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FFR_chap06.txt
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FFR_chap06.txt
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CHAPTER 6
CHEMICAL PROCESSING*
6-1. INTRODUCTION
One of the principal advantages of fluid fuel reactors is the possibility of
continually processing the fuel and blanket material for the removal of
fission products and other poisons and the recovery of fissionable material
produced. Such continuous processing accomplishes several desirable
objectives: (a) improvement of the neutron economy sufficiently that the
reactor breeds more fissionable material than it consumes, (b) minimiza-
tion of the hazards associated with the operation of the reactor by main-
taining a low concentration of radioactive material in the fuel, and (c) im-
provement of the life of equipment and stability of the fuel solution by
removing deleterious fission and corrosion products. The performance
and operability of a homogeneous reactor are considerably more dependent
on the processing cycle than are those of a solid fuel reactor, although the
objectives of processing are similar.
The neutron poisoning in a homogeneous reactor from which fission
product gases are removed continuously is largely due to rare earths [1],
as shown in Fig. 6-1. In Fig. 6-1 the rare earths contributing to reactor
poisoning are divided into two groups. The time-dependent rare earths
are those of high yield and intermediate cross section, such as Nd43
and Nd'#% Prl4l and Pm!'47) which over a period of several months could
accumulate in the reactor and result in a poisoning of about 209,. The
constant rare-earth poison fraction is due primarily to Sm'#® and Sm!5!
which have very large cross sections for neutron absorption but low yield,
and therefore reach their equilibrium level in only a few days’ operation.
Poisoning due to corrosion of the stainless-steel reactor system was cal-
culated for a typical reactor containing 15,500 {t* of steel corroding at a
rate of 1 mpy. It is assumed that only the nickel and manganese contribute
to the poisoning, since iron and chromium will hydrolyze and precipitate
and be removed from the reactor system; otherwise, corrosion product
poisoning would be four times greater than indicated in Fig. 6-1. The
control of rare earths and corrosion product elements is discussed in sub-
sequent sections of this chapter. Removal of solids from the fuel solution
also improves the performance of the reactor by diminishing the deposition
of scale on heat-transfer surfaces and reducing the possibility of erosion of
pump impellers, bearing surfaces, and valve seats.
*By R. A. McNees, with contributions from W. E. Browning, W. D. Burch,
R. E. Leuze, W. T. McDuffee, and 8. Peterson, Oak Ridge National Laboratory.
301
302 CHEMICAL PROCESSING [cHAP. 6
4.5 | !
A. Total Rare Ecrths
40 | B. Time Dependent Rare Earths
' C. Corrosion Products at 1 mpy
D. Constant (98.2% Rare Earths
3.5 + 1.8% Cd)
E. Sr8% 4 1c99
30} F. Alkali Metals ]
’ G. VIIB(13Y)
R H. Nobie Metals
e 2.5 (RR103)
2
z
0 30 60 90 120 150
Irradiation Time, days
Fig. 6-1. Poison effect as a function of chemical group in core of two-region
thermal breeder.
D,O
2 To Reactor
u, Th, Pa, Blanket
Fission Products
Slurry from DQ_O
Blanket | Recavery
Decay
! Storage
160 days)
Overflow Returned
to Reactor Core
U and
Fission
Products
F —
eed from—b\ Z——Hyd roclone
s /
Fission
Products
Reactor Core Solvent
v ‘ '{
Separation | Extraction
- - " Pa, T B
| Underflow Fission Products
Containing Decay | U
Insoluble | Storage
| Fission u (120 days) To Reactor
| Products To Reactor Core
Core
Fic. 6-2. Conceptual flow diagram for processing fuel and blanket material from
a two-region reactor,
The biological hazards associated with a homogencous reactor are due
chiefly to the radioactive rare earths, alkaline earths, and iodine [2].
The importance, as a biological hazard, of any one of these groups or nu-
clides within the group depends on assumptions made in describing ex-
posure conditions; however, I'3! contributes a major fraction of the radia-
tion hazards for any set of conditions. While the accumulation of hazardous
materials such as rare earths and alkaline earths will be controlled by the
processing methods to be described, less is known about the chemistry of
6-1] INTRODUCTION 303
Blanket
1.4 mUOQSO4
in D70 at
250°C
[—PDQO
1 D50 = Dissolution
Recovery [ | inHNO,
- Solvent
Extraction
Partition
Stripping
Solvent
=== Lrgnium Fission Plutonium Uranium
— Plutonium Product Waste
FiG. 6-3. Conceptual flow diagram for processing blanket material from a two-
region plutonium producer.
iodine in the fuel systems and methods for removing it. Ixisting informa-
tion on iodine processing is discussed in Section 6-3.
