= (1/2) [p(0) + p(I)] Pressure drop; Ap = p(0) — p(L) Tortuosity factor for binary mutual diffusion in a porous septum; g’ = (LC/L)2 Pore entrance radius Volume A measure of the relative effect of gas-surface collisions on gas transport; 5j = DjK/ Dk + D) | Total porosity or fractional void volume of a porous septum Flow porosity, that part of £, which actually contributes to gas transport Viscosity coefficient of gas j Mercury-graphite contact angle Radioactive decay constant of component ; A.¢p Decay constant including burnup; Aggp = )\j + T 2> Surface area of a given pore in a porous medium o Surface tension ;i Neutron capture cross section of species j ¢ Neutron flux ill. DESCRIPTION OF THE MSRE GRAPHITE The Molten-Salt Reactor Experiment utilizes Carbon Products Division (Union Carbide Corpora- tion) CGB graphite in the form of 6-ft-long bars which have a cross section of 3.08 in.2. The bars (565 in all) are stacked vertically in the reactor core to yield a graphite moderator volume of 77 ft3. The sides of each bar are slotted along the entire 6-ft length; these slots constitute the flow channels for the molten salt, The Base Stock Details of the actual fabrication of the moderator material are considered to be proprietary information and thus have not been made available to us. For the present study, however, specula- tions regarding the fabrication process seem warranted, inasmuch as the results obviously depend upon the manner in which the material was made. We have therefore liberally construed what might be at least a reasonable method for fabricating the MSRE graphite in view of the specifica- tions and the production techniques described in the open literature.? If the dimensions of the finished product must adhere to close tolerance specifications, a major cost item in the production of graphite is machine work. This temains true even if special procedures and materials must be employed in the manufacture of the graphite. Standard machin- ing practice therefore allows us to fix the dimensions of the starting billets (or base-stock bars) in the neighborhood of 2.5 in. x 2.5 in. x 6 ft. These values have recently been verified by meas- urement. The desire for maximum crystallite perfection suggests that the green mix employed to fabricate the base stock be composed of needle-coke graphite flour with a coal-tar pitch binder. Photomicrographs indicated that the flour was ‘‘fine grained.’’ In view of the size of the billets, a logical choice for forming the mix is extrusion; this sets the binder-flour weight ratio at about 3/10. After forming, the billets are baked to about 1000°C to produce a material with a density around 1.56 g/cm?® and a porosity of about 25%. The stock is then impregnated with a light pitch and graphitized at 2800°C in an Acheson furnace. At this stage the graphite characteristically 3. The base stock employed in the present work was found to has a density of about 1.70 g/cm have an average density of 1.67 g/cm?® and a porosity of 21%. (Henceforth this base stock will be denoted as CGB-BS.) 2See, for example, W. P. Eatherly and E. L. Piper, ‘“Manufacture {of Graphite),”’ chap. 2, pp. 21-51 in Nuclear Graphite, R. E. Nightingale, ed., Academic, New York, 1962, It has been established that a base stock suitable for impregnation must possess pores with sizes that range closely about a well-defined distribution peak;* CGB-BS meets this requirement. ‘ H It also has very large, but widely dispersed, voids that we term ‘‘vugs.’”’ These vugs are well connected to the overall open-pore system; thus small specimens used in certain characterization evaluations were selected to avoid as many vugs as possible. Examination of impregnant residues within regions that originally constitute vugs in the base stock permits reasonable speculation as to the impregnation schedule. Multiple Impregnations Once the base stock with suitable pore sizes has been acquired, the success of subsequent impregnation treatments is governed by the proper selection of the impregnant and careful control of the heat treatments. In each succeeding impregnation it becomes increasingly difficult to force the impregnant into the pores, because their size and number become smaller than they were in the previous treatment. Similarly, the heat treatment necessary to decompose the im- pregnant in the potes becomes more crucial; the rate of the operations must be retarded to avoid pressure buildups and stresses which invariably lead to spalling and fracture of the stock. We now speculate about the types of impregnant which might be employed. Pitch yields well- graphitized residues but is difficult to inject, whereas fluids which can be