an interactive code for a pressurized water reactor ... · calhoun: the nps institutional archive...

Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1980

An interactive code for a pressurized water reactor

incorporating temperature and Xenon feedback.

Heath, Gregory Garver

Monterey, California. Naval Postgraduate School

http://hdl.handle.net/10945/17616

ammHBE

HSS«

Pa

mmsSa9vSM

SXPSS2ESeww

BBttjtts«l

s

ttHSH

S8as

mmJP

»

DUDLEY KNOX *'"'

„«mNAVAL POSTGRADUATE SCHOOt

MONTEREY, CALIF 339*0

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESISAN INTERACTIVE CODE FOR A PRESSURIZED WATER REACTOR

INCORPORATING TEMPERATURE AND XENON FEEDBACK

by

Gregory Garver Heath

June 1980

Thesis Advisor P. J. Marto

Approved for public release; distribution unlimited

T196S81

UnclassifiedSECURITY CLASSIFICATION Of THIS *tSt fW*»m* Dmia EnffH)

REPORT DOCUMENTATION PAGErcrort nuuK*

READ INSTRUCTIONSBEFORE COMPLETING FORM

2. OOVT ACCKMIOM NO. » »ICi»iInT'$ CATALOG NUMIE*

4 TITLE rantf SuA«(((«)

An Interactive Code for a Pressurized WaterReactor Incorporating Temperature and XenonFeedback

»• TYPE OF REPORT * PERIOO COVERED

Master's Thesis: June 1980

• PERFORMING OMC. REPORT NuMIIN

7. AuTMORru i. CONTRACT OH GRANT NUMltMn

Gregory Garver Heath

# »(MO*MINd ORGANIZATION NAME anO ADDRESS

Naval Postgraduate SchoolMonterey, California 93940

10. PROGRAM ELEMENT. PROJECT taskAREA * WORK UNIT NUMIIM

II CONTROLLING OFFICE NAME ANO ADDRESS


12. REPORT DATE

June 1980II. NUMBER OF PAGES

93

IT MONITORING AGENCY NAME » » <• CSSCI » (it Itarmnt Irom Contrnlltnt OMIe«l


I*, security class. «h >m ( report)

Unclassified

li«. OBCLASBIFlCATSCHEDULE

ION/ DOWNGRADING

IE. DISTRIBUTION STATEMENT (ot t*i» *»»«/ii


17. DISTRIBUTION STATEMENT fat r^. f.-rmr, ~(m~4 In !•<>* 20. II dllfrmni Kmmon)

IS. SUPPLEMENTARY NOTES

IS KEY WORDS (Continue em r»w»r»» ><*• II n»c»*»arr and i4i\itty my bloc* nsm»mmr>

Pressurized Water Reactor, Xenon Feedback, Moderator Feedback

20. ABSTRACT (Conllnttm on rmvmrmm «/<»• II n»c»*»+rr an* Idrntitllr my mlmcM •»«j

An interactive computer model of a highly enriched pressurized water reactor

was developed, using the applicable plant parameters from Shippingport AtomicPower Station. The point reactor kinetics equations for one delayed neutronprecursor group were linearized using small perturbation theory. The model

included both moderator and Xenon-135 reactivity feedback effects, as well as

an automatic reactor protection and average reactor coolant temperature control

system. The thermal response of the model plant was simulated for normal

operating transients induced either by control rod or turbine load changes. The

nn womm*» I JAN 71 1473 EDITION O* ' MOV SS is OBSOLETE

S/N 0102-014- 4401:

Unclassified

Unclassified<"*>•• «•«• *««•*•*

post-shutdown Xenon transient response was also modeled. The interactive

program was coded in FORTRAN-IV language, and the simulation program was

coded in IBM CSMP-III language.

DD Form 1473 Unclassified,,J <la.1j3 .. . i i


An Interactive Code for a

Pressurized Water ReactorIncorporating

Temperature and Xenon Feedback

by

Gregory Garver HeathLieutenant Commander, United States Navy

B.S.M.E., United States Naval Academy, 1971

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN ENGINEERING SCIENCE

from the

NAVAL POSTGRADUATE SCHOOLJune, 1980

ABSTRACT

An interactive computer model of a highly enriched pressurized water

reactor was developed, using the applicable plant parameters from the

Shippingport Atomic Power Station. The point reactor kinetics equations

for one delayed neutron precursor group were linearized using small

perturbation theory. The model included both moderator and Xenon-135

reactivity feedback effects, as well as an automatic reactor protection

and average reactor coolant temperature control system. The thermal

response of the model plant was simulated for normal operating transients

induced either by control rod or turbine load changes. The post shutdown

Xenon transient response was also modeled. The interactive program was

coded in FORTRAN-IV language, and the simulation program was coded in

IBM CSMP-III language.

TABLE OF CONTENTS

I, INTRODUCTION - 9

II. MODEL DESIGN CONSIDERATIONS - 11

A. PRESSURIZED WATER REACTOR - - 11

B. MODEL AND PROGRAM FLEXIBILITY 13

III. MODEL DEVELOPMENT 15

A. POINT REACTOR KINETICS EQUATIONS - 15

1. Zero Power Reactor Transfer Function 17

2. Limitations 18

B. REACTIVITY FEEDBACK MECHANISMS — 19

1. Xenon-135 Transfer Function 21

2. Moderator Temperature Feedback 24

C. THERMAL ANALYSIS - 26

1. Reactor Heat Transfer Function 26

2. Heat Exchanger Transfer Function 29

3. Primary Piping Transfer Functions 35

D. OVERALL PLANT BLOCK DIAGRAM - - 37

E. MODEL CONSTANTS 38

IV. RESULTS 42

A. INTERACTIVE PROGRAM 42

B. SIMULATION PROGRAM - 48

V. CONCLUSIONS AND RECOMMENDATIONS - 54

APPENDIX A: DEVELOPMENT OF THE XENON FEEDBACK TRANSFERFUNCTION COMPONENTS 56

APPENDIX B: DEVELOPMENT OF THE REACTOR HEAT TRANSFERFUNCTION 61

APPENDIX C: DEVELOPMENT OF THE HEAT EXCHANGER TRANSFERFUNCTION 65

APPENDIX D: DEVELOPMENT OF THE PRIMARY PIPING FUNCTIONS -- 67

APPENDIX E: INTERACTIVE PROGRAM LISTING - 71

APPENDIX F: SIMULATION PROGRAM LISTING 78

APPENDIX G: INTERFACE PROGRAM LISTING 91

LIST OF REFERENCES 92

INITIAL DISTRIBUTION LIST 93

LIST OF FIGURES

1. Schematic of the Model Plant 12

2. Block Diagram of the Zero Power Reactor TransferFunction 18

3. Block Diagram of the Reactor Transfer Function withXenon-135 and Moderator Temperature Feedback Loops,and External Reactivity 20

4. Xe-135 Decay Scheme - - 21

5. Simplified Xenon-135 Decay Scheme 22

6. Block Diagram of the Reactor Transfer Functionwith Xenon-135 Feedback and External Reactivity 24

7. Block Diagram of the Reactor Heat Transfer Function 29

8. Block Diagram of the Heat Exchanger Transfer Function 34

9. Block Diagram of the Transport and Mixing DelayFunctions 38

10. Overall Plant Block Diagram 39

11. Interactive Program, Introduction and Instructions 43

12. Interactive Program, Initial Power Level andSimulation Choice Inputs 44

13„ Post-shutdown Xenon-135 Behavior 45

14. Interactive Program, Control Rod Movement Inputs 46

15. Interactive Program, Turbine Load Change Inputs 47

16„ Interactive Program, Logic Routine Example 49

17. Power, Reactivity, and Temperature Response to a

20 to 40% Turbine Load Change - 50


60 to 40% Turbine Load Change - 51

19o Power, Reactivity, and Temperature Response to a

10 second Inward Control Rod Movement 52


10 second Outward Control Rod Movement 53

D-l . Mixing Volume 69

I. INTRODUCTION

Computers have been used in the design and analysis of nuclear

reactors since the inception of reactor technology, and many codes have

been developed. More recently, digital computer programs have been used

as learning devices for nuclear engineering students. The formulation

of the computational problem of predicting the behavior of a nuclear re-

actor has been greatly facilitated with the use of high level computer

languages.

The purpose of this work was to develop a computer assisted learning

device to be used by students taking nuclear engineering courses at the

Naval Postgraduate School. The program graphically displays the simulated

kinetic and thermal transient responses of a pressurized water reactor

power plant. The reactivity feedback effects of Xenon-135 poisoning and

moderator temperature are incorporated into the model. Normal operating

transients, starting from a steady state critical condition, can be

induced by ramp changes in either control rod position or turbine load.

The initial reactor power level and reactivity change mechanism are

chosen by the program user. For user convenience, these inputs are

prompted and entered interactively, after which the simulation is run

with no further user action required.

A pressurized water reactor (PWR) was modeled as it is the most

common type of reactor used for power plant application. As a realistic

reference, the model design incorporated the applicable characteristics

of the Shippingport Atomic Power Station, whose nuclear parameters were

the most compatible, of available PWR core data, with the assumption of

a highly enriched core made in the model design,

9

The model was developed by treating the reactor kinetics and other

plant component thermodynamic relationships as transfer functions [1].

The point reactor kinetics equations were linearized using a Taylor ex-

pansion or small perturbation technique [2]. This same perturbation

technique and lumped parameter analysis were applied to the plant's

linear differential heat transfer and Xenon-135 equations [3]. The

individual transfer functions were then integrated into an overall plant

block diagram. The program also features a reactor protection and

average reactor coolant temperature control scheme.

IBM CSMP-III language was chosen to formulate the model simulation

as it has inherent routines to invert the transfer functions to the time

doma i n

,

10

II. MODEL DESIGN CONSIDERATIONS

Lumped parameter analysis and first order perturbation theory were

used throughout the model development. All the nuclear variables which

were used in the reactor kinetics and Xenon-135 decay equations were

considered to be averaged values of the variables over the neutron

energy spectrum. Similarly, the thermodynamic variables which were

used in the plant's heat transfer equations were considered to be

averaged values over the volume of the particular component.

Because of these approximations and other assumptions made in the

model development, the simulation should not be considered a design or

stability analysis. Instead, the simulation shows the model's large

scale reactor kinetic and thermal trends during normal operating

transients.

For similar reasons, although certain plant parameters of the

Shippingport Atomic Power Station were incorporated into the model, the

simulation cannot be considered to reflect the operating characteristics

of this power plant. The. Shippingport core is a seed and blanket type

whereas the model core is a uniform mixture of highly enriched fuel

and support materials.

A. PRESSURIZED WATER REACTOR

The pressurized water reactor (PWR) is the most widely used reactor

type in central power plant applications and the only type currently

used in naval propulsion.

A simplified schematic of the modeled PWR plant is shown in Figure

1. The modeled reactor contains a highly enriched core which is light

11

PRESSURIZER

COOLANTPUMP

THROTTLEVALVEa:

CONDENSATEPUMP

Figure 1. Schematic of the Model Plant

water moderated and cooled. The modeled plant contains two closed loop

thermodynamic systems coupled by a heat exchanger.

In the primary system, heat generated from thermal fission is trans-

ferred to the coolant as it passes through the reactor, raising the

coolant's temperature. The high temperature coolant leaving the reactor

is circulated by a pump through tubes inside of a heat exchanger where

it gives up some heat to a secondary fluid. A pressurizer maintains

the primary coolant at a sufficiently high pressure so that the bulk

temperature of the coolant is kept below the saturation temperature.

On the secondary side of the heat exchanger, the temperature of the

entering feedwater is raised to the boiling point and saturated steam

is produced. The steam is delivered to a turbine, is condensed and

returned to the heat exchanger, completing the second closed loop

12

B. MODEL AND PROGRAM FLEXIBILITY

The model was designed to simulate only normal operating transients

from an initial steady state condition. Reactor accidents and startup

were not considered in the model development. However, the model's re-

actor control module will simulate either a full or constant insertion

of control rods if certain parameters are exceeded. This feature was

not incorporated for accident analysis, but to keep parameters within

the limits of the assumptions made in the model development.

The applicable Shippingport plant characteristics are fixed in the

simulation program. User inputs are limited to choosing initial power

level, from which other initial parameters are adjusted, and the plant

perturbation mechanism, either control rod movement or turbine load

change. These perturbations occur at fixed rates which limit the amount

of reactivity that can be inserted during the simulation.

Originally it was envisioned that an overall program would feature

not only interactive input capability but also produce real time graphi-

cal displays of the transient for a user at a time sharing computer

terminal which had graphics capability. However, the computer language

(IBM CSMP-III) required to solve the model's algorithms was not avail-

able on the time sharing system, and furthermore, the programs long

execution time precluded any real time response.

In order to still provide as much user facility as possible with

these restrictions, the interactive feature was partially retained for

data input. Using a computer language available on the time sharing

system (FORTRAN-IV), a program which interactively prompts the user to

13

enter specified controlling parameters was developed. This program in-

corporates logic routines which permit inputs only within requested

ranges „ This feature allows for data reentry if a user error is made,

and ensures that only inputs compatible with the model development's

assumptions are used in the simulation.

After the input is completed, the initial transient conditions are

displayed at the terminal. A separate internal control program then

transfers the user supplied inputs into the simulation program. The

control program then transfers the simulation program to the batch

processing system for execution., The interactive program notifies the

user that this has been done. Hard copy plots of the transient are

subsequently produced. The post-shutdown Xenon behavior module is

located in the interactive program and produces real time graphical

displays at the terminal.

Thus there are three distinct programs:

1. An interactive program to prompt and receive user input,

and also simulate post-shutdown Xenon behavior.

2. A batch processed program which simulates the transientresponse to the user inputs.'

3. An internal control program which interfaces these two

programs.

14

III. MODEL DEVELOPMENT

A. POINT REACTOR KINETICS EQUATIONS

A lengthly and formal derivation of the point kinetics equations is

found in Reference 4 and will not be repeated here. More generally these

equations are obtained from one group neutron diffusion theory with the

assumption that the neutron flux is deparable in time and space, and

with the inclusion of delayed neutrons [5]. They are listed below.

djitl. £ltk£_ Ht)+ £ N C.(t) + Q(t) (1)

^.(t)iJ 1

0(t) - A,C,(t) 1 = 1,2,... (2)dt A y ^' Mi

where 0(t) = Flux amplitude function

/0(t) = Reactivity

C.(t) = Effective concentration of the ith delayedneutron precursor group

Q(t) = Extraneous delayed neutron source strength

a. = Effective delayed neutron fraction from

the ith group

*i = Decay constant of the ith group

and /3 » 2A s Total effective delayed neutroni fraction

These equations are referred to as the point reactor kinetics equa-

tions not because the reactor is considered as a single point in their

application, but since spatial variations are neglected, /3j,A;and A^

are assumed to be constant.

If the neutron flux spatial variation is assumed to be time invari-

ant, 0(t) can be considered to represent the number of neutrons in the

15

core. Equation (1) may then be seen as a neutron rate equation where

the three terms on the right hand side represent the rate of production

of prompt, delayed, and source neutrons respectively.

Equation (2) is a rate equation for the ith delayed neutron precursor

group. The two terms on the right hand side represent production and

decay rates respectively. The precursors are comprised of approximately

thirty isotopes which historically have been divided into six groups

-1 235with decay constants ranging from 0.0124 to 3.0 seconds for U. In

the model, the precursors were considered to be represented by one

effective group characterized by an averaged decay constant [2],

A. Z

-1

and an effective delayed neutron fraction

1*1 1

In equations (1) and (2), reactor power may be substituted for neutron

flux if the precursor concentration is modified by C = E. S*C . .

since

P-Ef Z,»

where P

Ef

If

= Reactor power

= Energy released per fission

= Macroscopic fission cross section

= Integrated one group neutron flux

For a reactor operating at power, the source term contribution to

the overall neutron population is negligible, i.e., Q « 0.

16

Incorporating these assumptions, equations (1) and (2) reduce to:

dPM = S&-Z* P(t) + A C (t) (3)

dCM = -£p(t) - XC(t) (4)

1 . Zero Power Reactor Transfer Function

Consider an initially critical steady state reactor at some power

level P at t £ 0. Equations (3) and (4) each yield:

C =-TX^ P (5)A.A ov

'

Now let P(t) = P + </Wt)

C(t) = CQ

+ </c(t)(6)

/>(t) =/Q

+ <#(t)

where the zero subscript denotes the initial steady state valueand the delta prefix a small perturbation imposed at t = aboutthis value.

Noting that /& =0 for a critical reactor and substituting equa-

tions (5) and (6) into equations (3) and (4) yields for t >

fa Mt) - % S/xt)- 4r Ht)+ x/c(t) (7)

fa <A(t) = -£<A(t) - \</t(t) (8)

where the —-^ term in equation (7) has been neglected.

Taking the Laplace transforms of equations (7) and (8):

s ^>( s ) = A.^($) - JjL<fp(s) +- A</C(s) (9)

SC(s) = —cPPts) - \<Pc& (10)

17

Solving equation (10) for C(s), substituting this into equation

(9), and rearranging, yields:

c/Vcs) _ ?o

tyw s(a* S+A -)

(ID

This is the zero power reactor transfer function, so called because

the reactor is assumed to be operating at a sufficiently low enough

power that no feedback effects are realized. These effects are examined

in the following sections.

Equation (11) may be represented in block diagram form as shown in

Figure 2.

e/>(s>

PGZ(s)

</*P<s)

Figure 2. Block Diagram of the Zero Power ReactorTransfer Function

where Z(s) =

S (a /3

S-hX -)

2. Limitations of the Point Reactor Kinetics Equations

The point reactor kinetics equations derivation is based on

the assumption that the spatial dependence of the neutron flux is

negligible. This assumption limits the validity of these equations to

transients where this remains a reasonable approximation such as those

which result in only small changes in reactivity. The small perturba-

tion technique used in the development of the zero power reactor

18

transfer function also requires only small changes in reactivity if the

first order approximation is to hold. Specifically, /> must be less

than 0.5/3 . Physically, when ^/Jis greater than /3 the reactor is

critical on prompt neutons alone. The simulated transients imposed on

the model were limited to ensure that excessive amounts of reactivity

were not introduced.

Bo REACTIVITY FEEDBACK MECHANISMS

In the zero power reactor point reactor, the power level is assumed

to be so low that it does not affect the reactivity, thus there are no

feedback effects. However, for a reactor operating at a useful power

level, feedback effects do exist and the reactivity becomes an implicit

function of the reactor power level (or neutron flux). This dependence

arises since reactivity depends on macroscopic cross sections which in-

volve the atomic number densities of material in the core:

X = nct

where S = Macroscopic cross section (cm""*)

N = Atomic number density (atoms/cm 3 )

C = Microscopic cross section (cm z)

The atomic number density can depend upon the reactor power level

since the concentrations of certain nuclei are constantly changing due

to neutron interactions. Material densities also depend upon tempera-

ture which is a function of reactor power level and hence the flux.

Duderstadt, J. J. and Hamilton, L. J., Nuclear Reactor Analysis ,

1st ed., Wiley, 1976.

19

The two feedback mechanisms considered in the model were Xenon-let and

moderator temperature.

Reactivity can also be changed directly by an external source such

as control rods containing a neutron absorbing material. Thus the over-

all reactivity can be written as:

where "fix = F P

<#>T= FT

P

cfo = Overall core reactivity

ofee = Externally added reactivity

<//Ox = Xenon-135 feedback reactivity

<fer = Moderator temperature feedback reactivity

Fx = Xeonon transfer function

Fj = Moderator temperature transfer function

Equation (12) with the previously developed zero power reactor

transfer function, given by equation (11), are incorporated in the

block diagram below:

(12)

<&>&)

u*

'*

\ <fal* .P Z(»)

</P<s)

J\*

FT(s)

Figure 3. Block Diagram of the Reactor Transfer Function

with Xenon-135 and Moderator TemperatureFeedback Loops, and External Reactivity

20

The next step in the model development was to derive the Xenon-135

and moderator temperature transfer functions.

1 . Xenon-135 Transfer Function

Xenon-135 is the most significant fission product poidon because

of its enormous thermal neutron absorption cross section and relatively

large fission yield. This isotope is not only produced directly from

fission but also from the decay of other fission products as shown in

Figure 4.

Figure 4. Xe-135 Decay Scheme

Since the /3>~ decay of Iodine-135 (

135I) and Xenon-135 (

135Xe), with

the largest half-lives, are the controlling steps in this decay scheme,

it was simplified by making the following assumptions:

1) All I is produced directly from fission (the production of

Antimony-135 ( Sb) and subsequent decay to I is consideredinstantaneous).

135m,2) The short lived metastable Xe is ignored.

1 353) The removal of I by neutron absorption is negligible for

the neuton flux levels used in the model (10 neutrons/cm sec)

21

4) All the135

I decays to135

Xe,

With these assumptions the effective decay scheme is shown in Figure

5.

