ML19351D307

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Viewgraphs Entitled, Safety/Relief Valve Actuation Overview
ML19351D307
Person / Time
Site: 05000447
Issue date: 09/10/1980
From: Hucik S
GENERAL ELECTRIC CO.
To:
Shared Package
ML19351D306 List:
References
NUDOCS 8010090500
Download: ML19351D307 (53)
v • d • e


Text

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o MARK III CONTAINMENT PROGRAM NRC - SRVA REVIEW

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SEPTEMBER 10, 1980 SRVA OVERVIEW STEVEN A. HUCIK JECHNICAL LEADER MK III CONTAINMENT ENGINEERING 4

SAH-1 9/10/80 8010090500

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SRVA - MULTIPLE SRV QUENCHER LOAD DEFINITION METHOD

. WHAT IS IT?

-METHOD FOR SIMULATING CONTAINMENT EOUNDARY PRESSURE LOADS DUE TO MULTIPLE SAFETY RELIEF VALVE ACTUATION.

  • HOW IS IT USED?

-SRV LOADS ARE APPLIED TO CONTAINMENT STRUCTURAL MODELS AND USED FOR EQUIPMENT QUALIFICATION.

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MARK III - SRVA METHOD'

. X-00ENCHER PERFORMANCE

- EXTENSIVE DATA BASE

- WIDESPREAD APPLICATION

. MULTIVALVE METHOD - SRVA

- INPUT CONFIRMED BY TEST DATA AND ANALYSIS

- REALISTIC LOAD COMBINATION

. BUBBLE ARRIVAL TIMES VARY

  • BUBBLE FREQUENCIES VARY j

- CONFIRMED RESULTS - CAORSO TESTS

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KARK 111

.SRVA METHOD - OVERVIEW

. MULTIPLE QUENCHER ACTUATION BUBBLE ARRIVAL TIME BUBBLE FREQUENCY 59 MONTE CARLO TRIALS BOUNDING CASES CHOSEN

. APPLICATION TO DESIGt!

DYNAMIC STRUCTURAL ANALYSIS SAH-4 9/10/80

O SRVA METHOD - OVERVIEW BUBBLE ARRIVAL TIME VARIABLE VESSEL PRESSURE RISE RATE - TRANSIENTS VALVE SET POINT DRIFT VALVE OPENING TIME - MECHANICAL STROKE BUBBLE DYNAMICS FREQUENCY VARIES DUE TO LINE LENGTHS GESSAR BUBBLE PRESSURE TIME HISTORY (GESSAR WAVE FORM)

POOL BOUNDARY LOADS DISTANCE ATTENUATION 2Ro/R ADDITION OF MULTIPLE QUENCHERS

. RESULT PRESSURE-TIME HISTORY AT 520 N0 DES (13 x 40)

BASEMAT FORCE TIME HISTORY OVERTURNING MOMENT TIME HISTORY FOURIER TRANSFORM OF BASEMAT FORCE AND OVERTURNING MOMENT AFTER EACH TRIAL s

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s SRVA METHOD OVERVIEW DESIGN CASE SELECTION AFTER 59 TRIALS e

PEAK FOURIER AMPLITUDE IN 4-12 Hz, 12-20 Hz, AND 20-28 Hz RANGES SELECTED FOR

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BOTH FORCE AND MOMENT UP TO NINE PRESSURE TIME HISTORIES USED IN -

STRUCTURAL ANALYSIS 15% PEAK BROADENING OF STRUCTURAL RESPONSES USED FOR DESIGN e METHOD APPLIED TO MULTIPLE SRV ACTUAT10t! LOAD CASES 1

i SAH-6 9/10/80

o SRVA METHOD LOAD CASES SINGLE VALVE FIRST ACTUATION SUBSEQUENT ACTUATION

  • TWO ADJACENT VALVES ADS VALVES ALL VALVES
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  • NORMALLY LIMITING CASES i