readily injected frequently yield rather poor residues. Obviously the latter would be chosen for the final im- pregnations, but the early impregnations would utilize pitch. Furfuryl alcohol polymers are a logical choice for the final impregnation treatments, since the viscosities of these fluids can be adjusted over a sufficiently broad range by careful control of phosphoric acid catalyst concentration and preimpregnation temperatures.? Ideally, the alcohol would break down in the following manner: Il w A HC C -— Cli — OH ——> {(2H, + H,0 + CO) + 4C (amorphous char) . H @] (Polymer intermediates have not been shown in this simplified formula.) Permeability reductions of about 10%, as a result of furfuryl alcohol impregnation treatments, have been cited in the literature;® comparisons between the base stock and the impregnated graphite, presented later, are in reasonable agreement with the reduction factor cited. Microscopic Examinations Inspection of photographs of base stock before and after treatment turns out to be one of the most revealing methods for demonstrating the structural changes resulting from impregnation. 31. W. Graham ef al., ““The Development of Low Permeability Graphite for the Dragon Reactor Experi- ment,’’ Proceedings of the Fifth Carbon Conference, vol. I, pp. 387—404, Pergamon, New York, 1963, PHOTO 86409 BASE STOCK AFTER TREATMENT (NC-CGB-BS) (NC-CGB) Fig. 1. Photomicrographs of Thin CGB Graphite Sections Before and After Impregnation. These sec- tions are mounted in pressurized clear epoxy resin (not furfuryl polymers) which has intruded and solidified in the connected pores. In low-magnification photos, entire impregnated regions give the appearance of open pores, as the resin seems to completely wet such regions. However, differences between the treated and untreated graphites become quite evident at higher magnifications. Photomicrographs of specially prepared ‘‘typical’’ sections of the graphites under discussion are shown in Fig. 1. These particular specimens were specially ground sections mounted in epoxy resin. While the resin was in a liquid state, they were subjected to pressures of about 7000 psi in an effort to fill the pores with a supporting material. These particular specimens were ground exceptionally thin to ensure maximum filling. A supporting material was required so that the true sizes and shapes of the pores would be maintained during the post-mounting polishing operations which are required for microscopic examination. Several grades of graphite pertaining to other studies were simultaneously subjected to the same treatment to afford comparisons of similar materials. We note that the tone of border areas around the structures at the top in Fig. 1 represents the plastic under the particular lighting conditions involved. In most cases, the presence of this tone appears over various regions within the structure, most frequently indicating the plastic- PHOTO 91133 Fig. 2. Low-Magnification Photos of CGB Base Stock and Impregnated Graphites. The base stock material is shown at a; several vug regions appear in the selected specimen. The impregnated material is shown at b, where manifestations of original vug regions are readily opparent. The pores do not contain epoxy mounting resin. Attention is called to the unusually large impregnated vug region in the upper left- hand corner of b. filled pores. This, however, is not always true, particularly in the case of impregnated graphite at low magnification (*~200x, upper photos in Fig. 1). Here, impregnated regions are saturated with mounting plastic, and the impregnant residue is obscured. The mounting plastic or resin should not be confused with carbonized impregnant. At fourfold higher magnifications, as in the lower photos, the plastic seems to become more transparent, the carbonaceous residues are clearly shown, and the differences between pore structures become quite evident. Examination of impregnated vug regions clearly reveals two types of impregnant residues in the material we have studied; thus our original speculations as to the treatments tend to be verified. Inspection of Fig. 2, which shows ‘‘resin-free’’ pores, gives some idea as to the size and frequency of vugs in the graphites before and after impregnation (Figs. 2a and 2b respectively). We note that the residues of the impregnation treatment obscure most of the original vug regions, but it is still possible to discern regions corresponding to unusually large vugs, as indicated in the upper left-hand corner of Fig. 2b. Photomicrographs of the latter region at higher magnifica- tions and after additional polishing appear in Fig. 3. Here is observed a single light-toned kernel surrounded by a dark ill-defined material which seems to be poorly graphitized. It will be- come obvious from pore size distribution curves to be presented later that even at these high magnifications it is practically impossible to discern the sizes and shapes of the pores. PHOTO 87044 Fig. 3. Large Impregnated Vug Region of Fig. 2b at High Magnification. X-ray analyses performed on such residues, after careful removal, reveal hard, turbostratic, anisotropic structures for the kernels.