Ax 135Cs

Figure 5. Simplified Xe-135 Decay Scheme

135

135Using this decay scheme, the resulting rate equations for I and

Xe are:

c/X(t)

(13)

where

5^= VxZ^tfCt) + AiI(*)-Ax X(t)-<3a x 0<:-t)X(t) (14)

135 3I = I number density (atoms/cm )

135 3X = Xe number density (atoms/cm )

2f = Macroscopic fission cross section (cm" )

= Integrated one group neutron flux (neutrons/cm sec)

1 35dr = Effective I fission yield

1 35^

x= Effective Xe fission yield

A_ = I decay constant (sec" )

1 35 -1

A x= Xe decay constant (sec )

<3" = Xe microscopic thermal neutron absorption crossa

section (cm?)

22

Again, using the first order perturbation technique, let

I(t) = IQ

+ cTl(t)

X(t) = XQ

+ o^X(t) (15)

0(t) = jB

Q+ c/fe(t)

where the zero subscript denotes an initial steady state value andthe delta prefix denotes a small perturbation about this value.

Upon substituting equations (15) into equations (13) and (14), and

taking the Laplace transform, the relationship between the perturbation

1 35in Xe and is derived (See Appendix A):

— = ; : —— = <=»x (S) (16)</*0<s} S 2 + (03X^o tV*Ai)st Ar(<3a

x ^ +

A

x )

135The change in reactivity caused by a small perturbation in Xe

concentration is also derived in Appendix A:

<7^X(S> 1? = *x (17)^<s > X + SL U

<5*

1 35where X = Equilibrium Xe number density before the

perturbation (atoms/cm^)

U = Uranium-235 ( U) number density (atoms/cm )

<% = Microscopic thermal neutron absorption cross

section of U (cm )

A perturbation in neuton flux ( o^0) is directly proportional to a

perturbation in reactor power ( cfp) as shown by:

23

where Ef

= Energy released per fission

O O C 1

Hf= Macroscopic fission cross section of U (cm )

or

c/<Zks)= k

The product of equations (17), (16), and (18) yields

(18)

^x(s) ^X(S) </fr(s) <^x(s) _= —I — ^X^X (S) K - rV(SJ</>X(s) ^(s) c^PCS) ^P(s)

x xwi* x (19)

Equation (19) is the transfer function relating reactor power and

135Xe feedback reactivity. This equation is shown in block diagram

form in Figure 6 where it has been incorporated with the previously de-

rived zero power transfer function given by equation (11).

<fp#)

d/Ogs)

«x ^ </X($)

QJ»^«/b(s)

K

c*

sP Zls)

</>(s)

)

Figure 6. Block Diagram of the Reactor TransferFunction with Xenon-135 Feedback andExternal Reactivity

2. Moderator Temperature Feedback

Reactivity feedback from changes in moderator temperature occurs

as a result of changes with moderator density. The density is also a

24

function of pressure, however, the pressure coefficient of reactivity is

typically two orders of magnitude smaller than the temperature coeffi-

cient, and was therefore not considered in the model development. The

moderator density affects the moderator number density and hence the

macroscopic scattering cross section of the moderator.

The primary mechanism for the thermal ization of the prompt and de-

layed neutrons is by elastic scattering interactions with the moderator

nuclei. Hence, variations in the macroscopic scattering cross section

will affect the rate at which neutrons become thermal ized. Changes in

the thermal ization rate affect the fission rate, or reactor power level.

Power level changes affect the moderator temperature, thus a feedback

loop is created.

Because the moderator is also the coolant in the model, its temper-

ature is not only a function of reactor power but also a function of the

heat transfer process occurring in the heat exchanger, thus complicating

the feedback loop.

Therefore, in order to develop this feedback mechanism analytically,

it is first necessary to model the plant's heat transfer processes.

This thermal analysis is done in the following section.

Another temperature feedback mechanism is the broadening of the

Uranium-238 resonance absorption cross section for neutrons with increas-

ing temperature. Because a highly enriched core was assumed in the

model, with little Uranium-238, this effect was not considered.

25

C. THERMAL ANALYSIS

1 . Reactor Heat Transfer Function

A lumped parameter model was assumed. This simplification pro-

vided a set of ordinary differential equation which were sufficiently

accurate for the simulated normal operating transients. In the lumped

parameter model, heat transfer in the reactor was assumed to occur at a

single point. Thus, spatial variations were neglected. The core was

considered to be a homogenized mixture of the uranium alloy fuel, the

fuel cladding, and other structural materials, with a constant thermal

capacity,,

The equation for the heat flow from the core was obtained from a

basic heat balance. The heat generated from fission equals the heat

required to change the temperature of the core materials plus the heat

transferred to the coolant. On a per unit time basis, the heat balance

is:

P(t) = C,

dTF(t)

dt+ h

FMTF Ct)-

TAV

(t) (20)

where P(t) = Total Power generated in the core (Btu/sec)

T-(t)= Average temperature of the core materials (°F)

T.v(t) = Average reactor coolant temperature (°F)

CF

= Total thermal capacity of the core materials (Btu/°F)

hF„ = Total heat transfer coefficient (Btu/° F sec)

A similar heat transfer balance must also hold for the heat being

transferred to the coolant and transported out of the core. This heat

is the last term of equation (20) and is transferred to the coolant as:

26

hF«[TFCt)-TAv(*)] = CM s!2*<S + mmc [V^-Tc,^] (21)

where CM= Total thermal capacity of coolant in the core

M(Btu/°F)

m = Coolant mass flow rate (lbm/sec)

TH

= Average reactor coolant outlet temperature (°F)

o

Tp

= Average reactor coolant inlet temperature (°F)L

i

C = Specific heat of reactor coolant (Btu/lbm°F)

For simplification, the average reactor coolant temperature is

assumed to be given by:

TAv(t) = [T^(0+ THo (t)] /2 (22)

Rearranging equation (20) yields:

TfC-O -ffi dl££l = TAvCO + li PCt) (23)dt Cp

where • l - tt—"fm

Substituting equation (22) into equation (21) to eliminate T"

Hyields:

TAv(t)[lt2|l *Ya <%£! = TF (t) + 2|Tc,(t) (24)L To J dt 'o 1

where Jo = —— , and

^FM

27

Now 1 et

P(t) = P + c/,

p(t)

Tp(t)= T

p+ cTT

F(t)

o

TAV

(t)= TAV

+ ^ TAV

(t) (25)

o

TH f*)- T

Ho+ ^T

Ho(t)

Tc.

(t)= Tci

+ ^c (t)

1

where the zero subscript denotes a steady state value and the

prefix a small perturbation about this value.

Substituting equations (25) into equations (22), (23), and (24),

eliminating the average temperatures TF(t) and T.„(t), and taking Laplace

transforms, the following relationship between reactor coolant inlet and

outlet temperature perturbations is derived (see Appendix B):

<^TH<> <s) = —(26)

where

tf = lj-'° =

This equation is the reactor heat transfer function for the reactor

coolant outlet temperature as a function of the reactor coolant inlet

temperature and reactor power.

A block diagram representation of this transfer function is shown

in Figure 7.

28

</*PU)

Figure 7. Block Diagram of the Reactor HeatTransfer Function

In Figure 7

BC(S) = {?-HH«)-<H

GH(S) =

{^-HfihHH2. Heat Exchanger Transfer Function

As in the derivation of the reactor heat transfer function, a

lumped parameter model was assumed for the heat exchanger . Two points

of energy storage were assumed, the primary coolant water and the water

on the secondary side of the heat exchanger. The thermal capacity of

the heat exchanger metal was included with that for the secondary water,

since the thermal resistance on the primary side is predominant. A

further assumption was made that the time spent by the primary coolant

29

while it passed through the heat exchanger was negligible in comparison

with the time spent in the primary piping.

The state of the steam produced on the secondary side of the heat

exchanger was assumed to always be dry and saturated and that the

secondary water is always at the saturation temperature for the existing

pressure. These assumptions were justified because moisture separators

and recirculation can provide high quality steam and preheating of the

feedwater.

With these assumptions, the following equations were obtained from

a heat balance per unit time:

%c [^Ctl-Tcfel] = Z» £E^> + h™[TAvecO-TsOo] (27)

hmffaeta -TsCtl ] = Cg sO|£} + pl(o (28)

where Tu .(t) = Heat exchanger coolant inlet temperature (°F)HI

Tr

(t) = Heat exchanger coolant outlet temperature (°F)

T.w (t) = Heat exchanger average coolant temperature (°F)AV

B

Ts(t) = Saturated steam temperature (°F)

h TM = Total heat transfer coefficient (BTU/°F.sec)In

C,. = Total thermal capacity of coolant in the heatn

exchanger (BTU/°F)

Cs

= Total thermal capacity of heat exchanger metal

and secondary water and steam (Btu/°F)

P.(t) = Power delivered by the heat exchanger (BTU/sec)

m = Coolant mass flow rate (lbm/sec)m

30

The total heat transfer coefficient, a function of the primary coolant

flow rate (a constant in the model) and the heat transfer characteristics

of the heat exchanger, was assumed to be constant. Also, the time delay

in transferring heat across the heat exchanger tubes was neglected.

This changed the shape of the initial thermal transient but had little

effect on the basic dynamics of the secondary loop.

Again, as a simplification, the average temperature of the coolant

in the heat exchanger was assumed to be given by

X - \ {\ +V (29)

The power delivered by the steam generator is proportional to the

product of the steam flow rate and the difference in enthalpy between

the steam and feedwater

Ktm [Tavb (0 - TsCt)] = m3 (HS - Hpv, ) * CS s!|£!

where m = Steam flow rate (lbm/sec)

H = Saturated steam enthalpy (Btu/lbm)

HF

= Feedwater enthalpy (Btu/lbm)

This equation assumes the steam and feedwater flow rates are always

equal and thus neglects any instabilities in the secondary steam.

As discussed in Reference 4, the enthalpy of saturated steam is

nearly constant over a wide range of pressure, varying from 1198 Btu/lbm

to 1204 Btu/lbm over a pressure range from 200 to 800 psig. The feed-

water enthalpy,which depends on condenser pressure, is usually between

50 and 100 Btu/lbm. Thus the enthalpy difference may be regarded as a

31

constant, and the power delivered by the heat exchanger is directly

proportional to the steam flow rate.

The impedance to steam flow caused by the turbine is nearly indepen-

dent of turbine speed. If constant backpressure is assumed, the steam

flow rate is directly proportional to the throttle opening at a given

pressure. Thus,

ms

= y*sA

2where /& = Saturated steam pressure (Ibf/in )

A = Proportionality factor which is a functionof the throttle setting 1 bm in^

Ibf sec

The numerous assumptions made in the heat exchanger model development

limit the accuracy of the resulting equations. However, the errors in-

volved in these assumptions are usually less than the amount of uncertainty

in the engineering valves of the coefficients used in the equations.

Recalling the previous assumption that

dTAV

B

(t)

-at— =° • and

Substituting equation (29) into equation (27), yields:

mMc[THl (t)- Tco(t)] = WT„r^[TH^t)+ TcoOo] - Ts(o]

Solving equation (30) for Tr , gives:Lo

(30)

Tc C*> = **(.)- tmi-O. (31)

fl+Kl)

32

where K, =

Ktm

Substituting equation (29) into equation (28) gives:

k™ (l [T̂ + Tci(^

J- Ts co . =r cs i^i1

+ put)

Rearranging this expression,

cs cJTsct) _ - r i i „(32)

Let THi

(t) = TH>

+ <AH<(t)

TC

f*)= T

Co °,

T e (t) = T v

PL(t) = P

L+

o

<As(t)

^Ts(t)

c/V,(t)

(33)

where the lowest zero subscript denotes a steady state value and

the delta prefix a small perturbation about this value.

By substituting equations (33) into equations (31) and (32), and

taking the Laplace transform, the following set of equations is derived

(see Appendix C)

:

<ATs (s) =Is + 1

(34)

^CoCS) = 2</Ts(s) - <AT^(s)[l-K±l

1+Ki

where T L = -r-*-

(35)

33

These equations are represented in a block diagram in Figure S.

JTC (s)

;rs*<LJ (

1

I

1 i

J

•Kl

<JTs(s>1

-

1*

Kl

Kl

1

' i

Jtc Is)

C- ;

v £+

J ^ ' \ji \

<*TH (rt

1

•

M

<S(!)

Figure 8. Block Diagram of the Heat ExchangerTransfer Function

With </tu and <P\>. as inputs, equations (34) and (35) form anH

iL

algebraic loop in </*Tr and c/t~. These two equations were solved

with the use of an inherent functional routine available in the CSMP-III

language which was used to formulate the model.

34

3. Primary Piping Transfer Functions

While circulating through the primary loop, the coolant under-

goes mixing and transport delay effects. For example, a transient in

the coolant temperature at the heat exchanger outlet does not appear at

the reactor inlet until sometime later. Where there are volume or flow

direction changes, as in the reactor coolant inlet plenum, mixing occurs

causing a smearing of a temperature transient. Both of these effects

were approximated in the model by combinations of two types of time

delays: a pure transport delay and a simple mixing delay.

Assuming no mixing in the primary piping and no heat loss with

perfectly insulated pipes, pure transport delays are encountered in the

piping runs between the reactor and heat exchanger. With these assump-

tions, the temperatures involved in the transfer of heat between the re-

actor and heat exchanger can be given as

TH

(t) = TH

(t - T3

)

where the inlet coolant temperature to the heat exchanger J u has theM

i

same form as the outlet temperature of the reactor T,, after a fixed

o

transport delay T-. This transport delay can be approximated by the

following differential equation which is derived in Appendix D.

i dt o

Similarly, the transport delay from the heat exchanger outlet to

the reactor inlet plenum is:

Y (t) r4

«c(t)=

'pdt

35

(37)

where Tp (t) = Reactor inlet plenum coolant temperature (°F)

Tr (t) = Heat exchanger outlet coolant temperature (°F)Lo

This can be approximated by

Tc .

p(t) 4-M ^ = fcoCt) (37)

As in the previous development, let

TH

(t) = TH

+ <AH

(t)

o o

TH

(t) = TH>

+ AH .(t)

(38)i p i po i p

v '

TC

(t) = TC

+ ^TC

(t)

o oQ

o

Tc

(t) = Tc

+ <AC

(t)

ip ipo ip

where again the lowest zero subscript denotes a steady state value

and the delta prefix a small perturbation about this value.

After substituting equations (38) into equations (36) and (37),

taking the Laplace transform, the following transfer functions are

derived (see in Appendix D).

A^ (5) = § (39)

</Tc,pC5) _ l(40)

</Yca (s) 14- HS

36

Combined mixing and transport effects are encountered at the reactor

and heat exchanger inlet and outlet coolant plenums. For simplification,

only the mixing effects at the inlet plenums were considered in the

model. Assuming perfect mixing and after performing a heat balance on

the plenum concerned, the combined mixing and transport effects are ex-

pressed by differential equations developed in Appendix D of the form

Y-£lil T <t)-T1<t)

whereT. (t) = Plenum inlet temperature (°F)

T (t) = Plenum outlet temperature (°F)

I= Mixing delay

As before, by using a small perturbation technique, and taking the

Laplace transform, the following transfer function is derived (see

Appendix D):

^2i!L = ,.., 1 (41)c/Th^(s) l tfs

Block diagram representations of the coolant piping transport and

mixing transfer functions is shown in Figure 9.

D. OVERALL PLANT BLOCK DIAGRAM

The transfer functions developed previously for the zero power point

1 35reactor, Xe feedback, reactor and heat exchanger heat transfer, and

the primary piping were interconnected resulting in the overall model

block diagram shown in Figure 10. The moderator temperature feedback

37

REACTOR<fT (s) / ^W s >

/•&TS

Jf

/ /

/^s /+%s1 1

i

HEATEXCHANGER

/

^o(s> / +fs Vtc

.csi

> r~

Figure 9, Block Diagram of the Transportand Mixing Delay Functions

loop is seen to consist of the heat transfer process and primary piping

transfer functions which yield v~[-. and <7T,, . These temperaturesi o

are summed, then halved, yielding T«v

, which is then multiplied by

the negative temperature coefficient °*T, generating the moderator

temperature feedback reactivity /^j.

E. MODEL CONSTANTS

The following plant parameters from the Shippingport Atomic Power

Station were obtained from Reference 6 and used in the model development,

38

/***

/*/&

hrn

<#htt)

t/Tc^s)

<*T

1

J

777T

—I

—

cT^ts]

'-

/-/ct

—*—

QH±K> c/*rHiis)

J+Ts

l+fts

Jtu#

GhOJ

<^>e<s)

O1

<&«s>V> + o^tts)

c^b(3)

A?fc)

cft^l

GhU)

</P(5)

<#<s)

G^S)

c^zka

Figure 10. Overall Plant Block Diagram

39

1

.

General Parameters

a. Reactor thermal power

b. Reactor coolant system pressure

c. Reactor coolant average temperature

d. Steam pressure at full load

2. Reactor Coolant System

a. Reactor coolant flow rate

b. Reactor coolant outlet temperature

c. Reactor coolant inlet temperature

d. Coolant volume in core

3. Reactor Core

a. Configuration

b. Size

c. Fuel load U (seed)

d. Composition (seed)

1

)

Water

2) Fuel alloy

3) Zircalloy

e. Control Rods

1

)

Total rod worth

2) Scram time

231 MW

2000 psia

523° F

600 psia

6280 lbm/sec

538° F

508° F

103 ft3

Right cyl inder

6.8 ft. dia X 6 ft. high

75 kg

43.5 v/o

30.0 v/o

34.1 v/o

0.256 k

0.35 sec time delay

1 .0 sec rod drop

4. Nuclear Data

a. Thermal neutron flux

b. Prompt neutron lifetime

14 22 X 10 n/cm sec

5.6 X 10" 5sec

40

c. Effective delayed neutron fraction 0.0077

-4d. Temperature coefficient of reactivity -3.1 X 10 a k/°F

5. Reactor Protection Setpoints

a. Scram

1) High reactor power 138%

2) High reactor coolant outlet temperature 550°F

b. Cutback

1) High reactor power 114%

2) High Startup rate 1.74 Decades per min,

41

IV. RESULTS

A. INTERACTIVE PROGRAM

Figures 10-16 are examples of the interactive program output. As

shown in Figure 10, the user is first given a description of the purpose

of the overall program and general instructions for input entry. As

shown in Figure 11, the user is then prompted to enter an initial steady

state power level, after which the corresponding major plant parameters

are displayed. The user is then prompted to choose the type of simula-

tion, either plant transient at power, or post-shutdown Xenon-135

behavior. The user must be at the Tektronix 4012 console in the computer

center if the latter is chosen.

If the post-shutdown Xenon-135 behavior is chosen to be examined,

graphs such as those shown in Figure 13 are generated and displayed on

the Tektronix' s screen. In addition to showing the time response of the

Xenon, the time of its peak and associated maximum reactivity are dis-

played.

If the plant transient simulation is chosen, the user is then prompted

to choose the mechanism for initiating the transient, either control rod

movement or turbine load change. In Figure 14, the user has chosen the

former. The program then prompts the user to enter the direction and

time length of the control rod movement. In Figure 15, the turbine load

change was chosen and the program request the final turbine load. In

either case, a summary of the transient inputs is displayed with a

notice that the interactive portion is complete.

42

i CDUI * <r Z Uien .^

i Li i-t 7*

2 — 2 — B H-

O 3 a 2 ^hk i_

*

en UI -J 2cn *** t~ u U t-UI ^ CJ 2 z2 cc 2 UI 2 H-l COo <X Um CJ w i

_j H i3 u. 2<r cj UI in ££ 2r « 2 n UI 2Lb. UI i—

i

Jl iH b cnUi 2 u 1 2 Uix CO <r 2 2 21— Q£ UJ B a z cc

LJ CJ Q 2 2Ui h- 2: UI UI — cx <Z c UI X £H 3 2 U. 1- I

^j 3 CJ« Q >- 2 2 i-i

UI UJ > (- C Z XH- N ili H* H-l 3<r >-H •> Ui 0£ •

_j lJJ Q H-

i

EC Ui <«» Ui3 3 JJ 1- 3 1— _i CJ e-2 Cfl h- U i— Z G z i—H-l en <r <Z <X Ui SB <r zcn Ui i—

i

Ui ii 2 wC <rQ£ i» BC UI > V _!

x 2 i—i j_ B cn z 2CJ 2 UI 2 UiH-l 9 —4 3 UI cn i— r> UiX UI H- |

—

• H Z HH X3a

>-1- OS

_iUI

Z Uiui ej

CO h-

r -H l-l • 2 — 2 2 UI U.<r GC J> B — c UJ L^ X occ 2 M « Q X cn 3 H-t HH

u. _J UJ Ui C h- x 1-X Cg 2" 2 cj K U.