SAH-7 9/10/80

D SRVA METHOD CONSERVATISMS IN METHODOLOGY GESSAR BUBBLE PRESSURES FOR SINGLE VALVE ARE e

CONSERVATIVE FOR MULTIPLE VALVE ACTUATION HIGHEST BUBBLE PRESSURE APPLIED AT EVERY SRV e CONSERVATIVE DESIGN CONDITI0t!S USED e PRESSURE-TIME ATTENUATION BOUNDS DATA

  • PRESSURE-DISTANCE ATTENUATION BOUNDS DATA e SELECTED CASES ENVELOPED
  • STRUCTURAL RESPONSE PEAKS BROADENED 15%

LOW DAMPING OF REG. GUIDE 1.60 USED IN STRUCTURAL ANALYSIS s

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RESULTS CONFIRMED BY CA0RS0 TESTS PRESSURE AMPLITUDE FREQUENCY TIME AND DISTANCE ATTENUATION CONCLUSIONS X-QUENCHER PERFORMANCE PROVEN TIME PHASING VALID CONSERVATISMS IN METHODOLOGY SRVA METHODOLOGY ADEQUATE FOR DESIGM hh!Uf00

SRVA MEETING OVERVIEW

. ADDRESS AREAS OF MAJOR CONCERT!

. QUESTIONS WITH SPECIFIC DATA REQUESTS WILL NOT BE FORMALLY PRESENTED

. ANY QUESTIONS YOU DO NOT tlEED FORMAL PRESENTATI0!!?

. IMPORTANT TO CONSIDER COMPLETE METHODOLOGY SENSITIVITIES SHOW SMALL EFFECT OF PARAMETER VARIATION COMPARISON OF METHOD TO CA0RSO TESTS SHOWS C0!!SERVATI s

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MK III.CONTAINMEllT PROGRAM 1

NRC - SRVA REVIEW 4

l SEPTEMBER 10, 1980

SUMMARY

- QUESTION 9 4

l STEVEf! A. HUCIK TECHNICAL LEADER MK III CONTAINMENT ENGillEERING i

SAH-1 9/10/80

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THE OBF DISTRIBUTION WHICH IS EMPLOYED BY THE PROPOSED M BASED ON DATA OBTAINED AT TWO GERMAN BWR FACILITIES (PLAN AND B).

THE DATA EXHIBIT A STANDARD DEVIATION OF ROUGHLY 20%

OF THE MEAN, THE LATTER BEING ABOUT 8-Hz.

THE QUENCHER PERFORMANCE SUGGESTED BY THE SELECTED DISTRIBUTION DIFFERS SUBSTAN THAT EXHIBITED BY THE DEVICE USED IN THE CA0RSO TESTS, WHICH WILL BE THE DEVICE USED ON ALL MARK Ills.

DIFFERENCES IN BOTH STANDARD DEVIATION (5% VS. 20%) AND IN MEAN VALUE (6 Hz VS HAVE BEEN FOUND.

PRELIMINARY INFORMATION INDICATES THAT' SIGNIFICANT DIFFERENCES IN MEAN QEF'S CAN ALSO BE DETECT THE RESULTS FOR PLANTS A AND B.

HOWEVER A CRITICAL FACTOR FOR ACCEPTANCE OF THE MSRVA METHO JS WHETHER IT PROVIDES A CONSERVATIVE DEFINITION OF THE L ALTHOUGH THE QBF DISTRIBUTION EMPLOYED BY THE PROPOS DIFFERENT FROM THE OBF DISTRIBUTION THAT CAN BE INFERR THE CA0RSO RESULTS, IT MAY WELL BE THAT THE METHODOLOGY IS S0 CONSERVATIVE WITH RESPECT TO PEAK PRESSURE AMPLITUD BOUND THE CA0RSO LOADS DESPITE THE FACT THAT THEY EX POWER AT 6 Hz MEAN BUBBLE FREQUENCY.