* Sampling and removal difficulties associated with the furfuryl-related residues permit the inference that these specimens possessed a weak and feature- less structure. The low degree of graphitization revealed by both residues tempts us to conclude that the impregnants have not been subjected to temperatures greater than 2200°C. Surprisingly, after such examinations (particularly of photomicrographs like Fig. 3 and in the absence of pore size data), no region of the resin-injected impregnated graphite showed any evidence of being porous. In fact, until recently we had not seen a region or feature which could be positively identified as a pore in the impregnated material, even with the aid of the electron microscope.® Although attempts with other porous graphites were highly successful, the first two attempts to replicate surfaces of specimens related to Fig. 1 for electron microscopy failed be- cause of polishing artifacts and limited surface areas available for replication. Since the entire impregnated regions were saturated by resin (Fig. 1), we could only speculate that the pores were an intimate part of the furfuryl-residue regions and that their radii were about the same size as the openings suggested by pore size distributions. Through continued efforts with resin-free specimens, we have recently obtained very good replicas. These permit one to obtain micrographs of much higher magnification than those indicated in Fig. 3. The new results are shown in Fig. 4. An inspection of this micrograph clearly reveals 4W. H. Cook and H. L. Yakel, private communication, March 1968, Sj. O. Stiegler, private communication, November 1966. Fig. 4. Electron Micrograph of a Surface Replica of Impregnated CGB Graphite. The surface involved is selected and not necessarily typical; the magnification is approximately 10,000x. The radius of the large pore shown here is about ten times greater than the most probable radius for large-pore entrances (see text ond Fig. 5). the small pores that control the flow behavior in the impregnated graphite. Although very large pores appear and attention tends to focus on such regions, it should be noted that the small pores with the highest frequency are of greatest importance, even though they constitute a rather nondescript background in Fig. 4. It is clear from the foregoing discussion that the impregnated material exhibits property variations along directions normal to the impregnation surfaces. Insofar as the MSRE graphite is concerned, however, we should note that the degree of nonuniformity has probably been mitigated somewhat, since the surface regions, where impregnation treatments should be particularly effective, have most likely been removed in order to produce the slots and final dimensions of the bars. We wish to stress this point because it was our original impression that the slots were milled either at the beginning or at some point during the multiple impregnation treatments. The impression was inferred from Carbon Products Division’s insistence that responsibility for the final permeability of the finished bars could not be assumed unless they were allowed to perform the final milling operations, as well as fabricate and impregnate the bars. There is no evidence, however, that additional treatment took place after milling. 10 IV. EFFECT OF IMPREGNATION TREATMENT ON FLOW PROPERTIES Comparison of Base Stock and Impregnated Graphite General Considerations. — In the preceding sections we have presented visual evidence con- cerning the effects of impregnation on CGB graphite structures. While this is pertinent and of interest, we are primarily concerned with the manifestations of impregnation treatments in a quantitative sense. Although the ultimate objective is to ascertain variations as a function of position in an impregnated bar, we shall first compare flow-related properties of base stock with those of impregnated materials presented in Report I. This approach has the particular advantage of demonstrating a maximum variation in values but is somewhat awkward in that we must pre- maturely preempt some definitions which would otherwise appear in other sections; thus it is immediately necessary