Ui.--> M a z |_ H-l H-l

:> i—

t

3 fi 2 k_ i—

1

a 3 cci-i x M rV M 2 3 2 ut— 3 t—

t

•_ Ui enb •» cn H rj^ -J u_ 2 Ui<c «-N Jj UJ — _j 12 _i Bci Ui CB 2 a Ui r^ B <X

» UI 3 2 2 2 H- u. J> U.• 1— £ <I <x <X k Ui* Z X 2 3 C£ UI u. ^ HH

en 1-4 CO U O CJ o X 2 a 2Z «0 i—

i

u. h- —* at-H 2 <»» Q i— r fi£ C Ui3 <r t- M CD O ce u_ CJ <rUI H cn y£ cj Ui H-l

a cn 3 1- o u 3 _1 o »-cny-t r 2 ft. H-l 03 C x Z Ui 3

z -

UI 3 a CI a UI LJ cnX u. Q cc UI i—

i

_j "T" UI O CJ

ui a CL 1- QC k- u. H B B A

COco

s_

to

-ac«o

co4->

o=5-aos-

Ei.C7»

Oi-o.

a;>

oA3s-cu

CUs-

CD

43

to4->

3Q.

t-»- 22 <rLU _l£j acc au ua.

aea© h-

© u~t <L u.

uiB CC © l£2 © UI<r ui • 3I m O

• i- N a.o in-* UJ U ii i-

H Ui UI <x2 <E 10 CC

ui a: 3 ^Ll! UI N M H- u u3 a. 2 2 <r u. <I(- O U CJ cc c BUI \ s UI u

-

: © BiZi a cn cn a. • m UI

i- 2 2 2 o u_i Q UI M UI uLU B CC H t- u: 1-( u <z> Ui cn 1- C ll UT 1—1 2LU 0£ UI

—

1

« UI II <T CO o-J i-i 1-4 Ll: r-j ae CC LU m u 23 cc UI 2 »-i i i _3 X • UI CC

cc a <r 3 — — —

1

t rv X 3UI LU »-» r in u <x <x \- o © u )^

3 CC _i *-4 «o cc cc <L in • 3 B 2>

c »-< «• © f\ UI UI L^ u •r 2 2 <X

a. si X CD in UI • — Ol UI UI © <I 2i—

i

3 £t • o © ~ r i. CL ~^ © UiUi <I Ui in 1-1 __ £ ^.

— 3 II © •• Ui Au- Jg — —

i

•II i— UI ^ UI • 2 :V

<X UI |— UI tH © 2 © u — - ,!_ <z o ~ c — 3 H- _ .C ui o _; L_i X3 N ii_ • _J cc rs 3 3 z Ui cc o 3 c^.

<x o QJ o u •—ii iw 3 1—

!

—Cl. • 2 2 2

:i TH UI Ui ll"5 2 *. o M U 3

U. ~r- 2 Ui QJ k V— f_> ^ z ii > cn H1 3

M u p. <r !! d u _^ i

—

1

2 2 •c <r BQ 3 »- J£ r^ 2 — b_ 1 <L UI ^J !! B Li r—

_i CI3 ll, — Q <z CJ _j — — B Ui 3 3<r 2 B 3 3 M Ci c O ~

cn cn CT l^ UI UI a C3 3 I-* c cnt- 2 <E — c_ z: 111 LL. cc tj U B B _; cn ccH-l t-« <r m 2 UI UI Ui UI H2 2 cn UI DC _l TH u UI cc cz u- — UI B ui CDH-l t-H UL u- o c 1 h- CD 1—

1

Q u u 

<T3

3E•p"

•ac<T3

a;>cu

uCU

o

E<as_CDOs.a.

cu>

CJITJ

s_cu

CNJ

CUU3cn

44

xiia POST SHUTDOWN XENON TRANSIENT

TINE CHRS)FPE-SHUTDOUN POUER - 10Q . OCXPC^K XENON TINE - 10.-43 HRSF£r,k! XENON LEVEL - O 953E IE AT0f1S/Cfl3PEhX XENON REACTIVITY - © SOOE-01 DELTA K

X10 11'••.?•' -

.

• •:••'

:

•'' '

POST^SHUTDOUN XENON ' TRANSIENT

'. .i • - , •

x .;•-/"•«'

f. ,« '...

uN '» ." '-*'.** •..•'.

"If

fi*^^_ *

*

Njj^.jSsV M

-

I- ' '

3S

A»'

!

T

NS p• '

C .

.-^^**"

N ..;•.•;..' ; -:A>-.\-

3• • \

' ' >:•'• •• •;. ;..;'

1'

1 ! i i 1 1 1 1 1 I "'»1 1 1

> f1 1 1 1

Til IE <HRS)PRE-SHUTDOUN POUER - 10. 00*.PEt-K XENON TINE - 6 IS HRSPE^K XENON LEVEL - . SEOE 13 AT0f1S'CI*»3PuAX XENON REACTIVITY - O.272E-0X DELTA tC

Figure 13. Post-shutdown Xenon-1 35 Behavior

45

CJ ZLU LUCO COX-<C Xl z

Ul<r iT. u <rO r-t O cc2

Ul 2a i_ G cc

• » Q <T :-h >^ CL3: 2 CC 1— ** •

cn CC 2 2 zM 1 2 LU h-l -~. — aZ O O CO X >^. 2 MC Ci H 2 CO 2 X 11

>-

X 1- 1— M _ i-t •^ <tu 2 cc a 1-1 !- 1 -JUl Ul >- h- CC X2: CJ CO

21- Li 0£

UlLUCO CO •

2HI

LU •s 1—1 1> -J CO 2 Mm h- CO

O 2 i—

1

O 2 i-t LU X2 <r >- I— CC t—

1

u- X Ul 2 Ul • ^ ^3 Ul 1-1 <L 2 >- h- r •i 1- >—

•

CJ

1

CD U. 3 X I— 1—

1

 iC s^ • X> HI <Z .\' 1- uh- x Ui ^ rj _1 jC 1—

1

u. Cl. m 2 UiHH u C5 CJ c 2 L5J u 1— 2 <: O <r Ul O Ul • Ul-i s <r CO uC X 1—

1

a <r Ul O • Cfl 1-1li d

1— 3 x ^ — X LU Uh 2 O Ul ccu 02 CJ —

j

co u, GE <r in s CC Xc x Q c Ul x c <: Ui u.Ul _j Q H- Of CJ LU r> CJ !! q t-

cc O «X m s Ul 2 1> 1—

1

11 _j 2 rJ£ q 5 _J LU CO —

H

1— > l-H 2 Ui Ul_ •—

«rf LU 3 LJ H-4 H h-

1

t— cc X LU u.

<x 2: -J CC CJ 00 K <T CO l-H LU —

1

2 2 coM <~^ lu _ X CN CJ X r» 3 II )_• —

i

Ul >-1— u ">-

Ld 2 Ul LU Ul u. 1—

1

O O A Ul CO>-* »-i z —

<t CC 2 •w h- u_ -jj U CC i9

Z ^ a <-i CJ h- t-t ^ u £ u X Xt-l 2 Ld t- O * a t- h-

LU |3Q i— Ui 2 • Ul l-H iV h- _l <r <rX x <r c >-\ x r

J 2 2 <x X 1X1

K 1- n S w h- _l c 1—

t

>-* 2• • • • <C Lu- j^ X t-i CO Ul

CC -H cn Q£ — cc i-t CM i-t CC cn CO u 1- XUi LU LU • Ul K X h-t- • t- r- O h- • 1-4 a.2 »* 2 O ••H 2 CM 2 2 a «-

U A LU 2 A Ul A HH 1-1 1- OS A

CO

c

CD

E>o

-0occ

o-+->

co

E(Os-cnos-Q.

>'T—

a03'-

cu+->

cu

cn

46

x05

uLU2LUaz<rX LUu a2

>• <rHIU1-1 U 3Z> 2t-i C5 <XH O Zu ca a<rlu -j a

Q£ O_J H- -J

HOlll>- u 2)-H l-H

<r 3

LU

2LU

<M

cmA

ULUcn\J*in

t~ •

2 OLUU u.cc aLUa. LU

H-* <r

cc

T-l aLU

u5 X2 t-t

<X L_

. <TO1-1 u.

<r2LU 'fLU 33 Uh- uuJ 3a

«JQ ,_J

_!<r s2 <i1—

1

b. -i

ae MLU LU •>— 1- tn2 r>»

LU 2 A

ena: HLU 3i- 3LU .V2 II OC ^C£ ^ •

<r ^ ind. in r^

u cnLU O LUa • CO 11

2 j

•c in —1 O cu • n 3

11

> 2h- CC 3 LUh-1 LU p—1 XI> 3 II h" MM O CJ —(- U. LU LU l£u 2 AC 3c cc h-

!

»~* r—u !- BLi •— _l

CJ C 2 <r_l <x >~1 •-1 2<Z LU x 2 M-1 i£ 01 LO U.

2LUCT

2LULUaen<x1xu

2<rccaocea.

2o

-i3

en

lu 22 3

C 3I- U2 LU1-1 XU

LU U.

2 2UJ LU

H-2 £f>

LU >LU cn03X

UJ uZ> 1-

<X <I2 Si

cn LU1- X3 (-

Cl2 O «•fH HiCA

to

cnc

-0

o

a>

-a-

EJ-cnos_Q.

CD>•r-+J

ai

c

LO

=3Cn

47

Figure 16 is an example of the interactive program's logic routines

which will only permit inputs within the requested ranges to be accepted

for the simulation.

B. SIMULATION PROGRAM

The program generates Versatec plots showing the plant's power, re-

activity, and temperature transient responses for the user's inputs.

Figures 17-20 are composites of these plots.

In Figure 17, the transient was initiated by a simulated 20 to 40

percent ramp change in turbine load at 1/2 percent per second. In

Figure 18, the transient was initiated by a simulated 60 to 40 percent

change in turbine load in the same manner. Both of these figures show

the characteristic power demand following and inherent stability response

typical of a PWR plant with a constant average temperature program and

negative temperature coefficient.

The inherent stability feature is further displayed in Figures 19

and 20. In Figure 19, the transient is initiated by a simulated 10 second

inward movement of the control rods at a reactivity insertion rate of

-4 n1.25 x 10 ok per second from an initial 50 percent power level. In

Figure 20, the transient response to an outward control rod movement

with the same parameters is shown. As seen in both cases, the reactor

power stabilizes about the initial turbine load and the average reactor

coolant temperature stabilizes at a new level to compensate, via the

negative temperature coefficient, for the reactivity inserted by the

control rods.

48

• H • t- • l-1- Z t- 2 l- zZ <X z « z <xUJ _i LU _J LU _iu o CJ O CJ occ o cc o CC oLU U LU u LU u0. a. 0.

CC CC cc• O * o • oO h- o fa* o h-O U o b o u<-« « »• <t T-i <xu LU UI

1=4 CC a OS a cc

z z z<r ui <r LU <l LUX X X

• H- * h- * Ko o o-( LU T-» LU i-t Ul

t- h- 1-

z <r z <r z <Tlu cc LU CC LU CCLU LU LU LU LU LU3 0. 3 u. 3 u_1- O t- O H- OLU LU LUa a A a a o

i- n- I—

j -J _iu a LU B LU a:> Lucn ^ lu cn z> lu cnlu a: lu LU as lu LU CC LUJ MH _l i—i i-t _J (-1 H-t

=3 CC 3 CC 3 CCas a <r CC 3 <X CC a <zUJ LU M LU LU *-> u LU i-t

3£t J 3 CC _l 3 CC _Jo <-i O i-t 3 l-l

(i. CD X u. cn x i. <n xHi 3 M X! i-t 3

LU <r LU <t UI cH- AC H- OS K cc<rujH c LU •— <c LU >-

H 3 Z l_ 3 Z t- 3 Zcn a <r cn ° * cn o <z

0.-1 <-- —

<

u. _1>- a. >• Ck > fiu

Q ^ Q 3 N! a a N!CO£ LU <r O CC LU <x © CCLU »N LU Qg LU -H UJ ££ LU ^ LUh- X LU i— x LU u- Xcn lu t- t- CO Lu (- i— cn U. h-o a 2 3 3 Z 3 3

-i LU -I LU -i<t z a <I r a <r Z aMDZ <I t-i 3 z <r l-l 3 Zt- z <r |_ (- z c H h- Z <Z1-4 H-t <r i-i 1-4 <r t-\ »-4

2205 Q z 2 cn a z z cnI-t l-l li. l-l i-t u. IH •H li.

z r t- z z H z z2 3 U 2 3 u z 3<t <t a. LU -d Cu. LU

CC<x <X u.

C£ ~ a: oe » fiC cc ••

LU LU © o LU LU O Ui LUt- K If) u t- 1- CJ p— i- Oz o -< z 2 O If) z z o inLU 2 A (-4

. LU 2 A M LU Z A

1)

I

—

Q.

(0X

os-Q_

cu>4->

o03S_cu

<o

cn

49

8?

o

o

oo"b

SIMULATION OF R PRESSURIZED WATER REACTORPONER AND LOAD RESPONSE leseno

POWER

LOAD O

REACTIVITY RESPONSE

/\

TEMPERATURE RESPONSE

LEGEND

rho a

RHOE <D

COOERNAL")

RHffT A(temperature:)

LEGEND

TRY m

TH O

TC A

00 10.00 20.00 30.00TIME (SEC)

40.00 50.00*10 l

60.00 70.00

Figure 17. Power, Reactivity, and Temperature Response

to a 20 to 40% Turbine Load Change

50

*

(To

u.

SIMULATION OF A PRESSURIZED WATER REACTORPOWER AND LOAD RESPONSE iegcnq

pokeh

Lam o

-g a a a a » a a a a a e g

REACTIVITY RESPONSE LEGEND

RH8

RttE O(EXTERNAL)

RHOI A(TEMPERATURC)-

^fw^^— 6B ~^> '' ^- ©

TEMPERATURE RESPONSE LEGEND

TOT

TH O

TC A

"b7oo 10. 00 20.00 30.00 40.00 50.00 SO. 00 70.00TIME (SEC) xlO'


to a 60 to 40% Turbine Load Change

51

o

c_3 <\j

SIMULATION OF fl PRESSURIZED WATER REACTORPOWER AND LOAD RESPONSE legeno

POWER E

LOflO O

REACTIVITY RESPONSE.LEGEND

RHO C

RHOE C(EXTHRKJAL)

RHOT A(TEMPERATURB

j Q-— o —a a g o agseesgoosse

TEMPERATURE RESPONSE LEGEND

TflV CD

TH O

TC A

o a e a a 9 e

* a g a n a a a-

"b.00 SO. 00 120.00 130.00TIME

240.00(SEC)

300.00 360.00 420.00

Figure 19, Power, Reactivity, and Temperature Response

to a 10 second Inward Control Rod Movement

I

52

SIMULATION OF P PRESSURIZED WATER REACTORPOWER AND LOAD RESPONSE legend

o

CO

GL

a a n a b b b

REACTIVITY RESPONSE

a . a a e a o a a a

>-

TEMPERATURE RESPONSE

-a a e a a a a a a-

a a o a b a a a b-

* *

"b.oo 10.00 ^0.00 30.00 HO. 00 50.00 60.00 70.00TIME (SEC) "10'

POWER

LORD

LEGEND

RHO CD

RHOE(EXTERNAL)

RHOT A(TEMPERATURE)

.LEGENO

TflV

TH O

TC A


to a 10 second Outward Control Rod Movement

53

V. CONCLUSIONS AND RECOMMENDATIONS

The model responds to normal operating transients with the charac-

teristics of a PWR plant. The interactive program provides the user with

the facility to initiate the simulation or examine a real time display

of post-shutdown Xenon-1 35 buildup and decay.

As previously discussed, the purpose of this work was to develop a

learning device for nuclear engineering students at the Naval Postgrad-

uate School. The result was a relatively simple model of a PWR power

plant and a simulation program that suffers from a long execution time.

The model's simplicity resulted mainly from the consideration of

an effective single group of delayed neutron precursors in the reactor

kinetic equations and the use of lumped parameter analysis in the plant's

heat transfer processes. The model's sophistication could be increased

by:

1. Expanding the reactor kinetic equations to consider six

delayed neutron precursor groups.

2. Developing a multi-section heat transfer model for the

reactor and the heat exchanger.

3. Incorporating variable reactor coolant mass flow rate and

heat transfer coefficients.

These additional features will also increase the complexity of the

simulation program, thus aggravating the long run time problem. This

concern might be eased by taking a different approach to the model's

formulation than the transfer function method* While this method was

readily coded using the CSMP-III language, physical insight to the plant

dynamic processes was lost when the Laplace transform and subsequent

grouping of constant terms was performed. The use of state variable

54

theory might not only allow this physical appreciation to be retained

but also result in shorter program run times.

Regardless of the formulation method, a real time response to the

simulation can probably only be achieved by using an analog computer.

The wide range of time constants associated with the equations (prompt

_5neutron life-times on the order of 10 seconds to Xenon decay half

lives on the order of hours) require a small numerical integration time

interval over a large time period. The result is a prohibitively long

run time on a digital computer for an interactive program.

It is hoped that refinement of the model will be continued. While

the existing model does reflect the general characteristics of a PWR

plant to normal operating transients, it does exhibit relatively large

power over/under shoots in response to turbine load changes as seen in

Figures 17 and 18.

55

APPENDIX A

DEVELOPMENT OF THE XENON FEEDBACK TRANSFER FUNCTION COMPONENTS

1 . Derivation of G (S)A

1 o f" IOCThe previously developed rate equations for I and Xe from the

135effective Xe decay scheme shown in Figure 5 are:

-— = *xZ£<z$<t) - ax ret) (A 1)

j^ = #x Z{£M + AxlCt) -Ax xa)-CaX^^)X(t) (A 2)

135 3where I(t) = I number density (atoms/cm )

135 3X(t) = Xe number density (atoms/cm )

_ 235 -121 f = Macroscopic fission cross section of U (cm )

2= Average integrated one group flux (neutrons/cm sec)

*I = Effective135

I fission yield

*X = Effective135

Xe fission yield

1 = I decay constant (sec" )

A X = Xe decay constant (sec" )

135 2g-X = Xe thermal neutron absorption cross section (cm )

Let I(t) = I + </l(t)

X(t) = XQ

+ (fX(t) (A 3)

0(t) =Q

+ ofy(t)

where the zero subscript denotes an initial steady state value and

the delta prefix denotes a small perturbation about this value.

56

With the reactor at an initial steady state with a flux level , the

135 135equilibrium values of I and Xe are found by setting their time

dependence in equations (A 1) and (A 2) equal to zero. Thus,

X = -i—2. (A 4)Ai

X. = hl£*l±2*ll (A 5)

*x + cr£ do

Substituting equation (A 4) into equation (A 5)

x.=^jMZpj.

(A5)

Substituting equations (A 3), (A 4), and (A 6) into equation (A 1)

and (A 2), neglecting the o0 J*X term (first order approximation)

^ cPr = a'rSfo^-Aio^: (A 7)

sL cPx = hxJl f (XxZp-q^Xoi^-CAx+QaV^^X (A 8)d-fc

Taking the Laplace transform of equations (A 7) and (A 8) and solving

for cA(S) and cfx(S)

^<s) - ski (A 9)

^X(s) = ^^ tUf-rfXo)^(aio)

57

Substituting equation (A 9) into equation (A10)

</X(s)

Expanding, collecting terms, and solving for ^g7s>

—— a . — ^xtS)

This is equation (16) on page 23.

2. Derivation of °^x

The effective core neutron multiplication factor k is given by

the familiar "six factor formula" found in the literature

k - fl*f>f PpNL PTNL

(A11)

where '{ = Thermal fission factor of the fule

€ = Fast fission factor of the fuel

p = Resonance escape probability

f = Thermal utilization factor in the core

PFNL

= Fast neutron non-leakage probability

PjNL

= Thermal neutron non-leakage probability

The core reactivity is defined as

^ 1 (A 12)

Consider a reactor at an initial critical steady state condition

1 35with an equilibrium Xe concentration Xo. By the definition of

critical ity

58

ko = 1 (A 13)

/^o =

In this condition

£-yCOKi - p v

( A 14)

where r-r F r , . . , . ..2»a

= Fuel macroscopic thermal neutron absorption crosssection

21 = Initial core macroscopic thermal neutron absorptiona° cross section

2, = Initial Xe macroscopic thermal neutron absorptioncross section

and the macroscopic thermal neutron absorption cross sections of the

moderator and other core materials has been neglected, a reasonable ap-

proximation in a highly enriched core.

