J.E.N. 338Sp ISSN 00*1 - 3397

CICLÓN: A neutronic fue!management program for PWR's

consecutive óyeles.

porAragonés, J. M.

JUNTA DE ENERGÍA NUCLEAR

MADRID, 1977

CLASIFICACIÓN INIS Y DESCRIPTORES

E21C CODESPWR TYPE REACTORSFUEL MANAGEMENTREACTOR CORESFUEL CYCLEREACTIVITYBURNUPOPTIMIZATION

Toda correspondencia en relación con este traba-jo debe dirigirse al Servicio de Documentación Bibliotecay Publicaciones, Junta de Energía Nuclear, Ciudad Uni- 'versitaria, Madrid-3, ESPAÑA.

Las solicitudes de ejemplares deben dirigirse aeste mismo Servicio.

Los descriptores se han seleccionado del Thesaurodel USTIS para describir las materias que contiene este in-forme con vistas a su recuperación. Para mas detalles consúltese el informe IAEA-INIS-12 (INIS: Manual de Indiza-cion) y IAEA-INIS-13 (INIS: Thesauro) publicado por el Or-ganismo Internacional de Energía Atómica.

Se autoriza la reproducción de los resúmenes ana-líticos que aparecen en esta publicación.

Este trabajo se ha recibido para su impresión enMarzo de 1976.

Depósito legal n2 M-790-1977 I.S.B.N. 84-500-1778-5

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I N D E X

Page

ABSTRACT . 3

1. PROGRAM DESCRIPTION 5

1.1. Definition of Problem 5

1.2. Methods and Procedures 10

2. PROGRAM CONSIDERATIONS 17

2.1. Function of Program Options 17

2.2. Program Structure and Flowchart 20

2.3. Program Restrictions 22

2.4. Machine Requirements and code Operation . 22

3. INPUT DATA AND OUTPUT 25

3.1. General Data Structure 25

3.2. Data Formats and Description 28

3.3. Output Description 38

3.4. Sample Problem 42

APPENDIX A - ALGORITHMS AND NUMERICAL TECHNIQUES• 49

APPENDIX B - SELECCTION OF RELOAD STRATEGIES ANDLOADING CONFIGURATIONS 59

APPENDIX C - SAMPLE PROBLEMS INPUT DATA, PRINTEDOUTPUT AND PUNCHED OUTPUT 81

APPENDIX D - COMPUTER CODE ABSTRACT 145

- 3 -

CICLÓN: A Neutronic Fuel Management Program fór

PWR's Consecutive Cycles

José M. ARAGONÉS

May 1975

ABSTRACT

CICLÓN is a neutronic fuel inanagement program for

PWR's transition cycles. With given fuel design characteris-

tics, cell burnup data, batch sizes, regionwise loading

schem'es and burnups and initial enrichments of previous

irradiated fuel, CICLÓN calculates cycle lengths or fresh

fuel enrichments for specified load factors and end of

cycle life condition. Regionwise burnup sharing in each

cycle is-also obtained, as well as discharge burnup and

isotopics. CICLÓN uses an Approximate Balance of Reactivity

Method, where whole core reactivity is calculated by inver-

sely weighting regionwise reactivities with its relative

burnups and is forced to match an input end of cycle core

reactivity, dependent of reactor size and end of cycle life

Sémdition. - Rsgionwise burnup sharing is calculated by a

simplified regional neutronic model, with approximated región

coupling. Regionwise reactivities and isotopics are obtained

as a function of regional burnup at end of cycle and initial

fuel enrichment from tables provided by the user through any

fuel cell burnup code. Summaries of batch burnup by cycle and

discharge isotopics for all cycles under study are printed

in the standard fuel inanagement format and optionally punched

for use in fuel cycle economic evaluation codes.

- 5 -

1. PROGR'AM DESCRIPTION.

1.1. Definition of Problem.

The basic objective of fuel management for nuclear

power reactors is the optimization of fuel cycle and reactor

operation to achieve a mínimum overall energy cost, within

the constraints given by design limits and technical speci-

fications for the operation of the reactor, and the requií-

rements of the overall generating system and of the fuel

resources structure.

The decisión variables associated with the general

optimization problem cover a broad range with complex in-

terrelationships.Because of the intrinsic complexity and

because decisions should be made at different time steps

and by different decisión centers, the general decisión

process of fuel management is approximated by a multi-stage

procedure, by grouping decisión variables into different

and f eqüen'tlly independent áreas of decisión. These decisión

áreas are:

a) Energy generation plan.

Where the energy production rate of the unit as a

function of time is selected. Cycle lengths and ave-

rage capacity factors, anual or by cycle, are then

determined, as well as the allowance for partial load

operation and henceforth the end of cycle life eondi-

t ion.

b) Fuel design.

The fuel design selection for a given unit is a function

of the state of the art in the fuel design field and of

the constraints imposed by reactor design and previous

- 6 -

fuel compatibility requirements. In this área all

fuel design limits are established.

c) Fuel recycling strategies.

The selection of fuel recycling strategies should be

made within the overall reactor system characteristics

and the fuel resources structure. The options of plu-

tonium recycle as well as the extensión of recycling

and fuel isotopic are established in this decisión área.

d) Fuel cycle definition.

After the three previous decisión áreas have been

covered, remainding decisión variables to define the

fuel cycle for consecutive reload cycles are:

- Quantity of fresh fuel loaded each cycle.

- Number of in-core cycles of each fuel batch and

eventual intermediate hold-out cycles .

- Feed enrichments of fresh fuel for each reload batch.

- Energy production sharing for each batch in each cycle.

- Discharge burnup and isotopics for each batch.

The selection of these variables, within the requirements

established in previous decisión áreas, should be made

well before the reloading of each cycle, because of time

schedule requirements for the different fuel cycle steps

(uranium concentrates, conversión, enrichment, fabrica-

tion and transportation), írequire - for anticipated deci-

sions. Previous long-term contracts would set up cons-

traints in the selection of thesé variables, that háve

to be included in the decisión process.

7 -

e) Reactor oparation.

PWR's reactor operation is given by detailed core

loading pattern and technical speci'fXcations, wich. .

are established in the core design study for the cycle

considered. Little margin is left for operation alter-

natives of reload cycles in PWR's, whithin constraints

• imposed in the first core design, with only a secondary

effect on the fuel cycle cost for given fuel cycle va-

riables. This área of decisión is closely associated

with the feasibility of the proposed fuel cycle defini-

tion, not only limited to peaking factors ¿Letermination.,

but including control rod worths, shutdown margins, axial

offset and kinetic parameters, among others . It should be

taken as late as possible before reloading, to take into

account actual operation of previous cycles, hencefórth' •

there is not incentive to include detailed core loading

pattern determinations in fuel management studies, feasi-

bility being considered through ground rules from core

design experience.

CICLÓN is intented to cover the neutronic calculation

of the decisión área (d), fuel cycle definition. Most frecuen-

tly the fuel management problem is restricted to this área.

The fuel cycle variables should verify the mass, energy

and reactivity balance relationships for each successive cycle.

A complete dependence is then established between the different

variables, by which if one of them is fixed all others will

be given through application of those relationships.

The first two variables for fuel cycle definition (batch

sizes and in-core plus hold-out cycles for each batch) are

related through application of mass balance relationships for

each cycle. They define what will be called the "reload stra-

tegy" for the cycles considered. For given initial and final

conditions a coll&c.t'ion of consistent alternatives for reload

- 8 -

strategies can be done using rules and criteria discussed

in Appendix B.

For given cycle lengths and capacity factors (which

would determine energy and burnup for each cycle) and gi-

ven initial and final fuel conditions (through given burnups

for fuel coming from previous cycles and continuing to next

cycles), if the reload strategy is established then the ave-

rage burnup of fuel discharged during ±he,; cyclés- coñsidered

is determined by application of energy balance relationships

Furthermore, average discharge burnup depends only of the

total sum of effective cycle lengths and of the total quan-

tity of fresh fuel loaded in the cycles coñsidered, being

independent of cycle by cycle reaload strategy, as discussed

in Appendix B. This fact is very important because average

discharge burnup is a primary factor in the fuel cycle cost,

while batchwise discharge burnup distribution has only a se-

condary effect on fuel cycle costs. Henceforth, in a first

optimization §-gág:é# primary effects of total length of cy-

cles and average discharge burnup on fuel cycle costs, can

be carried out by parametric selection of alternative re-

load strategies. In a second optimization stage, alternati-

ve cycle by cycle reload strategies would be selected and

the effect on fuel cycle costs evaluated, as well as tech-

nical feasibility features.

The fuel management neutronic problem, covered by

CICLÓN, is then reduced to the determination of (1) feed

enrichments for each reload batch, (2) energy production

sharing of each batch in each cycle, and (3) isotopics

of each bat-§li at discharge, for given reload strategies

and fuel designs for the sucessive cycles coñsidered.

Feed enrichments are given by reactivity requirements to

reach desired cycle lengths for whatever defined end of

cycle life condition, once core loading and operating

condictions for the cycle have been established. Because

- 9 -

feed enrichment is also a primary factor in fuel cycle cost,

its calculation should be accurate enough and good approxi-

mations for the balance of reactivity during the cycle should

be used. Batchwise energy production or burnup sharing has

only a secondary effect on fuel cycle cost by itself and its

contribution to the balance of reactivity has also a seconda-

ry effect on feed enrichments determination, however it has

a primary effect on batchwise discharge burnups that are

importáiit for feasibility evaluation. Isotopics is needed

for fuel cycle cost evaluation as well as for uranium and

enrichment future contracting needs.

Alternatively CICLÓN can adjust each cycle effective

length, in-terms of cycle burnup, for a given reload stra-

tegy with fixed feed enrichments, in order to match the ba-

lance of reactivity for each cycle. This option is needed

when a constant feed enrichment, or a small range of variation,

has been specified. Then if resultant cycle lengths are not

in the desired range, alternative reload strategies will have

to be tried.

CICLÓN deals consecutive cycles from an initial fuel

batch burnup state, which can be the EOC batchwise burnups

of any previous cycle, including hold-out fuel, or from the

first cycle. Fuel assemblies can be arbitrarily grouped in

iiatehes o*1 subbatches. The burnup history for every batch

is saved so that fuel reinsertion after any number of

hold-out cycles is allowed, and a summary performed after

all cycles considered have been successively calculated.

This summary provides all fuel cycle data for inultibatch-

multicycle fuel cycle cost calculations, including batch

burnups by cycle, and discharge burnup with isotopics.

It can be optionally punched for input in fuel cycle cost

codes.

- 10 -

1«2. Methods and Procedures.

CICLÓN performs.a cycle by cycle calculation of con-

secutive cycles. Each fuel batch or subbatch is associated

with a región in the core and different regionwise core

neutronic models can ]>e- used f or the balance of reactivity

and the burnup sharing calculations.

Fuel batches are defined as sets of fuel assemblies

with the same fuel design, initial uranium loading and

enrichment, cycle of loading and number of in-core cycles

of irradiation. Batches can be further subdivided in sub-

batches of fuel assemblies with fuel burnup and isotopics

within guia! 1 ranges .

For a given cycle, initial enrichments and batchwise

burnups at beginning of cycle are known for all fuel batches

coming from previous cycles. Quantity of fresh fuel loaded

in each cycle is also given to CICLÓN, with batch sizes pre-

selected using mass and energy relationships for selection

of "reload strategies" given in Appendix B.

The basic concept for the balance of reactiv%ity for

any cycle is that the core should be critical at the end

of the cycle life for whatever end of cycle life condition

be adopted. The exce.ss of reactivity necessary for a resi-

dual boron concentration or the defect of reactivity resul-

tant for coastdown conditions can be established from refe-

rence design calculations, providing the reference K-effec-

tive at EOC.

In PWR's local reactivity evolution with burnup can

be considered independent of irradiation history, because

local conditions along cycle are within a small range, re-

sulting in small spectral changes in relation with an ave-

rage cell burnup history, and henceforth in small changes

in isotopic composition for given local burnup. Local

- 11 -

reactivity for a given fuel design and initial enrichment,

can be considered as an exclusive function of local burnup

and can be obtained from cell burnup calculations at avera-

ge nominal operating conditions of power density, fuel

and coolant temperatures, no control and nominal boron

program with burnup. At the end of any cycle, power dis-

tribution is fíat énóugh to disregard reactivity effects

because of differences between local conditions and the

average nominal ones,

CICLÓN calculates local reactivity in terms of K-in-

finity as a function of local burnup and initial enrich-

ment, assuming all fuel regions are of the same fuel design,

through lagrangian interpolation from double entry tables

of K-infinity (at average nominal conditions, equilibrium

Xenón, no boron, no control) versus burnup and initial

enrichment. These tables have to be provided in the input,

from any suitable fuel cell burnup code.

The end of cycle core reactivity, in terms of

K-infinity, is calculated by the ratio between neutrón

source and absorptions throughout the whole core at EOC.

Both neutrón source and absorption;terms are additive,' ",

so that regionwise source and absorptions are simply summed

to yield whole core terms. As local absorptions are given

by the ratio between local neutrón source and K-infinity,

if neutrón sources are properly normalized to yield an

average neutrón source per assembly equal to unity, the

whole core K-infinity will be given by an inverse weighting

scheme of regionwise K-infinity, with regional neutrón sour-

ce as weighting factors. Algorithms are given in Appendix

A.l.

In the Approximate Balance of Reactivity (A.B.R.)

method, regional neutrón source at EOC are approximated

by the regional burnup sharing in terms of relative power

density averaged over the cycle, assuming that power dis-

- 12 -

tribution shift along the cycle is small. Core leakage

at EOC is assumed constant for any cycle, for whatever

cycle leng'tti and loading conf iguration, so that core

K-infinity at EOC can be directly used to check the end

of cycle life reactivity against a reference valué for

whatever EOC definitiom .There are compensation effects

between the approximations of constant radial and axial

leakage at EOC, constant power density for each región

along the cycle and regional K-infinity calculated at

core average power density and temperatures, that have

been numerdcally tested.

CICLÓN uses an iterative search procedure for ini-

tial enrichment of fresh fuel or cycle leng.th, in order

to yield the input reference core K-infinity at EOC.

An initial guess for the search variable should be input,

then CICLÓN calculates corresponding core K-infinity at

EOC, which compared with reference target provides a new

estimation, using built-in reactivity '.vró-rths of feed en-

richment or cycle length variations (standard in PWR cores),

afterwards a cuadratic extrapolation (using the two latest

iterations) is used for convergence accelaration, until

a convergence criteria of 0.0001 is met.

For the regionwise burnup sharing in terms of relative

power density averaged over the cycle, which is needed to

calcúlate EOC región burnups and to weight consequent región

K-infinity a EOC, input estimations based on previous design

experience can be used, but CICLÓN can perform a cycle de-

pendent burnup sharing calculation using either empirical

core models or explicit core models.

The empirical core models for burnup sharing calcula-

tion in each cycle use rules observed from regionwise bur-

nup data for different cycle of a given reactor core obtai-

ned from operating measurements or more sophisticated design

models. For each fuel región either the cycle relative power

- 13 -

density or the absorption ratio have to be given in the input.

For fuel regions to be loaded in the core periphery (the most

reactive fuel assemblies), their average burnup sharing

along the cycle has been observed to be nearly independent

of cycle length, feed enrichment or quantity of fresh fuel

for a given reactor core, with burnup sharing between periphe-

rical regions correlated to región sizes. The empirical rules

for a given reactor core have tobe investigáted" by^.theiuser.

Remaining fuel regions to be loaded in the core interior will

have absorption rates (ratio of cycle average power density

to K-infinity at EOC in the A.B.R. model), depending on the

number of previous cycles of irradiation according to the core

loading criteria adopted. Generally the absorption ratio.for

all interior regions will result nearly equal. Because whole

core burnup sharing has to be normalized, absolute valúes of

absorption ratios are not neccesary so that any valué can be

used when a constant absorption ratio is assumed for all in-

terior regions. An iterative procedure is used in CICLÓN for

burnup sharing. calculation ¿n regions not fixed by "input ,-••'•-

from'ari initial •' f lat '• guess-of cycle average power density,

EOC Bürnups and cor.r.esponding K-infinity for each interior

regions are calculated, then new cycle average power densi-

ties are calculated proporcionally to regional EOC K-infinity

(through input absorption ratios), which are properly nor-

malized and used in a new iteration until convergence is met

in very few iterations. No reference is needed for actual

core loading configuration in each cycle.

The explicit core models of CICLÓN, are based in a

simplified two dimensional nodal method, using cycle average

power density distribution as neutrón source and K-infinity

at EOC for the neutrón transport balance. Nodal balance equa-

tions, with each node representing axial averaged fuel

assembly conditions, are set assuming that the probability

for a neutrón born in one fuel assembly of being absorbed

in one of the four neighbors is constant throughout the core

and given by an empirical core average transport Kernel, W-

- 11+ -

The reflector effect for assemblies in the core periphery

is taken into account through empirical albedoes depending

on the border position. Nodal balance equations per-assem-

bly are summed over each core región, arbitrarily defined

(of any size and not necessarily conected regions), yiel-

ding a set of equations where regional neutrón sources are

given as a function of average neutrón source in neighbor

regions and regional k-infinity. The core average transport

kernel, W, and the eigenvalue, K, of the two-dimensional

problem, appear in all regional equations. Regional albedoes

terms appear only in equations for peripherical regions.

Coupling between regions is reduced to the calculation of

average neutrón source in neighbor regions, through diffe-

rent coupling models: (a) a direct matrix of vecinity

between regions which depends of core loading configura-

tion for each cycle, (b) a matrix of vecinity between given

core' zones and assigning the zone of loading for each región

in each cycle, and (c) empirical estimation of average neu-

trón source in neighbor regions for each región in each cy-

cle. Algorithms are given in Appendix A.2.

Neutronic balance is performed for the EOC reactivity

condition, with regional K-infinity calculated from input ta-

bles as a function of burnup at EOC and initial enrichment

at core average nominal conditions of power density and

temperatures, without boron and no control. Regional neutrón

source is substituted by cycle average power density, ne-

glecting power distribution shift along cycle. An inner ite-

ration loop is needed for each región, because regional K-in-

finity at EOC is a function of EOC burnup, which depends of

regional burnup sharing in terms of cycle average power den-

sity. An outer iteration loop is needed in models (a) and

(b), because of neutronic coupling between regions. The reac-

tivity balance search on feed enrichment or cycle length is

another overall iteration loop. Inner loop and search con-

vergence is fast, three or four iterations are normally

- 15 -

enough, but outer convergence is slower, with conventional

acceleration methods resulting frequently in oscillations

or divergence. Because running time is small, no further

effort has been devoted to improve convergence.

When explicit core models are used, the two-dimensio-

nal eigenvalue can be used as criticality check at EOC, ins-

tead of the core K-infinity at EOC in the A.B.R. method,

at user option. It can be regarded as the radial K-effective

at EOC, without axial leakage effects.

The empirical parameters for the explicit core models

(core average transport kernel,'W", albedoes in peripheric

regions and two-dimensional eigenvalue at EOC, K), can be

calculated using an inverse calculation option included in

CICLÓN. Feed enrichments, fuel burnup state, cycle lengths

and burnup sharing by región in each cycle are input to

CICLÓN from previous operating cycles data or reference

design methods. From equations for interior regions, where

there are not albedoes terms , .W" and K are obtained with

the condition of minimum square deviation between calculated

cycle average power density by región and reference valúes.

Albedoes terms for each peripheric región are calculated

from each regional equation, once W and K are given. Algo-

rithms are given in Appendix A.3.

The adjustement of the model should be consistent, so

that the same set of tables of regional K-infinity versus

burnup for different initial enrichments, to be used after-

wards, should be used in the inverse calculation of the

empirical parameters. Reference data should be for cycles

with similar loading criteria, and detail of core descrip-

tion as that to be used afterwards. Any abnormal cycle, be-

cause of special loading requirements or condition of end

of cycle for instance, should be excluded as reference';

- 16 -

CICLÓN provides a balance summary for each cycle

in the detailed fuel regions of the calculation and also

average; balance variables in a few batch scheme by cycle

of loading. After all cycles nave been processedj a summary

of burnups added by cycle to each detailed fuel región or

few batch is printed in standard fuel management format.

Regionwise fuel isotopics at discharge is calculated

as a function of discharge burnup and initial enrichment

through double lagrangian interpolation from tables , pro-

vided in the input to CICLÓN, of final to initial uranium

weight ratio, final enrichment and fissile plutonium con-

tent, which can be obtained from the same cell burnup cal-

culation as the K-infinity versus burnup and initial en-

richment. Discharge burnup and isotopic data for each de-

tailed región and few batch averages, are also printed

in a summary of all cycles processed. They can be punched

fSv: multib'.atch-multicycle fuel cost codes.

- 17 -

2. PROGRAM CONSIDERATIONS.

2.1. Function of Program Options.

The major CICLÓN options are the following

a) Direct calculation or search options for cycle reac-

tivity balance.

If fresh fuel enrichment and cycle length are given,

CICLÓN oarries out a direct calculation of the end of•

cycle core reactivity and proceeds to another cycle.

Searches can be done in one of those variables, with

the other provided in the inputs to yield an input end

of cycle core reactivity. This option can be indepen-

dently used in each cycle of the different consecutive

cycles considered. Reference end of cycle core reacti-

vity for search options can be unique or input cycle

by cycle. Alternatively the two-dimensional K-effective

calculated in the burnup sharing calculation option,

can be used as end of cycle reactivity reference para-

meter, and a cycle by cycle or an unique reference

valué can be input.

b) Burnup sharing calculation options.

Regionwise burnup sharing can be provided in the input

and no calculation is performed by CICLÓN. It can be

input in different ways,(l) as regionwise relative ener-

gy generation during the cycle (if unnormalized the

code will do it), (2) as regionwise burnup added during

the cycle, or (3) as regionwise end of cycle burnups.

In the last two cases the whole core cycle burnup will

be calculated from regional burnups if not given in

the input.

An empirical model can be used for the burnup sharing

calculation without any reference to the core loading

- 18 -

configuration. For some fuel regions relative energy

generation is fixed in the input, because they are

supossed to be loaded in the core periphery where

average power density along the cycle will be nearly

constant for different cycle lengths, feed enrichments

and fresh fuel quantity. For remaining fuel regions,

in the interior of core, relative energy generation

would by calculated proporcionally to regional

K-infinity at EOCa with input ratios (absorptions)

eventually different for each región according to

previous irradiation. An iterative procedure is per-

formed because K-infinity at EOC depends on EOC bur-

nups. At each step regional relative energy genera-

tions are normalized to yield an unity core average.

The procedure can be extended to calcúlate all fuel

regions through input absorption ratios.

Two models with explicit core representation are also

included in CICLÓN. A simplified mode.l does not consi-

der región coupling, but use input valúes for the ave-

rage relative burnup in neighbor regions for each core

región. A detailed model considers región coupling

through an input interaction matrix that expresses the

neigborhood between regions, an outer iteration loop

is performed in this case until point convergence for

regionwise relative burnup is achieved. Región coupling

can be directiy given cycle by cycle through regional

interaction matrices or indirectly through a unique

core description in zones , with coupling between zones

given through an unique interaction matrix, then for

each cycle the different regions are assigned to the

different core zones.

For core explicit burnup sharing calculations, the em-

pirical parameter W and albedoes by región should be

provided as input. They can be obtained by using an

- 19 -

inverse burnup sharing calculation option built up in

CICLÓN. In this option empirical burnup sharing for one

of more cycles is input using data obtained from previous

operating cycles or from design calculations . Región

coupling is also given through interaction matrices bet-

ween zones or regions. Then CICLÓN performs a región

by región neutronic balance obtaining W for each no pe-

ripherical región, The core uniqueW is obtained by mi-

nxmizing the sum of cuadratic differences between input

regional burnup sharing and that given as a function

of W, for internal regions. Using the calculated W, al-

bedoes for each peripheric región are calculated from

the regional neutronic balance relationships . Algorithms

are given in Appendix A.

c) Isotopics calculation option.

The calculation of final to initial uranium weight,

final enrichment and fissile plutonium content at dis-

charge is done if tables of local cell burnup data are

given in the input for those variables, as a function

of burnup for different initial enrichment. They should

be prsvided for the same burnup points and initial en-

richment used in the K-infinity tables.

d) Cycling and discharge data punch option.

If desired, batchwise burnups by cycle, discharge bur-

nup and isotopics for all cycles considered are punched

in standard format for multibatch-multicycle fuel cycle

cost calculations. Batches are regrouped after the su-

cessive cycles calculation by fuel design and initial

enrichments5 cycle of loading, number of in-core cycles

and cycle of discharge, averaging all variables for the

different fuel regions that can be in each batch.

- 20 -

2.2. Program structure and flowchart.

CICLÓN has a main program and six subroutines. The

main program perforas all code operations following the

flowchart given in figure 1. The six subroutines perform

auxiliary operations repeatedly used in the main program,

summarized as follows:

CHKNAC checks the total number of fuel assemblies

loaded in core each cycle and stops the execution

in case of negative check.

XAVE is a real function that averages a variable over

the different core regions by weighting with región

sizes (fraction of regional number of fuel assem-

blies to the core total number of assemblies).

ESCTAB performs the printing of each input table (for

K-infinity, final to initial uranium weight, final

enrichment or fissile plutonium content) as a

function of burnup points for different' initial

enrichments.

FXYTAB controls the double interpolation of tabulated

functions for given valúes of burnup and initial

enrichment.

FIND searches -the table entry points to be used in the

interpolation for a given valué. Four points are

used in the general case, three points are used

when given valué falls before thé first interval

or after the last interval and one point is used

when given valué is equal to a tabulated point.

TERP performs the lagrangain interpolation for single

entry n-points tables.

- 21 -

FIGURE 1 - CICLÓN Flow of Calculations

CALCÚLATE NEWVALÚES FORCYCLE LENGTHOR ENRICHMENT

READ TABLES oí KM, Uf, Enrf, Puf

vs. burnup and initial enrichment

PRINT TABLES

| READ REACTOR DATA AND INITIAL STATE

Yes READ í PRINT VECINITYMATRIX BY ZONE

READ REACTOR DATA AND BATCH LOADING STATE

READ $ PRINT VKCINITYMATRIX BY REGIÓN

CALCÚLATE AND NORMALIZE INITIALBURNUP SHARING BY REGIÓN

CALCÚLATE AVERAGE BURNUPSHARING IN NEIGHBGR REGIOS

PERFORM INNER ITERATIONFOR REGIONWISE BURNUPSHARING CALCULATION

CALCÚLATE EOC CORE REACTIVITYBy A.B.R. METHOD

PRINT A.B.R. RESULTS FOR DETAILED AND CONDENSED CYCLE LOADING

No

CALCÚLATE ¥ AND ALBEDOESFOR GIVEN BURNUP SHARING

¡ PRINT DETAILED SUMMARY OF BATCH BURNUPS BY CYCLE

CALCÚLATE

PRINT

f. PRINT

DETAILED

CONDENSED SUMHARY OF BATCH

1BATCH SUMMARY OF DISCHARGE

BURNUPS

BURN'UP í

BY CYCLE|

ISOTOPICS

CALCÚLATE í. PRINT CONDENSED BATCH SUMMARY OF DISCHARGE

PUNCH CONDENSED SUMMARIESIN UNIT 7 FOR ECONOMICS

- 22 -

2.3. Program Restrictions.

All array variables are dimensioned through parame-

ters defined in the main program and henceforth could be

easily changed at compilation time. The parameters used

to dimensión arrays and its present valúes are:

Maximun number of burnup points in table LBT=12

Máximum number of initial enrichments intable LET = 12

Máximum number of batches in all cycles LR=200

Máximum number of consecutive cycles to beconsidered LC=20

Máximum number of batches, regions or zonesin each single cycle LRC=35

Máximum number of batches in the reducedsummary LRD=50

2.4. Machine Requirements and Code Operation.

CICLÓN is written in UNIVAC FQRTRAN-V, but very

few special features different from ANSÍ Standard FORTRAN

have been used.

Standard FORTRAN Library routines are used, the only

exception being the FORTRAN-V Library routine FLD which

performs bit by bit manipulation and is used only for

alphanumeric identifications.

Less than 20.000 words of 36 bits of core memory

are needed on the UNIVAC-1106.

CICLÓN has been operated in the EXEC-8 Operating

System of the UNIVAC-1106.

- 23 -

Running time depends on the región coupling model used

and on the reactivity search option. For a ten cycles cal-

culation with fifteen coupled regions in each cycle and cycle

lengths search., total time is less than three minutes in the

UíTIVAC 1106, BPU time being two thirds of total time.

CICLÓN uses the following logical unit numbers:

Input unit for data reading 5

Output unit for printing . 6

Punch unit for output data set .. 7

Printed output is about four pages per cycle and five

pages for summaries by batch and cycle.

- 25 -

3. INPUT DATA AND OUTPUT.

3.1. General Data Structure.

CICLÓN input data follows a general structure that

can be observed In the program flowchart (figure 1). For

each problem the following data structure is needed:

Card 1 : Problem Identification Card.

Cards 2 to 6 : Tables of K-infinity and isotopics vs.

burnup for different initial enrichments.

Cards 7 to 10: Reactor data, initial state of fuel,

and, eventually, zonewise core description.

Cards 11 to 13: Data for each consecutive cycle conside^

red. Include a cycle data and options card,

batch loading data cards and, eventually,

regionwise vecinity matrix cards.

Any number of consecutive cycles can be considered,

provided the last cycle number is less than 20. No special

terminating cycle mark is needed, as CICLÓN proceeds trough

consecutive cycles until an EOF mark is encountered in the

card reader unit.

Further discussion should focus on the CICLÓN treatment

for identification, in-core loading, ordering and subdivisión

of batches.

Batch.es are identified through a six alphanumeric cha-

racters word. First character should be left blank by the

user, because the code will use it to differenciate subdivi-

ded batches. Second and third characters are intended for

alphabetic identification of batches, and the same string

should be used for batches of the same fuel design and ini-

- 26 -

tial enrichment, loaded in the same cycle . Hext'-. characters

are not considered by the code and can be arbitrarily used

by the user.

Batches are marked as charged or discharged in any

cycle according to the hundreds of variable NCR. If NCR<100,

batch is considered as charged in core during the cycle.

If NCR>100, batch is considered as discharged, being NCR/100

the last in-core cycle number.

At the beginning of calculation for each cycle all

previous batches are marked as discharged in previous cycle.

All batches are saved although being discharged at any cycle,

to keep histories for final summary and to allow reinsertion

at any cycle.

Batches loaded at any cycle are given in cards 12 for

each cycle. F.or each loaded batch a search is performed in

previous files, by comparing batch identification. If the

batch is found it is marked as charged, zeroing the hundreds

of NCR, increasing in one unit NCR which keeps the number

of in-core cycles• If the batch is not found in previous

files it is considered as fresh fuel, with zero initial

burnup, and it is added to the batch files with mark of

charged in this cycle.

For previous existing batches, if the number of fuel

assemblies, given in the input for the present cycle, is

greater than the previous batch size, a warning is printed

and batch size is set to the new valué. If the given batch

size is less than the previous size, a new batch is created

with a new identifications the new size and is considered

as charged, and the oíd batch is saved, marked as discharged,

with a size equal to the difference between previous and

new batch sizes in number of fuel assemblies. The new char-

ged batch is identified as the previous batch, adding one to •

the' fóurth' character and setting in the first character a

* 1 Fourth character is intended for numerical identificationo'f batches and should be used to differenciate subbatches

- 27 -

letter according to the number of fuel assemblies of the

previous batch, starting from A. The oíd batch can then be

loaded in this cycle or in any posterior cycle by simply

entering the oíd identification. All variables of the new

batch are set equal to the previous one. This procedure

allows a flexible way to subdivide batches.

Fuel batches are ordered into code memory in the order

they are firstly introduced at any cycle through cards 8 or

12. When a fuel batch is subdivided, the new batch (with the

new input size, new identification and marked as charged) is

inserted in core memory just after the oíd batch (with the

difference in sizes, oíd identification and marked as dis-

charged). That should be carefully taken into account when

considering in-core batch ordening ~aJt any cycle (as for ALFAN

and FV assignation in cards 12), because the prevailing order

is that in code memory and not the order in which fuel batches

are given at the input for the cycle considered through cards

12, which can be any other. Specially when a fuel batch is

subdivided in different batches and all are loaded in core,

new batches should appear first in the input (cards 12), but

they are located last in code memory, which is the prevailing

order, so that ALFAN and FV should not be input correspondingly

to the batch sizes, but inverted.

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3.2. Data Formats and Description.

CARD 1 : Problem Identification Card

Format (12A6)

Columns Content • Des cription

1-72 TITLE(I),1=1,12 Any alphanumeric identifica-tion for the problem.

PART I : CELL BURNUP DATA.TABLES

CARD 2 : Tables control Card

Columns

31-40

41-50

51-60

Format (4110, 2E10.6)

Content

1-10

11-20

21-30

NENRT

NBUT

IOPT

IMPRIT

ENRMIN

ENRMAX

Description

Number of initial enrichment fortable entry (<:12)

Number of burnups for table entrypoints (<;12)

Option for inclusión of isotopicstables

If <: 0, No isotopics tables(only Ka, tables)

If > 0, Isotopics tables are givenin cards 6.

Option for printing of tables

If *Z 0 3 No printing.

If > 05 All tables are printed.

Minimum initial enrichment (w/o)for searches.

I'f < 0, the first t.able entryenrichment is adopted.

Máximün initial enrichment (w/o)for searches.

If < 0, the last table entryenrichment is adopted.

- 29 -

CARDS 3 : Initial enrichments for table entry

Format (8E10.6)

Columns Content Description

1-10, 11-20, ..., 71-80

ENRT(J),J=1,NENRT

Initial enrichments (w/o) for table entry.Tables of cell.burnup data (K<x> and isoto-pics vs. burnup) are given for each ofthese initial enrichments. They should beproperly ordered in ascending valué.

CARDS 1 : Burnups for table entry points

Format (8E10.6)

Columns Content Description

1-10, 11-20, ..., 71-80

BUT(I),I=1,NBUT

Burnups (MWD/MTU) for table pointsordered in ascending valué.

CARDS 5 : K-infinity vs. Burnup table

. . Format. C8.E10 .6)

Columns Content Description

1-10, 11-20, ..., 71-80

TK(I,J),I=1,NBUT

K-infinity valúes (for no boron, nominalconditions) vs . burnup, for the differentBUT(I) burnups of the initial enrichmentENRT(J) .

- 30 -

CARDS 6

Columns

Isotopics vs. burnüp tables

Format (8E10.6) Only if IOPT>0

Content Description

1-10, 11-20, 71-80

TUR(I,J),I=1,NBUT -TENRF(I,J),I=1,NBUTTPUF(I,J),I=1,NBUT

Valúes of final to initial Uraniumweight ratio, final enrichment (w/o)and Plutonium fissile content (Kg ".Pu/MTU) vs. burnup, for the differentBTU(I) burnups of the initial enrich-ment ENR(J).

A new card should be starterd foreach of those .

NOTE: Cards 5 and 6 should be repeated for the NENRT initialenrichments.

