ML20101M561
| ML20101M561 | |
| Person / Time | |
|---|---|
| Site: | Crystal River  |
| Issue date: | 02/13/1996 |
| From: | Harrison D MPR ASSOCIATES, INC. |
| To: | |
| Shared Package | |
| ML20101M505 | List:
|
| References | |
| 102075DHH06, 102075DHH06-R00, 102075DHH6, 102075DHH6-R, NUDOCS 9604050441 | |
| Download: ML20101M561 (9) | |
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- Print page 1 l V EVALUATION OF MAKEUP TANK MAXIMUM PRESSURE PURPOSE:
1 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 calculations. Some parameters are also established by separate hand calculations.
CASE COVERED:
This is the nominal reference case except that the temperature in the makeup tank is assumed to be 100*F instead of 135'F. An expression for the difference in allowable pressure for the two temperatures is derived and evaluated, both as pressure and head.
PARAMETERS:
Vapor pressure of water in the makeup tank at 100*F:
Psat := 0.94924 b Psat = 136.691 b h*
n P m := 61.9963 Ib Density of water in the makeup tank at 100 F:
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Density of water in the BWST at 100 F:
p, := 61.9963 3
ft Acceleration of gravity: g := 32.17-h
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Minimum levelin the BWST:
Lm'm := 5.0 ft Minimum elevation of the surface in the BWST:
E := Lmin + 119.67 ft E, = 124.67 ft s
i Minimum margin between the top of the pipe at the tie-in and h
and the gas in the makeup tank:
Elevation of the top of the 6-in pipe at the tie-in point:
Ed := 104.5 ft + 3 in Ed = 104.75 ft Minimum elevation of the levelin the pipe from the MUT to the Ex := Ed+Xm Ex = 106.75 ft top of the 6 in pipe at the tie-in point:
1 Mole ratio of Nitrogen to Hydrogen in the MUT cover gas:
y := 0.1 c := 6.6641 Pipe flow velocity (in the 6-in pipe) at tie-in point:
u see Gage pressure in the BWST: Psg := 1.0 ft 62.4 E 3
ft 3 *b l
Absolute pressure in the BWST:
Ps := 14.7 b + Psg Ps = 2.054 10 in f;2 2
Total head loss from the BWST to the tie-in point at the centerline of the 6-in pipe:
AHac '= ll.8704 ft Combined Henry's Law and other constants for Hydrogen and Nitrogen, respectively:
DH := 0.018003 DN := 0.013609 O
The number of calculational steps to reduce the liquid volume in the makeup tank to zero:
k := 20
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Mathcad PLUS 6.0 EVAL 4RR.MCD 11:48 AM on 2/12/96 4
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MPR Associates,Inc.
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320 King Street, Alexandria, VA 22314 Calc 102075DHH06 Preparer:
Checker: ['/ A = [ S Print page 2 A
EXPRESSIONS USED:
The expressions below for the maximum pressure in makeup tank are derived in hand calculations:
vo t (j - 1) 6v t DH-(1 - v -j 6v) vo t (j - 1) 6v t D g(1 - vo-j 6v)
R H(j,v,6v) =
RN(I' V0'0V) ;*
vo + j 6v + D g(1 - vo-j 8v) vo +j 6v t D y(1 - vo-j.6v) k k
R H j,vo,
+t RN l'Y 5*
T(1,vo,k) :=
l 1+7 i
The maximum pressure in the makeup tank as a function of the initial gas volume fraction, vo,is as follows:
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-p m g E + p, g E,- (p,- p m) g Ed
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(psg 2g j Pmo(vo,y,k) := Psat +
y T(Y,vo,k)
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If we now define another quantity, Pxmo, as the allowable pressure at the maximum temperature in the makeup tank of 135'F, we can get the difference between the two pressures.
p The saturation pressure at 135'F is:
Pxsat := 2.5375-Pxsat = 365.4 b II k
The density at 135'Fis: p,x := 61.4628-ft The non-dimensional constants (from hand calculations) are: Dx H := 0.01892 Dx N := 0.01246 Now determine the new terms for the maximum temperature condition as above:
vo t (J - 1) 6vt Dx g(1 - vo-j 6v) vo + (j - 1) 6v+ Dx g(1 - vo-j 6v) l Rx H(j,vo,6v) ':
Rx N(I'V0'0V) ;*
vo +J 6v+ Dx g(1 - vo-j 6v) vo +j 6v+ Dx g(1 - vo-j 6v) k k
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k i k j Tx(y,vo,k) := j = 1 j=1 1+7 The maximum allowable pressure in the makeup tank, Pxmo, as a function of the initial gas volume fraction, vo, is as follows for the 135'F makeup tank temperature is:
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-p mx g E + p, g E,- (p,- p mx) g Ed + p s g-
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(psg 2g j Pxmo(vo,Y,k) := Pxsat +
Tx(7,vo,k)
The gas volume fraction, vo, is related to the measured level in the makeup tank, in inches, by the following relation (obtained from hand calculations):
vo(xm) := 0.9089- 0.0068355 in' x m
Mathcad PLUS 6.0 EVAL 4RR.MCD 11:48 AM on 2/12/96
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MPR Associates,Inc.
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320 King Street, Alexandria, VA 22314
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Print page 3 Calc 102075DHH06 Preparer:
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,O If we now define the difference between the two allowable pressures as AP (where Pmo is the allowable pressure at a makeup tank temperature of 100'F and Pxmo is the allowable pressure for a tank temperature of 135'F):
AP(vo,y,k) := Pmo(vo,y,k) - Pxmo(vo,y,k)
If AP is greater than zero, the allowable pressure at the makeup tank temperature of 100*F is greater than the allowable pressure at the 135'F temperature used in the original base calculation and it would show that the assumption of the higher (135'F) temperature is conservative because it results in a lower allowable pressure.
Range of level:
x,:= 0 in,5 in 100 in 10 l
l AP(vo(x m).7,k) 6 l
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20 40 60 80 100 As shown by the curve, the allowable pressure for 135'F is always lower than the allowable pressure at 100*F. This confirms that the use of the higher temperature in the analysis. Furthermore, it shows that the use of the higher temperature involves a substantial additional margin in the calculation. The curve of pressure difference can also be expressed in terms of feet of head as follows:
15 AP(vo(x m).T.k) 10 5Pm ft 5
0 20 40 60 80 100 l
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Mathcad PLUS 6.0 EVAL 4RR.MCD 11:48 AM on 2/12/96 1
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