Schematic flowshects for proposed processing schemes for two types of
two-region aqueous homogencous reactors are shown in Figs. 6-2 and 6-3.
In both cases, solids are removed by hydroclones and concentrated into
a small volume of solution for further processing. The nature of such
processing will be determined by the exact design and purpose of the
reactor. Thus, for a two-region plutonium producer, the core and blanket,
materials would have to be processed separately to avoid isotopic dilution,
while for a thorium breeder, core and blanket material could be processed
together. However, if an attractive method should be developed for leach-
ing uranium and/or protactinium from a thorium-oxide slurry without
seriously altering the physical properties of the slurry, the two materials
could be processed separately. In a similar way, the relation between
iodine control and fission product gas disposal is such that neither problem
can be disassociated from the other. A specific, complete, and feasible
chemical processing scheme cannot be proposed for any reactor without
an intimate knowledge of all aspects of design and operation of the reactor.
However, some of the basic chemical knowledge needed to evaluate various
304 CHEMICAL PROCESSING [crAP. 6
possible processing methods has been developed and is presented in the
following sections.
6-2. CorE PRrROCESSING: SoLIDs REMOVAL
6-2.1 Introduction. Early in the study of the behavior of fisston and
corrosion products in uranyl sulfate solutions at temperatures in the range
250 to 325°C, it was found that many of these elements had only a limited
solubility under reactor conditions. Detailed studies of these elements
were conducted and devices for separating solids from liquid at high
temperature and pressure were constructed and evaluated. Based on this
work, a pilot plant to test a processing concept based on solids separation at
reactor temperature was installed as an adjunct to the HRE-2. These
processing developments are discussed in this section.
6-2.2 Chemistry of insoluble fission and corrosion products. Of the
nongaseous fission produets, the rare earths contribute the largest amount
of neutron poison to a homogencous reactor after a short period of operation
(Fig. 6-1). Therefore, a detailed study of the behavior of these elements
TaBLE 6-1
SOLUBILITY OF LANTHANUM SULFATE IN
0.02 m U0:804,—0.005m HaSO4 as A FuNcTION OF
SoLuTioON TEMPERATURE
mg La2(S04)s/kg H20
Temperature,
°C True Concentration required to
solubility initiate precipitation
190 250 760
210 130 360
230 54 167
250 25 77
270 12 36
has been made. All the rare earths and yttrium showed a negative tem-
perature coefficient of solubility in all the solutions studied and a strong
tendency to supersaturate the solutions, as shown in Table 6-1. With the
exception of prascodymium and neodymium, which are reversed, the solu-
hility at a given temperature and uranyl sulfate concentration increased
with increasing atomic number, with yttrium falling between neodymium
6-2] CORE PROCESSING: SOLIDS REMOVAL 305
and samarium, as shown in Table 6-2. Increasing the uranyl sulfate
concentration increased the solubility of a given rare-earth sulfate, as
shown in Table 6-3.
TABLE (-2
SOLUBILITY OF VARIOUS RARE-IARTH SULFATES IN
0.02m U0s804—0.005m HoSO4 aT 280°C
Solubility, Solubility,
Salt mg/kg H20 Salt mg/kg H20
Las(804)3 10 Nd2(S04)5 110
Ce2(804)3 50 Y2(S04)3 240
PI‘2(804)3 170 SHlQ(SO4)3 420
TABLE 6-3
Errect oF URANYL SULFATE CONCENTRATION ON THE SOLUBILITY OF
NEODYMIUM SULFATE AT VARIOUS TEMPERATURES
Nd2(S04)3 solubility, mg/kg H20
U, g/kg H20
250°C 280°C 300°C
5.7 270 115 73
10.8 400 200 120
16.6 770 300 180
22 4 > 1000 o00 500
In a mixture of rare-earth sulfates the solubility of an individual rare
earth 1s less than it would be if it were present alone. For example, the
solubility of praseodymium sulfate at 280°C is 170 mg/keg H»0 with no
other rare earths present, as compared with 12 mg,/ke H>0 in a solution
made up with a rarc-earth mixture containing 6 praseodymiuin sulfate.
