Method and apparatus for filtering atomic or molecular contaminants from a gas

Tubular or rod shaped pieces of a filter material having a holding-back capability with respect to the contaminant are arranged in the interior of a containing cylinder through which the gas flows, so as to provide passages for gas flow along the surface of the filter material pieces, the latter being typically disposed with their long dimension parallel to the direction of gas flow. For a prescribed pressure loss through the filter, a maximum value should be obtained for a quantity that is equal to the filter length in the direction of gas flow times the second Stanton number divided by the hydraulic diameter, the latter term being equal to four times the volume of the space in the cylinder not occupied by the filter material divided by the surface of the filter material in contact with the gas. The second Stanton number is the quotient of the material transfer coefficient and the flow velocity of the gas. Favorable filter escape coefficients are made available with relatively low pressure drop, so that the filter can be interposed in the main cooling gas line of a nuclear reactor for removing contaminants as radioactive caesium.

This invention relates to a filter for cleaning a flowing gas with respect 
to contaminating material present in the gas as atomic or molecular 
particles by collecting the contaminating material on the filter and to a 
method of design and manufacture of such a filter. In particular, the 
invention relates to a method and an apparatus providing, in a cavity with 
gas-tight lateral walls, spaced pieces of a filter material having an 
effect of holding back the particles to be removed from the gas by a 
mutual effect therewith over a certain length in the direction of the flow 
of the gas and with a certain effective free diameter (or hydraulic 
diameter) d.sub.eff for the flow of gas. 
It is known to provide filters of the above-mentioned type in which the 
filter material is provided as a loose layer, for example, a granular 
material within the lateral casing of the filter through which the gas 
flows. Layers of material are used that provide so far as possible a 
maximum surface area of the filter material. For the design of the filter, 
for example the determination of the length of material through which the 
gas flows, the starting point is determined from experimental values that 
are available with respect to the particular material that is intended to 
be used. There is disadvantage in such arrangements, however, that for 
determination of what is a suitable filter for prescribed operating 
conditions, very expensive and troublesome experiments are necessary, in 
which various kinds of filters are subjected to the prescribed operating 
conditions. In the known filters of this kind, moreover, the filter layers 
produce very high pressure loss, so that in general they cannot be 
interposed in main gas ducts of an industrial facility. 
The Present Invention 
It is an object of the present invention to provide a procedure for 
designing and manufacturing a filter that makes it possible to produce a 
filter taking account of the material properties of the filter material, 
of the mutual reaction with the particles to be held back, as well as the 
dimensions of the filter mass, optimally suited to the particular task, 
without making it necessary to carry out expensive and time-consuming 
sequences of experiments for fitting the filter design to the particular 
requirements. 
It is also an object of the invention to produce a highly effective atomic 
or molecular filter having a low flow resistance. 
Briefly, the filter material consists of a material having the highest 
possible holding-back capability for the particles to be filtered out of 
the gas, and it is present within a flow-through cavity in a suitable 
geometry, preferably in the form of elongated elements such as rods, 
tubes, strips and the like, spaced from each other in the usual case in 
which there are more than one, providing through-passages for the flow of 
the gas extending over the length l of the filter material and having a 
hydraulic effective diameter d.sub.eff, and the dimensions are so 
determined that, for a given pressure loss .DELTA.p and for a given filter 
volume, the product 
##EQU1## 
is maximum, where the foregoing product is further defined as follows with 
reference to the quantities involved therein: 
##EQU2## 
is the hydraulic diameter in cm; l is the length l of the filter material 
in cm; 
V.sub.o is the cavity volume in cm.sup.3 within the lateral walls in the 
region of the length l left after deduction of the space occupied by the 
filter material therein; 
F is the surface of the filter material in cm.sup.2 ; 
St'=(h/v) is the second Stanton number; 
h is the mass transfer coefficient in cm/sec; 
v is the flow velocity of the gas in cm/sec; 
In order to fit the filter of the present invention as effectively as 
possible to prescribed operating conditions, it can be useful to 
investigate, as a preliminary step of design, a variety of filter 
dimensions for several filter materials, in order to obtain the most 
effective filter for the purpose, in a manner more particularly set forth 
below as the method of the present invention. It is particularly effective 
to constitute the filter of the present invention of one or more tubes of 
the filter material, and preferably a number of them are used in a cavity 
through which the gas flows, the gas-flow being in the logitudinal 
direction of the tubes. The filter material can also be provided in the 
form of rods so arranged in a gas-flow cavity that the gas flows either in 
the length direction of the rods or across them. The method of determining 
the constitution of a filter according to the present invention leads to 
particularly advantageous embodiments of the filter apparatus of the 
present invention. 