TO DEMONSTRATE THE METHODOLOGY'S CONSERVATIVENESS, PERFORM A t

VERIFICATION CALCULATION USING THE MSRVA TO PREDICT B PRESSURES FOR THE EXACT CONDITIONS OF CA0RSO TESTS FOLLOWING MODIFICATION; INSTEAD OF RANDOM SELECTION OF PRR AN THE VALVE ACTUATION TIMES RECORDED AT THE SITE SHOU A NON-STOCHASTIC INPUT.

THE CALCULATION SHOULD STILL INCLUDE THE VOT AS A RANDOM VARIABLE. COMPARISONS WITH ACTUAL TEST RESULTS SHOULD BE PRESENTED BOTH AS TRANSIENTS AS WEL POWER SPECTRAL DENSITIES.

SAH-2 9/10/80

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SUMMARY

- QUESTION 9 SRVA/CAORSO COMPARISON OBJECTIVE DEMONSTRATE THE SRVA METHODOLOGY CONSERVATISM.

APPROACH USED

-USE NRC REQUESTED PROCEDURE

-SRVA CALCULATION TO PREDICT BOUNDARY PRESSURES FOR EXACT CA0RSO TESTS

-NRC REQUESTED MODIFICATIONS TO SRVA METHOD

. USE CA0RSO RECORDED VALVE ACTUATION TIMES.

PRR & VST NOT USED.

. V0T AND QBF AS RANDOM VARIABLES.,

OBF MEAN ADJUSTED FOR CAORSO CONDITIONS SAH-3 9/10/80

SRVA/CA0RS0 COMPARISON

. COMPARISONS

-CA0RSO 4 - VALVE TESTS 27, 45-1, 30

. TEST 27 HAD TWO SRV'S SIMULTANE0USLY ACTUATED

. TEST 30 HAD HIGHEST MEASURED PRESSURES e TEST 45-1 HAD SHORTEST TIME SPAN FOR ALL VALVES TO ACTUATE

-PREDICTED BUBBLE PP.ESSURES COMPARED TO CA0RSO DATA

. MEAN PREDICTION COMPARED TO CA0RSO PEAK MEASURED BUBBLE PRESSURE

- ACTLAL CA0RSO CONDITIONS MEASURED USED FOR COMPARIS0N

-SRVA INPUT CALCULATIONS

- POOL B0UNDARY PRESSURE COMPARISONS AT P14, P23, P32 SAH-4 9/10/80

SRVA/CA0RSO COMPARISON PREDICTION SRY MEAN

  • MEASURED-27 A.

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9.4/-6.6 5.8/-1.9 E

9.2/-6.5 6.9/-3.5 F

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9.3/-6.6 4.6/-2. 8 45-1 A

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  • PREDICTED MEAN.FOR 4-SRV ACTUATION i

SAH-5 9/10/80

_ CONDITIONS FOR CA0RSO TESTS 27; 30 AND 45-1 TEST 27 TEST 30 TEST 45-1 VALVES ACTUATED A,

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AVG PIPE TEMP. ( F) 93 86 92 SRVDL AIR MASS (LBM) 4.60 4.70 4.70 STM. PART. PRESS.(PSIA) 0.77 0.62 0.51 WATER LEG LENGTH (FT) 17.7 17.7 17.7 POOL TEMPERATURE ( F) 77 80 80 DRYWELL PRESS. (PSIA 14.90 14.90 14.90 STM. FLOW RATE (LBM/SEC) 236,227,241,109 238,230,244,211 238,230,240,209 3

SRVDL VOLUMES (FT )

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AMPLIFIED RESPONSE SPECTRUM 120-

,,, g E

Etli MMPING 100-g 80

)p-j d 7

[j l

att s n aints I

6

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3 e

,: (

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ff/gj) p

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Si 20 s

s ctoaso c

Oo 10 i 10 2 10 8 FREQUENCY

( HZ )

PL 1

SRVA/CA0RS0 COMPARISONS

. RESULTS - CONCLUS10tlS

-SRVA CONSERVATIVELY PREDICTS CA0RSO MEASURED TEST DATA

-PEAK SPECTRAL VALUE SELECT 10tl PROCESS CONSERVATIVE SRVA METHODOLOGY ADEQUATE FOR DESIGN hb6fb0 l

j CUESTION 3 PROVIDE A DETAILED DESCRIPTION OF THE REGRESSION ANALYSIS USED TO DEDUCE THE PARAMETERS WHICH DO OR DO NOT INFLUENCE THE QBF.

