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Nuclear Engineering and Design/Fusion 1 (1984) 51-60
North-Holland, Amsterdam
W i l l i a m E. K A S T E N B E R G
School of Engineering and Applied Science, University of California, Los Angeles, California 90024, USA
Received May 1983
Afterheat and decay heat removal systems will be important safety features in fusion and fusion-fission hybrid power plants.
Decay heat removal considerations for fission power reactors are reviewed and design criteria discussed. Aspects of fusion and
fusion-fission afterheat and decay heat removal are also reviewed. It was found that afterheat thermal loads in fusion power
reactors are a factor of 5 to 10 less than decay heat loads in fission power plants. However, they remain relatively constant over
time periods of interest (out to a year in designs employing stainless steel), as compared to fission plants, whose decay heat
loads drop an order of magnitude during the first day.
Deterministic criteria for afterheat removal are presented. Although based upon fission reactor experience, they are modified
to account for these differences. A probabilistic criterion was developed which is based on public health and economic
considerations. A goal of 15 × 10 -6 per reactor year was established for afterheat removal in fusion.
For fusion-fission hybrid reactors, a goal ranging between 6 x 10 -6 and 30 × 10 -6 per reactor year was established. The
upper limit corresponds to the recent NRC safety goal quideline for core melt frequency (1 x 10-4/year), which has been
suggested for the decay heat removal function in Pressurized Water Reactors. These goals are to be applied to a reliability
analysis where major uncertainties can be quantified.
1. I n t r o d u c t i o n
An important phenomenon of power plants using
nuclear fuel is that they continue to produce energy at
low levels after the nuclear reactions cease. Because of
this phenomenon, systems a n d / o r features must be
incorporated into the design of these plants to remove
this continued production of energy, called decay heat
in fission reactors and afterheat in fusion reactors.
Although fission power reactors have been built and
operated for over 25 years, the subject of decay heat
removal is a very active design and regulatory issue [1].
In a fission plant, decay heat is primarily generated
by the radioactive decay of the fission products and
secondarily by the decay of actinides and the induced
activity in the structural material. In a fusion plant,
afterheat is primarily generated by the induced activity
in the blanket, e.g. the first wall, the magnet shields,
reflectors and the other structural material. Induced
radioactivity in either reactor is primarily due to neutron interaction with reactor components. The impor* Work performed while the author was a consultant to EPRI.
tance of decay heat or afterheat removal following
normal and off-normal operation of a plant is twofold:
to protect the economic investment by insuring the
structural integrity of the reactor, and to protect the
health and safety of the public by preventing the release
of radioactive material.
The objectives of this paper are as follows: (1) to
review the status of decay heat removal for fission
power reactors, (2) to discuss the afterheat and decay
heat removal question for fusion and fusion-fission
hybrid power reactors, and (3) to develop some guidance and criteria for dealing with these issues for
fusion and fusion-fission hybrid power reactors.
Although general design criteria exist for fission reactors [2], the results of several studies show that improvements in decay heat removal capability can significantly reduce public risk [3-5]. Moreover, with the
advent of quantitative safety goals for fission plants
[6,7], there is also a desire to augment these deterministic criteria with probabilistic criteria [8-10].
For fusion and fusion-fission hybrid power plants, a
number of conceptual design studies have been employed to explore the relative merits of candidate blan-
0 0 2 9 - 5 4 9 3 / 8 4 / $ 0 3 . 0 0 © E l s e v i e r S c i e n c e P u b l i s h e r s B.V.
( N o r t h - H o l l a n d Physics P u b l i s h i n g D i v i s i o n )
W.E. Kastenberg / Design criteria for afterheat and decay heat removal
ket materials with respect to induced activity, biological
hazard potential and afterheat [11-15]. It is a goal of
this paper to initiate further consideration of this essential issue as fusion and fusion-fission hybrids move
from the conceptual stage to the engineering design and
development stage.
2. Decay heat removal in fission reactors
Under normal operation, the energy produced in a
light water reactor (LWR) is removed as pressurized
water or steam to produce electricity via the turbine
generator. Following reactor shutdown, the reactor produces insufficient power to operate the turbine. Therefore other measures must be available to remove decay
heat to ensure that high temperatures and pressures do
not develop which could pose a threat to the reactor.