In dealing with filters of the type here concerned, it is useful to refer 
to the "filter escape coefficient," here given the symbol .delta., a Greek 
letter corresponding to the initial of the German name of this 
coefficient. The literal translation of the German term is "let-through 
coefficient" and refers to the letting through of a portion of the 
particles to be filtered out. This coefficient is a function of the filter 
length l and the expected service life t of the filter and is hence also 
symbolized .delta.(l,t). This coefficient is equal to 
##EQU3## 
defined as the quotient of the particle flow j(o,t) upon entrance to the 
filter and the particle flow j(l,t) upon exit from the filter. The 
negative natural logarithm of .delta.(l,t) is a related filter quality 
called the "coverage number" De. In mathematical expression: 
.delta.(l,t)=e.sup.-De. For effective filtering, De is large and .delta. 
is a small fraction of unity, whereas for the absence of a filter De is 
zero and .delta. is unity. 
In the design and manufacture of the filter, to put it briefly a filter 
escape coefficient .delta.(l,t), corresponding to a desired filter 
capability to be attained is selected and, the values of length l and the 
hydraulic (effective free) diameter d.sub.eff are so selected that, for a 
particular gas flow velocity and a particular mass transfer coefficient, 
the product of their quotient (l/d.sub.eff) and the second Stanton number 
St' is large enough for attaining said filter coefficient, said second 
Stanton number being the ratio (h/v) of said mass transfer coefficient to 
said gas flow velocity, both being expressed in cm/sec, and selecting a 
filter material from among those having a known sticking probability for 
particles of a particular contaminating material to be filtered out and 
making from said material at least one substantially rigid element to be 
disposed in a predetermined arrangement in said cavity, said material 
being selected on the basis of a predetermined service life t of the 
filter during which said contaminating particles held back by said filter 
material accumulate, and according to the following criteria: 
(a) the material has a sufficiently high surface sticking probability 
.alpha. for particles of said contaminant on the surface of said element 
of said material, (b) the material is one for which the desorption 
constant (.theta.) regarding said contaminant is sufficiently small, (c) 
the material is one for which the penetration coefficient (1-.beta.), and 
hence also the probability that said contaminant particles do not remain 
on the surface of the material but rather enter into the material and 
become irreversibly bound therein, is sufficiently large, in each case 
sufficiently so for attaining said filter oapability, and (d) that the 
saturation content (.phi..infin.) and the diffusion constant (D) are 
sufficiently large for the product 
##EQU4## 
to be smaller than unity, the quantities contributing to said product 
being defined as follows: 
##EQU5## 
A=mass number of the particles T=temperature of the surface of the filter 
material in .degree.K. 
Expressed differently, using the coverage number, and assuming that: 
##EQU6## 
De is determined by the following Equation I: 
##EQU7## 
wherein De, d.sub.eff, l and St' are defined as already given above; 
##EQU8## 
.alpha. is the sticking probability for the particles at the surface of 
the filter material (.alpha.approximately equal to 1 for partial pressures 
P.ltoreq.10.sup.-10 atm, if no activating processes are present); 
A is the mass number of the particles; 
T is the temperature of the surface of the filter material in .degree.K.; 
##EQU9## 
.omega..sub.o =.about.1,308.multidot.10.sup.11 T in sec.sup.-1 (Debye 
frequency); 
Q is the desorption energy in Cal/Mol; 
R is the universal gas constant in Cal/(.degree.)Mol; 
.lambda. is the decay constant for the substance in sec.sup.-1 ; 
I.sub.1 (x) is the modified Bessel function; 
##EQU10## 
1-.beta. is the penetration coefficient; the probability that the 
particles will become irreversibly bound; 
t is the expected service life of the filter; 
##EQU11## 
N.sub.G is the concentration of the particles in atoms/cm.sup.3, and 
.phi..infin. is the maximum number of particles that particular a filter 
material can take up (absorb) in atoms/cm.sup.3. 