1 35Now impose a small perturbation in the Xe concentration on the

1 35core. Neglecting the effect of the Xe perturbation on neutron leakage,

a reasonable assumption for a large reactor,

X = Xo + </x

k = ko + <fk

f - fb + cff

/>=/>o + <fy = d)C since /> =

The remainder of the terms in equation (A 11) are unchanged, thus

cA = <ff

and

k = k = * since ko - 1

59

where

r - *-*3 = =ti (a 15)

from equation (A 12) and (A 13)

(A 16)^= ^x= ^i= l--|

substituting equations (A 14) and (A 15) into equation (A 16)

&* = 1 = *x

This is equation (17) on page 23. Since fuel depletion effects are

not considered during the short simulated transients, the fuel number

density U is assumed constant and °^cis invariant in the time and the

Laplace domains.

60

APPENDIX B

DEVELOPMENT OF THE REACTOR HEAT TRANSFER FUNCTIONS

The previously developed equations describing heat transfer from the

reactor to the coolant are

TF(fc) * ti ^f£* = TAv(t) + 3k p(t ) (B 1)

TAv (t)[lM |]tf2^ = TF (t) + 2%TCl (t) (B 2)

TAvCtl = ICTHoC^ t Tc^Cfc)] (B 3)

where Tp(t) = Average core material temperature (°F)

T»v(t) = Average reactor coolant temperature (°F)

T„ (t) = Reactor coolant outlet temperature (°F)

T . (t) = Reactor coolant inlet temperature (°F)

P(t) = Total power generated in the core (Btu/sec)

Cr = Total thermal capacity of core materials (Btu/°F)

C., = Total thermal capacity of coolant in the core (Btu/°F)

C = Specific heat of coolant (Btu/blm°F)

m = Coolant mass flow rate (lbm/sec)m

and

hFM

= Total heat transfer coefficient (Btu/sec°F)

Jo =

r\pH

f2 = £m_Hfm

61

Let P(t) = ?n + <A(t)o

TF(t) = T

f(J+ c/*T

F(t)

TAV

(f) = TAV

+ <AAV

(t) (B 4)

THo

(t)=

THo

+ ^Ho (t)

o

Tc.(t) = Tcio

+ JVc^t)



From substitution of equations (B 4) into equations (B 1), (B 2),

and (B 3), with the reactor in a steady state at t ^ 0,

TAV*(i + 2 \) = TF^2^Tc id(B 5)

TAV = -|- ("ft*.* Tcio )

and

(B 6)

(/l>(o) » <^7av(o) b J%c io) a c/'Tc. (O) a C

Impose the perturbations at t=0. Substituting equations (B 4) and

(B 5) into equations (B 1), (B 2), and (B 3) with the initial conditions

given in equations (B 6),

</TP (.h) + Yi & <ftpfc) =* c/T/wCt) *•~ cPPdt) (B 7)

^TavCO * I jVrHo (fc) + o^ (t)] (B 9)

62

Taking the Laplace transform of equations (B 7), (B 8), and (B 9)

with the initial conditions given by equations (B 6)

Tf(5) [sfi+i] = Tav(s) *- ^rPCs) (B 10)

Tav(s) [sfz + i+z ±|] = TF( s) t a~Tc(s) (B 11)

TAV(S) = \ [ TN (S) + Tc (5)] (B 12)

where the delta prefix and lowest subscript have been deleted for

readability

Substituting equation (B 12) into equations (B 10) and (B 11)

TF (sfiti) = \ ( TH t Tc) + % P (B 13)

|(TH +TC ) (sTz + | + 2 £) = Tp + a^Tc (B 14)

where the s domain dependence notation has been deleted for

readability.

Solving equation (B 13) for TV and substituting into equation (B 14)

j<Jh + Tc) {sti+t+Z ^)(sfifl) = I (Th+Tc) + A p + 2 J| (sfi+ l)Tc

After expanding the products and collecting terms

After multiplying through by and solving for T„( <Pln (s))

o

63

where 5 = —-y and all notation has been restored^"2

This is equation (26) on page 28.

64

APPENDIX C

DEVELOPMENT OF THE HEAT EXCHANGER TRANSFER FUNCTION

(

The previously derived heat exchanger heat transfer equations are

[t + Kl]Tc (t) = r .

— 1(C 1]

£l ill^+TsU) = Y[THi (t)-hTCoa)] + h^pL(t) (c 2)

where T„.(t) = Heat exchanger coolant inlet (°F)

Tp (t) = Heat exchanger coolant outlet (°F)

T-(t) = Saturated steam pressure (PSIQ)

P. (t) = Power delivered by heat exchanger (Btu/sec)

C<» = Total thermal capacity of heat exchangermetal and secondary water and steam (Btu/°F)

C = Specific heat of coolant (Btu/lbm°F)

\\ = Total heat transfer coefficient (Btu/°F.sec)

m = Coolant mass flow rate (lbm/sec)

and 2mM C*i s "u

—

Ktm

Let Tm (t) = THi

+ </TH1

(t)

o

TCo

(t) = TC

+ Ato^ (C 3)

Ts(t) = T

s+ <A

$(t)

PL(t) = p

l+ dP

L(t)

o

where the lowest zero subscript denotes a steady state value and the

delta prefix a small perturbation about this value.

65

With the plant in an initial steady state at t < 0, equations (C 1)

and (C 2) are

aTSo -TH io [i+ Ki ]Tco„ =

[n-^i](C 4)

Ts = f ( TH. tTc0o )+ ^-PL (C 5)

and

JTu.^o) = cPTq (o) = <^Ts (o) = o

Impose the perturbations substituting equations (C 3), (C 4), and

(C 5) into equations (C 1) and (C 2)

(C 6)

(C 7)

Cs d

[£ 57 <*i<0 + Ate) = 1 [jYHiW + Ac.tel] - £VPL te) (c 8)

Taking the Laplace transforms of equations (C 7) and (C 8) with the

initial conditions given by equation (C 6)

jTs(s) = *

|[Ac (5) + C^Th.(S)]-4i^PL^

I5S + 1

where<-f

- Cs

Ktm

<^TCoC3) = (2c^rs (s)-(y)

TH.(s) [l-Kl]}/[l+*il

These are equations (34) and (35) on page 33.

66

APPENDIX D

DEVELOPMENT OF THE PRIMARY PIPING TRANSFER FUNCTIONS

1 . Transport Delay Transfer Functions

The transport delay of the coolant between the outlet of the reactor

and the heat exchanger inlet plenum can be expressed as

TH

. (t) -THo

(t-r3

) (Dl)p

where T„. (t) = Heat exchanger inlet plenum coolantHi

p temperature (°F)

TH

(t) = Reactor coolant outlet temperature (°F)

T*3 = Transport time delay (sec)

Rearranging terms and expanding equation (D 1) in a Taylor series

r Ji- 2.' dtdt 3t (° 2 )

For slow temperature changes, the second order and higher terms

in equation (D 2) may be ignored.

Tv*)*f3 ^S.T,..Wdt HoW(° 3)

Let

THi

(t) = TH

. + <Pl (t) (D 4)

po 1p

THo

(t) - th

+ eAHo (t)

°o



67

From substitution of equations (D 4) into equation (D 3) and for

the temperatures in a steady state at t^O

THi

= THo (D 5)1 po o

v ;

and

(D 6)

Impose the perturbations at t=0. Substituting equations (D 4) and

(D 5) into equation (D 3) with the initial conditions given in equation

(D 6)

Taking the Laplace transform of equation (D 7) and solving for

^THi / ^ T

Ho

C^THoCS) 1 + fzS

This is equation (39) on page 36,

By following a similar development, the transport delay between a

perturbation in the heat exchanger coolant outlet temperature and the

resulting perturbation in the reactor inlet plenum coolant temperature

can be expressed by the transfer function

tTTcoCs) 1-1- MS

where o *c^p = Reactor inlet plenum coolant temperatureperturbation (°F)

c^Tco = Heat exchanger coolant outlet temperatureperturbation (°F)

\. = Transport time delay (sec)

68

This is equation (40) on page

2 Mixing Delay Transfer Function

Let the reactor and heat exchanger coolant inlet plenums be represent-

ed by the control volume shown in Figure D-l

.

Tj,m *

m,T4

MT

M

T

o

m

= Mass of coolant in plenum (lbm/sec)

= Average plenum coolant temperature(°F)

= Plenum inlet coolant temperature(°F)

= Plenum outlet coolant temperature(°F)

= Coolant mass flow rate (lbm/sec)

Figure D-l. Mixing Volume

If perfect mixing is assumed, the coolant outlet temperature is equal

to the average coolant temperature in the plenum. At heat balance on

the volume requires that the net heat flowing into the plenum be equal

to the increase in stored energy. Assuming no ambient heat losses, and

assuming the temperature of the plenum structural material remains

constant, the heat balance per unit time over a time interval At is

mAtC [T\(t)-ToW] = MC ^gr^t = matedt

dTo(fc)

dt

where C = specific heat of coolant

The resulting equation is

m at dt(D 8)

69

where T =

Let

M— = mixing time delay.

m

V^ sTio

+ AwTo(t) = To

o+ A) (t)

(D 9)

where the lowest zero subscript denotes an initial steady state value

and the delta prefix a small perturbation about this value.

Substituting equations (D 8) into equation (D 9)

i ZJZ <^Tofc) + ofVoCt) * d%(±)dt

Taking the Laplace transform of equation (DlO)and solving for

(D10)

A/ AcTT (s)

This is equation (41) on page 37,

70

oooooooooocoooorooroocoom* <\im »* in «or- en &©-^ CM ro. sfr in «fi h- oc crO —4 f\|m >*•

OOOOOOQoO'-i^^-tH'^HHHHNINNNlMoooooooe-'OoooocooooocooooOOOOOOOOOOOOOOOOOOCOOOCO<x<r<i«i<r <r<r<ro r- co o>o -j <\im »* m vO r- oc >o o>o ro f»- <r o>(M cvj (\j <\j rvi tom rom ro r**immm in rn »*• in in en inOOOOOOOOOOOOOOOCoCOOOOCOCOOOOOOOOOOOOOOOOO^<r<r<t«4<r<i<T<j<r«j<i<i<r<c«i«i<r<i'<r<r777 :777Z7Z77Z777777777

CO<

0>

o

co

X cc—i C3Q Oz q:uj o.D_CL LU

CO

OmxLU

ooro

LU5"

©©

oOf*-

CO

mo>

LLvO

COX00

»C\J

•i

co7h-

— 300

ONCO

CvO

I— CO

300

TN

c_>r-

com03

nor«-

»

co

<nn6»

<\j

m«•

in

cvir\

Xni- co «*

m coI/10DZN

egm

ru O7co

» •>

*-•& moocot—r— r»-

» »•

torn m7oocococo h»

DO COUlOS7K <0

i- no

•»

mcoco

mfM

orjeopi

CVJ

mO

»•

(\j

ro•i

LUQ>O

»-«m

r> n in van i—

*

C0<IvO co co*-* •« •»•• ••

X LU"N. OJuj«s. LU>*_J OfC0_J _J

»—7 Kp-« •»— OJ >— CO0«"»»—'CO ^»—«GD —'CO

or"*-*-**— <r»— co»— «r »— <rLUCO—4 _!•>_! _i(J>7^X Cvllll LUainima< m_i«i >*_ji<r»— :rco<i— »-<rt— <i—Z^ôr^Zaoo^ —io<•hD_jCq r-coommco©

CO

COCO

~»o

l_j

•V7co«r

o»-h-CL<SCC— r-

to• • >•«"!

co»—

^

LUCOO

LULUQ.TOO<I oocTnrco<MlO

^-1 1

Z7T<r

Q-rorn

C5 I Izrr3:.-.--

LUUJ&*COCO-*

cocomcocorono-*arc^ i

cjouj

W

OOQcoi— •-•

COQ.^•rvii.u_no

COC3COO»—<I_JO. LUoo*-*

COQ.007art )0OCO»-iwDi/i5"fVco

« ^^^

rrtXro lu

i m>

»- I u77LU<nu.ry"7ll

yui

LL

cc

3•-a:CCLU—>LL

CO>7— »~«r

- LUlSV-co<r

n ô_i—2T«r <r

-* CCOU-!1 — _J TZU—

J

GUJU <t LU7COLUU , 3:>UJ^^co*— or »-•

X^*v<JLU»-

U w t— LUOl- "« U_

7»-Oc_JLLo<r7_iu_uj—

LUCO»- U I

<-7 CO CO <_><<_>>07COLU»-LU

t 50<tclOco

cot )<t770mCO UJ 1_)<T^ t— ta«

i— olu-J _i<rll oona;i-

LO OOLU7LUmiT\C_)CJ7UI>-^ro lu»—i— I

—*aroru_o»— lu I OO -D7ZI- 1— 3"LLIHt-iOt )t 5<JLLu r>7<r<riuuiu.nuiinu.i»—

n

LU»-«Xr«'0!rcOCJ

isj <U.XmXmX_jm 5" 5- ^- 5- ^- OO t—<jxvuocq s- *- srs- nar s:

t—^cococoocD—j-jsrox

no<ro

oan

On

ini

LU

•

C\l

X<ro?<j

mI

ininr^co•

r\j oo

<r rvifMLUv^cof~\ ./> • i >/>cnfMy _iiiiiii(Mmrvi«i * • tvavco__iLLU!co*tinooOSOffl • • • •

pj<ommi-ioovOO*r.n • -j^-i• _j-0 H II II II n *o>n » -îr\»-i5"ii<ru.Xi-<xO <r«r<r<f«r n u

LUO <N i—•-<»-•< 'U

ofUJ

n

co

>o o<r oclu 5:»— o.

<xooMvOOv— in*->nO •7*.tTN*-» ^«

LUot-oujorjiu

a2rf

o o O l->L.><-)LJ<î^H,S.LJLjL-3<J>LJt->LJl-} OLJin

71

oocooooocoooooooooroc ooooooooooooooooocooooor5-^csj(^>în^^cr(>0 <^<\Jmîn>oP--oo<T>Oi--tf\ifn«d-invi3N.oo<ô—*r\jeo*j-ir\NOr»-xor^-Of-«cvj«oo >o »o >o >o *o <o ^3 *or— h" r*> r*- p* f-^ h» h* r* oo oc oo co as oo oc <n co co cr»& o c?1 a* cr cr» oô^ cr*ooOoOOOOOGOOOOOOOOOOOOOOOOOCOOOOOOOOCOOOOCoO^t-*—*^-4OOOOOOOOOOOoOOOOOOOOOOOOOCOOOOOCOOOOoOoOOCCo<r<t<i, <r<3'<i<r<t<r <<i<i«j<r<r<r<r<i<r<r<i<r<i<r>- -j CLv, LL • 1— <T LL •>

iS> —

-

LL— era: * CDT wLLar lu X COO— LU «iua < Ki-m 0; LU Q-SI S •>

o •• =>3I =5 QiLUyLU O OCM t/"> UiCJ h- ZJotLH— •—

1

IMa: Z"V < !-=>»- co LJ

n LU -co—'CL <ll- 1- • »-»- 1— y\s\u rf <ari— lu X »

LU _jO a LUe£LL _J < co 21 LU»-<S Q_LU_I»-o < X»-LU zazr> s: X

ac LU^_)H UJSI^C < K«* < —1 LU »-LU -j

a ZOl— K»-K M IT* c• xn—-2>- ^ Z7 • oco LU T5«-i <* uit—«r<i-— ^V O aro>- *— II— *. I_»_|LU 1. Hi «-r *_ 1—-*ar <r.—LL<rt— mil 1- _ion •»»•-> n m* •>

»— >— »— iVmOx»—>7no to —

»

X —.Ifl v>o•Z C03Z»-i»l J n^-« iOluo. lu -i ^^ QTLL

OliJUJ rozn tu a:——

3

_i — <\J LUI-LU.J UJ V-->oiujj-aroc:i->-Q;QC3 »*s: LL -<(\J Ka: •< _

i

hUUODZZOOl-UJ^w * ^ • LUOat \- 1—

t

<tot37<i-i-<f<i-h<a: U, 4-0 sixi-n< LL LULULUOLUOca_u«3<a:r)QQ rt'<IOir~,C~)OiQiuiCO^<J 5"i u al(-\

aj-e < wn uiiiinounufiwon <J3 ^— ro <fxa»- t- aa>nir\a'auL)7ZSa)_ij »—

«

*rvj CL3<r «

i

<r _i "">mco 5" 11 iiuiiiry (A 0-^ •

»- Ul o <ror:r~)-*.-<Luiiifyfy ocii- luui * ni*» LI'LL<t • <*• firmer 1 1 c«»»-cio Z7 Lf\ 1 >f- 1— *Ooe£ _j -»—0^^<r 1-1-yy 5" ?•-"•-. m nr-50 »— • ^•5"

zo < 1—

n

> OOo£_J«_A } * »-oi-<o »— z.el LUZZ LU UJ «t <1 LU LU LULU CC CL rs 313 4. 1 cooio •j' t— «-LUÛ!LU>r3LUat-l— »— 1— -50 n* o.ao. 5" —

.

3LL) _ H-l e£nXX -rf u. at: /v 00 1/> inv 1— t— (V-» 1— -— <—

•

CO >.riOC zr> <J> HJX + * * X^CO sO O -QC *U- >-iCtL 2:_j_j_j_i_j_i_j_i_j_j_'_i_)_j mo.< "^5£r- • «Dooo-«o-^ o^ IIIO•_< »Of\l

UJ»—«o

3r<txt—

1—i<r<t<r<r<r<r<t<r<j<r<x<r<f<r • TPvJ* 5"

<f

—1 +O +»-ltyui<r

• • •

S-

1 â. »f> *

-* w_ • msr* <r1—O'—O^

LLlQ.1— -I

/—1 •— 1— 4—1 »— t— k— I 1 t— 1 1 •— t

noa:o3:0 LL

?777Z7?7777Z77 + 1

<-i•—O

Zw.-« CL—

<

3 •rmn«o'0•—OX -5-J I- mwn 1 (II 3T a.r\j3[ roorsry TUSKHfL »-<\0

ZoO-LUO (X—

1

h-3-O O DO <t\T\S.\-V- \-*-* X 11 z »»-t-«î_i- LUw «rny xn nnon QO it 11 v~ • wll 1 11 i-i»r)^-

X Q. i n i LL _i«m no:nni-"-tnr,n<t<f <M» II II II II II (M i wf>Oi OfiVO t/Hu -1-rjnTru.Xim it/iôn 5TO II II II OO 1—LUOujâio Zl- uaiLxofi- t-i— 1— 1— 1— »— 0-_j_j oxiin 0000 11 cq Z^<f»— <t- -J ccZ> ctOr^—»-ic oo«i •——cUJUL o/a: <r JjOSlLIOlO^WWOC cca:_jOm l-jt nu.x>-hi-i-i-K^f-a_iJ 0.3 »

uo o UONUUUOOUUUUUUUUUUUU 00

72

ocoooopcooooocroooocoooooooococcoccocoooooocooooocooo o<-«<-ihhoih^h—tt^f-4 e\j (\j(\j cnjcnj r\j<\j rsjf^ ofmv>mm row mcAmm >* st- -4- ^ >*• «*• >j- >fr <f >tmm in^^,—l^t—liM«—It—If^.—1^.—I^^^f—li—1,^»—l»î—|p-lf—lî—It—I.—1*^.^1—It—It—l»-4),-«»-<^.H —4— _4 _ ,-1 __i t— i _j—_4 —4OOOOOCOOOOOOOOOoOOOOOOOOCOOOCOOOOOCOOCOOOCOOCOOO<<r<<i<r <r«j<r<r<*«r<<r<r<i«a, <<i<r<r<i<r <<*<r<T<r<o <i<a:<r<r<j<x<x*T<r<r<' <"<r<r<i<r <<r«a7777727777Z727r77777r7r7r7Z77777r7777Z7777272777

H-t XX toCO OH **"*

K»- O Z"Z >4- LULU yy n LULU f- >> o

-E o c ar

V) r c >—

«

o a:> Z > o MM c V-

oc <3 OC o DC ti— X 1- rf • LU5* t 1 ? «->>. .-i

LU 11 < LU .Jn 1-

nar »-

<r <r or •Z 1- <r

o >- LU O H »- OLULU LU z o oUl < o LU < z LU_i _l o LUor O z a: O o ar »<r >—

•

o cc »-

MX *x LU in o LU »- UL LU u*- 1- X - >£»- »-S"< ^ K- LUZ oo c > z i ) ^ ^H-O «T z 7 Ot-VLU CCUJ LU nui T LUX k- <r LU cnrr'

Z <* > >-rf < uih <r CO LTI nn -f om<v 1— <r in /v m <-r I— O n <T inrit J

•-< *- r<"»>-0 •—

•

t— (flnn — LU LL 1— \--yt— «t (_> > «r <^« > u_ <r «fy _i O «J n *-*

<r O on? N4 o n ? a oriry <r o *-n_l »-CQ»— K »-.—.«-« ^C »—

•

z L5LLr> k- CJ h- —

.

K <rc_> w- o >- o C—ST l_> O— LL <r LJ nr\j LL- o cj »z »—

<

t—

•

L_> C5—> o_ orui ir> cr—

.