PART II : REACTOR DATA AND INITIAL FUEL STATE

CARD' 7 :• Reactor 'an'd "L'a's'f 'Frevious ' Cycle Data Card

Format (110, 2E10.6,

Columns

1-10

11-20

Content

NAC

CINF

21-30 PR

'Descript ion

Total nuiber of fuel assemblies inthe core.

Valué of. core K-infinity at EOC thatshb.uld be obtained in reactivity searchcases for each cycle.

Only used if IOP#0 in Card 11 for eachcycle.

If negative, a fíat source inverseweighting calculation of core K-infinityis made, inste.ad. of standard A.B.R.

If ZKEFF#0 is given in card 11, itsubstitutes CINF as reference valué forparticular cycle.

Core nominal power (Mwt).

- 31 -

31-40 ICO

1+1-50 NREG

51-60

61-70

NZ

LPERF

Last previous cycle number.

If the problem will study the first cycle,the valué IC0=0 can be entered. In thiscase any number of fuel batches with giveninitial state, for instance to have intoaccount partial fuel assembly reloading,can be given in cards'"8.

Number of fuel batches from previous cycles,with initial state described in cards 8.

If ^ 0, no previous fuel batches are-.:g i v e i i .••. • • - - • • ; .. ; . '. •> - • ;_• - "-.-;-

Number of zones to describe the core,with zone sizes and vecinity matrix givenin cards 9 and 10 (^35). If < 0, no corezone description is used.

Option control for punching the summaryof condensed batches through all cyclesconsidered. Complete data set for multi-batch-multicycle economic analysis ispunched in logical unit 7.

If = 0, no punching is performed.

If < 0, the first word for the first batchis the cycle number of loading

If > 0, LPERF is the first word for thefirst batch needed in economicscodes (month, day and year of thefirst cycle startup in columns65-67, 67-68 and 69-70 respecti-ve ly) .

CARDS 8 Previous fuel batches initial data

Format (A6, 14, 2E10.6, lio, E10.6)

Only if NREG >0, NREG cards (I=l,NREG)

Columns

1-6

Content

AR(I)

7-10

11-20

21-30

NAR(I)

ENR(I)

UIRCII

Description

Alfanumeric identification of the fuelbatch. Follow rules given in 3.1

Batch size in number of fuel assemblies.

Batch initial enrichment (w/o).

Batch initial uranium weight per assembly(Kgs).

- 32 -

31-UO NCR(I) Number of previous in-core cyclesfor the batch.

1+1-50 BUFR(I) Batch burnup.(Mwd/MTU) at the endof the last previous cycle. That willbe the initial state for posteriorcycles.

CARDS 9 : Size of core zones

.Format (1615) Only if NZ>0

Columns Content Description

1-5, 6-10, ..., 75-80

IZ(I),I=1,NZ

Size of core zones in number of fuelassemblies, for zones hereafter num-bered 1 to NZ. Total sum of IZ shouldbe NAC.

CARDS 10 : Vecinity or interchange matrix between zones

Format (16E5.2) Only if NZ>0

Columns Content Description

1-5, 6-10, . . . , 75-80

V(I,J), J=1,NZ, 1 = 1,NZ (new card for each I)

Elements of the vecinity or interchangematrix between zones . They are the num-ber of fuel assemblies of the core zoneI with four neighbor assemblies of thecore zone J, or also the number of commonassembly sides between core zones I andJ, divided by four. For peripheric zones,the number of exterior assembly sides,divided by four, is surnmed to the matrixelements V(I,I).

The vecinity or interchange matrix shouldverify. that the sums of elements for rowI or colum J be the number of fuel assem-blies for zone I or J, respectively. Thecode prints the whole matrix as well asrow and column sums but do not check forthat condition.

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PART III. CYCLE A O LOADED BATCH DATA

This part should be provided for eo.nsecu.tive cycles of

interest.

CARD 11 : Data and options for the cycle Card

Format (3110, E10.6, lio, 3E10.6)

Columns ' Coritent Déscription

1-10 IC Cycle number (^20) for data deck identi-fication. It is not used by the code,but calculated by consecutively adding oneto ICO.

11-20 HRC Number of in-core batches for this cycle.

21-30 I0P Option for cycle reactivity search

= 0, no search is performed. Input enrich-ments and cycle burnup are used and adirect core reactivity calculation atEOC is performed.

>, 2 , k cycle length or cycle burnup searchis performed to yield a core K-infinityat EOC, that differs from target §p(pin less than 0.0005. The core u-adia-1-K-eff at EOC can be also used as cyclereactivity parameter, using ZKEFF astarget valué•with the same convergencecriterium.

= 1, a feed enrichment search is perfor-med to yield the cycle reactivity asbefore. Batch enrichments subject ofthe search, are those entered as nega-tive in the in-core load descriptionfor the cycle (cards 12), the absolutevalúes being the initial guess and theincremental modification being the samefor all search enrichments. Normallyfresh batches will be the subject ofenrichment search and, when this optionis used;these batches should be inputin last place.

<: 0, The enrichment search is performedas in option I0P=l, but search enrich-ment are limited to rounded valúes of5 cents of w/o. If the enrichment searchyould yield valúes below or above EftRMINor ENRMAX given in card 2, the enrich-ment would be set to that valué and thesearch iw-itched-to a cycle length search

- 34 -

31-40 BC Cycle burnup in MWD/t

If í 0, it is calculated from batchburnups during the cycle given incards 12

For the cycle length search option(I0P^2), this is the initial guess.

41-50 IFCAL Option control for the batchwise burnupsharing calculation

= 0, no burnup sharing calculation isperformed. Input valúes from cards12, directly or from batch burnups,are used.

= 1, batchwise burnup sharing is calcula-ted by the coupled multiregion method.ALFAN valúes should be provided incards 12 for each batch or región.If a core zone description is used,FV valúes should also be provided toassign batches to the core zones .If no core zone description is used,vecinity or interchange matrix betweenregions should be provided in cards 13.

= 2, batchwise burnup sharing is calculatedby the uncoupled multiregion method.ALFAN an'd FV valúes for each batch orregión should be provided in cards 12.

= 3, batchwise burnup sharing is calculatedby an empirical model. For batcheswith zero or negative FV in card 12,then the batch relative power densityaiong cycle should by input ih DB andis kept constant by the code. Forremaining batches relative power densityalong cycle are calculated proportionalto their K-infinity at EOC, with ratiogiven through input relative absorptionsin FV in Card 12*.

=-1» no burnup sharing calculation is perfor-med, but the valúes of W and albedoesare calculated from input regionwiseburnup sharing by the coupled multiregionmethod. ALFAN valúes if positives causesa periferic región to be included in theVi calculation, if negatives are the ave-rage number of missing neighbors for pe-riferic regions. FV valúes or regionalmatrix should be provided as in optionIFCAL = 1 .

- 35 -

=-2, as in previous option (IFCAL=-1) ainverse W and albedoes calculationin performed from input regionwiseburnup sharing by the uncoupled multi-region method. ALFAN and FV valúesshould be provided as in option IFCAL=2.ALFAN effect is the same as in optionIFCAL=-1.

51-60 W Transport Kernel for neutronic interchangebetween neighbor fuel assemblies. It isthe core averaged probability for a neutrónborn in a given fuel assembly of being ab-r::'sorbed in one of the four horizontal neighborassembliés

It is needed only in the burnup sharing cal-culation options, IFCAL=1 ó 2. In the inver-se W and albedoes calculation options,IFCAL = - 1 6 -2, it is used, if input # 0,in the calculation of K (if imput ZKEFF=0)and albedoes ter.mslfó¿'-peripheric regions,instead of the calculated W for interiorregions .

61-70 ZKEFF Reference target reactivity at EOC for eachoptions (IOP#0) if #0. For detailed coremodels (IFCAL= 1 6 2), if given >0, is thetarget core radial K-effective includingaxial Leakage, but if <0 is the core K-infi-_'nity in the fíat source inverse weightingscheme of the A.B.R. Method.

In the inverse W and albedoes calculationoptions IFCAL = -1 ó -2, if input #0 isused in the calculation of W (if input W=0)and ALFAN and albedoes terms for perifericregions, instead of the calculated W and K _ .

for interior regions.

- 36 -

CARDS 12 : Tn-core batches f or this cycle -Data Cards .

Format (A6, 14, 5E10.6), NRC cards (I=1,NRC)

Columns

1-6

7-10

11-20

Content

DB

21-30

31-40

41-50

EN

UI

ALFAN(I)

51-60 FV(I)

Description

Alfanumeric Identification of thefuel batch. Follow rules given in3.1.

Batch size in number of fuelassemblies.

Batch burnup in this cycle (Mwd/t)or burnup sharing (relative energyper assembly generated in this batchduring the cycle).

If < 2.0, burnup sharing (relative).

If . 2.0, burnup in the cycle (Mwd/t).

If DB for the last batch in thecycle is <0, then all DB's are batchburnups at EOC in Mwd/t.

Batch initial enrichment (w/o)

Only used for fresh fuel batches, in-troduced in this cycle.

Batch initial uranium weight perassembly (Kgs). Only used for freshfuel batches.Negative for enrichmentsearches.

Valué of the n(l-a) t e n for thefuel batch loaded in-core in thiscycle in the order number I, accor-ding to rules given in 3.1.

n is the average number of missingneighbors per assembly for periferic.regions . ex is the average albedo forthe región. ALFAN should be zero forinterior regions.

If < 0, it is n for the a calculationin the inverse W and albedoes calcula-tion options, IFCAL = -1 ó -2.

When using the uncoupled multiregionscalculation options, IFCAL = 2 6 -2,it is the average relative energy perassembly along cycle for the fuelassemblies that are neighbors to theregión corresponding to fuel batchloaded in order number I in this cycle ,according to rules given in 3.1.

- 37 -

When using a core description byzones (NZ>0 in card 7) and the "coupled multiregions calculationoptions, IFCAL = 1 6 - 1 . it is thezone number to which the fuel batenloaded in order number I is located.

When using the empirical model option,IFCAL=3, it is the relative absorp-tion ratio for this batch (ratiobetween burnup sharing and K-infinityat EOC), the code normalizes inputvalúes to yiel a core average burnupratio equal to unity. If DB and FVare both input -£0, then FV is ::sét ::toóne , ' as:'well^as ""D'B , in :this option.-

CARDS 13 : Vecinity or interchange matrix between regiones.

Format (8E10.6)

Only if IFCAL = 1 or -1}and NZ$0.

Columns Contení Description

1-10, 11-20, ..., 71-80

V(I,J), J=1,NRC, I=1,NRC (new card for each I)

Elements of the vecinity or inter-change matrix between regions forthis eyele. I and J are the regionscorresponding to fuel batches in-coreloaded this eyele in the numbers oforder I and J, according to rulesgiven in 3.1.

Matrix definition and properties arethe same as discussed for zonal ma-trix in cards 10 .

3 Qo —

3.3. Output Description.

In each output page a heading is printed with problem

identification given in input card 1. CICLÓN printed output

constists of the following sections.

(i) Cell burnup data tables.

Tables of K-infinity, final to initial uranium weight

ratio, final enrichment and fissile plutonium content

versus burnup for different initial enrichments. As

given in input cards 2 to 6 from previous cell calcu-

lations. Tables are printed only if option IMPRIT>0

is selected in input card 2.

(ii) Reactor data and initial fuel state .

Number of fuel assemblies in the core, reference

K-infinity at EOC for search cases, nominal reactor

power and last previous cycle number are printed, as

given in card 7.

Initial data of previous fuel batch.es are printed as

given in cards 8. Calculated total uranium initial

lass, average specific power, average enrichment and

average burnup at EOC af previous cycle are also

printed.

If neutrón interchange is given by describing the core

in fixed zones (NZ>0 in Card 7), then zone sizes and

zonewise vecinity matrix as given in cards 9 and 10,

are printed. As the code does not check the input

vecinity matrix, it should be checked from this

output, verifying that row and cálum-wise sums are

equal to zone sizes (printed under NR heading).

- 39 -

(iii) Cycle and loaded batch data.

For each cycle, cycle number, search option, cycle

burnup (fixed or guess) and number of subbatches

loaded in the cycle are printed. Then5 eventual

warnings if any previous batch size is changed, are

printed, as well as a summary of batch data for this

cycle (as input in cards 12).

(iv) Vecinity matrix between regions.

If a regionwise core description is used for each

cycle ( llFCAL) =i; in card 11 and. NZ40 in card 7) the

vecinity matrix between regions, as given in cards 13,

is printed for checking purposes.

(v) Monitor printing for search options and iterative

burnup sharing calculations.

If a search option is .se.lected" ClOP#_0 in.card 11) -a moni-

tor print is performed at each iteration, giving the

search variable and corresponding K-infinity or K-effec-

tive valúes .

If an iterative burnup sharing calculation is selected

(IFCAL>0 in card 11) a monitor print is performed at

each iteration giving the averages of the neutrón balan-

ce terms F, FK and FV (see Appendix A) for the interior

fuel assemblies, the resultant constants A and B in the

assumed lineal relation between the transport kernel W

and the effective multiplication factor K, the itera-

tion number, the K-effective valué, the number of inner

iterations performed, the máximum relative change from

previous iteration and the unnormalized core average

burnup sharing.

- M-0 -

(vi) Batchwise balance summary of cycle at EOC.

Balance terms at EOC in the A.B.R. method are

printed for each subbatch in the detailed region-

wise core description and also for each baten in a

resumed core description, with batches defined by

the first three characters in the identification

variable, which is intended for fuel loaded at the

same cycle.

Following valúes are printed for each región:

- Fuel región identification .

- Number of assemblies.

- Initial enrichment.

- Initial uranium loading per assembly (Kgs).

- Number of in-core eyeles (irradiation eyeles).

- Initial burnup at BOC this cycle.

- Burnup irradiation during this cycle.

- Final burnup at EOC this cycle .

- K-infinity at EOC condition.

- Burnup sharing or cycle averaged relative powerdensity.

- Absorptions at EOC in the A.B.R. model.

Last line gives the core average value's of those va-

riables. It should be recalled that the core average

K-infinity is the inversely unity weigthed regionwise

K-infinity and the core average absortion is the in-

verse of the average regional absorption, wich is

taken in the A.B.R. method as the reference core

K-infinity. Core K-infinity as a function of coré .

average.enrichment and burnup at EOC, and calculated

by'. direct " áveraging and direct power density weighting

are also printed.

(vii) Burnup sharing calculation summary.

If the burnup sharing calculation options were selec-

ted (IFCAL#0) a inverse calculation of the transport

- 4-1 -

kernel and albedoes is performed from input or previously

calculated regionwise burnup sharing.

The neutrón balance terms in the A.B.R. method and the

transport kernel for each interior región are printed,

then from calculated averages for all interior regions

the averaged core transport kernel W and K-effective are

printed. With these W and K, the albedoes for each peri-

pheric región are calculated and printed, as well as

A.B.R. balance terms.

Averages for all peripheric regions are also calculated

and printed, as well as the total radial leakage fraction.

Output sections (iii) to (vii) are given for each cycle

in the problem.

(viii) Summaries of consecutive cycles in the problem.

After all the cycles have been processed the main fuel

management parameters for all cycles are printed in stan-

dard format. The first summary contents the following da-

ta for each detailed fuel región or subbatch: initial

uranium "weight per asse.mbly, initial enrichment, batch

size, initial burnup from previous irradiation and burnup

increments in each consecutive cycle. Cycle burnups in

Mwd/t, core uranium loading (MTU) and cycle lengths (Efec-

tive Full Power Days) are also given for each cycle consi-

dered.

The second summary contents fuel discharge data for each

detailed fuel región or subbatch, consisting of: batch

size, initial enrichment, initial uranium weight, cycle

of discharge, number of irradiation cycles, burnup at

discharge, final to initial uranium weight ratio, dis-

charge U-235 enrichment and fissile Plutonium contení

(Kg Pu/MTU).

- 4-2 -

The third and fourth summaries contení the burnup

increments by cycle and discharge data, respectively,

(as in the first and second), but for fuel regions

or batches formed by grouping all subbatches with

equal fuel design Cinitial enrichment and uranium

loading) and irradiation history Cequal cycle of

loading and discharge and number of in-core cycles).

Data of this summaries can be also pubched in logi-

cal unit 7 for multibatch-multicycle fuel cycle cost

calculations (LPERF#0 on card 7).

The fifth summary contents discharge data for fuel

batches grouped by its cycle of discharge and the

relative energy generation by cycle for fuel grouped

with the same criteria.

3.4-. Sample Problems.

Input data, selected printed output and punched output

for three example problems are given in Appendix C. The se-

lected problems represent the cycles 4 to 11 of a 160 Mwe

PWR, for the same reload strategy, but using three different

neutronic models optionally availables in CICLÓN.

Sample problem 1 uses a core description by zones,

with thirteen zones describing the 69 assemblies core with

1/8 simetry. Input data have in first place the K-infinity

and isotopics tables vs. burnup and initial enrichment. Six

enrichments and eight burnup points are used from 2.70 to

3.60 w/o and up to 35000 Mwd/t* Fuel state at the end of

last previous cycle (cycle 3) is given afterwards, with

the 69 fuel assemblies grouped in 20 subbatches. Fuel sub-

batches are identified by two letters, in columns two and

three, the first letter according to the cycle of loading:

and the second letter for special fuel assemblies, then a

" Obtained with a fuel cell burnuü code, such as LEOPARD(R.F.Barry, WCAP-3269-26. Sept."l963).

- 4-3 -

number in column four is used to distingish fuel subbatches

created by subdivisión in later cycles. Fuel state is given

by subbatch identificaction, size, initial enrichment, ini-

tial uranium loading per assembly, number of previous irradia-

tion cycles and burnup.

Afterwards zone sizes and matrix of vecinity between

zones are given for the adopted 1/8 simetry core description.

The matrix verifies that column and row sums are equal to

zone sizes. The zone pattern starts from center (zone 1) •

and orderly assigns zones with 1/8 simetry (zones 2 and 3

in second row from center, zones 4, 5 and 6 in third row,

zones 7, 8, 9 and 13 in fourth row and zones 10, 11 and 12

in last row).

Then, for each cycle (from 4 to 11), an option card

is given with cycle number, number of subbatches loaded, reac-

tivity search option C0 = no search with input cycle length,

2 = cycle length search), cycle length (fixed or first guess),

burnup sharing model option (-1 = inverse coupled regions,

1 = direct coupled regions), core average transport kernel

(W) and reference target core reactivity at EOC (in terms of

radial K-effective if positive).

For each cycle a card is given for every subbatch loaded

with identification sizes burnup sharing (in terms of absolute

burnup added during the cycle or as a fíat guess for direct

burnup sharing option), initial enrichment and uranium loading

per assembly (only needed for new subbatches), leakage terms

for regions in the core perophery (if negative is the number

of vacant neighbor positions in inverse calculation) and zone

number in which the subbatch will be loaded during the cycle.

A portion of the printed output is also given in Appen-

dix C. In the first page the input tables of K-infinity and

isotopic data vs. burnup and enrichment are printed. In page

2 fuel state at EOC of last previous cycle and zone vecinity

_ 1+1+ _

matrix are printed. In page 3 subbatch loading data for

cycle 4- are printed, Ttfith warnings for subbatch subdivi-

sions performed (new identifications assigned by the code

are printed for those subbatches). In page 4 the detailed

A.B.R. balance and a condensed balance» with fuel grouped

according to cycle of loading, are printed for the cycle M-,

which is an inverse non-search calculation. In page 5 the

inverse W and leakage terms calculation for input burnup

sharing and cycle length., is printed. From the interior

regions, W and K are obtained through best least square

deviation and simple averaging procedures. Leakage terms

for regions in the core periphery are obtained using input

valué of W and correspondent K. Rounded valúes of these

terms have been used for the direct calculation of posterior

cycles. Output for cycle 5, pages 6 to 8, has been reprodu-

ced to monitor the direct calculation option, which starts

in page 6 after printing of subbatch loading incidents and

summáry. Two monitor lines are printed in each outer itera-

tion, few inner iterations are needed to convergence within

each outer iteration (from about four or five iterations

per región in the first outer to about one or two in the

last), the outer convergence shows a very slow rate and

the limit of 20 outer iterations is f§ached--i-n th.e'first

search loop (with input cycle length). A monitor line is

printed for each search iteration and a total of three

search iterations is enough to yield target K-effective

within convergence criteria.•The conclusión from the obser-

ved convergence behaviour would be to introduce in the code

a good acceleration algorithm or to limit to 10 the number

of outer iterations within each search step and limit to 3

the number of inñer iterations within each outer, which can

be easily changed in the code. Pages 8, 12, 17, 22, 26, 31

and 35 are the printed summaries of A.B.R. balance terms

for cycles 5 to 11 respectively. In pages 37 and 38 the

summary for all cycles considered of burnup by detailed

subbatch in each cycle is printed, as well as cycle burnups,

_ 45 -

initial uranium loading by cycle and cycle lengths in effec-

tive full power days. In page 39 the summary of discharge

burnup and isotopic data for each detailed subbatch is prin-

ted. In pages 4-0 and 4-1 the burnups by baten and cycle and

discharge data are printed for condensed batches clasified

by equal cycle of loading and discharge and number of in-core

eyeles. In page 42 the discharge data and energy fraction

during each cycle summaries for fuel grouped by equal cycle

of discharge are printed.

The punched output for sample problem 1 is usted

afterwards, where fuel batches have been grouped by equal

cycle of charge, cycle of discharge and number of in-core

eyeles . The format is standard for multibatch-multicycle fuel

cost codes" Three cards are punched for each fuel batch, with

batch identification punched in columns 73 -to 80 of the :two

first cards (two letters related with cycle of loading and

fuel characteristicsa "fi^st " number equal to the number of

in-core eyeles and second number for- "the cycle of discharge).

The first card contains the cycle number of loading (date of

reactor startup_j given in the input^ for the first batch), the

cycle number of discharge, the core number and the number of

in-core cycle for the given subbatch, in format (2110, 13, 17)

The second card contains the discharge burnup, (Mwd/MTU), to-

tal initial uranium loading"• CMTU) , riñitial" enrichmeñt (w/o:---"

U-235), final to initial uranium weight ratio, final enrich-

meñt at discharge (w/o U-235) and fissile plutonium content

at discharge (Kgs, if positive or relative to initial uranium

loading, Kg/MTU, if negative), in format (F20.0, 5F10.4). The

third card contains the burnup increments (Mwd/t) during each

cycle from charge to discharge, in format (8F10.0).

Sample problem 2 uses a core des.cription by few regions

with a explicit core description through regionwise coupling

in each cycle for the burnup sharing model. Fuel is divided

in few regions, fresh fuel is taken as one región, and in its

second cycle is divided in two regions, one to be loaded in

* Such as FUELCOST-II (McLeod and Rodgers, NUS-U66. June 1970)

the core periphery and the other in the core interior,

subdivisión that is kept in consequent cycles .

Input data for sample problem 2 have been reprodu-

ced in Appendix C. The deck of K-infinity and isotopics :

tables is the same as sample problem 1.Last previous cycle

fuel state is defined with only five regions coinciding

w'ith fuel batches of equal cycle of loading and no core

zones are given. Inverse burnup sharing option is used

in cycle •+ without reactivity search, using input enrich-

ments and cycle lengthj and direct burnup sharing calcula-

tion, using valúes of W, K and leakage terms calculated

in cycle 4, with cycle length searches are selected for

cycles 5 to 11. In each cycle a matrix of vecinity between

regions is given depending on a regionwise core loading

configuration estimated for each cycle (following the

detailed zone wise loading configurations used in sample

problem 1).

Printed output of sample problem 2 has been partially

reproduced in Appendix C. In pages 2 and 3 the state at

EOC of last previous cycle and the regionwise loading

summary of cycle M- are práintéd, including the regionwise

vecinity matrix. In pages 4 and 5 the A.B.R. sumaries

and inverse calculation of W, K and leakage terms for input

cycle length and burnup sharing of cycle 4- are printed. In

page 6 loading incidents and summary and regional vecinity

matrix of cycle 6 are printed. In page 7 the monitor prin-

ting in the iterative burnup sharing calculation is repro-

duced, twelve outer iterations are needed to convergence

in the first search step, with inner iterations per región

and outer going from five in first iterations to one in

the last ones, another three outer iterations with very few

inners are enough to convergence and target K-effective

search in a total of three search steps . Pages 8, 12, 16,

20, 24, 2 8 and 32 with :A'..B .R. abalances •••(•.detailed and con-

- 1+7 -

densed) of cycles 5 to 11 are also reproduced. In pages 34-

and 36 the detailed and condensed summaries of burnup in-

crements by región or batch in each cycle are printed, with

summaries for discharge and isotopic data in pages 35 and

37 and summaries for fuel grouped by its cycle of discharge

in page 38. Pages 36, 37 and 38 with condensed summaries

are directly comparable with those of sample problem 1.

Punched output of sample problem 2 has been reprodu-

ced afterwards. Content is the same as for sample problem 1

except that batches labeled C2*03s ET3*05 and DA3*Q4 have

been included within batches D2«0 3, E3*05 and D3"0M- respec-

tively.

Sample problem 3 uses an empirical core model where

it is not necessary to describe core loading. Fuel is divi-

ded in few regións just identically as in sample problem 2.

Input data is very similar to that of sample problem 2

K-infinity and isotopics tables and fuel state at the end

of last previous cycle are the same. Cycles are calculated

with option IFCAL=3, using an empirical model adjusted from

results of sample problem 1. Cycle 4 is given a fixed input

length, regionwise relative power densities for regions in

the core periphery and regionwise absorption ratios. For

cycles 5 to 11 cycle length searches are performed, and an

unique relative power density for peripheric regions is

used, with absorption ratios for remaining regions adjusted

by the code. -Vecinity matrices for each cycle are not needed.

Printed output from sample problem 3 has been repro-

duced in Appendix C, selecting the same pages as for sample

problem 2. Iterative calculation of burnup sharing, without

search, performed for cycle 4 is given a monitor printing in

page 3, being equivalent to inner iterations in sample pro-

blems 1 and 2, with only three iterations needed to conver-

gence. Monitor printing of iterations for burnup sharing

calculations, with cycle length search, is given in

page 5 for cycle 5, with four iterat.ions in the first .

search step and two in the- second, which reached conver-

gence. The fastness of the calculation with the empiri-

cal model is confirmed in this sample problem.

Punched output from sample problem 3 has been also

reproduced afterwards with identical content as that for

sample problems 1 and 2.

The results of these sample problem provide basis

for comparison and validation of the different neutronic

models of CICLÓN. They have been extensively discussed

in Reference 2 of Computer Code Abstract with the main

conclusions being the ability of the empirical models

to provide a very fast and easy to prepare calculation

with accuracy enough for fuel management economic evalua-

tion. Few regions models yield comparable results with

empirical models while requiring more detailed input effort

Detailed zones models are prefered to detail regionwise •

models because of requiring less input effort and provide

results with enough accuracy for detailed discharge burnup

optimization and final calculation of fuel management

reload modes. Qua^iiification of detailed zone models has

been done by comparing results with data obtained from

in-core instrumentation measurements of previous operating

cycles and design data of a 160 Mwe PWR, as discussed in

Reference 2 of Computer Code Abstract (Appendix D).

- 4-9 -

APPENDIX A

ALGORITHMS AND. NUMERICAL TECHNIQUES INCLUDED IN CICLÓN

A detailed discussion of the Approximate Balance of

Reactivity (A.B.R.) method and of the models for burnup

sharing calculations included in CICLÓN can be found in

chapter 3 of Reference 2 in the Computer Code Abstract

(Appendix D). A brief review is the following.

A.l. Simple A.B.R. Method.

If the core is divided in spatial regions, denoted

by 1, the core K-effective at end of cycle (EOC), is given

by simple neutrón balance

Z Sf C

1KEOCK eff lEOC

1 + z LE 0 C

"F 0 0 EOC EOCwhere S , kro and L are the neutrón source, infinity

1 1 "

multiplication factor and neutrón leakage for región 1 at EOCi

Introducing the core average K-infinity at EOC, given by

the ratio between core source and core absorptions as

I SEOC

E 0 C = 1 (A 2)EÓC y&-¿>

CORE ^y

and the core leakage to absorption ratio, given by

- 50 -

EOC _CORE

Z1

1

CEOCSlEOC

*r

EOC

CORE

Z1

Z

TEOCLl

QEOCSl

(A.3)

the criticality equation is reduced to the one group equation

kEOC

KE 0 C - " C 0 R E

eff " . . TEOC1 + LCORE

The A.B.R. method uses equation (A.H-) to verify that enough

reactivity is provided at EOC., because whate>ver end of.life

definition can be easily expressed in terins of required

K-eff at EOC, with core K-infinity and leakage to absorption

ratio calculated through the following approximations of

(A.2) and (A.3).

i) Regional core representation.

For accuracy,the core should be divided in small re-

gions with homogeneous neutronic properties, such as equal

fuel design and enrichment and similar burnup, power density

and spectrum. For fuel management application, detail is

limited up to the fuel assembly level, without axial á.ix'e-r

rencing, and most frecuently core regions are given by fuel

batches with equal fuel design and initial enrichment and

number of in-core irradiation cycles.

With previous formalism, regions have not necessarily

to be conected in space, so that different fuel assemblies

in a scatter reload (chessbord like) loading pattern can be

part of a unique región. Equations (A.2) and (A.3) are used,

with 1 being core regions corresponding to fuel batches .

- 51 -

ii) Calculation of K-infinity for each fuel región.

The exact procedure would be to calcúlate regionwise

K-infinity as the ratio between neutrón source and absorptions

as given by the actual neutrón balance throughout the core,

or if pointwise source and K-infinity were known a exact

weighting equation similar to (A.2) could be used. As either

regional neutrón balance and pointwise source and K-infinity

would require a whole core neutronic solution, some approxi-

mation has to be done.

Regional K-infinity is calculated in CICLÓN as a func-

tion of región averaged condi->tions (moderator density, power

density, boron concentration and burnup). Furthermore the mo-

derator and power densities for all regions are assumed to be

equal to the core average densities, because at end o£ cycle

the power distribution is flattened and the effects on K-in-

finity involved are small. As there is no boron at EOC and

no control, the regional K-infinity is assumed to be a func-

tion of the región average burnup only, and is obtained in

CICLÓN by interpolation from input tables of K-infinity versus

burnup at core average conditions, previously obtained from

cell burnup codes..

^ f* hl (Bf ) (A.5)00 table 1

The regional average burnups at EOC are calculated usinga simple energy balance algorithm.

EOC = BOC g-CYCLE M

1 11 "i ' l • M c

EOCwhere, B is the región average burnup at beginning ofthe cycle (from preions cycles).

pynr r

S is the cycle averaged relative power densityfor the región (or the relative energy produc-tion alóng the cycle).

M p n p P and M are the core average and the región ave-rage masses of initial uranium per assembly.

AB is the cycle burnup (core average burnup increase)c

- 52 -

iii) Approximation of regional neutrón sources at EOC .

EOCThe regional sources at EOC, S , are needed as

weighting factors in the inverse K-infinity weighting

scheme in equation (A.2). A neutronic calculation of the

core at the EOC condition would be needed. Because thep y p T t1

cycle averaged regional relative power density, S ,

are also needed for the región burnup calculation at EOC

through (A.6), the approximation of using the cycle avera-p y p T 'P

ge power densities, S , instead of the sources at EOC,EO CS"1 , is made in CICLÓN. The approximation is good for mostcases, where the power distribution shift along cycle is

small, and would be exact for Haling hipothesis. As regional

sources are used only as weighting factors of K-infinity,

the error would be small in any case. There is also a com-

pensation between this approximation and the calculation of

regional K-infinity for nominal core average power and mo-

derator densities.

The problem is reduced to the calculation of regional

relative power densities averaged over the cycle (.related

to í>^gionwisé energy fractions and burnup sharing through

initial uranium masses per assembly). In CICLÓN they can

be input by user or calculated using models described later.

iv) Treatment of leakage.

To check the EOC condition, the criticality equation (A.4-)

should be used, where the core leakage to absorption ratio at

EOC, given by (A.3), has to be accounted for.

When consistent reload modes (such as the mixed reload

mode) are used for a given reactor core, the core leakage to

absorption ratio at EOC, will result nearly constant for con-

secutive cycles. Then the calculation of leakage can be avoided

and the EOC condition can be directly related to a reference

valué of the core K-infinity at EOC, given by (A.2), by using

(A.4) in a reference case. This approximation is valid in

- 53 -

most fuel management calculations, wheh fuel región sizes

and cycles lengths are similar through the consecutive cycles

considered.

CICLÓN can be used either with that simple EOC condi-

tion on the core K-infinity at EOC (a reference valué should

be given as input) or with a model for leakage calculation .

(using models described later) and a EOC condition on K-éffec-

tive (also given as input in order to include Xenón restart

capability, minimal boron concentration or whatever EOC defi-

nition) .

With the model described, CICLÓN needs that burnup

sharing (or relative regional power averaged over the cycle)

and reference core K-infinity at EOC be given by the user.

If there is previous experience with the reactor core consi-

dered and a regular cycling is expected for, this procedure

can yield accuracy enough for fuel management studies of

consecutive cycles. The simple A.B.R. method would allow

determination of feed enrichments or cycle lengths to achieve

the EOC condition.

A.2. Direct burnup sharing model.

CICLÓN also incorporates a simple core model for burnup

sharing and leakage calculation. Core is described by regions

defined by fuel assemblies of the different fuel batches, with

arbitrary detail. Core regions need not to be conected and

neutrón interchange between regions is described through a ge-

neral matrix of vecinity between regions.

Using nodal theory in two dimensionsy the neutrón balan-

ce equations for each fuel assembly 1, can be written as

S j

ce1

K i— = 4 w V + [l - (a-na., )W] Sn (A.7)k 1 w 1 1 J 1

Nodal theory has been used in different fuel managementcodes, referenced at the end of this Appendix.

- 54- -

where, K is the eigenvalue of the two dimensional pro-blem (core K-effective plus axial leakage effects)

S is the neutrón source in node 1.

k^ is the infinity multiplication factor of node 1.1

W is the core average transport kernel (averageprobability for a neutrón born in any node ofbeing absorbed in any of its four contiguousnodes.

V is the average neutrón source in the four nodescontiguous to node 1.

n number of missing contiguous nodes to node 1(sidés of node 1 facing to reflector).

a is the average albedo per exterior side ofnode 1.

Equation (A.7) assumes homogeneous fuel assemblies,

fíat flux within each asseinbly and neutrón interchange limi-

ted 'to the four contiguous assemblies. with transport kernel

constant throughout the core. The fíat flux hipótesis in

peripherical assemblies is very weak, so that a will s

differ from the physical albedo.

By summing equations (A.7) for all assemblies of an ar

bitrarily defined core región R and defining convenient re-

gional averages, results in the following regional equation

of balance

K -ü- = 4 W V_ + [l - O-n a )WJ S_ (A.8)coR

From this, a recursive equation for regional neutrón source

calculation can be obtained

W VL (A.9)R J£ ^ i - (i|-n a )w'j

co

R

- 55 -

And summing equations (A.8) for all core rsgions, the

criticality equation is obtained, which can be given in ex-

plicit K by

I \ I R R RK = -* 5 (A.10)

R

Equations (A.9) and (A.10) are used in CICLÓN in aconventional source iteration procedure to calcúlate regio-nal sources S and two dimensional eigenvalue K.

