2 =+/-0.18'F Converting to 16, A/D = t 0.18 °F/2 AID = t 0.09 °F 2.3.3 Calibration Error CAL2 The UO module is not calibrated. The calibration error for the loop is included in the verification of the indication for module 1 . Therefore, CAL2 = t0 2 .3.4 Setting Tolerance ST2 The PPC 1/O card has no adjustment . Therefore, there is no setting tolerance. ST2 = +/-0 2.3 .5 Drift Error D2 The vendor does not specify a drift error for the 1/O module . Per Section 3 .13, it is considered to be included in the Reference Accuracy . D2 - t0
APPENDIX B - RWCU TEMPERATURE LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 5 of 6 2 .3 .6 Random Input Error d2in o2in = c71 = +/- 1 .50°F cs2in = t 1.50°F 2.3 .7 Total Random Error v2 ts2 = :t [(RA2) 2 + (AlD2)2 + (CAL2)2 + (ST2)2 + (D2)2 + (d2in)2]"2 cs2 _ t [(0.45)2 + (0 .09)2 + (0) 2 + (0) 2 + (0)2 + (I .50)T r2 d2 = 11.569°F 2.4 PPC I/O Module Errors (Module 2) Non-Random Error, Normal Conditions Te2 2.4 .1 Humidity Error e2H No humidity effect errors are provided in the manufacturer's specifications (Ref. 4.5.1). Also, the 1/0 module is located in EQ Zone CIA, where humidity under normal conditions may vary from 20 to 50% RH (Section 2.3.6). Therefore, humidity errors are considered negligible (Section 5 .2). e2H = 0 2.4.2 Radiation Error e2R No radiation errors are provided in the manufacturer's specifications. Also, the instrument is located in the Control Room, EQ Zone CIA, a mild environment (Section 2.3.6). Therefore, it is reasonable to consider any radiation effect as negligible and capable of being calibrated out in accordance with Appendix I of Reference 4.1 .1 . Therefore, e2R = 0 2.4.3 Seismic Error e2S No seismic effect errors are provided in the manufacturer's specifications . A seismic event defines a particular type of accident condition. Therefore, there is no seismic error for normal operating conditions (Section 5.4). e2S - 0 2.4.4 Static Pressure Offset Error e2SP The UO module is an electrical device installed in the control room and is not subject to process pressure effects.
APPENDIX B -- RWCU TEMPERATURE LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 6 of 6 e2SP = 0 2.4.5 Ambient Pressure Error e2P The 1/0 module is an electrical device and therefore not affected by ambient pressure. e2P = 0 2.4.6 Non-Random Input Error e2in e21n Fret = 0 2.4.7 Total Non-Random Error Eel Eel = e2H + e2R + e2S + e2SP + e2P + e2in 0+0+0+0+0+0 Eel 0 2.5 RWCU Temperature Loop Uncertainty Total Error TE - a'2 + Ee2
+/- 1 .569°F + 0 [l cs]
Expressed at a 2a level of confidence TE = 2o2 + Eel
- t2* 1 .569 + 0 TE = t 3.138°F 3.0 Conclusion The total uncertainty in the RWCU Suction and Discharge temperature indications, expressed at a 26 level of confidence, is +/- 3 .138°F . This value is inserted into the table in Section 2.4 for the RWCU Suction and Discharge temperatures under Uncertainty.