Ul a: LU CS <—.~» LU LU — 7*7- 1— Ul UJOCO LU<V-» CM O a: LU a:— • o CO s: o^ »—'W u a: »-~ COOfNJ

3a: oc— UJO 3 CCa.—OluO ^ -< a: »ll X lu s: a:— —'vO

O toniu •CJfNJ _i CO Olu LUC-XM X noo— nw o: »-• n? —4 • 1— •>

Ul 5^« )3 w^-lCHt—lyO «3 •^ U"?h »»-««r> -r c/> i » o l-H »-< T f>*-i rsnâcn«v <r-5»tn nil— •> ••< <r tt«o - •• i— >- ? •lliO n to TT • II i7w»+MM . —*TT • •o.^m •—• * *-*z? • amv^r^ f^—i ^-<LULJO.I y —

.

Ml m«/MT* •

CO Of— <rr» z— r\J t-^—

.

O-OLU?—-f«*> Zir *^ Ot—vO ô LUvO«— LU t-uir-1luoou *-Ull/l zoo U-wLU3 LUOO LL •>— •• xo XOO LLX * rz»-f-POOhX • 7>-uin »—>oO »-.x • 00 >— LUf~i JOO »-< o*oir\ COO »-oo fc«»—

i

-> i i».i

sfiO »-"• <fZht- vOO *H Z^*-\- *c yZwrn l--^ vOO ll ^LT.ecctr\LU ».lfMiJU_Ol »-!»—»-. LU »in LUU_o0<f<—1»—

4

LU »Ln U'M •i LU ».lf\ LLI»-i»-t«/5Q.1CD2Tv£ Z«—z fxcrro Z-O z*-Z aa:o z^ • ZXt-UJO OLH Z>0 TT" XNM«m»m»—

i

<r^n T<1 »—««-»lTi -< <r«-.n sm ^—'^«•in M(fl7k-t- Li;_ •—iMtfin IM II ty-i •«.

y w7~ li •4 5" ^, S-II >-* *- w 5" fc— *—!•—• LL. y -» s: -i

(Vuj ry LL (VLU tt. u. 11 i «r (Vivo COLU OTIXi ^r LLlu»-oluco ^t-- LUI-O LUCO **»—

<

QHC aiâso Z»- LUt-O LUhh —

•

>-•-<rt-z l-l-H< l-Z oin

oom oo o ini^LJ

73

ooooooocooocoooooooooocooooocooooooooocoorccoooroû^>nfw ooc*o^-4f\jrn>*'ir\vor»coCT>Oi-<f\irr>>tir. ^r*-coON Of-t(\jrOsi'ir\ vof*-coo>> OM(\iro»i-Ln»£)c&oom in in in in inm »o >o >o »a «o %o >o -ao «o «o h» r*» h- r— f- r«- h» 1*- ^r*- co oo co ao oo co co co ao oo cr>& a- s

e*> cr» cr>o C*oMMMMI-IMMi-ImmMmi-IMi-IMM—4MMMMl-IMMMM.MMMMM.--lMMMMM f-4Mi-4MM.M:MMC\JOCOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO«r^ <r <t <t<. <t <r <r <x <t <s <t <r<r <r <t <J«l< <r <t <r <t <r <r z r»-

o •—

t

UL z5 o o 3** *

LUK O

o>- >• ar -1 O 1-»- *- •—

i

»—

i

o 3»-• ^ X u. X> > O CO —

.

CO*-* »—

1

< a <l 1—

1

l~ 1- o M h- • U> •—

•

till— 1— t—^^-> ^ t* 111 K J7 m-i ^-'

M •—

•

LU =) LU cc »—

i

O «LU LU QC hOSH- t~ _l »- -J M Z LU -1 o <X*vm < •— — o NH OlU.< t—

•

o 3mV) t3 U. _J LL LUOf— U- —1 m_io LU < o IU —

»

>-«T< < mu-OO- 3* < M «r 3T X UL ZCQ <t M 1—

t- — »— •d h- O LU_J V- 1— 1 *\— - < •—

•

< < »— <t z LU X(V <y o 3» o M O O «T CJ o III û.<rLU LU 1—

«

T »- -i 1— »LU ta-> h<oto co _l _i t—> «« «JCtf _J CO OTTy 3* < It < T 5" 02TQC d z Ot^< • •

»—

i

*-< •-* »-i CO •—

<

o <rO •-1 < HWJQO»— c »- h- X < »- »o »- QC co «o«o

o o >—

1

< •—

«

«» CO a cj Z H-

•

K X o»— »— zr o 3»LL 03"X _j LU — zu_ r)* 2"* *

i i> i _J mO X MM LL a: • mO z M <IZ z X «t t- OH LU O aou. < o cc:m mxO o OM LU no o Zcoco Z <f o—«o-* oo ^ cOrriM< 3* i-_j ô <r»—

o

»—

•

a t ) o y- _i Ul M(\l<fQO1- u- *--< III co -i ^ ttliO X j-iOrytJ o Y—. co ii <-» • II 2T—•— a:. MÛlOfM u — 5_ <<rLU UJ hO QfO oo t—OO Dr«

—

CD»—>i3 oo z o*<r-J_iQC Ofi XO DO <o LUK- XOO KOO LL •»- » <o 3 O _J•—

i

»—• • coO \-<t oo 3"Z woo OO »-• o«oo oo O 1UM It II

o • Om Om r» _J»-I ÛJ • 1— -(H -JvOO U.Z—'h- _i-^ o <hr-

1

1 •i _i_j »o »-3"0 • •• •> <r •LO UIO ».o »- LU3-Cii»-.X3T or QC—

I

< o:ho LU O fV^r-t z>o Z-LUO arô ZDU-jf- S!LU<I<I— II yft—1 It LU_ t it UJwfM Ul> II III——. ¥—>-_LO —T~\?rt-r- UJ«— f\J t—i <r <r "5*ooX X LL >—

«

u_ XO II LL. u. •*» X_i»-<>-i LL. w7j(.9ZrrWTOirtX com LLLL COLUO -srs: COLULU LU a? of rvO COLUO mO o<j-0 II 0_l_l>-x l-X <m t-< <•-. hOI« ^ »—<^* <M-< K <•-< C02T-JLUCOCUJCO CCOL LUO aroÔ LUC CO CO occâ: LUofLU LULL aâ:o oo<oCOOlSCOO 1-3 co_i >-ô CO(X»-0 »-33 a3a: Om l-JO auuM

o lo o in o mouuin omooôoo oo ooo-o oo uos oo o uon ocjcoo o

74

ooooooocooccooocoopcoocoocoooooooocoocoocooocoorr^,^CMecînor^cocro^cMcn^LOor^coc>©,Me\Jco>d'Lr>Or^co<>o.^cNjm

sooooooooo —«•-' »^ <-•—• »-* —* m* —* i-i r\j c\i cm cm cm r\j cmcm cm (Mm en en en (t*> en en enm en >t ^^ >*• si-^-^,î-t CM<N CM CM CM C\J CM CM CM CM CM <\J CMCM CM CMCM CM CM CM CM CM CM CM CMCM CM CM CM CMCM CM CM CM CM CM CMCMCM CMCM CM CM CM CM CM CMOOOOOOOCOOOOOOOOOOOOOOCOOOOOOCOOOCT'OOOOOOOOOOOOOO<r<i<i«3'<i!<r<r<i<r<i<r<r<r<t<t<<r«i<i» a. ««h 1- X< * Z <rcc N4 O X>- < z »-3" Q LU *LU 5" X •—

«

O <f 7* «rz _J z O oo 1 "3C M 5"

o mm o »- —

<

>-—XO. o <f X_l i-<r r

in -»<X h- a: < 1 >-< Xen -»OUJ X> O— »- Ow >SL *-~* -s- X »-«m z 2-Q. »—t5 »—

•

I w<r i on >xX UI-* «IX t—

«

OCz LU_l o< t >X_JLU «_)«/> no S" 1 — H- xr z< 1 CO <* oV «—i tr> « t— rrs- t-4 1 X HIT* _jLU 1— -*l— n —»*K. <_3l— <f <r airo «iX *Q— Q-— rgoj *C— 5- CM

X3TLUOO • X XX ZX3TXX z-> 00oo -»<r<3roco <r< << o«i<<j o* o^ '-Oît-in Norn o 5-3: zcr-is:* ZLOX »—

•

o 1 y-hrvxvyxi-t- LU5"«K UJfM< XLU i—<r^* X «— »-'<r<j«v** x<r»v* cm X »X a.z —JOX »-* _IC •o —icr.xx â << - I »-<o «« lu | z:hC o*: i «-•<< *w_J a:»— <<» oi- uJrvjrt-t-.^ 1 -1 o<— oy «J*v< OZÔQ * 5" 3" >C UU -er _j • <r »i 1 1 a. •« y x LUVC<r •._ix <tuj *-« xo>* —j • LTir> X <r r. <r« «\j

»_<->LL»ll«-«_J««r t— it-TMw J*.OCJ> LU «->_j + y >-4

too <t 1 •-< <I< vfl •III <r l LUCDX oZO II *Ow|_ II -1U-JQ+ HVITlI* Qw^4 X«-«< ^t•—en rra. X»-»«^5- XXOh 5-Q.X 1— co 2!

•»—»n<xi- —• *v »0(co *-»

r«->OX »"00-4<^ CMCO ill »ITN_I •• >»

-« «• » •LLl 7'Ln •> » cir\ •>

O rOl^TMMlÔMvfl ocm oonmk m>oir\_i>i"— *-f~-

«-l— rowww> lu or co_ilu w-«»—— . j^.^. ^^ --<« i.,^^-* w i -^ -^. I—hvX>i!<Ik oocdlui—nOK-lui-hi— x_jluqc:>— ii LU»^_i^-i3:3_«-»uix_iLU5_oo «uj »-i »-t-<o0 5- 3:o_j!<roc<rcD<rr»' c^»-!I- II — LU— 2 HKXH XOXOt- II II Z M^l-NMLJjai-DXI-UJlJJZ<r »— lu ii ii ii "^lu— »-• ii ii ii <r«r ii ii ii —i <r no^07Mfl.. uti/iHi in iorsir<j»—

•

_j s: ^s:»-2: h n 3r_j < it jxx ofMNî-i£ozwôo70s->7x>-u.X>LOi-i»-»cvjcno»-.'wCie'—<cMm I— -^.-icvim n X)<r<l »—OOOl-XXXul-XUJXXXXXwOXXXXhXXUlS: X II II II I I » t I^J :1_I_J_)_I_I_J_J_J^ i— <<<r<<j- _j<<<<r <kt_jclo o _j_j_j«j_j_i_j_j_j_j_j_i_j-j_i<o lus_

3:s:5:5:ll.<i3:3:3:2:o3:s'<*'_jx ai-^cMm<<r<r<<<'<K<<<r<<<<oo Qn-hi-i-t-'UXXxxLOXkL;<a h-_j_j_jooooooooooo«->ooc_»

ino oou lj& & o—i oo

oo Ln ooo o» o^

75

coooccoo^>a-^LOLO

oooo<<r<r<i7?r

oooooojci^loôloloiololofVJCVJtMCvjOlooooo

oooor^cooô

<\j<\jc\icooooor^-z^z

oooo

C\JC\JC\JC\Ioooo<r<i<x<r777Z

OOOOmvcf-oo

ojro<\ir\joooo??77

OOCOOOOOOOOOO .-• <\J fC ^C f*- CO OO r-»

>o h- r- f*- r* r*» r*» r- r» oo aof\J (\IC\J <\l CM f\Jf\l CM CMCMCMOOOOOOOOOOO«r< <r <r <i<r <r <s <t <x<

ooooocmco^lOvOoo CO oo co oocm cm cm cm cmooooo<X<X<X<<X

OOOOf-ccoo00 CO 00Ocm cm cm cmoooo<r<r<r<r

ooooo

cmcm CM CM CMOOOOO<r«i<t<i<t^^z^z

oz

of

zLU

ozno

a

z<a.oCot:

Q.

s: o•• —

i

CCLU CO az•—

1

LU UJh- X >

00 »- »—LU or I—X LU T • Li•- K •""•^ <r

LULL. O ofO X TO Qm LUz < << LUI- t—«t s: CCO cco z

o <_l LUo *0£ I Q. » »-LULU cc s: zx z3 m LUi— LUI1I <ro X CDXa. < Zoo Za: </>

3" <rn LUO «—

ctzr-x T - LULLon •» os: CC tn\-zr-x *-• s: »—

»

UUi< >x LULU X<xz »-oo >t- »-LU 1— •-"»- «Iooccr » > * TVoo •~o ooz>- cc Her; oo3X3 U3 H-ar0«TCL <ro. Oc> •Oy in o_i— ••

i_ •_ iV—

»

z<r v.Oli.o —i »-<CC—

»

-»«vICO _lO o (Njr\iv»

OO ^ <r>i- CtTuiO • • •>

1 >vO i— o LUXLO 00 CO*LU»- ••o \- O0)-sO >OvflCC~ oo ZsO 3 LL LL.LL-

Q.rs *- rr» -•~» o»n T) «tf«ff^p«

»—i >H->- T t— K-t—1— t—LUO t— Lu LL LU ++ <<I<?UKt- Zh .-«»-»- K zrr—.<! •—

•

i i>i i hZH Z (Octree:

orujoâ arc* Olu cc O OOOO-a'ScD a.3 ZW3 o LLU.LL

CQCZ »-u.o •• zctt-uj oov. lu- ixj»-»^»IZmZ »ujOlu luC<o*-1 *-*-"- x x 3ar_i•— •-•»- I h-LU>- »— LUO.CCOOO0_J< X LUCC2rLuaooc:oc»—o cc ccluoq.»/>*-lu - loujZ LUZ3- _J«->X

XQtfUJt/) »O0-»LU »—_jXO OZVOv>ctOxtJa:» z«s »zx.luluO «0 - 0SJ30«o—isoiuoa ozX»—o •• ooZoo» ara.<

CC* LO^»-iLU 'UJ•4- >—OO CT) LUd Ct. LU -* 6* «/1

—z t—uDo'OnoaLU<I- t ) i o.jnzo.-*r3_J U.Z L)D< o5:q->»u.o- z cclullo.

•U-Z •••—X »—

O

coa:» Lutu'vk*»c:z<>OLU I X>^ I-.LU&-2:•*3Zir: \al>wDoruQ »hij3»-< s:

* co«r •*--• r75"» ^r*> _j~5 jui<ti-«»

aroLUKDDOXsroo

•oo

- ex.

>xLO •

- X••inzOv

«acc_JLi—>-*

•.ZiiiLULUZr-iXuis: > *-o_^Sz • o<r*Z>< H-oO>-<_j«»»— LU

<—••->»— OCLU X<LU^ W*.Of ^-LUXl5»— »-_«^< kh» »

LLT0O5>ai—"Zm|-Oj O0<lr)o_LUt-iy muUmZh luco•LSKOJOaru z o oo

m 7U(- »— MlrVLU»—>m t ) III

nr«r«i Z>— UlT) » lliiii

SOTlU(/M?Q._j7'VQ!' XLL.**— OrvTO 111 <I«3- »>0 I—• t_J >-0 LU> - t- 2Lu<t>u'<uj>>X o? «o ccnOOUlCOXCtl— COI— «yiu>--<tf LU?'zot: »-Lu<r o^zin i-luo o ocnooi— sruja: ZxQ-OTLU OOJ-OLULUO LUOOLUI- •3TO-ZZLJ CCLU OUl»— <fQ OtLU t—i- LUX • y<v«-r»—i<rzr~i^"i—o »n i— »-cj

Tl— 0«-*CJLU-)X^ -»>._J «-*_! !?»—CCOS »LU» >».UJ<OZ oo»-<occixj ztSLUoo>-ui» t-iaci->. >-

LUt-Hi-t—^CC ^cf LUQi <TX a:— cd<i<0 »-h-h» Ocl<» ocl—~")*-*rYT 7ni/)-«*7ni-<«^moo>T507«-iO-LUf-<r _ii-Ol

LUOOh-.!— D2 <-i< Ot-H^S-xlui— s"h-.o_i 5- »(-xruHoroorOt-j<. cxro Dtfi-0-<Oof _J2T 0'-*0<0

OO LU U-» 0>-«'VLL LU LLC**

n. STOCK *>

» • oz> •+-•«LUOO»-« • •—

I

3TO0Ct»-'H- »«o0OOZ KO 2TO— «3 _Jnr"<—— CLZXOLULU- x^<octooct-*ooX »-Z 3" KUQZhjhQIui<tO dionrco>H 000c

LU 5C«»-0_J •

OLUZ> LUOfNJzz<*-»<roooc«<Ti-iCOV— \— -Xco onoozxoa: u.< lu <\io loDCuiu. lj »•

>- CfO< "VH- — X it •«

•-• OOLL »2"»> «LUO LU<-»•—(NJOOOri— »ffl7H- • w. .f-n— OO » . t7wll k»<txir - r-i»-

LUiTif—afO • rfct »Oi—OXZu-\zz« r-ooo

_J »LUO **-z<- JUXVHhi-ilu r- »>cjJ—OLUiC • LU>.

'ZtSt—i<S • 1—•»—

i—Xt— co- <ro>

III LU«»LJ_JHJt-TnlmujiUTot-n»-i-(/iot-<f

of Cv Ujec a:z^«tctcclu_ilu 1 UJt-Gh . <l"UJt-U-jZl^Z ••-OZ>LUh-LUV.J »UJ»—

-• ^ *LULO \~m m CO- • OrO» <Snf »• > ——. »f50«w •v.y^-LLV.LU»-i^^>w(— 1 ns.7>^Z>^XLU "V—<r •••«* •ooLOZ •>

I- 00- >-r\JO- 5»

LUCD- - ^1--

•-» »»! iV w^>——<l— 5^0OLUt— •

0<T- <iin-<O0<tf—

1

zy •.yy zy.LUCt XOTiuLUK-a: *XOLAO>K- ox

LL •U.DOU.in4* *A «A«A4A *^>

CC*V

CLIO•

•ooOil

OLU

CC

00

LULLLU3<rhLLKcc<

Oct

r-u >

_JLJO

111

CO*-*CC3

oLUCLLU

LU

O <

«•» #—t —1 1> —

LJU

OOOO O OOOO O OOOoonouu uroo-«m>o

oo

oo

>* LOo oo o

ooo

<r<r- -»<?Luyi-- srCCCCZLJCCOLLLUC

LULLLJOOLL

h- Oo oo r\i

*o

76

ocoocoooooccoooroooor- od <y>o «-• <vim «d" in <& r-co er*o—* <\i ro >$m >o0*ffff'OOOOCOOOOOHHH^HHHcvjc\jfvlcnfOromromcorOrOrornmrornrorOr<"»OOOOOOOOOOOOOOOOOCOO^ <i<r< < vûj ii <r>* 2"o •• zC »t/0O—IUJU1" LUV. Kt 20kOyot-a:. * xoo XX2 n»-oiuooZDtD »rsj 2: ir\in»-< -•»—< •+- eri-x • iÔ •• »-C0 KZ5U.J- <or: <rinsC <»— "vôr: <rocc 11 OKa »-u. u. < * .O _JLU• X» L-^LU»v •» Q. I— 3X3 mj<CL ••• • » ••O 2ILU

Xu<N<J£* H » • t/>LU_J •—mu. •luolullo Xn^ e:<yo—••-• LULLO »LU I— »._J Lb"—LU *LL I

• rVm O/v'LUfM "V. M 5"OJ» t—

y

••»— II <IO_J »LU ••• * <r • •• LU^DZclHZ^Z • ct^CX OKo£ ujOluo*— u_»— M 11 <Ku_if\ t— i/>

UJZ»-*X (£ KCl • •> Z>»— »— <ILUI— • CL »_I_J - -v *»</)

LU_j<i. arZ 11 ID cgu-iLULU •3T<Ior: • <LU»- »>o<j: II • CT<5-»-X »_lry» vOUJ 7 *-. LLOorTV5*u"\Xr"i-"i » ll i> wii.: «vi—•dmuj ir>m»—

x

»TT7 uj«fQ.TOV »o<iir> • 7muNw >— cd

»—Z *^ or" •« f~ • »— C 2LL). CT- QCLU'*^. llZCO> ll LL'LU

H- MJlL* CO. •• LUUH-3T«^ X<x u.t—z> ax •***«• 1 z»—*-mm» olu< lu - >x luto ••ro ••» <rt— _ 3:5^ *-n/» •• luo

V..-*C\J »-UJ (/> f".»l «Na;ya q-lu l> »—o» ZO •• <r a><ixo lui—

uitZ »u_xi— » ^c »«-!«v »s <r •»

K-5TLU» flTLnlNJ OX> >^ II TÎ/) X II - • 0O»—l_i »»-4 »