to consider the subject of nonuniformity of the flow specimen studied in Report I. The specimen used for these experiments was machined from the central portion of a bar that possessed a minimum number of large-scale defects and cracks (bar 23, lot 1). The cor- responding data were treated as though they were representative of a more or less uniformly im- pregnated material, even though this was not the case. To recapitulate, our purpose in this section is to compare the properties of the impregnated sample just described with like properties of the base stock in order to demonstrate the overall effect of impregnation on the gas transport characteristics of the graphite. We wish to re- emphasize, however, that the impregnated-sample data should be considered as representative of a material which has been subjected to moderate degrees of uniform impregnations. Characterization Parameters. — The first parameter we shall compare is the density d; next is the total porosity -, as ‘‘seen” by fluids (fraction of the bulk volume comprising connected pores), and third, the so-called pore size distribution function f_(r,) . The latter is of particular usefulness in our work; it is defined so that it represents the fraction of the total porosity - associated with pores having entrance radii between r and r, + dr,. Thus 0 O d”‘) (1) Aro)=s — | — |, 0 ~ dro S iegydrg - 1. ) Many porous materials display a multidisperse pore structure in that the distribution function exhibits several maxima. In such cases it is convenient to divide the distribution function into several parts, corresponding to the distribution in pore sizes about given maxima. These dis- tribution functions are defined by the relations 1/ d-, [ié(ro)__< 1>fi 1-‘:' 1!27"'1 (3) 4 dro 11 in which €, is the porosity contribution from the pores assigned to the ith group. The maxima frequently appear at considerably different values of the pore entrance radius, so it is generally not too difficult to make the apportionment. Flow Parameters. — We demonstrated in Report I that only three parameters are required to completely specify the gas transport characteristics of a porous medium. These are the viscous flow parameter B, the Knudsen diffusion coefficientDjK for any experimentally convenient gas i, and the diffusion coefficient Dji which describes the diffusion characteristics of any gas pair j-1 through the septum. In addition, it was also shown how these parameters can be obtained experimentally; the first two coefficients are derived from determinations of the pressure depend- ence of the permeability coefficient Kj. of given samples to a single pure gas j. The permeability coefficient relates to pressure in the following manner: K =®Bym)(p)+Dig, (4) where
is the arithmetic average of the pressures p(0) and p(L) on the two sides of the
sample and n; is the viscosity coefficient of the gas.
The third coefficient, D.,, on the other hand, can be obtained from only a few measurements
jr
of the counterdiffusion process for any two gases j and [ through the septum under isobaric,
isothermal conditions. Accordingly, just a few measurements of this kind involving base stock
were made in the present study. The reader is referred to Report I for further details regarding
procedures, equations, etc. Our present interest in Djl stems from the fact that this parameter
gives an indirect measure of the fraction of pores actually engaged in a linear flow situation;
that is, we are interested in the ratio (¢ /¢”) which appears in the equation
D = (E’/q');:'” ) (5)
in which 1‘3].1 is the so-called ‘‘free space’’ diffusion coefficient. Unlike Dfl, the quantity "jS
is independent of geometry. (Details regarding the experimental determination of the free space
diffusion coefficient are adequately described elsewhere.®)
We wish also to point out that the porosity ¢ should not be confused with the total porosity
€, introduced earlier. It is unfortunate that both quantities carry the same nomenclature, but
¢, refers to the total interconnected void volume, whereas € is only that part of ¢, which is in-
volved in gas transport. Furthermore, < cannot be determined directly; in the simplest case,
Eq. (5), it appears as the ratio (c"/¢”). In the majority of graphites that we have encountered,
the quantity (1/€t) (¢’/q”) ranges between 10~ 2 and 1073,
Comparison of Results. — Nominal values of the characterization and flow parameters for
each of the two types of graphite are listed in Table 1. First, we note the 12% increase in bulk
density of the treated material and the 57% decrease in the nominal porosity values, the latter
®A. P. Malinauskas, J. Chem. Phys. 42, 156 (1965); 45, 4704 (1966).