THIS DOCUMENTATION SHOULD INCLUDE:

(A) THE COEFFICIENTS FROM A STEPWISE REGRESSION RUN, THE ANALYSIS OF VARIANCE TABLE FROM THIS RUN, AND THE VARIANCE COVARIANCE MATRIX OF THE ESTIMATED COEFFI-CIENTSJ (B) THE SAME OUTPUTS AS (A) BUT WITH ALL VARIABLES INCLUDED (THAT IS, POOL TEMPERATURE, REACTOR PRESSURE, AND VALVE OPENING TIME); AND (C) PLOTS OF THE RESIDUALS FROM THE MODEL AGAINST PREDICTED AND AGAINST EACH VARIABLE USED.

P.V.

9/10/80 1

1 i

RESPONSE TO QUESTION 3 e

THREE DATA SETS ANALYZED FULL SCALE TESTS PLANT A FULL SCALE TESTS PLANT B HALF SCALE TESTS e

FULL SCALE TEST VARIABLES VALVE OPENING TIME (SERIES A ONLY)

~

WATEP TEMPERATURE REACTOR PRESSURE e

HALF SCALE TEST VARIABLES VALVE OPENING TIME AIR TEMPERATURE WATER TEMPERATURE AIR VOLUME BUBBLE SUBMERGEMCE ABSOLUTE PoESSURE (P.1 P.V.

9/10/80 2

EXPECTED FORP. OF CORRELATION e

RALEIGH BUBBLE 3YP.

}=.J_

2,g y

j -V k e

PERFECT GAS EQUATION AND ISOTHERFAL BUBBLE P.V = MRi V ~ T/P.

1 R ~ (T/P.)I f ~ T -h P. h e

OTHER CONSIDERATIONS:

e SUBP.ERGENCE - FREE SURFACE EFFECT (REDUCED VIRTUAL FASS, HIGHER FRE0.)

e POOL TEP.PERATURE - VAPOR PRESSURE (SAME EFFECT AS ADDING AIR) e BUB 3LE PRESSURE (PAPAPETERS AFFECT) 4G ITl HIGH PRESSURE BU3BLES DEFOR?. LESS P.V.

9/10/80 5

r 4

h 1

4 i

i RESULTS

i.

i e

FULL-SCALE (O 3

BF ~ T I w

T FROM 33 - 74 C y

f i

e FULL SCALE (B) 1 BF ~ (RP)I i

0 T

FROM 31.- 40 C g

d i

o-HALF SCALE I

.41

-2.13 BF ~ (VAIR)

(SUE) I (T )

4 W

i

)

P.,

, T333, VOT HAVE NO EFFECT o

j f

-l 1

i i

P.V.

(

9/10/80 4

..=

SOURCES OF DATA VARIABILITY e

UNKNOWN COMPOSITION IN LINE o-LEAKY val.VE-e UNKNOWN WATEP. LEG FOR SUBS. ACT,

-(PRESSURE, COMPOSITION) e FSI-IN HALF SCALE TEST l

e MULTIPLE VALVE ACTUATION (A & C ONLY) l

~

P.V.

9/10/80 l

5

'+7-#

m ea

-w g

3-7

--P e

ewe y-ey

-<ywyev-

e t --

i i.

j CONCLUSIONS i

i i

4 e

SIGNIFICANT PARAMETEP.S.

i AIR p

o

SUBM, t

e Ty

(

e P3 i

~ e ONLY PARAMETER OF SIGNIFICANT IMPORTANCE IN APPLICATION IS-V3ig, i

h v

t 4

l i.

P.V.

9/10/80 t

I l

r-

~,,. _., _.. cu

-.;-..._.~___._..

,.---..c__..