• • LU II sCC >— >^h-<r»«^ LO»_l » ryUJ lull 3 •o»-<&*' •—

2

<xroxr5Qt:» t- ^ x>s.<i- 3uiN- «Ln»— "~)U.<f» OO »LU»-«» • Q.CO»- nC •><! »— or 11 I • a. "Z. »-rsj 2!»-«U_ ,n»q^<- XLU UJ*/, t->(\| • .-.2Z » LUC* -\-CC CC.CCT •>£> LU»—i<» naiw<n q.tp,» >£>ll » 111

—4«.)^"Ol •t/it/^ - ^ »il » m• »-uj 1 1

. f ^ • <n » 11 iv. •> «»^•"» tn>-LUU_ »LU X »X\. m "Vc/l>v&f »— -Xa? >t(M v. 11 M^v<••• oj_j • ina. • »^ » 11 * »x• *5"m«^ it •• •—• nO<I» S' »•

(\Jt_)r)QC:LU>^5"« LULL, Or r»(M X•vû.oa: »«iiu» -a.* lu>-4 •• «_>

wvAi/i. »— ~>» tn^c«—» • «^'si_«n^x_i*-ll2 •<r*— llk- y$— »k—o«û »—

T

<r ^^xa:<r wi «rux<Q.LU •><!«5"- oriTiLUor:- - 3T OS" or"- 5: o.ocr it 1— «-olu »Cj »ct;Lu»-<Qf:or:»-< 0:2.00Oor:3'vOD.<NJUJ(\i03: COQHO<HZLLLULU *.3T3" •»- • LL »-. *»» LL. »- LLOCLOLU

«-H O •—

•

Oo 000m ** -^ un

77

ft ft* «« ftft*** O 1

* * fM Zlu* • t/> * L5 <ro •

* oror lu * <t LU* OLU»- K * —1 Ct 2!c/l •

* h22i4a: * LL 3 O—ft oo<nrfO * oo »- ^-> 0m, •

* <Q._J OH- * •i < hU 3T* lu cioao * PH Ct OLU «r •,

OTO OQT<r * t5 LU LUi/) or— LL o* t—LUOiOLU * < a. 1— o^ sto II

* cCT X t >or * -X y O? too or t5O ft UJOHJZ * a. LU QTLU —

<

< 1 <r0* * »-*- 0>-LU to 1- a-x CO JVH -jII * <<tllo: o * •> 3 001- < +o LLLU * 3 Ol-O** * o >- or QD z XX * »- ZtOo: * <r rr Oto oo LULL H•-« * OrVLL.O_|LU •» _i <r »-o (V«v aroo »K * iurti/~o<f •> * u. _i o«r O K O

* NQ.Z < * i— o <_) _JI/^ KO II

» * ^'OCas * «» o LULL OO Z<tZY- >*0* * orâ.Lu<n_) * o o or oro oor<or om * 0.-</?Xa.»~ * < LU »-a >—LUCOZ" <vO ft t/10_LU»—Ol- * _l or LUU^ z >-0l - _io—i * coa.a:«-'0<t * LL, D Xlu C--i »-"2"LL' LL II

o * lu,-. LUorar * X h- >-T on OLUor^- o»—:r * rt'T—l O-O * h- CJ \~ or T\- T30T • »

CD en M. o */i<r>. t_ » •k «*• /V LL l— <-> u-—

)

OO* ^CCui"^ * ch LU OLL O^V i )»— <r^— II II

h- • * OmiV X< * <J5 nr LLO •• oo Luoruj ror\j

<S) O * LUXLUO y- * <r -»^l )<f i^_jinor <**-M • * X»-Xlu O * _j LU -»2_jO ec ut-a <S »_J o * O H-O 2T » LU O <S)(D^*-*lLl— «so -JOs:

m * mX 3 .«j O < cc** ar»- o3 cooluh- LL II

X * anujQQ • * • ar oOf-Ka o »— 1— o-<h q: i— * ZarXzuj »S * m LU ZhU r>uj^ 31- 1- 1—3 C3 < * LUU-I—«-«f-Ûi * t5 5» <r<x:?*'iU'.or^(j3 « l^-J^- o: o UJ * •jcii— * •« <r U57?-1^ <r<tuu II o

X 4d ^</> »_!»—'tO •» _1 »-LL *-,}—+-» U'-ISTT fM II

V 4t _i*v •«/io»— >• Jt UL in O LI! /V<V >— onrui C5r\J

c z •» ft TLU_J»— 5"OCO * o X ÛJQt_JUJ~) <inn> <rt_r»o -» mm * f)»— lUÎ-ULI » •i »— «—x<r_icoo rvt >^n _I<T—41— m ^ * >-«ajnuji/)^-_i * IS] •«»— —>^l >

5" LL_JCO (\J * irDn OD -> IS c*« «• >-LUÔ o-atLu

-ôCoo-iUli

I— » * <i2Fcoujaror * < or to 1JJ LU, -LTl

= * in * <<v Zoro_H * -J LLX t5tOX LU LU cf 191— 1—^C tr> o •S » mm * > <r r^ l_> tA! rf <r II OCO

h» » * ooa_Xor aro * O —•« JT »-••-< 7Z _J<J <»— _J —« II

h» _l ft LU »--»- »00 * » <MCt LL»- 3|->-OLL»-LU3_JLU O-IO >v> * >-•— CO»— * H l-O M< jjui > oi/iaaon <ro—

i

< >a:s- * tf77tDlllOtll * ti «r> tnnfOUJuiy or _j<r«k wyy 4t _J«rfc-^,»'>«fry « <f —<_i TTiwi-i-tfnTTi-i-n it _i

1A II —>-5 * —> t i-.;?LUO # _l »-<! - « ilu rin /v rv e 1 1 'i >vy <v l 5LLCO UlOC5 ft :FO_Ol-<lori— tt LU ^0 "X _i ivi orm_> 1 1 1 hh i_ s"o uu ~<S)

o o ft »-« LU*JX ^ * O _l o«i CL0_00i»JXX»-Orvl o«—

1

<s » couicnor« » »-ar * ••r\j wn _i ^ II o—>o.oo* * _JOLU __ILLI # ou or or _i_ILU O II

Xi/lOO * 2. CO 0.00 0. # <r » U'»- OOXtlîNirO^Ci -^<NI <IC5COO. ft <<iluo<iocs: * _J^ \~-z. LLOT 3<tL5LS CO<OL50 _i<05-0 o ft r<c >n^ f-il— IU * LU— 70 >— . j«r<T«i<T .j^cTrf II -J-HS>m-i—O * cii-H<r_j_j^*- * Q x>o LU^1 •U l_l_l_JU-_J_i_l ou_O 3^^ ft n_i <r O * vnt- o XOQO LLLL LLLL X LL LLLL coi—

r-4 —!•—I •— * ^0-^XLUcJ|_ * o— H-LJ LUtOOOOOK— H— COO0or ooior^ * CLO-OOi^ z * ao h- CO ^CUOdfl.H * <»-.0»-'0:f«/) * to »—2!coO_J * XX _j ors: or or or oox<"^>-o>- * t-û'** fvocin ft *—**—» <r uil— ai3TO ^^LU«-*COotO * iihod o # LULL l— IVI"— f^ll— to •—

<

LU i— • • • * >-|-Whl-*>»,>*»*• *#**-**-»*** ft* ft^ft* **#*****##***

*

78

co

UJol-«

LL -»

u. «_•

UJ UJ

D 00o •» V.

* -tza <r»—

•

•- Kh- _» Zo —» UI ^s* rn Oin f-z> X" -mifMOu. O ^ffiZ,

v. Z 1 ~ioa: CO Ouj 1 OUJ Z t-iZZ 1

u_ O »->-o>'CO >- oo^<tz-» <«<fOUJUi«rm w« xY^.>r'jjYw u:u O1—.-. VcO U.U.

» »-—T'Oroar'z— •-• O COCM ••cOUJOTOCcoii i-^ cozzi-.j_ja:y-n »—uj«-oujujx>o » 7Qf-ai»-t-iOiLu- < Ui5*">->.UJco t\J 1— ttfU. OT

*• wiii,-.Q?2ai vi ^m minn•—i •. OS" ^«-«.-.;Ty-* i_J-"5:^«*coooO<rm 7n_ji/)(/iofiZ«~ 1— OCULil— t—t-l>-u_ Zin*-OU-U-Xo •• «roOX> UJi

«-» _j(\juû ujujâero a. 1 Z>>>O-' Z hhhQLLLU CO 3 •— 1— 1— I— UJi

•> Ze-iCLOlH )>.UI-« *-• ^5"Uln ill l<Ti

OrO »<nuLn u ii

<r— C'Of rt'U-U.U.UJa:o _IDClUJujUJO<o * _l

1 >-»

UI<NO0Z —5^««-fNJZ«tf ZO—KZO«-U._JOw <VUJ_4 Z^«Ct-ZO o

—

»

UJ»-«»— I— 00O—»UJ00»-O-J^.U-'C(- CJUIUI*GOUKoOUJOOO><coc£oogo wt<-**v O (/) I-— 1-<y t*. GOGO >- _l—'Cooont— ui

»- »-• OOCi—QZK>-ZQ£U>n.<zôu •-•

»-<UJ^-i Z»-UJcol— ooi— ZDcJl-7^zaOM<<nZMaiKi-ujtfi in ni/xiiv

i l^cooor*' -^^ uffn-nu.5-

M<ru.i/)nMo<r> cd iUJCJ*->00<>— COCU1I—<——* 2?~~aoaaouj

uj <oo»— »-.»—

>UJUJ« iUQ.1 >Z•-• ^> Of 1/5 COa •-. UJ!-*-« OOOU.Z( >»— Oo'lVoOU UJmODi )oOui>U. UI C£. i-. »-• OffoOU.U- ZZOllZLLjU 1 —ujOtnmXuio

in a'cnm rvOmmi— nj rvi inn oc^-imz i l mi--I —iOzz-*«r_Jui l U3") • ocOTT HM?IUe£MH5/T7nn »—

nai <riv ct'uiujO

«• u,u.a: -•NOJ 3. U.31- CD

m»CD3 VUJ-U_*-» r500U-^ > K>s.^5Qfar (fl3i >

y-Cx. -w »— ui00H-O CDlO»*OZ >^-*v<0 h- D-*

_IUJO Hit— I—O<ct:uj tj^roui -«*- to <rujwoo-»oU)Z Q.*-" ^.LJUJz»—o <okzuj u-,

Z UhZCOtOwa.K< u-uj_j—•

OZ _JU.^-w >f-<I_j <uuo_j<r ro»-.uj<ini—«rfou r>-

II if-iLLU. Ill It <r(vi >5"^.T"r»'Mior'

31- UJOU.U.U.I— U.n-5OCOcDUt/) O

«-«^-zoi-j>>> U_<UlU.y-h- H--»»—oru.«-MMOUl-(/)l/l(JOUVLU Zoo<r <y <r oo o. i— «r <Q.a.a.—co<rc«rz<r<r<r mi—UUOft»l-T t-

<I<.«J<(_l<IlU_Jzzza:n»-zooroôfuior* oUlUJUI^CJI-JOxxtui <r»-t-»-oorct:t-a:OQOO_i_j_jri- •— *— i— _i

t— y— i—uj<r<f<o<»— _inoai-ujujvujnnH i— >- co or ct: oo a:i tj

UJCO

—»*« ii

«

UI •

<_l_JUJUlOo

UJ

z»-» ui

uI—

y-zr<t

<r _i_JOooGOi )

oCDUJUJ_l

-JOiUIQui

UJZ

mZI-i »

ro3<iZO

CLUIz

y-—>man_I/VZZ3

-— Ocom u_

TOcoHÛI_JOCD<t<ICtk-Ooo»-UICO

l—X MX «3LLXl-<r <<t<«r«r<<ir

wmcLt-rysrs x«»ic5<iCLX»-«<\J_JUJ<l<T<r<I<IoOi-i»-*.-._IO'Hl ZOO_jXKODoo_J_ji_j«<coooco<rofrcjooCO<oo

Z OI— m>4"s/"><T

o_u_>-o<r«fl-<r_jUllJl-l-htf

CO—

'

I

UJ

>0int

»H t

II

••X •

<r

CD»0

COII

<

•

•oII

i zUJ-5

CO• »

• in »u• u»y

»UJr\IA• CDh- I I 1

(\1<-*UI

«too<t +i o •mujui •<Nirocooo ii it m• II Xli •

NrfQJ II

II 3TZOOO<l*r<x*—i 1— <r_Jco •Hid •

a3 •• »»0»m>i-o

•»«0 I rvjoo

vOooui l in-^roinin ii

ujocomof^- • •{> *•

ooNm •

• n ii ii r~>

>rti-t-i<rr)II <r<r<r-jins'Osrprim 5- ri") ii

ro<r<li-<u.TXO—ICiO

<CO

mii

m-<r

oo

mI inII o

y- •

<ro- X li

•nj.in

CON- OTNS UI•O »C0II v^N. »•

Z II oo— f\j «mOi lO •

Q fllNZ-«T II

•«—i2Tr-iOCvJcTO-<r\j_j»—o» •mo •» •ii ii in«*-

z-^ I I

i-oujujX îninvTXM•r>- • •

mO ii ii

in ii <f5"II v0Xi-iZ-)Q.Xu_<r_jcoTi-<<y

uiz<a:<

* * ****** ********»***********»*#

79

s:— -.uloir* u_«- -»

U)t-> uj XOUJ c£D _l—j-xr— o»- u_

i^<rû-— »-<r *tU^^wLL—<io: x

*» (/)> wU-Q^LU <rx >-<nu —ujo- s:— « rsi»-i|— otuu Q.Z *» OX X Zuo_j3o:uj2:lu c\j >-•

«/) •"* OZlUH-rJccTU-il— z to»— I •• ÛJO<I»— Oh- -»*i +«— too—ac<r»- - il>*.c3 x

O CL T uj«r<r»-UJ «U.7 <r

— Z h- ffiiit-saauH uj«ji- ?»f u. *- uj k cqi—tuaca-Zr: orwi- <r

•• —«- X Z 2. r5X>HUJ2L»-0 D U- «J</) > UJ UJ <T UJrD>— K Uj huiv^ <«•

o£ s:— > s: i-^Zhh i— i— •— <ycc ûj aro o uj <ro—' U7I- 3rz ocriuj o-»»— tôc 2T ^ a a. tn<r<ru-i»— «r< ujty-o xinuj O"* n i/ivmuj . • lit i ii nc/i • ~^<r>y «ô o ar tU'^.r^^Qfot— _irin yui^ _jr\i

< zr*~ a —. »— "n_i i or5rnn ma:> U.T5r*. *~ ec C & <ri-u7u.uriwuu i-q. * *< C«J O -»» H-cO OO «-» UJ U.Xa <uj _4 QC W-2Z of t-H-ar act &*2TS_i <t<

UJ> o — ou:i-ozzoo>-«h srzt- otuj ar _j u_ >ccoc:xuj^<<i-»— ujujh- Oc53? _J I— O O OUJH- 2i)JJ<f<0kl-0 >-«»-i

< ii 2 CC <r «T2r3XM<rrintfa:<JûifY' unoo_j cl o >- o ujoiu-ioujoou;iijn t * *s.

a. ar u-uj <_> z _j i—q.z«-«ujc£oo^z_iooh- m<ri— 0"« O •— tn <*** uiuj liiuj r«<r On

t— !T <IO i£ t) ry _J£CU.LUO?rr'OU5iiJI— i— uj co3T aCry2— v. OO. ^ r» jn^Maiinn 7<f<f7 m —>i9 T3I— Q.X CL HJJ CD 2 O MUtt'>-<0(yOO«£D^DcO ujoc:<-»towua o 2Ti— <r _i h-<uJOc)UJ<r<rujujc*:i— i— rr o*2h * *Z* luuj»-i— rD<<r-i --a< +03T* * II- O U 7ai- UJU^,<JOr o'cnoOl- oot^>i

—

• y mircji—X tî/) u. z »-• m t\j*3"n »h»-i

ok- s: a i o *- «j_i_j-H_i-j_j_j-j_j_j_j-j <.x • •

OOG I— »v »—I T cDu. 0<<f<f l <r««<i«^ «(\iCw25"Cj3r S'3rO 5"r~if~l fit—> 7i-1 »vO ?Mi_i»H7i^»->Mi>H»-ii-.t-i».i_4 —i + x. + I

Hwru.u -r^ t—teffV z?T ot ~)<r •—•*-— i— i— t—'

i— »— i-^ «— *— i— >— i— •

—

n*y • r->7v«tttJ Tuji 1 1 ii/* »»-</> »—rt t^-.«-.»-.^»-h-<»— fc-i»-.i— »-«to-»-H rvui<f^4 •nnnor**•-• •V.^'^-v (/1»-0. _ll— l-O _J nZ7ZOJ777777777 3 »5"

I CO (V CVC *-

3

«r^s:u_5:to-tf -oo o _j _j»-,hhmx^<-«>-mi^wm>-.»- CLr\js" wrriuaS" OUUU - — III— U -» <I— _i O* II IT* I— I— •- »-uj ii • n_io sro <ro 5^0 o 11 11 o 11

<v 11 11 11 11 <\j a:<to »—o (-"O 1—0 u. x ^«x 11 11 11 11 11

<. 3»->0 l-O OO U.OUJ »-o < o 1—0 < oUJS"o~4f\iir\ 11 o_>— ir\ in ir» mrv nir->^ mni-ono nynrnnnnno— y~>!D^"^ •— ». uj • uj » uj ».!D h-«vZj aofnn»-<n<rnn or—j q.oc:o»-i»-.o«j<<r<r<r<r<-^ ujîti 5"ir\ xm Xitiq <ti_jn_iTTi jTunmton J_in_iJToTtin_it9t-t— K->-:* aTn-.—' »—w 1-^ 1—wUJ _jcLU_x<ti— y- »— 1— •—Jha< a ulx<tk-»— 1— 1— »-_i

O QDQ OO OO OOO o_j uj<r< << <<t <Koi _j<r oluuj ujui ujuj ujiuq- <ro Oodty cyrct: ara: cceero o

a: 2a uj

80

u. «/>

o »-

< zO LU_J HI•. o ••

X i—it/-

x \i.y<S) LULUI— o*-ooX *•*

\T\ »-» «-»U,

• X U-LL.

O l/> t/IUJ

O 20o a: =5 O—

»

— O >-U_<

—

.

bf <t o z-• — ci _j z<r 1 —v? _i *• n«r x4 « i»- f"i _»_—. ,. <r• Out «« 1/1 K • C/15"

-4 o o a. oiui-t i— yw <r z uj * rar Z <o «* ar a dd+ uj o_l X <— t/> U.J- o 4.

O » a:acz> u. <t<ia— ui Q uj o ujuj<r u. xo —o»-< ti <r o *-» u-o.»— uj srx x»— « 1 Z n ^ t_> oott^*. o — «J«t <r

V. <t _J <T O0»— ZLU-M O UV5—J Q+ —. T T ft' •» <T»——J t —1 1 )»« 5"

<m « > uj it uio cC <tm —1 z * + <r

-»i ) 7 i—O 1— 1— i— «^ <r CI » er _i-^ l r\ »~> r\ ujt ui^,-^ w- .«« « i»— *it-% <r <x> <x x»- z_i T> * »— o pn*»-# <r • omx o o• </) -.1 r^ _) ofCi f-O t- (Vi Zrr>3 # * V w

~*i— 1— ri ^rv »—n • 3<\j_inx <r •*w^ LULL LU • O-X O (M* -V U_XUX<^._i *-C5 • ZQ U-in Z (vj - UKVw — <C **»X<r *lno •— <r n-* *- •» »— •> i/izo© —.—<-«*> Zo,u.xxrr,+ o.10 con •• rr\ -» 7n <jnn i-4WwOJui<i<<j<y s-

.—.^>v "™» ci—* —> n ii 1—ini- u~ 1 < m •> • ocii/xiiiowji •>_( 1x—o h- I *-• • i_ <r Q-q. xn 7mmm*aO »-m • o <o 11 11 » 11 » it ii 11 <r 00 </}</> 11 11 11 11 11

x<r ujo o • 00 —t uiir_j _j-^ z re**ujo xo uj-»^4 t • 1 xo—» <o ^— r=t —.———.——.———.————1— it 11 11 —.——.——.