The mass transfer coefficient h is conveniently calculated by the 
heat-mass-transport anology. If a filter is to be produced for an 
installation for cleaning a gas of radioactive particles, and if 
EQU .sqroot..lambda.D&gt;.eta., 
then the relation 
EQU .eta.*.sqroot.t&lt;1 
is fulfilled for all values of t and Equation I is always valid. 
The process according to the invention makes possible the production of a 
filter that is suited in an optimal fashion to the conditions required or 
presented, and thus it is also suited to the particularities of any 
installation. In general, the previously named magnitudes are so 
dimensioned that the magnitude of the coverage number is as great as 
possible, or at least reaches the value that is required by obtaining the 
predetermined value for the filter escape coefficient. By the 
establishment of the above set forth mathematical relation it is 
advantageously possible to carry out investigations of filters for large 
installations on the basis of a small-scale model in a cost-saving manner. 
Two filters are accordingly equivalent regarding their particle 
accumulation; hence with regard to their effectiveness, if they have the 
same filter escape coefficient and thus have the same value of the 
coverage number De. It is therefore also possible, proceeding from a 
simple variety of filter, for example, a piece of tubing through which the 
gas to be purified flows, to obtain the necessary parameter values for the 
manufacture of a filter for a large installation. In such a case the 
simple filter is subjected to different operating conditions and the 
parameter values are calculated according to Equation I. In the 
manufacturing method according to the invention, the diffusion of the 
particles in the filter material is also taken account of. It is therefore 
advantageously possible to manufacture filters that are also effective at 
temperatures above 400.degree. C. up to about 1000.degree. C. In contrast, 
in the manufacture of the known filters, merely the desorption and 
adsorption of the particles on the surface of the filter material, or 
chemical reactions of the particles with the surface of the filter 
material, are taken account of. Accordingly, designers heretofore have 
tried to provide filter material with as much surface as possible. This 
has had the result that the known filters have been inadequate for the 
required effectiveness in the temperature range above 400.degree. C. For 
this reason, users were required to keep the temperatures in the filter 
low by cooling. In order to increase the effectiveness of the known 
filters, moreover, several filters were connected one behind the other, 
which led to voluminous cleaning installations. 
An advantageous version of the design and manufacturing method according to 
the invention consists in that, at a temperature below about 400.degree. 
C., for a filter at which the prescribed operation time t for the 
materials available for selection as filter material, the 
adsorption-desorption equilibrium for the sticking of the particles is not 
obtained at the surface of the filter material, a material is provided for 
the filter material for which the relations hold: 
EQU 2.sqroot..zeta.t&lt;&lt;1 and (.lambda.+.theta.*).multidot.t&lt;&lt;1 (a) 
or for radioactive substances there holds the relation: 
EQU .lambda.&gt;&gt;.theta.* (b) 
Under these postulates--for example, when a filter is to be provided for 
cleaning a gas at low temperatures, as for a filter material temperature 
below 400.degree. C.--the equation for the coverage number simplifies 
itself into Equation II 
##EQU12## 
In a filter of the kind in which the filter material is selected so that 
the length l and the hydraulic diameter d.sub.eff are such that the value 
of the coverage number De reaches a prescribed value in accordance with 
the simplified formula given in Equation II, the sorption-desorption 
equilibrium for the sticking of the particles on the surface material is 
not reached. 
If the relation (b) is fulfilled, then the relation (a) holds for all 
values of t and a filter according to Equation II and is then effective 
without limit of time. According to the Equation II, with use of a 
material having a sufficient sticking probability for the particles to be 
held back, the dimensions of the filter are such that the expected filter 
escape coefficient .delta. is either as small as possible or corresponds 
to a predetermined value. 
