ML13043A657
Text
Enclosure 13 to NRC-13-0004 Fermi 2 NRC Docket No. 50-341 Operating License No. NPF-43 License Amendment Request for Measurement Uncertainty Recapture (MUR) Power Uprate Fermi 2 Calculation DC-6443, Volume I DCD 1, Revision A, "Reactor Core Thermal Power Uncertainty with Feedwater Flow Measured by LEFM CheckPlus C System" 50 Pages
DESIGN CALCULATION COVER SHEET Page 1 of 50 PART 1: DESIGN CALCULATION IDENTIFICATION A)
Design Calculation Number DC-6443 B)
Volume Number I DCD 1 C)
Revision A
D)
PIS Number E)
QA Level B2100/C1100/C3200/G3300 QNon-Q Q l 1M F)
ASME Code Classification NA G)
Certification Required Q Yes ZNo H)
Incorporation Code F
J)
Title - Reactor Core Thermal Power Uncertainty with Feedwater Flow Measured by LEFM CheckPlus C System K)
Design Change Documents Incorporated (Number and Revision)
None L)
Design Calculations Superseded (Number and Revision)
DC-6443 Volume I DCD 1 Revision 0.
M)
Revision Summary DCD 1 Revision A changes the title, incorporates new values for feedwater temperature uncertainty (for both fully functional and maintenance mode LEFM CheckPlus C) and feedwater flow uncertainty (maintenance mode LEFM CheckPlus C) from Cameron report ER-781 Revision 2. Added References 6.27 - 6.29. The QA Level is changed to 1M, and it is now identified as a Key Calculation. All pages are reprinted, including attachments and appendices. Revision bars indicate content changes.
N)
Review of Assumptions, Methods, and Inputs Completed (Step 4.3.2)
Q Standard review, completed in revision Key calculation review, completed in revision A
[Q N/A (For Non-Q)
O)
Key Calculations Review Incorporated in Revision A
[
N/A, Not a Key Calculation P)
PPRNs are required: Q Yes No Issuing DCD EDP 36969 QN/A Q)
Key Calculation:
Yes Q No Justification for Yes or No: Technical Specifications - supports licensed core thermal power limit PART 2: PREPARATION, REVIEW, AND APPROVAL A)
Prepared By R.PSE-52 Qualified and additional qualifications per Step 2.3:
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Date 2 13 B)
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ai L a_.
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Date /-S - 23 /1'3 D)
Design Calculation Utility has been updated [R Yes QN/A Approved By Print/Sign
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//Date./
/'C!// 13 t Decommissioning Related ISFSI Rel ed Q Yes Q No DTC: TPMMES DSN: MES15001 Rev. 9 Pi/1 File: 1703.22 Issued:
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CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO.2 of 50 Table of Contents Section Page Number 1.0 Purpose/Objective........................................................................................................
3 2.0 Sum m ary of Results and Conclusion...........................................................................
3 3.0 M ethod of Analysis......................................................................................................
4 3.11 Boundary Conditions and M ethodology Lim itations....................................................
9 4.0 D esign Inputs..................................................................................................................... 9 5.0 Assumptions...................................................................................................................... 12 5.1 V erified A ssumptions....................................................................................................
12 5.2 Unverified A ssumptions................................................................................................
13 6.0 References......................................................................................................................... 14 7.0 Calculation Details.........................................................................................................
17 8.0 Acceptance Criteria......................................................................................................
31 Appendices A
RW CU Flow Loop Error................................................................................................ 32 B
CRD Flow Loop Error..................................................................................................
35 Attachments
- 1.
N IST D ata on Therm ophysical Properties of W ater....................................................
39
- 2.
Excerpt from A SM E Fluid M eters.................................................................................... 40
- 3.
Excerpt from AN SI/A SM E PTC-6.................................................................................... 41
- 4.
Excerpts from NUREG/CR-3659......................................................................................
42
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 3 of 50 1.0 Purpose/Objective The purpose of this calculation is to determine the uncertainty in the reactor core thermal power (heat balance) calculation when using the Cameron Leading Edge Flow Meter (LEFM) CheckPlus System as the source for feedwater flow and temperature values. This calculation will evaluate the contribution of the uncertainties of the different instrument channel loops that provide the inputs that are used to calculate core thermal power (CTP). CTP is normally calculated in the Integrated Plant Computer System (IPCS), but may also be calculated manually. This calculation will detennine the overall uncertainty of the CTP calculation at the proposed Measurement Uncertainty Recapture (MUR) rated power when done either by the IPCS or manually, and with the LEFM CheckPlus in both fully functional and maintenance mode. Use of the tenn LEFM or LEFM CheckPlus within this calculation specifically refers to the Cameron LEFM CheckPlus C.
2.0 Summary of Results and Conclusion Results In terms of the Current Licensed Thermal Power (CLTP) rated power of 3430 MWt (Design Input 4.1) and the MUR rated power of 3486 MWt (Design Input 4.1), the total uncertainty to a 20, or 95.5%
confidence level, associated with the reactor thermal power (heat balance) calculation is:
Core Thermal Power Calculation Method Associated Uncertainty MWt
+/- 12.373 +/- 0.361
+/- 0.355
+/- 19.358 f 0.564 +/- 0.555
- 3. Manual Calculation with LEFM CheckPlus Fully Functional:
+/- 12.384 +/- 0.361
+/- 0.355
- 4. Manual Calculation with LEFM CheckPlus in Maintenance Mode:
f 19.364 0.565
+/- 0.555 Conclusion For Case 1 (Core thermal power calculated by IPCS with LEFM CheckPlus Fully Functional), the uncertainty is +/- 12.373 MWt (or +/- 0.361% CLTP). Per the Case 1 acceptance criterion in Section 8.0, the proposed MUR CTP (3486 MWt) plus the total positive uncertainty in MWt must remain bounded by 1.02% (3499 MWt) of Current Licensed Thermal Power (CLTP, at 3430 MWt).
3486 MWt + 12.373 MWt = 3498.373 MWt, which is less than 3499 MWt (1.02% of CLTP)
Thus, the Case 1 results are acceptable and support the proposed MUR rated power of 3486 MWt, or 101.64% of CLTP.
As stated in Section 8.0, for the remaining three cases there are no specific acceptance criteria and the uncertainties are simply stated in the table above.
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO.4 of 50 3.0 Method of Analysis The determination of reactor core thennal power (CTP) is based on the net heat output from the reactor vessel, which is based on the energy balance of heat flows into and out of the reactor vessel. The following figure is a simplified representation of the reactor energy balance (Ref. 6.6, 6.19, 6.23 and 6.24).
Punp Sal
/Flo R
Control Rod Drive From (,ndent Sy:tem Figure I Reucor Energy ialance Schematic 3.1.
The equation used to calculate core thermal power is (References 6.2, 6.4 & 6.19):
CTP = QFW + QCR + Qcu + QRAD - QP
[Equation 3.1]
where:
CTP = Core Thermal Power QFW = net power transferred to feedwater (MWt)
QcR = net power transferred to Control Rod Drive (CRD) cooling water (MWt)
Qcu = net power transferred to the Reactor Water Clean Up system (MWt)
QRAD = net power radiated to the Drywell and other thermal losses (MWt)
= net power input to the reactor coolant from the Reactor Recirculation (RR) pumps (MWe)
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 5 of 50 3.2.
Utilizing BTU/hr to MWt conversion constant Cl, the individual energy terms for QFW, QCR and Qcu in Equation 3.1 can be expressed in terms of mass flow (W) and enthalpy (h) as:
QFW = [WFW * ((hg - FM
- hfg) - hFW)]/C1
[Equation 3.2-1]
QCR = [WCR * ((hg - FM
- hfg) - hCR)]/C1
[Equation 3.2-21 Qcu= [WCU
- hCU1 - (WCU -WCUbd)
- hCU2]/C1
[Equation 3.2-31 Where: WFW is Feedwater Mass Flow Rate (Mlbm/hr) hg is Saturated Steam Enthalpy (BTU/lbm)
FM is Moisture Carryover Fraction hfg is Latent Heat of Vaporization (BTU/lbm).
hfg = hg - hf, where hf is saturated water enthalpy.
hFW is Feedwater Enthalpy (BTU/lbm) hCR is Control Rod Drive Water Enthalpy (BTU/lbm)
WCR is CRD Mass Flow Rate (Mlbm/hr)
WCU is RWCU Mass Flow Rate (Mlbm/hr)
WCUbd is RWCU Blowdown Mass Flow Rate (Mlbm/hr) hCU1 is RWCU Suction Enthalpy (BTU/lbm) hCU2 is RWCU Discharge Enthalpy (BTU/lbm)
Substituting hg - hf for hfg, Equation 3.2-1 can be re-written as:
QFW = [WFW * (hg * (1 - FM) + hf
- FM - hFW)]/Cl
[Equation 3.2-41 Substituting hg - hf for hfg, Equation 3.2-2 can be re-written as:
QCR = [WCR * (hg * (1 - FM) + hf*FM - hCR)]/C1
[Equation 3.2-5]
Per Section 5.1.4, RWCU blowdown flow is considered to be zero during steady state operation.
Thus Equation 3.2-3 reduces to:
Qcu = [WCU * (hCU1 - hCU2)]/Cl
[Equation 3.2-61 Substituting Equations 3.2-4, 3.2-5 and 3.2-6 into Equation 3.1, core thermal power can be calculated as:
CTP = [WFW * (hg * (1 - FM)+ hf
- FM - hFW)]/C1
+ [WCR * (hg * (1 - FM) + hf*FM - hCR)]/C1
+ [WCU * (hCU1 - hCU2)]/C1 + QRAD - Qp
[Equation 3.2-7]
3.3.
The energy input to the reactor coolant 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 = QPelec
- ETA where ETA is the RR pump motor efficiency.
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 6 of 50 3.4.
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 5.1.9).
3.5.
The determination of CTP uncertainty is based on the mathematical methodology of NUREG/CR-3659 (Ref. 6.20). Although Ref. 6.20 was written for Pressurized Water Reactors (PWRs), it details a mathematical methodology of determining instrumentation measurement uncertainty for power and flow. This mathematical methodology is based on a combination of measurement uncertainties in a rigorous statistical manner, and is applicable to evaluate the uncertainty of any multivariable system with measured input variables. This methodology is equally valid for either PWR or Boiling Water Reactor (BWR) power and flow measurements.
As stated in the executive summary of NUREG/CR-3659 (Ref. 6.20) "While the method is directed toward PWR power and flow determination, it is suitable for generalized application to instrument measurement uncertainties."
Based on Ref. 6.20, the mathematics of determining the uncertainty in CTP are developed as follows:
For a function Y of multiple variables (xn), such as:
Y = f (x 1, x2, x3,..., xn)
Equation 3.5-1 The change in Y due to changes in the individual x~ variables is:
dY=
- dxi
+
- dx
+...+
- dx Equation 3.5-2 ax1 2
axn Using o-to represent the standard deviation of each variable xn (which is the uncertainty of the individual variable x~), as developed within Ref. 6.20, the uncertainty (Uy) associated with multifunction variable Y may be represented as:
2 2
2 22 ax
\\ax 2 *x 2 +.
U Y
- xY +
-Y
+2 a a x a X 2
a Y
a x ax k
a y x
x U X +X
)
+.
ax+ 2a x
+
ax
- n m
n +
where letter subscripts designate cross products of dependent terms.