12
Tabie 1. Nominal Values of the Characterization Parameters of CGB Graphite
Before and After Impregnation
Base Stock Impregnated Graphite
(CGB-BS) (CGB)
Bulk density, g/cm? 1.67 1.87
Apparent solid density, g/cm? 2.09 2.05
Connected porosity,® % of bulk volume 21.4 9.2
Pore entrance radius at porosity distribution peaks, M
At primary peak 0.85 0.080
At secondary peak 0.01 0.01
Porosityb associated with pore-size distribution,
% of bulk volume
At primary peak 17.3 7.2
At secondary peak 3.0 3.1
Modified viscous flow parameter
(B,/m) for helium at 23°C, em? sec™ ! atm™! 1.57 x 10! 5.18 x 10~°
Knudsen diffusion coefficient Dijor helium 1.43 x 107} 4.70 x 10~4
at 23°C, cm?/sec
Normal diffusion coefficient D, for the pair He-Ar 1.04 x 1077 7.00 x 1074
at 23°C and 1 atm pressure, sz/sec
“Determined by helium expansion.
bDetermined by mercury injection; see Fig. 5.
having been determined in each case by the standard gas-expansion method.’” The information in
Table 1 relative to pore sizes and their distribution is clarified by an examination of the distribu-
tion plots shown in Fig. 5, where typical bidispersed systems for graphite are displayed. The
upper plot represents the porosity distribution function for the base stock, where maxima occur
at about 0.85 and 0.01 u. The lower plot illustrates the maxima exhibited by the impregnated
material at about 0.08 and 0.01 ;. Insofar as characterization parameters are concerned, a ten-
fold reduction in the size of the primary (large) pores is one of the major effects of the impregna-
tion. (The reader should note that a split abscissa with two scales has been employed for the
base stock plot at the top of the figure in order to show the entire dispersion of the primary large-
pore peak in a proper perspective and also that the ordinates differ by a fivefold scale.)
There are virtually no pores which contribute to the porosity of the base stock in the region
between 0.1 and 0.5 1. Also, the primary pores account for 85% of the total porosity of the base
stock. For impregnated graphite, however, a fair amount of overlap between the two maxima is
in evidence. Nevertheless, the primary mode still represents about the same percentage (70%)
of the total available porosity. We should note further that our experience with these and other
7’C. G. Rall, H. C. Hamontre, and D. B. Taliaferro, Determination of the Porosity by a Bureau of Mines
Method, U.S. Bur. Mines, Rept. Invest. 5025 (July 1953).
13
i ORNL-DWG 66-12743R
____BASE STOCK L
(NC-CGB—BS)‘ |
AFTER IMPREGNATION
- c-C
. - T ‘f—-:—u,——- - o . . . R .
s} 202 204 elels 208 o [SA N 014 016 018 02 022 024
Ty PORE ENTRANCE RADIUS (p)
Fig. 5. Effect of Impregnation on the Distribution of Pore Entrance Radii in CGB Graophites. Upper
plot, base stock; lower plot, impregnated material.
graphites suggests that the percent of bulk volume associated with secondary peaks ranges
about a constant value of approximately 3% of the bulk volume, even though the primary values
might vary considerably. We conclude that the size or number of the secondary pores is not
altered by the impregnation treatments; but the diffusion and flow behavior are nearly always
controlled by the primary, not the secondary, pores. Therefore, since primary pores sustain the
highest degree of alteration via impregnation treatment, it is not surprising that we found marked
differences in the diffusion and flow behavior of the two graphites cited in Table 1.
We shall reserve further discussion of the flow parameters in Table 1 for the general discus-
sion, since our major objective here is to demonstrate, on a magnified scale, some of the less
dramatic variations one might expect along the radial direction of an impregnated bar. One may
anticipate in the latter case that the density would remain essentially constant and the porosity
could change slightly, but the pore size distributions (and diffusion coefficients) might vary
appreciably.
14
Variation of Structural and Flow Properties with Position
Limitations of Sampling Procedures. — So far we have demonstrated that the overall effect
of impregnation, even for a ‘‘poorly impregnated’’ material, is a significant decrease in the large-
sized pores in the graphite and consequently a marked permeability reduction of the material to
fluids. In this section we consider the extent of permeability reduction; that is, we examine the
structural and flow properties as a function of position from the surface to the core of the bar.
Thus it is pertinent to review the history of the source material which we employed in the
previous and present investigations. We received a 15-in. section® of the original 6-ft bar 23.