Samples of the precipitating salts i1solated from solution at 280°C' have
usually been the sulfates and contained no uranium. However, under
special conditions a mixed sulfate salt of neodymium and uranium has been
observed [3].
The alkaline earths, barium and strontiun, also show a negative tem-
perature coeflicient, but not so strongly as do the rare earths; almost no
effect can be seen when the temperature of precipitating solutions is in-
306 CHEMICAL PROCESSING [cHap. 6
creased from 250 to 300°C. At 295°C in 0.02 m U02504—0.005 m H2S04
solution, the solubility of barium sulfate is 7 mg/kg HoO and that of
strontium sulfate is 21 mg/kg Ho0O. Both the alkaline and rare-earth
sulfates show a strong tendency to precipitate on and adhere to steel
surfaces hotter than the precipitating solutions, and this property can be
used to isolate these solids from liquids at high temperatures.
Other fission and corroston product elements hydrolyze extensively at
250 to 300°C and precipitate as oxides, leaving very low concentrations
in solution. Iron(III) at 285°C has a solubility of 0.5 to 2 mg Fe/kg Ho0
and chromium(III), 2 to 5 mg/kg HoO. At 285°C less than 5 mg of zir-
conium or niobium per kilogram of H20 remains in solution.
For other elements of variable valence, such as technetium, the amount
of the clement in solution is determined by the stable valence state under
reactor conditions. In general, the higher valence states better resist hy-
drolysis and remain in solution. Thus at 275°C in 0.02 m UO2S04 Te(VII)
is reduced to Te(IV) if hydrogen is present, and only 12 mg/kg H20 re-
mains in solution. However, a slurry of TcO» in the same solution but with
oxygen present dissolves to give a solution at 275°C with a technetium
concentration of more than 9 g/kg H»0. The same qualitative behavior is
observed with ruthentum. Selenium and tellurium in the hexapositive state
are much more soluble than when in the tetrapositive state [4].
A few eclements, e.g., cesium, rubidium, nickel, and manganese, intro-
duced into the fuel solution by fission or by corrosion of the system, are
very soluble under reactor conditions. Their removal and control are dis-
cussed in Section 6-1.
6-2.3 Experimental study of hydroclone performance. It is evident
from the preceding section that the amount of uranium withdrawn from
the reactor diminishes if the collection, eoncentration, and 1solation of the
insolubles can be effected at high temperature. One device capable of
collecting and concentrating solids at high temperature is a solid-liquid
cyclone separator called a “hydroclone,” or “clone.” A diagram of a hydro-
clone is shown in Fig. 6-4. In operation, a solids-bearing stream of liquid
is injected tangentially into the wide portion of a conical vessel. Solids
concentrate in a downward-moving layer of liquid and are discharged from
the bottom of the clone into the underflow receiver. Partially clarified
liquid leaves from the top of the clone through a vortex finder. Use of the
underflow recciver eliminates mechanical control of the discharge flow
rate and, by proper choice of hydroclone dimensions, any desired ratio of
overflow rate to underflow rate can be achieved. The driving foree for the
system is provided by a mechanical pump.
The factors influencing the design of an effective hydroclone for homo-
geneous reactor processing use have been studied, and hydroclone designs
6-2] CORE PROCESSING: SOLIDS REMOVAL 307
t/Overflow
] ——-DO
1%
Feed —-i
Hydroclone | //
Underfiow
Port
V5
3 £
e— Underflow
Receiver
Fig. 6-4. Schematic diagram of a hydroclone with associated underflow receiver.
based on these studies have been tested in the laboratory and on various
circulating loops [5]. All tests have shown conclusively that such hydro-
clones can separate insoluble sulfates or hydrolyzed materials from liquid
streams at 250 to 300°C. In the HRE-2 mockup loop a mixture of the sul-
fates of iron, zirconium, and various rare earths, dissolved in uranyl-
sulfate solution at room temperature, precipitated when injected into the
loop solution at 250 to 300°C. The solids concentrated into the underflow
receiver of a hydroclone contained 75% of the precipitated rare-earth
sulfates. When the lanthanum-sulfate solubility in the loop solution was
exceeded by 109, the concentration of rare earths in the underflow receiver
was four to six times greater than in the rest of the loop system; some
accumulation of rare earths was observed in the loop heater. A large
fraction of the hydrolyzed iron and zirconium was collected in the gas
separator portion of the loop. In the separator the centrifugal motion
given to the liquid forced solids to the periphery of the pipe and allowed
them to accumulate. Only about 109 of the solids formed in the loop was
recovered by the hydroclone, and examination of the loop system dis-
closed large quantities of solids settled in every horizontal run of pipe.