These measures have as their functional requirements:
(1) providing a means of transferring decay heat from
the reactor coolant system to an ultimate heat sink and
(2) maintaining sufficient water inventory inside the
reactor to ensure that the reactor coolant adequately
cools the reactor fuel.
Pressurized water reactors (PWRs) generally have
three means of removing decay heat: the auxiliary
feedwater system, the residual heat removal system and
the turbine bypass system. Reactor water inventory is
maintained by the high pressure safety injection system
or the chemical and volume control system [5].
Boiling water reactors (BWRs) usually combine these
two functions with the following systems: the residual
heat removal system, the reactor core isolation cooling
system (RCIC) and the turbine bypass system. The
RCIC system operates as a high pressure system, and it
is backed up by a high pressure core spray system. In a
BWR, the residual heat removal system can operate in a
number of different modes for both low pressure injection and decay heat removal [5].
A recent study [16] describes many of the design
variations that have evolved in the U.S. and abroad for
PWR and BWR decay heat removal systems. In general,
these variations involve the number of components or
equipment trains employed to make up the decay heat
removal systems. In the United States and abroad, the
following deterministic design criteria are used for decay heat removal systems [2]:
(1) Ensure that fuel integrity and pressure
boundaries are maintained.
(2) Withstand fire, sabotage, natural phenomena,
and other extreme conditions.
(3) Operate under normal and emergency power
(4) Provide manual backup control capability for
automatic systems.
(5) Monitor and maintain reactor coolant pressure
boundary through inspection, leak detection, and
isolation valving.
(6) Function despite the single failure of an active
component or the occurrence of small pipe
(7) Prevent shared normal or emergency equipment
from jeopardizing reliable safety operations.
(8) Provide uninterrupted cooling for thirty days.
Several non-U.S, countries have additional criteria:
(9) Initiate and operate automatically for a period
ranging from 10 minutes to 10 hours.
(10) Function despite the single failure of an active
or passive component in combination with a
maintenance outage involving a redundant system.
(11) Operate without on-site repair action for at least
12 hours and without offsite repair action for at
least 48 hours.
More detailed system information such as flow rates
and decay heat levels, number of trains and power
supplies are given in plant safety analysis reports (SARs).
However, much of this information presents design descriptions rather than criteria for a design.
The current regulatory interest in decay heat removal
comes as a result of the Reactor Safety Study [17] which
focused on the Surry PWR and Peachbottom BWR
whose decay heat removal systems were designed in
accordance with the general design criteria for U.S.
plants listed above. As noted by Berry and Sanders [5],
the following observations can be made for Surry (a
(1) Transients and certain small loss of coolant accidents (LOCAs) pose the highest probability for
core meltdown.
(2) Of all transients and small LOCAs, those involving the failure of high pressure injection and
auxiliary feedwater systems (for decay heat removal) pose the highest probability for core
Similarly the following observations can be made for
Peachbottom (a BWR):
(1) Transients, together with failure of the residual
heat removal, system, or the reactor protection
system, pose the highest probability for core
Recognizing the importance of decay heat removal in
preventing core meltdown, Ebersole and Okrent [3] were
the first to propose an alternative approach which included dedicated systems (the systems described above
W.E. Kastenberg / Design criteria for afterheat and decay heat removal
have other functional requirements as well as decay heat
removal), dedicated rather than shared power supplies
and was bunkered (i.e., especially protected from severe
internal and external hazards such as a turbine blade
missile, tornadoes, floods and sabotage).
Quantitative estimates of potential risk reduction
with improved decay heat removal has been the subject
of investigation at Sandia National Laboratory [5,16].
Their work can be summarized as follows:
(1) For the three-train Surry high pressure system
and auxiliary feedwater systems, system reliability improvements of as much as a factor of ten will result in
less than a factor of two decrease in overall core meltdown frequency.
(2) For the two train Peachbottom residual heat
removal system, improvements of as much as a factor of
ten in the reliability of either the residual heat removal
and high pressure service water systems, or the reactor
protection system will result in only about a factor of
two decrease in overall core meltdown frequency.
(3) In PWR's having two installed decay heat removal trains, estimated reductions in coremelt probability of at least a factor of ten were attained with the
addition of an auxiliary feedwater or high pressure
injection train.
(4) For BWRs, an add-on single train suppression
pool cooling/low pressure injection system gains a factor of about six reduction in coremelt probability.