A further advantageous variation of the manufacturing procedure according 
to the invention consists in that, in a temperature range above about 
600.degree. C., for a filter with which during the predetermined operation 
time t for the materials selectable as filter material, the 
adsorption-desorption equilibrium for the particles is obtained for the 
sticking of the particles at the surface of the filter material and a 
material is provided as a filter material that has a penetration 
coefficient that is as high as possible and for which the relations 
EQU 2.sqroot..zeta.t&gt;&gt;1 and (.lambda.+.theta.*)t&gt;2.sqroot..zeta.t and .theta.* 
&gt;&gt;.lambda. 
hold. The formula for the coverage number De then is simplified to Equation 
III: 
##EQU13## 
In this variation of the filter in accordance with the invention, the 
diffusion of the particles and the filter material is made use of. 
Also in this case, the dimensions of the filter are so measured that De is 
as large as possible or has a value for which the filter escape 
coefficient .delta. reaches the prescribed value. According to the choice 
of the filter material and the dimensions of the filter, such a filter 
obtains a high effectiveness even at high temperatures up to 1000.degree. 
C. 
Furthermore, a modification of the procedure according to the invention is 
very advantageous that consists in that for obtaining of the longest 
possible operation time t while holding constant the small filter escape 
coefficient .delta. that holds for the thickness .epsilon. of the filter 
material for radioactive substances, the following relation holds: 
##EQU14## 
and for non-radioactive substances, the following relation holds: 
EQU .epsilon.&gt;&gt;.sqroot.Dt 
in which D is the diffusion coefficient for the particles in the filter 
material. This form of filter and this version of the design procedure, in 
contrast with the methods of design and manufacture conventional up to 
now, not only is the adsorption-desorption behavior of the particles at 
the surface of the filter material considered, but the diffusion of the 
particles in the filter material is also utilized in the design of the 
filter. Whereas in the known filters, the installation life of the filter 
depended exponentially upon the reciprocal of the temperature, it is now 
possible by selection of a filter material with sufficient thickness to 
produce a filter that, by utilizing the diffusion of the particles in the 
filter material, has a long service life t, particularly at high 
temperatures. 
A filter built according to the procedure using Equation I is suited in 
optimum fashion to the specified operating conditions and hence to the 
special situations and pecularities of a particular installation. The 
magnitudes involved in the method of design are such that the magnitude of 
the coverage number is maximized, or at least brought up to the value 
which is necessary for obtaining the prescribed value for the filter 
escape coefficient. 
Since the filter of the present invention can be provided and operated at 
high temperatures as well as at lower temperatures more commonly used 
heretofore, the filter of the present invention is particularly 
advantageous for cleaning the cooling gases of a gas-cooled nuclear 
reactor. This application of the filter of the present invention makes 
unnecessary the usual cooling system required for conventional filters in 
such service. In fact, rather than merely substituting a filter of the 
present invention in a separate circulation system in which the cooling 
gas of a nuclear reactor is cleaned, a still more advantageous kind of 
operation can be provided by inserting the filter of the present invention 
directly in the main gas stream of a gas-cooled nuclear reactor.

EXAMPLE I 
For calculating the construction data for the provision of a filter of 
tubes arranged parallel to each other, the Equation I for the coverage 
number De is evaluated and the filter escape coefficient .delta. is 
calculated in dependence upon the mass throughput rate m of a gas flowing 
through a tube. 
The tube to which the calculation relates has the length l=800 cm and the 
diameter d=1 cm. The region of the mass throughput drawn into 
consideration comprises 10.sup.-2 to 12 g/sec. For the gas temperature, 
and at the same time the wall temperature of the tube, 950.degree. C. is 
assumed, and likewise it is assumed that the gas pressure p equals 40 bar. 
As particles that are to be filtered out of helium, atoms of caesium 137 
are taken into consideration. In this connection, two different wall 
materials are postulated, one having a penetration coefficient of 
1-.beta.=0.7.permill. and the other having 1-.beta.=100%. Whereas the 
value of 0.7.permill. for Cs 137 is characteristic for materials with 
cubic face-centered lattices, the penetration coefficient of 100% means 
that the material used is a perfect "diffusor." The symbol .permill. means 
parts per thousand. 
For effective showing of the characteristic of the filter, the mass 
throughput is varied in accordance with a parameter K, which is determined 
by the relation 
EQU m=K.multidot.m.sub.o 
in which m.sub.o is the mass throughput value which is taken into 
consideration as the reference magnitude. 