...,.. _. =.... - - _ - - _ - _...

QUESTION 6 THE MANNER IN WHICH THE RANDOMLY SELECTED VALUES OF VOT ARE EMPLOYED TO REDUCE AN ADJUSTMENT TO RELATIVE BUBBLE ARRIVAL TIMES SHOULD BE JUSTIFIED.

IT IS NOT'0BVIOUS WHY, IF TWO VALVES ARE ACTUATED SIMULTANEOUSLY AND ONE VALVE HAS A AT GREATER THAN THE OTHER, THAT THE DIFFERENCE IN " BUBBLE ARRIVAL" TIMES WILL ALSO DIFFER BY aT.

PR0v!DE THE BASIS FOR THIS PRO-POSED CORRESPONDENCE.

l P.V.

9/10/80 7

[

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I D * *'D)~ * ]D Y]f a m

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i

STANDARD DEVIATICN OF BUBBIZ AR?lVAL TI.v.E Valve 1

.m jl c

ACl 2l 1

W VOT --*=!

i 1

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m)

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+'AC1)

+

02

. _1.

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'D 3 "'VCT

'DL 1

V (B A) = V(t3)

  • 7 (VCT) + V(tg) p,y, V

fcBA)

/ v t3A) 9/10/80 Q

T 4

JUT.TIFICATION e

DEA 9 TINE DATA (DIKKERS - 40 TESTS)

MEAN 2 52 MS.

-0 7

DEV.E 6 MS e

VALVE OPENING TIME STD, DEV.

9.2 To 9.7 MS USE 9 MS 1/3 STD DEV. = 3 AIP. CLEARING TIME DIFFERENCE DUE TO PIPE LENGTH e

= 5 To 17 MS (MK III)

ASSUME 8 MS = 4r

( = 2 MS 5'(EA) = (36 + 9 + 4)I = 7 MS es l

i P.V.

E/10/80 la i

CI CCKPA.YY FRCPRIETARY Class III N.

I t*

_1 1

as l

O g

G 2

3 f

F 1

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c i

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(

.=

0

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I M [L II WVA WC$st$ 773d D P*D

~ " I~D oI.W Til1 IbIeL p,

n wa 9/10/80

//

CONCLUSIONS e

9 MS IS A REASONABLE VALUE FOR STD DEV. OF BUBBLE ARRIVAL TIME e

IT IS COMPAPABLE TO RESULTS OF MORE RIG 0ROUS ANALYSIS e

THE FORCING FUNCTION IS NOT SENSITIVE TO SMALL VARIATIONS IN STD. DEV. OF B.A.T.

e NO CHANGE IN SPllA RESULTS EXPECTED.

P.V.

9/10/80 i

QUESTION 7 THE EFFECT OF SRV LINE LENGTH AND HYDRAULIC RESISTANCE ON BUBBLE ARRIVAL TIME REQUIRES ADDITIONAL CLARIFICATION.

EXPLAIN WHAT THE " MAXIMUM FOURIER IRANSFORM" SHOWN IN FIGS 15-17 REPRESENTS IN THE RESPONSE TO QUESTION 11.*

IS IT THE ENVELOPE OF ALL THE MONTE CARLO TRIALS?

IF SO, HOW MANY TRIALS ARE INVOLVED?

THE RESPONSE ALSO STATES THAT THESE CALCULATIONS WERE PERFORMED FOR A TYPICAL MARK II PLANT.

IS THIS AN ERROR OR WAS IT REALLY DONE FOR MARK II?

IF IT WAS DONE FOR A MARK II PLANT, JUSTIFY THE APPLICABILITY OF RESULTS FOR MARK 111 GEOMETRY.

IN ADDITION, PROVIDE ADDITIONAL INFORMATION TO JUSTIFY THAT THE LINE LENGTH AND ASSOCIATED HYDRAULIC RESISTANCE FOR THE SRV LINES FOR ALL MARK lll CONTAINMENTS WILL RESULT IN NEGLIGIBLE EFFECT ON BUBBLE ARMIVAL TIME AS WELL AS BUBBLE FREQUENCY.

l P.V.

