Energy and Power Engineering, 2013, 5, 510-516
doi:10.4236/epe.2013.54B098 Published Online July 2013 (http://www.scirp.org/journal/epe)
Modeling of Fuel Elements Cycling System in Pebble Bed
Reactor Based on Timed Places Control Petri Nets*
Hongbing Liu1, Peng Shen1, Dong Du1, Xin Wang2, Haiquan Zhang2
1Department of Mechanical Engineering, Tsinghua University, Beijing, China
2Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing, China
Received January, 2013
ABSTRACT
Pebble bed reactors use cycling scheme of spherical fuel elements relying on fuel elements cycling system (FECS). The
structure and control logic of FECS are very complex. Each control link has strict requirements on time and sequence.
This increases the difficulties of description and analysis. In this paper, timed places control Petri nets (TPCPN) is ap-
plied for the modeling of FECS. On this basis the simulation of two important processes, namely uploading fuel ele-
ments into the core for the first time and emptying the core is finished by simulation software Arena. The results show
that as TPCPN is able to describe different kinds of logic relationship and has time properties and control properties, it’s
very suitable for the modeling and analysis of FECS.
Keywords: Timed Places Control Petri nets (TPCPN); Arena; Pebble Bed Reactors; Fuel Elements Cycling System
(FECS)
1. Introduction
In recent years, the concept of the fourth generation of
advanced nuclear energy systems is put forward in the
world. Pebble bed HTGR is considered to be the pre-
ferred technology for the fourth generation of advanced
nuclear energy systems [1,2]. Pebble bed reactors use
cycling scheme of spherical fuel elements. Its running
process can be summarized as following: spherical fuel
elements are uploaded from the reactor core and trans-
ported in the near equal diameter pipeline; the burn-up
measurement device measures the burn-up of the element;
if the element has reached the target burn-up, or say it’s a
spent element, it will be transported to th e spent elements
tank; if not, the element will be lifted up to return to the
core; new fuel elements with the same number of the
spent elements will be up loaded into the core at the sa me
time. The realization of the running relies on a very im-
portant support system of the reactor, namely fuel ele-
ments cycling system (FECS) [3]. The control logic of
FECS is very complex. Each control link has strict re-
quirements on time and sequence. So it’s difficult to de-
scribe it with natural languages, flowcharts, etc.
Petri nets (PN) is a powerful graphical modeling tool.
It has a strict mathematical basis as well as intuitive
graphical expression. Relationship such as parallel, con-
current and conflict can be described very well with Petri
nets [4]. Control Petri nets (CPN) can describe some easy
control systems. Multi-level description of complex con-
trol systems can also be realized with the concepts of
macro-place and macro-transition [5]. However, many
control systems cannot be described with PN or CPN
because the systems have requires on time.
In order to describe and analyze the control logic of
FECS accurately, timed places control Petri nets (TPCPN)
is used for the modeling of FECS. On this basis some
simulations are done to analyze the operation process,
including uploading fuel elements into the core for the
first time and emptying the core. The results show that as
TPCPN has the advantages on describing complex con-
trol system and contains time properties, it can describe
the control logic of FECS very accurately. It also facili-
tates the simulation with software Arena.
2. The Function of Fuel Elements Cycling
System (FECS)
The structure of FECS is very complex. The key features
of FECS include uploading fuel elements into the core
for the first time, the main cycling, uploading new fuel
elements into the core, discharging the spent elements
from the core and emptying the core.
When the system begins to run for the first time, hun-
dreds of thousan ds of fuel elements will be u ploaded into
the core. This process is called uploading fuel elements
into the core for the first time. During the period of the
*Supported by the Nation a l S&T Major Project (Grant No. ZX06901).

H. B. LIU ET AL. 511
main cycling, fuel elements are uploaded from the core
one by one and transported in the near equal diameter
pipeline. Along the pipeline there are many kinds of de-
vices including single conveyers, distribution devices,
burn-up measurement devices, stop devices, etc. The
elements which have reached the target burn-up are
transported to the spent elements tank. The elements
which have not reached the target burn-up are lifted in
the lifting system for cycling (lifting system A) to return
to the core. Some new fuel elements will be uploaded
into the core at the same time. When there are special
circumstances, hundreds of thousands of fuel elements in
the core will be transported to the temporary stor age sys-
tem for spent elements (temporary storage system B) in
succession. Then they will be transported through the
lifting system for the spent ele ments (lifting system B) to
the spent elements tank.
The reliable operation of FECS relies on a variety of
devices and media, including more than 50 sets of deliv-
ery devices, more than 100 counters, nearly 200 elec-
tronic gauges, more than 1000 meters of pipeline, etc.
3. The Timed Places Control Petri Nets
Model of Fuel Elements Cycling System
Considering the complex control logic of FECS, TPCPN
can be used for its modeling.
3.1. The Timed Places Control Petri Nets Model
of the Head Control Room
The head control room can control the operation of the
subsystems, including inputting new fuel elements into
the temporary storage system which is also called
temporary storage system A(P1), transporting the fuel
elements from temporary storage system A into the core
(P3), discharging the spent fuel elements (P4), the main
cycling (P6) and emptying the core (P10).
The TPCPN model of the head control room is shown
in Figure 1. The relationship between the subsystems
can be seen clearly from it, including parallel, concurrent,
conflict and so on. For example, as both of P1 and P4
need to use the gas changing system, they cannot be car-
ried out at the same time. In this case, an initial place
Figure 1. The TPCPN model of the head control room (TPCPN1).