Since there is a linear relation between the Reynolds number Re and the 
mass throughput m, there also holds the following relation: 
EQU Re=K.multidot.Re.sub.o 
Here Re.sub.o designates the Reynolds number for the mass throughput 
m.sub.o. 
As can be seen from the graphical representation given in FIG. 1 and FIG. 
2, the filter characteristic has a jump at a value of K=0.077. The value 
for K corresponds to a value for the Reynolds number of about Re=2300. 
This discontinuity is produced by the fact that the Sherwood number Sh and 
accordingly the material transfer coefficient h or the Stanton number St', 
likewise show a discontinuity at the transaction from turbulent to laminar 
flow. The step or jump height is dependent upon the geometry, which is to 
say from the ratio .delta./d of the tubular wall material. 
It is further possible to read off from the graphs the flow region in which 
the filter coefficient reaches the smallest value and where the coverage 
number is correspondingly great, so that the activity of the filter 
accordingly reaches its highest value. As can be seen from the graphical 
representations, these minimum and maximum values lie in the region of 
strong laminar flow and in the transition region, about at the Reynolds 
numbers between 2500 and 5000. In the construction of a filter, it is 
possible to provide both regions at the same time in which, for example, 
bundles of tubes are arranged in the filter so that the gas flows along 
their lengths both internally and externally. 
From the above illustration it follows that although the absolute values 
given in the graphical representations strictly have validity only for the 
particular case involved, yet the filter characteristic thus given makes 
possible, however, a qualitative statement also for other operating 
conditions and other geometrical arrangements of the filter material. The 
desired absolute magnitude of the activity of the filter can be directly 
obtained by the arrangement of a corresponding multiplicity of tubes 
arranged in parallel. 
EXAMPLE II 
In order to test the effectiveness of a simple filter consisting of a 
straight piece of tubing, contaminated helium was caused to flow through a 
piece of tubing of 95.5% pure titanium in two completely separate tests at 
different temperatures. The helium gas contained the fission products 
Cs-137, Cs-134 and Ag-110m. A catch-all filter was connected downstream of 
the tube under test for measuring all of the quantity of fission products 
coming out of the tubular filter. The content of fission products in the 
helium thereby measured was different for the two tests. The tubes had a 
length of 2370 mm, an outer diameter of 24.5 mm and a wall thickness of 
1.65 mm. The temperature of the helium entering the filter in the first 
case was 825.degree. C. and in the second case 750.degree. C. In both 
cases the exit temperature was 210.degree. C. The temperature of the tube 
walls was stable and therefore readily measurable during operation. 
During operation of the filter, the flow of the helium was so adjusted that 
the mass throughput of 15 Nm.sup.3 /hr. was obtained. The duration of the 
filtering operation was 785 hours in the first test and 1029 hours in the 
second test. 
For calculation of the filter coefficient of the filter and thus of the 
effectiveness of the filter, the following values were substituted in 
Equation I: 
EQU For Cs-137:1-0,2.permill.; Q=38(Kcal/Mol) 
EQU Cs-134:1-.beta.=0,1.permill.; Q=38(Kcal/Mol) 
EQU Ag-110m:1-.beta.=0,04.permill.; Q=50(Kcal/Mol) 
EQU and .omega..sub.o =1,308 10.sup.11 sec.sup.-1. 
On account of the temperature gradient in the tube the filter was 
subdivided into several sections for the purpose of calculation by 
Equation I. With the calculated filter escape coefficient .delta., there 
were calculated the aggregate radioactivity values in .mu.Ci for the 
fission products getting through the filter and these were compared with 
the values measured in the catch-all filter. There are given below the 
calculated and experimental values in opposite columns: 
TABLE I 
______________________________________ 
Calculated 
Measured 
______________________________________ 
First Test: 
Cs-137 1.00 1.20 
Cs-134 0.79 0.84 
Ag-110 m 11.4 11.7 
Second Test: 
Cs-137 0.52 0.59 
Cs-134 1.6 1.7 
Ag-110 m 5.1 5.6 
______________________________________ 
EXAMPLE III 
In a manner corresponding to the tests of the Example II a filter 
consisting of a tube of stainless steel .times.10 CrNiTi 189 (former 
designation 4541) of the same diameter and wall thickness given in the 
case of Example I, but having a length of 140 cm was tested. The 
temperature of the gas upon entry into the filter was in both cases 
625.degree. C. and upon exit from the filter, 210.degree. C. The duration 
of the operation was 810 hours in the first case and 790 in the second. 