APPENDIX C -- CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 1 of 16 The purpose of this appendix is to calculate the uncertainty in the measurement of CRD flow for input to the table in Section 2.4 of the body of the calculation. 1 .0 CRD Flow Loop Characteristics 1 .1 Each analyzed instrument loop consists of a flow element supplying a differential pressure to a transmitter, and a PPC input/output (UO) module with a precision resistor (8 5Z) across the input. The loop is shown as (Ref. 4 .3.4): MODULE 1 Flow Element - 2C11-N003 0-200 inWC dp MODULE 2 Flow Transmitter - 2C11-N004 4-20 mA MODULE 3 Comp Point - 271'1 Resistor at Input terminals 0.1 The loop components evaluated in this document (and the applicable performance specification and process parameter data) are as follows: 1 .2 Flow Element, EPN: 2C11-NO03 (Ref. 4.4.2 and 4.6.2) GE flow element part number 158B7077AP016 (Ref. 4.4.3) Maximum differential pressure 200 inWC at 100 GPM Accuracy t1%
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE 1 .3 Flow Transmitter, EPN: 2CI I-NO04 (Ref. 4.6.2) Rosemount Model 1151DP5E (Ref. 4.6.2) Flow Transmitter performance specifications (Ref. 4.5.3). These are considered 26 numbers per section 5.6: Upper Range Limit (URL): 750 inWC Output Span : 4 - 20 mA Accuracy: +/-0.2% calibrated span [2cf] Temperature Effect : +/-(0.5% URL + 0.5% calibrated span)/100°F (-20 to 200 °F) [2cs] Drift: +/-0.2% URL for 6 months [26] Temperature Operating Limits : (-) 20°F to 200°F Static Pressure Effect Zero Error +/-(0.25% URI J2000 psi) Static Pressure Effect Span Error +/-(0.25% Input Reading/10(10 psi) Vibration Effect 0.05% URL/g Power Supply Effect < 0.005% output span/volt EMI/RFI Effect < 0.1 % span for 30 V/m between 20 and 1000 MHz Calibration information (Refs. 4 .6.2): Calibration Range: 0 - 200 inWC Corresponding Process Range: 0 -100 GPM Span 200 inWC 1 .4 PPC UO (low level analog input) cards for computer point IA2711 . (Refs. 4.3 .4 & 4.3.8): RTP 8436-32 8 Channel Isolated Low Level Analog Input Card performance specifications (Ref. 4.5.1) Accuracy : -+/--0.50% of full scale (32°F to 131'F) Full Scale Voltage: 1160 mV 1 .5 The signal resistor at the input terminals of the UO card (Module 3) is a precision 8 ohm resistor with a tolerance of 0.10% (Ref. 4.3 .4). This is considered to be a 2Q number because all resistors supplied meet this tolerance .
APPENDIX C -- CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 3 of 16 1 .6 Process Parameters (Refs. 4.5.4, 4 .6 .1, 4.6 .2 and 4.6.8): Process Fluid Water Process Press Max 1410 PSIG Steam Dome pressure - rated 1005 PSIG Process Temp Max 95 °F Process Temp at Rated Power 80 °F Process Temp Min 40°F Process Flow-Rated 64 gpm 1 .7 Calibration Instrument Data Per reference 4.6.9, the following M&TE are required . Druck DPI-610 (15 psi), a 1 ohm precision resistor, and a Fluke 45 multimeter. 1 .8 Local Service Environments (
Reference:
4.6.1): Pmesure Transmitters Plant Process ComnuM EQ Zone 4 1 Location Rector Id . Control Room Com uter Room Tem erature 94°F to 118°F 50°F to 104°F Nominal: 65 to 85° Pr ssure 1 0,25 'WC 10 . 125 to 3.0 *wc Humidity 23 to 35% RH 2 .6 to 90% RH (Normal expected : 20-50%)
APPENDIX C -- CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 4 of 16 2.0 CRD Flow Loop Uncertainty 2.1 Flow Element (Module 1) Random Error, al The flow element is a mechanical device mounted in the process and cannot be calibrated . Therefore, CAL = ST1= D1= QIPS = (s1T = 0 2.1 .1 Reference Accuracy RAl Per reference 4.4.3, the accuracy of the flow element is +/-I % of span. This is considered a 2Q number per section 5.3 . Therefore, Converting to I cr value, RAI,, - t 1 % 12 RAI,, = t 0.5 % d.P span 2.1 .2 Temperature Effect on Element Expansion TN1 Per paragraph 1 .6, the maximum temperature of the water passing through the flow element is 95°F and