.As noted in item 10 under design criteria, a philosophy has evolved in several European countries that
requires safety systems to be able to sustain both a
random failure of one train and a simultaneous maintainence outage of another train, and still retain 100%
operational capacity. This philosophy was not adopted
for improving decay heat removal reliability nor for
reducing the probability of coremelt. Rather, it was
adopted over a concern for special emergencies (e.g.,
airplane crash and explosive pressure waves, etc.), characterized by low frequency. Hence, effort has been
placed on providing three, four and sometimes six trains
for decay heat removal, even though the safety benefits
tend to decrease in a probabilistic sense beyond three
It is important to recognize that the Reactor Safety
Study, as well as the Sandia studies, are based upon
probabilistically evaluated events which do not include
special emergencies (e.g., plane crashes, severe floods,
tornadoes, etc.). The occurrence frequency and significance of special emergencies are not easily predicted,
and hence are difficult to quantify. On the other hand,
recent Probabilistic Risk Assessments (PRAs) for the
Zion [18] and Indian Point [19] power plants have
treated severe external events parametrically and deduced that while they do not dominate coremelt probability, they do contribute significantly to risk.
Before turning to the question of afterheat in fusion
and fusion/fission hybrid reactors, it is of interest to
mention decay heat removal in liquid metal, fast breeder
reactors (LMFBRs) and in gas cooled reactors (GCRs).
The decay heat removal system for the Clinch River
Breeder Reactor (CRBR) is typical of what one might
expect with a low pressure system and liquid metal
In addition to the normal decay heat removal path
consisting of the balance of plant steam/feedwater system (turbine bypass system) there are three backup
systems [20]. The first are protected air-cooled condensers which cool the steam drums, on each of the
three coolant loops. A second heat sink can be made
available by opening the safety relief valve in the steam
line between the steam drum and the turbine and venting steam to the atmosphere. A protected water storage
tank is available for supplying make-up (auxiliary) water,
while two of the auxiliary feedwater pumps are electrically driven and one is steam driven. Lastly, a completely separate "direct heat removal service" (DHRS),
is provided to remove decay heat directly from the
in-vessel, primary loop, and has as its heat sink, an air
blast heat exchanger. The latter represents diversity
from the water system in the steam loop.
The decay heat removal systems using the primary
and intermediate coolant loops depend on forced circulation by the main coolant pumps driven at approximately 10% speed by small pony motors which depend
on a source of electric power. Similarly the DHRS air
blast heat exchangers rely on electric power. Although
CRBR is designed with redundant and diverse power
supplies, the capability for decay heat removal by natural circulation is a desirable feature. With natural circulation, the inherent safety of the plant is enhanced since
no electric power is required to provide adequate circulation in the heat transport or steam generator systems
following shutdown.
Although CRBR and several other LMFBRs (the
German SNR-300 and the French Phrnix) are designed
for natural convection cooling, and the transition from
forced to natural circulation has been verified at the
Fast Test Flux Facility [21], several questions must still
be answered. These include demonstration under actual
LMFBR normal and off-normal conditions, as well as
the passivity of the ultimate heat sink (e.g., the air
cooled condensers) [22].
Gas cooled fast reactors (GCFRs) and high temperature gas cooled thermal reactors (HTGRs) have also
W.E. Kastenberg / Design criteriafor afterheat and decay heat removal
been designed with alternate and diverse decay heat
removal systems, For GCFRs, there are three separate
systems [21]:
(1) Steam bypass to the condenser using the normal
power conversion system,
(2) Operation of three shutdown cooling system loops
using the steam generators, and main helium circulators (pumps) driven by pony motors, and
(3) Three Core Auxiliary Cooling System (CACS)
The CACS loops have their own independent auxiliary circulators and cooling water loops. An air-blast
type heat exchanger provides the ultimate heat sink. The
CACS is designed to provide core cooling following all
design basis events, including the depressurization of
the primary cooling system. It has also been argued that
the heat transfer components within the CACS are
located at sufficient elevation differences such that natural circulation will transfer decay heat from the core to
the ultimate heat sink, provided the system is pressurized [23], although this was never verified.
For HTGRs there are two main modes for removing
decay heat:
(1) The Main Loop Cooling System (MLCS), composed of the steam generators, the main helium
circulators, the main loop isolation valves, and
the associated ducting.