For calculating the filter escape coefficient .delta., the following values 
were inserted into Equation I. 
EQU For Cs-137 1-.beta.=0,7.permill.; Q=45 Kcal/Mol 
EQU Cs-134 1-.beta.=0,33.permill.; Q=45 Kcal/Mol 
EQU Ag-110m 1-.beta.=0,2.permill.; Q=28 Kcal/Mol 
EQU and .omega..sub.o =1,308 10.sup.11 T sec.sup.-1. 
TABLE II 
______________________________________ 
Calculated 
Measured 
______________________________________ 
First Test: 
Cs-137 2.1 2.2 
Cs-134 1.07 0.96 
Ag-110 m 6.2 6.5 
Second Test: 
Cs-137 1.92 2.1 
Cs-134 1.03 1.1 
Ag-110 m 3.26 3.51 
______________________________________ 
EXAMPLE IV 
The constructional data for a filter consisting of parallel arrangement of 
tubes illustrated in FIG. 4 were calculated for predetermined operating 
conditions. 
As is evident from FIG. 3, the filter consists of a multiplicity of 
parallel tubes arranged witn uniform spacing from each other, the entire 
group arranged in the interior space enclosed by an outer tubular lateral 
enclosure 2. The outer diameter of the individual tubes of the tube bundle 
is d.sub.a, the inner diameter of each of the tubes is d.sub.i, the length 
is 1, and the inner diameter of the lateral enclosure is D.sub.i. The gas 
to be purified flow not only through the tubes of the filter, but also in 
the spaces around them within the lateral enclosure. 
The gas to be purified is helium that contains fission products Cs-137 and 
Ag-110m. 
The contemplated operating conditions are: Mass throughput of helium: 
m=11.25 kg/sec., Helium temperature at filter input: T=950.degree. C., 
Helium pressure: p=40 bar, Contemplated operation duration: t=30 years. 
Material for the tubes: heat resistant steels were provided which have a 
body-centered cubic structure or which, as for example, Incoloy-802 and 
Inconel-625, have a face-centered cubic structure. For the materials just 
mentioned, the penetration coefficient for Cs-137 is 1-.beta.=0.7.permill. 
and for Ag-110m is 1-.beta.=0.2.permill.. For the binary diffusion 
constant which is used to calculate the mass transfer coefficient h, the 
following values, for T=950.degree. C. and p=40 bar, were used: 
EQU D.sub.Cs-He =0.146 cm.sup.2 /sec. 
EQU D.sub.Ag-He =0.272 cm.sup.2 /sec. 
The values of h and St' needed for calculation of the coverage number De 
were obtained from the German Industry Association (VDI) heat atlas and 
from volume 14, Int. J, Heat Mass Transfer, pp. 1235-1259 (Pergamon 
Press). Since in the present case, the conditions: 
EQU 2.sqroot..zeta.t&gt;&gt;1 and (.lambda.+.theta.*)t&gt;2.sqroot..zeta.t and 
.theta.*&gt;&gt;.lambda. 
are fulfilled, the calculation of the construction data for the filter was 
carried out according to Equation III. 
Under the assumption that the volume of the filter does not exceed 40 
m.sup.3, that the pressure loss is not greater than 0.1 bar and the filter 
coefficient .delta. for silver is between 6.multidot.10.sup.-4 and 
8.8.multidot.10.sup.-3 and for caesium is between 1.2.multidot.10.sup.-5 
and 2.multidot.10.sup.-3, the construction data in the table given below 
were calculated for the filter. The values there for d.sub.i and d.sub.a, 
as well as those for D.sub.i and l are given in cm. N is the number of 
parallel tubes in the filter. Along with the constructional data, there 
are given the values for the pressure drop .DELTA.p in the filter, in bar, 
as well as the values for the respective filter coefficients. The value 
for .DELTA.p was calculated according to the VDI heat atlas and volume 14 
Int. J Heat Mass Transfer, pp. 1235-1259 (Pergamon Press). 