If all the variables are independent, the cross product terms become zero, and this simplifies to:
2 2= /Y 2
2 Y
2 2
uY Y
ax. /
- axx2
+
aaa
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO.7 of 50 Per Section 5.1.9 all variables are considered to be independent so all of the cross product terms from the squaring operation are zero. Thus the uncertainty of multifunction Y is:
Uy
- Qxl)2 + (--*
x2)2
______ e 2
Equation 3.5-3 This calculation applies Equation 3.5-3 to the variables in Equation 3.2-7 to determine the overall uncertainty in core thermal power.
3.6.
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 (T), pressure (P) and the enthalpy read from the steam tables (I). 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 5.1.9 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 3.6-1 below and is used as the basis for detennining the enthalpy uncertainties:
/ah Sh h
- ah rT) 2
+/-(-h
- UP) 2 +(j
- UIf 2
[Equation 3.6-1]
aT aP al Per sections 5.1.5, 5.1.6 and 5.1.7, the variation of enthalpy with respect to T and P is considered to be linear. Since h is enthalpy, and I is the enthalpy read from the steam table, the change in h with respect to I is constant, thus ah/aI = 1. Therefore Equation 3.6-1 can be expressed as:
Ah *)2 Ah 2
S=
AT T
P I
[Equation 3.6-2]
The calculation of uncertainty for saturated steam and water enthalpies, Ohg, and Uhf use a modified form of Equation 3.6-2 above since temperature input is not required to determine saturation enthalpy. Thus AWAT is set to 0 and the uncertainties associated with the saturated steam and water enthalpies are expressed as:
Ahg h
h
=
(
- up) 2 + 612
[Equation 3.6-31 uf (Ahf *Q) 2 +
2
[Equation 3.6-4]
AP Where:
hg is the enthalpy of saturated steam (BTU/lbm) hf is the enthalpy of saturated water (BTU/lbm)
P is the steam dome pressure (psia).
I is the enthalpy read from the steam table.
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 8 of 50 The uncertainty associated with the control rod system water enthalpy is expressed as:
AhCR AhCR
- 2 + 6 2
[Equation 3.6-51 hCR ATCR TCR P
I Where:
hCR is the enthalpy of CRD system water (BTU/lbm).
P is the steam dome pressure (psia).
TCR is the CRD water temperature (°F)
I is the enthalpy read from the steam table.
The uncertainty associated with the feedwater enthalpy is expressed as:
AhFW AhFW 2+
2
[Equation 3.6-6]
chFW ATFWFW P)
+(AP Where:
hFW is the feedwater enthalpy (BTU/lbm).
TFW is the feedwater temperature (°F).
P is the steam dome pressure (psia).
I is the enthalpy read from the steam table.
The uncertainty associated with the RWCU suction enthalpy is expressed as:
oru
= (AhCU1 *
)2
+ AhCU1 *o) 2 +
1
[Equation 3.6-71 ATCU1 AP Where:
hCU1 is the RWCU suction enthalpy (BTU/lbm).
TCU1 is the RWCU suction temperature (°F).
P is the steam dome pressure (psia).
I is the enthalpy read from the steam table.
The uncertainty associated with the RWCU discharge enthalpy is expressed as:
AhCU2 AhCU22 hCU2 = (
)2 +(
)2 +
[Equation 3.6-81 h~2 ATCU2 T~2 AP P
1 Where:
hCU2 is the RWCU discharge enthalpy (BTU/lbm).
TCU2 is the RWCU discharge temperature (°F).
P is the steam dome pressure (psia).
I is the enthalpy read from the steam table.
3.7.
The rated Reactor Dome Pressure value is used to calculate the different enthalpies (Section 5.1.10).
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 9 of 50 3.8.
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 Cl-4180 "Setpoint Validation Guidelines" (Reference 6.1).
3.9.
These indication loops evaluated in this calculation are non-safety-related, but the indications are used to calculate Core Thermal Power, which is a licensing limit. Thus the random errors are combined via Square Root Sum of the Squares (SRSS) and taken to a 2-value for conservatism.
3.10. An enthalpy value uncertainty of +/-0.1% [2c] will be applied in the overall enthalpy uncertainty evaluations in Section 7.1 of this calculation, based on Input 4.5.
3.11. Boundary Conditions and Methodology Limitations Because the input values used are for normal full power operation, this calculation methodology determines the uncertainty of the reactor core thennal power only for normal operation near the rated thennal power. No attempt is made to quantify uncertainties for other modes of operation.
4.0 Design Inputs 4.1.
Nominal values of the core thermal power calculation input parameters for operation of Fenni 2:
- 1. At 100% of current licensed thermal power (CLTP), 3430 MWt, are listed in UFSAR Figure 1.2-32, "GE Reactor System Heat Balance Rated Performance" (Reference 6.6),
- 2.
At 101.64% of CLTP, or the proposed MUR rated power (3486 MWt), are listed in MURFTRTO100 Figure 3-2a, "Revised Reactor Heat Balance - TLTP (101.64% CLTP)"
(Reference 6.26), and
- 3.
Also per Reference 6.26, 1.02% of CLTP is 3499 MWt.
4.2. Conversion factors:
4.2.1.
For MBTU/hr to MWt: C1 = 3.413 MBTU/MWt-hr (Ref. 6.2) 4.2.2.
For HP to MWe: 1 HP = 0.7457 KWe = 0.0007457 MWe (Ref. 6.1) 4.3.
From DC-4567 Volume I (Ref. 6.9), the uncertainty of the RWCU flow indicator is f 11.02 gpm
[1.645 a]. Using the density (52.363 lbm/ft3) at the RWCU discharge temperature of 435.9°F and 1045 psia to convert this to mass flow, and taking it to 2Q:
owcu = [(* 11.02 gpm)*(52.363 lbm/ft3)*(1 ft3/7.480519 gal)*(60 min/hr)]*2/1.645 wcu =*+/- 5627 lbm/hr = t 0.0056 Mlbm/hr
[2Q]
4.4. From Ref. 6.14, 6.15 and 6.24 each Recirc pump motor is rated at 7500 HP. There are two pumps (Loop A and B). Converting this to MWe to get the bounding pump motor energy input:
QP = (2
Reference 6.16 evaluates the effect of the use of enthalpy values from four major sources:
Keenan & Keyes 1936, ASME 1967, NIST Version 2.2 and IAPWS-IF97. It states that the uncertainty of the enthalpy as read from any of these four sources is bounded by +/- 0.1% of the value. This calculation applies the bounding +/- 0.1% uncertainty to the enthalpy values.
Because this bounding enthalpy uncertainty is included in the overall uncertainty determination, the calculation results are conservative as long as this calculation and the plant's core thermal
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 10 of 50 power determination utilize any of these four sources. This calculation utilizes the NIST source.
Per References 6.2 and 6.22, the process computer and the manual calculation both use Keenan
& Keyes.
4.6. The table below lists the input parameters to the proposed MUR rated core thermal power calculation and the source of these values:
Table 4.6-1 CTP Input Parameters (at MUR conditions)
Description Term Nominal Value Units Source Reactor Dome Pressure P
1045.0 PSIA Ref. 6.26 Feedwater Flow Rate WFW 15.111 Mlbm/hr Ref. 6.26 CRD Flow Rate WCR 0.032 Mlbm/hr Ref. 6.26 RWCU Flow Rate WCU 0.133 Mlbm/hr Ref. 6.26 Feedwater Temperature TFW 426.5 OF Ref. 6.26 Control Rod Drive Temperature TCR 100.0 OF Ref. 6.3, 6.6 RWCU Suction Temperature TCU1 533.8 OF Ref. 6.26 RWCU Discharge Temperature TCU2 435.9 OF Ref. 6.26 Radiated and Misc Thennal Losses QRAD 2.1
- MWt Ref. 6.3 Recirc Pump Motor Energy Input QPelec 11.185 MWe Input 4.4 Recirc Pump Motor Efficiency ETA 95.2 Ref. 6.3 Pump A & Pump B Saturated Steam Enthalpy hg 1191.7 BTU/lbm Ref. 6.7 (Att. 1)
(at dome pressure)
Steam Moisture Content FM 0.001 Ref. 6.19 (at dryer exit)
Saturated Water Enthalpy hf 549.87 BTU/lbm Ref. 6.7 (Att. 1)
(at dome pressure)
Feedwater Enthalpy hFW 404.89 BTU/lbm Ref. 6.7 (Att. 1)
CRD Enthalpy hCR 70.834 BTU/lbm Ref. 6.7 (Att. 1)
RWCU Suction Enthalpy hCU1 529.17 BTU/lbm Ref. 6.7 (Att. 1)
RWCU Discharge Enthalpy hCU2 415.20 BTU/lbm Ref. 6.7 (Att. 1)
The total radiated and miscellaneous thermal losses value of 2.1 MWt is based on 1.1 MWt (Ref. 6.19) for radiative heat loss through the vessel wall, in the recirculation piping, RWCU piping, feed lines and steam lines and 1.0 MWt for the Recirc Pump Seal Purge flow from CRD (Ref. 6.3).
- The value of 100.0°F for control rod drive temperature is not changed by increasing the power level.
Thus the existing 100°F value from Ref. 6.3 and 6.6 is used instead of the 97.2°F value from Ref. 6.26.
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 11 of 50 4.7. References 6.2, 6.3 & 6.25 identify the instrument or computer point displays that provide CTP input indications. The table below lists the uncertainties associated with various core thermal power input parameters and the source of these values:
Table 4.7-1 CTP Input Parameter Uncertainties (all 20 unless noted otherwise)
Description Term Indication Uncertainty Units Source Reactor Dome Pressure - IPCS C32DP1732
+/- 18.9 [1.6450]
DC-4556 Vol. I Reactor Dome Pressure - Indicator C32R609
+/- 12.7 [1.6450]
(Ref. 6.8)
Feedwater Flow Rate - LEFM LEFM 4Plus ER-781
/Plus Fully Functional indication or
+0.28% of 15.111 Rev. 2 OWFW LEFM VPlus input Mlbm/hr (Ref. 6.11)
Feedwater Flow Rate - LEFM to IPCS N21CF6138 M.51%
(e 6.11)
VPlus in Maintenance Mode N21CF6035 (Loop A)
- 0.51% of 15.111 N216036 (Loop B)
CRD Flow Rate - IPCS C11CF6001 0.0025 Appendix B aWCR ~
C C1DF1052Mbmh CRD Flow Rate - Indicator C11R800 f 0.0029 Appendix B RWCU Flow Rate - IPCS G33DF1055 (A7+/-16) 0.0022 Mlbm/hr Appendix A uWCU G3F05(76 RWCU Flow Rate - Indicator G33R609
+ 0.0056 Mlbm/hr Input 4.3 or G33R623 Feedwater Temperature - (LEFM LEFM VPlus VPlus fully functional indication or 0.55 ER-781 aTFW input to IPCS OF Rev. 2 Feedwater Temperature - (LEFM N21GT2804 g 0.58 (Ref. 6.11)
,/Plus in Maintenance Mode N21GT2805 Control Rod Drive Temperature uTCR N/A
+/- 10 OF Section 5.1.1 RWCU Suction Temperature TCU1 G33DT2502
- IPCS or indicator G33R607 RWCU Discharge Temperature aTCU2 G33DT2503 10 F
Section 5.1.1
- IPCS or indicator G33R607 Radiated and Misc Thermal Losses UQRAD N/A (1 10% of nominal)
MWt Section 5.1.2 Recirc Pump Motor Energy Input aQP N/A
(+ 10% of nominal)
MWe Section 5.1.8 Recirc Pump Motor Efficiency aETA N/A
(+ 1% efficiency)
Section 5.1.3 Saturated Steam Enthalpy ahg N/A
+/- 1.522 BTU/lbm Section 7.1.1 (at dome pressure)
Saturated Water Enthalpy uhf N/A
+ 3.504 BTU/lbm Section 7.1.1 (at dome pressure)
Feedwater Enthalpy - LEFM f 0.725 Section 7.1.4 VPlus Fully Functional OhFW N/A BTU/lbm Feedwater Enthalpy - LEFM
+/- 0.752
,Plus in Maintenance Mode CRD Enthalpy ahCR N/A
+/- 9.947 BTU/lbm Section 7.1.5 RWCU Suction Enthalpy ahCUl N/A 12.541 BTU/lbm Section 7.1.2 RWCU Discharge Enthalpy ohCU2 N/A 11.018 BTU/lbm Section 7.1.3
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 12 of 50 5.0 Assumptions 5.1.