(2) The Core Auxiliary Cooling System (CACS),
composed of a core auxiliary heat exchanger, an
auxiliary circulator, an auxiliary circulator service
system, and a core auxiliary cooling water system.
The CACS for an H T G R is an engineered safety
feature for decay heat removal in the event the main
loops are unavailable. A typical 1100 MW c H T G R
design calls for six main loops and 3 auxiliary loops,
each with its own circulators, heat exchangers and steam
generators. A recent study by Washburn [24] indicated
that the initiating events of greatest importance to
coremelt frequency are, (a) loss of adequate a-c power,
(b) loss of CACS shutdown heat-removal and (c) the
loss of main loop shutdown heat removal.
decay heat is primarily generated by the fission products, and although the relative yields change with neutron spectrum, the decay heat curve is somewhat universal. It is approximately 7% of operating power at shutdown, 2% at 1 hour, 1% at 5 hours, 0.5% at 1 day and
0.1% at 10 days.
3.1. Fusion systems
Since afterheat in fusion power plant conceptual
designs is due to neutron induced activity in the blanket, and primarily in the first wall, it is material dependent. Vogelsang et al. [11] examined afterheat as a
function of both time after startup and time after shutdown for three structural materials making up the first
50 cm of the blanket, in the UWMAK-I design (5000
MWth ). After 10 weeks of operation, the three materials
(type 316 stainless steel, vanadium-20% titanium and
niobium-l% zirconium) approached an afterheat value
of 22 MW at shutdown, or 0.4% of operating power. At
ten years of operation the type 316 stainless-steel (316
SS) and the niobium-l% zirconium ( N b - l Z r ) afterheat
reach 0.6% of operating power at shutdown. The
vanadium-20% titanium (V-20 Ti) remained relatively
constant between 10 weeks and 20 years at 0.4% power.
Following shutdown (after 10 years of operation) the
N b - l Z r structure afterheat remained fairly constant
( - 0.5% operating power) out to 10 days. Thereafter, it
drops drastically (a factor of 10 reduction after 10
weeks). The Type 316 SS afterheat remains fairly constant beyond 1 day (at 0.4% operating power), drops to
0.2% operating power at 1 year, and to 0.06% (an order
of magnitude) at 2 years. The V-20 Ti structure afterheat
decayed the quickest; from 0.4% operating power to
0.1% in 1 hour, to about 0.05% in 1 day (an order of
magnitude reduction). It appears then, that the 316 SS
blanket structure maintains, on the average, a relatively
constant afterheat value for several years after shutdown compared to other materials.
In a further study of first wall/blanket materials,
Conn et al. [12] compared induced activity and afterheat
in five design studies as follows:
3. Afterheat considerations in fusion and fusion/fission
Before attempting to postulate design criteria for
fusion and fusion/fission hybrid reactors it is of interest
to examine the nature of afterheat in these systems.
Decay heat removal in fission power reactors is based
upon a standard decay heat curve which gives the
percent of operating power as a function of time. Since
Afterheat as % power
1 Week
316 SS
316 SS
PE-16 b
SAP = Sintered Aluminum Product (88~ AI, 12% Al203).
b Pc-16 = 43% nickel, 39% iron, 18% chrome.
W.E. Kastenberg / Design criteria for afterheat and decay heat removal
A detail of the first 100 minutes (1½ hours) showed a
fairly constant power rating for all cases but the niobium
which dropped by a factor of 5 within the first six
seconds and then remained constant.
Blankets including the materials TZM (0.45%
titanium, 0.1% zirconium, remainder molybedinum), and
2024 A1 (aluminum) were also compared in UWMAK-I
by Vogelsang [13]. The total afterheat, at shutdown
following two years of operation for TZM and V-20 Ti
was 1.4% and 1.5% of operating power respectively. The
2024 AI and 316 SS had afterheat on the order of 1%
full power. Except for the V-20 Ti which dropped a
factor of 5 in the first hour, the others remained fairly
constant out to one day. In this study, the entire blanket
was considered, rather than 50 cm.
Recently, Youssef and Corm [15] have examined
induced radioactivity and influence of materials selection in DD and DT fusion reactors. For the SATYR
design using a deuterium-deuterium fuel cycle, a SAP
blanket at shutdown has a power rating that is 13% of
operating power. For a ferritic steel blanket (HT-9), the
afterheat is 0.6% operating power. Within 1 hour, the
SAP blanket is down to 1% afterheat, and down to ½%
at one day. In the HT-9 blanket the afterheat is constant to 1-hour, and then drops an order of magnitude.