R

The core average transport kernel W and regional valúes

of the product n a , should be provided in the input forK R

the direct burnup sharing calculation.

K-infinity by región is calculated using equation(A.6) as a function of burnup at EOC. Because of the presen-ce of S in equation (A.6) an inner iteration loop for each

R

región has to be performed, using equations (A.6) and (A.9)

consecutively. This procedure converges faster than using

equation (Á.6) only one time in the outer step .

To calcúlate V , the ayerage neutrón source in the no-R

des contiguous to nodes of región R, CICLÓN uses a matrix

of vecinity between core regions given in the input, where

matrix terms V(R,R'), are the number of cominon sides between

fuel assemblies of regions R and R', divided by four. If N

is the number of assemblies in región R, then the V term for

región R is calculated by

v = -i- E V(R,R')S (A.11)

where the assumption that all fuel assemblies of región R',

have the same neutrón source S . has been done.R

- 56 -

In this model, the calculation should be performed for

the EOC condition, in order to check EOC reactivity, but be-

cause cycle averaged regional relative power densities are

needed for EOC burnup calculation, trough eqúation (A.6),

the model should be adjusted (through input W and n a ) toR R

yield regionwise cycle averaged power densities, instead

of sources at EOC.

The EOC condition is input through a reference valué

for the two dimensional core K-effective, including axial

leakage .and EOC def inition . ef f ects .

A.3. Inverse burnup sharing model.

In order to allow optimal adjustement of core model

narameters (W and regional n ci terms), a inverse burnupR K

sharing option has been included in CICLÓN. Given a refe-

rence regionwise distribution of cycle averaged relative

power density (either directly or through BOC and EOC re-

gión burnups) and provided tabulated functions of K-infinity

for each fuel type versus burnup, the core average transport

kernel, W, K-effective at EOC, K, and regional leakage termsn am are fitted as follows .K R

For regions in the interior of the core, leakage terms

n a vanishes, so that npc = 0 in eqúation (A.8). Summing

equations (A.8) for all the interior yields a. relationship

between K and W as follows

E S 4 E V - 4 s S

R- + R- + R

K = i n t + —i£Í ^ £ i = A + B_ „

y SR y SR m t m th -—- L

R »int R

where A. and B. are constants calculated from reference' - xnt m tburnup sharing for interior regions.

- 57 -

W is adjusted to yield the minimal sum for all interior

regions of cuadratic differences between reference valúes of

S and valúes obtained from the left hand side of equation

(A.8), when reference valúes are used in the right hand side.

It will be:

F =R

. .>> A . + B . ^mt mt mtí — ¥ UWVR+SR-4WSR)-SR ) = MIN (A. 13)

When the condition dF/dW=0 is imposed, the following

equation £ar W is obtained

sX-aZ

where following sums for interior regions have to be perfomed

* = RE „ 5R ; a = RE. t r R t

mt .: m t =°R mtr - ; v =

RZ VR u-15)

.. \ l Rmr R mt

Y = V RE V R V R " S RE-, k'Rmt R , . IHT R

» SR " S H L k~ S^«

After-w-'hás been- calculated using CA-'.14), K' is evaluated' using

XA. 12). Both- par^me'ters depend of po.wer sharing " between :.

interior core regions. With these W and K, the terms nBao for

regions in the core periphery are calculated using (A.8), which

yields:

- 58 -

V R " M 1 " S7> * í (kT

For better accuracy the inverse calculation in

CICLÓN to adjust i, K and n aB terms, should be done

for a detailed description of the core, with one región

for each fuel assembly, which would yield the reference

valúes of W and K and n a terms for each peripheric

fuel assembly position. For particular problems, with

regions make up of a number of fuel assemblies, after

a loading pattern has been selected, the n-Rap ^erins

the regions comprising the fuel assembly locations 1,

can be calculated by the following aproximation

E n a S1 ~ JL. E niai (A.20)

x 1 R

Because regions should comprise fuel assemblies

with similar powers, the arithmetic averaging is norma-

lly a good approximat ion. If Broader'regio-ns áre'-üsed,

relative powers of a reference case can be used to

weight the n a . terms per assembly of the región.

A.4. References.

Three dimensional nodal codes

- FLARE. Delp, D.L. et al., GEAP-4598. July 1964.

- NUTRIX. Kim, Y.S., NUS-657. July 1970. See also TransAm.Nucl.Soc. , 1_7_, 305. Nov 1973.

- TRILUX. Goldstein, L. et al., Trans.Am.Nucl.Soc.,10, 300. Oct 1967.

- MÉDIUM. Müller, A., Wagner, M . R. , Trans.Am.Nucl.Soc.,18, 152, Nov 197M-.

Two dimensional nodal codes:

- CYREP-II. Pilat, E.E., NUS-533. Jan 1971.

- MODFLA. liót'óda, H. et al. s Nucí. 1-%'éhíi©!- , 2_5_, 477.March 1975.

- 59 -

APPENDIX B

SELECCIÓN OF RELOAD STRATEGIAS AND LOADING CONFIGURATIQNS

The "reload strategy" for a given number of consecutive

cycles, is defined by: (a) the quantity of fresh fuel to be

loaded each cycle (batch size), and (b) the number of in-core

cycles and eventual intermedíate hold-out cycles for the

different parts of each fuel batch (subbatch sizes and irra-

diation scheme). The mass balance equations are given by the

condition that the total number of fuel assemblies in the core

should be constant for every cycle.

The fuel burnup at discharge has a primary effect on

fuel costs, and henceforth plays an important role in the

selection of reload strategies, that should be consistent al-

ternatives for the transition between a given initial fuel

state (state of in-core and stored fuel at the end of a given

previons cycle) and a final fuel state (given by an equilibrium

cycle state" previonsly'optimized), in order to allow the eco-

nomic optimization through evaluation of parametric alternati-

ves. The energy balance equations relate the average discharge

burnup of fuel in the cycles considered with the total effec-

tive length of the cycles at rated power and the total mass of

fresh fuel loaded, taking into account the mass and burnup of-

fuel coming from previons cycles and remaining in posterior

cycles.

A detailed discussion of criteria and rules for selection

of alternative reload strategies in consecutive cycles of tran-

sition (as well as equilibrium cycles) for fuel management op-

timization, was done in chapter 2 of reference 2 in the Compu-

ter code Abstract (Appendix D). A brief review will be done

here .

CICLÓN perforas searches of feed enrichments or cycle

lengths for each consecutive cycle to assure neutronic balance

- 60 -

for every given reload strategy and computes burnup sharing

Betweeñ fuel batches for each cycle, as well as discharge bur-

nup and isotopics, which are needed for multibatch multicycle

fuel cost calculations. By using CICLÓN options of empirical

models for the neutronic calculation, the explicit core loading

configuration for each cycle is not needed, because burnup

sharing is calculated through adjusted empirical models in-

dependently of actual location of fuel batches in the core,

But when CICLÓN options for burnup sharing calculation are

selected for more accurate neutronic evaluation, the core

loading configuration for each cycle should be provided in

its input , using different detail in the assignement of fuel

batches to core regions or zones, with core geometry descri-

bed through a matrix of vecinity between regions or zones.

Some considerations for selection of loading configurations

with different detail, effort and accuracy will also be

discussed here.

B.l. Procedures for selection of alternative reload stra-

tegies in cycles of transition.

Basic criteria and rules, considering plant operation

requirements and fuel design limits, are applied in a step by

step process of selection, resulting in a consistent selec-

tion of alternatives for the different variables, in order

to allow a parametric optimization.

B.l.l. Analysis of previons fuel for assesment of use in

the transition.

The most recent available data of fuel state at the

end of the last previons cycle should be analized, including

fuel design limits and contractual requirements, materials

and dimensions, initial uranium loading and enrichment, and

fuel burnup and irradiation history for each fuel assembly

in the core and storage pool.

- 61 -

Fuel will be grouped in batches by equal fuel design and

initial uranium loading and enrichment, and in subbatches by

similar burnup and isotopics. f-psyipus fuel design limitis and

contractual requirements would restrain: máximum or batch ave^e

rage discharge burnups. Expected cycle lengths would give an

estimation of added burnup for each subbatch if inserted in

posterior cycles, so that the number of cycles of aditional

irradiation for each subbatch can be estimated. Different al-

ternatives would eventually rise in the approximate analysis.

B.1.2. Selection of final state and number of cycles of tran-

sition.

The final state will generally be an equilibrium cycle

previously optimized, whereby effective cycle length, quantity

of reload fuel and feed enrichment- are known. Transition cycles

are those where reload batch size and enrichment, and eventua-

lly cycle lengths, are allowed to be différ.ent-lfrom equilibrium

variables. In principie the optimum transition strategy has

to reach the equilibrium state as shortly as possible. A prac-

tical way to define the number of transition cycles is to con-

sider as such the cycles with fuel from previons design, so

that if fuel is allowed to be irradiated a máximum of n+1 cy-

cles, the number of cycles of transition would be n . If reload

batch. enrichments and cycle lengths of transition cycles are

different from equilibrium, another n cycles of pseudoequili-

brium will result before the equilibrium cycle is reached, be-

cause although reload batch sizes and enrichments are equal

to equilibrium variables^ sizes and reactivity of previons irra-

diated batches will be different. Of course there will be reload

strategies with shorter transition and pseudoequilibrium, but

they can be included as alternatives in this general scheme.

- 62 -

B.1.3. General relationships between reload batch sizes.

Reload strategy for the transition and pseudoequilibrium •

cycles will depend on loading scheme of the core in consecu-

tive cycles at r batch detall. A general reloading strategy can

be established using variable reload batch sizes for any tran-

sition cycle and allowing for variable number of fuel assem-

blies hold-out in the reactor storage pool in transition cycles

Hold-out for posterior reinsertion would be limited to transi-

tion cycles, excluding the last one, in order to reach the equi-

librium condition in short term and would also be limited to a

part of the less reactive fuel batch (batch with highest num-

ber of previons irradiation cycles and with lowest initial en-

richment), because of the need to reduce cost penalties asso-

ciated with fixed charges for hold-out fuel.

Let be N., N , N , ... the sizes of fuel batches with3. ¿. ó

previons irradiation of 1, 2, 3, ... cycles at the end of last

previons cyclei F., F. , ;.. the sizes of reload batches for

each transition cycle j ; F the reload batch size for pseudo-

equilibrium and equilibrium cycles and F! the subbatch size

that remains n + 1 eauilibrium cycles (with the diference F -FT

e ebeing n cycles of in-core irradiation); N' N', N', ... and

X Á vJ

F! , F1 , ... the sizes of subbatches with n+1 cycles of

in-core irradiation (with the differences being the sizes of

subbatches discharged after n in-core cycles); and P. the si-

zes of fuel subbatches hold-out during each transition cycle j.

A general reload strategy can then be established as

that of table B.l^where sizes of each batch, according to cy-

cle of loading and previons in-core cycles or enrichment

(for the transition from cycle 1) are represented. The mass

balance equations are obtained from the condition that the

total number of fuel assemblies in the core at any cycle

should be constant (T). Considering n transition cycles and

n pseudoequilibr-ium cycles the 2n equations of "tai?-le. B.l are

obtained. The restrictions expressing that subbatch sizes

- 63 -

should be minor or equal to corresponding bath sizes are also

given in table B.l. Every baten or subbatch size should be

positive or zero.

Following variables are previously known:

- N. , N . N , . . . , N and P . „ from last- previous eyele1 2 3 n ~] -1

- n, F , F' from equilibrium eyele

There are the following unknowns:

- F., F. , •••» F. (n): reload batch sizes fortransition cycl.es .

- P., P. , ..., (n-1): number of hold out assemblies^ -1 each eyele.

- N ' , N • . , . . . , N • and F!, F '.n' n-1 1 •} ]

, . . . , F I

(2n): size of subbatches thatstay:- n + 1 irradiation eyeles .

Other reload principies could nave been taken into

account in the elaboration of a general reload strategy, such

as leaving a general freedom for hold-out at any eyele and

from any fuel batch, allowance for any number of irradiation

eyeles for previous fuel batches or reload batches of transi-

tion eyeles and others , but generally the problem can be dealt

in a similar way to table B.l.

B.1.4. Relationships between average eyele length, quantity

of fresh fuel and average discharge burnup.

The energy balance applied to the total of eyeles of

transition and pseudo-equilibrium provides the relation between

average discharge burnup from these eyeles as a function of

average eyele length and quantity of fresh fuel loaded in th-ese

eyeles.

TABLE B.l - GENERAL RELOAD SCHEME, RELATIONSHIP3 AND CONTRAINTS FOR THE TRANSITION BETWEEN AN INITIALFUEL STATE AND A FINAL EQUILIBRIUM CYCLE.

RELOAD SCHEME (BATCH SIZES)

DISCHARGE

HOLD-OUT

IN-CORE

Number ofpreviousirradia-tióncyclos.

ií+1

n

n

n

2

1

0

PREVIOUSCYCLE

CYCLE

—

Pd-1

Nn +1

N 3

N2

Nl

TRANSITION CYCLES (n)

CYCLlCd

Nn +1

Nn"NA

-Pd

NA-pd+pd-i

N2

Nl

Fd

CYCLEd+i

NA"VPd-lNn-1"NA-1

Pd + 1

N 1 ,+P^-P - ,n-1 d J+l

• • •

N l

Fd

Fd + 1

...

* • •

• • •

• • •

• • •

CYCLEj+n-1

N2-Pd+l-2+PJ+n-3

Nl-Ni

-

Ni+Pd+n-2

• • •

Fd+'>-3

Fd+n-2

j+n-1

PSEUDOEQUILIBRIUM CYCLES (ri)

CYCLEj+n

N'+P, o1 d+n-2

Fd"Fd

-

Fd• • •

Fd+n-2

Fj+n-l

Fe

CYCLEd+n+1

Fj

Fd+1-Fd+1

-

d+i

• • #

Fd+n-l

FeFe

• • •

* • •

* • •

• • •

• • •

• • •

• • •

• • •

CYCLE0+2n-l

j+n-2

F -F1

d+n-1 ,i+n-l

-

F1

J+n-1• * •Fe

Fo

Fe

EQUILIBRIUMCYCLE

CYCLEj + 2n

Fj+n-l

F -Ve e

-

fe •

fe fe

fe

Transición: Cyole j dCyclo j+1 : F

MASS BALANCE EQUATIONS

+ N,

+ FJ

+ N,

"i

- P

+ ... + Nn-1

j

j+l

+ Pd-i

= T

= T

CONSTRAINTS

N1

n

•j+lNA-i Nn-1

Cyclo d+n-1: Pj + n_ x d+n-2 * N x

Pseudoeqiii-librium Cycle

Cycle d+n+1 "•

+ Fd+n-2 +

+ F. , +d+n-1

+ F'

+ F1

d+i= T F1. .

J+l

Equili-brium

Cycle d+2n-l: Fm

Cycle j+2n : HF

F« .d+n-1

F'e

= T

rn

F1 S Fj+n-1 < d+n-l

F1 í Fe * e

- 65 -

Let be P the nominal thermal power of the. reactor (Mwth')j

D. the individual cycle length '(EFDD; nT:'vthé iñitiál" ura-'1 • -1 v

nium loading per fuel assembly (MTU) in reload fuel (assumed

to be equal to equilibrium cycle feed fuel); m., B. and N. the

average initial uranium loading per fuel assembly, average

burnup and number of fuel assemblies of fuel from previous

cycles to be used in the transition; B „ and N the average

burnup and number of fuel assemblies left for the equilibrium

cycle; and B the average discharge burnup (Mwd/MTU) of fuel

from transition and equilibrium cycles. The balance of energy

would yield

N-m. B . - N ^ m B ^ + E P . D .3- i i f r f . ]

B = , 3 ; , (B.l)d

N . m . - N m + S F . mi i f r j ] r

Thereby, for given initial and final fuel átate,"average

discharge burnup depends only on total duration of cycles

(E D .-) and total quantity of fresh fuel (I F.)j ] ' j 3

If average discharge burnup and cycle length is given

from equilibrium cycle optimization and operating requirements,

then equation (B.l) provides the total number of fresh fuel

assemblies to be loaded in the transition. If discharge burnup

and cycle length can be also optimized, then B.l provides a

tool to parametrically select different alternatives.

B.l.5. Selection of alternative reload strategies.

By using general relat ionships from B.l.3 and B . 1 . M- and

particular constraints for the problem, a consistent set of

alternatives for the reload strategy should be selected in

order to allow a parametric economic optimization.

The problem of table B.l is too general so that further

- 66 -

constraints, depending of the problem, should be introduced,

First the total number of fresh fuel assemblies loaded in

the transition cycles can be fixed using B. 1 .4- to a unique

valué or to a limited number of alternatives. Then, from

the analysis of previous fuel, done in B.l.l, the sizes of

subbatches with n+1 cycles of irradiation (N!, N', ..., N')1 ¿ n

can be defined or limited to few alternatives, so that the

number of unknown is reduced to reload batch sizes (n),

hold-out subbatch sizes (n-1) and reload subbatches with

n+1 cycles of irradiation sizes (n).

Application of equations in table B.l (2n) and cons-

traints, reduces the problem to manageable proportions ,

pg-fisaining only (n-1) independent variables, that are redu-

ced to (n-2) if total quantity of fresh fuel is fixed.

B . 1. 6 . Examüle.

In Reference 2 of Computer Code Abstract (Appendix D)

an example of reload strategies selection was given, in

2.3.6, for the transition cycles of a 160 Mwe PWR from its

fourth cycle to a given equilibrium cycle. Here an example

will be discussed for the transition from the first cycle

of a 1100 Mwe PWR" with 193 fuel assemblies in the core,

to an equilibrium cycle with atinuai reload (80 % load factor)

of 64 fresh fuel assemblies.

Initial state is the end of first cycle, with 65

assemblies of 2.1 w/o, 64 assemblies of 2.6 w/o and 6 4

assemblies of 3.1 w/o, having average burnups of 17930,

19110 and 12885 Mwd/t.

Final state is an eq_uilibrium cycle with anual reload,

at 80 % load factor, of 64 fresh fuel assemblies of 3.25 w/o

initial enrichment and 0.461 MTU of initial uranium loading• . •* ** •

p"e~r fue 1- a-ssembly-. Nominal-'power rating is 3411 'Mwths core

* All data are from Westinghouse , DOCKET-RESARA-7, Rev.3s

Vol.2. June 1972.

** Equilibrium cycle was precalculated with CICLÓN.

- 67 -

loading is 89 MTU,and'annual cycling at 0.8 load factor

yields a core burnup by cycle of 11185 Mwd/t. Reloading of

6U-/193 of the core at equilibrium yields an average dis-

charge burnup of 33730 Mwd/t.

Reloading of 64- fresh fuel assemblies of 3.25 w/o

initial enrichment .will start in cycle four in order to : .' .'.

achieve an equilibrium state as soon as posible. Transition

cycles are then cycles two and three with unknown reload

batch size and enrichment. Hold-out is' allowed only in cycles

two and three, and will be limited to the less reactive fuel

batch.

Further assumptions are in relation with allowed cycles

of additional irradiation for fuel batches of first cycle and

number of in-core cycles for reload of cycles 2 and 3, which

are the following:

a) The whole fuel batch of minor enrichment in first cycle

(65 assemblies) is limited to another cycle of irradia-

tion, well in cycle 2 or in cycle 3 after hold-out during

cycle 2. Hold-out in cycle 2 is limited to a part of

this batch (P assemblies).

b) Fuel batch of intermediate enrichment in first cycle

(64 assemblies) is allowed to be irradiated a total of

2 or 3 cycles. The whole batch will be in-core during

cycle 2 and after two cycles of irradiation a part will

be discharged (6 4- - N' assemblies), a part will be hold-

• out- during cycle • 3 (P assemblies) for reinsertion in

cycle 4-, and a third part will remain in-core during

cycle 3 (N' - P assemblies). So that N' assemblies

will be 3 in-core cycles and 64--N' assemblies will be

2 in-core cycles.

c) The whole -fuel'. batch of major enrichment in first cycle

(64 assemblies) is limited to three cycles of irradia-

- 68 -

tion, so that it will remain loaded in cycles 2 and 3.

d) Reload batches of cycles 2 and 3 will be irradiated

three or four cycles. Cycle 3 reload baten (F assem-

blies) will be in-core during cycles 3, 4 and 5,

afterwards one fuel assembly will remain for cycle 6

with the others being discharged. Cycle 2 reload baten

(F assemblies) will be in-core during cycles 2, 3 and

4-, with F' fuel assemblies remaining in-core for cycle

5 and F -F' being discharged after three irradiation

cycles .

The resulting reload scheme, with batch or subbatch

sizes for each cycle, is given in table B.2. The relations-

hips and constraints that should verify the batch or sub-

batch sizes are also given in table B.2 from the condition

of total number of fuel assemblies in-core for each cycle

equal to 193, positivity of each batch or subbatch size

and subbatch sizes minor or equal to correspondent batch

size.

There are six variables (F , F , ?2, N£, Pg, F£)

with four equations and the constraints given in table B.2,

Equations are reduced to express all variables as function

of F and F , selected as the two independent variables2. ó

for parametrie selección, in the following way

P2 = F2 iE'±)

P3 = 129 - F2 - F3 (E.2)

N' = 258 - 3F - 2F (E.3)

F^ = 65 - F3 (E.4)

The constraints are expressed also in terms of F

and F , being reduced to the following•O

0 •< F * 65 (C.l)

97 - 3/2 F « F « 129 - 2F (C.2)

TAB.LE B.2 - RELOAD SCHEME (BATCH SIZES) FOR TRANSITION

AFTER FIRST CYCLE OF A 1100 Mwe PWR

PISCHARGE

HGLD-OUT

IN-CORE

Number ofprevious

t ioncycles

4

3

2

2

1

3

2

1

0

Preyiouscycle

Cycle1

0

0

. . .0.

0

0

0

0

0

65 ,64,64

TRANSITION

CYCEE2

0

0

0

0

? 2

0

0

65-P 2364s6i+

F2

CYCLE

CYCLE3

0

0

65-P2,64-N2

o3

0

N'-P 64¿ oP2^F2

F3

PSEUDOEQUILIBRIUM

CYCLE4

0

N2-P3,64

P2

0

0

0

P F3 2Fo3

64

CYCLE5

0

F 3 ' 2 *20

0

0

F2F.3

. 64

64

2YCLES

CYCLE6

F2

0

Q

0

1

64

64

64

EQUILIBRIUMCYCLES

CYCLE7

1

63

0

0

0

1

64

64

64

enid

• MASS BALANCE EQUATIONS

Cycle 2 : 65 - P2 t 64 + 64 + F2 = 193

Cycle 3 : N' - P + 64 + P + F + F = 1932. ó J. 2. o

Cycle 4 : P + F + F = 64 = 193o 2. o

Cycle 5 : F' t F + 64 + 64 = 1932. ó

CONSTRAINTS

0

0

< F

< • 65 ; F2 > O

< N 2 < 64 ; F,

. ; F_ < 65

- 70 -

These constraints are represented graphically in

figure B.l, taking F and F as independent variables,

including also the lines of equal valué for dependent

variables P2, P

3 >N2 a n d F2 a s w e l 1 a s F2 + F3'

In figure B.l the valúes of F and F giving points

within the triangle are the alternatives for the reload

strategy within the constraints adopted. In order to op-

timize the reload strategy a number of points covering

the triangle has to be selected and the graph would yield

all variables in the problem. Using the condition of reload

batch sizes múltiple of four assemblies, in order to keep

1/4- or 1/8 core simmetry, there are 24 points within the

triangle. A convenient selection is given by the six points

encircled in figure B.l yielding the six reload strategies

with batch and subbatch sizes given in table B.3.

B.2. Selection of Loading Configurations.

For burnup sharing calculations using core explicit

neutronic mo.dels, CICLÓN needs the core loading descrip-

tion for each cycle in two .alternativel • ways, zonewise

or regionwise core description.

Zonewise core description consists of an unique

assignation of zones in the core, fuel assembly positions

of similar neutronic importance are assigned to the same

zone (assuming for instance 1/8 core simmetry), that remains

for all cycles. For each cycle, it is necessary to specify

at which core zone is located every fuel subbatch. Because

a single fuel subbatch can only be assigned to an unique

core zone, fuel will have to be subdivided at least in as

many subbatches as core zones . On the other hand it is

possible to assign various fuel subbatches to the same

core zone.

Regionwise core description consist of a cycle by

cycle descrdption with regions given by location of each

- 7 1 -

-J O Jg tSÍO iO IO lf>

(£>

OCO

(£>LO

CMLO

CO

COUJoUJu

ce1—loUJ

Q

O

UJce

ÍO

UJ

coCO

ro U.

coes

es

Oes

TER

_j*> <

•—

mUJ

ce

u_

TABLE B.3 - ALTERNATIVE RELOAD ESTRATEGIES FOR TRANSITION

AFTER FIRST CYCLE OF A 1100 Mwe PWR.

ALTER-NATIVE

1

2

3

4

5

6

RELOAD BATCH SIZES

CYCLE 2

(F2)

52

48

ko

4 o

32

28

CYCLE 3

(F3)

20

32

ho

48

6h

56

HOLD-OUT

CYCLE 2

(P2)

52

48

4o

4o

32

28

SUBBATCH

CYCLE 3

(P3)

57

49

49

49

33

45

CONGER IN-CORE SUBBATCH SIZES

THREE CYCLES

BATCH1-A

(N|)

0

0

0

0

0

0

BATCH1-B

(N¿)

62

50

58

42

34

62

BATCH1-C

(N3)

64

64

64

64

64

64

FOUR CYCLES

BATCH2

<F2>

45

33

25

17

l

9

BATCH3(F3)

1

1

1

1

1

1

TOTALNUMBEROF FRESHASSEM-BLIES

(F2+F3)

72

80

80

88

96

84

I

- 73 -

fuel subbatch. A matrix of vecinity between core regions has

to be coraputed for each cycle and provided to CICLÓN, which

needs a detailed core- configuration description and compu-

tation regardless of the number of fuel regions considered.

B.2.1. Procedures for zonewise core loading description.

Each fuel assembly location in the core has to be

assigned to core zones of similar neutronic "importance. Most

frequent approach will be to keep 1/8 core simetry, which

results in 31 zones for a reactor core with 193 fuel assem-

blies, with zone sizes of 1 , 4- or 8 fuel assemblies.

Following criteria will be used for selection of loading

configurations in each cycle:

a) Fresh fuel will be positioned in the core periphery,

starting with positions of less neutronic importance. If

core peTtpheTy locations would not be enough, fresh fuel

will also be positioned in locations contiguous to core

periphery in next less important positions avoiding that

such interior fresh assemblies have more than one neighbor

fresh assembly.

b) If fresh fuel was loaded in the core interior, their

neighbors will be loaded with leást"reactive:fuel subbat-

ches (tne mostburned for equal initial enrichment;)., ta;:

compénsate 'reáctivit ies . Remaining least"reactive ~' assemblies

will- be"located following a chessboard pattern with the

previous.

c) Fuel subbatches with intermedíate reactivity will be

loaded in a chessboard pattern of more and less reactive

zones, starting from the pattern given in the core periphe-

ry, most reactive fuel occupying diagonal positions with

thase of fresh fuel if that was loaded in the interior, or

following rules given in a) for fresh fuel .If it does not

complete the core periphery locations. The rule of simi-

lar average reactivity for each four neighbor assemblies

should be used.

An example of zohe loading pattern for cycles 1 to 7,

in the reactor considered previously in B.1.5, followiing

one of the reload strategies selected there, is given in

table B.4. Fuel is subdivided initially according to the

zonewise loading in its first in-core cycle and subbatches

are further subdivided when they nave to be assigned to

different zones. This loading pattern has not been through-

fully optimized, it is just an example to illustrate the

procedure. In the upper right córner of that table is given

the zoning scheme of the core in 1/8 simmetry.

The zone sizes and matrix of vecinity between zones

is given in table B.5 where the property of row and column-

wise sums equal to zone sizes is shown.

B.2.2. Procedures for regionwise core loading description.

Each fuel región has to be assigned to the core p'osi-

tions pn a detailed loading description. Loading criteria

for zonewise loading can be followed. There is no limitation

for regiónosizes, but previous fuel subdivisión in subbat-

ches has to be conserved. When using few regions all fuel

assemblies of each reload batch are assigned to an unique

región if its size do not exceed the loading positions in

the core periphery, then fuel batches with assemblies in the

core periphery would be subdivided in two regions grouping

fuel assemblies in the core interior and in the periphery.

If s'ize of reload batch exceeds periphery positions then

the batch would be subdivided in two regions from its first

in-core cycle.

An example of core loading description by regions is gi-

ven in table B.6, corresponding to the cycle 6 of table B.1

• (equilibrium cycle). Seven regions are used by subdividing fuel

batches of 6*4 assemblies in two regions of 20 and 4-4 assem-

blies, according to the loading in the core interior or in

the periphery during the first cycle of irradiation. Matrix

of vecinity between regions is also given in table B.6 for

that loading configuration.

Loading description by regions is very flexible respect

to the detail used. A proper selection of.regions would allow

to take into account any peculiar loading configuration. But

the effort necessary to compute vecinity matrix for each cycle

is independent of the number of regions, because it always re-

quires an assembly by assembly- vecinity computation. Zonewise

loading description requires more input data than few-regions

loading description but avoids tedions vecinity matrix compu-

tation for each cycle. Furthermore regionwise vecinity matrix

has to be :• recompüted: if changes in the loading conf iguration

are done.

- 76 -

TABLE B.4 - ZONE¥ISE CORE LOADING DESCRIPTION FOR TRANSITIONAFTER FIRST CYCLE OF A 1100 Mwe PWR

SUB-BATCH

NumberAssem-blies

ZONE OF LOADING BY SUBBATCH AND CYCLE

AlA2A3A4A5A6A7A8A9Al OAllAl 2

BlB2B3B4B5B6B7B8B9B10

ClC2C3C405C6C7C8C9

DID2D3D4

D5ElE2E3E4E5

144484488848

4848884488

848884888

88888

88888

CYCLE1

CYCLE2

CYCLE3

CICLE4

CYCLE5

CYCLE6

1346810111317192224

2579121415161823

202125262728293031

1

1820

225391214101622,72382111,15134,6281719242627293031

71618

1820

232025

(1)112

534,68

10,152291314

2,1128,271924172627293031

22241917

(1)1154,1013

16,36,115820

2,79121418

1

2

47

n

16

22

28

358

12

17

23

29

6

9

13

18

24

30

COREZONES

10

14

19

25

31

15

20

26

21

27

(1) 1171924

22,420813

10,11 (1) 1

- 77

CTT"QbU-D —BATCH

PlF2F3F4F5F6F7F8F9

GlG2G3G4G5G6G7G8G9

HlH2H3H4H5H6H7H8H9

TABLE B.

NumberA ^ k ^_a ^ ^ fcW

Assem—blies

488884888

48888

4888

488884888

4 (Cont.)• • • / •

ZONE OF LOADING BY

CYCLE GYCLE CYCLE1 2 3

SUBBATCH

CYCLE4

212325262728293031

AND CYCLE

CYCLE5

395

6,15122

147,1618

212325262728293031

CYCLE

2224177,H203

136,1019

1612182,45

1589

14

212325262728293031

TABLE B.5 - ZONE SIZES AND VEGINITY MATRIX POR A 1100 Mwe PWR CORE

MATRIX OP VECINITY BETWEEN ZONES

ZONE SIZE 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

123456789

10

1112131415

161718192021

22232425262728293031

1444844884

48884

488884

4888884888

1 - 2 12 - 01 0 -

2 2

1

22

O2

O2

1O

- 0 0 2

0 - 2 0 0O 2 ¿' 2 O2 0 2 - 2

2 ~

1

2

7

11

16

22

28

3

5

8

12

17

23

29

6

9

13

18

24

30

1

COREZONES

10

14

19

25

31

15

20

26

02

21

27

Oo2

1OOO

O O -2OO

2OO

O2

2O

0 0 0- 2

O

oo2

O2

oo

_ 2

2 -OOO2

OOOO2

OOO2

2OOO

- 22 -O 2O OO O

O2

2OO

O2

2O

OO2

2O 2

O OO O2 O_ o

2 -

OOO2

OOOO2

OOOO2

OOOOO2

1OOOOO

2OOOO

- 22 -O 2O OO O0 O

1 O2

2OOO

O2

2OO

OO2

2OO

OO2

2O

OOO2

2O

OOO222

OOOO

OOOO24

oooo

1ooo

12Oo

2OO

--j

00

2O

22 22 2 2O 2 4

TOTAL 193 4 4 4 8 4 4 4 8 8 8 4 4 8 8 8 8 4 4 8 8 8 8 8 4 8 8

- 79 -

TABLE B.6 - LOADING CONFIGURATION BY REGIONS AND

VECINITY MATRIX FOR A 1100 Mwe P¥R CORE

A2

C2

C2

B2

B2

B2

C2

C2

Cl

B2

C2

B2

B2

C2 C2

Cl Bl Cl B2 B2 DI

Bl DI Bl DI D2 D2

D2 D2 D2 D2

REGIÓN

A2

Bl

B2

Cl

C2

DI

D2

TOTAL

SIZE

1

20

kk

20

kk

20

kk

193

VECINITY

A2

0

0

0

0

1

0

0

1

Bl

0

0

0

9.

0

8

3

20

MATRIX BET¥EEN REGIONS

B2

0

0

6

9

23

k

2

kk

Cl

0

9

9

0

2

0

0

20

C2

1

0

23

2

18

0

0

kk

DI

0

8

k

0

0

0

8

20

D2

0

3

2

0

0

8

31

kk

- 81 -

APPENDIX

SAMPLE PROBLEMS INPUT DATA, PRIHTEP OUT-PUT

AND PüNCHED OUTPUT

- 82 -

CICLON-2 INPUT DATA FOR SAMPLE PROGLEM 1 PAGE 1

000001000002000003000004000005000006000007000008000009000010000011000012000013000014000015000016000017000018000019000020000021000022000023000024 .00002500002600002700002a0000290000300000310000320000330000340000350000360000370000380000390000400000410000420000430000440000450000460000470000460000490000500000510OÜ052000053000054000055000056000057000058000059000060

UUÜ000

. 000000000000

. 000000000000000000000000000000000000000000

• 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

cou000000000

-SAMPLE PROBLEM 1ó

2.70200.