X-ray analyses of this section revealed that the bar was of exceptionally good quality in compari-
son to some of the other source materials available to us, even though there were two small
cracks approximately 4 in. from each end of the 15-in. section. We selected an unusually good
portion for the fabrication of a 6-in. diffusion cell and a 2-in.-OD porosity plug, data for which
appear in Report I,
After fabricating these two specimens, some 6 in. was available for the present investigation,
thus precluding a study of variations along the bar axis; we were limited therefore to a study of
properties along the equivalent radius. Nevertheless, the axial variations could be estimated by
comparisons of the present data with comparable data which were reported for the specimens of
Report 1.
A study of property variations as a function of position demands small specimen sizes that
would produce results equivalent to differential measurements. However, the need for small
sizes must be balanced by the need for good representation of the material, particularly when the
presence of macroflaws is suspected. Acquisition of representative samples is of great im-
portance in permeability (diffusion) studies. For these reasons, we chose to fabricate two series
(and types) of specimens.
The first series, shown at the top of Fig. 6, comprised relatively small specimens that were
used for density and porosity determinations. Samples from both sides of the midpoint were ob-
tained to ascertain the degree of symmetry of the property variations. Each of these samples was
smaller than a dime. Such sizes could be employed for porosity and density determinations be-
cause of the availability of a suitable volumetric mercury-porosimeter pressure cup and the rela-
tive insensitivity of these parameters to macrocracks and fractures (not, however, to poorly im-
pregnated vugs).
Specimens comprising the second series, shown at the bottom of Fig. 6, were considerably
larger than the density-porosity samples, for reasons given above. Although it might seem that
a weakness of the sampling technique might stem primarily from employing large increments
(thicknesses) along the z direction, this is not the case. When a steady-state flow pattern is
visualized, wherein the outer surface of an entire bar is held at a constant potential while a sink
or source acts at the center of the bar, one realizes that the isobars tend to be nearly rectangular
8The specimen bar was furnished by W. H. Cook, April 1964.
15
ORNL-DWG 66—-12744
I ! I
l
SPECIMENS H
—|VA THRU J |
=
{
1\7 | 0.0813 - 0.345 =
L 1.596 TJ ’{ F '
. WSS
l t0 THRU 4
POROSITY
DENSITY
IiI SPECIMENS
Iq /] | ‘\ ;—5 L-
e Y 7 | | b
| | | / 1 b
| ; | : / I
| R | |
- T - L — - + -
) 1 / z 1
eat— 4 - .-—2——-«/-—3-, -—4-/1-—5-— t
} /‘ : | | 1
R 1a, | / I I _-—:50_-_ a
4N A % I
/ vd !
_—0.125
# 0.0862 =1,/ j=— ——‘ |
/ / PERMEABILITY SPECIMENS
12¢=0
DIMENSIONS ARE IN INCHES
Fig. 6. Cross Section of CGB Graphite Bar 23 Showing Specimen Geometries and Locations. Upper
figure, porosity-density specimens; lower figure, permeability samples.
near the surface, but quickly revert to cylindrical patterns as the center is approached. Most
’ several steady-state isobars, and thus it is clear that
interior samples would ‘‘cut across’
ambiguities are introduced mainly because their radii (not thickness normal to z) were too large.
As in Report I, however, we must again caution the reader of the possibility that the data to
be presented may not be typical of the bulk of the graphite actually employed in the MSRE. Most
of the bars made available to us contained large-scale flaws, fractures, and/or cracks. These
defects probably result from the impregnation treatments, and, while not likely to be important
insofar as reactor operation is concerned (since these defects can become filled with salt if
16
Table 2. Variation of Density with Locotion Relative to the Center of a CGB Graphite Bar
(Porosity-Density Specimens)
Distance from
Specimen Identification Density (g/cms)
Center”
Lettered Numbered (cm) Lettered Numbered .