the normal temperature is 80'F . Since the system temperature operation band is small, there is a minor change in the element expansion factor. The change is in order of 0.0007 or less for the temperature range of 70 °F to 95 °F. Therefore the temperature effect on element expansion can be neglected. TNl = 0 2.1 .3 Temperature Effect on Density TDl Per paragraph 1 .6, the maximum temperature of the water passing through the flow element is 95°F and the normal temperature is 80 °F. The change in water density for a temperature range of 70°F to 95 °F is approximately 0.2% . Therefore density effects are considered negligible . TD1 - 0 2.1 .4 Random Input Error 61in The flow element is the first device in the instrument loop. Therefore;
APPENDIX C -- CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 0{11 PAGE NO. 5 of 16 alin 0 2 .1 .5 Total Random Error al al = t [(RAI) 2 + (CALI)2 + (STI)2 + (D1 )2 + (alpS) 2 + (a1T)2 + (al in)2 + (TN 1)' + (TD1)21 112 al - t [(0.5%)Z + (0)2 + (0) 2 + (0)2 + (0)2 + (0)2 + (0)2+ (0)2 + (0)2112 al -- t 0.5 % dP Span 2.2 Flow Element (Module 1) Non-Random Error, Eel The flow element is a mechanical device mounted in the process and its output is not subject to environmental or vibration effects. Therefore; e1H = elR = elP = elT = 0 2.2.1 Seismic Error e1S A seismic event is an abnormal operating condition and is not addressed by this calculation (Section 5 .4). Therefore; 2.2.2 Static Pressure Error elSP The flow element is constructed of stainless steel and is not affected by process pressure . Therefore, e1SP = 0 2.2.3 Non-Random Input Error elin The flow element is the first device in the instrument loop . Therefore; 2.2.4 Total Non-Random Error Eel Eel = elH + eIR + elP + e1T + e1S + elSP + elin Eel - 0+0+0+0+0+0+0 Eel -- t0
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 6 of 16 2.3 Flow Transmitter Errors (Module 2) Random Error, Normal Conditions d2 2.3.1 Reference Accuracy RA2 Reference Accuracy is t0.2% of span (paragraph 1 .3). RA22,, 0.2% [2a1 Converting to a l a value
= RA2Id +/- 0.2%/2 = RA2ia +/- 0.1 % dP span 2.3.2 Calibration Error CAL2 The pressure loop is calibrated using a pressure source to simulate pressure input to the transmitter (measured by a digital pressure indicator for MTE1 IN), and reading the pressure on the computer point (Ref. 4.6.9). Therefore, only the digital pressure indicator contributes to the overall calibration error at the transmitter.
Measurement & Test Equipment Error MTEj 2 Pressure Indicator Per paragraph 1 .7, the pressure indicator used for calibration is a DRUCK DPI-601 gage with a range of 415 inWC. The measurement uncertainty, MTEi 2, for this indicator is specified in Reference 4.6.4 for an ambient temperature of 104 °F as: MTEjn2 = t 0.606 inWC [ 1 a1 Converting to % dP span, MTE;n2 = +/- (0.606 inWC/200 inWC)* 100% MTEj.2 - 0.303 % dP span
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE 2.3 .3 Calibration Standard Error STD2 The calibration standard error is considered to be negligible (Section 5.8). STD1o2 = 0 2 .3 .4 Calibration Error CAL2 The total calibration error for the M&TE is: CAL2 = t [MTE;n22 + STD X22 ] 112 t [0.303 2 +021 112 CAL2 = t 0.303 % dP span 2.3 .5 Setting Tolerance ST2 The transmitter is calibrated as part of a loop calibration, and the PPC output is verified to +/- 3.04
% (3 .04 gpm) (Reference 4.6.9). This is considered a 3tr value since all calibrations meet this tolerance.
Converting to 16 ; ST2 - +/- 3.04 gpm /3
= t 1 .013 gpm Expressed as a percent of nominal flow at rated conditions :
ST2nom +/- 1.013 gpm/64 gpm
- 100
+/- 1 .583 %
Converting to % of dP span at 64 gpm using equation G10 from Reference 4.1 .1 :
% full span dP error = (2* % nominal flow error)/(Fn,,
.,/ Fnom)2 where F ,, and Fnom are expressed in % of Fnem
% F.,, -- (100/64)
- 100
- 156.25%
ST2 .- (2
