ML20101M544

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Combination of Mut Pressure & Level Errors
ML20101M544
Person / Time
Site: Crystal River Duke Energy icon.png
Issue date: 01/17/1996
From: Harrison D
MPR ASSOCIATES, INC.
To:
Shared Package
ML20101M505 List:
References
102075DHH04, 102075DHH04-R00, 102075DHH4, 102075DHH4-R, NUDOCS 9604050436
Download: ML20101M544 (10)
v • d • e


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MPR Associates, Inc.

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MPR Associates,Inc. Page b 320 King Street Alexandria, VA 22314 -

.9 r n Calc 102075DHH04 Preparer: .

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Print page 1 b EVALUATION OF MAKEUP TANK MAXIMUM PRESSURE PURPOSE:

The purpose of this calculation is to evaluate the maximum pressure in the makeup tank as a function of levelin the tank. The expressions are derived in hand calculatiols. (See MPR calculation 102075DHH01, Reference 2.)

CASE COVERED:

This is the nominal reference case with an attemate method of accounting for the effects of instrument errors. This alternate method is detailed in hand calculations. It is a root mean square combination of i:

the pressure and level errors where those errors are weighted by their sensitivity coefficients. It involves  ;

evaluation of the derivative of the allowable pressure vs. level at various values of level to obtain the necessary sensitivity coefficients. ,

I PARAMETERS:

Vapor pressure of water in the makeup tank at 135 F: Psat := 2.5375 b Psat = 365.4 b 2 2 in ft Density of water in the makeup tank at 135 F: P m := 61.4628-Density of water in the BWST at 100 F: p , := 61.9963-l ft Acceleration of gravity: g := 32.17 h 2

sec l Minimumlevelin the BWST: Lmin := 5.0 ft l

Minimum elevation of the surface in the BWST: E, := Lmin + 119.67 ft E, = 124.67 ft Minimum margin between the top of the pipe at the tie-in and i and the gas in the makeup tank: Xm := 2 h l

Elevation of the top of the 6-in pipe nt the tie-in point: Ed := 104.5 ft e 3 in Ed = 104.75 ft

! Minimum elevation of the levelin the pipe from the MUT to the l top of the 6-in pipe at the tie-in point: Ex := Ed + Xm Ex = 106.75 ft Mole ratio of Nitrogen to Hydrogen in the MUT cover gas: y := 0.1 Pipe flow velocity (in the 6-in pipe) at tie-in point: u e := 6.664see --

Gage pressure in the BWST: Psg := -1.0 ft 62.4 b 3

ft Absolute pressure in the BWST: Ps := 14.7- + Psg Ps = 2.054 10' -

m ft Total head loss from the BWST to the tie-in point at the centerline of the 6-in pipe: AHac := 11.8704 ft Combined Henry's Law and other constants for Hydrogen and Nitrogen, respectively:

DH := 0.01892 DN := 0.01246

% The number of calculational steps to reduce the liquid volume in the makeup tank to zero: k := 20 Mathcad PLUS 6.0 EVAL 4RE.MCD 7:46 AM on 01/16/96

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MPR Associates,Inc.

320 King Street, Alexandria, VA 22314 Page7

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EXPRESSIONS USED:

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The expressions below for the maximum pressure in makeup tank are derived in hand calculations
I vo + (j - 1) 6v + DH-(1 - vo - ) 6v) vo + (j - 1) 6v + DN'( I - VD - l'0V)

RH(j,vo 6v) := -

RN(j,v .6v) :=

vo + j 6v + D H-(1 - vo - j 6v) vo + J 6v + DN'(I - VO - l'0V)-

k k f i -

f 1 - vo,i R HI J ,vo ,1 - vo '

+ y- R i i k j j=1 N (l'V0 'k j l T(y,vo,k) := j = 1 1+y The maximum pressure in the makeup tank as a function of the initial gas volume fraction, vo, is as follows: j I u 2)

Ps

-P m g Ex + p , g E , - (p , - p m) g Ed + P s g- - AHac - e - Psat Pmo(vo,y,k) := Psat +

P s 8 2 g;.

1 T(y,vo,k) l The maximum pressure can also be expressed in gage units by subtracting one atmosphere:

I O Pmog(vo.7,k) := Pmo(vo,y,k) - 14.7 psi The gas volume fraction, vo, is related to the measured levelin the makeup tank, in inches, by the following relation:

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xm vo(xm) := 0.9089 - 0.0068355 in~I MAXIMUM ALLOWANCE FOR INSTRUMENT ERRORS The maximum instrument (:cors in the level, et, and in the pressure, op, are 2.7 in and 1.12 psi, respectively; One method to account for these errors is to assume that both of these errors occur at the same time. This can be done by offsetting the level and pressure by these full amounts. This is accomplished by calculating the following quantity:

Pmog(vo(xm- 2.7 in),y,k) - 1.12 psi For a range of values of level: x ,:= 0 in,5 in 100 in The amount of this reduction in the allowable pressure is APm, where, APm(x m) := Pmog(vo(xm),y,k) - (Pmog(vo(x m - 2.7 in),y,k) - 1.12 psi)

This can be shown graphically as:

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1 MPR Associates,Inc. Page7 l 320 Kng Street, Alexandria, VA 22314 .

, [ i p Cale 102075DHH04 Preparer- .

- Checker: D '! P.".nt page 3 Q  ;

This can also be expressed in terms of head, where Hm(x m) I* I PsE 14 12  ; i

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AHm(i a

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y l 2

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0 20 40 60 80 100 l

l COMBINATION OF ERRORS (rms) l As derived in hand calculations, the statistical combination of the errors in the pressure and level, emp. can be expressed as follows, where the values of the error in pressure and level are:

a p := 1.12 psi o g := 2.7 in l

o m,(x m) .= o ,' . , 2. 'd 1 \,m emo,(ve(x m).y.uf}

This can be evaluated for a range of levels to obtain the following:

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o mp(xm) 3 i

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in U mp(*m)

This can also be expressed in terms of head, where AHs(x m)

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AHs(xm) 8 10 - - I ft 6 l 4 _.

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0 20 40 60 80 100 The two methods of accounting for instrument errors can be compared by graphing them against the 0 allowable pressure curve that has no allowance for instrument errors.

Mathcad PLUS 6.0 EVAL 4RE.MCD 7:46 AM on 01/16/96

MPR Associates,Inc. Pagef 320 King Street, Alexandria, VA 22314 -

Calc 102075DHH04 Preparer- /w Checker: Print page 4 G

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\ 0 10 20 30 40 50 60 70 80 90 100 l 'To e k; /Cs c l DS! ) xm 5 i The difference between the two curves with instrument errors, ape, can also be plotted, where ape (x m) := -(Pmog(vo(x m - 2.7 in),y,k) - 1.12 psi) + (Pmog(vo(x m),y,k) - o ,p(x m))

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MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By

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