1.2bOÜ47.999o6

2.6767.1263

1.267146.99966

2.8706.1223

1.274242•999Ü7

2.976b- .12021.291771.99967

3.22660.11581.298206.99967

3.3265.1143

1.312U70.99953

3.5765.1116

69A 13B 2C 1ET4 2DI 2D2 2

H 03 6D3 1

E D5 4G 05 2DA 1EA1 4EA2 4EA3 4El 4E2 1E3 7E4 1E5 4Eó 4

1 41.0

1.02.01.0

2.905000.1.183685.99211

2.1¡3ia2.34321.201603.99215

2.36922.30511-206056.99219

2.47342.28601.225945.99224

2.71762.24301.232570.99227

2.81562.22681.247979.99229

3.06222.22070.02.4252.903.603.603.60•3.60 •3.603.603.603.603.002.902.902.903.603.603.603.603.603.604

2.0 1.0

2.0 2.0

1.0

CYCLES 4 TO6 1

3.0010000.1.122011.98497

1.76223.80101.14Q565.98502

1.93773.77311.147210.98506

2.03643.75911.166125.98512

2.26833.72541.173206.98515

2.35183.71231.190026.93521

2.59S83.6743510.2&6.20266.25263.40249.10257.85

. 257.35257.a5257.35257.85257.85260.50259.00259-00259.00260.60260.60260.6026C.ÓÚ260.60260.60

4 8 4

2.02.0

2.02.0

I

2.02.0

11 •CORE

3.2515000.1.066858.978311.41324.76291.089053.97634

1.57404.76121.094602.976371.66524.76031.114218.97641

1.68114.75531.121616.97843

1.96864.75261.139571,97643

2.19354.7936

4

1.02.0

2.02.0

2.01.0

1

3222122222221111111116

OEbCRIPTION BY ZONES2.403.35

20000.1.022637•97190

1.12085.46121.042098.97192

1.26515.4£661.048214•97193

1.34765.49931.0óa079.97195

1.54485.52581.075602'•971961.62545.53521.094060.97199

1.83555.5572

2027090.20665.22931.9900.

19645.19168.18490.11460.161d8.17046.18040.12160.10378.7730.

11380.7966.7966.5794.5794.7368.

8 4

2.01.0

2.0

1.0

3.903.60

25000.0.980506.96581.8782

5.6807O.c*9857• í.^580

1.00525.93541.005838.96579

1.07825.96271.025824.96578

1.25516.02451.033484•.965731.32826.04761.052786.96573

1.52046.1509

13

8 4

2.02.0

2.0

30000»0.94^820.95982.6797

6.224Ó0.960697.95979.7891

6.29-350.96?9?o.95977• S524

6.33690.988390.95973

1.00*26.42520.995921-95972

1.07?26.45Q21.013564.95966

1.24446.5307

13169

8

2.0

35000.G.ql5óO•95393.5281

6.39130.92166•9539S.6194

6-UB290.93752.95396• 6725

6.^2370.9557»•95383.8060

6.64100.9'=>292.95326.fí62?

6.ñ-<3530.97,329•94803

1.00716.8076

- 93 -

CICLON-2 INPUT DATA FOR SAMPLE PROBLEM 1 PAGE 2

000061000062000063000064000065000066000067000068000069000070000071000072000073000074000075000076000077000076000079000080

ooooai000032000083000084000085000086000087

ooooaa0000890000900000910000920000930000940000950000960000970000980O0O99000100000101000102000103000104000105000106000107000108000109000110000111000112000113000114000115000116000117

ooona000119000120000121000122000123

000000000000000OOÜ000000000000000000000000000000000000000000000000000000000000000 .000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

ET4Di0202

H 03H 03

03E D5E 05G D5DAEA1

• . E A 2

EA3ElE2E3E4E5E6FlF2 .

ET4EA2EA3ElE2E3E4E5E6FlFlF2F26162

GH

EA1E5E6Fl

H F2F2

H F3H F3eiGlG2G2G3G4G4HlH2H3

422114213121444417144885244417144264428486

• 444624311144

• 4

17388

14200.12400.12480.12500.12630.12510.1354Ü.13060.12580.12790.11610.12820.12540.12780.13300.14720.12310.12780.9610.7660.9770.7330.

22

3.3.

17

3.3.3.3.

18

3.3.3.

i600.600

0000

353535

2.

0 11300.

265.93265.93

2 8065.

267.6267.6267.6257.6

2 8065.

267.6267.6267.ó

022

-1.-2--1.-2,

1.

1.2.2.

1.

2.2.1.2.

«0• 0

• 0.0.0• 0

.50

.45,30.60

50

30304560

2.0 2.02.0

2.0-1 0.105

7.5.- 5.4.

. ' :- : 3.5.7.7.4.3.5.2.6.8.8.1,9,9,

10.12.11.13.

1 0.1055.6.3.4.1.8.8.2.7,5.9,9.

10.9.

11.12.13.

1 0.1054.3.6.8.8.2,1,5.5.g.7,10.5.g.12.12.11.13.

2.0

4.0

1.0128

1.0128

CICLCN-2

00012400012500012600012700012a000129000130000131000132000133000134000135000136000137000136000139000140000141000142000143000144000145000146000147000146000149000150000151000152000153000154000155000156000157000156000159000160000161000162000163000164000165000166000167000168000169000170000171 .0001720001730001740001750001760001770001780001790001600001610001320001630001840Ü018D000186

INPUT

000000000000000000000000000000000000000000000000000000000000000 .000 -000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000OOÜ000000000000000000000000000

DATA

H

H0

8

H

H

H

H

H

cH

H

HH

DH

H

FlF2F2F3F4SIG2G2G3G3G4G5HlH2H3H3JiJ2

G3G3G4G4G5HlHlH2H2H3H4JlJlJ2J2J2KlK2K3

H2H2H3H3H4JlJ2J2J2J3J3KlKlKlK2K3K3LlL2L3

JlJ2

FOR SAMPLE

722413114H .471384'4

a8844 •34• 121444462.4228289144442422244222448281012

PROBLEM 1

18

• 3.253.25

19

3.253.253.25

20

3.253.253.25

21

2 8065.

267.6267.6

2 8065.

267.6267.6267.6

2 8065.

267.6267.6267.6

2 8065.

1.502.301.452.60

2.301.501.452.302.60

2.301.50

1.452.302.60

PAGE 3

1 0.1054.4.

• ' • 3.6.6.7.1.8.8.2.5 . •

5.7.9.

10.12.11.13.

1 0.1053.6.4.8.

a.• • i .

• 5 .

2.8.7,5,5.9.9.

12.10.11.12.13.

1 0.1051.4.3.6.

- 8.2.7.8.5.5.5.2.7.9,

12.10.9.

11.12.13.

1 0.1051.8.

1.0128

1.0123

1.0128

1.0128

- 85 -

CM

O

wo O

•o oro in

OJ

woo¿t ro vD

o pro in

CM CM CM

in o o* ro \0

CM CM

v0 \ 0 vO in• • • vO

r- r- r- ovO sO >-0 COCM CM CM

<M

vD \ 0 vO• • •

i— r— r-<J3 '.Q vOCJ CM CM

_ lCDOcro.UJ_JQ.

<

CM CM CM• « •

ro ;o ro

LO tn inCM CM CM

O

Q a x Q x

CM CM CM ;O J- f-i CM CM CVJ rO .=r r-t -j t-i CM rO rO <-H CM

a x x a x x

3a. oooooooooooooo

ooooooooooooooooooooooaoooooooo

ooooooooo ooo ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

CM

ouo

CM " 3 O O CM ¡O 3- CM .-O J- m o ¿r -n -o'JOJ<\¡

CU CM CM

J^ i r - i r-4 - ^ .rH ,-H r-\ <-) <r-( »H •r-í y-i —I CM CM CM CM OJ OJ CM CM CM CM -" \ CJ C\i C\J T\J C\! CM CM CM CM CM C\¡ i\J C\¡000000 0000000000000 00000 0000 0000 00003 0 00oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

- 86 -

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1 P A G E í

SAMPLE PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZOfJES

TABLA DE K-INF (SIN BORO) VS QUEMADO PARA DIFERENTES ENRIQUECIMIENTOS INICIALES

QUEMADLO EI=2.700 EI=2.9Q0 EI = 3.000 EI=3.250 EI=3.350 El=3.600 (;«/-=)

200.5000.

10000.15000.20000.25000.30000.35000.

1.25001.18391.12201.06891.0226.9805.9448.9156

1.26711.201b1.14061.08911.0',21.9099.9607.9217

1.27421.20811.1472

09460482

.9689

.9375

1.29181,22591.16611.11421.06311.0258.9834.9558

1.29821.23261.17321.12161.075o1.0335.9959.9629

312924801900

1.1396.0941.0528.0136.9783

TABLA DE U-RES (KGUR/K6UI) VS QUEMADO PARA DIFERENTES ENRIQUECIMIENTOS INICIALES-

EI=2.700 EI=2.900 ,EI=3.000 EI=3.250 EI=3.350 El=3.600 f,w/o)QUEMADO

200.5000.10000.15000.20000.25000.30000.35000.

.9997

.9921

.9850

.9783

.9719

.9658

.9598

.9539

.9997

.9922

.9850

.97u3

.9719

.9658

.9598

.9540

.9997

.9922

.9851

.9784

.9719

.9658

.9598

.9540

.9997

.9922

.9851

.9784

.9720

.9658

.9597

.9539

.9997

.9923

.9852

.9784

.9720

.9658

.9597

.9539

.9997

.9923

.9852

.9784

.9720

.9657

.9597

.9480

TABLA DE ENR-F (Vi/O) • " VS QUEMADO PARA DIFERENTES ENRIQUECIMIENTOS INICIALES

EI=2.700 EI=2.900 EI=3.000 EI=3.250 EI=3.350 EI=3.600 (w/o)QUEMADO

200.5000.

10000.15000.20000.25000.30000.35000.

2.67672.18181.76221.41321.1208.Í57S2.6797.5281

2.67062.36921.93771.57401.26511.0052.7891.6194

2.97662.47342.03641.66521.34761.0782.8524.6725

3.22662.71762.26831.88111.54481.25511.0082.8060

3.32652.81562.3618.9686.6254.3282.0732.8623

3.57653.06222.59882.19351.83551.52041.24441.0071

TABLA DE. PU-FlS.(KGPU/TUI) VS QUEMADO PARA DIFERENTES ENRIQUECIMIENTOS INICIALES

QUEMADO EI=2.700 EI=2.900 EI=3.000 EI=3.250 EI=3.350 EI=3.600 íw¿a)

200.5000.

10000.15000.2Q000.25000.30000.35000.

.12632.34323.Ü010

'• 4.76295.46125.68076.22466.3913

.12232.30513.77314.76125.43665.93546.29956.4829

.12022.28603.75914.76035.49935.96276.33696.5287

.11582.24303.72544.75535.52586.02456.42526.6410

.11432.22683.71234.75265.53526.04766.45926.6853

.11162.22073.67434.79365.55726.15096.53076.8076

- 87 -

CICL0N-2 PKINTEO OUTPUT FRCM SAN'PLE PROBLEM 1

SAHPLE PROBLEM 1 CYCLLS 4 TO 11 CORE DESCRIPTION BY ZONES

PAGE 2

NÚCLEO CON 69 ELEMENTOS K-INF EOC r ,000000

ESTADO AL FINAL DEL ULTIMO CICLO (CICLO 3)

LOTE

ABC

ET4DID2

H D303

E D5G 05DAEAlEA2EA3ElE2E3E4E5E6

POTENCIA NOMINAL = 510.00 MWT

HENTOS

1321222614214444171 •44

ENR INIC

2.4252.9003.6003.6003.600

• 3.600-'. 3.600

3.6003.6003.6003.0002.9002.9002.9003.6003.6003.6003.6003.6003.600

KG U-INIC

266.200266;250263.400249.100257.850257.650257.650257.850257.850257.850

. 260.500259,000259,000259.000260.600260.600260.600260.600260.600260.600

CICLOS

2221222222211111

• 1111

QUEMADO EOC

27090.0020665.0022931.009900.0019645.0019168.0013490.0011460.0016188.0017046.0018040.0012160.0010378.007730.0011380.007966.007966.005794,005794.007368.00

MATRIZ DE INTERCAMBIO ENTRE REGIONES VECINAS

REGIÓN NR SUMA 10 11 12 13

1234567a9

10íi121369

1444

a44884848

69

1.004.004.004.008.004.004.008.008.004.008.004.008.0.0

69.00

.001.00.00.00.00.00.00.00.00.00.00.00.00

1.00

1.00.00

2.001.00.00.00.00.00.00.00.00.00.00

4.00

.002.00.00.00

2.00.00.00.00.00.00.00.00.00

4.00

.001.00.00.00

2.00.00

1.00.00

. .00.00.00.00.00

4.00

.00

.002.002.00.00

2.00.00

2,00.00.00.00.00.00

8.00

.00

.00

.00

.002.00.00.00.00

2.00.00.00.00.00

4.00

.00

.00

.001.00.00.00.00

2.00.00

1.00.00.00.00

4.00

.00

.00

.00

.002.00.00

2.00.00

2.00.00

2.00.00.00

8.00

• 00• 00• 00.00• 00

2.00.00

2.00.00.00.00

2.002.008.00

.00

.00

.00

.00

.00

.001.00.00.00

1.002.00.00.00

4.00

.00

.00

.00

.00

.00

.00

.002.00.00

2.002.00.00

2.00G.OO

.00

.00

.00

.00• .oo.00.00.00

2.00

.no

.002.00.00

4.00

.00

.00

.00

.00,00.00.00.00

2.on,0n

2.00.00

4.008.00

ClCLON-2 PKINTED ÜUTPUT FROM SAMPLE.PROBLEM 1 - P A G E 3

SAMPLE PROBLEM 1 CYCLES 4 TO 11 . CORE DESCRIPTION BY ZONES

CICLO 4

OPCIüN 0 QUEMADO DEL CICLO =11300.00 22 SUBLOTES

ADVERTENCIA = EL SUBLOTE D2 TIENE AHORA SOLO 1 ELEMENTOS CUANDO ANTES TÍiNlA 2LA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

ADVERTENCIA = EL SUDLOTE H D3 TIENE AHORA SOLO 4 ELEMENTOS CUANDO ANTES TENIA 6LA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

ADVERTENCIA = EL SÜULOTE E D5 TIENE AHORA SOLO 3 ELEMENTOS ' CUANDO ANTES TENIA 4• LA DlhERENClA St CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

SUBLOTES CARGADOS EN ESTE CICLO

NJ NO. ELEMENTOS

221124113214444171448b

NO,LOTE

45678910111213141516171619202122232425

IDENTIF.

ET4DID2

B D3H D'áF D4

D3E DbD D6G DbDAEA1EAEEA3ElEkE3E4EbEbFif'¿

REG

1234b67a91011121314151617Ití19¿Ü2122

oaco

ENR-INIC

3.6003.6003.6003.6003.6003.6003.6003.6003.6003.6003.0002.9002.9002.9003.6003.6003,6003.6003.6003.6003.600 .3.600 •

U-INIC

249«10257.85257.85257.85257.85257,85257.85257.85257.85257.85260.50259.00259.00259.00260.60260.60

• 260.óO260.60260.60260.60265.93265.93

BU-INIC

9900.. 19645.

19168.19168.18490.18490.11460.16188.16188.17046.10040.12160.10378.7730.11380.7966.7966.5794.5794.7388.

0.

o.

DB-INPUT

Í4200.000012400.000012500.000012480.000012510.000012630.000013540.000012580.000013060.000012790.000011610.000012820.000012540.000012780.000013300.000014720.000012310.000012780.00009610.00007660.00009770.00007330.0000

ZONA

7554•3

57743526a8i991012ll13

-1

-1

ALFAN

.0000

.0000

.0000

.0000• nono.0000.0000• oono.nooo• nono.0000.0000• nono.0000.0000.ooon.0000.0000.0000.oono.nooo.oono

FV-INPUl

7.noot5.000Cs.onoc4.nonc3.oon(s.onoí7.Q00C7.nnnc4.0 0 0C3.0 0 n c5,onn(2.00ÍK6.onocB.onnc••B.oonc

. 1.O00C9.000C9.onoc

ío.onoc12.000Cíi.ocnc13.000C

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1:

SAMPLE PROBLEM 1 CYCLES 4 TO i! CORE DESCRIPTION BY ZONES

PAGE 4

BALANCE DEL CICLO A EOC

IDENTIFSUBLOTE

ET4DiD2

B D3H D3F D4

D3E D5D 06G D5ÜAEAlEA2-EA3ElE2E3E4E5£6FlF2

NÚCLEO

NO.ELEM

22112411321444417i

88

ENRIÓINIC.

3.6003.6003.6003.6003.6003.6003.6003.6003.6003.6003.0002.9002.9002.9003.6003.6003.6003.6003.6003.600S.bOO3.600

KG UIELEM.

249.10257.85257.85257.852b7.85257.85257.85257.85257.85257.85260.50259.00259.00259.00260.60260.60260.60260.60260.60260.60265.93265.93

CICLOSANTIG.

23 •

3 .33 •33333322222222211

69 3.470 260.55

QUEMADOINICIAL

9900.19645.19168.1916e..18490.18490,11460.16188.16188.17046,18040.12160,10378.7730.

11380.7966.7966.5794.5794.7388.

0.0.

8999,

CICLO 4

DELTA-B . QUEMADO. CICLO FINAL

K-INF\ EOC .

14194.12395.12495.12475.12505.Í2625.13535.12575.13055.12785.11605.12815.12535.12775.13295.14714.12305.12775.

9606.7657.9766.7327.

24094.32040.31663.31643.30995.31115.249^5.28763.29243.29831.29645.24975.22913-20505.24675-22680.20271.18569.15400.15045.

9766.7327.

.0600

.9987

.0014

.0015

.0062

.0054

.0528

.0230

.0193

.0148

.97140001017003760554071509171066

1.1358 •1.13911.19251.2198

FRACCIÓNEMERGÍA

1.20101.08561.09431.09261.09521.1057l.ltia'J1.10131.14331.11971.02691.12731.10271.12381.17681.30241.08921.1308.8503.6778.8821.6618

ABSORCIONESEOC

,0870,09p8,09n9,08A4.0993.1259>07fi6

1.081886 K-INF(ENRfBEOC)

11300. 20299. 1.080652 1.0000

1.086199

1.12171.10331.05711.1273 ,1.0843 ro

1.0831 «o1.1150 11.2155 •.9977 •••

1.0218.7'ia7.5950.7397.5426

1.069383 PESADO INVERSO

1.074195 PESADO DIRECTO

BALANCE DEL CICLO A EOC CICLO 4

IDENTIFSUBLOTE

ETDÜAEAEF

NO. ENRIQELEM INIC.

2171

122116

KG UI CICLOS QUEMADOELEM. ANTIG. INICIAL

3.6003.6003.0002.9003.6003.600

249.102l>7.ü5260.50259.002t>Ú.6O265.93

233221

9900.17581.18040.10089.7989.

0.

DELTA-BCICLO

14194.12713.11605.12708.11231.8547.

QUEMADOFINAL

24094.30293.29645.22798'.19220.8547.

K-lNFEOC

060001149714018010092059

FRACCIÓNENERGÍA

1.20101.1134

0269118099417720

ABSORCIONESEOC

1.13291.10f)51.0571

.9074

.6411

NÚCLEO 69 3.470 260.55 8999. 11300. 20299, 1.080652 1.0000 1.06g383 PESADO INVERSO

CICLON-2 PRlNTED OUTPUT FROM SAMPLE PROBLEM 1

SAMPLE PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZONES

MEDIA 45. ELEMENTOS INTERIORES F-INT = 1.123029 FK-INT = 1.0S6454

PAGE 5

FV-INT = 1.066215 A = 1.033665 I

REGIÓN

ET4DID2

ü D3H 03F 04D3

E D5 •D Ü6G D5DAEA1EA2EA3ElE2E3E4

JUSTE

ALORES

NO EL.

221124113214444171

K-INF-EOC

1.060045..9986951.0013931.0015371.0062291.0053561.0520281.0229731.0192961.014Ü36.971372

1.Ü00U591.0170191.037b451.0553851.0715471.0917321.106o21

POR MÍNIMOS CUADRADOS

PROMEDIOS OBTENIDOS

FRACCENERGIA

1.2009641.0855681.0943221.0925711.0951981.105703

. 1.1853701.1013261.1433481.1197101.0268521.1273421.1027201.123b251.1767771.3024181.0891821.130767

755435774352688199

W = .104065

•• IN = .107695

ABSORCIONES F-VECINOS

1.1329371-0869861.0928001.0908951.0884181.0998131.1258911.0765931.1217031.1033411.0571151.1272751.0842671.0830531.1150221.215455.997664

1.021020

K = 1.

K = 1

1.0703861.1227821.1227821.1195701.1083661.1227821.0703861.0703861.1195701.1083661.1227821.1619951.0918851.0595131.0595131.127342 ', .898148.898148

011898

.011138

N*<1-ALFA)

. 0 0 0 0 0 0 ••;•

.000000

.000000

.000000

.000000

.000000

.000000

.000000

.000000

.000000

.000000. .000000.000000.000000.oooooo •.000000.000000.000000

W-CftLC

.104744

.101036

.102991•104255.106519.104351.096136.113486• H5524.112047.108873.101182.098379.140385.102694.103224.104297.104010

I

o

CALCULO DE LOS ALBEDOS EN LAS REGIONES PERIFÉRICAS (USANDO W = .105000 K = 1.01170? )

REGIÓN NO EL. K-INF-EOC FRACCENERGIA ABSORCIONES F-VECINOS N*U-ALFA) N-ExT ALFA

E5E6FlF2

4 1.1357554 , 1.1391408 1.1925196 1.219783

.850288 10 .748654

.677753 12 .594968

.882125 11 .739716

.661819 13 .542571

.946673

.886066

.886133•825036

MEDIA DE LOS 24. ELEMENTOS EXTERIORESFRACCIÓN DE ENERGÍA = .769321

1.4936682.2948911.4622332.611126

-l.flOOOOO-2.000000-1.000000-2.000000

ABSORCIONES = .651366 F VECINOS = .875846

-.493668

-.462233-.305563

r» R r> Y AI

Lf I lyn u i

CICLO 5

OPCIÓN 2 QUEMADO DEL CICLO = 8065.00 17 SUBLOTES

ADVERTENCIA = EL SUBLOTE Fl TIENE AHORA SOLO 2 ELEMENTOS CUANDO ANTES TENIA BLA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

ADVERTENCIA = EL SUBLOTE . F2 TIENE AHORA SOLO 4'ELEMENTOS CUANDO ANTES TENIA 8LA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUüLOTE SE INCLUYE EN LA LISTA

SUBLOTES CARGADOS EN ESTE CICLO

MO.LOTE

41617181920212223242526272fl293031

MEDIA 45ITERACIÓN

MEDIA 45ITERACIÓN

MEDIA 45ITERACIÓN

MEDIA 45ITERACIÓN

MEDIA 45ITERACIÓN

MEDIA 45ITERACIÓN

MEDIA 45ITERACIÓN

MEDIA 45ITERACIÓN

MEDIA 45ITERACIÓN

IDENTIF. 1

ET4EA2EA3ElE2E3E4E5EbFl

H F2F¿

H F3GlG2G3G4

. ELEMENTOS1 K-EFF

. ELEMENTOS2 K-EFF

. ELEMENTOS3 K-EFF

. ELEMENTOS4 K-EFF

. ELEMENTOS5 K-EFF

• ELEMENTOS6 K-EFF

. ELEMENTOS7 K-EFF

. ELEMENTOSB K-EFF

. ELEMENTOS .9 K-EFF

ÍÍE6I0N NO.

123456789

1011121314151617

INTERIORES= 1.045120

INTERIORES= 1.027874

INTERIORES= 1.023653

INTERIORES= 1.021615

INTERIORES= 1.019730

INTERIORES= 1.019461

INTERIORES= 1.018425

INTERIORES= 1.018500

INTERIORES= 1.01789Ü

ELEMENTOS , ENR-INIC U-INIC

2 3.6004 2.9004 2.9004 3.6001 3.6007 3.6001 3.6004 3.6004 3.6006 3.6002 3.6004 3.6004 3.6002 3.0008 • ; • 3.0004 •; 3.0008 3.000

F-INT = 1.000000ITER INT = 72

F-INT = 1.068938ITER INT = 72

F-INT = 1.086592ITER INT = 70

F-INT = 1.104865ITER INT = 67

F-INT = 1.110714ITER INT = 65

F-INT = 1.118395ITER INT = 64

F-INT = 1.120591ITER INT = 63

F-INT = 1.124357ITER INT = 61

F-INT = 1.125179ITER INT = 5a

249.10259.00

, 259.00' 260.60260.60260.60260.60260.60260.60265.93265.93265.93265.93267.60267.60

. 267.60267.60

FK-INTDIFMAX =

FK-INTOIFMAX =

FK-INTDIFMAX =

FK-INTDIFMAX =

FK-INTDIFMAX =

FK-INTDIFMAX =

FK-INTDIFMAX =

FK-INTDIFMAX =

FK-INTDIFMAX =

BU-INIC

24094.22913.20505.24675.22680.20271.18569.15400.

• • 15045.9766.9766.7327.7327.

0.0.0.0.

= .956828,335155

= 1.020439.183094

= 1.042892.105509

= 1.058797.083904

= 1.067430.065336

= 1.073565.059038

= 1.077483.044092

= 1.080207.039700

= 1.082120.028504

DB-INPUT ZONA

1.0000 51.0000 61.0000 31.0000 41.0000 11.0000 81.0000 81.0000 21.0000 7

•••' 1 . 0 0 0 0 ••• 5 '

l.oooo gl.oooo g1.0000 lo1.0000 g1.0000 111.0000 • 12

. 1.0000 13

FV-INT r l.OOOOoOSUMA F = .948670

FV-INT = 1.021189SUMA F = .975007

. FV-INT = 1.041278SUMA F = .989052

FV-INT = 1.049669SUMA F = .989601

FV-INT = l.O578olSUMA F = .996560

FV-INT = 1.061403SUMA F = .994842

FV-INT = 1.065219SUMA F = -i 998863

FV-INT = 1.066841SUMA F = .997231

FV-INT = 1.068772SUMA F = .999603

ALFAN

.0000• 0000.0000.0000.0000.0000..0000.oono• cono.oono.oono.0000

1.5000.0000

1.45002.30002.6000

A =

' • A = •

A =

A =

A =

A =

A —

A =

A =

; FV-INPUT

5.00006.00003.00004.00001.00008.00008.00002.00007.0000

. "5.00009.00009.0000

10.00009.000011.000012.000013.0000

1.045120

1.047527

1.041903

1.043510

1.040550 .

1.041758

1.040009

1.040872

1.039791

B =

B =

B =

B =

B =

B =

B =

B =

B =

i

ÍD

' 1

.000000

-.187171

-.173802

-.208525

-.198284

-.212346

-.205561

-.212982

-.208504

MEDIA 4b. ELEMENTOS INTERIORES F-INT = 1.127165 FK-INT = 1.083402 FV-INT = .1.069502 A = 1.040394 B

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1

ITERACIÓN 10 K-EFF = 1.018040 ITER INT = 55 DIFMAX = .025639 SUMA F =

PAGE 7

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 11 K-EFF = 1.01766Q

MEO!A 4b. ELEMENTOS INTERIORESITERACIÓN 12 K-EFF = 1.017796

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 13 K-EFF = 1.017568

MEDIA 45. ELtMENToS INTERIORESITERACIÓN 14 K-EFF = 1.017667

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 15 K-EFF = 1.017523

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 16 K-EFF = 1.017598

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 17 K-EFF = 1.017504

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN Id K-EFF = 1.017556:

MEDIA 4b. ELEMENTOS INTERIORESITERACIÓN 19 K-EFF = 1.017499

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 20 K-EFF = 1.017537

F-INT = 1.127432 FK-INT =1.084371 FV-INT = 1.070523ITER INT = 52 DIFMAX = .018266 SUMA F = .999997

F-INT = 1.128530 FK-INT = 1.084990 FV-INT = 1.070036ITER INT = 5o DIFMAX = .016592 SUMA F = .999094

F-INT = 1.128563 FK-INT = 1.085482 FV-INT = 1.071393ITER INT = 47 DIFMAX = .011965 SUMA F = 1.000120

F-INT = 1.129202 FK-INT = 1.085793 FV-INT = 1.071522ITER INT = 47 DIFMAX = .010916 SUMA F = .999450

F-INT = 1.129141 FK-INT = 1.0Ü6036 FV-INT = 1.071323ITER INT = 47 DIFMAX = .007874 SUMA F = 1.000130

F-INT = 1.129524 FK-INT = 1.086193 FV-INT = 1.071867ITER INT = 47 DIFMAX = . .007194 SUMA F = .999662

F-INT = 1.129447 FK-INT = 1.086320 FV-INT = 1.072039ITER INT = 47 DIFMAX = .005224 SUMA F = 1.000113

F-INT = 1.129680 FK-INT = 1.0&6399 FV-INT = 1.072046ITER INT = 43 DIFMAX = .004788 SUMA F = .999779

F-INT = 1.129606 FK-INT = 1.086460 FV-INT = 1.072143ITER INT = 39 DIFMAX = .003497 SUMA F = 1.000086

F-INT = 1.129751 FK-INT = 1.086503 FV-INT = 1.072145ITER IMT = 35 DIFMAX = .003178 SUMA F = .999873

A

A

A

A

A.

A

A

A

A

A

= 1.039710

= 1.040129

= 1.039689

= 1.039979 ,

= 1.039690

= 1.039892

= 1.039700

= 1.039839

= 1.039713

= 1.039805

B =

B =

B =

. B =

B =

B =

B -

B =

B =

B =

-.209924

-.212698

-.210674

-.212490

-.211108

-.212325 •<

-.211385

-.212201

-.211561

i

-.212079 ">

ITERACIÓN 1 ENR O QUEMADO = 8065.000 K-lNF O K-EFF =1.017537 VALOR BUSCADO = 1.012B00

MEDIA 4b. ELEMENTOS INTERIORESITERACIÓN 1 K-EFF = 1.013226

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 2 K-EFF = 1.013300

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 3 K-EFF = 1.013302

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 4 K-EFF = 1.013322

F-INT = 1.129697 FK-INT = 1.091113 FV-INT = 1.072189ITER INT = 35 DIFMAX = .002834 SUMA F = .'.000229

F-INT = 1.1294S9 FK-INT = 1.090869 FV-INT = 1.0720«2ITER INT = 26 DIFMAX = .001359 SUMA F = 1.000045 .

F-INT = 1.129363 FK-INT = 1.090768 FV-INT = 1.072016ITER INT = 25 DIFMAX = .001065 SUMA F = 1.000086

F-INT = 1.129320 FK-INT = 1.090697 FV-INT = 1.0719R6ITER INT = 25 DIFMAX = .000683 SUMA F = 1-000003

A

A

A

A

= 1.035362

= 1.035403

= 1.035383

= 1.035411

B =

B =

B =

B =

-.210822

-.210501

-.210300

-.210378

ITERACIÓN 2 ENR O QUEMADO = 8538.677 K-lNF O K-EFF = 1.013322 VALOR BUSCADO = 1.012800

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 1 K-EFF = 1.012790

F-INT = 1.129257 FK-INT = 1.091220 FV-INT = 1.071944 A = 1.034857 B = -.210088ITER INT = 22 DIFMAX = .000536 SUMA F = 1.000070

ITERACIÓN 3 ENR O QUEMADO = 8597.310 K-lNF O K-EFF = 1.012798 VALOR BUSCADO = 1.012800

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1 •

SAMPLEPROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZONES

PAGE 8

IDENTIFSUBLOTE

ET4EA2EA3ElE2t3E4E5 •E6 .Fl

H F2F2

H F3GlG2G3G4

NÚCLEO

NO.ELEM

24441

. 714462442a4a

69

1

BALANCE DEL CICLO

ENRIQINIC.

3.6002.9002.9003.6003.6003.6003.6003.6003.6003.6003.6003.6003.6003.Ü003.0003.0003.000

3.328

.078194

KG UlELEM.

249.102b9.002b9.002b0.602b0.60260.60260.602bO.6O200.60265.932b5.93265.93265.932b7.602D7.602b7.60267.60

263.55

CICLOSANTIG.

. 3333 :3333322Z21111

K-lNF(ENRrBEOC)

A EOC

QUEMADOINICIAL

24094.22913.20505.24675.22680,20271.18569.15400.15045.9766.9766,7327.7327.

0.0.0. .0.

1091Q.

CICLO 5

DELTA-BCICLO

9221.«869.9328.9623.9892.9460.9711.10321.9847.10918.9331.9758.6999.10295.7010.6702.5409.

0597.

QUEMADOFINAL

33315.31782»29833.34298-32573.29731.28280.25721.24892-20685-19097.17085.14326.10295.7010.6702.5409.

19515.

K-INF FRACCIÓNEOC

.9897

.9468. .9620.9830.9949

1.01561.02671.04701.05361.08821.10191.12001.14601.14391.18261.18641.2028

1.080023

1.086864

ENERGÍA

1.01371.01381.06621.10681.13781.08801.11691.18701.13261.28151.09511.1452.8215

1.2159.8278.7915.6388 •

1.0000

ABSORCIONESE O C • • '•

1.02421.07n71.10fl31.12591.14361.07131.08791.13381.07491.1776.9938

1.0225.7166

1.0629.7000.6671 ---.5311

1.069979

1.076111

t

<DCO

1

PESADO INVERSO

PESADO DIRECTO

BALANCE DEL CICLO A EOC CICLO 5

IDENTIFSUDLOTE

ETEAEFG

NO.ELEM

2

e211622

ENFUQINIC.

3.6002.9003.6003.6003.000

KG UlELEM.

249.102b9.00260.60265.93267.60

CICLOSANTIG.

333 .21

QUEMADOINICIAL

24094.21709.19220.8547.

0.

DELTA-BCICLO

9221.9098.9761»

• • 9450.' :

6670.

QUEMADOFINAL

33315.30807.

. 28982* •;- 17997'.

6670.

K-INFEOC

.9897

.95441.02131.11171.1868

FRACCIÓNEMERGÍA

1.01371.04001.12271.1091,7878

ABSORCIONESEOC

1.02421.0E951.0985T.0006.6656

NÚCLEO 69 3.328 263.55 10918. 8597. 19515. 1.080023 1.0000 1.069979 ' PESADO INVERSO

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1

SAMPLE PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZONES

PAGE 12

BALANCE DEL CICLO A EOC CICLO 6

IDENTIFSUBLOTE

EAlE5E6Fl

H F2F2

H F3D F4Gl

B G2G2 ,

h G3G3

H G5HlH2H3

NÚCLEO

NO.ELEM

44462413114447138

a

1

ENRIQINIC.

2.900 .3.6003.6003.6003.6003.6003.6003.ÓÜÜ3.0003.0003.0003.0003.0003.Ü0O3.0003.3503.3503,350

3.299

.080648

KG UIELEM.

259.00260.60260.60265.932o5.93263.93265.93265.93267.60267.60267.bO267.60267.60267.60267.60267.602ü7.60267.60

265.90

CICLOSANTIG.

••;••• 3

4433 •33322222 .2 .,2111

K-INF(ENR»BEOC)

QUEMADO:INICIAL

24975.25721.24892.20605.19097.17085.14326.14326.10295.10295.7010.7010.6702.5409.5409.

0.0.0.

10600.

DELTA-BCICLO

8541.9451.9226.9137.9364.9972.10918.9972.9677.8399.9676.6578.10319.9219.5B63.6559.7249.5554.

8401.

QUEMADOFINAL

33516.35172.34118.29822.28461.27057.25245.24298.

. 19971.18694.16686.13587.17021.14628.11272.65í>9.7249.555.4.

19001.