308
Reactor
Cell
Pump
CHEMICAL PROCLESSING
Underflow
Pot
Hydroclone
Recombine:
-Condenser
10 gal
Separator
Lsad
e
DZO Receiver
g Decay Tank {2)
Recombine:
-Condenser
HZO to Waste
Separator
100 gal
\
[cHAP. 6
Dissolver
7 gal @7\
Dissolver
Solution
DO Addition 67
»+ Fuel Addition Sampler o
]
Carrier
Transfer Tank
Fie. 6-5. Schematic flow diagram for the HRE-2 chemical processing plant.
TaBLE 64
Dmaensions oF HRE-2 HypROCLONES
Dimension, in.
Symbol Location . . _
0.25-in. 0.40-1n, 0.56-1n.
hydroclone hydroclone hydroclone
D1 Maximum inside 0.25 0.40 0.56
diameter
L Inside length 1.50 2.40 3.20
Dy Underflow port
diameter 0.070 0.100 0.148
Do Overflow port
diameter 0.053 0.100 0.140
Dy Feed port effec-
tive diameter 0.051 0.118 0.159
2] CORE PROCESSING: SOLIDS REMOVAL 309
Samples taken from the loop after addition of preformed solids and without
the hydroclone operating showed an exponential decrease in solids concen-
tration with a half-time of 2.5 hr; with the hydroclone operating, the half-
time was 1.2 hr. In the HRIE-2 chemical plant [5], operated with an aux-
iliary loop to provide a slurry of preformed solids in uranyl sulfate solution
as a feed for the plant, the half-times for solids disappearance and removal
were 11 hr without the hydroclone and 1.5 hr with it. The efficiency of the
hydroclone for separating the particular solids used in these experiments
was about 109, With gross amounts of solids in the system, concentration
factors have been as large as 1700.
Correlation of these data with anticipated reactor chemical plant oper-
ating conditions indicates that the HRE-2 chemical plant will hold the
amount of solids in the fuel solution to between 10 and 100 ppm. If neces-
zaryv. performance can be improved by increasing the flow through the
chemical plant and by eliminating, wherever possible, long runs of hori-
zontal pipe with low liquid veloeity and other stagnant areas which serve
to accumulate solids.
6-2.4 HRE-2 chemical processing plant.* An experimental facility to
test the solids-removal processing concept has been constructed in a cell
adjacent to the HRI-2. A schematic flowsheet for this facility is shown
in Fig. 6-5.
A 0.75-gpm bypass stream from the reactor fuel system at 280°C and
1700 psi ig circulated through the high-pressure system, consisting of a
heater to make up heat losses, a screen to protect the hydroclone from
plugging, the hydroclone with underflow receiver, and a canned-rotor
circulating pump to make up pressure losses across the system. The
hydroclone is operated with an underflow receiver which is drained after
each week of operation, at which time the processing plant is isolated
from the reactor system.
At the conclusion of each operating period 10 liters of the slurry in the
underflow pot is removed and sampled. The heavy water is evaporated
and recovered, and the solids are dissolved in sulfurie acid and sampled
again. The solution is then transferred under pressure to one of two 100-gal
decay storage tanks, Tollowing a three-month decay period, the solution
1= transferred to a shielded carrier outside the cell and then to an existing
sulvent extraction plant at Oak Ridge National Laboratory for uranium
decontamination and recovery. The sulfuric acid solution step is incor-
porated n the HRIS-2 chemical plant to ensure obhtaining a satisfactory
<umple. This step would presumably not be necessary in a large-scale
plant.
*Contribution from W. D. Burch.
310 CHEMICAL PROCESSING [cHAP. 8
Fic. 6-6. HRE-2 chemical plant cell with equipment.