9/10/80 /3

RESPONSE TO QUESTION 7 e

THE " MAXIMUM FOURIER TRANSFORM" IS THE ENVELOPE OF FOURIER TRANSFORMS FROM 22 MONTE CARLO TRIALS e

THE CALCULATIONS WERE PERFORMED FOR A MARK II PLANT e

THE RESULTS B0UND MARK III APPLICATIONS OF THE METHOD e

ADDITIONAL RESULTS FROM A MARK II DL VOLUME SENSITIVITY ANALYSIS AND COMPARISOf! WITH MARK III DL VOLUME VARIABILITY l

P.V.

9/10/80

/4

60 -

a 0-0 a

-3

, ),76 x 10 sec/ft3 0&

N (V - 57.2) sec at =

V e

3 40

  • e*

D e

a k

a g 30 2

e u

3 8; 20

,e s

e VALVE tD e

AC 10 D

g r, JA 0

55 60 65 70 75 80 85 90 SRV Discharge Line Volume (ft )

FIGURE 1 - Air-Clearing Time vs. Discharge Line Volume l

P.V.

9/10/80 i

/5 1

t

N Effects of SRV Discharge Line Volume on Bubble Frequency and Delay Time I

3 Discharge Line Volume (ft )

Plant Vmax(Valve #)

Vmin(Valve #)

AV(ft )

Af Af

^ ("#

^ (5"C 3

2 gx min

-Mark II 88.1 (SC) 57.2 (IB) 30.9 0.83 0.96 1.05 0.054 Mark III -- Plant 1 53.36 (VI) 45.65 (V6) 7.71 0.98 1.03 0.41 0.014 Plant E 64.41

( 9) 54.51 (14) 9.90 0.92 0.97 0.41 0.017 Plant 3 50.167 (12) 46.937 (17) 3.23 1.00 1.02 0.16 0.006 Plant 4 57.78 (16) 55.00 ( 3) 2.78 0.95 0.97 0.16 0.005 Plant 5 49.9 (12) 46.7 (17) 3.2 1.00 1.02 0.16 0.006 Plant 6 57.596 (16) 49.600 ( 8) 7.996 0.95 1.00 0.41 0.014 Plant 7 50.0

( 1) 40.6 (12) 9.4 1.00 1.07 0.57 0.017 Notes:

laV " Y

-Y mx min 2

=3 adjustment factor AF 3af

  • IO I IIZ) IAf

- AFmin}

m

=(AV)(slope)where" slope"ishbasedonFigure1.

4aT P.V.

~

9/10/80

/4

2(c).2 MARK III

~

SRVA REVIEW RESPONSE TO QUESTION 2(c): (CONTINUED)

TABLE 2(c).1 TWO SAMPLE MEDIAN TEST AB0VE BELOW GROUP 1 5

5 CHI. SQUARE =.125 GROUP 2 20 20 NOT SIGNIFICANT TABLE 2(c).2 T-TEST N

MEAN VARIANCE STD. DEV.

GROUP 1 10 53.300 74.678 8.642 GROUP 2 40 51.225 26.487 5.147 T = 0.728 ON APPROX. 10.65 DEGREES OF FREEDOM NOT SIGNIFICANT i

PRELIMINARY RP-1

A 3.4 TABLE 3.1.2

. PLANT A CORRELATION MATRIX (1)

(2)

(3)

(4)

(1) 1.000 (2)

-0.486 1.000 (3)

-0.219

-0.414 1.000 (4) 0.282

-0.508 0.363 1.000 VAR -1 = LN V0T VAR 2 = LN IW VAR 3 = LN RP VAR 4 = LN BF PRELIMINARY RP-2 i

-....I

Ao3.5 TABLE 3.1.3 PLANT A A. FULL MODEL (ALL VARIABLES FORCED) 2 R

= 0.3096 SEE = 0.1081 VARIABLE COEFFICIENT STD. ERR F-RATIO LN TW

-0.8487 0.5064 2.81 LN RP 0.0746 0.0402 3.44 LN V0T 0.0673 0.0535 1,59 CONSTANT 6.2222 DEGREES OF FREEDOM = 48 RESIDUAL SUM OF S0VARES = 0.5608 B. REDUCED MODEL (SIGNIFICANT AT.05 LEVEL) 2 R