K-INF FRACCIÓNEOC '

.9332

.9771

.98421.01491.02531.03631.050B1.05841.04851.05991.07841.10871.07521.09331.13311.21311.20471.2255

1.081773

1.089128

EMERGÍA

.99021.10251.07631.08771.11471.18721.29981.18711.15921.00611.1592.7880

1.23621.1044.7024.7857.8664.6653

1.0000

ABSORCIONESEOC

1.06111.12831.09351.07171.08721.14561.23691.12161.1056.94931.0749.7107

1.14971.0055.6198.64 77.7208.5429

1.070963

1.077387 PESADO DIRECTO

BALANCE DEL CICLO A EOC CICLO 6

IUENTIFSUBLOTE

EAEFGH

NÚCLEO

NO.ELEM

48162219

ENRIQINIC.

2.9003.6003.6003.0003.350

Ktí UIELEM.

2b9.00260.602 Ü 5 . 9 3267.60267.60

CICLOSANTIG.

34321

69 3.299 265.90

QUEMADOINICIAL

24975.25307.17997.6670.

0.

10600.

DELTA-BCICLO

8541.9338.9642.8853.6426.

QUEMADOFINAL

33516.34645.27639.15523.6426.

K-INFEOC

.9332

.98071.03171.08951.2147

FRACCIÓNENERGÍA

.9C021.08941.14781.0605.7698

8401. 19001. 1.001773 1.0000

ABSORCIONESE O C • . .

1 . 0 6 J . 1 ' •••1.11091.1118

.9752

. 6 3 4 4 ••.••

i.070963 PESADO INVERSO

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1

SAMPLE PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTIoN BY ZONES

PAGE 17

IDENTIFSUBLOTE

F F2H F2

F2H F30 F4

GlD G2

G2H G3

G3G4

H G5 •Hl ,H2H3

H mJlJ2

NÚCLEO

NO.ELEM

2241311 •444713a44a8

69

i.

BALANCE DEL CICLO

ENRIQIN1C.

3.6003.6003.6003.600.3.6003.0003.0003.ÜO03.0003.0003.0003.0003.3503.3503.3503.3503.2503.250

3.259

080607

KG UIELEM.

265.93• 265.93,265.93265.93265.93267.60267.602&7.60267.60267.60267.602o7.60267.60267.602o7.60267.60267.60267.60

267.31

CICLOSANTIG.

. 4

... . n

.... n443333333222211

K-lNF(ENRrBEOC)

A EOC

QUEMADOINICIAL

29822.28461.27057.25245.24290.19971.18694.16686.13587.17021.14628.11272.6559.7249.5554.5554.

0.0.

11382.

CICLO 7

DELTA-BCICLO

7138.7271.6998.7851.7959.7152.6014.7969.839B.6985.7799.8279.9563.6545.6705.5545.6819.5191.

7260.

QUEMADOFINAL

36960. •, 35731.

34055. '33095.32257.2712't.25508.24655.21985.24007.22427.19551.16122.15794.12260.11099'.6819»5191.

18642.

K-ÍNFEOC

.9655

.9735

.9847

.9913

.9972

.98951.00181.0086 •1.03081.01391.02711.05221.11091.11401.14911.16131.20311.2235

1.082056

1.089048

FRACCIÓNEMERGÍA

.9782

.9963

.95901.07581.0907.9£63.9396

1.09891.15(31.90.33

1.07551.14171.31881.1783.9247.7647.9404.7158

1.0000

ABSORCIONESEOC '

1.01311.0235.9739

1.08531.0938.9968 -•.9379

•.- 1.0096'•• 1.1234

.95011.04711.08511.18721.0578.8047.6585.7816.5851

1.075643

1.081979

BALANCE DEL CICLO A EOC CICLO 7

1DENTIFSUüLOTE

FGHJ

NÚCLEO

NO.ELEM

12221916

69

ENRIQINIC.

KG UIELEM.

3.600 265.933.000 2o7.603.350 267.603.250 2o7.60

3.259 2t,7.31

CICLOSANTIG.

4321

QUEMADOINICIAL

26911.15523.6426.

0.

11382.

DELTA-BCICLO

7378.7739.7687.6005.

7260.

QUEMADOFINAL

34289.23262.14113.6005.

18642.

K-INFEOC

.98311.02001.13031.2132

FRACCIÓNENERGÍA

1.01111.06711.0600.8281

1.082056 1.0000

ABSORCIONESEOC

1.02801.0456.9409.6833

1.075643 PESADO INVERSO

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1

SAMPLE PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY 20NES

PAGE 22

IDENTIFSUBLOTE

H G3G3

. 64G G5H G5Hl

C H2H2

H H3H3

H H4Jl •

H J2 .J2

0 J3H J3

KlK2K3

NÚCLEO

IDENTIFSUBLOTE

GHJK

NÚCLEO

NO.ELEM

44

• ' 4 •3112444

2622

828

69

1.

NO.ELEM

16191618

69

BALANCE DEL CICLO

ENRIQINIC.

3.0003.0003.0003.0003.0003.3503.3503.3503.3503.3503.3503.2503.2503.2503.2503.2503.2503.2503.250

3.220

080798

KG UIELEM.

267.60267.60267.60267.60267.60267.60267.bO267.60267.602o7.60267.60267.60267.60267.60267.60267.602b7.60267.602o7.60

267.60

CICLOSANTIG.

444443333332222 .2 .11

,. 1

K-INF(ENR»BEOC)

BALANCE DEL CICLO

ENRISINIC.

3.0003.3503.2503.250

3.220

KG UIELEM.

267.60267.60267.60267.60

267.60

CICLOSANTIG.

4321

A EOC

QUEMADOINICIAL

21985.24007.22427.22427.19551.16122.16122.15794.15794.12260.11099.6819.6819.5191. •5191.5191.

0.0.0.

10503.

A EOC

QUEMADOINICIAL

22532.14113.6005.

0.

10503.

CICLO 8

DELTA-8CICLO

8235.7929.8179.7644.7972.9329.8625.8965.8945.8934.9395.9999.8682.8969.5753.6687.6884.6212.5270.

7793.

QUEMADOFINAL

30220.31936.30605.30071.27523.25451,24747.24760'.24739.21193.2Ü494.16818.15501.14160.

' 10944.11877.6884.6212.5270.

18297.

CICLO 8

DELTA-BCICLO

8017.9028.8017.6092.

7793.

QUEMADOFINAL

. 30549»23142.

• 14022.6092.

18297.

K-INF FRACCIÓNEOC

.9674

.9561

.9648

.9685

.98651.02991.03551.03541.03561.06521.07131.09691.10941.12251.15581.14581.20241.21061.2225

1.081888

1.089649

K-INF FEOC

.96521.04861.12381.2121

1.081888

ENERGÍA

1.05661.01751.0494.9808

1.02291.19701.10671.15041.14781.14631.20551.28301.11401.1508.7302.8580.8834.7970.6763

1.0000

-RACCIONENERGÍA

1.02871.15841.0287.7817

1.0000

ABSORCIONESEOC

1.0922I.O64I1.0877 -•1.01281.03691.16231.06871.11101.10831.07621.12531.16971.00411.0252.6387.748R.73U7.6584.553¿

1.072410

1.079333'

ABSORCIONESEOC

1.06571.1044

' : .9179.6455

1.072410

I

10

PESADO INVERSO

PESADO INVERSO

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1

: SAMPLE PROBLEM 1 . CYCLE.S 4 TO 11 CORE DESCRIPTION BY ZONES

PAGE 26

BALANCE DEL CICLO A EOC CICLO 9

IQENTIFSUBLOTE

B H3H2

H H3H3

H H4JI :

H Ü2F J3J2

D ü3H J3

Kl '0 K2 'H K2

K2K3

H K4LlL2L3

NÚCLEO

NO.ELEM

14444224224224244ü28

69

1

ENRIQINIC.

3.3503.3503.3503.3503.3503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.250

3.275

.079291

KG UIELEM.

267.60267.60267.60267.602b7.602b7.60267.60267.60267.60267.60267.60267.60267.60267.602fa7.60267.602b7.602o7.602o7.60267.60

267.60

CICLOSANTIG.

4444 .433 .3333222222111

K-INF(ENR»BEOC>

QUEMADOINICIAL

24747.24760.24739.21193. •20494.lóQia.15501.15501.14160.10944.11877.6684.6084.6fl84.6212.5270.5270.

0.0.

:• o.10486.

DELTA-BCICLO

9027.8958.9018.9306.8870.9119.8944.9429.9611.10146.9986.10796.10391.9432.6113.7091.9731.7330.6684.5643.

8460.

QUEMADOFINAL

33775. •33717.33757.30499.29364.25937.24445.24930.23771.21090.21863.17681.17275.16316.12325.12361.15001.7330.6684.5643.

18945.

K-INFEOC

.9706

.9710

.9707

.99241.00041.01841.03031.02641.03581.05851.05181.08891.09261.10161.14111.14081.11421.19701.20481.2177

1.081752

1.088497

FRACCIÓNENERGÍA •

1.06711.05891.06601.10011.04861.07801.05731.11461.13621.19941.18041.27621.22831.1150.7227.8382

1.1503.8665 •.7902.6671

1.0000

ABSORCTONESECC

1.09951.09061.09H21.10851.0.4811.05851.02621.08601.09691.13311.12221.17201.12421.0121.6333.7348

1.0324• .7239

•-• . 6 5 5 8

• .5478 .

1.071355

1.077346

BALANCE DEL CICLO A EOC CICLO 9

IDENT1FSUBLOTE

HJKL

NÚCLEO

NO.ELE.M

17161818

69

ENRIQINIC

3.3503.2503.2503.250

3.275

KG UIELEM.

267.60267.60•267.60267.60

267.60

CICLOSANTIG.

4321

QUEMADOINICIAL

22911.14022.6092.

0.

10486.

DELTA-BCICLO

9037.9581.8867.6509.

8460.

QUEMADOFINAL

31949.23604.14960.6509.

18945.

K-INFEOC

.98251.03721.11461.2070

1.081752

FRACCIÓNENERGÍA

1.06831.13261.0482.7694

1.0000

ABSORCIONESEOC

1.08711.0914.9431.6381

1.071355

I

PESADO INVERSO

CÍCLON-2 PRINTED OUTPUT. FROM SAMPLE PROBLEM 1

: SAMPUE PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZÓNES

PAGE 31

1DENTIFSUBLOTE

B J2H J2F J3J2

D J3H J3 !Kl

D K2H K2

K2 •K3

H K4 :

Ll 'ü L2H L2L2L3

H L4MiM2M3

NÚCLEO

• N O .

.ELEM

124224224244224244828

69

1

BALANCE DEL CICLO

ENRIQINIC.

3.2503.2503.2503.2503.2503.2503.2503.250

. 3.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.250

3.250

.079946

KS UIELEM.

267.60267.60267.60267.60267.60267.60267.60267.60267.60267.60267.60267.60267.602t>7.60267.60267.60267.60267.60267.60267.60267.60

267.60

CICLOSANTIG.

44444433333

. ' 3222222111

K-INFCENRiBEOC)

A EOC

QUEMADOINICIAL

25937.24445.24930.23771.21090.21863.17681.17275. ,16316.12325.12361.15001.7330.7330.7330.66Ü4.5643.5643.

0.0.0.

10698.

CICLO 10

DELTA-BCICLO

8277.7872.B318.8439.8760.8524.8516.8748.8882.8966.9357.8949.10170.9809.8854.5745.6816.9152.7025.6329.5387. :

7967.

QUEMADOFINAL

34214.32317.33248.32210.29850.30387.26197.26023.25199.21291.21718.23950.17500.17139.16184.12429.12460.14795.7025.6329.5387.

18664.

K-INF FRACCIÓN

EOC: ••.9606.9727.9667.9734.9894.9857

1.01641.01781.02421.05681.05311.03431.09051.09391.1028 -1.14011.13971.11621.20061.20921.2210

1.081990

1.089060

ENERGÍA

1.0390.9882

1.04411.05931.0996 •1.07001.06901.09801.11491.12541.17461.12331.27661.23131.1114 ..7211.8556

1.1488.8818.7945.6762

1.0000

ABSORCIONESEOC

1.0816 .1.01591.08011.0ña21.11131.00551.05171.07891.08851.06501.11541.08601.17061.12561.0078.6325.7507

1.0292.7345.6571.5538

1.072188

1.078489

BALANCE DEL CICLO A EOC CICLO 10

IDENTIFSUEiLOTE

JKLM

NO.ELEM

1518ia18

ENRIQINIC.

3.2503.2503.2503.250

KG UIELEM.

267.60267.602b7.60267.60

CICLOSANTIG.

4321

QUEMADOINICIAL

23448.14960.6509.

0.

DELTA-BCICLO

8386.8956.8374..6220.

•• QUEMADOFINAL

• 31834.23916.14683.6220.

K-INFEOC

.97591.03461.11541.2105

FRACCIÓNENERGÍA

1.05261.12421.0512.7807

ABSORCIONESEOC

1.07831.0862.9449.6456

CD

NÚCLEO 69 3.250 2o7.60 10698. 7967. 18664. 1.081990 1.0000 1.07?l88 PESADO INVERSO

CICLON-2 PKINTED OUTPUT FROM SAMPLE PROBLEM 1

SAMPLE PROBLEK 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZONES

PAGE 35

IDENTIFSUBLOTE

B K3H K2K2K3

H K4H

D L2H L2

L2L3

H L4 >Mi ,

D M2H M2

M2M3

H M4PlP2P3

NÚCLEO

IOENTIFSUBLOTE

KLMP

NÚCLEO

NO.ELEM

14244224244224244828

69

1

NO.ELEM

1518lala

69

BALANCE DEL CICLO

ENRIQINIC.

3.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.250

3.250

.079873

KG UIELEM.

267.60267.60267.60267.60267.602b7.602&7.60267.60267.60267.60267.60267.60267.60267.60267.602fa7.60267.602b7.60267.60267.60

267.60

CICLOSANTIG.

44 •44433333322

• • 2 ••

222111

K-INF(ENRfBEOC)

BALANCE DEL CICLO

ENRIQINIC.

3.2503.2503.2503.250

3.250

KG UIELEM.

267.60267.60267.60267.60

267.60

CICLOSANTIG.

432

, 1

A EOC

QUEMADOINICIAL

26023.25199.21291.21718.23950. ,•17500.17139.16184.12429.12460.14795.7025.7025.7025.6329.53B7.5337.

0.0.0.

10607.

A EOC

QUEMADOINICIAL

23471.14883.6220.

0.

10607.

CICLO 11

DELTA-BCICLO

8232.8334.8346.8647.8421.8442.8887.9023.9084.9373.9010.

10115.10009.9052.5893.6959, •9347.7154.6458.5484.

8065'.

QUEMADOFINAL

34255.33533.29637.30365.32371.

. 25942.• 26026.25207.21514.21833.23806.17140.17034.16077.12222.12346.14734.7154.645a.5484.

18672.

CICLO 11

DELTA-BCICLO

8436.9025.8526.6335.

8065.

QUEMADOFINAL

31907.23908.14746.6335.

18672-

K-lNF FRACCIÓNEOC

.9603. .9649

.9909

.9858

.97231.01841.01771.02421.0548 .1.05211.03551.09391.09491.10391.14221.14091.11681.19911.20761.2198

1.081913

1.088949

K-lNF 1EOC

.97541.03471.11671.2091

1.081913

ENERGÍA

1.02071.03341.03491.07211.044»1.04671.10201.11881.12641.16¿21.11721.25421.24101.1224.7307.8629

1.1590.8871.8008.6800

1.0000

-RACCIONENERGÍA

1.04601.11911.0572.7855

1.0000

ABSORCIONESEOC

1.062B1.07111.04431.0875 .1.07391.0278

. 1.08281.09241.06781.10471.07B91.14661.13351.0168.6397.7563

1.0378.7398.6631.5575

1.072592

1.078886

ABSORCIONESEOC

1.07211.0811.9491.6503

1.072592

íD

PESADO INVERSO

I •

CICLON-2 PFUNTED OUTPUT FROM SAMPLE PROBLEM 1 • ' ••.••

SAMPLE PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZONES

INCREMENTOS DE QUEMADO POR LOTE EN CICLOS SUCESIVOS

PAGE 37' •

SUBLOTE

ABCET4DID2

B D3H 03F D4

03E 050 06G DíiDAEA1EA2EA3ElE2E3E4EbE6Fl

F F2H F2

F2H F3D F4

GlB G2

G2H G3

G364

G G5H G5

HlC H2B H3

H2H H3

H3H H4

NO. EL

132

; 122

, 1:: i• 2

4ii3

, 21

• 4

444

• 1

• 7

144422

1•3

11.44

431111444

W/0 I

2.4252.9003.6003.6003.6003.6003.6003.60Ü3.6003.6003.6003.6003.6003.0002.9002.9002.9003.6003.6003.b003.6003.6003.6003.6003.6003.6003.6003.6003.6003.0003.0003.0003.0003.0003.0003.000 .3.0003.3503.3503.3503.3503.3503.3503.350

KG UI

266,20266.25263,40249.10257.a52b7.852b7.85Üb7.d52b7.852b7.85257.85257.85257.85260.50259.002b9.002b9.002bO.6O260.60260.602b0.60260.bO260.60265.93265.93265.932o5.93265.93265.93267.60267.60267.60267.60267.60267.60267.60267.60267.60267.602t>7.60267.60267.60267.602t>7.60

BU INIC

27090.20665.22931.9900.19645.19168.19168.18490.lb490.

. 11460.16188.16188.17046.18040.12160.10378.7730.11380.7966.7966.5794.5794.7388.

0.0.0.0.0.0.0.0. :0.0.0.0.0. .Ot0.0.0.0.0.0.0.

CICLO 4

0.0.0.

14194t12395.12495.12475.12505t ,12625.13535.12575.13055.12785.11605.12815.12535.12775.13295.14714.12305.12775.9606.7657.9766.9766.9766«7327.7327.7327.

0.0.0.0.

o.Ot0.

o.O«0>0.0.0.0.0.

CICLO 5

0.0.0.

9221.0>0.Ot

0.0.0.0.

• 0 .

o.0.0.

8869t9328.9623.9892.9460.9711.10321.9847.10918.10918.9331.9758.6999.6999.10295.10295.7010.7010.6702.5409.5409.5409.

0.0.0.0.0.0.0.

CICLO 6

0.0.OtOt0.Ot

0.0.0.0.0.0.

•••• 0 .

0.8541.

0.0.0.0.0.0.

9451.9226.9137.9137.9364.9972.1091B.9972.9677.8399.9676.6578.10319.9219.9219.5863.6559.6559.6559.7249.7249.5554.5554.

CICLO 7

0.0.0.0.0.0.0.0.Ot0.Ot0.0.0.0.0.0.0.0.OtOt0.Ot

0«7138.7271.6998.7851.7959.7152.6814.7969.8398.6985.7799.7799.8279.9563.9563.9563.8545.854516705.5545.

CICLO 8

Ot

0.0>Ot0.OtOt0»0.

• Ot

0.Ot0.0.0.0.OtOt

0.0.0>0.0.0.0.0.

• • Ofo.Ot

Ot0.0.

8235,7929.8179.7644t7972.9329.8625t8625.8965t8945t893419395.

CICLO 9

o.OtOt0.0.0.Ot

0.0.OtOtOtOtOt

Ot0.0.Ot

0.0.0.Ot

OtOt

0.••• o.

0.OtOt

0.Ot

0.0.0.0.OtOt0.0.

9027.• 8958.

90lP.9306.8ñ70t

CICL010

0.0.0.0.Ot

0.0.0.0.0.0.Ot0.Ot

• • • o .

• . 0 . ' •

Ot

0.0.0.0.Ot

o'.o.Ot0.oi0>0.0.o. •0.OtOt

. • • • • • o .

• • • • • . • o .

0.

o'.0.0.OtOt

. Ot0.

CICL011

t

' oot

-

OtOtOt0.0.0.0.0.0.Ot

0.0.0.0.0.Ot

0.0.0.0.0.0.0.0*OtOtOt0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

CICLON-Z

SU'dLOTE

Ulb J2H J2F u302

D J3H J3Kl

D K2B K3H K2K2K3

H K4Ll

D L2H L2L2L3

H L4Mi

D M2H M2M2M3

H [-'4PlP2P3

> PKINTED OUTPUT FROM

NO.EL W/0

112422

• 4

211

. 424' 422

, 424n224244828

3.2503.2503.2503.250

. 3.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.250

• 3.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.250

1 KG UI

267.60267.60267.60267.60267.60267.60267.60267.60267.bO267.60267.60, .267.602t>7.60267.60267.60267.60267.60267.60267.60267.602o7.60267.60267.602b7.602fa7.60267.60267.60267.60267.60

QUEMADO DEL CICLO (MWD/MTU)

MASA TOTAL DE

DURACIÓN DEL

U INIC

CICLO

(MTU)

(EFPD)

SAMPLE.

BU INIC

0.0.0.0.0.0.0.0.0.0.

... o.0.0.0.'0.0.0.0.0.0.0.0.0.0.0.0.

•.,- 0 .

• o .

0.

0.

.000

• 00

PROBLEM 1

CICLO 8

0.0.

. •• ... .-o..

.; ••• - .• O . ' ,

0.

o.0.• o .

0.0. .

.... . , o.0.

.. . o.0.0.0.

.-,•.;• 0 .

•..'•; o .

o.0*0-o-0.

. 0.0.0.0.0.0.

11300.

17.978

,398.33

CICLO 3

0.0.0.0.0.0.0.

• • 0 .

0.0.

..,.,. 0.. . 0.

•••,,-: 0 .

0.0.

• ..-••• 0 .

• , • 0.0.0.0.0.0.0.0.0.0.0.0.0.

8597.

18.185

306.55

CICLO S

0.

o.0.0.0.0.0.0.0.0.

:;, ,-• ' 0 .

0.0.0.

, .0.o..0.0.0.0.

•••., •' o .

0.0.0.0.0.0.0.

. 0.

8401.

18.347

• 302.23

CICLO 15

6819.6819.6819.6819.5191.5191.5191.

0.0. • .

• o . ;

0.0.0.0.0.0.0.0 . ••

0.. :. 0 . •0.0.0.0 . •

0.0.0.0.0. '

7260.

18.444

262.55

CICLO 8

9999.9999.8682.8682.8969.5753.6687.6884.6884.6884.6884.6212.5270.5270.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

7793.

18.464

282.16

r.

CICLO 1

9119.9119.8944.9429.9611.

10146.9986.10796.10391.

••'• 1 0 3 9 1 . -

943?.6113.7091.9731.7330.7330.7330.6684.5643.5643.

0.0.0.0.0.0.0.0.0.

8460.

18.464

306.27

' • '•>

CICLO<0

0.8277.7872.8318.8439.8760.8524. .8516.-8748.8748.,8882.8966.9357.8 9 4 9 . '•••

10170,•-• 9809. .

8654.5745.6816.9152.

; 7025.• 7025.'

7025.6329. •5387.

• 5387.0.0.0.

7967..

18U64

288.43

-101-

CICL01*

0.0.0.0.0.0.0.0.0.

8232.8334.8346.

-• 8647.8421.

• 8442.8887.

• 9023.908».9373.9010.10115.10009.9052.5893.6959.9347.7154..6458.5484.

8065.

18.464

291.99

- 102 -

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1

SÁMPL.E PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZONES

SUMARIO DE LA DESCARGA

PAGE" 39

IDENTIFSUBLOTE

ABCET4

BHF

EDG

DID2D3D3D4D3D5D6D5

DAEAlEA2EA3

FH

HD

B

H

GH

CB

H

H

BHF

DH

D

ElE2E3£4E5E6FlF2F2F2F3F4GlG2G2G3G3G4G5G5HlH2H3H2H3H3H4ülÜ2J2J3J 2 •

J3J3KlK2

NO.ELEM

J321221124-11321444 '417144 .42241311H4443111144.4

. 4112422421

ENRIQINIC.

2.4252.9003.6003.6003.6003.6003.6003.6003.6003.6003.6003.6003.6003.0002.9002.9002.9003.6003.6003.6003.6003.6003.6003.6003.6003.6003.6003.6003.6003.0003.0003.0003.0003.0003.0003.0003.0003.3503.3503.3503.3503.3503.3503.3503.2503.2503.2503.2503.2503.2503.2503.2503.250

KG UITOTAL

3460.60532.50263.4049S.20515.70257.85257.65515.70

1031.40257.85257.85773.55515.70260.50

1036.001036.001036.001042.40260.601824.20260.bO1042.401042.401063.72531.86

•• 531.861063.72265.93797.79267.60267.60

1070.401070.401070.401070.40802.80267.60267.60267.60267.60

1070.401070.401070.401070.40267.60267.60535.201070.40535.20535.20

1070.40535.20267.60

CICLODESCARGA

33•7

t"

44444444446555555666777777778888888999999101010 .1010101010

CICLOSPERMAN.

2223.33333333.333333333443« •

4

n4H3334444

n33444443444- -44433

QUEMADODESCARGA

27090.20665.22931.33315.32040.31663.31643.30995.31115.24995.28763.29243.29831.29645.33516.31782.29833.34298.32573.29731.28280.35172.34118.29822.36960.35731.34055.33095.32257.27124.25508.24655.30220.31936.30605.30071.27523.25451.24747.33775.33717.33757.30499.29364.25937.34214.32317.33248.

. 32210.29850.30387.26197.26023.

U RESIDUAL(UF/UI)

.9633

.9711

.9683

.9526

.9556

.9564

.9565

.9578

.9575

.9657

.9615

.9608

.9599

.9602

.9557

.9577

.9600

.9500

.9544

.9601

.9621

.9475

.9505

.9599..9420.9459.9507.9531.9551.9632.9652.9662• 9595.9575.9591.9597.9627.9652.9661.9553.9553.9553.9591.9605.9646.9548.9570.9559.9571.9599.9593.9643.9645

ENRIQ.DESCARGA

.66491.22781.64581.08271.14291.16121.16211.19411.18811.52071.30911.28371.2531.8669.6649.7233.7956

1.03811.11751.25831.3350.9996

1.04611.2536.9246.9756

1.04901.09291.1325.9768

1.05321.0953.8435.7773.8282.8495.9587

1.30341.3422.9099.9122.9106

1.05021.10321.2055.8348.9089.8718.9133

1.0150.9909

1.19201.2010

PU FIS.(KG/MTU)

5.95135.55815.92876.72586.65616.63426.63306.59406.60146.15046.45066.48256.52026.31536.44736.38566.28976.77496.68606.51396.41736.81536.76626.51966.88816.83956.76326,71436.66856.13806.00635.93576.34926.43236.369A6.34096.16856.09026.02556.64706.64506.64646.49016.41546.10976.61936.54826.58646.54346.41556.44856.13266.1173

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1 '

SAMPLE PROBLEM 1 CYCLES 4 TO-il ••• CORE DESCRIPTION BY ZONES

*** BALANCE POR LOTES DE.IGUAL.CICLO DE CARGA Y DESCARGA ***

INCREMENTOS ÜE QUEMADO POR LOTE EN CICLOS SUCESIVOS

PAGE

SUDLOTE

A2*03H2*03C2*Ü3

ET3+05D3 + 04

DA3+Ü4EA3*Ü6EA3*05t¿3*05L4*06F3 + U6F4*Ü7G3*Ü7G4*oaH3*ÜÜH4 + U9J3 + Ü9J4*10K3*10K4*0üL3*00M2 + 00

. P1*OÜ

QUEMADO

NO.EL W/0

1321217, 14

• 8

8• 4.12• 6162171

153151818la

2.4252.9003.6003.6003.b003.0002.9U02.9003.6003.6003.6003.6003.0003.ÜO03.3503.3503.2503.2503.2503.2503.2503.2503.250

I KG UI

2b6.20266.25263.40249.10257.85260.56 .2b9.002b9.002b0.60260.60265.93265.93267.602o7.60267.60 ,267.60267.60267.60267.60267.60267.60267.602o7.60 •

DEL CICLO (MWD/MTU)

MASA TOTAL DE

DURACIÓN

U INIC

DEL CICLO

(MTU)

(EFPD)

BU INIC

27090.20665.22931.9900.17581.18040.12160.9054.8849.6591.

0.0.0.0.0.0.0.0.0.0.0.0.0.

0.

.000

.00

CICLO 4

o.o.o.

14194.12713.11605.12815.12655.

. 12831. .8632.9766.8140.

0.0-0.0.0.0.0»0.0.

o.0.

11300.

17.978

398.33

CICLO 5

0.0.0.

9221.0.0.0.

9098.9563.10084.10918.8961.8105.6132.

0.0.0.0.0.0.0.0.0.

8597.

18.185

306.55

• CICUO. 6

0... 0.0.0.0.0.

•• 8 5 4 1 .

• 0 •0.

9338.9137.9810.9464.8624.6559.6411.

0.0.0.0.0.0.0.

8401.

18.347

302.23

CICLO 7

0.0.0.0.0.

. 0.0.0.0.0,0.

7378.7641.7775.9563.7466.6819.5951.

0.0.0.0.0.

7260.

18.444

262.55.i-

CICLO 8

0.0.

• ••• o .

0.0.

• 0.0.0.0.0.

'• • o .

••• 0 .

0.8017.8977.9034.'9999.

. 7885.6884.5934.

0.0.0.

7793.

18.464

282.16

CICLO 9

0.0.0*0.0.0.0.

o.0.0.0.0.0.0.0.

9037.9119.9612.10661.8509.6509.

o.0.

8460.

18.464

306.27

CICL010

0.o . •

0.0.

• 0.0.0.0.0.0.0.0.0.0.

• • 0 .

0.0.

8386.8593.9029.8374.6220.

0.

7967.

18.464

288.43

CICLO11

0.0.0.

• •• o .

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

. 0.8436.9025.8526.6335.

8065.

18.464

291.99

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 1

SAMPLE PROBLEM 1 CYCLES 4 TOlí CORE DESCRIPTION BY ZOÑES

PAGE 41

*** BALANCE POR LOTES DE IGUAL CICLO DE CARGA Y DESCARGA *** o

I

A2*Ü3B2*03C2*ü3

ET3*05Ü3*Ü4

DA3*Ü4EA3*06EA3*05£3*05E4*Ü6F3*0oF4*Ü7G3*0764*08H3*Ü8H4*09J3*Ü9Ü4 + 1ÜK3*1UK4*ÜÜL3*Ü0M2*Ü0P1*ÜO

132121714a13a4126162171

15315ialala

SUMARIO DE LA DESCARGA

IDENTIF NO. ENRIQSUBLOTE ELEM INIC.

2.425900600.600600000

2.9002.9003,6003.6003.6003.60033

.000

.0003.3503.3503.2503.2503.2503.2503.2503.2503.250

KG UI CICLO CICLOS QUEMADO U RESIDUAL ENRIQ. PU FIS.TOTAL DESCARGA; PERMAN. DESCARGA (UF/UI) DESCARGA (KG/MTu)

3460.60• 552.50•263.40••• 49a.204383.45260.50

1036.002072.003387.802084.801063.723191.161605.604281.60535.20

4549.20267.60

4014.00802.bO

4014.004816.804816.804816.80

3335446556677889910100000

22233333343434343434321

27090.20665.22931.33315.30293.29645.33516.30807.31243.34645.29822.34289.;::2ü9.30549.25099.31949,25937.31834.26139.31-907.2.3908.14746.6335.

.9633 ••

.9711

.9683

.9526

.9588

.9602

.9557

.9588

.9567

.9490

.9599

.9497 • "

.9655

.9591

.9657 '

.9574

.9646

.9576

.9644

.9645

.9645

.9645

.9645 =

.6649-1.22781.64581.0e271.2316.8669.6649.7595

1.18561.02291.25361.04061.0686.8315

1.3228.9891

1.2055.9307

1.19501.20101.20101.20101.2010

5.95135.5581 .5.92876.72586.54486,31536.44736.33766.60006.79086.51966.76895.98126.36246.05786.55506.10976.51fi26.12756.11736.11736.11736.1173

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROÜLEM 1

SAMPLE PROBLEM 1 CYCLES 4 TO 11 CORE DESCRIPTION BY ZONES

PAGE 42

*** BALANCE POR LOTE DE DESCARGA *** OenI

SUMARIO DE LA DESCARGA.

IDENTIF NO. ENRIQSUBLOTE ELEM INIC

KG UI CICLO CICLOS .: .QUEMADO U RESIDUAL ENRIQ. PU FIS.TOTAL DESCARGA PERMAN. -DESCARGA (UF/UI) DESCARGA (KG/MTU)

0304050607

oa091011

16la231618

lala180

2.5573.5663.3573.4273,3993.0393.344

• 3.250 ...000

4256.504643.955958.004184.524796.764816.804816.804816.80

.00

345678910

. 11

34567a91011

26029.30257, •3 1 2 6 5 . •••

33139.31250.29943.31615..30885.

0.

.9646

.9569

.9571

.9534

.9550

.9599

.9578

.9587

.0000

.79601.21111.0288.99291.0499.88601.0011.9747.0000

5.90076.53196.5193'6.63686.50536.32866.53026.4531.0000

ENERGÍAS RELATIVAS EN CADA CICLO DE LOS LOTES DE DESCARGA

LOTE34567891011

NO. EL16182316181818180

CICLO 326029.17606.9006.6294.

0.0.0.0.0,

CICLO 4.0000

1.10861.1336• .6844.4902.0000.0000.0000.0000

CICLO 5.0000.0000

1.0715.9003

1.0202.6438.0000.0000.0000

CICLO 6

1.1.1.• •V

o

0000000000000642156500567253 .0000 .0000

CICLO 7

111

.ooo'ó.

.0000

.0000

.0000

.0253-

.0996

.0246

.6838

.0000

CICLO 8.0000.0000.0000.0000

• • .00001.04241.1661.9904 .• 0000

CICLO 9,0000.0000.0000

• ,0000.0000.00001.06891,1569.0000

CICLO 10.0000.0000.0000.0000.0000.0000.0000

1.0570.0000

- 106 -

CICLON-2

ODATAiL 7.

ÜUUüui000002000003ooooot000005000006000007

oooooa00000900001000001100001200001300001400001500Q016000017

ooooia00001900002000002100002200002300002"+00002500002600002700002800002900003000003100003200003300003400003500003600003700003600003900004000004100004200004300004400004500004600004700004800004900005000005100005200005300005400005500005600005700005800005900006000006100006200006300006400006600006b000067000066000069

PUUCHEO OUTPUT FROM

1010*

27090.3

20665.3

. 22931.3

9900.3

• .

17581.3

18040..-• - 3

12160.3

9054.3

8849.• • . • • • 3

6591.4

... 9766.4

8140.5

8105.5

6132.6 .

6559.6

6411.7

6819.7

5951.6

6634.8

' 5934.9

6509.10

- 6220.11

6335.

327090.

320665.

322931.

533315.14194.

430293.12713.

429645.11605.

633516.12815.

530807,12655.

531243.12831.

634645.8632.

629322.10918.

734289.8961.

725209.9464.

830549.8624.

825099.9563.

931949.7466.

925937.9999.

1031834.7885.

1026139.10661.

1131907.&509.

1123908.8374.

1114746.8526.

116335.

SAMPLE PROELEM

1

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

3

3

3

3

4

13.4606

1.5325

,: 1.2634

3.49829221.

24.3834

2.2605

41.0360

0.3

2.07209098.

33.38789563.

42.084810084,

31.06379137.

43.19129810.

31.60567641.