Thereafter, it remains fairly constant (-0.02%) in the
time frame of 1 day to 1 year; after which it drops
drastically (an order of magnitude) due to the decay of
the Fe 55.
These reactors were compared with the WITAMIR-I
design [25] using HT-9 and the STARFIRE design [26],
using PCA (2% molybdenum, 16 nickel, remainder steel).
The afterheat at shutdown in the two reactors are approximately 0.9% operating power, or about 30 and 40
MWth respectively. Both are fairly constant for several
3.2. Fusion-fission systems
Afterheat in fusion-fission (hybrid) power plant designs is due to structural activation (first wall/blanket),
fission product decay, and decay of actinide and transuranic elements. Hybrid systems have been proposed as
power producers, fissile fuel producers and actinide
For a fast fission blanket, Kastenberg et al. [27]
determined that the fission product inventory of a hybrid should not differ significantly from that of fission
reactors. In this regard then, a hybrid reactor would
posses both the afterheat requirements of pure fusion
with respect to the first wall and structural materials
and the decay heat removal requirements of a fission
Recently there has been interest in fission suppressed
blankets for producing fissile fuel [28-30]. Since the
fission product decay heat would dominate a hybrid, the
suppression of fission for breeding purposes, should
also lower the decay heat removal requirements. This is
shown in table 1, which is reproduced from ref. [28].
Examination of table 1 shows several important trends.
For fast fission blankets the decay heat power density
produced in the fertile zone, approaches the afterheat
produced in the first wall, in about a day. For the
fission suppressed blanket, the first wall afterheat
dominates within an hour of shutdown.
3.3. Remarks
The brief survey presented here indicates that
afterheat removal in fusion systems is materials dependent. However, a general trend seems to be present;
afterheat thermal loads will be about a factor 5-10 less
than fission decay heat thermal loads, but will remain
Table 1
Total volumetric afterheat production rates a (W/cm3) at shutdown, and at 1 h and 6 h after shutdown
Blanket concept a
Hours after shutdown
First wall
Uranium fast-fission
Thorium fast-fission
Thorium fission suppressed
Pure fusion
a Based on 4000 MWth total power.
Fertile zone
W.E. Kastenberg / Design criteria for afterheat and decay heat removal
relatively constant over periods of interest (from shutdown to 1 day, for stainless steel out to one year). This
latter attribute differs from fission decay heat which
drops an order of magnitude within 1 day. For
fusion-fission hybrids, the combined heat load (decay
plus afterheat) is also sensitive to the blanket design.
For the first day, fast fission blankets resemble fission
reactor decay heat loads. For fission suppressed blankets, afterheat dominates after 1 hour.
4. Criteria for fusion and fusion/fission afterheat and
decay heat removal systems
It has been recognized that loss of afterheat and
decay heat removal capability in fusion and fusion-fission hybrid power plants will be a major contributor to
risk [29-31]. In this context, risk can be taken in the
probabilistic sense: frequency times consequence. Furthermore, consequence includes both health effects and
economic loss.
A number of conceptual designs have been completed for various fusion and fusion-fission systems,
but little attention has been paid to this safety question
as a design issue. Balance of plant designs usually
include systems and components for normal power operation (e.g., pumps, steam generators, loops, turbines,
etc.), but not for afterheat and decay heat removal.
From a safety viewpoint, calculations are performed for
a variety of scenarios such as loss of flow and loss of
coolant, and time-to-melt or time-to-structural failure
are used as figures of merit. Although these considerations are important in determining the consequences of
accidents, and in the initial choice of materials and
coolants, they are of little use to the designer in laying
out the balance of plant. In this section two types of
criteria are proposed for design consideration.
4.1. Deterministic criteria
In section 2, eleven general design criteria were given
for decay heat removal systems in fission power plants.
Before determining the applicability of these criteria
a n d / o r modifying them, several points should be discussed. Afterheat generation in first wall/blanket
materials represent a smaller percentage (on the order of
1~ or less operating power) than fission reactor decay
heat (on the order of 7~) at shutdown. On the other
hand, afterheat generation tends to be fairly constant
for up to a year (for stainless steel) following shutdown,
while decay heat generation drops an order of magnitude within a day. Hence, up to 50 MWth may have to
be removed for periods of 1 week to 1 year in a fusion
With these comments in mind, the following criteria
appear to be appropriate:
1. Ensure that blanket and fuel structural integrity,
and pressure boundaries are maintained.