6-2] CORE PROCESSING: SOLIDS REMOVAL 311
All equipment is located in a 12- by 24- by 21-ft underground cell located
adjacent to the reactor cell and separated from it by 4 ft of high-density
concrete. Other construction features are similar to those of the reactor
cell, with provisions for flooding the cell during maintenance periods in
order to use water as shielding. Figure 6-6, a photograph of the cell prior
to installation of the roof plugs, shows the maze of piping necessitated by
the experimental nature of this plant.
Dimensions of the three sizes of hydroclones designed for testing in this
plant are shown in Table 6—4. These three hydroclones, which have been
Blind Flange ;‘
Closure ‘{? !
1
i Y:‘X‘E:\'Y- AN !
b m&\ A0 Sy \\\\T{\*\
G
e < .:\‘.\\ .
i
i
o
N
Hexagonal Head —
ol oo
it :
Cap Plug
L R
|
|
o f For
*~" ]lLeak Detector
Spider
Overflow
Pressure Screw
Hydroclone
Retaining Plug
Gold Wire Gasket
F1c. 6-7. HRE-2 chemical plant hydroclone container.
selected to handle the range of possible particle sizes, are interchangeable
at any time during radioactive operation through a unique, specially ma-
chined flange, shown in Fig. 6-7. Removal of the blind closure flange ex-
poses a cap plug and retainer plug. Removal of these with long-handled
socket wrenches permits access to the hydroclone itself. This operation has
heen performed routinely during testing with nonradioactive solutions.
In processing homogeneous reactor fuel, a transition from a heavy- to a
natural-water system is desirable if final processing is to be performed in
conventional solvent extraction equipment. Such a transition must be ac-
complished with a minimum loss of D20 and a minimum contamination of
312 CHEMICAL PROCESSING [cHAP. 6
the fuel solution by H20 in recycled fuel. Initial tests of this step in the
fuel processing cycle have been carried out [6]. In these experiments a
mixture of 59, D0, 959%, H:20 was used to simulate reactor fuel liquid.
The dissolver system was cycled three times between this liquid and or-
dinary water, with samples being taken during each portion of each cycle.
Isotopic analysis of these samples showed no dilution of the D20 in the
enriched solution and no loss of D20 to the ordinary water system.
At expected corrosion rates, approximately 400 g of corrosion products
will be formed in the reactor system per week, and the underflow receiver
was therefore designed to handle this quantity of solids. The adequacy of
the design was shown when more than three times this quantity of solids
was charged to the underflow receiver and drained in the normal way with-
out difficulty.
Full-scale dissolution procedures have also been tested [6]. To minimize
the possibilities of contaminating the reactor fuel solution by foreign ions,
a dissolution procedure was developed using only sulfuric acid. This con-
sists of a 4-hr reflux with 10.8 M HoS04 in a tantalum-lined dissolver fol-
lowed by a 4-hr reflux with 4 3 H2S04, and repeated as required until
dissolution is complete. Decay storage tanks and other equipment required
to handle the boiling 4 3 HoSO4 are fabricated of Carpenter—20 stainless
steel. Tests have repeatedly demonstrated more than 99.59, dissolution
of simulated corrosion and fission products in two such eycles.
The HRE-2 hydroclone system has been operated as an integral part
of the reactor system for approximately 600 hr and for an additional
1200 hr with a temporary pump loop during initial solids-removal tests.
During this operating period, in which simulated nonradioactive fuel
solutions were used, the performance of the plant was satisfactory in all
respects.
6—3. Fission Propuct Gas DisposaL*
6-3.1 Introduction. To prevent the pollution of the atmosphere by
radioactive krypton and xenon isotopes released from the fuel solution, a
system of containment must be provided until radioactive decay has re-
duced their activity level. This is accomplished by a method based on the
process of physical adsorption on solid adsorber materials. If the adsorber
system 1s adequately designed, the issuing gas stream will be composed of
long-lived Kr®, oxygen, inert krypton isotopes, inert xenon isotopes, and
insignificant amounts of other radioactive krypton and xenon isotopes. In
case the activity of the Kr®5 is too high for dilution with air and discharge
to the atmosphere, the mixture may be stored after removal of the oxygen
*Contribution from W. E. Browning.