Verified Assumptions 5.1.1.
A conservative assumption has been made that CRD and RWCU temperature variations are bounded by +/-10 °F of the nominal value based on engineering judgment. The 10%
is consistent with the 10% error assigned for all non-feedwater flow related error in existing calculations DC-4568 Volumes VII and VIII (Refs. 6.12 and 6.13), which determine the overall uncertainty in the IPCS and manual calculations of core thermal power when using the feedwater flow indication from the differential pressure flow measurement system.
5.1.2.
A conservative assumption has been made that the radiated and miscellaneous thermal loss value listed in Reference 6.2 is bounded by a +/-10% variation. The 10% is consistent with the 10% error assigned for all non-feedwater flow related error in existing calculations DC-4568 Volumes VII and VIII (Refs. 6.12 and 6.13).
5.1.3.
A conservative assumption has been made that the RR Pump motor efficiency when the Unit is operating at design basis conditions is bounded by a +1% variation. Per Ref.
6.21 the B pump efficiency changes from 94.65% to 95.18% for a loading change from 75% to 125% of rated load. Since the core thermal power is determined for normal operating conditions near 100% loading, a 1% variation conservatively bounds any expected efficiency variation. This 1% variation is conservatively assumed to apply to both the A pump and the B pump, due to their similarity in type, size and operating characteristics (Ref. 6.14 and 6.15).
5.1.4.
It is assumed that RWCU blowdown flow during steady-state normal operations is 0 gpm, because blowdown is not utilized during normal steady-state operations.
5.1.5.
It is assumed that a +/-1 degree variation in steam temperature is sufficiently small such that the variation of enthalpy with temperature is linear for the calculation of steam enthalpy uncertainty. This is based on engineering judgment from review of the steam tables.
5.1.6.
It is assumed that a +/- 5°F variation 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.
5.1.7.
It is assumed that a +/- 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.
5.1.8.
A conservative assumption has been made that the RR Pump motor power reading is bounded by a +10 % variation. The 10% is consistent with the 10% error assigned for all non-feedwater flow related error in existing calculations DC-4568 Volumes VII and VIII (Refs. 6.12 and 6.13).
5.1.9.
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 insensitive to pressure and all flow and temperature measurements are provided by different instruments.
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 13 of 50 5.1.10. 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 6.2.
5.1.11. A conservative assumption is made that the uncertainty of the CRD flow nozzle is bounded by +5.0%. Per Table II-V-1 of Ref. 6.17 the worst case uncertainty of a flow nozzle is +/- 2.0%. Per Ref. 6.18, the worst case uncertainty of an uncalibrated flow section is 3.2%. The selected value of +/-5.0 conservatively bounds either of these cases. Thus this assumption is conservative.
5.1.12. It is assumed that there is no significant uncertainty associated with the digital transfer of data from the LEFM to the IPCS. The LEFM has a direct digital connection to the IPCS. Per engineering judgment, no significant error is introduced to the data that is transferred via this direct connection.
5.1.13. It is assumed that there is no significant uncertainty associated with the digital calculations performed within the IPCS. Per engineering judgment, the digital calculations performed by the IPCS do not in themselves create an additional source of error.
5.2. Unverified Assumptions None
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 14 of 50 6.0 References DOCUMENT INTERFACE
SUMMARY
Ref DTC DSN or Rev Title Ref In Out How document is used Document Type put put in calculation 6.1 TDPINC C1-4180 C
Setpoint Validation Guidelines Q
Q Methodology for instrument (DECO File No.
loop accuracy determination C1-4180) in Appendices 6.2 TRVEND 520 2311300 06E 1
IPCS -Detailed Design Manual Q
Q Formulas and inputs for the (DECO File No.
Appendix E NSSS CTP calculation M14-886) 6.3 TPNPP 57.000.02 33 Core Thermal Power Evaluation Q
Inputs to CTP calculation 6.4 TCEDP 36238.A024 0
Feedwater Ultrasonic Flow Q
Formulas and inputs for the Measurement System (Markups to CTP calculation 520-231100-06E) 6.5 TSICSS G33N042-SS A
RWCU Bottom Head Drain Q
Q Inputs on RWCU temp Temperature instrumentation - to App. A 6.6 TDFSAR UFSAR 18 Updated Final Safety Analysis Q
Q Section 1.1 and Figures 1.2-Report Chapter 1 and Chapter 5 32 & 5.1-la - nominal CLTP variable inputs 6.7 Thermophysical Properties of Fluid Q Q
Data Retrieved October 16, Systems, Chemistry WebBook, 2011.
NIST Standard Reference Database Enthalpy and density data Number 69 included as Attachment 1 6.8 TDPINC DC-4556 H
Remote Shutdown Reactor Q
Q Inputs on reactor dome Vol I Instrumentation pressure instrumentation accuracy 6.9 TDPINC DC-4567 D
Q Inputs for RWCU flow Vol I Instrumentation Surveillance instrumentation accuracy Procedure Validation 6.10 TDPINC DC-5924 E
CRD Flow Instruments Calibration Q Q
Inputs on CRD flow Vol I Specification instrumentation accuracy 6.11 TRVEND ER 781 2
Bounding Uncertainty Analysis for Q Z
Q LEFM CheckPlus C (DECO File No.
Thermal Power Determination at measurement accuracy of C1-7406)
Fermi Unit 2 Using the LEFM C FW flow and temperature System 6.12 TDPINC DC-4568 0
Maximum Probable Error in Q
Q 10% uncertainty for non-FW Vol VII DCD Process Computer Calculation of flow parameters Core Thermal Power 6.13 TDPINC DC-4568 0
Maximum probable Error in NPP-Q Q
10% uncertainty for non-FW Vol VIII DCD 57.000.02 Manual Calculation of flow parameters Core Thermal Power
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 15 of 50 DOCUMENT INTERFACE
SUMMARY
Ref DTC DSN or Rev Title Ref In Out How document is used Document Type put put in calculation 6.14 TMINSL VMR1-39 A
General Electric 295X271 Nuclear Q
Z D RR pump A motor rating Reactor Water Recirculating Pump Motor 6.15 TMINSL VMRl-96 0
Vertical Induction Motor for Q
RR pump B motor rating Nuclear Reactor Water Recirculating Pump "B" 6.16 TDVEND DRF A13 00461 0
Impact of Steam Table Basis on Q
Uncertainty of Enthalpy as 02 Process Computer Heat Balance read from steam table (PROPRIETARY)
Calculations (GE Nuclear Energy) sources 6.17 ASME Fluid Meters, Their Theory Q
Q Typical Uncertainty of flow and Application, Sixth Edition, nozzle - used for 1971 Assumption 5.1.11 (Table included as Att. 2) 6.18 ANSI/ASME PTC-6 Report 1985, Q
Q Typical Uncertainty of Guidance for Evaluation of uncalibrated flow sections -
Measurement Uncertainty in used for Assumption 5.1.11 Performance Tests of Steam (Table included as Att. 3)
Turbines 6.19 TDDATA NEDC 32805P 1
Fermi 2 Process Computer Reactor Q
Heat Balance Equation, (DECO File No.
Heat Balance Review conversion constant for R1-7306)
BTU to MW-hr, radiative heat loss value, moisture fraction 6.20 NUREG/CR-3659 A Mathematical Model for Q
Q Uncertainty Methodology Assessing the Uncertainties of (applicable pages included Instrumentation Measurements for as Attachment 4)
Power and Flow for PWR Reactors 6.21 TDDATA 218098 1
Induction Motor for Nuclear Q
RR pump motor efficiency (DECO File No.
Reactor Water Recirculating Pump vs. loading - used for C1-7119)
Assumption 5.1.3 6.22 TMINSL GEK 73527A
--- GEK 73527A Q
Q States which steam table is used for manual calculation
- used for input 4.5 6.23 TDDBD Cl 1-00 C
Control Rod Drive Hydraulics Q
Information on CRD flow System 6.24 TDDBD B31-00 B
Reactor Recirculation System Q
Q Info on RR system and pumps 6.25 TRVEND 520 2311300 06A 2
IPCS - Detailed Design Manual Q
Q Formulas and inputs for the (DECO File No.
Appendix A NSSS CTP calculation M14-884) 6.26 TRVEND MURFTRT0100 0
Project Task Report Detroit Edison Q Q
Proposed MUR CTP Fermi-2 Thermal Power variable inputs Optimization Task TO 100: Reactor Heat Balance
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 16 of 50 DOCUMENT INTERFACE
SUMMARY
Ref DTC DSN or Rev Title Ref In Out How document is used Document Type put put in calculation 6.27 TRVEND ER 157PA 8
Supplement to Caldon Topical Q
Q (and Rev. 8 Report ER-80P: Basis for Power Errata)
Uprates with an LEFM Check or (DECO File No.
an LEFM CheckPlus System C1-7303) 6.28 TMINSL VMC1-510 0
LEFM CheckPlus C User's Manual L
Q 6.29 TRVEND SD 36238 983 01 3
Leading Edge Flow Meter (LEFM)
Q L and Integrated Plant Computer System (IPCS) Interface
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 17 of 50 7.0 Calculation Details 7.1.
Evaluation of the Enthalpy Uncertainties. The equations in section 3.6 are used to calculate enthalpy uncertainty to a 2Q level. The largest error in steam dome pressure from Table 4.7-1 is applied for the pressure uncertainty, so the results are conservative for both manual and IPCS uncertainties. In each enthalpy uncertainty detennination, the uncertainty of reading enthalpy from the steam table (Ref. 6.7) is 10.1% = + 0.001 per Input 4.5.
7.1.1.
Saturated Steam and Water Enthalpy Error The rated dome pressure for the heat balance calculation is 1045.0 psia, which has a saturation temperature of 550.02 OF (Ref. 6.7). Per section 5.1.5 a f10F variation is used to determine the variation in steam and water enthalpies with pressure. The temperatures that bound this value (549.02 OF and 551.02 °F) are used to determine the corresponding pressures at saturation per Ref. 6.7, and to establish the change in saturation steam enthalpy, hg, and saturated water enthalpy, hf, relative to the change in temperature.
Saturated Steam Enthalpy (BTU/lbm)
T P 1036.5 1045.0 1053.5 549.02 F 1192.0 550.02 F 1191.7 551.02 F 1191.3 Using Equation 3.6-3:
BTU 2
I(1192.0 -1191.3) lbTU 189s BTU 2 hg (1036.5-1053.5)psia 1.*(2*
)
+0.001*1191.7 lbm BTU Oh = +1.522 hg b
Saturated Water Enthalpy (BTU/lbm)
T P
1036.5 1045.0 1053.5 549.02 F 548.59 550.02 F 549.87 551.02 F 551.15 Using Equation 3.6-4:
BTU 2
(548.59 - 551.15) lbm 18.9 psi
/
BTU 2 ohf
- (2 *
)
+ (0.001 *549.87 hf (1036.5-1053.5)psia 1.645
\\l.
bm BTU ohf =*3.504 lbm
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 18 of 50 7.1.2.