2. Withstand fire, sabotage, natural phenomena, and
other extreme conditions.
3. Operate under normal and emergency power conditions.
4. Monitor and maintain coolant boundary through
inspection, leak detection and isolation valving.
5. Prevent shared normal or emergency equipment
from jeopardizing reliable safety operations.
6. Initiate and operate automatically for a period ranging from 1 hour to 1 day.
7. Provide manual backup control capability for automatic systems.
8. Provide uninterrupted cooling for up to two months.
9. Function despite the single failure of an active or
passive component in combination with a maintainence outage involving a redundant system.
10. Operate without on-site repair action for at least 5
days and without off-site repair action for at least 1
The basic approach in formulating these criteria was
to adopt fission reactor criteria as appropriate but
account for the prolonged generation of afterheat. It
should be pointed out that the varying time scales
reflect the dependence of the afterheat load on the
materials employed. A more conservative approach was
taken to the single failure criterion (number 9) because
of the potentially large economic loss should afterheat
removal fail.
4.2. Probabilistic criteria
Quantitative or probabilistic safety criteria to provide guidance to reactor designers have been used in the
U K for several years and have been found to be a useful
tool in the design process [32]. With the increased
emphasis on the use of a quantitative approach in the
US, there is now an interest in developing quantitative
criteria for the main safety functions of fission reactors,
both for assessing the adequacy of the safety systems in
existing plants and for providing guidance to the designers of new plants.
Recently Cave et al. [10] developed a screening
criteria for evaluation of decay heat removal in PWRs.
The starting point is a set of safety goals for LWRs that
was published by the NRC for public comment [7]. The
principal goals in this set are based on public health
W.E. Kastenberg / Design criteria for afterheat and decay heat removal
Table 2
Risks for evaluation of afterheat removal
Public health
Onsite economic
Offsite economic
Early fatalities
Cost of energy replacement
Delayed fatalities
Early illness
Delayed illness
Genetic effects
Repair costs
Clean up costs
Occupational health costs
Capital investment loss
Public damage (loss of gross national product
due to interdiction)
Lost wages
Decontamination costs
Public health costs
Evacuation/rehousing costs
Secondary costs (higher electricitycosts affect
industrial production)
risk, and there is a supporting goal relating to the
acceptable probability of coremelt, i.e., 10 -4 per reactor
year, median value. An allocation scheme was developed which appropriated 25 x 10 -6 per reactor year to
the shutdown decay heat removal phase (scram to hot
shutdown) and 5 × 10 -7 for the residual heat removal
phase (hot shutdown to cold shutdown) for PWRs.
Because fusion power plants will have very large
capital costs, economic as well as public health risks
should be included in developing criteria for afterheat
removal. Examples of the risks that should be considered are shown in table 2.
The work of Kazimi and Sawdye [33] is particularly
useful in developing criteria for afterheat removal systems. Beginning with the premise that the potential
radiological hazards associated with accidents in fusion
reactors should be less than those of commercial light
water reactors, Kazimi and Sawdye determined maximum tolerable frequencies for large accidents. These
frequencies were defined so as to assure that releases of
fusion reactor induced radioactivity (not tritium) do not
imply a greater radiological hazard than in either the
WASH 1400 PWR or BWR.
Utilizing the UWMAK-I (316 SS blanket) and the
UWMAK-III (TZM blanket) designs, it was determined
that maximum tolerable release frequencies were 10 -5
and 4 x 10 -6 per reactor year, respectively. Noting that
the radioactivity inventories used were among the highest
possible in Tokamak reactors, and that no release mitigation factors were employed, it was concluded that
these numbers represent lower bounds.
From an economic viewpoint, the work of Stucker et
al. [34] and Strip [35] are particularly useful. Stucker et
al. focused on the costs of closing the Indian Point
Nuclear Power Plants (two units) before their useful life
was over. They estimated that the costs would be between $7.7 billion and $17.4 billion and was composed
of the incremental generating costs (Indian Point pro-
duces the cheapest electricity in the New York City
area), one time costs and savings, business costs and
secondary costs (net costs to the local economy). The
major component was the replacement power cost,
estimated at about $8 billion for the two units (approximately 2000 MWe).
