ML20101M511
| ML20101M511 | |
| Person / Time | |
|---|---|
| Site: | Crystal River  |
| Issue date: | 01/11/1996 |
| From: | Harrison D MPR ASSOCIATES, INC. |
| To: | |
| Shared Package | |
| ML20101M505 | List:
|
| References | |
| 102075DHH01, 102075DHH01-R00, 102075DHH1, 102075DHH1-R, NUDOCS 9604050423 | |
| Download: ML20101M511 (38) | |
Text
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_j Calc 102075DHH01 Preparer _ Mm Checker: O[MtW Printpage 1
(
L EVALUATION OF MAKEUP TANK MAXIMUM PRESSURE PURPOSE:
The purpose of this calculatkm 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:
I Thisis the nominalreference crire.
l l
I PARAMETERS:
Vapor pressure of water in the makeup tank at 135 F:
Psat := 2.5375-Psat = 365.4 -
A P m := 61.4628 Ib Density of water in the makeup tank at 135 F:
Density of waterin the BWST at 100 F:
p,:= 61.9963 b A'
Acceleration of gravity: g := 32.17
- see, Minimumlevelin the BWST:
Lmin := 5.0 A Minimum elevation of the surface in the BWST:
E,:= 12nin + 119.67 A E, = 124.67 A Minimum margin between the top of the pipe at the tie-in and Xm ;" 2 A and the gasin the makeup tank:
Elevation of the top of the 64: pipe at the tie-in point:
Ed := 104.5 A + 3 in Ed = 104.75 A Minimum elevation of the levelin the pipe from the MUT to the Ex := Ed+Xm E = 106.75 A top of the 6-in pipe at the tie-in point:
x Mole ratio of Nitrogen to Hydrogen in the MUT cover gas:
y := 0.1 l
Pipe flow velocity (in the 6-in pipe) at tie-in point:
u, := 6.664 - -
sec Gage pressure in the BWST:
Psg := - 1.0 A 62.4 lbf A'
Absolute pressure in the BWST:
Ps := 14.7-
+ Psg Ps = 2.054 10' -
4 A
Total head loss from the BWST to the tie-in point at the centerline of the 6-in pipe:
Allac := 11.8704 A l
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 4R.MCD 1:58 PM on 01/04/96
l, Pagelo MPR Associates,Inc.
320 King Street, Alexandria, VA 22314
/
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Printpage 2
~ O. Calc 102075DHH01 Preparer // w,*m Checker:
G EXPRESSIONS USED:
The expressions below for the maximum pressure in makeup tank are derived in hand calculations:
I w + (j - 1) bv + D r(1 - vo - j 8v) q 3
RH(30V)"
w + j-6v + D yy(1 - vo - j 6v) vo + (j - 1) 5v + DN'(I~V"~l'0V) f RN(l'*0 '0V) '"
vo + j 6v + D g-(1 - vo - j Sv) k k
1,
- 1. yo\\
1, 1 - vo\\
l RH J,v,
I + y-
.R N (J.W. k j t
k 3 i
j=1 P(y,vo,k) := j = 1 l
1+y The maximum pressure in the makeup tank as a function of the initial gas volume fraction, vo,is as foHows:
f 2) u Ps - AHac p, f3
-p m g Ex + P s g E,- (p,- p m) g Ed + p s g-
- Psat Pmo(vo,y,k) := Psat +
k k
f,
- 1. mi f
- 1. voi j,vo,
+ y-R I
R p(A k j N(J'V0' k j j=1 j=1 1+y The maximum pressure can also be expressed in gage units by subtracting one atmosphere:
Pmog(vo,y,k) := Pmo(vo,y,k) - 14.7144 lbf 2
A The gas volume fraction, vo, is related to the measured levelin the makeup tank, in inches, by the foHowing relation:
vo(x,) := 0.9089 - 0.0068355 in" 3 x m The aRowable pressure can be adjusted for the maximum instrument errors in the level and in the pressure of Level error = 2.7 in, l
Pressure error = 1.12 psi l
It win be assumed that both of these errors occur at the same time.
j Mathcad PLUS 6.0 EVAL 4R.MCD 1:58 PM on 01/04/96 l
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MPR Associates,Inc.