3] FISSION PRODUCT GAS DISPOSAL 313
40
r— 171717 1 ©° © B 1 oo
20—
10 —
- oh
E 5 SieYes —
'g Mo\ecu\c“
o -1
3 Vot Sieqes
E N\O\ecu 5 1 0",\ —
o cutes Sieve
3 o
E 2 12 ]
- gitico &2
0
<
3 5
» a0
g 1.0 3\2’5 S‘“COG —
e Tr e ]
e
.g_ | oW Hi-Sil %-303
> | —
x — /4 Dr\OCe\ —
05 —
gihca Gel-70
0.2 \at Gieves- AR —]
Zeo-Dur MoleculS
Micro Cel-A
(1 1 1 [ [ [ |
0.1l
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Krypton Pressure, mm
Fic. 6-8. Adsorption of krypton on various adsorbents at 28°C.
or further separated by conventional methods into an mert xenon fraction
and a fraction containing Kr®5 and inert krypton.
6-3.2 Experimental study of adsorption of fission product gases. Evalu-
atiou of vartous adsorber materials based on experimental measurements of
the equilibrium adsorption of krypton or xenon under static conditions is
in progress [7]. Results in the form of adsorption isotherms of various
solid adsorber materials are presented in Fig, 6-8,
A radioactive-tracer technique was developed to study the adsorption
efficiency (holdup time) of small, dynamic, laboratory-scale adsorber
systems [8]. This consists of sweeping a brief pulse of Kr8 through an ex-
perimental adsorber system with a diluent gas such as oxygen or nitrogen
314 CHEMICAL PROCESSING [cHAP. 6
and monitoring the efluent gases for Kr®5 beta activity. The activity in
the gas stream versus time after injection of the pulse of Kr®5 is recorded.
A plot of the data gives an experimental elution curve, such as shown in
Fig. 6-9, from which various properties of an adsorber material and ad-
sorber system may be evaluated.
Among the factors which influence the adsorption of fission product
gases from a dynamic system are (1) adsorptive capacity of adsorber ma-
terial, (2) temperature of adsorber material, (3) volume flow rate of gas
stream, (4) adsorbed moisture content of adsorber material, (5) composi-
tion and moisture content of gas stream, (6) geometry of adsorber system,
and (7) particle size of adsorber material. The average time required for
the fission product gas to pass through an adsorber system, fmax, 1s influ-
enced by the first five of the above factors. The shape of the experimental
elution curve is affected by the last two.
The temperature of the adsorber material is of prime importance. The
lower the temperature the greater will be the adsorption of the fission gases,
and therefore longer holdup times per unit mass of adsorber material will
result. The dependence of adsorptive capacity, k, on temperature as de-
termined by holdup tests with some solid adsorber materials is shown in
Table 6-5.
TABLE 6-H
ADsSoRPTIVE CaprAcITY OF VARIOUS MATERIALS AS A FUNCTION
oF TEMPERATURE
ce gas/g adsorbent*®
Gas Diluent Adsorber
273°K 323°K 373°K
Xe Oy Charcoal 4.7 x 103 4.0 x 102 80.0
Kr He Charcoal 1.8 x 10° 34 9.6
Kr Oz or N» Charcoal, 68 24 11.0
Kr O; Linde Molecular 23 9 4.5
Sieve SA
Kr O Linde Molecular 11 5.7 3.5
Steve 10X
*(Gas volume measured at temperatures indicated.
6-3] FISSION PRODUCT GAS DISPOSAL ald
1 | i
Average Holdup Time (rmax) _l
Kr85 Activity in Effluent Gas Stream —»
Breakthrough Time (1}
l I J
Time After Injection of Kr85 —
F1ac. 6-9. Experimental Kr83 elution curve.
At a given temperature, the average holdup time, fyax, 18 inversely pro-
portional to the volume flow rate of the gas stream. If the volume flow
rate ix doubled, the holdup time will be decreased by a factor of two.
All the solid adsorber materials adsorb moisture to some degree. Any
adsorbed moisture reduces the active surface area available to the fission
gases and thus reduces the average holdup time,
The geometry of the adsorber system influences the relation between
breakthrough time, f,, and average holdup time, ¢max, as shown in I'ig. 6-9.
Ideally, for fission product gas disposal, a particular atom of fisslon gas
should not emerge from the adsorber system prior to the time #,... Since