I III 3.180 1.874 1.871
Iv II 3.180 1.868 1.867
A 1 1.962 1.853 1.865
B 2 1.766 1.854 1.865
C 3 1.570 1.862 1.863
D 4 1.374 1.853 Lost
E 5 1.177 1.864 1.864
F 6 0.981 1.860 1.858
G 7 0.785 1.856 1.856
H 8 (.589 1.862 1.861
I 9 0.392 1.859 1.850
J 10 0.196 1.855 1.856
Center Center 0 1.850 1.850
“Relative position in bar shown in Fig. 6.
near the surface), they do render the samples unsuitable for gas transport characterization. In-
spection and selection of the stock we received was performed with these facts in mind, so that .
our choice of a particular section of one bar (bar No. 23) was made on the basis of a minimum
number of such flaws. .
Density Determinations. — The apparent or bulk density of a regular geometric body is
probably the most convenient property to determine accurately; one merely weighs the sample
and then calculates the volume in which the solids are contained from appropriate measurements
of the geometry. The densities derived in this manner for the porosity-density specimens are
listed in Table 2. All of the samples which were employed to obtain the density and porosity
data were machined from the graphite bar normal to the extrusion axis; the position, geometry, and
identification of these specimens are shown in the upper portion of Fig. 6.
On preliminary examination, the material as a whole appears to be quite uniform; indeed, the
average density of the bar is 1.86 + 0.03 g/cm®. On closer inspection, however, we note a
slight decrease in density near the center of the bar. This becomes obvious when one compares
results for specimens I-IV with those taken at the center of the bar. Results for all other
samples indicate no definite trends. For a more sensitive test, we now focus on the porosity
determinations.
Total Porosity Determinations. — The porosities exhibited by selected disks of the porosity-
density specimens are listed in Table 3. These results have been obtained as an adjunct to
those obtained by the standard mercury-penetration technique, in which mercury is injected into
a previously evacuated sample by compression and the difference in weight of the sample after
17
Table 3. Porosity, Determined by Mercury Injection of Selected Small Disks
of CGB Graphite, as a Function of Bar Position
a Distance from Center Open Porosity
Specimen Identification (cm) (% bulk volume)
I and III 3.180 10.1
)| 1.962 10.2
2 1.766 10.6
3 1.570 10,2
5 and E 1.177 10.8
6 0.681 10.9
9 0.392 11.0
Center 0 11.1
“Relative position in bar shown in Fig. 6.
and prior to injection is determined. Unlike the bulk density values, the porosity data display
an unmistakable trend; the surface specimens are approximately 10% less porous than the
sample which had been machined from the center of the bar.
According to our speculations as to the manufacturing process, specimens near the surface
should be most dense and least porous. Moreover, if we were cotrect in contending that the ef-
fectiveness of the impregnation treatments would diminish from the surface to the center of the
material, the density should decrease and the porosity should increase as one proceeds toward
the core of the graphite body. It appears as though we have gained experimental support for this
contention.
Porosimetry Determinations
That pore size spectra encountered in this work might be more readily comprehended, we
shall preface this otherwise brief section with a cursory description of the experimental and
theoretical aspects of porosimetry. The experimental facets divide into two distinct parts: (1)
evacuation and mercury charging of a penetrometer containing a sample and (2) injection of the
mercury into the pores of the specimen utilizing pressurized isopropyl alcohol.®
A drawing of the penetrometer is shown in Fig. 7. Components A, B, and D are employed to
exert a sealing pressure on the glass sample holder E, part of which forms a calibrated capillary
F. The actual seal occurs between the ground cup lip of E and the glass disk C; the O-ring B
merely serves to ensure uniform compression for the glass-to-glass seal. High-pressure seals
9An Aminco-Winslow porosimeter (American Instrument Co., Silver Spring, Md.) was employed in this
work. Although the major part of the purchase price is for the auxiliary pressure equipment, the main com-
ponent from the standpoint of the experiment is the penetrometer. Detailed discussions relative to an
older mode! have been presented by N. M. Winslow and J. J. Shapiro, ‘“‘An Instrument for the Measurement
of Pore-Size Distribution by Mercury Penetration,’”” ASTM Bull.. February 1959, pp. 490-54.