Page7 j[j/
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320 King Street, Alexandria, VA 22314 Preparer: Av#/,'h Checker: -/,,,f,"f,/
Printpage 3
'C Calc 102075DHH01 The allowable gage pressure without and with maximum instrument errors in the makeup tank level and pressure are shown graphically below as a function of the makeup tank level:
m := 0 in,5 in.100 in Range oflevel:
x 60 55 50 l
45 I.
40
/
l Pnns(vo m),y,k) 35
,7 30 Pmos(vo(x,- 2.7.in),y,k)- 1.12 psi
[', '.
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Mathcad PLUS 6.0 EVAL 4R.MCD 1:58 PM on 01/04/96
MPR Associates,Inc.
Page f
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320 King Street, Alexandria, VA 22314 f
Preparer./N/
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Printpage 1 Calc 102075DHH01 hts. Checker:
EVALUATION OF MAKEUP TANK MAXIMUM PRESSURE PURPOSE:
The purpose of this calculation is to evaluate the maximum pressure in the makaup 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 and its results are compared to the allowable pressure values from FPC calculation M94-0053, Rev. 2. Attachment 1, sheets 11 and 12 (the original values) and the i
preliminary values for Revision 3 of that calculation provided by R. Clauson (FPC) on January 3,1996.
!4 PARAMETERS:
[,
Vapor pressure of water in the makeup tank at 135 F:
Psat := 2.5375-Psat = 365.4 -
m A
lb Density of water in the makeup tank at 135 F:
p m := 61.4628 Density of waterin the BWST at 100 F:
p, := 61.9%3-
^
Acceleration of gravity: g := 32.17 A j
- sec, O-j!
Minimumlevelin the BWST:
Lmin.= 5.0 A Minimum elevation of the surface in the BWST:
E,:= Lmin + 119.67 A E, = 124.67 A Minimum margin between the top of the pipe at the tie-in and Xm := 2 A and the gasin the makeup tank:
Elevation of the top of the 6-in pipe at the tie-in point:
Ed := 104.5. A + 3 in Ed = 104.75 A i
Minimum elevation of the levelin the pipe from the MUT to the j
Ex := Ed+Xm E = 106.75 A top of the 6-in pipe at the tie-in point:
x 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:
e := 6.664 - -
u see Gage pressure in the BWST:
Psg := - 1.0 ft 62.4 b 3
A N + Psg 3 b Absolute pressure in the BWST:
Ps := 14.7 Ps = 2.054 10 t-2 g
g.,
Total head loss from the BWST to the tie-in point at the centerline o!the 6-in pipe:
AHac := 11.8704 A Combined Henry's Law and other constants for Hydrogen and Nit ogen, respectively:
DH := 0.01892 DN := 0.01246 The number of calculational steps to reduce the Equid volume in the makeup tank to zero:
k := 20 Mathcad PLUS 6.0 ECOMP4R.MCD 2:04 PM on 01/04/06
MPR Associates,Inc.
Pagef
[g 320 King Street, Alexandria, VA 22314 Preparer /Wir/
//
/
f.WMhecker: M/'lY' Printpage 2 Calc 102075DHH01-O EXPRESSIONS USED:
The expressions below for the maximum pressure in makeup tank are derived in hand calculations:
vo + (j - 1) 8v + D g(1 - w - j 8v)
RH(l'VD*0V)"
vo + j 8v + D g(1 - vo - j 8v) l vo + (j - 1) 8v + DN'(I - VD -I'0V) l RN(j,vo,8v) :=
vo + j 8v + DN'(I-VO-IOV) l k
k H'tj,vo,1-yo f
- 1. vn\\
f t
R I + y-RNll We l
k i
\\
k }
9'(y,vo,k) := j = 1 j=1 1+y The maximum pressure in the makeup tank as a function of the initial gas volume fraction, vo,is as foHows:
I 2) u Ps - AHac -,
- Psat
-pm g Ex + p, g E,- (p,- pm) g Ed + p, g-n (psg 2 gj
(
Pmo(vo,y,k) := Psat +
H I'**
k R
N I'**
k
+y.