- 1 .583 %)/(156.25/100)2 ST2 - 1.297 %dP span 2.3 .6 Drift Error D2
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 Drift error for the transmitter is t 0.2% of URL / 6 months, taken as a random 20 value (paragraph 1 .3). The calibration frequency is 2 years, with a late factor of 6 months . D221 = +/- (0.2%
- URL)
Drift is applied to the surveillance interval as follows (Reference : 4.1 .1 Appendix A)
- D22a t [0.002 URL] [(24 months + 6 months) / 6 months] 1/2 (0.002
- 750 inWC) (30 /6)1n
= t 3 .354 inWC Converting to a 16 value = D2,a +/- 3.354 inWC / 2 D21, = +/- 1 .677 inWC Converting to % dl? span, D21, = +/- (1 .677 inWC 1200 inWC)
- 100%
D21,, = +/- 0.839 % dP span 2.3 .7 Power Supply Effects o2PS Power supply effects are considered to be negligible (Section 5 .7). Therefore, o2PS = +/-0 2.3 .8 Ambient Temperature Error o2T The temperature effect is -~ (0.5% URL + 0.5% calibrated span)/100°F [2(y] (paragraph 1 .3). The maximum temperature at the transmitter location is 118°F, and normal temperature during calibration is considered to be 73°F, so the maximum difference =118-73°F = 45°F a2TZ1 _ +/- [(0.005
- 750 inWC + 0.005 x 200 inWC) / 100°F] x 45°F [26]
v2T2, = +/- 2.138 inWC Converting to a 1 a value a2T1, = + 2.138 inWC / 2 a2Tla= +/- 1 .069 inWC Converting to % dl? span,
APPENDIX C -- CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 9 of 16
- 1 62T1,= +/- (1 .069 inWC / 200 inWC)*100%
o'2T ICF~ t 0.534% dP span 2.3.9 Random Input Error o2in Random input error to Module 2 is equal to the random output error from Module 1, therefore o2in = cs1 - t 0.5% dP span 2.3.10 Total Random Error o2 02 - t [(R .A2)2 + (CAL2 )2 + (ST2)2 + (D2)2 + (ts2pS)2 + (o2T)z + (o2in)2] m 02 - +/- [(0.1)2 + (0.303) 2 + (1 .297)2 + (0.839)2 + (0)2 + (0.534)2 + (0.5)2]'r2 d2 +/- 1.739 % dP span 2.4 Flow Transmitter Errors (Module 2) Non-Random Error, Fe2 2 .4.1 Humidity Error e2H No humidity effect errors are provided in the manufacturer's specifications, and the humidity conditions at the instrument location are within the operating limits of the module . Therefore, humidity errors are considered negligible during normal conditions. (Reference 4.1 .1, Appendix 1) e2H = 0 2.4.2 Radiation Error e2R No radiation errors are provided in the manufacturer's specifications. Therefore, it is reasonable to consider the normal radiation effect as negligible and capable of being calibrated out in accordance with Appendix I of Reference 4.1 .1 . Therefore, e2R - 0 2.4 .3 Seismic Error e2S No seismic effect errors are provided in the manufacturer's specifications . A seismic event defines a particular type of accident condition. Therefore, there is no seismic error for normal operating conditions (Section 5.7) e2S = 0
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 16 of 16 2.4.4 Vibration Effect e2V The error due to vibration is considered to be negligible because it is small and there is no difference between normal operating and calibration conditions with respect to vibration effects (Section 5 .7). e2V - 0 2.4.5 Static Pressure Error e2SP The transmitter has a Zero Error of +/-0.25% of URL per 2000 psi and a Span Error of +/-0 .25% of Input Reading per 1000 psi (paragraph 1 .3). Therefore the total Static Pressure Error is e2SP = +/-0.25% of URL per 2000psi + 0.25% of Input Reading per 1000psi The nominal process pressure is 1005psig (paragraph 1 .6) . Therefore, the Zero error is: e2SPz = t 0.25%
- 750 "WC
- 1005 psig / 2000 psi
= t 0.942 "W.C.
Calculating the input dP at 64 gpm : Input dP = (64 gpm/100 gpm)2
- 200 "W.C.
81 .92 "W.C. Calculating the Span Error: e2SPsp = t 0.25%
- 81 .92 "WC
- 1005 psig / 1000 psi e2SPsp = t 0.206 "W.C.
Therefore, the combined Zero and Span error, e2SP, is: e2SP = e2SPz + e2SPsp e2SP = +/- [0.942 "W.C. + 0.206 "W.C.) e2SP = +/- 1 .148 "W.C. Converting to % dp span, e2SP = +/- (1 .148 "W.C./200 "W.C.)