H. B. LIU ET AL.
512
Figure 2. The TPCPN model of the main cycling (TPCPN2).
named P0 is used to avoid the two subsystems running
simultaneously. Likewise, P5 can avoid P3, P6 and P10
running simultaneously.
3.2. The Timed Places Control Petri Nets Model
of the Main Cycling
The TPCPN model of the main cycling is shown in
Figure 2. When P6 in TPCPN1 gets a token, Pin is given
a token. Then the main cycling starts. If there are fuel
elements before the single conveyer (T1), one of the
elements will be transported to the next section of the
pipeline by the single conveyer (P1). When counter A
detects the signal of the element passing by (T2), the
burn-up measurement device begins to measure the
burn-up of the element after a period of time(P2, P3). If
the element has not reached the target burn-up (T4)and
there are no elements in lifting system A(P5), the element
will be transported to liftin g system A by the locator(P6).
When counter B detects the signal of the element passing
by (T6), the stop device will let the element into the co re
after a period of time (P7, P8). Then the stop device
returns to the former status(P9). If the element has
reached the target burn-up and there are no elements in
temporary storage system B(T11), the distribution system
will connect with temporary storage system B (P11). Then
the element is transported to temporary storage system
B(P12). When counter C detects the signal of the element
passing by(T13), the distribution system will return to the
former status to connect with lifting system A(P13). Then
the judgment that whether there are elements before the
single conveyer starts again.
When the command of stopping the main cycling is
received, T8 in PN1 is fired. Then the discharge device is
turned off. If there are no elements in the pipeline, T10 in
PN2 is fired. Pout gets a token and gives out the signal
that the main cycling is over.
The meanings of the places, transitions and time used
in Figure 2 are listed in Table 1.
3.3. The Other Timed Places Control Petri Nets
Models
The TPCPN models of the other processes are shown in
Figures 3-6, including inputting the new fuel elements
into temporary storage system A, transporting the fuel
elements from temporary storage system A into the core,
discharging the spent fuel elements and emptying the
core. The operation process will not be discussed in de-
tail any more.
4. The Simulation of Fuel Elements Cycling
System with Arena
Based on the TPCPN models of FECS, the simulation is
conducted with the software Arena. Arena is widely used
for system simulation. TPCPN models can be converted
to Arena models very conveniently. Referring to the pa-
rameters given by reference [6], some input data for si-
mulation are listed in Table 2.

H. B. LIU ET AL. 513
Table 1. The meanings of the places, transitions and time in TPCPN2.
Place Meaning Time Meaning TransitionMeaning
P1 The single conveyor operates. d1 The operation time of the single
conveyor. T1 There are elements before the single conveyor.
P2 Delay. d2 Delay. T2 Counter A detects the signal of the
element passing by.
P3 The burn-up measure operates. d3 The operation time of the burn-up
measure device. T3 Designed for sequence, T3=1.
P4 Designed for status. d4 Meaningless, d4=0. T4 The element has not reached the target
burn-up.
P5 The status that there are no
elements in lifting system A. d5 Meaningless, d5=0. T5 Designed for sequence, T5=1.
P6 The locator operates to transport
the element to lifting system A. d6 The operation time of the locator. T6 Counter B detects the signal of the element passing by.
P7 Delay. d7 Delay. T7 Designed for sequence, T7=1.
P8 The stop device transports the
element into the core. d8 The operation time of the stop device.T8 Designed for sequence, T8=1.
P9 The stop device returns to the for-
mer status. d9 The length of time for the stop device to return to the former status. T9 Designed for sequence, T9=1.
P10 The stop device has returned
to the former status. d10 Meaningless, d10=0. T10 The command of stopping the cycling
is received and there are no elements
in the pipeline.
P11 The distribu tion system connects
with temporary storage system B. d11 The length of time for the distribution
system to connect with temporary
storage system B. T11 The element has reached the target
burn-up and there are no elements in
temporary storage system B.
P12 The locator operates to transport the
element to temporary storage sys-
tem B. d12 The operation time of the locator. T12 Designed for sequence, T12=1.
P13 The distribution system connects
with the lifting system for cycling. d13 The length of time for the distribution
system to connect with lifting
system A. T13 Counter C detects the signal of the
element passing by.
- - - - T14 Designed for sequence, T14=1.
Figure 3. The TPCPN mode l of inputting the new fuel elements into temporary storage system A (TPCPN3).