44.28167775.

3.53528977.

44,54929034.

3.26769119.

44.01409612.

3.80286593.

44.01409029.

34.81639025.

24.8168

14.8168

1

2.4250

2.9000

3.6000

3.6000

3.6000

3.0000

2.9000.8541.

2.9000

3.6000

3.60009338.

3,6000

3.60007378.

3.0000

3.00008017.

3.3500

3.35009037.

3.2500

3.25008386.

3.2500

3.25008436.

3.2500

3.2500

3.2500

.9633

.9711

.9683

.9526

.9588

.9602

.9557

.9588

.9567

.9490

.9599

.9497

.9655

.9591

.9657

.9574

.9646

.9576

.9644

.9645

.9645

.9645

.9645

.6649

1.2278

1.6458

1.0827

1.2316

.8669

.6649

.7595

1.1856

1.0229

1.2536

1.0406

1.0686

.8315

1.3228

.9891

1.2055

.9307

1.1950

1.2010

1.2010

1.2010

1.2010

• n « J->

-5.9513

-5.5581

-5.9287

-6.7258

-6.5448

-6.3153

-6.4473

-6.3376

-6.6000

-6.7908

-6.5196

-6.7689

-5.9812

-6.3624

-6.0578

-6.5550

-6.1097

-6.5182

-6.1275

-6.1173

-6.1173

-6.1173

-6.1173

A2*03A2*03

82*0362*03

C2*03C2*03

ET3*05ET3*05

03*04D3*04

DA3*04DA3*04

EA3*06EA3*06

EA3*05EA3*05

E3*05E3*05

E4*06E4*06

F3*06F3*06

F4*07F4*07

G3*07G3*07

64*08G4*08

H3*08H3*08

H4*09H4*0O

J3*09J3*09

J4*1ÓJ4*10

K3*1OK3*1O

K4*00K4*00

L3*00L3*00

V2*00M2*00

P1*OOP1*OO

- 107 -

CICLON-2 INPUT DATA FOR SAMPLE PROBLEM 2 PAGE 1

0000010000020000030000040000050000060Q0007

oooooa00000900001000001100001200001300001400001500001600001700001800001900002000002100002200002300002400002500002600002700002800002900003000003100003200003300003400003500003600003700003tí000039000040000041000042000043000044000045000046000047000046000049000050000051000052000053000054000055000056000057000058000059000060

000000000000000000000000000000000000000000000000000

.• 000- •000-000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

SAMPLE PR08LEM 26

2.70200.

1.250047.99966

2.676?.1263

1.267146.99966

2.870c.1223

1.274242.99967

2.9766.1202

1.291771.99967

• 3.2266 .0.11581.29820o.99967

3.3265.1143

1.312870.99968 •

3.5765.1116

69AO 13BO 1DO 20EAO 12EO 23

4DO 18

EAO 12EO 8EO 15FQ 169.06.02.50.5 '0.0

• . , 5

EAO • 8EO 15

W El 8FO 4FO 12GO 2

v ei 200.01.02.04.50.00.50.0

2.905000.1.183885.99211

2.18182.34321.201603.99215

2.36922.30511.206056.99219

2.47342.28601.225945.99224

2.71762.24301.232570.99227

2.81562.22681.247979.99229

3.06222.22070.02.432.903.602.903.60

12700.12725.8520.

13105.8435.6.00,05.00.01.0

1.02.05.0 •• '4.50.00.52.0

CYCLES 48

3.0010000.1.122011.98497

1.76223.8010

• 1.140565.98502

1.93773.77311.147210.98506

2.03643.75911.166126.98512

2.26833.72541.173206.98515

2.36183.71231.190028.98521

2.59883.6743510.266.20266.20257.80259.00260.60

5

3.602.55.02.02.53.0

7

3.003.002.05.00.00.01.00.00.0

TO 11 CORE DESCRIPTIOH BY1 1

3.2515000.1.066858.97831

1.41324.76291.089053.97634

1.57404.76121.094602.97837

1.66524.76031.114218.97841

í.asii4.75531.121616.97843

1.96664.75261.139571.97843

2.19354.7936

32221

. • •• 1

0 11300,

265.900.50.0'2.53.02.0

2 8065.

267.60267.604.5.4.50.00.00.00.03.0

2.403.35

20000.1.022637•97190

1.12085.46121.042098.97192

1.26515.48661.0482'.'*.9719 3

1.34765.49931.068079.97195

1.54485.5258 •1.075602.97196

1.62545.53521.094060.97199

1.83555.5572

527090.24039.17580. '10090.8120.

— 1

-1.50-1.500.01.03.02.010.0

1

1.19

1.980.00.01.00.01.00.02.0

3.903.60

25000.0.980506.96581• 8782

5.88070.999857.96580

1.00525.93541.005838.96579

1.07825.96271.025824.96578

1.2551 •

6.0245 ••1.033484.96578

1.32826.04761.052786.96573

1.5204 .6.1509

0.115

0.115

0.50.50.00.00.00.01.0

FEW REfilONS

30000.0.944820.95*382• 67°7

6.22460.960697.95979.7891

6.29950.-96S936.95977.8524

6.33690.988390.95973

•• 1.00326.42520.995921.95972

1.07326.45Q21.013564.95966

1.24446.5307

0 013169

• -

1.0100

• • 0.02.00.03.02.01.0

12.0

35000.0.915606.95393• 5281

6.39130.921662.95398.6194 .

6.48290.937525.95396.6725

6.52870.955788.95388.8060

6.64100.962921.95386.8623

6.68530.978291.94803

1.00716.8076

- 108 -

CICL.ON-2

0000610000620000630000640000ÓS000066000067000068000069000070000071000072000073000074000075000076000077000078000079

ooooao000081000082000083000084000085000066000087000088000089000090000091000092000093000094000095000096 '000097000098000099000100000101000102000103000104000105000106000107000108000109000110000111000112000113000114000115000116000117000118000119000120000121000122000123

INPUT

000000000000000000000000000000000 ..000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ooo. ..000000000000000000000000000000000000000000000000000000000000

DATA FOR SAMPLE

EAOW ElFO

P Fl

eoV GlV 61HO0.00.01.00.750.51.750.00.0

FOP Fl

GOV 61T G2HOHOJO0.00.00.753.53.00.750.00.0

V GlT 62HO

S HlJOJOKO ...0.0 .0.02.04.04.250.00.75

HOS Hl

JO •P JlKOKOLO0.00.02.54.02.50.0

648124251519

784215581116

811511861018

99810661218

0.00.02.01.51.03.50.00.0

0.00.00.251.750.02.00.00.0

0.00.03.51.00.50.00.0

0.00.03.01.03.00.0

PROBLEM 2

8

3.351.02.00.01.750.54.750.02.0

8

3.25• 0.75

0.250.00.750.00.00.250.0

7

3.252.03.51.02.01.250.01.25

7

3.252.53.0 .0.01.02.00.5

2 8065.

267.600.751.501.750.00.00.0 .0.00.0

2 8065.

267.603.5 '1.750.753.500.03.500.02.0

2 8065.

267.604.01.02.00.00.01.00.0

2 8065.

267.60. . 4.Ó

1.0 . •1.00.00.00.0

1.321.970.51.00.50.00.00.00.00.0

1.681.923.00.00.00.02.00.00.00.0

1.481.96

• 4.25Q.A1.250.00.01.03.0

1.481.962.53.02.00.00.01.5

1 0.115

0.00.00.50.01.52.0

PAGE 2

1.0100

1.753.504.750.00.00.01.53.50.115

- o.o0.00.00.00.01.5r.5.2.0 :

1.0100

0.0• 0.0

2.00.00.03.52.011.5

0.752.00.03.50.00.02,752.00.115

0.00.00.250.00.02.753.02.01.0100

0.00.00.02.00.02.02.010.0

0.00.00.01.01.02.02.00.115

0.750.0

• 1 . 2 5

0.03.02.011.01.0100

0.01.01.00.03.02.0

- 109 -

Wo

oo

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cg

o- I

O C3 O O O O O O O O O O 3 O 3 O O O O O O O O O O O O O O O 300000000000000000000000000000000000000000000000000000000000000

- 11Q -

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEH a CYCLES 1 TO 11 CORE DESCRIPTION BY FEW REGIONS

PAGE 2

NÚCLEO CON 69 ELEMENTOS K-INF.EOC = .000000 POTENCIA NOMINAL = 510.00 MwT

ESTADO AL FINAL DEL ULTIMO CICLO (CICLO 3)

LOTE

AOBODOEAOEQ

NO.ELEMENTOS

131

201223

ENR INIC-

2.4302.9003.6002.900 .'3.600 .

KG U-INIC

266,200266.200257.800259.000

, 260.600

CICLOS

22211

QUEMADO EOC

27090.0024039.0017580.0010090.008120.00

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2 PAGE 3

SAMPLE PROBLEM 2 CYCLES 4 TO 11 CORE DESCRIPTION BY FEW REGIONS

CICLO 4 . ••• •

OPCIÓN 0 QUEMADO DEL CICLO =11300.00 5 SUBLOTES

ADVERTENCIA = EL SUBLOTE DO TIENE AHORA SOLO 16 ELEMENTOS CUANDO ANTES TENIA 20LÁ DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

ADVERTENCIA = EL SUBLOTE EO TIENE AHORA SOLO 8 ELEMENTOS CUANDO ANTES TENIA 23LA-DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

SUBLOTES CARGADOS EN ESTE. CICLO

10.LOTE IDENTIF. REGIÓN NO.ELEMENTOS ENR-INIC U-INIC BU-IMIC DB-INPUT

181215816

45678

T DIEAO

. EO.-,..W E l ••• -..•- FQ

12345

3.6002.9003.6003.6003.600

257.80259.00260.60260.60265.90

17580.10090.8120.8120.

0.

12700.000012725.000013105.00008520.00008435.0000

NA

00000

ALFAN

• .0000

.oono• oono

-1.5000-1.5000

FV-INPUT

.0000

.0000

.0000

.0000

.PO00

MATRIZ DE INTERCAMBIO ENTRE REGIONES .VECINAS

REGIÓN NR SUMA 1 2 3 4 5

12345

T DIEAOEO

W ElFO

NÚCLEO

1812158

16

69

• 18.0012.0015.008.0016.00

69.00

9.00ó.úO2.50.50.00

18.00

6.00.00

5.00.00

1.00

12.00

2.505.002.002.503.00

15.00

.50

.002.503.002.00

8.00

.001.003.002.0010.00

16.00

- üi -CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLE.M 2 •

SAMPLE-PROBLEM 2 • • CYCLES "i JO. 11 CORE DESCRIPTION BY FEW REGIOMS

PAGE

BALANCE DEL CICLO A EOC CICLO 4

1DENTIF ÑO. ENRIQ KG UISUBLOTE ELEM INIC. ELEM.

T DI . 18 3.600 257.80EAO 12 2.900 259.00EO 15 3.600 260.60

W El 8 3.600 260.60FO Í6 3.600 265.90

NÚCLEO 69 3.478 260.82

CICLOSANTI6.

T

• • 2 •

21

RÍBEOC)

QUEMADOINICIAL

17580.10090..8120.8120.

0.

8980.

DELTA-BCICLO

12700.12725.13105.

. S520.8435.

11300.

QUEMADOFINAL

30280.22315.21225.16640.8435.

20280.

K-INFEOC

1.01151.01781.08361.12411.2071

1.081521

1.086697

FRACCIÓNEMERGÍA

1.11091.11831.1588..7534.7610

1.0000

ABSORCIONES'EOC

1.09831.09871.0693.6702.6304

1.070736

1.075256

BALANCE DEL CICLO A EOC CICLO 4

IDENTIFSUBLOTE

DEA A

. EF

NÚCLEO '

NO.ELEM

18122316

ENRIQINIC.

KG UIELEM.

3.600 257.802.900 259.003.600 260.603.-600 265.90

CICLOSANTIG.

3221

69 3.478 260.82

QUEMADOINICIAL

17580.10090.8120.

0.

- 8980.

DELTA-BCICLO

12700.12725.11510.8435.

QUEMADOFINAL

30280.22815.19630.8435.

K-lNFEOC

1.0115•1.01781.09731.2071

FRACCIÓNENERGÍA

1.11091.11831.0178.7610

11300. •• 2028Q. 1.081521 1.0000

ABSORCIONES •EOC

1-09831.0937.9305 :.6304

1.070736 PESADO INVERS

PAGE 5CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEM 2 CYCLES 4 TO 11 CORE DESCRIPTION BY FEW REGIONS

•MEDIA 45. ELEMENTOS INTERIORES F-INT = 1.128821 FK-INT = 1.088738 FV-INT = 1.067869 A = 1.036816

CALCULO DE Vi EN LAS REGIONES INTERIORES CICLO 4

REGIÓN

T DIEAOEO

JUSTE

ALORES

NO EL.

,-.. la .•• 1 2 ..•

15

POR MÍNIMOS

PROMEDIOS

K-INF-EOC

1.0114831.0178391.08363d

CUADRADOS

OBTENIDOS

FRACC.ENERGÍA

111

W

w

.110898 0

.118266 0

.158774 0

= .115087

= .115173

ABSORCIONES F-VECINOS

111

.098286 1

.098666 1

.069337

K = 1.011044

K = 1.011025

•110072.101689.990170

N*Ü-ALFA)

.000000

.000000

.000000

W-CALC

•114669• H6007•115111

CALCULO DE LOS ALEEDOS EN LAS REGIONES PERIFÉRICAS (USANOO W = .115000 K = 1,011064 )

REGIÓN NO EL. K-INF-EOC FRACC.ENERGÍA ABSORCIONES F-VECINOS N*<1-ALFA) N-EXT ALFA

W ElFO

ti1 6

1.1241321.207107

.753358

.761011.670169.630442

•904310•856963

1.6761191.916582

-1.500000-1.500000

MEDIA DE LOS 24. ELEMENTOS EXTERIORESFRACCIÓN DE ENERGÍA = .758460 ABSORCIONES = .643684 F VECINOS = .872746

-.117412-.277722

FUGAS RADIALES = .055731

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROQLEM 2 PAGE 6

SAMPLE PROBLEM 2 CYCLES 4 TO H CORE DESCRIPTlON BY FEW REGIONS

CICLO 5

OPCIÓN 2 QUEMADO DEL CICLO =8065.00- 7 SU8L0TES

ADVERTENCIA = EL SUBLOTE EAO TIENE AHORA SOLO- • B ELEMENTOS CUANDO ANTES TENIA 12LA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

ADVERTENCIA = EL SUULOTE FO TIENE AHORA SOLO 4 ELEMENTOS CUANDO ANTES TENIA 16LA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

SUBLOTES CARGADOS EN ESTE CICLO

NO.LOTE

67891011

IDENTIF

LEA1EU

W ElFO

P FlGO

12 V Gl

1 82 15ó , 84 125 46 27 20

R-INIC •

2.9003.6003.600'3.6003.6003.0003.000

U-INIC

259.00260.60260.60265.90265.90267.60267.60

BU-INIC

22815.21225.16640», 8435.

• 8435.0.0.

DB-INPUT

1.00001.00001.00001.0000

•, 1.00001.00001.0000

NA

0000000

ALFAN

.0000

.0000

.0000

.00001.1900.0000

1.9800

FV-INPU

,000.000.000

.ono

.ono• .000

.ono

MATRIZ DE INTERCAMBIO ENTRE REGIONES VECINAS

REGIÓN NR SUMA

1234567

LEA1

w

p

V

EOElFOFlGOGl

815

. a1242

20

8,0015.008.00

, 12.004.002.00

2Ü.00

124

.00

.00

.00

.50

.00

.60

.00

1.002.005.004.50, .00 ..50

2.00

2.5.

•1.

•

00000000000000

44

3

.50

.50

.00

.00

.00,00.00

1

1

2

.00

.00

.00

.00

.00

.00

.00

.50

.50

.00

.00,00,00

1,00

.002.00.00

3.002.001.00

12.00

NÚCLEO 69 69.00 8.00 15.00 8.00 12.00 4.00 2.00 20.00

- 113 -

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2P<\GE 7

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 1 K-EFF = 1.044497

MEDIA 45, ELEMENTOS INTERIORESITERACIÓN 2 K-EFF = 1.026914

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 3 K-EFF = 1.021098

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 4 K-EFF = 1.017539

MEDIA 45. ELEMENTOS INTERIORESITERACIUN 5 K-EFF = 1.015942

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 6 K-EFF = 1.015027

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 7 K-EFF = 1.014611

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 8 K-EFF = 1.014367

MEDIA 45. ELEMENTOS INTERIORES •ITERACIÓN 9 K-EFF = 1.014262

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 10 K-EFF = 1.014192

MEDIA 45. ELEMENTOS 1NTERIORFS •ITERACIÓN 11 K-EFF = 1.01+165

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 12 K-EFF = 1.014145

F-INT = 1.000000 FK-INT = .957398 FV-INT = 1.000000ITER INT = 30 DIFMAX = .313516 SUMA F = .947594

F-INT = 1.068700 FK-INT = 1.020986 FV-INT = 1.024710ITER INT = 30 DIFMAX = .148129 SUMA F = .973616

F-INT = 1.089484 FK-INT = 1.046278 FV-INT = 1.043545ITER INT = 28 DIFMAX = .060174 SUMA F = .987796

F-INT = 1.107059 FK-INT = 1.062295 FV-INT = 1.050251ITER INT = 26 DIFMAX = .043119 SUMA F = .992678

F-INT = 1.112265 FK-INT = 1.069133 FV-INT = 1.055552ITER INT = 24 DIFMAX = .023436 SUMA F = .996942

F-INT = 1.117298 FK-INT = 1.073492 FV-INT = 1.057136ITER INT = 22 DIFMAX = .015530 SUMA F = .997969

F-INT = 1.118408 FK-INT = 1.075221 FV-INT = 1.058675ITER INT = 20 DIFMAX = .008978 SUMA F = .999283

F-INT = 1.119914 FK-INT = 1.076429 FV-INT = 1.059002ITER INT = 18 DIFMAX = .005996 SUMA F = .999411

F-INT = 1.120084 FK-INT = 1.076843 FV-INT = 1.059469ITER INT = 18 DIFMAX = .003510 SUMA F = .999848

F-INT = 1.120572 FK-INT = 1.077200 FV-INT = 1.059520ITER INT = 13 DIFMAX = .002348 SUMA F = .999835

F-INT = 1.120575 FK-INT = 1.077299 FV-INT = 1.059670ITER INT = 13 DIFMAX = .001288 SUMA F = .999950

F-INT = 1.120731 FK-INT = 1.077406 ^V-INT = 1.059675ITER INT = 12 DIFMAX = .000796 SUMA F = .999960

A =

A =

A =

A =

A =

A =

A =

A =

A =

A =

A —

1.044497 •

1.046734

1.041295

1.042138

1.040343

1.040807

1.Q40166 ;

1.04039B i1 :

1.040156! 1C i

1

1.040263 I

1.040171

1.040213

ITERACIÓN 1 ENR O QUEMADO = 8065.000 K-INF O K-EFF = 1.014145 VALOR BUSCADO = 1,010000

MEDIA 45* ELEMENTOS INTERIORESITERACIÓN 1 K-EFF = 1.010416

MEDIA 45. ELEMENTOS INTERIORES--.ITERACIÓN 2 K-EFF = 1.010472

F-INT = 1.120715 FK-INT = 1.081392 FV-INT = 1.059716 AITER INT = 11 DIFMAX = .002507 SUMA F = 1.000142

F-INT = 1.120517 FK-INT = 1.081201 FV-INT = 1.059660 AITER INT = 8 DIFMAX = .000509 SUMA F = 1.000050

1.036364

1.036364

ITERACIÓN 2 ENR O UUEMAOO = 8479.480 K-lNF O K-EFF = 1.010472 VALOR BUSCADO = 1.010000

MEDIA 45. ELEMENTOS INTERIORESITERACIÓN 1 K-EFF = 1.010006

F-INT = 1.120480 FK-INT = 1.081664 FV-INT = 1.059625 A = 1.035886ITER IMT = 8 DIFMAX = .000436 SUMA F = 1.000042

ITERACIÓN 3 ENR O QUEMADO = 6532.755 K-INF O K-EFF = 1.010006 VALOR BUSCADO = 1.010000

CICL0N-2 PhlNTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROQLEM 2 CYCLES 4 TO 11 CORE DESCRIPUON BY FEW REGIONS

PAGE 8

IDENTIFSUDLOTE

LEA1EO

V. ElFO

P Fl60

V Gl

NÚCLEO

NO.ELEK

a15a1242

20

69

1

BALANCE DEL CICLO

ENRIQ1NIC.

2.9003.6003.6003.6003.6003.0003.000

3.328

.077775

Kü UIELEM.

259.00260.60260.60265.902o5.902t»7.60¿b7.60

263.88

CICLOSANT1G.

3. '.. 3

32211

K-lNF(ENRfBEOC)

A EOC

QUEMADOINICIAL

22815.21225.16640.8435.8435.

0.0.

11030.

CICLO 5

DELTA-BCICLO

8909.. .9405.

9629.10255.6942.10282.6438.

8533.

QUEMADOFINAL

31724.30630.26269.18690.15377.10282.6438.

19562.

. . . . . , • •

K-INFEOC

.9472•1.00891.04261.10551.13601.14401.1897

1.079452

1.086154

FRACCIÓNENERGÍA

1.02481.08851.11441.2111.8198

1.2220.7651

1.0000*

• • • - • • • • ' . • •

ABSORCIONESEOC

1.08191.07891.06891.0954.721.6

1.0681-.6431

1.071080

1.077202

• .

PESADO INVF1?

PESADO DTREC

BALANCE DEL CICLO A EOC CICLO 5

IDENTIFSUBLOTE

EAEF6

NO.ELEM

a231622

ENRIQIN1C.

Kti UIELEM.

2.900 259.003.600 2D0.603.600 2b5.903.ÜÜ0 2u7.6Ü

CICLOSANT1G.

332

. 1

QUEMADOINICIAL

22815.19630.8435.

0.

DELTA-BCICLO

8909.9483.9427.6787.

QUEMADOFINAL

31724.29113.17862.6787.

K-INFEOC

.94721.02031.11301.1654

FRACCIÓNEMERGÍA

1.02481,09751.1132.8067

ABSORCIONESEOC

1.08191.075'+1.0020»6818

NÚCLEO 69 3.328 263.88 11030. 8533. 19562. 1.079452 1.0000 1.071080 PESADO INVERS

CICL0N-2 PRINTED OUTPUT..FKOMSAMPLE PROBLEM 2

SAMPLE PROBLEM 2 • CYCLES 4 TO U CORE DESCRIPUON BY FEW REGIONS

.P.AGE 12

BALANCE DEL CICLO A EOC CICLO 6

IDENTIFSUBLOTE

EAOn ElFO

P FlGO

V Gl 'T G2HO

NÚCLEO

NO.ELEM

48124215519

69

1.

ENRIQI1MIC.

2.9003.6003.Ó0Ü3.6003.0003.ÜO03.Ü003.350

3.299

Ü80352

KÜ UIELEM.

259.002b0.602b5.902o5.902b7.602ü7.602o7.60267.60

265.90

CICLOSANTIG.

34332221

K-INF(ENR»BEOC)

QUEMADOINICIAL

22815.26269.18690.15377,10282.6438.6438.

ü.

10593.

DELTA-BCICLO

8694.. 9148.'

9361.9878.9659.9648.6685.6602.

8441.

QUEMADOFINAL

31509.35416.28051.25255.19941.16006»13123. .6602.

19034.

K-INFEOC

. .9489.9755

1.02851.05071.01*871.08411.11351.2126

1.081606

1.088541

FRACCIÓNENERGÍA

1.00331.06221,10901.17031.15171.1504.7971.7871

1.0000

ABSORCIONESEOC

1.05731.08881.07831.11381.09821.0611.7158.6492

1.072071

1.078230

PESADO INVEr?S

PFSADO DlRrCl

BALANCE DEL CICLO A EOC CICLO ó

IDENTIF NO. EIMKIQ KG UI CICLOS QUEMADO DELTA-B QUEMADOSUBLOTE ELEM INIC ELEM. ANTIG. INICIAL CICLO FINAL

EAEF6H

NÚCLEO

48162219

69

900600600

3.0003.350

233

259.00260.60265.902b7.60267.60

34321

3.299 265.90

22815,26269.17862.6787.• 0.

10593.

8694.9148,9490.8976.6602.

8441.

31509.35416.27352.15763.6óÜ2«

19034.

K-INFEOC

.9489

.97551.03401.08721.2126

1.081606

FRACCIÓNENERGÍA

1.1.1.1.

0033062212440702.7871

1.0000

ABSORCIONESEOC

1.1.1.

05730888087298606492

I

1.072071 PESADO INVFRS

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEM 2 CYCLES• H'. TO 11 CORE DESCRIPTION BY FEW REGIONS

PAGE 16

IDENTIFSUBLOTE

L FlP Fl

GOV G l -•T G 2 ••

HO •S HlJO

NÚCLEO

NO.ELEM

64 .2

. 15511a16

• 69

BALANCE DEL CICLO

ENRIQINIC.

3.600. 3.6003.0003.0003.0003.3503.3503.250

3.259

KG UIELEM.

2o5.90265.902b7.602b7.60267.60267.60267.602o7.60

267.30

CICLOSANTIG.

44333

••. 2

21

A EOC

QUEMADOINICIAL

28051.25255.19941.16086.13123.6602.6602.

0.

11543.

CICLO 7

DELTA-BCICLO

7330»7657,7014.'7638.8065.8702.5904.5726.

7153.

QUEMADOFINAL

35381.33112.26955.23724.21188.15304.12506.5726.

18695.

K-INF' 1EOC

.9758

.9911

.99081.01621.03771.11871.14651.2167

1.081620

FRACCIÓNENERGÍA

1.01941.0927.9817

1.06911.12881.2180.8264.8014

1.0000

ABSORCIONESEOC '

1.04471.1024.9909

1.0520: 1.0878

1.0888.7208.6586

1.073942

1,080326 K-ÍNF(ENRi 1.0.88822 1.080513 PESADO DlRcTC"

BALANCE DEL CICLO A EOC CICLO 7

IDENTIFSUBLOTE

FG ;

HJ

NO.ELEM

12221916

ENRIQINIC.

KG UIELEM.

3.600 265.903.000 2b7.603.350 267.603.250 267.60

CICLOSANTIG.

4321

QUEMADO DELTA-BINICIAL': CICLO

. 27119.15763.6602.

0.

7506.7678.7524.5726.

QUEMADOFINAL

34624.• 23441.14126.5726.

K-INFEOC

.9808 •1.01851.13021.2167

FRACCIÓNENERGÍA

0438074705318014

ABSORCIONESEOC

1.06401.0546.9338.6586

1

en1

NÚCLEO 69 3.259 267.30 . 11543. 7153, 18695. 1.081620 1.0000 1.073942 PESADO IMVER5

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEM 2 • CYCLES 4 TO ll CORE DESCRIPTlON.BY FEW REGIÓOS

PAGE 20

IDENTIFSUBLüTE

0 G2T G2HO

S HlJO

P JlKO '

NÚCLEO

' NO.ELEM

115

11

a106la

69

1

BALANCE DEL

ENRIQiNlCt

•: 3.000. 3.0003.350

, 3.3503.2503.2503.250

3.220

.060097

CICLO

K6 UI CICLOSELEM. ANTIG.

267.60267.60267.602b7.60267.602b7.60267.60

267.60

K-INF(£NRi

4433221

rBEOC)

A EOC

QUEMADOINICIAL

23724.21188.15304. .12506.5726.5726.

0.

10535.

CICLO 8

DELTA-BCICLO

7943.8220.8819. ••

8984.9287.6512.6202.

7840.

QUEMADOFINAL

31667.•> 29408.• 24122.

21490.15013.12237.6202.

18374.

.K-INFEOC

.9579

.97301.04061.06261.11411.14211.2107

1.081184

1.088917

FRACCIÓNENERGÍA

1.01321.04861.12491.14601.1846.8306.7911

1.0000

ABSORCIONESEOC

1.05781.0776

-•1,0810 •1.07851.0633 ..7273.6534

1.073072

1.080079

PESADO -I.NVER

PESADO DIREC

BALANCE DEL CICLO A EOC CICLO 8

1UENTIFSUBLOTE

GHj :K. '

NO.ELEM

16191618

ENRIQINIC.

KG UIELEM.

3.000 267.603.350 2u7.603.250 267.603.250 2b7.60

CICLOSANTIG.

4: 3

21

QUEMADOINICIAL

22931.14126.5726.

0.

DELTA-BCICLO

8030.8888,8246.6202.

QUEMADOFINAL

30961.23014»13972.6202.

K-ÍNFEOC

.96251.04971.12441.2107

FRACCIÓNENERGÍA

1.02421.13381.0519.7911

ABSORCIONESEOC

1.06401.0800.9373.6534

i

I

NÚCLEO 69 3.220 267.60 10535. 7840. 18374- 1.08118" 1.0000 1,073072 PESADO INVER

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEM 2 CYCLES 4 TO 11 CORE DESCRIPTION BY FEW REGIONS

PAGE 2M-

IUENTIFSU8L0TE

K HlS HlJO

P JlKÜ '

H Kl .LO

NÚCLEO

NO.ELEM

98106126ia

69

1.

• BALANCE DEL CICLO

ENRIQINIC

3.3503.3503.2503.2503.2bO3.2503.250

3.275

076811

Kü UIELEM.

2o7.60267.602o7.60267.602b7.60267.60267.60

267.60

CICLOSANTIG.

4433221

K-1NF(ENR»BEOC>

A EOC

QUEMADOINICIAL

24122,21490,15013.12237.6202.6202.

0.

10496.

CICLO 9

DELTA-B••... C I C L O .-•-•

9077.8996,9375,9918.10027,6854.6574,

8503.

QUEMADOFINAL.

33200.30486.243Ü8.22155.16230.13066.6574.

18999.

K-INFEOC .

,9743' '•,9925

1.03081.04931.10241.13361.2062

1.081181

1.087730

FRACCIÓN•ENERGÍA-

••• •• 1 . 0 6 7 6 '

1.05801.10251.16641.1793.8060.7731

1.0000

ABSORCIONESEOC

1.09571.0660- .1 . 0 6 9 6 " •1 . 1 1 1 5 •;1 . 0 6 9 7 ••••

.7110

.6410

1.071489

1.077364

BALANCE DEL CICLO A EOC CICLO 9

PESADO

IÜENTIFSUBLOTE

HJK :

L

NÚCLEO

NO.ELEM

17161818 .;

69 •

ENRIQINIC.

3.3503.2503.2503.250

3.275

Kb UIELEM.

267.60267.60267.60267.60

2u7.60

CICLOSANTIG.

432i :

. QUEMADOINICIAL

22884.13972.6202.

0.

10496.

.DELTA-BCICLO

9039.9579,8969.6574.

• 8503.

QUEMADO .FINAL ;'

31923.23550.15172.

• 6574.

18999.

K-INFEOC

.98271.03761.11251.2062

1.08118

FRACCIÓNENERGÍA '

1.06311.12651.0549.7731

.". 1.0000

ABSORCIONESEOC

1.0S171.0854.9502.6410

1.071489

I-I

C»

PESADO INVEF

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEM 2 CyCLES 4 TO 11 CORE DESCRlPTlON BY FEW REGIONS

PAGE 28

BALANCE DEL CICLO A EOC

IDENTIF NO. ENRIQ Kb UI CICLOS QUEMADOSULsLOTE ELEM INIC, ELEM. ANTIG. INICIAL

CICLO 10

J JlP Jl

KOR Kl

LO 'R Ll •

MO

NÚCLEO

9612ó12618

3.2503.2503. ¿503.2503.2503.2503.250

257.60267.60267.602D7.60

2b7.60267.60267.60

4433221

24388.22155.16230.13056,6574.6574.

0.

69 3.250 267.60 10780.

1.079533 K-INFÍENRrBEOC)

DELTA-BCICLO

8243.8441.8675.9001.9400.6485.6251.

7930.

QUEMADOFINAL

32631.30595*24905.22057.15974.'.13059.6251.

18710.

K-INFEOC

.9706

.93431.02661.05021..1C481.13361.2101

FRACCIÓNEMERGÍA

1.03951.06441.09401.13511.1854.8177.7882

1.081513 1.0000

1.038454 • • •

ABSORCIONESEOC

1.07101.08141.06571.08091.0729.7214.6513

•'1.072624

1.078692

PFSADO INVEHÍ

PESADO DIRFCI

BALANCE DEL CICLO A EOC CICLO 10

IDENTIF NO. ENRIQ KG UI CICLOS QUEMADO DELTA-B QUEMADOSUOLOTE ELEM INIC. ELEM. ANTIG. INICIAL CICLO FINAL

JKL :

M

NÚCLEO

15Id1818

69

3.250 267.60 4 23495. • 8322.3.250 2b7.ó0 3 15172. 8784.3.250 267.60 2 6574. 8428.3.250 267.60 1 0. 6251o

3.250 2b7.60 • 10780. 7930.

31817*23956.15002.6251.

K-INFEOC

.97601.03431.11421.2101

FRACCIÓNENERGÍA

1.04951.10771.0629.7882

i

18710. 1.081513 1.0000

ABSORCIONES•-• E O C

1.07511.0708.9557.6513

1.072624 PESADO IMVF.Rí

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2 ,

SAMPLE PROBLEM 2 CYCLES 4 TO 11 COFíE. DESCRIPTION BY FEW REGIONS

PAGE 32

IDENTIFSUBLOTE

L Kl .R Kl

LOR Ll

HOR Mi '

PO .

NÚCLEO

IDENTIFSUBLOTE

KLMP

NÚCLEO

NO.ELEM

9612612618

69

1.

NO.ELEM

1518 :1818

69

BALANCE DEL CICLO

ENRIQIN1C.

3.2503.2503.2503.2503.2503.2503.250

3.250

079275

KG UIELEM.

267.60267.602b7.60267.60267.60257.60267.60

267.60

CICLOSANTIG.

4433221

K-1NF(ENR»BEOC)

BALANCE DEL CICLO

ENRIQINIC.

3.2503.2503.2503.250

3.250

KG ulEuEM.

257.60¿o7.602o7.602b7.60

267.60

CICLOSANTIG.

4"X ' . •\J >

21

A EOC

QUEMADOINICIAL

24905.22057.15974.13059.6251.6251.

0.

10711.

A EOC

QUEMADOINICIAL

23766.15002.6251.

0.

10711.

CICLO 11

DELTA-BCICLO

8281.8549.8788.9082.9551.6603.6331.

8028.

QUEMADOFINAL

33186.30606.24762.22140.15801.12854.6331.

•••.. 1 8 7 3 9 .

CICLO 11

DELTA-BCICLO

8388.8886.8568.6331.

8028.

QUEMADOFINAL

32154.23888.14819.6331.

18739.