- 100%
e2SP = t 0.574 % dp span
APPENDIX C -- CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 11 of 16 2.4.6 Ambient Pressure Error e2P The flow transmitter is an electrical device and therefore not affected by ambient pressure . e2P = 0 2.4.7 Temperature Error e2T Temperature error is considered to be a random variable for a Rosemount transmitter. Therefore e2T - 0 Non-Random Input Error e2in e2in Total Non-Random Error Eel 1e2 -- e2H + e2R + e2SP + e2S + e2V + e2P + e2T + e2in 0+0+/-0.574+0+0+0+0+0 F.,e2 = +/- 0.574 % dp span 2 .5 PPC VO Module Errors (Module 3) Random Error, (Y3 2.5.1 Reference Accuracy RA3 Reference Accuracy is specified as +/- 0.50% o¬ full scale voltage (paragraph 1 .4) and considered to be a 2a value (Section 5.6) RA32Q = +/- 0.50% x FSV RA32Q = +/- 0.005 x 160 = 0.8mV Converting to inWC and 1 a, RA3tQ = +/- [0.8mV * (200 inWC l (160mV - 32mV))J 12 RA3 i Q = +/- 0.625 inWC Converting to % dp span, RA3 1 a = +/- (0.625 inWC/200inWC)
- 100%
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 12 of 16 RA31a = t 0.313 % dp span 2.5 .2 Calibration Error CAL3 The I/O module is not calibrated ; the indication is verified during the calibration of Module 1 . Therefore, CAL3 = t0 2.5.3 Setting Tolerance ST3 The UO module is not calibrated and no operator adjustments are made which could introduce errors due to a calibration process. The computer output is verified to read t 2.2 gpm as part of the loop calibration. Therefore, the Setting Tolerance is included as part of the transmitter calibration. ST3 = t0 2.5 .4 Drift Error D3 The vendor does not specify a drift error for the 110 module . Per Section 3.13, it is considered to be included in the specification for Reference Accuracy . D3 = t0 2 .5.5 Input error due to Signal Resistor Q3r A t 0.1 % tolerance resistor is connected across the input to the I/O card to develop the voltage signal read by the card (Section 2 .4.1). The t 0.1% tolerance is considered to be a 2cs value (Section 5 .6). The transmitter is scaled to provide a 4-20 mA output for 0-200 "W.C. dP input . At nominal flow (64 gpm), the dP presented to the transmitter is: Calculating dP at 64 gpm: rated = (64 gpm / 100 gpm)2
- 200 "W.C.
= 81 .920 "W.C.
At this dP, the transmitter output is: Flow Signal Out = (81 .920/200)
- 16 mA + 4 mA
- 10.554 mA
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 13 of 16 Therefore, the maximum error due to the resistor at rated flow (64 gpm) with the 1/O card scaled for 32 -160 mV equal to 0 - 200 "W.C. (paragraph 1 .2) is 63r2a = t(0.001)*892
-- t 0.008 St Converting to voltage error at the input to the UO card :
a3r7a = t (0.008 S2
- 10 .554 mA
- t 0.084 mV Converting to " W.C .:
a3r2o = t [(0.084 mV/(160 - 32 mV))
- 200 "W.C.]
a3r2a = t 0.132 "W.C. Converting to a I a value; a3ri, = t 0.132 "W.C./2 a3r, Q = t 0.066 "W.C. Converting to % of dP span; a3rla = t (0.066 "W .C. / 200 "W.C.)* 100 a3r, Q = t 0.033 % of dP span 2 .5.6 Random Input Error v3in a3 in - 02 - t 1.739 % dp span vain = :t 1.739 % dP span 2.5.7 Total Random Error a3 cY3 - t [(RA3) 2 + (CAL3 )2+ (ST3)2 +((;3r)2 +(crD3)2 + (cs3in)2]lrz a3 - t [(0.313)2 + (0)2 + (0) 2 + (0.033)2 + (0)2 + (1 .739)21'2 v3 f 1.767 % dP span 2.6 PPC UO Module Errors (Module 3) Non-Random Error, Fe3 2.6.1 Humidity Error e3H No humidity effect errors are provided in the manufacturer's specifications . Also, the I/O module is located in EQ Zone CIA, where humidity under normal conditions may vary from 20 to 50%