Strip estimated the financial risks of. nuclear power
accidents as a function of accident severity and location
for several power plant types. Included were onsite and
offsite health costs, and onsite and offsite economic
costs. Strip's results, although site dependent, indicate
that onsite costs (including replacement power costs)
dominate, with offsite costs a close second. Onsite costs
varied between $1 and $10 billion, with clean-up costs
contributing $1 and $2 billion. For the most severe
accidents, offsite costs were as high as $10 billion. For
less severe accidents, the replacement costs could be
less, if the plant was repaired, and put back on-line.
For the purposes of the analysis here, the following
can be considered. A large accident at a fusion or
fusion-fission power plant involving loss of the blanket
and part of the primary coolant system due to a loss of
afterheat or decay heat removal would involve loss of
capital investment, replacement power costs and clean
up costs. Nuclear power plants costs such as CRBR and
Shoreham are approaching $3 billion. Fusion plants
have been estimated to cost between $2 and $10 billion.
Replacement power for a large fusion plant might be on
the order of the two units at Indian Point ($8 billion)
and clean-up costs might be similar to those estimated
for Three Mile Island ($2 billion). Although it is recognized that the capital investment cost must account for
depreciation, it can be assumed that loss of a fusion
plant might approach 10 billion dollars. If the blanket
wa repairable or replaceable, the loss might approach 5
billion dollars.
Taking 10 -5 per year as an upper limit for loss of
the blanket, and 10 billion dollars as the total potential
W.E. Kastenberg / Design criteria for afterheat and decay heat removal
loss, the expected risk (loss) is l0 s dollars/year,
($100000/year). If the goal were relaxed to 10 -4 per
year, the expected loss would be 106 dollars/year ($1
million/year). An expected loss of 106 dollars/year
appears to be at the high end of acceptability. Since
10 -5 per year for a loss of the blanket may be conservative from a public health viewpoint, and 10 -4 per year
intolerable from a financial viewpoint, a value between
them of 5 × 10 -5 per year might appear appropriate. If
this value is adopted, two other considerations must be
dealt with:
(a) The provision for adequate margin against the
effects of uncertainties in the estimation of the
risks, and
(b) an appropriate allocation of the goal due to loss
of afterheat removal and to other functions whose
failure could lead to loss of the blanket structure,
and release.
Uncertainties can be divided into three categories:
(1) Uncertainties due to variations in data and which
can be quantified;
(2) uncertainties due to describing extreme events
such as severe earthquakes, floods, etc., and extreme phenomena (the so-called special emergency
situations described in section 2), and
(3) uncertainties due to human errors, design errors,
and extreme human acts (sabotage).
Category 1 uncertainties are those included in design. Category 2 and 3 uncertainties are unquantifiable
at present, and can be treated as design margins.
Following Cave et al. [10], adequate margin can be
attained by assigning 40% of the goal to Category 1
uncertainties, with the remainder divided equally between Category 2 and 3. Hence for system design, the
loss of blanket frequency goal would be 20 × 10 -6 per
The allocation between the afterheat removal function and the others required to prevent loss of blanket
integrity should be arrived at from a plant specific
probabilistic risk assessment. Examination of the relative demand for these functions would optimize the
suballocation. In PWRs, experience leads to a 75%
allocation to decay heat removal function and 25% to
others, such as large break loss of coolant accidents and
other transients [17].
The most effective mechanism for releasing radioactive blanket material is oxidation following a lithium
fire in the U W M A K systems with lithium coolant following a loss of coolant [33]. Plasma disruption may be
a further cause for release, but appears to be localized in
nature [36]. For gas (helium) cooled systems, depressurization accidents have also been shown to be less of a
contributor to risk than loss of decay heat removal
capability [24]. In summary, there is little evidence to
believe that the split between the afterheat removal
function and the other safety functions will be much
different than that for fission reactors. Hence a 75/25
split is assumed, and will be varied below.
This final allocation yields a reliability requirement
of 15 × 10 -6 per year for afterheat removal in a fusion
reactor. This value may not be too far from optimum
for the following reasons. If the Category 2 and 3
uncertainties were reduced by a factor of five (12%
allocation), the allocation for afterheat removal would
double; i.e., it would be 33 × 10 -6 per reactor year.