R j=1 j=1 1+y
)
. The maximum pressure can also be expressed in gage units by subtracting one atmosphere:
Pmog(vo,y,k) := Pmo(vo,y,k) - 14.7144 lbf 2
ft The gas volume fraction, vo,is related to the measured levelin the makeup tank, in inches, by the following relation:
vo(xm) := 0.9089 - 0.00683SS in-I
'X m The allowable pressure can be adjusted for the maximum instrument errors in the level and in the pressure of Level error = 2.7 in, Pressure error = 1.12 psi it will be assumed that both of these errors occur at the came time.
!O t
Mathcad PLUS 6.0 ECOMP4R.MCD 2:04 PM on 01/04/96
MPR Associates,Inc.
Page /0 320 King Street, Alexandria, VA 22314 f
- /
. w.w_s Checker:
/.~j,'A '/ '
Print page 3 Calc 102075DHH01 Preparer:
C The original and preliminary results can be put in the form of vectors at 5 inch levelincrements:
1.49 2.00 2.05 2.65 2.65 3.35 3.30 4.11 4.01 4.93 1
l 4.78 5.83 l
5.62 6.82 The revised allowable The original aPsable 0'
l values from the prel.
values from the pbnt l
Rev. 3 of FPC Ca'c.
7.55 procedure as Estedin 9.10 M94-0053 as provided C Calc. W@53 8.68 10.44 by R. Clauson on Rev. 2, Att.1, sheets '
January 3,1996.
Par:.
9.93 psi 11 and 12 of 18.
Pao :=
11.93 psi l
11.33 13.62 12.92 15.53 14.73 17.71 16.81 20.24 19.23 23.20 i
22.09 26.70 O'
25.50 30.92 29.67 36.09 34.85 42.59
,41.50,
,50.99, i
i v
l i
l i
l Mathcad PLUS 6.0 ECOMP4R.MCD 2:04 PM on 01/04/96
MPR Associates,Inc.
Page //
// /
j 320 King Street, Alexandria, VA 22314 Preparer: /,.
MNhecker: %d (61'-/
Printpage 4 Cale 102075DHH01
/
The allowable gage pressures with maximum instnament errors in the makeup tank level and pressure are shown graphically below as a function of the makeup tank level. On this curve:
Pmogis the MPR calculated value, Par is the FPC revised calculated value, and @ ----
Pao is the or!ginal FPC procedure value (before revisions). @~~~~
m := 0 in,5 in.100 in Range oflevel:
x 60 55 SO I
45 f
Pmog(vo(xm-2.7 in) y,k)- 1.12 psi
'/
j Pu f
Par 35
/
j 30 f
g'q) 1 Pa
/
Pao 25 l
20 7.-
,sg Y
/
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s--
0 10 20 30 40 50 60 70 80 90 100 TCtV/C bgIC/, /J1 1
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MPR Associates, Inc. 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By to2075D/MIof / g,' 4,)7 g,kj
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10 ukva $Ud ['NNebN35 CR3 EP OFFICE F.d g, gor gg/1he t Pf' C*l-l0:07(bHU0/ ~ Crystal River Unit 3 Chemistry Report mapont Date:Nomiqy. Decem6er 07.1985 SAMP12 POINT DATE MODE MEASURETYPE RESULT 8 UNITS b 85.1 %VOL (*J,3l, f, " f */ m CE 118 114/9511:16:00 AM 1 %H2 GAS = 10.26 %VOL / G 118 114/9511:16:00 AM 1 %N2 GA5 = I Gellt 11/6/9511:16:00 AM 1 %O2 GAS = 0 %VOL ) 0.01 uCVcs G418 11/6/9511:16.00 AM 1 ARAL = 0.99 uCi/cc j CE41s 11/6/9511:16:00 AM 1 XE 133 = f CE 118 11/6/9511:16:00 AM 1 XE 135 = 0.571 uCFcc 3.92 uc#ce G-118 114/95 11:16:00 AM 1 Xc.Egulv = { = - - - _ _ 0.01 uCVcc CE118 11/13/95 2:10;00PM 1 AR41 = 0.975 uCFcc CE 115 11/13/95 2:10:00 FM 1 XE 133 = CE 118 11/13/95 2:10:00 PM 1 XE J35 = 0.541 uc#cc 4 3.79 uCuee CB418 11/13/95 2:10:00PM 1 Xe49uiv = E7.51 %VOL G-118 11/13/952:30:00PM 'l %H2 GAS fI.30 /f,C L = $J5 MVOL ) CE418 11/13/95 2:30;00PM 1 %N2 GAS = CE418 11/13/951:30:00 PM 1 %O2 GAS =_ 0 %VOL x -- 90 %VOL 'l CE-118 11/20/9510.45:00 AM 1 %H2 OA3 = 91 37 l,f.f) 1.37 MVOL s CE lit 11/20/9510:45 00 AM 1 %N2 GAS = = 0 %VOL CE-114 11/20/95 10:45:00 AM 1 %O2 GAS 0.007 ~ uCVcc G-118 11/20/9510:45:00 AM 1 AR 41 = CE418 11/20/9510:45:00 AM 1 XE 133 = 0.828 uCl/cc = 0.352 uCl/ce CE-115 11/20/9510:45.00 AM 1 XE-135 a 2.89 aCl/cc l CE.118 11/20/9510:45:00 AM i Xc Equiv = = 85 %VM, CE418 11/27/9512:3100 FM 1 %H2 OAS 5 i Page 1 O %d 4 "'"A ^ i i i
w r m e u w - ./0207[bHilol pay ;3 4 'LE POINT DATE MODE MEA 511 RETYPE RESULTS ITNTT5 g ^ 13.4 %YOL 5 ff,'/#f f,593 / CE-118 11/274512:31:00PM 1 %N2GA5 = 0 %VOL CE 118 11/27/9512;31:00 PM 1 %C2 GAS 0.006 uCuce CE-118 11/27/9512:31:00 PM 1 AR-41 = = 0.79 uCl/cc G-Ils 11/27/9512:31:00PM 1 XE 133 0.3ss uCFec CE.118 11/27/9512:3120 PM 1 XE 135 = 2.75 oCI/cc C5118 11/27/9512:31:00PM 1 Xe-Equiv = ^ w 85.67__ %VOL CE.118 12/M512:20:00 PM. ,1 %H2 QAS gj = 11.14 %VOL CE-118 12/0512:20;00PM 1 %N2 GAS ' = 9 0 %VOL CE 118 12/4/9512:20.00 PM 1 %C2 GA5 = 0.008 uCuce CE.118 12/M512:20:00PM 1 AK-41 = CE-113 12/4/951220:00PM 1 XE.123 = 1.043 uCi/oc 0.547 uCuce CE-118 12/M512:20:00 PM 1 XE.135 = 3.9 nCVcc CE 11s 12/4/9512:20:00 PM 1 X4-Equiv = 1 l I l e a 4 1 4 Page 2 fon)jiwt?b W/ j l cLea 9. gg 4 Y
MPR Associates, Inc. D 320 King Street K Alexandria, VA 22314 Calculation No. Prepared By Checked By /0:075 Dill /O/ Jh/p,.l yf,)g),, /
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t I ~ MPR Associates. Inc. 320 King Street Alexandria, VA 22314 (' O d Calculation No. Prepared By Checked By I020H0440I $?(!w dr~ O/i):i) Picosure in dwSr l l In Hu ff ble (lbfotua 2 ) flu pousun in Hu I!!uSr th a c c u me o' fu be slig hMy /u s M ou ak:orpleni, i. e., / foot of % o de/ow o%phush pawn. Tias sow-<. anumpRon te'll k. Jush. for flusc eolculokar.s. (fu. o4.o funnua.7). y.{ = t'47 :ws - /. o Giz.o (nom &p ) i ys = / 4 7 x lH - /.ox 4:.9' = 0 OGY,9 /W/4 s- .2/i G.s - & Z. Y = I } f. Ec/ shen n' klawa &etev. 6 /.!e,inp &L %.! a 1 Re:m 4 4 a n ex. R, pm 'I/ LG = o. 9 021 - 0. oo if 35Y Xm tyhere % = lcic/in makeup huk in iuclus 1 i
MPR Associates. Inc. MPR 32o ximo street Alexandria. VA 22314 i Prepared By Checked By h Calculation No. !O2075DHH0/ k)(by -/,4sjp) Al' w l A. /??mo mum le>.</in /$k/S/ l ~ AM/ ininimum lea /in r3wsr t swihl,our = {0 g. o ihm ifefemuce 3 p :4 o/ rs : G le va A*a n o f le x / = lndicokd icec/ + //t). 67,9 (see pid i!n-3 e? r!H-oon, &/. 8, :Jutn) So of an oth<alindito&/ Gocl<;fMpu sch<a/ /eic/ 6/cyclion of f)e curfo* c in h r3 c /M.474e / } (O E, = 50 + / /9. 67 = .,,,,y =-- ~ d. /tec/ /hr.:nt s'n. /// sheep Twk 5m Opero/>i/ih; fouc.tme f6ofu Krs & p a t, / / 3, /46u. 7 f lua ler coluws a l on & d< =.?. o 4 /f &n, poinf is for ; pipe, (f + Sin flevod'av el pipe cuk hht = Jost.C 4ef /&A f/YorP5t.d,2 y dw o \\ i O l11fl4 {!$YA O l1 lA/O Y $ U f f3CA. l E Ex = lo Y,5 * / z +.l. o = _/ 0 (,. 7 5 #- ufc /cn/ in e//>o w of Ao /hur ef /}ob Mo/ Nuip% make up /sek. u t h / /u u /o i