APPENDIX C - CRD FLOW LOOP CALC ULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 14 of 16 RH (Ref. 2.4.8). Therefore, humidity errors are negligible during normal conditions. (Reference 4.1 .1, Appendix I) e3H - 0 2.6.2 Radiation Error e3R No radiation errors are provided in the manufacturer's specifications . Also, the instrument is located in the Control Room, EQ Zone CIA, a mild environment (Section 2.4.8) . Therefore, it is reasonable to consider the normal radiation effect as negligible and capable of being calibrated out in accordance with Appendix I of Reference 4.1 .1 . Therefore, e3R - 0 2.6.3 Seismic Error e3S No seismic effect errors are provided in the manufacturer's specifications. A seismic event defines a particular type of accident condition. Therefore, there is no seismic error for normal operating conditions (Section 5.7). e3S 0 2.6.4 Static Pressure Offset Error e3SP The I/O module is an electrical device and therefore not affected by static pressure . e3SP = 0 2.6.5 Ambient Pressure Error e3P The YO module is an electrical device and therefore not affected by ambient pressure . e3P = 0 2.6.6 Process Error e3Pr The UO module receives an analog current input from the flow transmitter proportional to the pressure sensed . Any process errors associated with the conversion of pressure to a current signal have been accounted for as errors associated with module 1 . Therefore, e3Pr = 0 2.6.7 Non-Random Input Error e3in e3in = Ee2 = t 0.574 % dp span Total Non-Random Error Ze3
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 15 of 16 F,e3 = e3H + e3R + e3S + e3SP + e3P + e3Pr + e3in
-- 0+0+0+0+0+0+/-0.574 Ee3 = +/- 0 .574 9'o dp span 2.7 CRD Flow Rate Uncertainty Total Error, TE TE = 2*63 + Ee3 To convert % dp span to Ibm/hr Converting 0.0320 Mlbm/hr to GPM :
Weight of water at 4 °C (=40 °F) 1000 kg m"3 (specific gravity = 1) 1 kilogram = 2.2046226218 lbs Therefore 1 m3 of water at 4 °C weighs 1000 kg m-3
- 2.2046226218 lbs/kg = 2,204.623 lbs M-3 1 gallon = 0.003785 m3 [US, liquid]
1 gallon = 2,204.623 lbs M-3
- 0.003785 m-3 1 gallon = 8.3445 lbs Or 1 lb = 0.1198 gal (gallons/lb) 1 hour = 60 min (min/hr)
Lbm
- gal/lb/[(hr*min/hr)
- sp] = gal/min (at specific gravity sp) 1 Lbm/hr = (1
- 0.1198)/(60
- 1) = 0.0020 GPM At a temperature of 80 °F, the specific gravity of water is 996.56 kg/m3/ 1000 kg m-' = 0.997 Therefore, 1 Lbm/hr = (1
- 0.1198)/(60
- 0.997) = 0.0020 GPM At 80 °F: 0. 0320 Mlbm/hr = 64 gpm
APPENDIX C - CRD FLOW LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 16 of 16 Converting errors to % nominal flow (using Equation G10 in Ref. 4.1 .1) Nominal flow = 64 gpm = 100% flow Full Span =100/64* 100 =156.250% flow
% flow error = (% dp span / 2) * (F.,JF,,or,)2 + (% dp span / 2) * (Fma,JFr~,',)2
= (1 .767 / 2) * (156.250 % / 100%)2+ (0.574/ 2) * (156 .250 % / 1()0%)2 a'3 + 1e3 = t [2 .157 % flow + 0 .701 % flow] [ 1 a]
Converting to a 2cs value, TE - t [(2*2 .157 % flow) + 0.701 % flow] TE -- t 5.015 % flow 3.0 The uncertainty calculated for the CRD flow at rated conditions of 64 gpm is :t 5.015 % of flow. Therefore; TEflow = +/- (5.015 %
- 64 gpm)/100 l i+~_Ylow = +/- 3 .210 gpm [2a]
Converting to lbm/hr for water at 80 °F TE,bm = -+/-- (3.210 gpm) * (8 .3445 lbs/gal C sp. Gr. = 1) * (0 .997 sp. Gr. C 80 °'F)
- 60 min/hr TEIbm = t 1602.329 lbm/hr This value is entered into the table in Section 2.4 for CRD flow under Uncertainty .
APPENDIX D - REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 1 of 9 The purpose of this Appendix is to calculate the uncertainty in the measurement of Reactor Recirculation Pump Motor Power for input to the table in Section 2.4 of this calculation. 1 .0 Recirculation Pump Motor Power Measurement Loop Configuration 1 .1 Each analyzed instrument loop consists of Current Transformers, Potential Transformers, a Watt Transducer, a Watt Transducer Filter, and a PPC input/output (UO) module . There is a separate instrument loop for each of the Reactor Recirculation Pump motors . Since the two loops are identical, the instrument uncertainty of one loop will be calculated and then the two uncertainties combined SRSS to provide the uncertainty in the combined power measurement for both pumps The vendor specifies a combined accuracy for the watt transducer and watt transducer filter which is considered to include the CT and PT inputs . 