TABLE III 
______________________________________ 
.delta. 
.delta. 
N d.sub.i 
d.sub.a 
D.sub.i 
l Cs-137 
Ag-110 m 
.DELTA.p(bar) 
______________________________________ 
95000 0,55 0,75 300 500 1,53 8,76 10.sup.-3 
0,063 
10.sup.-3 
95000 0,55 0,75 300 600 4,64 4,18 10.sup.-3 
0,076 
10.sup.-4 
145000 
0,35 0,55 300 600 3,162 5,26 10.sup.-3 
0,085 
10.sup.-4 
190000 
0,35 0,55 325 600 1,26 6,29 10.sup.-4 
0,089 
10.sup.-5 
190000 
0,35 0,55 325 500 4,886 2,129 10.sup.-3 
0,074 
10.sup.-4 
190000 
0,35 0,55 325 400 1,97 7,228 10.sup.-3 
0,059 
10.sup.-3 
______________________________________ 
EXAMPLE V 
As in Example IV, the constructional data for a filter consisting of 
parallel tubes were calculated for the same operating conditions, except 
for input gas temperature which was 300.degree. C. in this case. As 
material for the tubes, a feritic steel of type 15 mo03 was selected. For 
this material, the penetration coefficient and the desorption energy Q 
have the following values: 
For Cs-137: 
EQU 1-.beta.=1,2.permill.; D.sub.Cs-He =0,039 cm.sup.2 /sec. 
EQU Q=65 kcal/Mol, 
and 
EQU .omega..sub.o =1,308 10.sup.11 T sec.sup.-1. 
For Ag-110m 
EQU 1-.beta.=0,3.permill.; D.sub.Ag-He =0,072 cm.sup.2 /sec. 
EQU Q=52 kcal/Mol 
and 
EQU .omega..sub.o =1,308 10.sup.11 T sec.sup.-1. 
Since in the present case, the conditions: 
EQU 2.sqroot..zeta.t&lt;&lt;1 and (.lambda.+.theta.*) t&lt;&lt;1 
and fulfilled, the calculation of the constructional data for the filter 
was carried out according to Equation II. 
Under the assumption that the volume of the filter does not exceed 17.2 
m.sup.3, that the pressure loss .DELTA.p is much greater than 0.11 bar and 
that the filter coefficient .delta. for a caesium amounts to 
1.06.multidot.10.sup.-4 and for silver amounts to 5.61.multidot.10.sup.-6, 
the following constructional data are obtained: 
______________________________________ 
N = 10.sup.5 D.sub.i = 230 cm 
d.sub.i = 0.3 cm 1 = 350 cm 
d.sub.a = 0.55 cm 
______________________________________ 
The pressure drop amounts to .DELTA.p=0.105 bar. 
EXAMPLE VI 
For the operating conditions given in Example V, the constructional data 
were calculated for a filter consisting of a multiplicity of parallel and 
equally spaced rods, that, just like the tubes in Example V, were located 
within a surrounding casing. In this case, the following values were 
obtained for the materials specified in Example V: 
For the filter escape coefficient, .delta.=1.62.multidot.10.sup.-3 for 
Cs-137 and .delta.=4.4.multidot.10.sup.-5 for Ag-110m and, with the 
assumption that the volume of the filter is not greater than 10.5m.sup.3 
and that the pressure loss .DELTA.p is not greater than 0.125 bar: 
______________________________________ 
N = 1.2 .multidot. 10.sup.5 
1 = 250 cm 
d.sub.a = 0.5 cm 
D.sub.i = 230 cm 
______________________________________ 
The pressure drop amounts to .DELTA.p=0.124 bar. 
For the filter escape coefficient .delta.=5.814.multidot.10.sup.-3 for 
Cs-137 and .delta.=3.272.multidot.10.sup.-4 for Ag-110m and for the 
otherwise identical values for N, d.sub.a, d.sub.i, the length 1 was 200 
cm and .DELTA.p was 0.11 bar.