_j h- <r <v r^ooo i-Ot/i ho Qo^-trvim^-KNira—4(\J f-4<\ji-*(Mro

II II O 1-1O II —I II II CO II »CD »- O (.wwwwwv«,w2rii^^«v.-wwII UJ. 00 ujo<t mvti ujf >u« ti ioQr\(i«irn >• tt iujimu-u.ii

On »— <rnnoooo »- Z •- 1— <s(/lion <3" 11 LUo<r»— <r<r»— <j <r 11 11 —**a <tin uj»-Q-«I _J X_jO OO CI _J w -icf. XDo •- _IO_J—IO-J OQO K-UJ D

I- OO -QOOotCC 0<< Zl- Oet _J<r >— jOn •-••-> _in <n uju. <*_j_i o^ft' <tto o—

1

«/>*-< occ>- 0.3 ooz

o ir> h- o

81

•-> raw mm z—o *m. u_ —»—• LL -» OLLLU —» LO «x LULU —»- U. -i»i ~CO

—4CO ——i(JJ wLULU— I- LLlu<iujw

<\i < 1 2 OOLUa: ZLU (V— LLILU —-co a:s: »- lui ) -r'vrj—oar zr> o'a: arrjzo -J X*v OÎ-LL^r)—Of-Zr5"5 z!Di-ov. LU ^tO «v <T— 1— t-LL»—<0»' >— -.<-)»-<•-<—

—

aw CO O 5^5"—to<Jar •a'ajwaârt— <r<f u-N-Krari-^LuW Z w cmZf-LULucDa: <Lui-a:a: wi—lulu <r>— «—w O

or<r»— 3TO _io. a: a: uj lu cc o.< lu lu

>- >-<i<_>»-Lu:rz>r5 0.tt:ttr.:rcoa.a.<O-O-C0cO

lucc 3To:q-uj-J <— h- i- _Jw«v<tcuji-»-rrr3r)ujc3r5-s: a:arLUUJ—j— ar

to LU ô •—)-»LU l^wk <OfUJ»-l— t-DLULU rsrjofi-i- rat— •5» H-iLU >^Qvr otLUi— <rot i— i— fr— \-\-rs ofLui—Z LU 5"^ <—i ^»— n^»>-*— luq. «;lu»— *v <r«:i— >— tU(y<r•—

i

—1 -»"»^"—

'

l-«I *-l— OKÔ. J-LU'O LULUI-I— cx:lu<tujq.z>cc:LU •• LJC^ Oh->-CO<»-*»— <I-TU. LUC _JO-LUZ LUO-ai-J COLUO CO •• ec LLILUZ <f_jh-z<-»t->_jLuar-J2a Z _i<r O u. Dlucoo.*-* LU Z LU tOOO Luu-t—u. <»->OH-r5*— LUCr:>-'LL»— «J SLUCOCXLU-TLL s: a 3 Vrfw -«a:o>0>cCi-o t-^5v-r> aro luots 3qc:luu. •-M •-..-.a Dui— ^ «^«-« Kauut-«1D 1—1—300 H- OLUl-h-Q-l-LU »— l-»*Q. ——LUI— v: >-(y»-"T3<r z«! >-<?, t- o i-i— 7<ro U« 1*mo<r <ro>tJLuuo»-Lur^<ru I— LUoc<r«tf >- j-<r •tfa:3

_ 5_

O _j LU /V »W<»CO 1— *SV- <X rc\T nf *vn jn ^_jiu ifV-yT ixirvi— _m;<f <rn tooro rV jffiîjjyujuj LnT<n-a.rui«*"t iin^nciuLU

Z or Ull— T^Û-I —

»

luO"!xvooo-ili lOnunynaîZ 5^0.^0 5-L-l—O i- uxuont-»—ou >-h r* r-)<rt iLOniiiumu! •-^"-JtJUtC^tO-< z -<0<tin-ii—>^ cC ^ ^lui— ll ar> LU O h- LUO-J LUO t-t- a STO-LUt-l— e£UJ LL oOlTMU»-iJ-a:QC»-Oh- aTKOQ- Hi-oa qoo o < a£«I< 0-<T> -luluz ZdC i3JCDQ. KK-Luuji-^-tS'tûiLUf— <rar<uj»— »— o:k <!- I-UJI— 1—

3 <r LU >caic* <*->:>< _l»-'C^r»'Z 1 X5Z»-i<J?(_)_jO_UI<IlijOUJ _iuj3r <r_j«r<u. »— 7 c»-1~—>r5i— r>n i>~i lu^'T'uj* i<r<r-i^-oi— a:_j»_ _j o_j-5oc:>-£ya:

LU •—

»

<_><ti— i— of _irn-i»-v:»-'0 QHrfuinunnaiZuz C^ZUJ^-iT)a! ec CO Z<»-ioc"c*<J'LL^.h<fuuzm u_LU(r< ><rooz»-.<i*- UMUjâi-KLU #v i—UlitOLUint— Oor'«r»-<iiipri(Vii "^ LU ui LU —• _ilu <r<lLL + -1 a: ia_a LO ,^'^<rMicrLL v-HLuuxf uirvoJi-jf i— t^rr'a'Qdu-oi'i— o oartototO n 1- O > oi-ujo-oll i oom tso 07 o o««,07 Oz ar<r UitoOofofOSTrVi—ior:y uilulot'5'i jco<t^ toi— <r3"i— to»— \— <r u- 5" \— to to< to O 1/ )3 «t UJ LULU *-> Luiuorioo r)o:i )3i )_j<r<m<r?'(_)_iuj<£<i'T)ôr. O.Z Z r)Oiii33^D»-ioi-u oozziuotij<io<tOLUtt:OQ.o<ro_Juja.C;0K <r «r LLL-OnOLUI- CI LLiUi rr-LL>LLUJuiO»-tIlUJui.-.<LUOZI— LLlU'LU

*_j t/>7l/iQ.n o.7i •iC^cv-LOia^XlOO^'^rv^'fVtltO^T'T'L-Crt )«ol77ZCO * o «*< <s Ororo<r cok <f <t u <ruj<r lu<t<io <<< o lu i- _j a: cy cc -J lu «j»- -* ~hk _j -< <r j- _j u.j h- _» at —i cd»- C cc _jcc cc —io i- 1-wnCTi fr *-Z«tOOO<«y o<r i i z<r i tfZ'<o?'<ra< z «<on< zzl-wro. o o y a <i»-iit— 1— 1—T QCTrr ^^<r»—•T'U '<Tfc-«3'<I»-.>— fc-5"<r2T ~^»— U- *- »-.3"<I<TLU-r»— >-nn v-»— *v»— i— t J »_.-r^_rfr»— *--« >« m_<ti_ i—

Â ..•<r<i«~i ^rnm ^ftOt—

t

<t <r<r iwrf^f^Trîrt*—.5*5"tn>—.LUcOta<<Tt_i n iiAULJr»'»-<<r<J«—*intO to»—

4

t~< « (A • or7?aia;aixnOriu:uj?ziiiai7'7>7ru'?'H?:Kui7ujiu7(-2'3'* II ii ii it it »-ot-o î—<»-«iDtc^Qfi-uu5!Xx>-t- i XK>- | t-t<jM*-a:»-<(/)Mi//a»Ha'c<t-tc/)»HM

Zll ll II

»—

<

*-*C\JOXluiikt

o.

OHNîvjm 1-Za.

xrin u-

Ull— >^T—4 TO f-i n rtLlTTT*-*—**— i— vr o o o< iflytn jitocaiyoc-ianrno. i o.5»arrv ofi-tt— »-4 HMwOnhLLU > >+ '•—•_! D.nt?^-)JTTTTjllin _J<r5"*S-TXXTTl >T OOOl 5CJtOtOOf _JI-

CO<I—

t- to

I— CO O.O.Ic*o-s<r

Qlo cou.o!'Qff/o:<xxx<h i- i— i— i— i— i— i— t- i- »-i-i-»-i-a»-

a: ujoto

sr

»* **»«*•***-* **#*•«• <*>*•* R-*-******* *****

82

UJV)

n

.—

I

— U'O Xwzz *m% imi mCOI- 3

LUc**- «rZDUJ l-»-i|— trt «CD n? 3:CCUJUJ o h-DI> cC Xl-H_j at ^

<t UJ •-• —

.

oo> »- -4»-»- M O X

LU O a:On_l »- 3 •

UJnH— » O i-l

OTiVl— 1—

<

1 — muuujf-i X 1— "V o!>5»<V K <J5 — —— <rhhI » oo — -HCVJ O-i_rt- i—

#

Qt—^ LULU -JUJLU O— 3>:* XX co-»ocai OOQ- a: 1

•—•*- •*oZ l-UIW<f • »-K o_<r

c£.r*>— ••»- , >H^ ^*'«* ynLULUCO X l-LL t (.r>~ Q.Q. «S_J35 CC X X — .«.'«» -»—

»

oc ' <S)# •^ XX 0:1—Or->—

>

« » U- »-—

»

on. na <vu_ • •>*-« •—

<

<r<r «-r

Q.O t— «» <r hi c£>— o»-< Th 3 »f\JLOX o Qô? ft Q_XO m _• lY 30 »-o l-X fOCLOf><^3l— v> X

(/>(•>(/> nx Q X n Q.I— •1— — 4. -ni— <r CM *ft n<r=>=53 xa: LU Z5 a •• •> ^ •> (T» • UJ»-qjO>- 1 u <f (Xooo oc UJ _) _J OCJ D>a "DsO OtToCO •> 1 X5" _IOLUUIUJ Xrocgu. U. <r •• •• <rZ> «fZ3 _i«/>UJt— ot^) «• !-••—i<\JO_J*z-rz + •>+ <-4 V- •• .—IC\J 1— <JO_»— <t •Qt -+ •»- 1- ITu cLcf<<x<: -hLU-VLLK • LU I— •• » -*~n »- <\II5»-h-O* to COCOCl- Ct-H»- »_ «»<MJJcf Xrg •XZQ-OOfMO -CO -O O-OXw t I- aa:xz*<ZZZ OmHQ3as w* <f<0 •• »-o »o_i »o • *«Uh- _J<N <— oco n<f <r<r X •- • • »-_j.-»X •TjOlMMTO • <~) • <""> O-l- ^ - — C5 -» * On.)»-(_*— nrrM<\Jf\jrfT<r N-il MJ.O.O _Jwt- >-.<->_i«ôo OOw . 1 con i -a-or

-

f/M/H/) to «~ £* l }*T • _l LLLL _i«-»<r_i«»-j ton_i ii <r ii >— _i XX LUi—Z7Z D+ ll* -»lu* *-co(\j<rx —Jcooo i Q-_JXo 1 tJ5a:_JO. LU <r —Ifc-C r—l-J_Jft»-<»—<•—« 1—• l/~! CL + o«- «zz _iaoc_ja#w3 x>oco 4-^ xxLui-a (\j

KLUXae'ae'Xtt'OUJLLft iuX<r<t.-*<i.jUJ<r_j aro. II »-i«: o ^^ •yitoni- o<rLUO<3 3UIXXLUOO y- a: ecaCCuKX lu< <r3 < it »- OCL OCX0 4. u_ uox _i wa: O i

oca »-»ctl— w <t X »- a: a: ii o C0<VlOUJ»— LU O II II T.C-ie/tot V II II rV il LO(V ii ni- ii ii ti >• ii II l— »— <""></>!>— || (V Cf II I--jQ^QCrV II II O ii m»— ^ n ii a: ii c_o CO CJ1 —

)

II II &-.-ICM <r33 Cf kXhh •—

<

X«j>.-4rvj O. <tO. GOiOoOLUI- Q T'LUIULULU II II

Q.o-<r ooa:a:z><fCicx: I tin <vooc)•—it—iO«—i»-fr»f<rr^Qf LU»-»- ooonz ii

l-I22Jfl:i2Z itf<nrooziiô3D CJCOl/) UIII:»-.^<njoa Q.Q- lluj cc\-oXarox H-t— t-i- \- Ch>- o. —icl o Oh-a ot:a:ct:cc<<<

o < O z \->— o UJ CK a a:1—4 LU n LU i~)C£. LU o a o 3X ec X X <fa I/) O o cc i-< LU Qi zz>

a; Q. UJ

** * t* « * •ft* ft ft* *

83

• >*• u.~* -4-

9- >-» vf(M A inO a: A<r uj x-J 3 1-

u. o -.l) t-» z a

•. >f <-• O — CO»-* »o u, —« —CD «S" O H- Z X<r «_i m —» a luj u. m o i—U. ».0 A Z *- ÛK • —» X O i— O

•• »X W I- O O •-OfNJ • CO «- O 2" KO 2"

•ih-O fO uj *r O nhC> o_uj_i *x -« z ex. o o mc <rs:U_,-_) • A o «; < in 037D _J*-Oi— »~ err »-* uj cd *nOK ni- <r»—co »o — uj »~ _i »- u woo •»

«-ti\il— O of; -*r h- » "") -sm— >— n v-T"coin •• uj —

>

no o coi—x yco n»-u<rn x to e_ :r co oi— uinof xnf__i»--» cr: •— ««-• r"> «r —>>o"">c*> 0<— »——U-O O X CO >*• UOS _i • ^

it ooi- u. uj z oomi*-o a.'^«r«*' ujo• •• o_ »- os: ôuj* •-or—<t^ ** uo—to uj <t »-H<ooc:-4UJ »_j i— mt5^»-"0

C_.t3X O. OS. *- OfT <IICS0A02^<f «0 «T »- •>

x<r»— co m o m rmwt»nH ox •jiionooen i f o. (i o. o co i— —<of. &-^^-UJ»— UJLL 3"«—o•U.O UJ UJ O Z OOO-Ock.— O • _jX(J5o_of"i i— I— »—-—

.

in n m i »«» tO"^N*T »T u. »i-«ft-ujn yi— ».T" co uj nrry X-- iftomoco _J5^ oofôuif-c3i— _jrr»-»— <r•»13I~ X <Tuj X—4 --J CM-iroto U_ -<** •m<_5 «t X»— U_h-«--> ofX<r •» Zin<r i- 1 »— co--iX i— -do -it-î • u_ _j vr »-lux ft: ryn ui— _io: 0-*ac coo »—o</> <a<on v co —.llowcoj— q-3cd couj•clx *--h< o. ori-u <d cc i— or »—•-•—•o •»-• -of-cr. xuj x!>•—»— i— o_ at: » o <*\-o u.i >h<oiujoujvi-iu. or—.<r •. •« <rn am-o oocn cor-so-rûi couj cdu_3o—'t>«— in»—t~oO ort-coc*. 3aO _jcoc osoa •»- • or • ouj 3 ••

•><oi O Z53: OS • <. etOoC UJ aCO C *.0-XU» oam_ix aiocaoc o-o-O — a. uj^.»—— ujO'-<u.o<o^tji-» o_ujcom •— »—ouj xo»-> w 7in —"« • »v • is "du.1 3-^t » 3^ i-*i-Tt ivnr># no7^nmTn7 ll<tvcotu xouii— ct: »-4^»2^ i_ t_ C« •—i •-• o mOtn^^Mjt )wi »m tOaX ••"« ^<f-i+ +>-rrf- l-O • —ii— in O U.UJ t-»

••mo. O Kcr* + + OUlO o XOX »X lL<fÛlU. X-*ocrto •• •-• »cojco o<oQ uj •<3mf,t~- iwju«-'0»-« inuj<io jujZaaocxiu a: i-ujoc: •»~oqc:uj u_uj ujo2_IOfT <T7m xo«— OfT II 3 n_J( » x •OOVUTIL uoou-3 > • ii t—xcj ii tv at: »coo a. «u-Um »— soev« •»« uj »-v- uji— o «rof'of' uj »- »

u-ct-of: ii m*-n ii uju—iciuyiiu. n«ooUJ ^.llxTiu ii h rrxj-O of:Xt-<u.u_3:oi-o»-« ^>^si-ot: uj-j3> -«_joc:c£ o»-h o ouj«X ^^20<IUOj32D »-t-^cOiiO.XU_ h-UJOc o—-oahHf-xoo.co o—-owO'-o*-' Zi— »-UJ UJ _l _J < UJ Uj i—i—.

o Xll< <r uju.Xu.xu_ rtrafTOO 0»—O O CE.»-C_)»-«0«-' 0-30

o_in

84

o —UJ XQ£ << QCLU O_J o COo UJ

zz < to-

1

O UJ

G to-i _i HLL »- CJ _Joc to-> o X<r O UJ z coin Z rv n UJ_j n <r 1—4 <v

UJ L_> i) UJ 1— zk _j »-< _J o< z * o o -1 to*

C£ o o z to-l Ks 1—

1

<t z o 3 to-l

< z - aj ' o o oQ. O •—I *- tod ^ z-5 — ^ o oCO 1— z

o—(Olil^ X

MMo

<_)UJ<5"

<CO

oIII III i

)

/Vto- z m to—

i

1— ^111o*a" CO OLUt— r> 1— >~ D «» O?"O*- z *: to-3 to ocn-5 o -^ <J—

.

i— •-« — x oo nof. ôa: C5 CQh-<TI- ; <r 2: <f LOOO.LU *.*^ r> o <s 1- •>

(* * z x or <t U.I CD O 3 o or</) z _J Xrt'luX to-

•

<f O Of. _1 l-O xo <nX to-

1

U_ cjOO.K » «v to OITM— r>»--»oa cot— co a: «r t_) COX • • <_> t/imf- o ••—

•

H- UJ o Of •UJOC COZ 00 t- •o • OOl- DCIS o o Da:l-UJ a:n af. CLÔf. •—

1

artoo h- oooo o of COUl"^ ii i*—* o i-» l lO /V--X UJ isj xotso. iiiCJ /V co «/> m»- • toHvrt D»\j — a: >* C9CLto* XUJ o> uj uiuj LULL! a. LUI— * oo • ujoo UlUJto* to-l

X-» <a: •jhcioiz •XX •OOÔtfi -HUO X X ro X—>o xo • Z«-»IT\ X to-O to-

1

to4(\|H -J oujO <o 1 oco »- i v- 1—< in (JDUJ C3 • I— «o 5^|-»-t0 cS in UJOCJO CL »~ UJ uj ivo i ii —

^

h-i tari-Oin i—ujo •• o < 1 i < ii —

*

oo«->>o o ii z ii x it x ii r> • II II II Li- —* X UJZK-I- xoz>o < II II -1 _J -H »-inO«"-I

*- to tt-» o _ ton I—O O C5 lO:*—..-. • —

'

CO LLMU ff» i— »0*0 < acx i_>x i——i »— (m OOOW<fO IKnoCrr-n LL \— IU to-—

1

(MOCDCJCDO Ovfi II oZ<~ re m h in mo. ii <i<j<r __n— •""-JO-Q-JICD HffZl- rsiLiuj <r <r>— Z— h-

Uhlhlt-ShSM OCTOJ-U- LLw 71 to-l to- usri-_jH- _j »*

H-UJ coujcoujcowi-<tjjto-.a:o_j_J-JujOO *0 ^COOf-Of to-l I-.LUU.UJU.O haiooZJ- wowa:v)H- coh »—<Ooo»—oocoo O— u_ o«-»a3 at-i-tooôo Zh<h> It 1 »- UJ to* LU o to-ito-t_Jr£rv ULI xu. XLL »- crra'U.O0-3 </) <_>•— o»-< CO G-^<->i3

O o lf\ O en O*m# **^-# * * * **»t * *ir\* *-*in * * * *vO

85

X *r>- CD»»i

or M1-O

-1 z<r w2: UJUJ or»- X)CO h-> <rCO or

z UJ< _l aa: a s: O

CC UJ Z«/-

ZK

CD

z a OZ 1—

>

UJ O z I-

a IV M nT H* to «r «w »- w tr-> - 2" UJ ^> <r O*M •—

•

•»

1

—1 <r or T UJK OO 1- »- tu <t O>_ O _J O ^. a CD MO a D UJ Z ao COz CO or O UJ r-l »- h-o UJ < »-4 a _;^ O 3t

>

1—

1

Zinor UJ

_j t—

t

n1—

<zn in

O*: tc r- * O <r Z CC\~ (T«UJ 1-

o O <_> Z QtL c O Q Z*» <r -n «d-LU z 111 k>» zn n»-. 11

1

tn V S CD 1— CO 3" 1 ) Q. 1— CD c-co 3^- < >© z y- UJ 1— 1-. — 3T »M UJ c-T3 <-r cc •• .— 3 -JO T5I- »-o rr LU n a— nn orl 1LU (33 COS O • h-O U • —•0^ orUJ l- z<—<•—

.

