ciclÓn: a neutronic fue! management program for pwr's ... · j.e.n. 338 sp issn 00*1 - 3397...
TRANSCRIPT
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
- 1 -
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
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.
- 28 -
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.
- 33 -
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
o o
oo
oininooooo .oininoooo
inO »-i
• «OJ O
in
oooininoo^-4
OOOO«-IOJ<\ÍO
o o o in m o o
o o o o «-< CM cu
co \0 CO \ 0
o
oin
O vO• O
O CO
C\]
inmtnooino
cvio j o o o a
oo
04
_1
o
i n o o o u o o o L ncg . . . . . . .• sf »H <\! •H ( \ |OH
m o o o i í i o o i f )C\J. . . . . . .«cl-r-«CM»HC\)O^
ro
tu
o
o o o in o o m
o o «-t •-» ro o o
o o o LO o o tnO O «H tO O O
a> \0 c\j co
o»
oO r-t O T-t O O O
• a. ce
o o o un <S) o o oooininoo
2: • cr
oooaoooooooooooooooooooooooooooOOQOOOOOOOOOOOOOOOOOOOOOOOOOOOO0000000000000000000000000000000
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
* •O O o o
<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
.9581
.9669
.9575
.9663
. .9577
.9656
.9656
.9656
.9656
• 9656
1
2
1
1
1
1
1
1
1
1
1
1
1
1
.6668
.0516
.0031
.2316
.7301
.7297
.22l6-:
.9891 .
.3546
.0310
.0682
.7983
.3793
.9925
.2774
.9353
.2491
.2491
.2491
• 2491
.2491
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.