RWCU Suction Enthalpy Error The conditions used in the heat balance to describe the RWCU suction enthalpy, hCU1, are a nominal pressure of 1045 psia and a rated temperature of 533.8 °F. Per Sections 5.1.6 and 5.1.7, a +/-5 °F temperature variation and a +/- 30 psi pressure variation are used to determine the variation of liquid enthalpy with temperature and pressure. Reference 6.7 is used to develop the entries in the following table to calculate the uncertainty in the enthalpy for the RWCU suction.
RWCU Suction Enthalpy (BTU/lbm)
T P
1015.0 1045.0 1075.0 528.80 F 522.94 533.80 F 529.22 529.17 529.12 538.80 OF 535.47 Using Equation 3.6-7:
2 2
(535.47-522.94) BTU (529.12-529.22) BTU 18.9__
lbm *(10 F)
+
lbm *(2*18.psi (538.80-528.80)"F (1075.0-1015.0)psia 1.645 hCU1
+0.001*529.17 BTU\\ 2 lbm /
oU
=
12.541 BTU hCU1 ibm
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 19 of 50 7.1.3.
RWCU Discharge Enthalpy Error The conditions used in the heat balance to describe the RWCU discharge enthalpy, hCU2, are a nominal pressure of 1045 psia and a rated temperature of 435.9 OF. Per Sections 5.1.6 and 5.1.7, a +/-5 OF temperature variation and a +/-30 psi pressure variation are used to determine the variation of liquid enthalpy with temperature and pressure. Reference 6.7 will be used to develop the entries in the following table to calculate the uncertainty in the enthalpy for the RWCU discharge.
RWCU Discharge Enthalpy (BTU/lbm)
T P
1015.0 1045.0 1075.0 430.9 OF 409.71 435.9 F 415.18 415.20 415.23 440.9 OF 420.72 Using Equation 3.6-8:
(420.72-409.71) BTU 2
(415.23-415.18) BTU 2
2 lbm *(10F)
+
lbm *(2* 18.9 psi)
+/0001*41520 BTU hCU2 (440.9-430.9 ) F (1075-1015 ) psia 1.645 lbm hCU2=
11.018 hCU2 Ibm
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 20 of 50 7.1.4.
Feedwater Enthalpy Error The conditions used in the heat balance to describe the feedwater enthalpy, hFW, are a nominal pressure of 1045 psia and a rated temperature of 426.5 °F. Per Sections 5.1.6 and 5.1.7, a +/- 5 °F temperature variation and a +/- 30 psi pressure variation are used to determine the variation of liquid enthalpy with temperature and pressure. Reference 6.7 will be used to develop the entries in the following table to calculate the uncertainty in the enthalpy for Feedwater, hFW.
Feedwater Enthalpy (BTU/lbm)
T P
1015.0 1045.0 1075.0 421.5 F 399.44 426.5 OF 404.87 404.89 404.92 431.5 OF 410.37 Using Equation 3.6-6, for LEFM fully functional:
2 2
(399.44-410.37) BTU (404.92-404.87) BTU 2
Ibm *(0.55*F)
+
Ibm *(2*18.9psi)
+ 0.001*404.89B (421.5-431.5)*F (1075-1015)psia 1.645 lbm hFW=
0.725 Bbm Using Equation 3.6-6, for LEFM in Maintenance Mode:
(399.44 410.37) BTU 2
(404.92-404.87) BTU 2
2
/
44 lbm *(0.58*F)
+
Ibm *(2*18.9psi)
+ 0.001*404. 89 BT hFW (421.5-431.5) iF (1075-1015)psia 1.645 Ibm hFW=* 0.752 Bbm
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 21 of 50 7.1.5.
CRD Enthalpy Error The conditions used in the heat balance to describe the CRD system water enthalpy, hCR, are a nominal pressure of 1045 psia and a temperature of 100.0°F. Per Sections 5.1.6 and 5.1.7, a
+/- 5F temperature variation and a +/- 30 psi pressure variation are used to detennine the variation of liquid enthalpy with temperature and pressure. Reference 6.7 will be used to develop the entries in the following table to calculate the uncertainty in the enthalpy for the CRD water.
CRD System Water Enthalpy (BTU/lbm)
T P
1015.0 1045.0 1075.0 95.0 F 65.861 100.0 OF 70.755 70.834 70.913 105.0 F 75.808 Using Equation 3.6-5:
BTU 2
BTU 2
(75.808 - 65.861) lbm(70.913
-70.755)
(10 F)18 2)
(105.0 -95.0) °F (1075-1015)psia 1.645 hCR BU2
+ 0.001 *70.834 BTU lbm BTU hCR =
9.4 lbm
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 22 of 50 7.2. Feedwater Flow Energy Uncertainty 7.2.1.
IPCS Calculation, with LEFM CheckPlus Fully Functional Recalling Equation 3.2-4, which represents the feedwater flow energy:
QFW = WFW*(hg*(1 - FM) + hf*FM - hFW)
Taking the partial derivatives with respect to the individual terms, to show the effect with respect to CTP:
aCTP = hg*(1 - FM) + hf*FM - hFW aCTP = WFW *(1 - FM) aWFW ahg aCTP = WFW
- FM aCTP = -WFW ahf ahFW Based on Equation 3.5-3, the uncertainty in core thennal power due to uncertainty in feedwater flow energy (UFW) is:
UFW =
[(aCTP *U WFW)2 + (
hCTP
- O hg) 2 + ( aCTP *a 1f)2 +/- (aCTP
- J hFW)2 1/2 aWFW ahg ahf ahFW Substituting the partial derivatives from above:
UFW = [((hg*(1 - FM) - hf*FM - hFW)* U WFW) 2 + ((WFW*(1 - FM))
- Q hg) 2
+ (WFW*FM
- U hf)2 + (- WFW
- hFw)2 1/2 Equation 7.2-1 Solving Equation 7.2-1 will determine the contribution of the uncertainty in the feedwater flow energy to the overall core thermal power uncertainty.
Input values from Table 4.6-1:
hg
= 1191.7 BTU/lbm hf
= 549.87 BTU/lbm FM
= 0.001 at dryer exit hFW
= 404.89 BTU/lbm WFW = 15.111 Mlbm/hr Uncertainties from Table 4.7-1:
UWFW (i 0.28 %)*(15.111 Mlbm/hr)= 0.0423 Mlbm/hr [2a]
aig
= +/- 1.522 BTU/lbm [2Q]
ohf
=
3.504 BTU/lbm [20]
o sw
=
0.725 BTU/lbm [2a] (LEFM fully functional)
Using these values to solve Equation 7.2-1:
UFW = {[((1191.7 BTU/lbm)*(1 - 0.001) - (549.87 BTU/lbm)*0.001
- (404.89 BTU/lbm))*( 0.0423 Mlbm/hr)]
2
+ ((15.111 Mlbm/hr)*(1 - 0.001) * (1.522 BTU/lbm))
2
+ ((15.111 Mlbm/hr)*0.001*(3.504 BTU/lbm)) 2
+ ((-15.111 Mlbm/hr)* (0.725 BTU/lbm)) 2 1/2 UFW = E 41.842 MBTU/hr Converting to MWt, with the conversion factor from Input 4.2:
UF
= (+ 41.842 MBTU/hr) / (3.413 MBTU/MWt-hr) = +/- 12.260 MWt
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 23 of 50 No Moisture Carryover Case The case will be run with FM = 0 (no moisture carryover) to demonstrate which case is the most conservative. For FM = 0, Equation 3.2-4 reduces to:
QFW = WFW*(hg - hFW)
The partial derivatives with respect to the individual tenns reduce to:
BCTP = hg - hFW DCTP = WFW BCTP = - WFW BWFW ahg ahFW Based on Equation 3.5-3, the uncertainty in core thermal power due to uncertainty in feedwater flow energy (UFW) is:
UFW =
[(8CTP *u WFW) 2 + (aCTP
- U hg) 2 + (CTP
- U 11FW)2 1/2 BWFW ahg ahFW Substituting the partial derivatives from above:
UFW = [((hg - hFW)* Q WFW) 2 + ((WFW
- a hg) 2 + (-WFW
- LFW) 2 1/2 Equation 7.2-la Solving Equation 7.2-1 a will determine the contribution of the uncertainty in the feedwater flow energy to the overall core thermal power uncertainty, for the case of no moisture carryover.
Input values from Table 4.6-1:
hg
= 1191.7 BTU/lbm hFW
= 404.89 BTU/lbm WFW = 15.111 Mlbm/hr Uncertainties from Table 4.7-1:
QWFW
= (E 0.28 %)*(15.111 Mlbm/hr) = 0.0423 Mlbm/hr [2v]
o+g
=
1.522 BTU/lbm [2Q]
ahFW
= E 0.725 BTU/lbm [2Q] (LEFM fully functional)
Using the values from above to solve Equation 7.2-la:
UFW = [((1191.7 - 404.89) BTU/lbm*(0.0423 Mlbn/hr)) 2
+ ((15.111 Mlbm/hr)*(1.522 BTU/lbm)) 2 + ((-15.111 Mlbm/hr)*(0.725 BTU/lbm))2 1/2 UFW = + 41.913 MBTU/hr Converting to MWt, with the conversion factor from Input 4.2:
UFW = (E 41.913 MBTU/hr) / (3.413 MBTU/MWt-hr) = +/- 12.280 MWt Comparison of these values to those above for FM = 0.001 at the steam dryer outlet, shows that a slightly higher uncertainty is calculated for the case of no moisture carryover. Inclusion of the moisture carryover term reduces the total calculated uncertainty, because the uncertainty is higher when the full effect of the steam enthalpy term (1191.7 BTU/lbm) is not reduced by the influence of the water enthalpy from the moisture carryover.
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 24 of 50 7.2.2.
IPCS Calculation, with LEFM CheckPlus in Maintenance Mode When in Maintenance mode, per Table 4.7-1 the LEFM feedwater flow accuracy is +/-0.51% of nominal.
Thus the input values to solve Equation 7.2-la are:
Input values from Table 4.6-1:
hg
= 1191.7 BTU/lbm hFW
= 404.89 BTU/lbm WFW = 15.111 Mlbm/hr Uncertainties from Table 4.7-1:
QWFW (i 0.51 %)*(15.111 Mlbm/hr) = 0.0771 Mlbm/hr [26]
o g
=
1.522 BTU/lbm [2Q]
-hFW
= E 0.752 BTU/lbm [26] (LEFM in Maintenance Mode)
Solving Equation 7.2-la:
UFW = [((1191.7 - 404.89) BTU/lbm*(0.0771 Mlbm/hr)) 2
+ ((15.111 Mlbm/hr)*(1.522 BTU/lbm)) 2
+ ((-15.111 Mlbm/hr)*(0.752 BTU/lbm)) 2 ]1/2 UFW = +/- 65.864 MBTU/hr Converting to MWt, with the conversion factor from Input 4.2:
UFW = (+ 65.864 MBTU/hr) / (3.413 MBTU/MWt-hr) = +/- 19.298 MWt
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 25 of 50 7.3.