00 zz l-OCt >- or <ll O + co • )-

en-i Dl-LUZ K r»- O— ors 2n -J*-1 \- 0—^1— CO -»orUJI- k- or m nrtn ZCO CK «fl- Z 1i~n ^z z3 » olui-i <r X • »-« •> O » <3 «J 11 # i- UjUJ 1—

1

occ UCZh >- f H-O a: a: c l-X -J O^ UJ •w xzQ.UJ Z <Io vO xw Zt5 n»- O or»- _i j«t-1 n

"« *«—»eTUI UJLL UJ • 03 cf X n 1— co • HlCl—J l» •—

^n <v^^«3'«v •nyy ^•IILTi • on <r—

.

t—— 1 > •^.-*»•—• f-4 »«T II

1

00- -> Q.i—_jf-»- . »— 1 >-l»-i_l t —

1

no. _i »o fM CJr-* • —J 11 Z it riI—

I

O • Ol l-l-O CD «0 l UJ <r>*<r UJO or O oror + tou. »—

t

IDI— OO^! UJ <r 11 or Q£-« 4" -J OO •zz <ll-OI-»-o nujoo 11 z 11 11 u_ rso 11 —4 i-unu..-41—lyD 1— 0rOH-^(NJ_j < UJ ««

UJ«—I UJ •<(") »-. ^i-«i U)UJ UJ-4 n x 1— ZUJ *-»-U-l— —IK-5" —

1

OO <V COoTZ >— #-l(\Jt ) n 1 •s-s: OO T •!- 11 no 0 l-UJ Z-" Uj »-^CD II —•(/)!— COI— »— •

t— •«• wiOkli-yri- %*— 1 i-»-ir\ 1— » ttrttt <v* or«') ^r r»OU3 n<O UJCO lii•— *— UJ U- CC LL mi n>oo U_ »Q£«Jl— UJ n«cr^ (sju- 1 UJz«- U-_J cOnCO»_J— cOOl—

«

II 11 II -* Z~-sJ- •-1 UJ_JZI- UJ U lOwl-w •

U_»- xiniu.*—>*-* O 1J-UJ CN1—tu ttUUJ CQQO l-UJO *»-ujXarar <r *i-xu H-l-Zl- O'—CO <<<»- Zl-I- O>-0C|- o_3 a: o-— «_>•— «H>

> l> 1 UJ ooa •—••—« UJ UJ UJ II

a*a* xu- _l^l_JO ororo XU > Xu. u_a.3 o»-* QtOHO Q.313 o«-> <3 O'>—

t

i-i-

in IT* O in 1O infro****-** * -» * h- # »C0 »* 00-* * * * *» 0* * * a*

86

oZ<tCD

t-Ozo

iii

h- ofs:

z oa: z3 u. «at- CM <fi

UJ

in "v on to + in7h- UJ -i T-

GC 0-*0 N-t

o tt z i- xtu q o <o COa: uj oi cci—

o

•-H \~ O- UJ «* _i!3 5" UJ I—O^tn r-* oa h* _i ?mncDtfr tfl cLoj x Q- >-*-*z 3i-i2:<r i—ofin- to yo -* -»»—»—•—• i zor a o y n uj *Xil o^ w**-* 2 o ii •—«o— •ardent/') omQ uj Z> ZL~*iS> Z act- _iO Q.»-i-z s: o •—o câ: »s: o<v o

J- O CD »- r x<r_Jt5Z)v-i—

—

alix 1 I—+• UJOm h~ l/l_l<T I— CO >4-HfsJ to to

cr Z> uj crro*- z u_a;-»u_ •uioz— ujujo a:h-h uj -»»-<ict • »-< o —» o -Jcoi-^cr: uoo orr »— —4« Ml 1

5" 5"n vT> (V «rT II ill I— ""

5

3TV— *-<-*c» (-nor: i-h O-jxn iii ^ -^»— »—5^^.3". i S" ii h h nco <r OvOujujooiliuj ujX • i »-ir\a: o »cc • — i— u_r\j««- n <_>o<T | O »UOU.JS 2TcO»— 2T >0-*t-i UQ2 U-tOI-UJ COOl— ^<\JOiO O_J UJ • »-*nO I—I—'r-4 —> __!»-« II w^<-> • UJK- —*•—lOQZI- Q- <f uiUJI±j<JO II II

u-oiftTUja:i-t5i- ^vî-»-c5^»-uj »x ^-<ir>ot • i*> <i-i*-.c>-_i»-s:s'M_icr:I— ^-l»- 3"X_J<m>OUJ < ^ t/)3FUI03: ^3? U-<Ii£ cfCC\r~ IUU- U J»-i»-hUJU-UJ^(\J

II —i ^h>— •_JP'«-S" II II _J II II (-HOC Mkh•— II »^H-r\l»-'_jt_)«"-Q.;jcOcOCOCOK>— CCl— M»— h- UJtn uji— u_ _ u_ rri-iM t O ii tu <vrtTCDOl— U.UJco»— ujI— -4<\Jco(J>^rvl— UJcoof'(-)t0 5-OU-«*iî/">TiJ- ULOuj<r»— <r ii i—y—?!- ihuj <ruiuj^»*/)Cj3Kt'i mKhjUvOm tooM_J _1 I— >-<*-«l— STSTH _J3Tt- l-X U.UJ ÛJujiloD-<^t-u.a:oiuj>-^-iUJU.«-iUJu. ujooo^voiu. *—ljoci-coujo««'i-'a3</)i-»-wooi-0'-< wooo-ut" »—

c

_|2IUJ UJ ZCC<mtu. iu. no.

zo in o itmuo o -H ^

Q r>Z z<r *-

CO 2:

i-n —

<

7 t/^

UJ AUl »—o "» Q»— z ZCO *-> <t

t- s: CO3n o >-

-^ ycc 7" —

>

Y A Xh- irtuj CO

Qif\.^r>u- 3»"^-^»- _ls: <r-(1 to n— CO ni- ujet:

t~ oi-rari-i~»- C~Z

u_ a n i-tô 70Cn' 0

87

LLXOU.»—U-* m - _i a. •• oc;-> <ih- in oo_: uj< _: >-XLOn —CO — * x <r • o» »-i/> > »- <i_. _l»— Ul«_ LO• -O- of- x V * 21- t^> o 1— X UO l-co >»- — —II V. II O II tO W m (_ II _3C UJ2 UJUJ •• o K- -4- Xcc ^ctxxt^'Z - • O OUJ <IZ >o -i_l - o * < •> X -UJ- Oof- OX r. _i z> re JO »-»- O >_ •• OfX >x —jTU-H--) »m of of <r Oit J <iuj »— _) UJ OLT> Tin lo - bfC Ol— XI—

-

< <t UJK OUJ ><s> Of) </) < • »- - UJ - o-CL- <KLOOf -J UJ o- ZL0 of <r ceo *< ^l>s LU

•JJJCf LLO <_!»-• UJ- x_: u'-»i-uj m » »~ •> »-<\l—of <n of lux ofz U 1/iX r- _J K 1- O- 3 * z» »-• <r •-o •- ©_ »—o -» r-to 1— l-<N C i/H J» -.*« nw »—'vOl/)

t-O -_> QO h- Z _) » <N I- • u-o —:o h cc- af- i-a.oUU-XtU< LU O of o>» O • o-o _:< oz *uj ar •—X - -« -z< -mi-i—>_:to x < UJ-O C-U. •-uj—'<ooi- OCM- »- CM z- oLU- - COi—

•

H- _J -»- ZkL X •> C0<_» CDOUJ< H- «v^ • - II o<_ ii \rm» w <a—• ujoo ar »-• a:- iî— Luoia: vOolusO Of LU* lu <r </> » —» » 3>LU 3» II D Q3(^«t - U.ZZU. 3TUJO0W- UJ- • (M UJ- UICO<rl— I— it UJUJ l-XÔ LUQ. » -0«—« 9- <I3»xou_>- - - • ofo-cra*-—) UJUJ ZI too - _JX X- occ- ofO •»

IO|- CTOJXnO DDrz<-Z CCS. 1 l» 1 » »o •> •k_)>— * II UJOf II OO-fNJ-<r- •loll hZI-C »- •-H £E»- vujorvj cc - Qfl/>_>Of in •

xof »Q>o - " <0<(JU'S UJ>- (_• x »-i/)u •_:< OUJ KLU of >0

UjrOU-U_X» ofoof LUce: ar- rs * •• QfvOOh- UJT- 3 - an Of• 0. •!— - -II LL,UJUJ</-_>0 _> •• »-x • &*• <X LL»—O0 hQ — C j— o••X _<- • UJ Q.C0O. h-—

1

^x tn O- *4_ *>K * <ro_<M ••(_ ^.o- \-

v/HUti-Of II "3" X *•• <t <ru*\ m •> U OJ_J» •—1 •• - •>» <r it ofVl— -~»U •«/>_ UJ* in ^/T-^y » ••X. i- (\j •« ^ ii r\x —. nr.n -<v - UJUJ <rLU - t—ryt-t- >- fH-^JllXS-i» us X. <r »»ft ujx'lo i—nu.- n 7(V5 UJt-»_ it <—)0 rvi »o. X(/ifi » » MsOa—rn •• ~'I— -Ol- r-i- i—

>

ofUJZUJCAi/ie. ?" i— .i-vori-oy» — . >f l-U- Ct-l )V —>C3- U'O •— !—2r<os> oozw ujsOuju-uj :ZLUU. - o- •—< •>« •—<h- > < hi-< K X- Of<JD »UJ»-'X _IU 1 -f-UJO»- Clu » Z- II I-- ^» _LL;L»J<rUJ •-LO - UJOOQtDt-Xc^ 00 1— >>-• ofo • IJJI-CM »— II UI»-« »<_)d* OOf ZTi—Of O -X l-t)-l-<o<too.i-- Z>» _» 11 1— OUJI— MLO< • crox<- <r- •—'i—

-

ZXIO <aua: - z o ii nuj^'5-oozf\j<H-.sO 2"UJi—ZLOCC —— CD »l' >i < — o - III

aivriuy'— UJ 5"«r <T •!LUKLL *j.~£.\—D •+-«M <» »-^- T^t* o- x 1— »—

lu<vo_ »<rt-nn • I— _Tl— •—• la? < _JnOO«—i •• »:o» OV.X) •ir>~>lo ••-<lo o o\—oy- ujoo *i>*?mZI-00 »T^.U. Z- OO. •• KJOQi) f-X •• —lUJ- Ul>><ri—luu-I— 7*x » X^» U_^ X.LT»>^X nar XI <f <tI—o»- i/i<r •._!• _J •.<_) •t )• O of CfLOO^PUJ O— •>*«.)•' <ro-o_ —<l— 1

—

l/Xf - Of - AJO MTIX U_CT> It Q?3TLU LUO »«*• 1—.. <_)»—• x.<r» CO<-iO rrf -> —III*— »Ol-— •O xo lo <v in u_ if uj I— <r ~z ori— xcD *<riiuj«fl, 5' »<r>^ K-Qf ->ao

>ofiuc\iuj r _c;ir\o »>C3 •0^>_'<vO Oo •— (NrfaCv/OcrrO- 1—O Or-- cn a »— aoi— UJ(M UJ_I_Iujcsou-a'xo * n »o« < + uj<r» Of a. of U-rjo OhC h-i«»<j:^ • ofl-<0 I? -z ii i—- k-u-uj :

:' _ -OarO ix. • • of !— crui— oo ofto- z_isO o.a.Qftoo: - »-- ii cuiLO ofu-i—_:xOuji- o. •• «>uj» of • arO- ujCt/)«—<ru. UJUJ

uj»— ii <r&*—

4

<r . IfV •./VfMt'JO *<')«w« >n LU I— ».«r>A LUtyOI— i/iO •a or~i —>ih ii it Q.O.!-«• _J—* -C\J- rvi •<r^x«r »—• rr- xii T o.. »—i vft »—1« >o_juj o

«-»»— ^3i-x .^tuX • XvOcr'<rLn<v- hl. x »-»ir!i<iir?ii isuioi-i- »-»-fO »-iXO<LO vO «-• ZCvOOU-liliD »-ujc<o o» oao—uio »<9 tôi—

<

zoo•^moof -u-s MMlL»-t f> «v>7F 5T»-'X •—>o ii •—• »-«ofs:>—<o- *->o UJ(-\tV oxx

COf— - LUX - II CDI t-X- <L" »«rOim XUJLLiXOfX- •-•XI- II TI-<» Qfcr: -Of of_• Vtfd — —•of- • I?' CD»- •• O. Of O »4— Ul t-a 1— ».

U_- -OS- II 1—

) || • »-• t-il-L- _)• X. - o_X)» »-» X<» - Ol— - OCNJ- H-_> <ru'ujw—'. i_imi O _• 1— «• 1—wC1 -«^ I— wt'»«i'«— • —>»_. I— ««(_)««IA ••^»ii l<f««LU • -«• i— jnnH-WUh < i-ni-ii~<f. t-:^ . l-» p-nr'^l— <rl— ••:X »— O. Of V- O. >0 1— UJ rf oxx<*<r. <r . n- _»<X<II— <I<v <j »—

i

•<: O <I*-Of<lLU<IX.LO<rO_ <O.H <tT,

<S Sof Of5"5" -UJI— _! <n-r. tujcnis- !— xûi T UJ2Tof^ •> rMQ.?M Si-h — •- •-

ofof c\iafZc\j côt. of -ofo. •_:<Ln_:_. OfUJ_.Of. of- xofof _>Of Of- Of COCO v/-oa_j oo •- <r »uj ••—o -cxoo-oao: ••CiQ- G>—"O HDO Ol- »—Ol— II Oof- XX<X U-U- -0 f_lNOZ-J-U-U.XU.LOll. 1J.lLLUSU-t-'«-U IU1U.XU.UJ>» u. (yu. UJU.O - of of~" *«»m<fl4VI* W* «A «»4r> <AM <^«^ <^ ** *& •^nA ±PnA «><» <»<>I—

•

LUH-UJX OO ^h <n m >* Lf\ •O 1— CO 0> o —

*

-JZC5Of OO o o o o O o o o o ~« ix| »-<-.ZUJ OO o o o o O o o o o o o •-•Qf <r

*K*LOvO vO nO «o vO vO sO nO -o vO xO vO #H-aof*

88

• •• O

in m inin -« m

cc » O QC cc »o • • c O •

1 1- Ko M O<r ir\ 1- <r OO «rr inUl w n LU <r<r LU MC O m X Ct 00 .V «»

>- ct _i_i »- U'ct » • •» Ct •- • Ct • ^ toLU -» MM • LU ctct LU O -» z»— t OUJ •-4 in 1- LULU »- OLU •

< OUJ -*00 Olu it <r 33 < -ÔO OLU O-

3 LO«/> -z • OO _j 2 OO 2 -Z LOoO 00inZ 00 •.2- LU 1— Q.O- OPI- Ln2"i- LL'I-

o O •a -<n O O^ •• •• O •0.3* ô^ ctzLU • O. OoO OO. ct LULU>> LU OOOLU • O.LU LUrvl OW win • 00 a. i«u^-.<r<l i-sl — — i->or)fc- 11 '•—

<— OUJ Oct 1 Ut *~tr>t— 1— »-m Oct 00 OU'oO —ct 00OH in<v <r «nf ^ rf2 • Ct <r ^ nct^ • -)3ro «• 00 Ul *^ ~5«riniO rs oO- • wofmm V) _J<IOt XLLCt m<rocoo t-O" c Ih O OOt— >-*-* OO »Of- Kctl— ir»ctj-LU 0 -»_l ao- it LU UJUJ LU — _J 0 •-LU

GC -»t_r>- • r- >t»- _i o^rxv Ct • 7T*- — l-T'h- • 0. ^r-a. •< OO "^to-i LU 0.0 • * 0. OOO •<ro 020

Oct 11 OZ II ^K II O :?XX ozz 11 OctZ II ouuz 11

< tr\Lu w4< OU t- <tluc: «f ~*<t LU ITLULU lAKLUinn x - X •<rx X) :XXX XX l^CLXl — XX

ii •-^-t— oiyi- »ini— u_ <VfV LL o«v 1— 5- l- "5>t0 >_a •lliO •111O ^r/rî O » •> O tLU O • ai <lr> O

Ol-M o3»-« -* l->- 02 •-• 01— <-• 1— <r ^tz O 3 -02 • 3 • z nc zr wO 3 O 3 3o LO CtO- 1 O XX ara. in mo•—• — * UJ > »» * •—

1

ctct •—

1

UJ » «« m^1— > in 2 in n in l- •. • %- r in > m —t<r in< < x II < LULU < C < LU_J »— 11 0. II ct 11 3- _j OO _i a. 11 1— 11 XLU ,1

rs •1 •» > »—

<

-) XX * •» ••X3- LU l-l- LU 1— h- LU »->- »— 3- ctct » LU t—t— LU 1— 1— LU 1— 1-

1— 5- IO 3" IG 3- ia Z M « » »—

<

•sr xo s: xo 3" XO00 .— C5_J +~ O—l « O-J •—

>

OO OO 00 •-. O—

1

»-' O—J •—• O—

1

H- »-«0. h- >—Cl 1— •—id. LL K XX >- «—iCL »— chO. »— â.LU> UJ>- LU> O CLcC LU> LU> LU>

I- XX t- XX 1- XX a. 1- XX V- XX 1- XX_i =>_! o_J X>_Ji Ct I-Z»- LULL'LUf- _ D-J-J D_|_J X>_j_jUJ O.LULL.LU Q.UJLUUJ Q.LULULU LU 0<-«LU _J.jOz LU O. LULULULU Q.UJLUUJLU O. LULULULUCO KcOOcQ -COOtD I— COtSO 5" 00.000 1— 1-z«~« CD h-COCCOO »—COCOOO 1— OOCOCQO<r 0<r<r<r -5<r<<r 3<tf<r<r •—

«

772UJ t-tt—i<Tct «r ^><x<t<t<t 0<r<r<r<r "^•rf^-J"*_j*o_jaa*a_io-a-*a_jca*^*LU«-<ujct#H-Kctei.*_j*o—i_io-o.*o_i_jo-q.«- o_i_iq.q.

89

ot

11

XoXcc»mmm4O•

m•Ho•

11

l-cXonm omm •

•H oOUI o•CO II

»ZI- _J-oz LUOO.LU o• OOt—

1

fV1 UI</> Q_<-(yZ *•

lu <r oox* •

Xt-»- —*

a:*~ II

->z?r- _J—..-.o LU-•t-z: ii oOcjLU »-• «5 XX X)•oil v- n—4*V f~\ •i

o <-• m• 3 +» LU** •• >*o in •

X LA«• II II

» XLU »->- i—

i

x xa 1—»-i o_j zt— «-»Q- mt »-

LU> li- 3H- XX a. cd=5_I-J ar f-z oQ-UJLULUUJ LU 3«-«a.~3»—cocooo :r QA.OOOx><t<r<r«j •-• ZZ2TH-Z

•W-O—»_IO_CL* I— »LU«— LUOOI

90

a

»—

Z kTOTJ^j

<rco to

Co ° t:^t)

_l _l—*>-r\J

<—iUJ«-«l<sCC Q-Q.Q-°- -I

^j 0.0-0-0.{_> TTTej; Q.cOtOcO

ceTLX.ll »

COCD I )•—'COCO

o <t (V<r<r«rto i— p_i_J_Jco < uao-a

Oen p-<>—i . ii i

I <3 —

.

CO l_TTr\ Q.Q.Q-Q.

co yof to toCOCOo_Ot—f-t )00U2"

lucdco ex to

n n i7i/>m i—— >— »—

err V_jC~» zr^^T1 *-Cf^Oiinu I— <f«J<r<r7UiOtOt- 2T-^c.)_i_J_J_J<f

s- MO<aQ-ao—

i

i— t— 2»— i

—

J» h- a.

—lTJO UL^UlUIUJtJl

luuj <ru.;o •->•-« »-<»—»-<

Q. O-t-- CD COLLI Ci CO CO CC CD 2l

hhtojaMOnOooDcj to>0 OU. —JOOOOCO

91

LIST OF REFERENCES

1. Schultz, M. A., Control of Nuclear Reactors and Power Plants , 2nded., McGraw-Hill, 1961.

2. Bell, G. I. and Glasstone S., Nuclear Reactor Theory , 1st ed.,

Van Nostrand, 1963.

3. Radkowsky, A. (ed.), Naval Reactors Physics Handbook , vol. I, USAEC,1964.

4. Henry, A. F. , Nuclear Reactor Analysis , 1st ed., MIT, 1975.

5. Duderstadt, J. J. and Hamilton, L. J., Nuclear Reactor Analysis ,

1st ed., Wiley, 1976.

6. The Shippingport Pressurized Water Reactor , personnel of the Naval

Reactors Branch, AEC, and Westinghouse Electric, Addison-Wesl ey,1958.

92

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Technical Information Center 2

Cameron StationAlexandria, Virginia 22314

2. Library, Code 0142 2


3. Department Chairman, Code 69 1

Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

4. Professor Paul J. Marto, Code 69Mx 1

Department of Mechanical EngineeringNaval Postgraduate School

Monterey, California 93940

5. Professor Gil 1 es Cantin, Code 69Ci 1

Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

6. CDR C. J. Garritson, USN, Code 34 1

Naval Engineering Curricular OfficerNaval Postgraduate SchoolMonterey, California 93940

7. LCDR G. G. Heath, USN 1

Department Head Class 67

SW0SC0LC0M, Bldg. 446Newport, Rhode Island 02840

93

Thesis

c.lHeath

109507

An interactive codefor a pressurized waterreactor incorporatingtemperature and Xenonfeedback.

Thesis 189507H^4l7^5 Heathc.l An interactive code

for a pressur : ze J water

reactor incorporating

temperature and Xenon

feedback.

an interactive code for a pressurized water reactor ... · calhoun: the nps institutional archive...

Documents