'Therefore, they will be addressed as one module . The loop is shown as: PTs Us MODULE I Watt Transducer - 2833-K655A, -K655B Watt Transducer Filter - 2833-K656A, -K656B MODULE 2 Comp Point - 2725, 2726 1 .2 Watt Transducer EPN 2B33-K655A, -K655B (Refs. 4.4 .1, 4.2.4 & 4.6.2): Volts: 120 Amps: 0-5A Output Range 0-1 mA Setting Tolerance +/-5% of full scale Location 2H13-P612
APPENDIX D -- REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 2 of 9 1 .3 Watt Transducer Filter EPN 2B33-K656A, -K656B (Refs. 4.4.1, 4.6.2 and 4.6.14) : Amps : 0 -- 1 mA Output Range: 0-100 mV Process Range: 0-14.4 MW) Location 2H13-P612 1 .4 The Watt Transducer and Filter have a combined accuracy of t 0.5 % (Ref. 4.4.1) 1 .5 Pump Motor Efficiency (Ref. 4.4.1): At 100% Load: 94.4% At 75% Load: 93 .5% At 50% Load: 91 .5 At 25% Load: $5 .0% 1 .6 PPC UO (low level analog input) cards for computer point LA2725, IA2726 (Ref. 4.3 .9 &4.5.1): RTP 8436-32 8 Channel Isolated Low Level Analog Input Card performance specifications (Ref. 4.5.1) Accuracy: +/-0.50% of full scale {32°F to 131 °F} Full Scale Voltage: 1160 mV 1 .7 Local Service Environments (Reference : 4.b.1): 2H13-P612 Plant Process Computer E Zone ClA 1A Location Aux. Elec . Equip. Rm . l Room (Computer Roo Temperature Range 50°F to 104°F Normal : 65 to 85°F 50°F to 104°F Normal : 65 to 85°F Pressure 0.125 to .0 " 0.125 0 . " __ Humidity 2.6 to 90% RH (Normal: 20-50%) 2.6 to 90% RH (Normal: 20-50%)
APPENDIX D - REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATIO N PAGE, 2 .0 Reactor Recirculation Pump Motor Power Measurement Loop Uncertainty 2.1 Watt Transducer and Filter (Module 1) Random Error, a1 2.1.1 Reference Accuracy RAI Per paragraph 1 .4, the combined accuracy of the transducer and filter is +/-0.5% of range. Per Section 5.6, this is considered to be a 2cs number. Therefore, RA 12,1 = +/- 0.5090
- 14.4 MW RA 121 = +/- 0.072 MW Converting to l a value, RA1 16 = +/-0.072!2 MW RAI1Q = +/-0.036 MW 2.1 .2 Calibration Error CAL1 The test equipment used to calibrate the Watt Transducer and Filter are assumed to be at least as accurate if not better than the equipment being calibrated . Therefore, the M&TE uncertainty will be taken as the Reference Accuracy of the Watt Transducer and Filter. Per Section 5 .6, this is considered to be a 2a number .
M&TE = RA I = +/-0 .590 of range M&TE = +/- 0.072 MW CALI = M&TE = +/- 0.072 MW Converting to 16 value, 1 CAL 1, = +/- 0 .072!2 MW CAL1 Ia = +/-0.036 MW
APPENDIX D - REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATION PAGE 2.1 .3 Setting Tolerance ST1 The setting tolerance is +/-5% of full scale (Reference : 4.6.2). This is considered to be a 3a number. Therefore, ST1 3Q =+/-5%
- 14.4 STIR, = +0.72 MW Converting to la value, ST 1 j Q = +/- 0.72/3 MW ST1 IQ = +0.24 MW 2.1 .4 Drift Error D1 The vendor did not publish a separate drift specification.
Therefore, per Reference 4.1 .1 Appendix A, a drift error of t 0.5% of span per refueling cycle is assumed for electronic components . This is considered to be a 26 number . Therefore, D1 = +-0.5% *14.4 MW D1 = +/- 0.072 MW Converting to l6 value, D1 = +/-0.072/2 MW D1 - +/-0.036 MW 2.1 .5 Power Supply Effects a1PS Power supply effects are considered to be negligible (Section 5 .10). Therefore, a1PS = 0 2.1.6 Ambient Temperature Error (TIT The vendor did not publish a separate temperature effect specification. The Watt Transducer and Filter are'located in the auxiliary electrical room which is a controlled environment. Therefore, per Section 5 .any temperature error is considered to be included in the reference accuracy.