Control Rod Drive Flow Energy Uncertainty Recalling Equation 3.2-5, which represents the CRD flow energy, and setting FM=0 to obtain the most conservative (largest) uncertainty:
QCR = WCR*(hg - hCR)
Taking the partial derivatives with respect to the individual terms, to show the effect with respect to CTP:
aCTP = hg - hCR aCTP = WCR aCTP = - WCR aWCR ahg ahCR Based on Equation 3.5-3, the uncertainty in core thermal power due to uncertainty in CRD flow energy (UCR) is:
UcR =
[(OCTP *o WCR)2 (aCTP
- h 11g)2 + (OCTP *0 hCR)2 1/2 BWCR ahg ahCR Substituting the partial derivatives from above:
UCR = [((hg - hCR)*
WCR) 2 + (WCR
- O hg) 2 + (- WCR
- 1,CR) 2 1/2 Equation 7.3-1 Solving Equation 7.3-1 will determine the contribution of the uncertainty in the CRD flow energy to the overall core thermal power uncertainty.
Input values from Table 4.6-1:
hg
= 1191.7 BTU/lbm hCR = 70.834 BTU/lbm WCR = 0.032 Mlbm/hr Uncertainties from Table 4.7-1:
=WCR E 0.0025 Mlbm/hr [26] (IPCS indication)
QWCR =
0.0029 Mlbm/hr [20] (manual indication) o
= + 1.522 BTU/lbm [2Q]
O'hCR
= E 9.947 BTU/lbm [2a]
Using these values to solve Equation 7.3-1, for IPCS indication:
UCR = [((1191.7 - 70.834) BTU/lbm*(0.0025 Mlbm/hr)) 2
+ ((0.032 Mlbm/hr)*(1.522 BTU/lbm)) 2 + ((-0.032 Mlbm/hr)*(9.947 BTU/lbm))2 11/2 UCR = E 2.8 2 1 MBTU/hr Converting to MWt, with the conversion factor from Input 4.2:
UCR = (E 2.821 MBTU/hr) / (3.413 MBTU/MWt-hr) = +/- 0.827 MWt Using these values to solve Equation 7.3-1, for manual indication:
UCR =
[((1191.7 - 70.834) BTU/lbm*(0.0029 Mlbm/hr)) 2
+ ((0.032 Mlbm/hr)*(1.522 BTU/lbm)) 2 + ((-0.032 Mlbm/hr)*(9.947 BTU/lbm))2 11/2 UCR =
3.266 MBTU/hr
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 26 of 50 Converting to MWt, with the conversion factor from Input 4.2:
UCR = (E 3.266 MBTU/hr) / (3.413 MBTU/MWt-hr) = + 0.957 MWt 7.4. Reactor Water Clean Up Flow Energy Uncertainty Recalling Equation 3.2-6, which represents the RWCU flow energy:
Qcu = WCU*(hCUl - hCU2)
Taking the partial derivatives with respect to the individual terns, to show the effect with respect to CTP:
OCTP = (hCU1 - hCU2) aCTP = WCU BCTP = - WCU aWCU hCUl ahCU2 Based on Equation 3.5-3, the uncertainty in core thermal power due to uncertainty in RWCU flow energy (Ucu) is:
Ucu =
[( DCTP
- a wcu) 2 + ( BCTP
- O hcul) 2 + ( aCTP *U hcu2)2 112 aWCU ahCU1 ahCU2 Substituting the partial derivatives from above:
Ucu = [((hCU1 - hCU2)* a wcu) 2 + (WCU* O hcui) 2 + (- WCU
- O hcu2) 2 1/2 Equation 7.4-1 Solving Equation 7.4-1 will determine the contribution of the uncertainty in the RWCU flow energy to the overall core thermal power uncertainty.
Input values from Table 4.6-1:
hCU1
= 529.17 BTU/lbm hCU2
= 415.20 BTU/lbm WCU = 0.133 Mlbm/hr Uncertainties from Table 4.7-1:
awcu
=* 0.0022 Mlbm/hr [2a] (IPCS calculation) a wcu
=* 0.0056 Mlbm/hr [2a] (manual calculation) alcui
=
- 12.541 BTU/lbm [2a]
ahcu2
=
- 11.018 BTU/lbm [2a]
Using these values to solve Equation 7.4-1, for IPCS calculation:
Ucu = [((529.17 - 415.20 BTU/lbm)*(0.0022 Mlbm/hr)) 2
+ ((0.133 Mlbm/hr)*(12.541 BTU/lbm)) 2 + ((-0.133 Mlbm/hr)*(11.018 BTU/lbm))2 11/2 Ucu =
- 2.234 MBTU/hr Converting to MWt, with the conversion factor from Input 4.2:
Ucu = (+ 2.234 MBTU/hr) / (3.413 MBTU/MWt-hr) = + 0.655 MWt
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 27 of 50 Using these values to solve Equation 7.4-1, for manual calculation:
UcU = [((529.17 - 415.20 BTU/lbm)*(0.0056 Mlbm/hr)) 2
+ ((0.133 Mlbm/hr)*(12.541 BTU/lbm)) 2 + ((-0.133 Mlbm/lr)*(11.018 BTU/lbm)) 2 ]12 UcU =
2.310 MBTU/hr Converting to MWt, with the conversion factor from Input 4.2:
UcU = (+/- 2.310 MBTU/hr) / (3.413 MBTU/MWt-hr) = t 0.677 MWt
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 28 of 50 7.5. Radiated Heat Uncertainty The radiated and other heat losses in Table 4.6-1are a constant of 2.1 MWt, which per Ref. 6.3, is based on 1.1 MWt radiated heat loss and 1.0 MWt heat loss to recirculation pump seal purge flow.
Because CTP varies directly with QRAD, the partial derivative of CTP with respect to QRAD is 1:
aCTP
=1 aQRAD Based on Equation 3.5-3, the uncertainty in core thermal power due to radiated and other thermal losses (UQRAD) is:
UQRAD = [( aCTP
- O QRAD) 2 1/2 8QRAD Per Table 4.7-1, the uncertainty associated with this heat loss is conservatively taken as +/-10 %
oQRAD =
10% * (2.1 MWt)=
0.21 MWt Substituting the values from above:
URAD= [((1
- 0.21 MWt)2 11/2 = g 0.21 MWt
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 29 of 50 7.6.
Reactor Recirculation (RR) Pump Heat Uncertainty As described in Section 3.3, the energy input to the reactor coolant 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 (ETA).
QP = QPELEC
- ETA Taking the partial derivatives with respect to the individual terms, to show the effect with respect to CTP:
aCTP = QPELEC CTP = ETA aETA aQP Based on Equation 3.5-3, the uncertainty in core thermal power due to RR Pump energy uncertainty (URCP) is:
URCP = [(aCTP
- U ETA)2 + (CTP
- 0 QP)l 112 aETA 8QP Substituting the partial derivatives from above:
UCU = [(QPELEC
- U ETA) 2 + (ETA
- U QPELEC) 2] 1/2 Equation 7.6-1 Solving Equation 7.6-1 will determine the contribution of the RR pump energy uncertainty to the overall core thermal power uncertainty.
Input values from Table 4.6-1:
QPELEC = 11.185 MWe (combined, for both pumps)
ETA
95.2% = 0.952 Uncertainties from Table 4.7-1: UQPELEC = E 10% (11.185 MW)
1.119 MWe [2U]
UETA=
1%=+ 0.01 2U]
Using these values to solve Equation 7.6-1:
URCP = [((11.185 MWe)*0.01)2 + (0.952 *(1.119 MWe))2] 1 2 URCP=
1.071 MWe =
1.071 MWt
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 30 of 50 7.7.
The total CTP Uncertainty is the combination of the individual uncertainties calculated in Sections 7.2 through 7.6 above. Because the individual uncertainties are independent, they are combined via the square root sum of the squares.
UCTP = (UFW 2 + UCR 2 + UCU 2 + UQRAD 2 + URCP 2) 1/2 Fully Functional LEFM CheckPlus, IPCS Calculation Substituting in the uncertainty values from Sections 7.2.1, and 7.3 through 7.6:
UCTP = ((12.280 MWt)2 + (0.827 MWt)2 + (0.655 MWt)2 + (0.21 MWt)2 + (1.071 MWt)2)1/2 UCTP = +/- 12.373 MWt In terms of percent of current licensed thermal power (CLTP) at 3430 MWt (Input 4.1):
PCLTP = (E 12.373 MWt) / 3430 MWt PCLTP = E 0.361 % CLTP In tenns of percent of MUR rated core thermal power (CTP), at 3486 MWt (Input 4.1):
PMUR CTP = (E 12.373 MWt) / 3486 MWt P MUR CTP = + 0.355 % MUR CTP Maintenance Mode LEFM CheckPlus, IPCS Calculation Substituting in the uncertainty values from Sections 7.2.2, and 7.3 through 7.6:
UCTP = ((19.298 MWt)2 + (0.827 MWt)2 + (0.655 MWt)2 + (0.21 MWt)2 + (1.071 MWt)2)1 /2 UCTP = N 19.358 MWt In terms of percent of CLTP, at 3430 MWt (Input 4.1):
PCLTP = (i 19.358 MWt) / 3430 MWt PCLTP = E 0.564 % CLTP In terms of percent of MUR CTP, at 3486 MWt (Input 4.1):
P MURCTP = (i 19.358 MWt) / 3486 MWt P MURCTP = E 0.555 % MUR CTP Fully Functional LEFM CheckPlus, Manual Calculation Substituting in the uncertainty values from Sections 7.2.1, and 7.3 through 7.6:
UCTP = ((12.280 MWt)2 + (0.957 MWt)2 + (0.677 MWt)2 + (0.21 MWt) 2 + (1.071 MWt)2)1/2 UCTP = +/- 12.384 MWt In terms of percent of CLTP at 3430 MWt (Input 4.1):
PCLTP = (E 12.384 MWt) / 3430 MWt PCLTP = i 0.3 6 1 % CTP In terms of percent of MUR CTP, at 3486 MWt (Input 4.1):
P MUR CTP = (E 12.384 MWt) / 3486 MWt P MUR CTP = + 0.355 % MUR CTP
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 31 of 50 Maintenance Mode LEFM CheckPlus, Manual Calculation Substituting in the uncertainty values from Sections 7.2.2, and 7.3 through 7.6:
UCTP = ((19.298 MWt)2 + (0.957 MWt)2 + (0.677 MWt)2 + (0.21 MWt)2 + (1.071 MWt)2)112 UCTP = +/- 19.364 MWt In terms of percent of core thermal power, for CTP = 3430 MWt (Input 4.1):
PCLTP = (E 19.364 MWt) / 3430 MWt PCLTP = E 0.5 6 5 % CTP In terms of percent of MUR CTP, at 3486 MWt (Input 4.1):
P MURCTP = (E 19.364 MWt) / 3486 MWt P MUR_CTP = E 0.555 % MUR CTP 8.0 Acceptance Criteria For operation at the proposed MUR CTP (3486 MWt, per Ref. 6.26), this calculation determines the uncertainty associated with the determination of core thermal power for the following four cases:
- 3.
Manual Calculation with LEFM CheckPlus Fully Functional, and
- 4. Manual Calculation with LEFM CheckPlus in Maintenance Mode.
For Case 1 (Core thermal power calculated by IPCS with LEFM CheckPlus Fully Functional), the acceptance criterion is that the proposed MUR CTP (3486 MWt) plus the total positive uncertainty in MWt remains bounded by 1.02% (3499 MWt) of Current Licensed Thermal Power (CLTP, at 3430 MWt).
For the remaining three cases (Core thermal power determined by IPCS with LEFM CheckPlus in Maintenance Mode, Manual Calculation with LEFM CheckPlus Fully Functional, and Manual Calculation with LEFM CheckPlus in Maintenance Mode), there are no specific acceptance criteria.
The uncertainty is determined and simply stated.