MPR Associates, Inc. 320 King Street Alexandria, VA 22314 Calculation No. Prepared By Checked By l0207%4llO1 ldt/Y .ch4rp / / OG $6"u$/77t/<7Jr [t/A Lud77OAJS
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MPR Associates,Inc. Page f/ /Mf'r/) / 320 King Street, Alexandria,VA 22314 gj Prbtpage 1 Calc 102075DHH01 Preparer: EdN4A Checker: - 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 calculations. Some parameters are also established by separate hand calculations. CASE COVERED: This is the nominal reference case, but with various values of the mole ratio of nitrogen to hydrogen in the makeup tank cover gas to evaluate the sensitMiy of the results to the mole ratio. i i j PARAMETERS: 5 5 Prt = 365.4 Vapor pressure of water in the makeup tank at 135 F: Psat := 2.5375 I" A P m:= 61.4628 lb Density of water in the makeup tank at 135 F: Density of waterin the BWST st100 F: p,:= 61.9963 S A' Acceleration of gravity: g := 32.17 A O see Minimum levelin the BWST: Emin := 5.0 A Minimum elevation of the surface in the BWST: E,:= Lmin + 119.67 A E, = 124.67 it Minimum margin between the top of the pipe at the tie-in and Xnu= 2 A and the gas in the makeup tank: Elevation of the too of the 6-in pipe at the tie-in point: Ed := 104.5 A + 3 in Ed = 104.75 A Minimum elevation of the levelin the pipe from the MUT to the Ex := Ed+Xm B =106.75 A x top of the 6-in pipe at the tie-in point: Mole ratio of Nitrogen to Hydrogen in the MUT cover gas: y := 0.1 This is the nominal value, extremes of 0.0 and 0.5 are also evaluated. Pipe flow velocity (in the 6-in pipe) at tie-in point: u, := 6.664 - - see 5 Gage pressurein the BWST: Psg := - 1.0 A 62.4 A' 85 Absolute pressurein the BWST: Ps := 14.7 - + Psg Ps = 2.054 10 '2 2 m g Total head loss from the BWST to the tiet point at the centerline of the 6-in pipe: AHac := 11.87% A Combined Henry's Law and other constants for Hydrogen and Nitrogen, respectively: D g := 0.01892 DN := 0.01246 O The number of calculational steps to reduce the liquid volume in the makeup tank to zero: k := 20 Mathcad PLUS 6.0 E4RGAM.MCD 12:37 PM on 01/04/96 I
l MPR Associates,Inc. Page JO 320 King Street, Alexandria, VA 22314 f fj i Calc 102075DHH01 Preparer:. s M hecker: # '_/ J '-r Printpage 2 l l EXPRESSIONS USED: The expressions below for the maximum pressure in makeup tank are derived in hand calculations: I w + 0 - 1) 8v + D g(1 - w-j 5v) RHQ,w,5v) = w + j 6v + D g(1 - w -j 6v) i w + d - 1) 8v + D -(1 - vo - j 5v) N R pG,vo,5v) := w + j 8v + DN-(1 - w - j 6v) k k f. 1 - wi f. 1 - voi R p'i R }{i J,vo, I j,vo, I+r l k j k j 4'(y,w,k) := i" 3"' I+y The maximum pressure in the makeup tank as a function of the initial gas volume fraction, vo, is as foRows: - AHac -, \\ f 2 u Ps ~PmgEx + p, g E,- (p,- p m) g Ed+Psg- - Psat Pmo(vo,y,k) := Psat + I 1 - voi ,f. 1 - voi lRH ),vo, l + y-RNIJe*0 i i k j ( k j j=1 j=l' 1+y l l ' The ma::imum pressure can also be expressed in gage units by subtracting one atmosphere: [ ? ] Pmog(vo,y,k) := Pmo(vo,y,k)- 14.7144 lbf A The gas volume fraction, vo, is related to the measured level in the makeup tank, in inches, by the foRowing relation: 1 ]. w(x ) = 0.9089 - 0.0068355 in'I x m 1 V l i l B j 4 Mathcad PLUS 6.0 E4RGAM.MCD 12:37 PM on 01/04/96