Similarly, if it were found that other safety functions
were equal to afterheat removal; (as in BWRs) the goal
becomes 10 × 10 -6 per reactor year. Hence the range
10 x 10 -6 to 33 x 10 -6 , with a goal of 15 x 10 -6 appears reasonable. This analysis is summarized in table 3.
For fusion-fission hybrid reactors, the combined
afterheat and decay heat removal functions must be
considered. At one extreme, the blanket could be considered a fission reactor, and the N R C safety goal
applied. Using the arguments above, (40% for Category
1 uncertainties, 75% for decay heat removal function)
one arrives at an allocation of 30 × 10 -6 per reactor
Table 3
Allocation of afterheat removal reliability goal
Base case
Afterheat function
Other functions
15 × 10- 6/year
5 × 10- 6/year
20 x 10- 6/year
15 × 10-6/year
15 x 10- 6/year
Category 1 uncertainty (40%)
Category 2 uncertainty (30~)
Category 3 uncertainty (305g)
5 x 10- 5/year
Reduced uncertainty
Afterheat function
Other functions
33x10 -6
l l x l 0 -s
44×10 -6
3×10 -6
3X10 -6
Category 1 uncertainty (88~)
Category 2 uncertainty (6~)
Category 3 uncertainty (6~)
5 x 10-5/year
Reduced function
Afterheat function
Other functions
Category I uncertainty
10×10 -6
lOxlO -6
20x10 -6
W.E. Kastenberg / Design criteriafor afterheat and decay heat removal
year as the design goal. This extreme represents public
health. From an economic viewpoint, the loss of a
hybrid also represents the loss of an assured fuel supply
to a number of fission reactors. Hence some multiplier,
in terms of expected loss must be used.
Assuming that the monetary loss of a hybrid is a
factor of 5 greater than the monetary loss of a pure
fusion power reactor, or 50 billion dollars ($50 × 109),
and that the upper limit on expected loss is 1 million
dollars per year; the goal would become 20 × 10 -6 per
reactor year. Allocating for uncertainty and function as
before, the combined afterheat-decay heat function-goal
would be 6 × 10 -6 per reactor year. Hence a range of
6 × 10 -6 to 30 × 10 -6 per reactor year may be appropriate for hybrids.
and can be used in a variety of ways. They can be used
to determine the number of loops, steam generators
a n d / o r heat sinks required in the balance of plant. Or,
on the subsystem level, they can determine the number
of trains, pumps, valves, etc. needed to provide such
things as auxilliary feedwater.
It should be noted that one approach for insuring the
decay heat removal function in liquid metal cooled
systems is by natural circulation. Although some fusion
systems are designed with lithium coolants, the geometries employed might preclude its use as a viable option.
For fusion-fission hybrids, gas cooling appears to be
the favored approach, which necessitates high pressure.
Since depressurization is a design basis event, natural
circulation might be precluded as well.
5. Summary and conclusions
Design criteria for afterheat and decay heat removal
in fusion and fusion-fission power plants were proposed in this paper. Deterministic criteria were derived
by reviewing the general design criteria for fission plants
and modifying them to account for the different features of fusion and fusion-fission after- and decay heat.
The fraction of full power for afterheat (fusion)
tends to be an order of magnitude less than that for
decay heat (fission) and it decays rather slowly by
comparison. However, if fusion reactors produce high
thermal power (5000 MWth) the total heat load will be
comparable over the time of interest (1 day to 1 week).
As a result, it is proposed that the general design
criteria for fission plants be made more conservative for
fusion reactors: in particular it is proposed that the
afterheat removal system function despite both a single
failure of an active or passive component in combination
with a maintenance outage involving a redunant system.
Moreover, the time for automatic operation, and on-site
and off-site repair action are extended.
Probabilistic criteria were developed from both an
economic and a public health viewpoint. Using a lower
limit for public health risk and an upper limit for
financial loss, an allocation scheme was proposed to
account for uncertainty and function. The following
design criteria are proposed:
This work was supported by the Electric Power
Research Institute. The author wishes to thank Dr. Noel
Amherd for his interest, support, and encouragement.
Afterheat removal
decay heat removal
15 × 10-6/year
6 × 10- 6 to
30 × 10-6/year
These values are meant to be target values for design
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