APPENDIX A - RWCU FLOW LOOP ERROR CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 32 of 50 The purpose of this Appendix is to deternine the channel instrument error (CIE) in Reactor Water Clean-Up (RWCU) mass flow rate at MUR rated conditions of 3486 MWt for insertion into Table 4.7-1 of the base calculation.
NOTE: References are listed in the main body of the calculation. Paragraph references refer to steps within this Appendix. Section references refer to steps within the main body of the calculation.
Al Reactor Water Clean-Up (RWCU) Flow Loop Configuration The RWCU flow input to the plant computer is addressed in calculation DC-4567 (Ref. 6.9) as Channel 7.
This loop consists of a Rosemount transmitter measuring differential pressure across a flow element. The transmitter provides a 4-20 mA signal to a signal converter/isolator that sends a 10-50 mA signal to the PPC for display in the Control Room. The analyzed instrument loop may be represented as follows:
0-400Comp Pt g -p40 G33N035 0 - 14.9 G33N036 4-20 G33K805 10 - 5 A716 0 -400 m
m G33DF1055 gpm Flow AP Signal Element Transmitter Converter/Isolator Input Module A2 Reactor Water Clean-up (RWCU) Flow Instrument Data and Uncertainty Values Calculation DC-4567 provides the following parameters and uncertainties for the instruments in this flow loop. Page numbers are referenced from DC-4567 where the information is found.
A2.1 Flow Element (G33N035) (page 14 & App. A page 7 of 22):
Full Scale Inlet Flow: 400 gpm dP @ Full Scale Inlet Flow: 146.79 inwc Flow Element Uncertainty (PEA) = + 1% of span = +/- 4 gpm
[20]
A2.2 Transmitter (G33N036):
Rosemount Model 1152DP4E22PB Normal accuracy (page 25): t2AN = +/- 0.468 inwc =
0.638 gpm
[20]
Drift (page 25), adjusted for 25% late interval:
t2DDa = +/- 0.575 inwc = + 0.782 gpm
[20]
From page 42, Calibration Error t2CC = +/- 0.86 gpm
[2Q]
APPENDIX A - RWCU FLOW LOOP ERROR CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 33 of 50 A2.3 Signal Converter/Isolator (G33K805):
TEC Model 156L: 4-20 mA input to 10-50 mA output Normal accuracy (page 31): i2A =
0.195 mA (input scale)
[2a]
Convert to gpm, at full flow of 400 gpm, per Equation 8 on p. 46 of Ref. 6.1:
i2A = (400 gpm)*((1 2 + (0.195 mA/40 mA))112 - 1) i2A =
0.974 gpm
[2v]
Drift (page 31): i2DD = +/- 0.111 mA (input scale)
[2Q]
Convert to gpm, at full flow of 400 gpm, per Equation 8 on p. 46 of Ref. 6.1:
i2DD = (400 gpm)*((1 2 + (0.111 mA/40 mA))11 2 - 1) i2DD =
0.555 gpm
[2Q]
Using the methodology from page 41 and values from page 40:
Calibration equipment effect: i2CX = (xi2 * (i2CLI2 + i2CLO2) 1/2 i2CX = (1 * (0.2752 + 0.3502) 12 i2CX = 0.445 gpm
[3Q]
From page 31: i2ALT = 0.240 mA [3Q]
Convert to gpm, at full flow of 400 gpm, per Equation 8 on p. 46 of Ref. 6.1:
i2ALT = (400 gpm)*((1 2 + (0.240 mA/40 mA))1/2 - 1) i2ALT = 1.198 gpm
[3Q]
Per Ref. 6.1, Calibration Procedure Effect: EP = ALT if ALT > CX, otherwise, EP = CX if ALT < CX. In this case: i2ALT =
1.198 gpm > i2CX =
0.445 gpm.
Therefore since ALT > CX:
i2EP = i2ALT = + 1.198 gpm Calibration Error, i2CC, using the methodology of page 42:
i2CC = (2/3 * (i2CX2 + (i2CX/rt) 2 + i2EP2) 1/2 i2CC = (2/3 * ((0.445 gpm) 2 + (0.445 gpm/2) 2 + (1.198 gpm) 2)1/2 i2CC = + 0.865 gpm [26]
A2.4 I/O card (G33DF1055):
Accuracy (page 36): celA = + 0.5% of span = + 2.0 gpm [2v]
Drift: included in accuracy so celDD = 0 No calibration instrument error, CX, but per page 36, celALT = +/- 3.0 gpm [30]. Thus per the methodology of Ref. 6.1, celEP = celALT =
3.0 gpm Thus total calibration error is:
celCC = 2/3*(celEP) = 2/3*(3.0 gpm) = + 2.0 gpm [2Q]
APPENDIX A - RWCU FLOW LOOP ERROR CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 34 of 50 A3 Reactor Water Clean-up (RWCU) Flow Loop Channel Uncertainties The total uncertainty is the SRSS of the uncertainties due to instrument accuracies, drift, and calibration.
Combining the individual uncertainties:
Channel Accuracy:
LANcel = (t2AN2 + i2A 2 + celA2) 1/2 LANcel = ((0.638 gpm)2 + (0.974 gpm)2 + (2.0 gpm)2) v2 LANcel =+ 2.314 gpm [20]
Channel Drift:
LDcel = (t2DDa2 + i2DD2 + ce1DD 2) 1/2 LDcel = ((0.782 gpm) 2 + (0.555 gpm) 2 + (0)2) 1/2 LDcel = + 0.959 gpm [2a]
Channel Calibration Error:
LCcel = (t2CC2 + i2CC2 + celCC211 2 LCcel = (0.86 gpm)2 + (0.865 gpm) 2 + (2.0 gpm)2) /2 LCcel =+/-2.343 gpm Channel Instrument Error per page 44 methodology, but taken to a 20 confidence level:
CIEcel = (LANce1 2 + LDcel 2 + LCcel 2 + PEA2) 1 2 ClEcel = ((2.314 gpm) 2 + (0.959 gpm)2 + (2.343 gpm)2 + (4 gpm)2) 1/2 CIEcel = + 5.269 gpm to a 20, or 95.5% confidence level The density at the RWCU discharge conditions (from Table 4.6-1) of 435.9 °F and 1045 psia (52.363 lbm/ft3, from Attachment 1) is used to convert this to terms of Mlbm/hr for inclusion in the CPT determination:
ClEcel = (+/- 5.269 gpm) * (52.363 lbm/ft3) * (1 ft3/7.480519 gal) * (60 min/hr)
CIEcel= + 2213 lbm/hr = t 0.0022 Mlbm/hr This value is entered into the Table 4.7-1 of the base calculation as the uncertainty of the RWCU Flow Rate when using the TPCS input based on G33CF6004/G33DF1055.
APPENDIX B - CRD FLOW LOOP ERROR CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 35 of 50 The purpose of this appendix is to calculate the uncertainty in the measurement of Control Rod Drive (CRD) mass flow at MUR rated conditions of 3486 MWt for input to the Table 4.7-1 of the base calculation.
NOTE: References are listed in the main body of the calculation. Paragraph references refer to steps within this Appendix. Section references refer to steps within the main body of the calculation.
B1 CRD Flow Loop Configuration (Reference Calculation DC-5924 Rev. E, Ref. 6.10)
The instrument loop consists of a differential pressure transmitter tapped across a flow element.
The transmitter provides a 4-20 mA output to a computer input card. The loop is shown as:
Computer Point Flow Element Flow C11DF1052 Cl 1N003 Transmitter C 1N004 Indicator C11R800 Per Ref. 6.25 Section 4.2.2, the IPCS converts the volumetric flow input to point C11DF1052 to mass flow read at point C11CF6001.
The loop components evaluated in this document, the applicable perfonnance specifications and process parameter data are as follows:
B2 CRD Flow Instrument Data and Uncertainty Values Calculation DC-5924 provides the following parameters and uncertainties for the instruments in this flow loop. Page numbers are referenced from DC-5924 where the information is found.
B2.1 Flow Element (C11N003) (Design Basis Document C11-00 Rev. B Section 4.1.3.3.3, p.
4-25 & 4-26):
Maximum differential pressure: 200 inwc at 100 gpm (p. 2 & p. 9)
Flow Element Uncertainty (PEA) =
5 % of span = t 5 gpm [2Q] (Sect. 5.1.11)
B2.2 Transmitter (C1 1N004):
Rosemount Model 3051S1CD2A2F12A1AB2 (p. 13)
Calculation DC-5924 page 14 states the following uncertainties:
Accuracy VA = + 0.400 inwc [3u]
Convert to gpm, at full flow of 100 gpm, per Equation 8 on p. 46 of Ref. 6.1 and take at 2Q:
tAN = VA*(2/3) 0.400 inwc)*(2/3) = +/-0.267 inwc tAN = (100 gpm)*((1 2 + (0.267 inwc/200 inwc))/ 2 - 1) tAN = 0.067 gpm [2a]
Drift DD1 = +/- 1.764 inwc [2Q]
Convert to gpm, at full flow of 100 gpm, per Equation 8 on p. 46 of Ref. 6.1:
APPENDIX B - CRD FLOW LOOP ERROR CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 36 of 50 tDD = (100 gpm)*((1 2 + (1.764 inwc/200 inwc))'/ 2 - 1) tDD = +/- 0.440 gpm
[2o]
Calculation DC-5924 page 26 recommends that this transmitter be calibrated with a pressure gauge of accuracy +/- 0.15%, and a DMM of accuracy +/-0.05 mA, or better.
Taking the error at the maximum 200 inwc, for a 0.15% accuracy, per the method on p.
29 of Ref. 6.1:
Calibration equipment effect: tCX = (tCLI2 + tCLO2) 1/2 tCX = (((0.15%*(200 inwc)*(16 mA/200 inwc)) 2 + (0.05 mA) 2)1/2 tCX = +/-0.055 mA
[3v]
Convert to gpm, at full flow of 100 gpm, per Equation 8 on p. 46 of Ref. 6.1:
tCX = (100 gpm)*((1 2 + (0.055 mA/16 mA))v 2 - 1) tCX = +/- 0.172 gpm
[3a]
From page 14: tALT = 0.400 inwc [3a]
Convert to gpm, at full flow of 100 gpm, per Equation 8, p. 46 of Ref. 6.1:
tALT = (100 gpm)*((1 2 + (0.400 inwc/200 inwc)1 /2 - 1) tALT = 0.10 gpm
[3a]
Per Ref. 6.1, Calibration Procedure Effect: EP = ALT if ALT > CX, otherwise, EP = CX if ALT < CX. In this case: tALT = +/- 0.10 gpm < tCX = +/- 0.172 gpm. Thus, tEP = tCX
=
0.172 gpm Calibration Error, tCC, per p. 30 of Ref. 6.1:
tCC = (2/3 * (tCX2 + (tCX/rt)2 + tEP2) 12 tCC = (2/3 * ((0.172 gpmn) 2 + (0.172 gpm/2)2 + (0.172 gpm) 2) 12 tCC = +/-0.172 gpm
[2Q]
B2.3 I/O card (C11-DF1052 with Resistor C11AR4A) (Refer to DC-5924 Page 15):
Accuracy: ceA =
0.5 % of span =
1.000 inwc [2Q]
Convert to gpm, at full flow of 100 gpm, per Equation 8, p. 46 of Ref. 6.1:
ceA= (100 gpm)*((1 2 + (1.000 inwc/200 inwe))1 2 - 1) ceA = 0.250 gpm [2Q]
Drift: included in accuracy so celDD = 0 No calibration instrument error, CX, but per page 15, ceALT = +/-1.500 inwc [30].