H. B. LIU ET AL.
514
Figure 4. The TPCPN model of transporting the fuel elements from temporary storage system A into the core (TPCPN4).
Figure 5. The TPCPN model of discharging the spent fuel elements (TPCPN5).
Figure 6. The TPCPN model of emptying the core (TPCPN6).
Table 2. Some input data for simulation.
Data Unit Value
The design capacity of temporary storage sys-
tem A. - 100
The length of time for the fuel element lifting in
lifting system A. s 9.6
The length of time for the fuel element lifting in
lifting system B. s 3.0
The operation time of the delivery device. s 1.0
4.1. The Simulation of Uploading Fuel Elements
into the Core for the First Time with Arena
During this stage, 6 thousand to 12 thousand fuel
elements will be uploaded into the core. The pro cesses of
inputting the new fuel elements into temporary storage
system A and transporting the fuel elements from
temporary storage system A into the core will be carried
out. The gas needn’t be changed.
Considering the capacity of temporary storage system
A, a group of 100 fuel elements will be put into tempo-
rary storage system A at regular intervals. Then the ele-

H. B. LIU ET AL. 515
ments will be lifted in lifting system A and transported
into the core.
The simulation result shows that if the time period
be
and shorten
th
fuel elements into
th
able 3 that as the
nu
able 3. The relationship between the number of elements
the number of the minimum time the time it costs
tween each two groups is 9 min, the utilization rate of
lifting system A is 80.07% while the utilization rate of
temporary storage system A is as high as 92.22%. In this
case, it will take 14.70 hours to transport 10 thousand
fuel elements into the core. If the task is 12 thousand
elements, the time cost is 17.65 hours. The utilization
rate of temporary storage system A is so high that the
speed o f uploading fuel elements is li mited.
In order to improve the speed of uploading
e consuming time, a method called grouped tandem
pneumatic lifting (GTPL) given by reference [7] can be
used for the lifting process of the fuel elements. This
method can realize several elements lifted together. The
process of lifting is steady. Thus the lifting and trans-
porting efficiency is much higher.
The task is to upload 10 thousand
e core. If the maximum utilization rate of lifting system
A is limited to below 90%, the relationship between the
number of elements lifted together and the time it costs
to finish the task is listed in Table 3.
A conclusion can be got from T
mber of elements lifted together increases, there is a
marked decrease in the minimum time between each two
groups. The time required to finish the task is reduced.
T
lifted together and the time it costs to finish the task.
elements lifted
together period between each two groups (min) to finish the task (h)
1 9.3 15.50
2 5.3 8.83
3 4.0 6.67
4 3.4 5.67
5 2.9 4.83
Thn bfueo
the fta
pleteorter tim
he core is simulated. The result
s
-
celle speed of emptying the core is limited by
aximum speed
of
be emptied in a shorter time.
quirements on
TPCPN has time properties and con-
an describe the control logic accu-
orld Development of Nu-
Temperature Gas-cooled
Reactor,” Chinese Journal of Nuclear Science and Engi-
neering, 2000(
gdes.2009.02.023
able 4. The simulation result of emptying the core with
mber of the maximum number of the time it costs
T
GTPL.
the nu
elements lifted
together uploading elements from the core (min-1) to empty the core (day)
1 9.6 43.40
2 17.6 23.67
3 24.5 17.01
4 30.0 13.89
5 35.3 11.80
6 40.0 10.42
e method ca
e core for th
d in a sh
e used for uploading
irst time so that the
e.
l elements int
sk can be com-
4.2. The Simulation of Emptying the Core with
Arena
The process of emptying t
shows that the process of lifting the spent elements ha
been the bottleneck as the burn-up measurement is can
d. So the
the process of lifting the spen t elements.
In order to meet the requirements of the speed, the
method of GTPL is used. The simulation result is shown
in Table 4.
It can be seen from Table 4 that the m
uploading elements from the core increases as the
number of elements lifted together increases. In this way
the core can
5. Conclusions
FECS of pebble bed reactors has very complex control
logic. Every control link has very strict ac
time and sequence.
trol properties. It c
rately. So it’s very suitable for the modeling of FECS. In
addition the simulation of FECS can be conducted to
analyze the control logic. This provides the basis for the
design opt i mizati o n of react o r s.
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