I MPR Associates,Inc. Page j/ eg / 320 King Street, Alexandria,VA 22314 / q Calc 102075DHH01 Preparer Wm Checker: Td C/MU/ Printpage 3 The alowable gage pressure in the makeup tank for the range of values of the mole ratio of nitrogen to hydrogen in the cover gas are shown graphically below as a function of the makeup tank level: m := 0 in,$ in.100-in Range oflevel: x Q y: 0-(y) y:0./ -- - ss $)y =o,f-- 3, ) l 45 Pmog(w(xm),0.0,k) D M i 7 2 w 3s Pmog(vo(xm),0.I,k) &8 M 30 u.. Pmon(=(xm),0.s.k) " / o 5 / V s-- Is / / hk / bt%Vil s j / 86/j 0 10 20 30 40 so 60 70 80 90 100 Yos.A:lett',fu
- m in This can also be evaluated for a specific set of conditions:
y := 0,0.05. 0.5 34.8 / 34.2s wea).,.k> 34.7 34.6s 0 0.2 0.4 0.6 7
== Conclusion:== The fraction of nitrogen in the cover gas has a maximum effect of about 0.1 psi and is, therefore, noi a significant varleble. i Mathcad PLUS 6.0 E4RGAM.MCD 12:37 PM on 01/04/96 i
t MPR Associates,Inc. Page81 1 320 King Street, Alexandria, VA 22314 I Calc 102075DHH01 Preparer: Mu/. Checker: -f Printpage 1 EVALUATION OF MAKEUP TANK MAXIMUM PRESSURE PURPOSE. l 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: These are he same parameters as the nominal reference case except for one case the solubility of the gas in the makeup tank water is zero. This should bound the effect of gas coming out of solution and indicate the sensitivity of the solution to the assumptions of gas solubiRty. PARAMETERS: 5 Psat = 365.4 5 Vapor pressure of water in the makeup tank at 135 F: Psat := 2.5375 N A2 Density of water in the makeup tank at 135 F: Pm := 61.4628-Density of waterin the BWST at 100 F: p,:= 61.9%3 5 A' Acceleration of gravity: g := 32.17 A Minimumlevelin the BWST:
- = 5.0 A Minimum elevation of the surface in the BWST:
E, := Lmin + 119.67 A E, = 124.67 A Minimum margin between the top of the pipe at the tie-in and h;=2A and the gas in the makeup tank: Elevation of the top of the 6-in pipe at the tie-in point: Ed := 104.5 A + 3 in Ed = 104.75 A 1 Minimum elevation of the levelin the pipe from the MUT to the Ex := Ed+Xm E = 106.75 A top of the 6-in pipe at the tie-in point: x i Mole ratio of Nitrogen to Hydrogen in the MUT cover gas: y := 0.1 i Pipe flow velocity (in the 6-in pipe) at tie-in point: u, := 6.664 A see l Gage pressure in the BWST: Psg := - 1.0- A 62.4 Ibf l A' 5 + Psg Ps = 2.054 10' 5 Absolute pressure in the BWST: Ps := 14.7 i d A 2 Total head loss from the BWST to the tie-in point at the centerline of the 6-in pipe: Blac := 11.8704 A Combined Henry's Law and other constants for Hycirogen and Nitrogen, respectively: l DH := 0.01892 DN := 0.01246 The number of calculational steps to reduce the liquid volume in the makeup tank to zero: k := 20 j 1 Mathcad PLUS 6.0 E4RSOLMCD 12:57 PM on 01/04/96
l l l l l MPR Associates,Inc. Page JJ 320 King Street. Alexandria, VA 22314
- s. / m' Checker:'f# (Cc '/