Therefore since ALT > CX:
ceEP = ceALT = +/- 1.500 inwc [3a]
Thus total calibration error is: ceCC = 2/3*(ceEP) = 2/3*(1.5 inwc)=
1.0 inwc Convert to gpm, at full flow of 100 gpm:
ceCC = (100 gpm)*((1 2 + (1.0 inwc/200 inwc))/ 2 - 1) ceCC = 0.250 gpm
[2a]
APPENDIX B - CRD FLOW LOOP ERROR ICALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 37 of 50 B2.4 CRD Indicator (Cl1R800)(Refer to DC-5924 Page 17):
Accuracy: i2A =
2% of span =
2.000 gpm [2c]
Drift: included in accuracy so i2DD = 0 No calibration instrument error, CX, but per page 17, ALT4 = +/-3.000 gpm [3Q]
Therefore since ALT > CX: i2EP = ALT4 = t 3.000 gpm
[36]
Thus total calibration error is:
i2CC = 2/3*(i2EP) = 2/3*(3.000 gpm)=
2.000 gpm [26]
B3 CRD IPCS Flow Loop Channel Uncertainties The total uncertainty is the SRSS of the uncertainties due to instrument accuracies, drift, and calibration. Combining the individual uncertainties:
Channel Accuracy:
LANce = (tAN2 + ceA 2) 1/2 LANce = ((0.067 gpm)2 + (0.250 gpm)2) 1/2 LANce =
0.259 gpm [2c]
Channel Drift: LDee = tDD =
0.440 gpm
[2o]
Channel Calibration Error: LCce = (tCC2 + ceCC 2) 1/2 LCce = ((0.172 gpm)2 + (0.250 gpm)2) 1/2 LCce = + 0.303 gpm
[2c]
Channel Instrument Error CIEce = (LANce 2 + LDce2 + LCce2 + PEA2) 112 CIEce = ((0.259 gpm) 2 + (0.440 gpm) 2 + (0.303 gpm) 2 + (5.0 gpm) 2) 12 CIEce =
5.035 gpm to a 2c, or 95.5% confidence level The density (from Attachment 1) at the rated conditions of 100.0°F and 1045 psia (62.188 lbm/ft3) is used to convert this to terms of Mlbm/hr for inclusion in the CPT determination:
CIEce = (+ 5.035 gpm) * (62.188 lbm/ft3) * (1 ft3/7.480519 gal) * (60 min/hr)
CIEce = +/-2511 lbm/hr =
0.0025 Mlbm/hr This value is entered into the Table 4.7-1 of the base calculation as the uncertainty of the CRD Flow Rate when using the TPCS input based on Cl1CF6001/Cl1DF1052.
APPENDIX B - CRD FLOW LOOP ERROR CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 38 of 50 B4 CRD Indicator Flow Loop Channel Uncertainties The total uncertainty is the SRSS of the uncertainties due to instrument accuracies, drift, and calibration. Combining the individual uncertainties:
Channel Accuracy:
LANi = (tAN2 + i2A2) 1/2 LANi = ((0.067 gpm) 2 + (2.000 gpm) 2) /2 LANi=+ 2.001 gpm
[2Q]
Channel Drift: LDi= tDD = t 0.440 gpm
[2Q]
Channel Calibration Error: LCi= (tCC 2 + i2CC2) 12 LCi = ((0.172 gpm) 2 + (2.000 gpm) 2)1/2 LCi = + 2.007 gpm
[2u]
Channel Instrument Error CIEi= (LANi2 + LDi 2 + LCi2 + PEA2) '2 CIEi= ((2.001 gpm) 2 + (0.440 gpm) 2 + (2.007 gpm) 2 + (5.0 gpm) 2) 1/2 CIEi = + 5.764 gpm to a 2Q, or 95.5% confidence level The density (from Attachment 1) at the rated conditions of 100.0°F and 1045 psia (62.188 lbm/ft3) is used to convert this to terms of Mlbm/hr for inclusion in the CPT determination:
CIEi = (+/- 5.764 gpm) * (62.188 lbm/ft3) * (1 ft3/7.480519 gal) * (60 min/hr)
CIEi = +/- 2875 lbm/hr = +/- 0.0029 Mlbm/hr This value is entered into the Table 4.7-1 of the base calculation as the uncertainty of the CRD Flow Rate when using the indicator input.
ATTACHMENT 1 NIST Data on Thermophysical Properties of Water CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 39 of 50 NIST Data on Thermophysical Properties of Water Isothermal and Isobaric Properties of Water Temperature (F)
Pressure Density Specific Volume Enthalpy Phase (psia)
(lbm/ft)
(ft3/lbm)
(Btu/lbm)
Isothermal 533.80 1015.0 47.044 0.021257 529.22 liquid 533.80 1045.0 47.065 0.021247 529.17 liquid 533.80 1075.0 47.086 0.021238 529.12 liquid 435.9 1015.0 52.352 0.019102 415.18 liquid 435.9 1045.0 52.363 0.019097 415.20 liquid 435.9 1075.0 52.375 0.019093 415.23 liquid 426.5 1015.0 52.775 0.018949 404.87 liquid 426.5 1045.0 52.786 0.018945 404.89 liquid 426.5 1075.0 52.796 0.018941 404.92 liquid 100.00 1015.0 62.182 0.016082 70.755 liquid 100.00 1045.0 62.188 0.016080 70.834 liquid 100.00 1075.0 62.193 0.016079 70.913 liquid Isobaric 538.80 1045.0 46.732 0.021398 535.47 liquid 533.80 1045.0 47.065 0.021247 529.17 liquid 528.80 1045.0 47.390 0.021102 522.94 liquid 440.90 1045.0 52.134 0.019181 420.72 liquid 435.90 1045.0 52.363 0.019097 415.20 liquid 431.50 1045.0 52.562 0.019025 410.37 liquid 430.90 1045.0 52.589 0.019015 409.71 liquid 426.50 1045.0 52.786 0.018945 404.89 liquid 421.50 1045.0 53.006 0.018866 399.44 liquid 105.00 1045.0 62.122 0.016097 75.808 liquid 100.00 1045.0 62.188 0.016080 70.834 liquid 95.000 1045.0 62.250 0.016064 65.861 liquid Saturated Steam Properties Temperature Pressure Density Specific Volume Enthalpy Phase (F)
(psia)
(lbm/ft3)
(ft3/lbm)
(Btu/lbm) 549.02 1036.5 2.3337 0.42850 1192.0 vapor 550.02 1045.0 2.3553 0.42458 1191.7 vapor 551.02 1053.5 2.3770 0.42070 1191.3 vapor Saturated Water Properties Temperature Pressure Density Specific Volume Enthalpy Phase (F)
(psia)
(lbm/ft3)
(ft3/lbm (Btu/lbm) 549.02 1036.5 46.017 0.021731 548.59 liquid 550.02 1045.0 45.952 0.021762 549.87 liquid 551.02 1053.5 45.887 0.021793 551.15 liquid "Thennophysical Properties of Fluid Systems" by E.W. Lemmon, M.O. McLinden and D.G. Friend in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P.J. Linstrom and W.G. Mallard, National Institute of Standards and Technology, Gaithersburg MD, 20899, http://webbook.nist.gov, (retrieved October 06, 2011).
Table I1-V-1 Tolerances for Discharge Coefficients and Flow Coefficients Primary Element Coefficient from Pipe Size, D Rd or RD Tolerance (per cent)
Square-Edged Concentric Orifices Flange taps Equations (1I-11), (I-I11-2) or Table 114-1-2 D & if D taps Equations 0.20 < (<0.70
+/-1.0 or less D
(11-I-3), (11-111-4)
D > 2.0 in.
Rd j 5000 D 0.11 -#
g 0,20
+/- 2.25 to L
I.0 linearly with #
or Table 11-111-3 0.70
~ 70.75
+/- 1.0 to +/-2.25 linearly with S Vena contracta taps Equatins V..taps only (e c-In
-Sr, (11-U M1-)
0.70 C S 0.80
+/- 1.0 to i 2.5 linearly with #
or Table U1-11-4 1.0 < D < 2.0 in.
As above Above tolerances to be multiplied by a factor of 1 to 2 increasing linearly as D decreases As above 4000 R < 5000 D As above Above tolerances to he multiplied Asaoedby a factor of 1 to 2 increasing 4-o linearly as Rd decreases H
Long-Radius Flow i6zzle Equation (Fig. 11-111-14)
(11-121-12) 2.0 D< 16 in. 104 Rd 7 2.5x 106 0.22 0.8
+/- 2.0 Pipe-wal taps at D & z D or Table 11-111-5 Long-radius Flow Nozzle Calibration (Fig. 11-111-14)
(See Par. HI-IV-6) 2.0 D < 16 in.
Rd 105 0.2 j #
0.5 As determined (or +/- 0.8)
C Taps at 1 D and nozzle throat 1932ISA FlowNozzle Kby Fig. 11-111-23 2
D 7 40 in.
2x 104 RD 10*
0.32<
<0.8 +/-1.0 (Fig. 11-111-22)
Corner taps Venturi Tube Par. --
38 4 < D % 32 in.
2x 10' RD 10 0.3.8< 0.75
+/- 0.75 Rough-cast inlet cone Venturi Tube Par. 1-111-38 2 7 D 10 in.
105 RD 10 0.4 0.5 1.0 Machined inlet cone Venturi Tube Par.
-11138 8
D < 48 in.
2x105 2 Rg22 x00 0.4
'$ 0.7 1.5 Welded sheet metal inlet cone Ecceotric,0rifice Flange taps Fig. 11-111-9 4 < D 4 14 in.
10 RD 10*
0.3 0.3 D
4 in.+/- 1.9 Vena contracta taps D>4in,+/-1.4 Segmental Orifice Flange taps Fig. 11-111-10 4 4 D4 14 in.
10 { RD Z 104 0.35 8
0.85 +/- 2 Vena contracta taps
ATTACHMENT 3 Excerpt from ANSI/ASME PTC-6 ICALCULATION NO. DC-6443 Vol I DCD 1-Revision A PAGE NO. 41 of 50 Excerpt from ANSU/ASME PTC-6
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ATTACHMENT 4 Excerpts from NUREG/CR-3659 CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 42 of 50 Excerpts From NUREG/CR-3659 iG/CR--3659 TI5 008128 A Mathematical Model for Assessing the Uncertainties of Instrumentation Measurements for Power and Flow of PWR Reactors Manuscript Compatd Novombr 1984 Dote Pub shod: Fabru ry 1985 Prepared by G. M. Hanon, W. C. Cif, D, L Sevens PocI NOrthwest taboriatry Rihand, WA932 Prepared for Division of Systens Intgratlon Office of Nuclear Reactor Regulation US. Nuclear Regulatory Commission Washington, DC. 205 NRC FIN B261 DISCLA MER T14 rt m-pou
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ATTACHMENT 4 Excerpts from NUREG/CR-3659 I
CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 43 of 50 EXECITlVE SltiMMARY Neitner the power nor flow of pressurtled water reactors (PWR) are measure directly.
[nstead, values of both are calculated from data of severai other variables which are directly measured, Each of these directly measured variables has an uncertainty in ts value.
An assessrnent model 'as developed which gives the appropriate statistical method of combining the uncertairties in the measured variables to give the uncertainty in the power or flow measureients for use in technial specification input.
While the method is directed toward PWR power and flow determinatIon, it is suitable for generalized application to insttrument measurement uncertainties, The method defines the paramters considered with references tb reactor power and reactor coolant flow, The report next deffrnes the classification of errors, systematic and random, together with a discussion concerning the proper handling of each. The sources of possible errors are provided to all of which must he considpred to ensure that all uncerta intis are included.