= 0.2585 SEF. = 0.1097 VARIABLE COEFFICIENT STD ERR F-RATIO LN IW

-1.4862 0.3560 17.43 CONSTANT 10.6053 DEGREES OF FREEDOM = 50 RESIDUAL SUM 0F SQUARES = 0.6022 PRELIMINARY RP-3

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TABLE 3.1.4 i

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3 2.1/94 2.1701

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A.3.10 TABLE 3.1.5 PLANT A' ANALYSIS OF VARIANCE FULL DEGREES OF SUM 0F MEAN SOURCE FREEDOM SQUARES SQUARE F-RATIO REGRESSION 3 0.2514 0.0838 7.1726 REMAINDER 48 0.5608 0.0117 TOTAL 51 0.8122 REDUCED DEGREES OF SUM 0F MEAN SOURCE FREEDOM SQUARES SQUARE F-RATIO REGRESSION 1 0.2100 0.2100 17,4361 1 REMAINDER 50 0.6022 0.0120 TOTAL 51 0.8122 PlELI::INARY RP-6

A.3.11 f TABLE 3.1.6 PLANT A VARIANCE - COVARIANCE MATRIX OF COEFFICIENTS FULL LN IW LN RP LN V0T LN TW 0.2564 0.012149 0.01770 LN RP 0.001616 0.001139 LN VOT 0.002862 REDUCED VAR LN TW 0.1267 = PRELIMINARY RP-7

A.3.15 i TABLE 3.2.3 HALF SCALE A. FULL MODEL (ALL VARIABLES FORCED) 2R = 0.8610 SEE = 0.0730 VARIABLE C0 EFFICIENT STD. ERR F-RAf10 LN VAIR -0.4145 0.0638 42.17 LN SUB -0.4764 0,2492 3.65 LN PRES 0.5904 1.0006 0.35 LN IW -2.2066 0.2919 57.14 LN TA -0.1997 0.7424 0.07 LN V0T -0.0237 0.0192 1.52 CONSTANT 15.5718 DEGREES OF FREED 0f1 = 28 RESIDUAL SUM 0F SQUARES = 0.1493 l PRELIMINARY RP-8

A.3.16 TABLE 3.2.3 (CONT.) . HALF SCALE B. REDUCED MODEL (SIGNIFICANT AT.05 LEVEL) 2 R = 0.8492 SEE = 0.0723 VARIABLE COEFFICIENT STD. ERR F-RATIO LN VAIR -0.4103 0.0625 43.07 LN SUB -0.3302 0.0322 105.19 LN IW -2.1317 0.2543 70.28 CONSTANT 13.8760 DEGREES OF FREEDOM = 31 RESIDUAL SUM 0F SQUARES = 0.1619 PRELIMINARY RP-9 n -e

A 3.28 4 TABLE 3.1.3 . PLANT B A. FULL MODEL (ALL VARIABLES FORCED) 2R = 0.3621 SEE = 0.2227 VARIABLE COEFFICIENT STD. ERR F-RATIO LN TW 0.0203 3.5524 0.00 LN RP 0.3431 0.0638 28,94 CONSTANT 0.7084 DEGREES OF FREEDOM = 51 RESIDUAL SUM 0F SQUARES = 2.5298 B. REDUCED MODEL (SIGNIFICANT AT.05 LEVEL) 2 R = 0.3621 SEE = 0.2206 VARIABLE COEFFICIENT STD. ERR F-RATIO LN RP 0.3431 0.0631 29.52 CONSTANT 0.8244 DEGREES OF FREEDOM = 52 RESIDUAL SUM OF SQUARES = 2.5298 PRELIMINARY RP-10}}

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