APPENDIX D - REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO.5of9 alT = 0 2.1 .7 Random Input Error alin The watt transducer and filter are the first devices in the instrument loop. Therefore, alin = 0 2.1 .8 Total Random Error al al = t [(RA1)2 + (CAL1)2 + (ST1)2 + (D1)2 + (alPS) 2 + (alT) 2 + ((7l in)2] 112 al = t [(0.036)2 +(0.036)2+ (0.24)2+ (0 .036)2 + (0) 2 + (0)2 + (0)2] 111 al - t 0.2480 MW 2.2 Watt Transducer and Filter (Module 1) Non-Random Error, Fel The watt transducer and filter are electrical devices and their output is not subject to environmental or vibration effects. Therefore; e1H=e1R=e1P=e1T=0 2.2.1 Seismic Error e1S A seismic event is an abnormal operating condition and is not addressed by this calculation (Section 5.7). Therefore; 2.2.2 Static Pressure Error e1SP The watt transducer and filter are electrical devices not affected by process pressure . Therefore; e1SP = 0 2.2.3 Non-Random Input Error elin The watt transducer and filter and their associated CTs and PTs are the first devices in the instrument loop. Therefore; elfin = 0
APPENDIX D - REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO.6of9 2.2.4 Total Non-Random Error .Eel Eel .- e1H + e1R + e1P + e1T + e1S + e1SP + elin Eel - 0+0+0+0+0+0+0 Eel = t0 2.3 PPC 1/O Module Errors (Module 2) Random Error, Q2 2.3.1 Reference Accuracy RA2 Reference Accuracy is specified as t 0.50% of full scale (paragraph 1 .6) and considered to be a 2a value (Section 5.6) RA22, = t 0.50%
- full scale RA22Q = t 0.50%
- 14AMW = 0.072 MW Converting to ba, RA21 , = 1 0.072 / 2 RA21,, = t 0.036 MW 2.3.2 Calibration Error CAL2 The UO module is not calibrated ; the indication is verified during the calibration of Module 1 . Therefore, CAL2 = t0 2.3.3 Setting Tolerance ST2 The UO module is not calibrated and no operator adjustments are made which could introduce errors due to a calibration process. The output of the PPC UO module is verified as part of the loop calibration of Module 1 . Therefore, ST2 +/-0 2.3 .4 Drift Error D2 The vendor does not specify a drift error for the 1/O module. Therefore, per Section 3 .13, it is considered to be included in the reference accuracy.
APPENDIX D -- REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 7 of 9 2.3 .5 Random Input Error oZin a2in = al = 0.2480 MW o2in -. t 0.2480 MW 2.3.6 Total Random Error d2 cF2 = t [(RA2)2 + (CAL2 )2+ (ST2)2 +(cvD2) 2 + (a2in)2J "2 a2 - +/- [(0.036)2 + (0)2 + (0) 2 + (0) 2 + (0.2480)']"2 cY2 t 0.2506 MW 2.4 PPC 1/0 Module Errors (Module 2) Non-Random Error, Fk2 2.4.1 Humidity Error e2H The UO module is located in EQ Zone C1 A, where humidity may vary from 20 to 50% RH (Ref. 4 .6 .1). Humidity errors are negligible during normal conditions. (Reference 4.1.1, Appendix 1) e2H = 0 2.4.2 Radiation Error e2R The instrument is located in the Control Room, EQ Zone CIA, a mild environment (Section 2.5.7). Therefore, it is reasonable to consider the normal radiation effect as negligible and capable of being calibrated out in accordance with Appendix I of Reference 4.1 .1 . Therefore, e2R = 0 2.4.3 Seismic Error e2S No seismic effect errors are provided in the manufacturer's specifications. A seismic event defines a particular type of accident condition. Therefore, there is no seismic error for normal operating conditions (Section 5.7). e2S 2.4.4 Static Pressure Offset Error e2SP The 1/0 module is an electrical device and therefore not affected by static pressure . e2SP = 0
APPENDIX D -- REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 PAGE NO. 8 of 9 2.4.5 Ambient Pressure Error e2P The PPC UO card is an electrical device and therefore not affected by ambient pressure . e2P 2.4.6 Process Error e2Pr The PPC UO card is an electronic device mounted in the Control Room and is not subjected to any process effects. . Therefore, e2Pr = 0 2.4.7 Non-Random Input Error e3in e2in = Eel = t0 2.4.8 Total Non-Random Error Eel Ee2 - e2H + e2R + e2S + e2SP + e2P + e2r + e2in
= 0+0+0+0+0+0+0 Ee2 = 0 2.5 Recirculation Pump Motor Power Total Error (one pump motor)
TEIQ -- 62 + Ee2
- +/-0.2506 MW +0 TEI, = t 0.2506 MW Converting to a 2a value, TEza = 2*cs2 + Ee2
- t 2*0 .2506 MW + 0 TEW1p = t 0.501 MW
APPENDIX D - REACTOR RECIRC PUMP MOTOR POWER LOOP CALCULATION PAGE CALCULATION NO. L-003445 Revision 001 2.6 Total Recirculation Pump Motor Power Error (two pump motors) TEW2 p f ((0.501 MW)2 + (0.501 MW)2)~A TEW2p - t 0.709 MW The total uncertainty in the measurement of Reactor Recirculation Pump Motor Power is t 0.709 MW. This number will be entered in the table in Section 2.4 for RR Pump Motor Power under Uncertainty.}}