K-INF FRACCIÓN •'EOC ENERGÍA

.9671

.98421.02771.04951.10651.13571.2091

1.081313

1.088329

K~INF 1EOC

.97381.03481.11601.2091

1.081313

1.03151.U6491.09461.13121.1896.8225.7886

1.0000

; • • • • • • • • •

FRACCIÓNEMERGÍA

1.04481.10681.0672.7886

1.0000 •-,•

ABSORCIONESEOC

1.06661.08201.06511.07791.0751.7242

. .6522

1.072663

1.079009 '

ABSORCIONESEOC

1.07271.0693.9582.6522

1.072663

PESADO INVERSi

•• PESADO DIRFCTi

iH-toO|

PESADO INVEPS

CICL0N-2 PKINTED OUTPUT FHOM SAMPLE PROBLEM 2

SAMPLE PK03LEM 2 CYCLES 4 TO 11 CORE DESCRIPTION BY FEW REGlONS

PASE 31

INCREMENTOS ÜE QUEMADO POR LOTE EN CICLOS SUCESIVOS

SUBLOTE NO.EL W/O I K6 UI BU INIC CICLO 4 CICLO 5 CICLO 6 CICLO 7 CICLO 8 CICLO 9 ClCLOlO CICLO11

AOBODO

T DIEAO

LEAlEü

to ElFO

L FlP Fl

GOV GlO G2T G2

HOK hlS HlJO

J JlP ül

KOL KlH Kl

LOR Ll

MOR MI• P O

1312IB4815

a4. a42411529a1963.•96126126

la

2.4302.900

600DÜO900900

3.6003.6003.6003.6003.600

000000Ü00000

3.3503.3503.3bO3.2^03.2503.2bO3.2503.2503.2503.2503.2503.2503.2503.250

266.20266.202D7.Ü0257.80259.ÜO259.002bO.6O260.602o5.90265.90265.902b7.60267.602t>7.60267.60267.602b7.602to7.602o7.602o7.60267.602t>7.óO267.60267.60267.60267.60267.60267.602O7.60

QUEMADO DEL CICLO (MWü/MTU)

MASA TOTAL DE U INIC (MTU)

ÜURACION ÜEL CICLO (EFPD)

27090.24039.17580.17580.10090.10090.8120,8120.

0.0.0.0.0.0.0.0.0.0.0.

: 0.Ú.0.0.0.0.0.0.0.0.

0.

.000

.00

o.o»o.

12700.12725.12725.13105.8520.8435.8435.8435.

0.0.0.0.0.0.0.0.0.0.0.0.

: •• • 0 •

o.0.

.-. . 'o»-o.

11300.

17.997

398.75

0.0.0.

¡.... 0.• o .8909.

.•9405.9629.10255.10255.6942.102Q2.6438.6438.6438.

0.0.0.0.0.0.0.0.0.0.0.0.

• • .-,••• o .

• .• • • o.

8533.

18.207

304.63

0.0.0*

• . 0.8694.

0.0.

•9148.9361.9361.9878.9659.9648.9648.6685.6602.6602.6602.

0.0.0.0.0.0.0.

• • .• • 0 . •

0.0.0.

. 8441.

18.347

303.65

0.0.0.

. 0.• ••• o.

0.0.0.

• o .

7330.7357.7014.7638.7638.8065.8702.8702.5904.5726.5726.5726.

0.0.0.0.0.0.0.

• . .• 0 .

7153.

18.444

258.67

C.0 .0 .0 .

• 0 .• • • • • • o .

0 .0 .0 .0 .0 .

o .0.

7943.8220.8819.8819.8984.9287.9287.6512.6?02.6202.6202.

0.0.0.0.0.

7840.

18.464

283.83

0.0.0.0.0.0.

. 0.0.0.0.0.0.0.0.0.0.

9077.8996.9375.9375.9918.10027.10027.6854.6574.6574.

0.0.0.

8503.

18.464

307.85

0.0.0..0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

8243.8441.8675.8675.9001.9400.6485.6251.6251.

0.

7930.

j8.464

287.10

0.0.0.0.0.0.0.0.0.0.

I °*0.

i o.1. • o.0.0.0.0.0.0.0.0.

8281.8549.8788.9082.9551.6603.6331.

8028.

18.«64

290.66

CICL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEM 2 CYCLES 4 TO 11 CORE DESCRIPTION BY FEW REGIONS

SUMARIO DE LA DESCARGA .. . .: . ••• ... . •••

PAGE 35

IÜENTIFSUELOTE

AObODO

T DI-EAOLEA1EO

W ElFO

L FlP Fl

GOV Glü G2T G2HO

K HlS Hl

JOJ JlP JlKO

NO.£LEM

131

• . 2 •

, la4 •01584842 .411529ai9ó3

ENRIQIN1C.

2.4302.9003.60 03.60 0~2.9002.9003.6003.6003.6003.6003.60 0

. 3.000'3 . ü 0 03.ÜÜ03.0003. 3503.3503.3503.250

. 3*2503.2503.250

KG UITOTAL

3460.60266.20515.60

4640.401036.002072.003909.0020d4.b01063.602127.201063.60535.20

1070.402943.601338.00535.20

2406.40¿140.60267.60

240b.401605.60802.80

CICLODESCARGA

3. 33465566777

' 7 - .888999101010

CICLOSPERMAN,

2223333434433443443443

. •QUEMADO•••DESCARGA

! 27090.24039.17580.30200.31509.31724.30630.35416.28051.35381.33112.26955.23724.31667.29408.24122.33200.30486.24388.32631.30595.24905.

U RESIDUAL(UF/UI)

.9633

.9670

.9751

.9592

.9580

.9578

.9585

.9468

.9624

.9469

.9531

.9634

.9673

.9578

.9605

.9669..•• .9559

.9591

.°C65

.9566

.9590

.9659

EMRIQ.DESCARGA

.6668 "1.05162.00311.2301.7330.7253

1.2124.9891

1.3474.9906

1.0922.9846

1.1426.7873.8768

1.3772.9331

1.05081.2882.8962.9818

1.2602

PU FIS..ÍKG/MTU)

•' .5.95295.86165.22036.548g6.37396.38326.57136.8260.6.40106.82456.71516.124a5.86036.42116.30035.96986.62536.48935.97226.56186.46066.0165

I

I .

CICL0N-2 PKINTED OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEM 2 CYCLES 4 TO U CORE DESCRIP.JION BY FEW REGlONS

*** BALANCE POR LOTES DE IGUAL CICLO DE CARGA Y DESCARGA ***

INCREMENTOS DE QUEMADO POR LOTE EN CICLOS SUCESIVOS

PAGE 3 6

SUBLOTE

A2*03U2*0302*03D3 + Ü4 ,

EA3*üó .EA3*Ü5E3 + 05E4*üóF3*üóF4*07 .G3*07G4*08H3*Ü8H4*Ü9J3*Ü9J4*10K3*1ÜK4*00L3*00M2*Ü0Pl + UO

QUEMADO

NO.EL W/0

1312 -10. 4& .

. 15ü

' 412616

• 2

171

153

15ia18lü

2.4302.9003.6003.6002.9002.9003.6003.6003.6003.6003.0003.0003.3503.3503.2503.250•3.2503.2503.¿bO3.2503.250

I KG UI

2o6.20266.20257.80257.60259.00259.00260.602o0.602o5.90265.90267.bO267.602O7.60267.602o7.60267.602Ü7.60267.60267.60267.602b7.6Q

DEL CICLO (MWD/MTU)

MASA TOTAL DE

DURACIÓN DEL<

U INIC

:ICLO

(MTU)

(EFPD)

BU INIC

27090.24039.17580.17580.1Ü090.10090.8120.8120.

0.0.0.0.0.0.0.0.

•••• •:".••.•.' 0 . .

... 0.0.0.0.

0.

.000

.00

CICLO 4

0.

o.o.

. 12700.' 12725.12725.13105.8520.8435.8435.

o.o.o.o.o.o. .

. . • • o . •••

' o . •

0.o.o.

11300.

17.997

398.75

CICLO 5

0.0.0.0.0.

8909.9405.9629.10255.9151.7719.6438.

0.0.0.0.

.• • 0 .

0.• 0 .

0.0.

8533.

18.207

304.63

CICLO 6

0.0.

- 0.

. ;,.\ . o.8694.

0.0.

9148.9361.9533.

• 9652.8722.6602.6602.

0.0.

••• • • 0 .

o.0.0.0.

8441.

18,347 .

303.65 .

CICLO 7

0.0.

•-0.•:'• •• 0 .

0.0.0.0.0.

7506.7430.7772.8702.7385.5726.5726.

0.0.0.0.0.

7153.

• 18.444

258.67

CICLO 8

0.0. .

- . .-•:.•' • 0 ¿ :

• • • ' • " • - • • ' 0 • '

0.0.0.0.0.0.

o.8030.8819.8897.

:••••. 9 2 8 7 .

•8177.•• • 6 2 0 2 . •

6202.0.0.0.

7840.

18.464

• 283.83

CICLO 9

•-••• o .

0.. • ' • • • • o . .

• • ' ' • • • • • • • o . ' •

o.0.0.0.0.0.0.0.

• • • • o . ••

9039.9375.959?.

10027.• • -875fl.

6574.

o,.0.

8503.

18.464

307.05

CICLO10

o'.o'.0.0.0.

o'.0.0.0.

o.0.

• o.o.0.0.

8322.8675.

:: 8806.B428.6251.

0.

7930.

18.464

287.10

CICLO11

0.0.0.0.0.0.0.0.0.0.0.

•••• • o .

• o .

0.0.0.0.

8388.RB86.8568.6331.

8028.

18.464

290.66

I

CICLON-2 PKINTEÜ OUTPUT FROM SAMPLE PROBLEM 2

SAMPLE PROBLEM 2 CYCLES 4 TO 11 CORE Í)ESCRIPTION BY FEW REGIONS

PAGE 37

*** BALANCE POR LOTES DE IGUAL CICLO-DE'CARGA Y DESCARGA ***

SUMARIO DE LA DESCARGA

IÜENTIF NO. ENRIQSUBLOTE •ELEM INIC

KG UI CICLO : CICLOSTOTAL DESCARGA PERMAN.

A2*03B2*03D2*03D5*04

EA3*06EA3*05E3*Ü5£4*06F3 + Ü6F4*07(¿3*07G4*0tiH3*08H4*09J3 + Ü9J4*1ÜK3*10K4*0 0L3+00M2*üüP1*ÜO

1312 ..1848158412616217115315181618

2.4302.9003.6ÜÜ3.6002.9002.9003.6003.6003.6003.6003.Ü00

, 3.000. 3.3503.3503.2503,2503.¿503.2503.2503.250

. 3.250

3460.60• 266.20

515.604640.401036.002072.003909.00¿084.6010o3.603190.801605.DO42til.6O535.20

4549.20267.60

4014.00802.60

4014.004816.804816.804816.80

. 333465566778a9910100000

22233334~S434343434321

QUEMADO U RESIDUAL ENRIQ. PU FIS.DESCARGA (UF/UI) DESCARGA :(KG/MTU)

27090.24039.17580.30280.3J.509.31724.30630.35416.28051.34624.24801.30.961.24122.31923.24388.31017.24905»32154.23888.14819.6331.

.9633

.9670«9751,9592.9580.9578.9585.9468.9624.9490.9660.9586.9669.9575.9665.0t:76.9659.9659.9659.9659.9659

.6668'1.05162.00311.2301.7330.72531.2124.9891

1.34741.02451.0899.8153

1.3772.98851.2882.9305

1.26021.26021.26021.26021.2602

. 5.95295.86165.22036.54896.3739•6.38326.57136.82606.40106.78805.94856.38345.96986.56135.97226.52136.01656.01656.01656.01656.0165

C I C L 0 N - 2 P R I N T E D O U T P U T F R O M S A M P L E P R O B L E M 2 ' • ••• •.••• •,._ = ....

SAMPLE PR08LEM 2 CYCLES 4 TO 11 CORE DESCRIPTION BY FEW REGIONS •••••••

*** BALANCE POR LOTE DE DESCARGA ***

: SUMARIO DE LA DESCARGA' \ ••

PAGE 38

IDENTIFSUBLOTE

030405060708091011

NO.ELEM

1618231618iala180

ENRIQINIC.

2.6023.6003.3573.4273.3993.0393.3443.250.000

KG UITOTAL

4242.404640.4059dl.004184.404796.404816.804816.áO4316.bO

.00

CICLODESCARGA

3456789

1011

CICLOSPERMAN.

345ó7a9

10ii

QUEMADODESCARGA

25743.30280.31009,32577.31336.30201.31504.30665.

0.

U RESIDUAL(UF/UI)

.9650

.9592

.9582

.9535

.9547

.9596

.9580

.9590

.0000

ENRIQ.DESCARGA

.85331.23011.04361.01671.0464.8777

1.0051.9854.0000

PU FIS.(KG/MTU)

5.85026.54396.50616.60606.50706.33746.52866.4372.0000

I

Cn

I

ENERGÍAS RELATIVAS EN CADA CICLO DE LOS LOTES DE DESCARGA

LOTE34567tí91011

NO.EL16ia2316181818180

CICLO 325743.17580.8ÍJÜ2.6544.

0.0.0.0.0.

CICLO 4.0000

1.11091.1447.6465.5073.0000.0000.0000.0000

CICLO 5.0000.0000

1.0664.8600

1.0262.6801.0000.0000.0000

CICLO 6• 0000• 0000.0000

' 1.05921.13661.0119.7434• 0000.0000

CICLO 7

111

.0000

.0000

.0000

.0000

.0425

.1022

.0208

.6678

.0000

CICLO 8

*

•1.1.1.

• ' •

000000000000000000000354137600100000

CICLO 9.0000.0000

: • .0000.0000.0000.0000

1.06531.1366..0000

CICLO 10.0000.0000.0000.0000.0000.0000.00 00 •

, '1.0569 •• • .0000

CICLO 11.0000.0000.0000.0000.0000.0000• 0000.0000.0000

- 126 -

CICLON-2

QDATArL 7

00000100000200000300QQ04000005000006000007

oooooa00000900001000001100001200001300001400001500001600001700001800001900002000002100Ú02200002300002400002500002600002700002800002900003000003100003200003300003400003500003600003700003800003900004000004100004200004300004400004500004600004700004800004900005000U05100005200U05300005400005500005600005700005800005900006Ü000061000062000063

PUNCHED OUTPUT

•

13169

27090.3

24039.• • • • : 3

17580.3

17580.3

10090.. .. 3 .

10090.3

8120.. 3

8120.4 -

.,-8435.4

8435.5 -

7719. ' -. 5

6438.6

6602.6.

. 6602.7

5726.7

5726.8

6202.8

6202.9-

6574.10

6251.11

6331.

FROM

327090.

324039.

317580.

430280.12700.

631509.12725.

531724.12725.

530630.13105.

• 6

35416.8520.

628051.10255.

734624.9151.

724801.9652.

830961.8722.

824122.8702.

931923.7385.

924388.9287.

1031817.8177.

1024905.10027.

1132154.8756.

1123888.8426.

1114819.8568.

116331.

SAMPLE PROBLEM 2 •

1

1

1

3

1

1

1

- 1

1

1

2

2

2

2

2

2

3

3

3

3

4

13,4606

1.2662

1-.5156

Z4.6404

41.0360

0.•• 3

2.07208909.

33.90909405.

• 4 •

2.08489629.

31.06369361.

43.19089533.

31.60567430. .-

44.28167772.

3 ••'

.53528819.

44.54928897.

3.26769375.

44.01409592.

3.80288b75.

44.01408806.

34.81688886. •

24.8166

14.8168

2.4300

2.9000

3.6000

3.6000

2.90008694.

2.9QQ0;

3.6000

3.6Q009148.

3.6000

3.60007506.

3.0000

3.00008030.

3.3500

3.35009039.

3.2500

3.25008322.

3.2500

3.25008388.

3.2500

3.2500

3.2500

.9633

.9670

.9751

.9592

.9580

.9578

.9585

.9468

.9624

.9490

.9660

.9586

.9669

.9575

.9665

.9576

.9659

.9659

.9659

.9659

.9659

.6668

1.0516

2.0031

1.2301

•' .7330

• .7253

1.2124

.9891

1.3474

1.0245

1.0899

.8153

1.3772

• 9885

1.2882

.9305

1.2602

1.2602

1.2602

1.2602

1.2602

PAGE 1

-5.9529

-5.8616

-5.2203

-6.5489

-6.3739

-6.3832

-6.5713

-6.8260

-6.4010

-6.7880

-5.9485

-6.3834

-5.9698

-6.5613

-5.9722

-6.5213

-6.0165

-6.0165

-6.0165

-6.0165

-6.0165

A2*03A2*03

B2*03B2*03

D2*03D2*03

D3*04D3*04

EA3*06EA3*06

EA3*05EA3*05

E3*05E3*05

E4*06E4*06

F3*06F3*06

F4*07F4*07

G3*0763*07

G4*08G4*08

H3*08H3*08

H4*09H4*09

J3*0vJ3*09

J4*10J4*10

K3*10K3*10

K4*00K4*00

L3*00L3*00

M2*00M2*00

Pl*00

Pl*00

- 127 -

CICLON-2 INPUT DATA FOR SAMPLE PROüLEM 3 PAGE 1

UÜÜOÜ1O0OÚ02000003000004000005000006000007oooooa00000 .'000010000011000012000013000014000015000016000017000018000019000020000021000022000023000024000025000026000027000028000029000030000031000032-00003300003400003500003600003700003a000039000040000041000042000043000044000045000046000047000043000049000050000051000052000053000054000055000056000057000053000059000060

000000000000000000000000000OúO000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

SAMPLE PROBLEM 36

2.70200.

1.250047.99966

2.6767.1263

1.267146. .999662.8706.1223

1.274242.99967

2.9766. . .12021.291771.99967

3.22660.11531.298206.99967

3.3265 '.1143

1.312870.99968

3.5765

8

.1116

AOBODO

EAOEO

• DO 'EAOEOEOFO

EAOEOElFOFOGO

V Gl

EAOV« El

FOP Fl

GOV GlV Gl

HO

FOP Fl

2.90. 5000.1.183885.99211

2.18182.3432'1.201603.99215

2.36923051208056.99219

2.47342.28601.225945.99224

2.71762.24301.232570.99227

2.81562.22681.247979.99229

3.06222.2207

69 1.072013 2.43

2.1,

0.764

0.772

W

12012234

18128151658

1564 0.79

122

20 0.7964812425 0.791519

90609060

CYCLES 4

3.0010000.1.122011.98497

1.76223.80101.140565.98502

1.93773.77311.147210.98506

2.03643.75911.166126.98512

2.26833.72541.173206.98515

2.36183.71231.190028.98521

2.59383.6743510.266.20266.20257.80259.00260.60

TO 111

3.2515000.1.068858.97831

1.41324.76291.089053• .978341.57404.76121.094602.97837

1.66524.76031.114218.97641

1.88114.75531.121616.97843 •

1.9686 •4.75261.139571.97643

2.19354.7936

3.60

3.003.00

EMPIRICAL1 2.40

3.3520000.1.022637•97190

1.12085.46121.042098.97192

1.26515.48'jó1.040214•97193

1.34765.49931.0&8079.97195

1.54485.52531.075602.97196

1.62545.53521.094060•97199

1.83555.5572

O 11300.

265.902 8640.

267.60267.60

2 8240.

CORE MODEL3.903.60

25000.0.980506•96581-8782

5.88070.999857.96580

322211

1.00525.93541.005838.96579

1.07825.96271.025824.96578

1.25516.02451.033484.96578

1.32S26.04761.052786•96573

1.52046.1509

27090.24039.17580.10090.8120.

30000.0.944820.95982.6797

6.22460.960&97.95979.7891

6.29950.968936.95977.8524

6.33fi90.988390.95973

1.00H26.42520.995921.95972

1.07326.45921.013,564.95966.2444.5307013169

1.6.

1.09901.09831.0614

35000.0.915606.95393• 5231

6.39130.921662.95398.6194

6.48290.937525.95396.6725

6.52870.955788•9538a• 8060

6.64100.962921.95386• 8623

6.68530.97fi291•94803

1.00716.8076

0.79 3.35784

267.607150.

- 128 -

w<CU

o •\0 O• o

r- r-

<M

O •vO O

• o

oj

- • sf

r-- o•D coC\]

vO O• *

{v. oOJ

_ Jenoceo.

inCM

in

fO

o.

ceo

o

r-o

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<Q

a

O r-l Cvj O O O -H 04 O r-i O O OO O X X ~3 O 1¿

O r-i O

X X T~J

LO n

O O OÜ i¿ -I

a o o O <H O O O

_J _s s: s a.

00000000000000000000000000000000000000o oooooooooooooooooao o0000000000000000000000000000000000000000000000000000000

I

O

O

O

»-< C\j ?O ;}• l í i O r*- ÍD CT» O <H <M rO á" LO -O t"~ 33 "J1 O >-i Al rO d" '-D ¿3 f~ CO G^ O •—I CU

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0o o o o o o o o o o o o o o o o o o oO O O O O O O O O O O O O O O O O O O

o o o o o oo o o o o o

o o o o o o o o o o o o o o o o o o oooooooooooooooooooo

- 129 -

-2 • PHINTED O U T P U T FROM SAMPLE PROQLEM 3 . . . PAGE 3

SÁMPLE PROBLEM 3 " CYCLES 4 TO 11 EMPIRICAL CORE MODEL

•: 4 • • . ' - . - • • • • • - - . . .• • . - . - ; • - • . •

........ -• OPCIÓN 0 QUEMADO DEL CICLO =11300.00 • 5 SUBLOTES

ENCÍA = EL SUBLOTE DO TIENE AHORA SOLO •18 ELEMENTOS CUANDO ANTES TENIA 20: LA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

ENCÍA = EL SUBLOTE EO TIENE AHORA SOLO S ELEMENTOS CUANDO ANTES TEMÍA 23LA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE.EN LA LISTA

SUBLOTES CARGADOS E N ESTE CICLO

ON

ON

ON

IDENTIF.

T DIEAOEO

W ElFO

1

2

3

DIFMAX

DIFMAX

DIFMAX

REGIÓN NO

12345

=

=

.023987

.002327

.000232

•ELEMENTOS

181215816

SUMA

. SUMA

SUMA

=50

=50

=50

ENR-INIC

3.6002.9003.6003.6003.600

.704554

•702460

.702640

U-INIC

257.80259.00260.60

• 260.60-, 265.90

DIFSUM =

DIFSUM =

DIFSUM =

BU-INIC

17580.10090.8120.8120.

0.

.003335

.000041

.000004

DB-INPUT

111

.0000

.0000• 0000.7640.7720

ZONA

11100

ALFAM

. .0000.0000• 0000.0000.0000

FV-INPUT

111

.0990

.0983

.0614

.0000

.0000

-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 3

SÁMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

BALANCE DEL CICLO A EOC CICLO 4

BALANCE DEL CICLO A EOC CICLO 4

PAGE

NO.LEM

ia1215816

69

1

ENRIQ•INIC.

3.6002.9003.600

. 3.6003.600

3.478

.082693

KG UI CICLOSELEM. ANT1G,•

257.80259.00260.60260.60265.90

260.82

K-INF(ENR

32221

•6E.0C)

QUEMADOINICIAL

17580.10090.8120.8120.

0,

8980.

DELTA-BCICLO

12669.12683.12978.8640.8557.

11300.

QUEMADOFINAL

30249.22773.21098.16760.8557.«-

20280.

• -...»

K-INFEOC

1.01171.01821.08471.12301.2057

• 1.081516

-1.086605

FRACCIÓNENERGÍA

1.10821.U461 1476.7640.7720

1.0000

ABSORCIONESEOC

1.095*+1.09471.0579.6803 ••.6403

1.071284

1.075771

NO.ELEM

18122316

69

ENRIQINIC.

3.6002.9003.6003.600

3.478

KG UIELEM.

257.80259.00260.602Ó5.90

260.82

CICLOSANTIS.

3221

QUEMADOINICIAL

17580.10090.8120.

0.

8980.

DELTA-bCICLO

12669.12683.11469.8557.

11300.

QUEMADOFINAL

30249.22773.19589.8557.

20280.

K-INFEOC

1.01171.01821.09761.2057

1.081516

FRACCIÓNENERGÍA

1.10821.11461.0141.7720

1.0000

ABSORCIONESEOC

1.09541.0947.9266 •.6403

1.071284

PESADO INVERSO

PESADO DIRECTO

PESADO INVERSO

C I C L O N - 2 P k l N T E D 0 U 7 P U T F R O M S A M P L E P R Ó B L E M 3 • •,• . .-•• • • P A G E 5

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

CICLO 5

OPCIÓN 2 QUEMADO DEL CICLO = 8640.00 7 SUBLOTES

ADVERTENCIA = EL SUBLOTE EAO TIENE AHORA SOLO 8 ELEMENTOS CUANDO ANTES TENIA 12LA ÜIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

ADVERTENCIA = EL SUbLOTE FO TIENE AHORA SOLO 4 ELEMENTOS CUANDO ANTES TENIA 16LA DIFERENCIA SE CONSIDERA DESCARGADO Y EL NUEVO SUBLOTE SE INCLUYE EN LA LISTA

NO.LOTE IDENTIF

6789101112

LEA1Eü

W ElFO

P Fl60

V Gl

REüIOK

1234567

SUBLOTES CARGADOS EN ESTE CICLO

NO.ELEMENTOS ENR-INlC U-INIC

81561242

20

2,9003.6003.6003.6003.6003.0003,000

259.00260.60260.60265.90265.90267.60267.60

ITERACIÓN 1

ITERACIÓN 2

ITERACIÓN 3

ITERACIÓN 4

ITERACIÓN 1

ITERACIÓN 1

ITERACIÓN 2

ITERACIÓN 2

BU-INIC DB-INPUT

22773.21098.16760.8557.8557.

0.0.

DIFMAX = .113604 SUMA =46.600944 DlFSUM = .068726

DIFMAX = .010199 SUMA =46.584311 DlFSUM = .000357

DIFMAX = .001019 SUMA =46.585672 DlFSUM = .000029

DIFMAX = .000101 SUMA =46.535553.. DlFSUM = .000003

ENR O úUEMADO = 8&40.000 K-lNF O K-EFF = 1.070781

DIFMAX = .000375 SUMA =16.635652 •'•DlFSUM = .001075

DIFMAX = .000037 SUMA =46.635612 DlFSUM = .000001..

ENR O QUEMADO = 8518.103 K-lNF O K-EFF = 1,071902

1.00001.00001.00001.0000.7900

.1*0000.7900

ZONA ALFAN • FV-IMPUT

00ooooo

.0000

.0000

.0000

.0000

.0000

.0000

.0000

VALOR BUSCADO = 1.072000

.0000

.0000

.0000

.oono,nnoo.oono.0000

o

VALOR BUSCADO = 1.072000

CICL0N-2 PRINTED OUTPUT FROM .SAMPLE PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

PAGE 6

BALANCE DEL CICLO A EoC CICLO 5

IDENT1FSUBLOTE

L£AlEO

W ElFO

P Fl60

v Gi:

NO.ELEM

815a1242

20

ENKIQINXC.

2.9003.6003.6003.6003.6003.0003.000

Kb UIELEM.

2b9.00¿60.602bO.6Q265.902o5.902o7.602b7.60

CICLOSANTIG.

3332>211

QUEMADOINICIAL

22773.21098.16760.. 8557.8557.

0.0.

DELTA-ÜCICLO

8829.9350.

. 9639.10036.6678.10308.6636.

QUEMADOFINAL •

31603.30448.26400.18592.15235.10308.6636.

K-INFEOC

.94821.01021.04151.10641.13731.14371.1872

FRACCIÓNENERGÍA

1.0174 -1.U8401.11751.1872.7900

1.2272.7900

ABSORCIONESEOC

1.07301.07301.07301.0730.6946

1.0730.6654

NÚCLEO 69 3.328 263.88 11040.

1.077Ü14 K-INF(ENRfBEOC)

BALANCE DEL CICLO A EOC

8518, 19558. 1.079414 1.0000

1.085939-

1.071902 PESADO INVERS

1.077929 PESADO DIRECT

CICLO 5

IÜENTIFSUBLOTE

EAEFG

NÚCLEO

NO.ELEM

6231622

69

ENRIQINIC.

2.9003.60Ü3.6003.000

3.326

Kb UIELEM.

259.00250.602b5.90267.60

263.68

CICLOSANTIG.

3321

QUEMADOINICIAL

22773. •19589.8557. .

. o.11040.

DELTA-BCICLO

8829.• 9450.9196.6970.

8518.

QUEMADOFINAL

31603.29040.17753.6970o

19558.

K-INFEOC

.94821.02Ü81.11391.1831

1.0794

FRACCIÓNENERGÍA

1.01741.09571.0879.8297

14 1.0000

ABSORCIONESEOC

1.07301.0730.9784.7025

1.071902 PESADO INVERS

CICLON-2 PUINTED OUTPUT FROM SAMPLÉ PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

,PAGE 8

IÜENTIFSUBLOTE

EAOw El : .FO

P FlGO

V GlT G2

HO ',

NÚCLEO

NO.ELEM

48124

•• 2

15519

Ó9

1.

BALANCE DEL CICLO

ENRIÓ.INIC.

2.9003.6003.6003.6003.0003.0003.0003.350

3.299

080170

K6 UIELEi'-i.

2b9.00260.60265.90265.90267.602u7.602b7.60267.60

265.90

CICLOSANTIG.

3433

. 2 - ••

221

K-INF(ENRrBEOC)

A EOC

QUEMADOINICIAL

22773.26400.18592.• 15235.10308.6635.6636.

0.

10639.

CICLO 6

DELTA-BCICLO

8818.:9016.9325.9551.9453.9732.6606.6606.

84-15. '

QUEMADO .FINAL—-

3 1 5 9 1 . •••• •

35415.27917.24786.19761.16368»13241. •

6606»

19054.

*

K-INFEOC

.9483

.97551.02951.05451.05031.08141.11231.2125

1.081360

1.088263

FRACCIÓNENERGÍA

1.02061.05001.10811.13501.13051.1639.7900.7900

1.0000

ABSORCIONESEOC

1.07631.07631.07631.07631.07631.0763.7102.6515

• 1.072000

1.078134-

BALANCE DEL CICLO A EOC CICLO 6

IÜENTIFSUBLOTE

EAE :

FGH

NÚCLEO

NO.ELEfo

4

a16221969

ENRIQ• INIC .

2.9003.6003.6003.0003.350

3.299

KG UIELEM.

259.00260.60265.90267.60267.60

265.90

CICLOSANTIG.

343 •

2 •••

1

QUEMADOINICIAL

22773.26400.17753.6970.

0.

10639.

DELTA-BCICLO

8818.9016.9382.8996.6606.

8415.

QUEMADOFINAL

31591.35415.27135.15966.6606»

19054.

K-INFEOC

.9483

.97551.03571.08521.2125

1.081360

FRACCIÓNEMERGÍA

1.02061.05001.11481.0759.7900

1.0000

ABSORCIONESEOC

1.07631.07631.0763.9931 ..6515

1.072000

PESADO INVERSC

LO

PESADO IMVERS(

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

PAGE 10

IDENTIFSUBLOTE

L FlPFI:GO

V GlT 62HO

S HlJO '

NO.ELEM

84215511816

BALANCE DEL CICLO

ENRIQINIC.

3.6003.6Ü03.0003.0003.0003.3503.3503.250

KG ÜIELEM.

265.902b5.902o7.602b7.60257.602ó7.60267.60267.60

CICLOSANTIG.

44

. 3332 .2 ,1

A EOC

QUEMADOINICIAL

27917.24786..19761.16368» .13241.6606.6606.

0.

CICLO 7

DELTA-BCICLO

7566.• 7723.7614,,:7806.7997.8630.5653.5653.

QUEMADOFINAL

35483.32509.27375.24174.21239.15235.12259.5653.

K-INFEOC

.9751

.9954

.98761.01251.03731.11931.14911.2176.

FRACCIÓNEMERGÍA

1.05061.07241.06411.09091.11761.2060.7900.7900

ABSORCIONESEOC

1.07741.07741.07741.07741.07741.0774.6075.6488

NÚCLEO 69 3.259 2b7.30 11566.

1.080016 K-lNF(ENRfBEOC)

7164. 18730. 1.081287 1.0000

1.088676

1.072010 PESADO INVERS

1.078744 PESADO DIRECT

BALANCE DEL CICLO A EOC CiCLO 7

IDENTIF NO. ENRIQ KG Ul CICLOS QUEMADO DELTA-B QUEMADO K-INF FRACCIÓNSUBLOTE ELEM INIC. ELEM. ANTIG. INICIAL CICLO FINAL EOC ENERGÍA

3.600 255.90 4 26874. 7618. 34492. .9817 1.05793.000 2b7.60 3 15966. 7832. 23798. •• '1.0156 1.09453.350 267.60 2 6606. 7376. 13962. 1.1316 1.03083.250 2o7.60 1 0, 5653. 5653. 1.2176 .7900

FGHJ

12221916

ABSORCIONESEOC .

1.07741.0774.9132.6488

NÚCLEO 69 3.259 267.30 11566 7164. 18730. 1.081287 1.0000 1.072010 PESADO

CICLÜN-2 PKINTED OUTPUT FROM SAMPLE PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MOPEL

PAGE 12

BALANCE DEL CICLO A EüC CICLO 8

1DENTIFSUbLOTE

0 G2T G2 .HO

S hlJO

P JlKO ;

NÚCLEO

1ÜENTIFSUBLOTE

GHJ :K

NÚCLEO

NO.ELEM •

11511810618

69

1.

NO.ELEM

16191618

69

ENRIQINIC

3.0003.0003.3503.3503.2503.2503.250

3.220

079445

KG UIELEM. .

2D7.6Q2b7.60267.60267.60267.602ü7.60267.60

267.60

CICLOSANT1G.

. 4433221

K-INFíENRrBEOC)

BALANCE DEL CICLO

ENf<IQINIC.

3.0003.3503.2503.250

3.220

KG UIELEM.

267.60267.60267.60267.60

267.60

CICLOS •ANTIG.

4321

QUEMADOINICIAL

24174.21239.15235.12259.5653.5653.

0.

10554.

A EOC

QUEMADOINICIAL

23257.13982.5653.

0.

10554.

DELTA-BCICLO

8111.8268.8850.9049.9464.6235. •6235.

7893.

QUEMADOFINAL

32285.29506.24086.21307.

. 15117.

. 11888. .•• 6 2 3 5 . • • •

18446.

CICLO 8

DELTA-BCICLO

8160.8934.8253.6235,

7893.

QUEMADOFINAL

31417.22916.13906-.6235.

18446.

K-INF FRACCIÓNEOC ENERGÍA

.9539 .

.97231.04091.06421.1131

. 1.14571.2103

1.080617

1.088531

K-INF FEOC

.95951.0r,C51.12501.2103

1.080617

1.02771.C4751.12131.14651.1991.7900.7900

1.0000

. •• • • „ •• .

-RACCION"EMERGÍA

1.03391.13191.0457.7900

1.0000

ABSORCIONESEOC

'•1.0773-1.07731.07731.07731.0773

• :•• . 6 8 9 5 .

' ••••: . 6 5 2 7

1.-072000.

1,079193

. • :•• .

-•ABSORCIONESEOC

1.07731.0773.9319.6527

1.072000

PESADO IMVERS

PESADO DIRECT.

PESADO INVERS<

CICL0H-2 PKINTED OUTPUT FROM SAMPLE PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

PAGE 14

BALANCt DEL CICLO A EOC

IDENTIF NO,SUBLOTE ELEM

K hlS Hl i

JÜ ,P Jl

KOR Kl

LO

NÚCLEO

9O10612618

ENRIQINIC.