fj f M Printpage 2 y Calc 102075DHH01 Preparer: f l j i EXPRESSIDNS USED: The expressions below for the maximum nressure in makeup tank are derived in hand calculations: vo + (j - 1) 5v + D g(1 - vo - j Sv) R (I'* *0V) " H vo + j 5v + D g(1 - vo - j 8v) ) vo + (j - 1) 5v + DN-(1 - vo - j 6v) RN(3****0V)" vo +j 8v + DN-(1 - w -j 8v) k k i i i 1 - voi f Nlil*** 1 - vo l RH ',vo, i+r R k j l k j i=1 j=1 4'(y,vo,k) := ' I+y The maximum pressure in the makeup tank as a function of the initial gas volume fraction, vo, is as foBows: 1 2) -p gg Ex + P s g E,- (p,- p m) g Ed + P g- - AHao - - Psat (p, g 2'8 ) l Pmo(vo,y,k) := Psat + k k RH I+"a + y-Ry j,vo, {b s k j=1 j=1 1+y l The maximum pressure can also be expressed in gage units by subtracting one atmosphere: Pmog(vo,y,k) := Pmo(w.y,k) - 14.7144 lbf 1 2 i ft The gas volume fraction, vo, is related to the measured level in the makeup tank, in inches, by the following relation: vo(xm) := 0.9089 - 0.0068355 in'I x m and D are zero and i If the solubility of gas in the water in the makeup tank is zero, the constants Da N l Rs H(j,v,5v) := "
- O ~ I}' #
Rs p(j,vo,6v) := *
- 0 ~ O'
- L vo +j 8v w +J 6v I
The maximum pressure in the makeup tank as a function of the initial gas volume fraction, vo, is as folows: f "c) 2 Ps l -pmgEx + p, g E,- (p,- pm) g Ed + P s'B' - AHao - - Psat l Pmos(vo,y,k) := Psat + k k r l ' f, t _ vol f,
- 1. voi l
Rs N'i J,w, 1 +t Rs p1j,w, ( k 3 i k j j=1 j=1 1+y Ibf Pmosg(w,y,k) := Pmos(vo,y,k) - 14.7 1443it Mathcad PLUS 6.0 E4RSOL.MCD 12:57 PM on 01/04/96 r l-l
i MPR Associates,Inc. Page 8 Y /[,/ / 320 King Street, Alexandria, VA 22314 f,/ Preparer:// Ajfv/mmChecker: 7' / LAW Printpage 3 Calc 102075DHH01 g~ l The snowable gage pressures with and without considering gas solubility are shown graphically below as a i function of the makeup tanklevel: Range oflevel: x, m 0 in,$.in 100 in 60 i @.:folubllo'hf /11eh!b$ 35 (p fohibEl*N 1 / 50 t.n on/-- - '): I 45 40 Pmog(vo(xm).7,k) @l E 35 /,' 2 a +- & ){ Pmg(w(x,),y,k)30 1 M 25 b L-~ 20 0 s a / / 'o / \\ / 5 p 0 10 20 30 40 50 60 70 80 90 100
== Conclusion:== The solubility of gas in the makeup tank Equid orh has an effect when the tank levelis high (over about 90 inches). The maximum effectis 1 to 2 psi. O Mathcad PLUS 6.0 E4RSOL.MCD 12:57 PM on 01/04/96
9 MPR Associates,Inc. Pagej[ 320 King Street, Alexandria, VA 22314 Calc 102075DHH01 Preparer: / h checker: //l Printpage 1 l 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 l levelin the tank. The expressions are derived in hand calculations. Some parameters are also l established by separate hand calculations. l CASE COVERED: This is the nominal reference case, but with various values of the number of calculational steps, k. used in the determination of the makeup tank pressure. These cases are being run to establish that the number of steps usedis sufficient. 1 PARAMETERS: Vapor pressure of water in the makeup tank at 135 F: Psat := 2.5375-Psat = 365.4
- A Pm := 61.4628 lb Density of water in the makeup tank at 135 F:
Density of waterin the BWST at 100 F: p,:= 61.9963 5 3 ft A Acceleration of gravity: g := 32.17 2 m Minimum levelin the BWST: 12nin := 5.0 ft Minimum elevation of the surface in the BWST: E, := 12nin + 119.6711 E, = 124.67 ft Minimum margin between the top of the pipe at the tie-in and Xm := 2 A and the gasin 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 E =106.75 A x top of the 64n pipe at the tie-in point: Mole ratio of Nitrogen to Hydrogen in the MUT cover gas: y := 0.1 This is the nominal value, extremes of 0.0 and 0.5 are also evaluated. Pipe flow velocity (in the 6-in pipe) at tie-in point: e := 6.664 u see Gage pressure in the BWST: Psg := - 1.0- A 62.4 Ibf 3 A 3 Absolute pressurein the BWST: Ps := 14.7- + Psg Ps = 2.054 10 A Total head loss from the BWST to the tie-in point at the centeriine of the 6-in pipe: AHae := II.8704.ft Combined Henry's Law and other constants for Hydrogen and Nitrogen, respectively: DH = 0.01892 DN := 0.01246 s i I The number of calculational steps to reduce the liquid volume in the makeup tank to zero: k := 20 l (This is the nominal value used in other calculations, this calculation wiB use others.) i Mathcad PLUS 6.0 E4KR.MCD 11:52 AM on 01/04/96
MPR Associates,Inc. Page 3 6 J 320 King Street, Alexandria, VA 22314 !.w m, Checker: -l
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Printpage 2 Calc 102075DHH01 Preparer: EXPRESSIONS USED: The expressions below for the maximum pressure in makeup tank are derived in hand calculations: w + (j - 1) 8v + D g(1 - w - j 8v) RH(5 **'0V) w + j 8v + D g(1 - w -j 8v) w + (j - 1) 8v + DN-(1 - w -j 8v) RN(j,v,8v) := vo +j 8v + DN-(1 - vo - j 8v) k k [ i f i H 5 ** 1 - w N(5 ** l - vo R R k j k 4'(y,vo,k) := j = 1 J=1 1+y The maximum pressure in the makeup tank as a function of the initial gas volume fraction, vo, is as follows: (Ps " 2) - AHac - c - Psat -pm g Ex + p, g E, - (p, - p m) g Ed+psg. p (P s'8 '8 ) Pmo(vo,y,k) := Psat + 1 1 - yn\\ 1, } - yn> i R g l(J,w, RH j,vo, ! + y-i k j k j .j=1 j=1 1+y l ' The maximum pressure can also be expressed in gage units by subtracting one atmosphere: b f Pmog(w,7,k) := rmo(vo,y,k)- 14.7144 lbf P i A The gas volume fraction, vo, is related to the measured levelin the makeup tank,in inches, by the foDowing relation: !i I j! vo(xm) := 0.9089 - 0.0068255 id x m 1 l. Mathcad PLUS 6.0 E4KR.MCD 11:52 AM on 01/04/96 l
an 4 e MPR Associates,Inc. Pagej[ // Preparer:$ dN/w Checker: V(//bMI-r Print page 3 / f 320 King Street, Alexandria, VA 22314 Calc 102075DHH01 J The allowable gage pressure in the makeup tank for various values of the calculational constant, k, as a function of the makeup tanklevel: m := 0 in,5s_100 in Range oflevel: x @ ks3 - 60 g:to. k = 20 - - ss A, 40 50 %s(-(.).1.3) j 0; M 4s i 2 7 h 40 r-s(-(.).1.io) / M 3s / w-- P-s(-(=.).r.20) 30 / h M 25 k' Pmog(vo(,),y,40) e 5" / 1 / 10 TOMk 2 3 fit $$t.itc [ #8 0 10 20 30 40 50 60 70 30 90 100 Tork lo ef M. y The effects can also be evaluated at specific conditions for a range of k values, for example at 90 inches: k := 2,3. 50 3s.2 i 1 3s Pmog(vo(90 * ),y.k) m l-34.s 0 20 60 k Conclusion
- The number of iterations is not a significant variable and 20 is an adequately large value.
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