Sources of numerical values of the several possible errors are given, A mathematical model is developed by which the numerical values of the measurement errors are comined to give the overall error in the desired parameter. An example calculation using the model is given.
A background section on statistics is provided giving the underlying basis for the model and the statistical Uiplications of the results.
Ix
ATTACHMENT 4 Excerpts from NUREG/CR-3659 ICALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 44 of 50 to be of little use because In th4 field different electrical leads'or different lengths of electrical leads were used, and the system did not perform as expected. When possible, instrument systems should be using the total system from sensing elempent to the final output as shown in. the previous schematic.
- Drift data are usually obtained by prior experience, in observations of how tne measurements of a particular sensor change over time, Instrument drift errors can be reduced through more frequent calibration of the instrumentation and crosscheckts with comparable instruentation, Drift over a specific time interval is obtained by noting the differences between the calibration at the start of the interval and the calibration at the end of the interval.
Orift uncertainty is somewhat difficult to deffne since intermediate values of drift are rarely obtained for the time interval desired; the assu ption that drift is a linear function of time i
sometimes used, which iay not necessarily be valid, The representat iveness of the data is an area f uncertainty.
In many cases, a iocal measurement or temperature, pressure, or flux is used to represent bulk properties associated with a volume or area that is much larger than that sensed by t h sensing element.
The degree of uncertainty in this case may be handled by theory or additional experimental data, An example of poor representativeness would be the use of a point temperature measurement in a thermally stratified fluid, without regard to the thermal stratification.
- Detailed des anal sis can also provide input into an uncertainty analy ne a
nalysis can calculate the effects of the geometrical configurations used, sensing locations, site, and flow blockage introduced, as well as a host of other factors associated with the pnysical and electrical design of a sensing system and the system Into whic the sensing system is placed,
- The data spread about empirical curve fits of correlation data can be used to e3imatThi uncertainty of the empirical correlation value, DEVELOPMENT UF TUE UNCERTAINTY MtETHOD The uncertainty of a quantity is the maximum reasonably expected departure of a measurement from the true value of the quantity, It is necessary to establish a permissible percentage of time during which this error can be exceeded.
For instance, a 95% uncertainty analysis permits up to 5% of the values obtained to exceed the tolerance intervai calculated from the uncertainty analysis, The following discussion develops a systematic model for estimating the uncertainty of a result.
ATTACHMENT 4 Excerpts from NUREG/CR-3659 SCALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 45 of 50 A result, e.g, mass flow rate or poer, is a ailue which has been computed using an equation, the terms of, which are variables, each with an uncertainty in its value.
The following mndel examines how the uncertainties in the variable propagate into the uncertainty in the desired result.
The procedure for calculating the uncertainty in any result will consist of the fol owing two steps:
1, Obtain an estinate of the uncertainty in each of the variables, e.g.
temperature, pressure.
These uncertainty estimates may be calculated using the following model or may simply come from vendor specifications or other sources of uncertainty data listed in the previous section.
- 2.
Combine the uncertainties obtained for each of the variables according to the foll owing model to obtain the total uncertainty in the result 4 This analysis assumes that any vendor-supplied UnCertainties have been evaluated and are valid.
RATHE$ATIp-0F THE MOn1t Generally, the desired result i a function of many variables (xe) g9 mass flow rate, power, That is, Result R 3 f(X,3 3*"
n The change in 4 resulting from changes in the variables (XI's) Would be dR 1 dX1 +
dX 2 ".
dXn
(
Each variable Xy XXi can he either negative or positive. This may be handled statist cally by averaging, <(),
the square of dR.
+ 2 (
ddX XdX
+..
d 4
-d df3>
rXlX-)l2
ATTACHMENT 4 Excerpts from NUREG/CR-3659 CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 46 of 50 For any two ndependent variables X and X, the cross product is zero:
6 R"R dX dXn>
- 0.
That Is, the cross-product germs involvinq independent variables in Eq. (2) are equal to zero and may be deleted from the equation. For those variables that wre dependent (correlated) the cross-product ternis remin. For these dependent varl7bles Schwarz's inequal ty (Parzen 960) shows that aRY' dX dX 4
0
(
where C and a are the square root of the variances of XI and Xip eq.
S(<(dX1 ) )
The term ax is sometimes referred to as the RMS Root Mean Square) value of Xi or tie stan ard deviation of Xi; in either case, It is the square root of the variance of X about X11s ean.
Usi ng Eq. (3) in Eq. (2) results in c(dR2 2R 4j 2
2 +4 2 2
2 2
+ 2 (
I
+
+'
,}
(4) ox kn x e
.}ta where the cross products subscripted with a letter are the cross products of dependent terms.
If all the variables were independent, akl the cross-product terms would be zero, and the variance of the result, a
, would simply equal the sum of the variable variances times their respective coefficients, Or:
2,
)20Z 2 +
4 2O (for independent variables)
I 1
2 X
n n
t5)
ATTACHMENT 4 Excerpts from NUREG/CR-3659 CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 47 of 50 Where some of the Variables are dependent, Eq. (4) may be written:
+
+ '
+
(for independent and dependent variables (6) where the terms subscripted by integers are independent, those subscrited by 1,
, k...
are dependent one to another, and those subscripted by n m,.
are dependent ony to another.
Eq, (6) provides a conservative estimate of the value of the variance of the result:
that is, Eq. (6) will give a value which exceeds or equals the expected vanidnCe of the result.
The RMS value of the result is simply the quare root of the variance or upa(md ) it rrib t side of Eq. {61 1{I?
U The uncertainty in R may now be expressed in terms of toe uncertainty of each of the variables. For instance, both sides of the equation could be multiplied b, giving us a vale of 2
, Assuming that R is normally distributed, a a value infers that toe probability is greater than 9 that the actual vl;a of R lies between the measured ye of R + 2 0 and R4 2 a Many times uncertainty is written as a ratio of the uncertainty, Up of the result to the value of the result, R. That is, from Eq. ()
U~
ux U
12 7 +,,i,
(( ) ( +(
+
(8) where U is the uncertainty in the variable Xi and where the numerical subsroipt5 denote independent variables and letter subscripts denote dependent variables, Unless otherwise specified, it is assumed that UX is equal to (a) By the central limit theorem, the mre variables R is a function of, the more assured we are-that R is normaly distributed, Also, if each of the variables were normally distributed, R would be normally distributed, If some of the variables were normally distrfiuted and some uniformly distributed or if all ware uniformly distributed, the assumpt on of normality of R would be conserva ie for the uncertainty analysis, 12
ATTACHMENT 4 Excerpts from NUREG/CR-3659 jCALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 48 of 50 Many times when differentiation is difficult it is more convenient to numerically calculate the sensitivity coefficient, M/aX 4, by Calculating R+AR from an equation using X1 + Ax, and using the ratio a /AX1 in lieu of 6R/ aX One must be cautious, hwwever, to keep AX1 small so that AR/AX1 represents the local slope of a curve relating R and X1 may also be written lix Some experimentalists prefer the foram of Eq. (9) because the coefficients in front of each variable uncertainty are a measure of the percentage of the a ount that the result would vary for a 1% change in the uncertainty of the
- variable, This is sometires useful in deter mining which variables cause the largest uncertainties in the result, At this point, a value for tlie uncerta nty of a result has been determined.
If conservatism has been bilt into obtaining this result, such as some of the variables being dependent, having uniform density distributions, or simply that conservatye estimates in the uncertainties of the variables were used, no further cormutation may be warranted.
- However, one may wish to impose a confidence limit on the uncertainty value obtained. For instance if the uncertainty ana ysis were performed for the ta value of the reSult, i.e., 95%
tol rance interval, one may also wish to be 95% confident that this tolerance will not be exceeded.
To evaluate tnis confidence limit, one should use the statistics associated with the noncentral t-distribution.
It snould also be noted that the analysis developed in this report assumes that the uncertainties associated with each variable act over a region which can be considered linear.
[f extreely large uncertainties are expected and they occur over strongly nonlinear calibrati n region;, then a Taylor series expansion using higher-or.er terms my be warranted (Golden 1982),
It should also be noted that the model presented is consistent with the International Organization for Standardizati Committee (1981), Kline (1953), and with NUREG/cR-24r, except that the model presented addresses the issue of dependent variables. The model presented uses a conservative form fir evaluating the uncertainties associated with deperdent variables.
A less restrictive rodel should be used only if the joint frequency distribution of dependent variables is known, for which case Eq. (2) could be used directly, 13
ATTACHMENT 4 Excerpts from NUREG/CR-3659 ICALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 49 of 50
- Further, note that the uncertainty of a variable, e.g., temperature.
can be reduced by a factor of 1//r when taking the average of readings from independent sensors, An exarrple of this would be using the mean value of t..tersperature obtained by avraging the te iPeratare obtained frot n sirilar independent sensors, T + T + T3 +
- T From Eq, 5) the uncertainty In Tave Ta would be ae a T(
(
2 +
(
)
TT T +,,'
1 1 T 2 /
Tave Ta IT n
T T2 Tn (1
Since the uncertainty of each similar temperature sensor would be the same, the uncertainty in the average temperature value would be MT ave I
rn Where Uy is the uncertainty associated with any one of the similar temperatbre sensors, Summary of the Uncertainty Method The uncertainty of a result, such as flow rate, may be computed by:
1, estimating the uncertainty of each variable 2
computing the uncertainty of the result from the equation that relates the variables to the result and using the relations given by Eq. (7),
E9.
(S)h or Eq. (9).
Estimating the uncertainties in the variables tay itself require an uncertainty analysis.
That is, the variables may be functions of other parameters; for example enthalpy, which is a variable used in computing power absorbed in a steam generator, is a function of temperature and pressure.
In this case, an uncertainty analysis on the variable, enthalpy, is required to obtain the variable's uncertainty to be used in the uncertainty analysis of the final result--power transferred in a steam generator of a PWR.
14
ATTACHMENT 4 Excerpts from NUREG/CR-3659 CALCULATION NO. DC-6443 Vol I DCD 1 Revision A PAGE NO. 50 of 50 j
Note that the equations formulated for adding variances to obtain the variance of the result are conservative when any of the variables are uniformly distributed. Also conservative is the practice of sumaing the RMS0 values of dependent variables and then squaring this sum to add to the variances of the independent variables.
Representative lists of variables that should te considered are given in Appendix E.
Eanple of the Uncertainty Method Suppose that the uncertainty in the value of the power transferred i a steam generator is desired. For this case the following equation relates power (PA),
to the inlet enthalpy (o), outlet enthalpy (h ), and the pass flow rate through the steam generator ()and the system loss t (0).
PA a (0
- hi)m + 0 (13)
The numerical values fn the exarple are deliherately chosen to represent no particular nuclear reactor or operating condition, The first step in assessing the uncertainty la P is to determine the ?a uncertainty in ho, ip m, and QL For 100% power tie nominal conditions are assumed to be 6
a 1x10 lbm/hr, L - 2x06 Stu/hr Pi 83O psi, Po 830 psi, Ti
- 434*F, To 622,6"F hi 413 Stu/lbn, h
1195 Btu/lba P, *(h
- hi)
+ j t1.1732x10 10 Mtu/hr.
DETERMINING THE 2 UNCERT'iNTIES OF THE VARACLE$
The value of h Is a function of temperature, T, pressure, P, and the accuracy of the steam teble interpolation, I. All parameters may be considered independent and thus Eq. 6) may be used, yielding; 0T2 +
)
op + (gtO I
or 15