3.3503.3503.2503.2503.2503.2503.250

Kü UIELEM.

267.60267.602b7.60267.60267.60267.60267.60

CICLOS QUEMADOANTIG. • INICIAL.

4433221

24086.21307.15117.11888.6235.6235.

0.

69 3.275 267.60 10463,

1.078602 K-lNlr<ENR»BEOC>

CICLO 9

DELTA-B QUEMADOCICLO. • FINAL

8973.9135.9469 •9699.10131.6762.6762.

B559.

33058.30442.24586.21588..16366.•12997.

6762»

K-INFEOC

«g752.9928.0292.05421011

1.13421.2039

1.1.1.

FRACCIÓNEMERGÍA

1.04831.06731.10631.13321.1837.7900.7900

19022. • 1.080909 1.0000

1.087303

ABSORCIONESEOC

1.1.1.1.

0750075007500750

•1.0750.6965.6562

le072000

1.077780

PESADO INVERS-

PESADO DIRECT

BALANCE DEL CICLO A EOC CICLO 9

IDENTIF NO. ENRIQ Kü UI CICLOS QUEMADO DELTA-B QUEMADOSUBLOTE ELEM INIC. ELEM. ANT1G. INICIAL CICLO FINAL

HJKL

NÚCLEO

17 3.350 267.60 4 22778. 9049. 31827.16 3.250 267.60 3 13906. 9555. 23462.Í8 3.250 2b7.60 2 6235. 9008. 15243.18 3.250 267.60 1 0. 6762. 6762»

69' 3.275 267.60.. . -. 10463. . 8559. 19022.

K-INFEOC

FRACCIÓNENERGÍA

1.0572.98331.03841.1119 • 1.05251.2039 . .7900

1.080909 1.0000

ABSORCIONES • 'EOC ^

<x>en

1.0750 ,1.0750

••.. . 9 4 8 8. 6 5 6 2 '•'• .

1.072000 PESADO INVERS

CICLCN-2 PKINTED OUTPUT FROM SAMPLE PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

pAGE 16

IÜENTIFSUBLOTE

J JlP Jl'

KO .K Kl

LOR Ll

MO

NÚCLEO

IDENTIFSUBLüTE

JKL ;

M

NÚCLEO

NO.ELEM

9612612618

69

1.

NO.ELEM

15ia1618

69 ..

BALANCE DEL

ENRIQINIC.

3.250•3.2503.2503,2bÜ3.2503.2503.250

3.250

079162

CICLO

Kti UI CICLOSELEM. ANTIG.

267.602o7.60 .267.60267.602o7.602O7.602o7.60

267.60

K-1NFÍENR

• • BALANCE DEL

ENRIQINIC.

3.2503.2503.2503.250

3.250

44332 • .

21 .•

tBEOC)

CICLO

KG UI CICLOSELEM. ANTIG.

267.60267.60267.60267.60

267.60

4321

A EOC

QUEMADOINICIAL

24586.21588.16366.12997.6762.6762.

0.

10824.

A EOC

QUEMADOINICIAL

23307.15243.6762.

0.

10824.

CICLO 10

DELTA-BCICLO

8269*-8432.8745.8967.9410.-6262.6262.

7927.

QUEMADO.- FINAL

32855..30019.25111.21964.16172.

.- 13024.6262.

18752.

CICLO 10

DELTA-BCICLO

8334.8819,8361..6262.

7927.

QUEMADOFINAL

31721.24062.15123.6262.

' 18752.

K-INF••••,•• E O C

.9692

.98831.02491.05101.1030

,1.13391.2100

1.081135

••-- 1.088061

• K-INFEOC

.97661.05:541.11301.2100

1.081135

FRACCIÓNENERGÍA

1.04311.06371.1031. i1.13121.1871.7900.7900

1.0000

FRACCIÓNENERGÍA

1.05131.11251.0547.7900

1.0000

ABSORCIONESEOC

1.07631.07631.07631.07631.07&3.6967

. .6529

1.072000

1.078252

ABSORCIONESEOC

1.07631.0763.9498 '.6529 •;

1.072000

PESADO INVERS

PESADO DIREC1

ai

PESADO INVERS

CICL.0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

PAGE 18

1DENT1FSUBLOTE

L KlR Kl :

LOR Ll

KOR Mi

PO

NÚCLEO

IDENTIFSUBLOTE

KLMP

NÚCLEO .

NO.ELEM

9612612618

69

1.

NO.ELEM

151618

la69

BALANCE DEL CICLO

ENRIQINIC.

3.2503.2503.2503.2503.2503.2503.250

3.250

078906

KG UIELEM.

267.60267.602b7.60267.60267.60267.602u7.60

2o7.60

CICLOSANT1G.

443322

•' 1 ', :

K-lNF(ENRrBEOC)

•..,••, . BALANCE DEL CICLO

ENRIQINIC,

3.2503.2503.2503.250

3.250

KG UIELEM.

267,60267.60267.60267.60

2o7.60

CICLOSAMTIG.

4321

A EOC

QUEMADOINICIAL

25111.21964.16172.13024.6262.6262.

. o, ;

10764.

A EOC

QUEMADOINICIAL'

23852.15123.6262.

0.

10764.

CICLO 11

DELTA-DCICLO

8331.8501.8851.9060.

• 9548.

6333.6333. .

8016.

QUEMADOFINAL

.. 33442.30465.25023.220B4.15810.12595.

... 6333.

• 18780.

CICLO 11

DELTA-BCICLO

8399.8921.8476.6333o

8016.

•QUEMADO•FINAL

32251.24043.14738.6333.

18760.

K-ÍNF FRACCIÓNEOC ENERGÍA

.9654

.98521.02561 . 0 4 9 9 ••'•.

1.10641.13831.2091

1.080981

• 1.088091

K-INF 1EOC

.9731l.OHi'61.1168

• 1.2091

1.080981

1.03931.C6051.1041

. .1.1303'-1.1910.7900.7900

1.0000

FRACCIÓNENERGÍA

1.04781.11281.0574.7900

1.0000

ABSORCIONESEOC

1.07651.0765

:. 1.0765•~ 1 . 0 7 6 5

••..•• 1 . 0 7 6 5

.6940

.6534

1.071977

1.078418

ABSORCIONESEOC

1.07651.0765.9490.6534

1.071977

PESADO INVERSí

PESADO DlRECTí

i.

CJ

-J

1

PF.SADO INVERSi

I -

C1CL0N-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

INCREMENTOS DE QUEMADO POR LOTE EN CICLOS SUCESIVOS

PAGE 19

SUBLOTE

AOBODO

T DIEAO

LEA1EO

W ElFÜ

L Fl 'P FlGO

V Gl0 G2T G2HO

K HlS HlJO

J JlP JlKO

L KlR KlLO

R Ll, MOR Mipo

QUEMADO

NO. EL

131218481584

a. 4

2' 411529a196396126126

: 18

W/O I

2.4302.9003.6003.6002.9002.9003.6003.6003.6003.6003.6003.0003.0003.0003.0003.3503.3503.3503.2503.2503.2503.2503.2503.2503.2503.2503.2503.2503.250

KG

266.2b6.257.257.259.259.2bO.260.265.2o5.265.267.267.267.2b7.267.267.2b7.2b7.267.2b7.267.2b7.267.267.267.267.267.267.

UI

2020ao800000606090 .9090606060606060606060606060606060606060

DEL. CICLO (MwD/MTU)

MASA TOTAL UE

DUliACIOtN

U 1NIC (MTU)

J DEL CICLO (LFPD)

BU-INIC

27090.24039.17580.17580.10090.10090.8120.8120.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0.0.0.0.0.0.0.

•••••• o . .

.000

.00

CICLO 4

0»o.0.

12669.12633.- ..12683.12978.8640.8557.8557.8557.

0.o.0.0. ;0.o.o.o.o.o.o.

'• o .

o.o.o.0.0.0.

•• 11300»

• "17.997

. 398.75

CICLO 5

0.. 0.

0.. 0.

, • o .

8829.9350.9639.10036.10036.. 6678.. 10308.

6636.6636.

' 6636.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

8518.

18.207

304.10

CICLO 6

0.0.0.0.

8818.0.0.

9016.9325.9325.9551.9453.9732.9732.6606.6606. .6606.6606.

0.0.0.0.o.o.0.

o.0.0.

o.8415.

18.347

302.73

CICLO 7

0.0.0.0.0.0.0.0.0.

7566.7723.7614.7806.7806.7997,'8630.8630.5653.5653.5653.5653.

0.0.0.-0.0.0.0.0.

7164.

18.-444

259.07

CICLO 8

0.

o.0.

. • o .

0.0.0.

o.0.0.o . •••

0. ::• 0 .

•-•:..• 8111..•<.-, • • 8 2 6 8 .

V,r 8850.•. 8850.

9049.9464.9464.6235.6235.6235.6235.

o.-0.0.

o.0.

7893.

18.464

285.75

CICLO 9,

0.0. .

. - • - - • ( ) . •

0.0.

o.o.

• • o .

0.o . •

• . • • ' • ' • • • o . •

• ''•• 0 .

• :•••••• • • o .

• •• o .

0*0.

8973.9135.9469.9469.9699.10131.10131»6762.6762.676?.

0.0.

o.- 8559.

18.464

309.87

XICL010

0.

o.0.0.0.0.0.

o'.0.0.0.0.0.0.0.0.0. .0.0.

8269.8432.8745.8745.8967.9410.6262'.6262.6262. •

0.

• 7927.

'•• 18.464

287.00

CICL011

0.0.0.

•'- ' o.• o .

0.0.0.0.0.0.0.0.

• 0 .

0.0.0.0.0.0.0.0.

8331.8501.8851.9060.9548.6333.

. 6333.

8016.

18.464

290.22

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 3

SAMPLE PK03LEM 3 CYCLES H TO 11 EMPIRICAL CORE MODEL

SUMARIO DE LA DESCARGA

PAGE 20

IDENTIFSUÍSLOTE

1 AOBODO

T DIEAOLLA1EO

W ElFO

L FlP FlGO

V Gl0 G2T G2HO

K Hl .S Hl

vjOü JlP JlKO

NO.ELEM

131218481584

. a4241152 .9 ,:•B1963

ENRIQINIC.

2.4302.9003.6003.oOO2.9002.9003.6003.6003.6003.6003.5003.0003.0003.0003.000

. 3.350, 3.3503.3503.2503.2503.2503.250

KG UI, TOTAL

3460.60266.20515.60

4640.401036.002072.003909.002084.8010o3.602127.20iUb3.60535.201070.402943.601338.00535.20

2408.402140.60267.60

2408.401605.bO802.60

CICLODESCARGA

33346 ,5566.7777688999

•=• 1 0 . ••.••••

• 1 0 . ,.;•

1 0 •

CICLOS•PERMAN.

22233334344334434434

•-• ' 4

3

QUEMADOv, DESCARGA

• 27090.24039.175dO.30249.31591.31603.30448.35415.27917.35483.32509.27375.24174.

'• '322B5..'29506.• 24066.• .33058.

30442.24586.

• 32.855.•• '.30019.

25111.

U RESIDUAL(UF/UI)

.9633

.9670

.9751

.9592

.9579

.9579

.9588

.9468

.9625

.9466

.9545

.9629

.9663

.9571

.9604

.9669

.9561

.9592<?663.9564.9597.9656

ENRIQ.DESCARGA

.66681.05162.00311.2316.7301.7297

1.2216..9891 •1.3546.98621.1205.9653

1.1196-.7645.87271.3793.9390

1.05281.2774.8873

1.00731.2491

PU FIS.(KG/MTU)

5.95295.86165.22036.54706.37756.37806.55976.8260

. 6.39146.82896.68256.15735.89736.44726.30655.96646.61956.48675.93936.5711-6.42646.0348

10

I „

CICLON-2 PklNTED OUTPUT FROM SAMPLE PROBLEM 3

SAMPLE PROBLEM 3 CYCLES 4 TO 11 . EMPIRICAL CORE MODEL

*** BALANCE POR LOTES DE IGUAL CICLO DE CARGA Y DESCARGA ***

INCREMENTOS DE QUEMADO POR LOTE EN CICLOS SUCESIVOS

PA6E 21

SUBLOTE

A2*0302*03D2*Ü3D3*Ü4 '

EA3*ÜóEA3*ü5 'E3*Ü5E4*06F3 + Ü6F4+Ü7Ü3*ü7 '.G4*Ü8 'H3*08H4*Ü9J3*09J4*10K3+10K4*ÜUL3*Ú0M2*00P1*OO

QUENADO

NO.EL w/0 ,

1312184a15a

• 4126162171153

15181818

2.4302.9003.6003.6002.9002.9003.6003.6003.6003.6003.0003.0003.3503.3503.2503.2503.2503.¿503.2o03.2503.250

I KG UI

266.20266.202b7.tíO2b7.80259.002b9.002b0.60260.60265.90265.902b7.602o7.60267.60267.60267.60267.602b7.60267.60267.60267.60267.60

DEL CICLO Ü1WD/MTU)

MASA TOTAL DE

DURACIÓN DEL (

U INIC

:ICLO

(MTU)

(EFPD)

BU INIC

27090.24039.17580,17580. .10090.10090.8120.

. 8120,• 0.0.0.

• • • o .

0.0.0.0.0.0.

••'., 0 .

••• . - o .

0.

0.

.000-

: .00

CICLO 4

0.o.o.

• 12669.12683.12683.12978.8640.8557.8557.

o.o.0.0.

• . o.o.o.o.o.o.0.

11300.

17.997

• 398.75

CICLO 5

• •••••-. . o .

0.0.

• 0 .

0.8829.9350.9639.

• 10036.8916.

• 7060.•••:•• 6 6 3 6 .

•>..-., o .

• . . .: • o .

0.. o .' 0.0.0.0.0.

8518.

18.207

304.10

CICLO 6

0.0.0.0.

8818.0.o.

9016.9325.9400.9639.8755.6606.

•••• • 6 6 0 6 . • =

0.0.0>0.

o.0.0.

8415.

18.347

302.73

CICLO 7

o..•••'"'•

0.0.o . - •

0.0.o . •

0.0.

7618.7742.7866.8630 •.•--

, 7229,:-5 6 5 3 . ••'••

' 5653. '•0.0.0.0.0.

7164.

18.444

259.07

CICLO 8

0.0.0.0.0.0.0.o.0.0.0.

8160.,-8850.'•8944.. 9464.• 8173.6235.6235.

0.

o.o.

7893.

18.464

285.75

CICLO 9

0.0.0.0.0.

- • ' •: 'O. .0.o.0.0.0.0.0.

9049.9469.

. • 9561.10131.8783.6762.

0.o.

8559.

18.464

309.87

CICLO10

• 0. .o'.0.0.0.0.0.0.0.0.0.0.0.0'. '•0.

8334.8745.8834.6361.6262.

0.

7927.

18.464

287.00

CICLOll

0.0.0.0.0.0.0.0.0.0.0.0.0.

- •• •• • o .

0.0.0.

••••• fi399.

P921.8476.6333.

8016.

18.464

290.22

O1

CICL0N-2 PKINTED OUTPUT FROM SAMPLE PKOBLEM 3

SAMPLE PR08LEM 3 CYCLES 4 TO 11 EMPIRICAL CORE MODEL

PAGE 22

*** BALANCE POR LOTES DE IGUAL CICLO DE CARGA Y DESCARGA ***

SUMARIO DE LA DESCARGA

IDENTIF NO. ENRIQSUBLOTE ELEM ' INIC.

KG UI CICLO CICLOSTOTAL DESCARGA PERMAN.

QUEMADO U RESIDUAL ENRIQ. PU FIS.DESCARGA (UF/UI) DESCAIGA (KG/MTU>

A2*03d2*Ü3D2*Ü3Ü3*04

LA3*0óEA3*05E3*05E4 + 06F3*Ü6F4 + Ü763*07GM*oaH3+ÜÜH4 + 09J3*09J4*1ÜK3 + 10K4*00L3 + Ü0M2*00Pl + ÜÜ

1312104815. 8

••.••, 4 .

• 12616217115315181818

2*1302.9003.6003.6002.9002.9003.b003.60 03.6003.6003.0003.0003.3503.3503.2503.2503.2503.2503.2503.2503.250

3460.60266.20515.60

4640.401036.002072.003909.00 ,2064.60 ,1063.603190.601605.6042dl.6O535.20

4549.202b7.60

4014.00802.60

4014.004816.604816.804816.80

•• .• - 3 • •'

.3• • • - 3

65

. 5ó677.8 .• 8

-••.9

......g10100000

222333343434343434

. 321

27090.24039.17580.30249.31591.31603.30448.35415.27917.34492.25241.31417.24086.31827.24586.31721.25111.32251.24043.14738.6333o

.9633 '•

.9670

.9751

.9592

.9579

.9579

.9588

•" , 9625'•:•:-•

.9492 •

.9655

.9581,9669.9576 ..9663.9577.9656.9656.9656.9656.9656

.66681.05162.00311.2316.7301 •:

.72971.2216.9891

•-. 1.35461.03101.0682.7933

1.3793.9925

1.2774.9353

1.24911.24911.24911.24911.2491

5.95295.86165.22036.5470

' 6.37756.37806.55976.82606.39146.78015.98406.40325.96646.55705.98936.5132

• 6.0348' 6.02486.03486.03486.0348

CICLON-2 PRINTED OUTPUT FROM SAMPLE PROBLEM 3 .

SAMPLE PROSLtM 3 CYCLES 4 TO H EMPIRICAL CORE MODEL

PAGE 23

*** BALANCE POR LOTE DE DESCARGA ***

SUMARIO DE LA DESCARGA

IDENTIFSUBLOTE

0304G5060708 ;09 /• .

1011

NO.ELEM

16182316

• 18 .18.

• l aia

,,.. o

ENRIQINIC.

2.6023.6003.357. 3.4273.3993.0393.344•3.2bO

.000

KG UITOTAL

4242.404640.405931.004184.404796.404816.804816.804816.80

.00

CICLODESCARGA

3456789 ;

1011

CICLOSPERMAN.

3 ... '' 4567 .a910íi

QUEMADODESCARGA

25743.• 30249.

'•••• 30846.32563.31395. .:•'30602.

,. 31425..•: 30619.

0.

U RESIDUAL(UF/UI)

.9650

.9592

.9585

.9536•... .9547.-

.9591

.9580

.9590 •

.0000

ENRIQ.DESCARGA

.85331.23161.05121.01791.04 34.8629

1.0083.9876.0000

PU FIS.(KG/MTU)

5.85826.547o6.4967ó.6045

••;; 6.5136' 6.35476.5255

. 6.4335• .0000

ENERGÍAS RELATIVAS EN CADA CICLO DE ..LOS LOTES DE DESCARGA

LOTE34567891011

NO. EL16182316181818180

CICLO 325743.17580.,büÜ2...6544.

0.0.0.0.o . •

CICLO 4.0000

1.10621.1361.6536.5147.0000.ÜÜOO.0000.0000

: CICLO 5• .0000

.00001.0608• .85561.0151..7022.0000.0000.0000

CICLO. "6

111

.0000

.0000

.0000

.0572

.1290

.0185

.7461

.0000

.0000

CICLO 7.0000.0000.0000.0000

1.06591.1111.9980.6583.0000

CICLO 8.0000.0000.0000.0000.0000

1.04361.1368.9946.0000

CICLO 9.0000.0000.0000.0000.0000.0000

1.06001.1282.0000

CICLO 10.0000.0000.0000• OOoO.0000.ooon.0000

1.0600.0000

CICLO 11.0000.0000.0000.nooo.0000.nooo.0000.0000.0000

- 143 -

CICLON-2 ,

3DATA»L 7.

Oüüüül0OUOO2300003D00G04300005300006300007300008300009300010300011300012300013500014)00015J00016J00Q17loooia)OüO19 ;

100020100021IOÜ022100023100024100025I0Ü02&I0Ü02710002a .¡00029100030100031'000320003300034000350003Ó0003700038000390004000041000420004300044000450004Ó000470004800049000500005100U520005300054000550D0560005700G53000590006000061ÜÜ0620OCb3

PUÍ4CHED OUTPUT FROM :

• 131oV

27090.3

24039.3

. ' - . < • , . . . . . . " . . . : • • .

-•-, 17580.-. • - • 3

.17580. ;-• .•:•..-.•• -•, 3 -•,

, . 1 . -• , ,

10090.3

10090.3

8120.3

•.-.8120..•• : ••••• 4 - .

8557.4

8557.5

7860.5

6636.ó

6606.• - 6

6606.. 7

5653.7

5653.8

6235. .8

6235.9

6762.10

6262.11

6333.

327090.

324039.

3• 17580.

430249.1Í.Ó69.

631591.12663.

• 5

31603.12633.

53044S.12978.

635415.

; 8640.- -6

27917.10036.

734492.' 8916.

725241,9639.

831417.6755.

824086.8630.

931327.7229.

924586.9464.

1031721.8173.

1025111.10131.

1132251.8783.

1124043.6361.

1114738.6476.

116333.

5AMPLE PROBLEM 3 .

• 1

1

1

1

1

1

1

1

1

1

2-

2

2

2

2

-2-

3

3

3

3

4

13.4606

1.2662

1.5156

24.6404

41.0360

0.3

2.07208829.

33.90909350.

42.08489639.

31.06369325.

43.19089400.

31.60567742.

44.28167866.

3• .53528850.

44.54928944.

3,26769469.

44.01409561.

3.80288745.

44.01408834.

34.8168'8921. •.. 2

4.8168

14.8163

2.4300

2.9QQ0-

3.&000

3.6000

2.90008318.

2.9000

3.6000

3.60009016.

3.6000

3.6Q007618.

3.0000

3.00008160.

3.3500

3.35009049.

3.2500

3.25008334.

3.2500

3.25008399.

3.2500

3.2500

3.2500

.9633

.9670

.9751

.9592

•.9579

.9579

.9588

.9468

.9625

.9492

.9655

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PAGE 1

-5.9529

-5.8616'

-5.2203

-6.5470

-6.3775

-6.. 3780

-6.5597

• -6.8260

-6.3914

-6,7801

-5.984Q

-6.4032

-5.9664

-6.5570

-5.9893

-6.5132

-6,0348

• -6.0343

-6.034a

-6.0348

-6.0348

A2*03A2*03

D2*03. B2*03

D2*03D2*03

D3*04D3*04

EA3*CÓEA3*06

EA3*05EA3*05

•• E3*05E3*05

E4+06E4*06

• F3*06F3*06

F4*07F4*07

G3*07G3*07

G4*08G4*08

H3*08H3*0fi

H4*09H4*09

J3*09J3*09

• J4*10J4*10

K3*10K3*10

K4*00K4*00

L3*00L3*0Ü

M2+00M2*0 0

P1*OOP1*OO

- 145 -

APPENDIX D

COMPUTER COPE ABSTRACT

1. Ñame or designation of program.

CICLÓN

2.. Computer for which program is designed and other upon which

it is operable.

UNIVAC 1106

3. Nature of phisical problem solved.

Neutronic calculation of consecutive cycles'for survey

fuel management studies of PWR's transition cycles. With given

fuel design characteristics, batch sizes, initial enrichments

and burnups of previous irradiated fuel, CICLÓN calculates cy~

cle lengths or fresh fuel enrichments for specified load fac-

tors and end of cycle life condition. Burnup sharing by batch

in each cycle is also obtained as well as discharge burnup and

isotopics.

4-. Method of solution.

A method of Approximate Balance of Reactivity at end of

cycle is used, where whole core reactivity is calculated by

inversely weighting regionwise reactivities with relative bur-

nups. A search is done in fresh fuel enrichment or in cycle

length to match an input, user selected, end of cycle core

reactivity "dependitig of reactor size. and end of cycle life

condition. Regionwise reactivities are obtained as a function

of regional burnup at end of cycleiand initial enrichment from

tables provided by the user. Regionwise burnup sharing is

either input provided or calculated by a simplified neutronic

- 1H-6 -

model, where-a two dimensional nodal model is condensed by

región, with región coupling described with different appro-

ximations using empirical parameters that can be obtained

through an special option of the program from previous or

otherwise calculated cycles.

5 . Restrictions on the complexity of the problein.

Arrays are dimensioned through parameters defined in

the main program, that can be easily changed. Their present

valués are:

Maximun number of burnup points in tables = 12

" " " initial enrichments in tables = 12

" " " batches in all cycles = 200

" " " succesive cycles to be considered = 20

" " " batches, regions or zones in one cycle = 35

" " " batches in the redúced summary = 50

6. Typical running time.

Depends on the región coupling model and reactivity search

option. For a ten cycles calculation with fifteen coupled regions

in each cycle and cycle lengths search, total time is less than

three minutes in the UNIVAC 1106, CPU time, being two thirds of

total time.

features of the program.

A very simple procedure is used to input batch loading in

each cycle. Batches can be divided in subbatches at any reload.

Different number of in-core or hold out cycles for every batch

are allowed. Irradiation history is saved for every batch and

isotopics for the discharge burnup is calculated printing the

summary of batch burnups by cycle;and discharge data in stan-

dard format in fuel-management.

- 147 -

8. Related and, auxiliary programs.

Tabulated sets of K-infinity, final to initial uranium

weight ratio, final enrichment and fissile plutonium contents

versus burnup for different Initial enrichments should be

provided in the input. Tables can be obtained from previous

files or from cell burnup calculations at nominal operating

conditions.fReload strategies and regionwise loading schemes

should be ppre'éalcülated^ by users . A complete set of data

summarizing all cycles considered can be punched in the for-

mat of the program FUELCOST.

9. Status.

Tested on UNIVAC 1106 at JEN.

10. Rgfgranees .

1. J.M. ARAGONÉS" "CICLÓN: A Neutronic Fuel Management

Program for PWR's Consecutive Cycles". Report JEN-

to ..be published (this report).

2. J.M. ARAGONÉS, M.R. CORELLA, J.M. MARTINEZ-VAL:

"Métodos y Programas de Cálculo para Gestión en PWR:

Programas SOTHIS y CICLÓN". Report JEN-to be published

11. Machine requirements.

Less than 20,000 36-bits words on the UNIVAC 1106 and

standard input, output and punch devices.

12* Programming languages used.

FORTRAN V, with very small use of special features

different from ANSÍ standard.

13. Operating system or monitor under which program is executed

UNIVAC EXEC-8.

- 148 -

14. Other programming or operating information or restrictions

15. Ñame and establishment of authors.

José M. ARAGONÉS "Junta de Energía NuclearAvda, Complutense, 22Madrid-3SPAIN

16. Material available.

Program Source (1081 cards)

Sample Problem input data and EXEC-8 Control Cards

(459 cards).

17. Category: D

KEYWORDS: PWR," Fuel" Management, Fuél Cycle , Enr.ichment,

Burnut) .

J.E.N. 336

Junta de Energía Nuclear. División de Teoría y Cálculo de Reactores. Hadrid." C I C L Ó N : Un p r o g r a m a n e u t r ó n i c o de G e s t i ó n de l

Combustible para ciclos sucesivos de reactores de aguaa presión".ARAGONÉS, J.H. (1977), 146 pp., 2 f igs . 2 refs.

Se recoge la descripción del programa y el manual de uso de un nuevo programa de

computador. CICLÓN efectúa el cálculo neutrónico de ciclos sucesivos de recarga para

i optimizanón de la Gestión del Combustible en reactores PWR. Las características y da-

tos de quemado del combustible, tamaños de regiones o lotes, esquemas de carga y está-

do del combustible irradiado previamente se dan como entrada al programa. Las duracionesj

de los ciclos o enriquecimientos de alimentación y el reparto del quemado entre cada . .

región o lote se calculan usando diferentes modelos neutronicos del núcleo y se impri- '

¡men o perforan en el formato normal en gestión del combustible.

CLASIFICACIÓN INIS Y DESCRIPTORES: E21. C codes. PWR type reactors. Fuel management.

Reactor cores. Fuel cycle. Reactivity. Bumup. Optimization.

J.E.N. 336

Junta do Energía Nuclear. División de Teoría y Cálculo de Reactores. Madrid." C I C L Ó N : Un p r o g r a m a n e u t r ó n i c o de G e s t i ó n de l

Combustible para ciclos sucesivos de reactores de aguaa presión".ARAGONÉS, J.H. (1977), 146 pp., 2 f i gs . 2 refs. '

Se recoge la descripción del programa y el manual de uso de un nuevo programa decomputador. CICLÓN efectúa el cálculo neutrónico de ciclos sucesivos de recarga paraoptimización de la Gestión del Combustible en reactores PWR. Las características y da-tos de quemado del combustible, tamaños de regiones o lotes, esquemas de carga y esta-do del combustible irradiado previamente se dan como entrada al programa. Las duracionesde los ciclos o enriquecimientos de alimentación y el reparto del quemado entre cada .reglmo lote se calculan usando diferentes modelos neutronicos del núcleo y se Impri-men o perforan en el formato normal en gestión del combustible.CLASIFICACIÓN INIS Y ESCRIPTORES: E21. C codes. PWR type reactor. Fuel management.

D n - H •••<•> . vMnr t

J.E.N. 336

Junta de Energía Nuclear. División de Teoría y Cálculo de Reactores, Madrid."CICLÓN: Un p r o g r a m a neutrónico de Gestión del

Combustible pa ra ciclos sucesivos de r e a c t o r e s de aguaa presión".ARAGONÉS, J.M. (1977), 146 pp. , 2 f i g s . 2 r e f s .

Se recoge la descripción del programa y el manual de uso de un nuevo programa de

computador. CICLÓN efectúa el cálculo neutrónico de ciclos sucesivos de recarga para

optimización de la Gestión del Combustible en reactores PWR. Las características y da-

tos de quemado del combustible, tamaños de reglones o lotes, esquemas de carga y esta-

do del combustible Irradiado previamente se dan como entrada al programa.Las duracionesj

de los ciclos o enriquecimientos de alimentación y el reparto del quemado entre cada

región o lote se calculan usando diferentes modelos neutronicos del núcleo y se impri-

men o perforan en el formato normal en gestión del combustible.

CLASIFICACIÓN INIS Y DESCRIPTORES: E21. C codes. PWR type reactors. Fuel management.

Reactor cores. Fuel cycle. Reactivity. Bumup. Optimization.

J . E . N . 336 •

Junta de Energía Nuclear. División de Teoría y Cálculo de Reactores. Madrid."CICLÓN: Un p r o g r a m a neutrónico de Gestión del

Combustible pa ra ciclos sucesivos de r e a c t o r e s de aguaa p re s ión" .APAGONES, J.M. (1977), 146 pp., 2 f i g s . , 2 refs.

Se recoge la descripción del programa y el manual de uso de un nuevo programa decomputador. CICLÓN efectúa el cálculo neutrónico de ciclos sucesivos de recarga paraoptimización de la Gestión del Combustible en reactores PWR. Las características y da-tos de quemado del combustible, tamaños de regiones o lotes, esquemas de carga y esta-do del combustible irradiado previamente se dan como entrada al programa.Las duracionesjde los ciclos o enriquecimientos de alimentación y el reparto del quemado entre cadaregión o lote se calculan usando diferentes modelos neutronicos del núcleo y se impri-men o perforan en el formato normal en gestión del combustible.CLASIFICACIÓN-INIS Y DESCRIPTORES: E21. C codes. PWR type reactor. Fuel management.

C o lno I r\m i r-f i ui + w PIÍWII in On-t-1 mí 7Q+ í nn.

J.E.N. 336

Junta de Energía Nuclear, División de Teoría y Cálculo de Reactores. Madrid.

"CICLÓN: A Neutronic Fuel Management Program forP W R ' s C o n s e c u t i v e C y c l e s " .ARAGONÉS, JJ.-(1977), 146 pp., 2 figs. 2 refs.

The program description and user's manual of a new computer code is given. CICLÓN

performs the neutronic calculation of consecutive reload cycles for PWR's fue! mana-

gement optimization. Fuel characteristics and burnup data, región or batch sizes, loa ,-

ding schemes and state of previously irradiated fuel are Input to the code. CycVe ' :

lengths or feed enrichraents and burnup sharing for each región or batch are calculated'

using different core neutronic models and printed or punched in standard fuel raana-

gement format. • •,

INIS CLASSIFICATION AND DESCRIPTORS: E21. C codes. PWR type reactors. Fuel management.

Reactor coros. Fuel cycle. Reactivity. Bumup. Optimization.

J.E.N. 336

Junta de Energía Nuclear, División de Teoría y Cálculo de Reactores. Madrid.

"CICLÓN: A Neutronic Fuel Management Program forPWR's Consecutive Cycles".ARAGONÉS, J.N. (1977), 146 pp., 2 f igs . 2 refs.

The program description and user's manual of a new computer code Is given. CICLÓN

performs the neutronic calculation of consecutive reload cycles for PWR's fuel mana-

gement optimization. Fuel characteristics and burnup data, región or batch sizes, loa-

ding schemes and state df previously Irradiated fuel are input to the code. Cycle

lengths or feed enrichments and bumup sharing for each región or batch are calculated

using different core neutronic models and printed or punched In standard fuel mana-

gement format.

INIS CLASSIFICATION AND DESCRIPTORS: E21. C codes. PWR type reactors. Fuel management.

Reactor cores. Fuel cycle. Reactivity. Burnup. Optimization.

J.E.N. 336

Junta de Energía Nuclear. División de Teoría y Cálculo de Reactores. Madrid." C I C L Ó N : A N e u t r o n i c F u e l M a n a g e m e n t P r o g r a m for

PWR's Consecutive Cycles".ARAGONÉS, J.M. (1977). 146 pp. 2 f i g s . 2 refs.

The program description and user's manual of a new computer code is given. CICLÓN

performs the neutronic calculation of consecutive reload cycles for PWR's fuel mana-

gement optimization. Fuel characteristics and burnup data,- reglón or batch sizes, loa-

dihg schemes and state of previously irradiated fuel are Input to the code. Cycle

lengths or feed enrichments and burnup sharing fo r each región or batch are calculated

using different core neutronic models and printed or punched in standard fuel mana-

gement format.

INIS CLASSIFICATION AND DESCRIPTORS: E21. C codes. PWR type reactors. Fuel management.

Reactor cores. Fuel cycle. Reactivity. Burnup. Optimization.

J.E.N. 336 '

Junta de Energía Nuclear. División de Teoría y Cálculo de Reactores. Madrid.

"CICLÓN: A Neutronic Fuel Management Program forPWR's Consecutive Cycles".ARAGONÉS, J.M. (1977}. 146 pp. 2 f igs . 2 refs.

The program description and user's manual of a new computer code is given. CICLÓN

performs the neutronic calculation of consecutive reload cycles for PWR's fuel mana-

gement optimization. Fuel characteristics and bumup data, región or batch sizes, loa-

ding schemes and state of previously irradiated fuel are input to the code. Cycle

lengths or feed enrichments and bumup sharing for each región or batch are calculated

using different core neutronic models and printed or punched in standard fuel mana-

gement format.

INIS CLASSIFICATION AND DESCRIPTORA E21. C codes. PWR type reactors. Fuel management.

Reactor cores..,Fuel cycle. Reactivity. Bumup. Optimization.