18
ORNL- DWG 68-5315
x
—— \:')1;7_-?-:‘_:;1:1:]_: Gl SrloorlTrro i e
SAMPLE INCH
Fig. 7. Sketch of the Penetrometer for the Aminco-Winslow Porosimeter. The varicus components are
identified and described in the text.
are unnecessary, since the entire penetrometer is subjected to the same pressure in the course
of the mercury injection.!?®
It is imperative that the size of the sample to be employed in the experiment be judiciously
chosen, since an improper size can easily result in the entire volume of mercury in the capillary
being forced into the specimen at a prematurely low pressure. This possibility can be lessened
either by determining the total porosity by the usual gas expansion method or through a computa-
tion based on the bulk density and the assumption that the density of solids is 2.08 g/cm?.
In the first stage of the experiment, the sample is weighed and then sealed in the penetrometer.
Then the penetrometer is placed within a glass enclosure, and the assembly is evacuated.
Mercury is then admitted into the penetrometer through the capillary under the application of
atmospheric pressure. The sample has now been subjected to mercury injection at 1 atm pressure,
so that pores with equivalent radii greater than about 7 u have already been filled with the
penetrant. Hence, if pores of this size are suspected, the specimen should be reweighed and the
procedure above repeated before proceeding further.
In the second phase, the mercury-filled penetrometer is transferred to a pressure chamber
which contains alcohol. Pressure is then applied in a stepwise manner to the system, which
causes further penetration of the mercury into the specimen. In a typical step, the meniscus of
the mercury in the capillary is noted and then pressure applied until a predetermined volume
change, after the system has been allowed to equilibrate, is observed.
10More recent penetrometers use plastic rather than brass for components A and D and a metal fitting
instead of the glass plate C. In this manner the O-ring is eliminated. Also, the need to observe volumetric
changes of the mercury visually through a high-pressure sight port is obviated by using a platinum wire
resistance system in place of the graduation marks on the capillary.
19
The capillarity formula which relates the pore dimension to the applied pressure is given by
V —ocosf
< — (6)
2 p
where V represents the volume of a pore which has been filled with mercury at the hydrostatic
pressure p, X is the surface area of the pore, o is the surface tension of mercury (473 dynes/cm),
and # represents the mercury-graphite contact angle (130 or 142° is commonly used). In the case
of cylindrical pores of radius r and length I,
and if we employ this relationship as the definition of the ‘‘equivalent pore entrance radius,”’
then Eq. (6) takes the form
—20 cos 0
Tg= —————— . (7)
p
The experimental data are thus of the form of a series of pore volume —Ar, (or A p) pairs;
these are plotted as a continuous pore size distribution curve by first defining the porosity dis-
tribution function,
() - — 27 (8)
o Vo L\ro ,
in which V., is the total volume of mercury injected, and by referring each f(¢) to a characteristic
radius which is calculated from the relation
0
r. = rg + (Aro)i/Q + iiol [(Aro)i] . )
The calculations are made in reverse order; rg represents the pore entrance radius corresponding
to the minimum value of r, as determined by Eq. (7), that is, at the maximum applied pressure,
and the (Ar ), represent succeeding increments.
The distribution of porosity as a function of pore opening radius was determined for several of
the impregnated samples. Surprisingly, only small differences were obtained for specimens rang-
ing about E or 5, as defined in the upper portion of Fig. 6. Thus we were forced to select samples
from diverse positions to demonstrate that variations in porosity characteristics would be signif-
icantly greater than the variations introduced by the reproducibility of the method, as suggested
by the curves in Fig. 8. The result is that the pore size distributions do not give a high degree
of distinction regarding flow properties as we had originally imagined. Part of the difficulty is
unquestionably due to our inability to distinguish between pore number and pore length in con-
structing the porosity distribution curves. Unfortunately, these have opposite effects on the flow
20
ORNL-DWG 66-12745
50 T T T T T T - T
3 DISTANCE FROM TOTAL BULK
®) SPECIMEN NO. BAR CENTER POROSITY DENSITY
5 40 (cm) (vol%) (g/cm3)
2 M T
ST : ————— 0 9 0.39 1.0 1.85
L — i —_—— E 118 10.8 1.86
z 2 - e I 3.48 10.4 1.87
Q - 30 —is < —
S S
o
xr T
o |
(2 —
0 :O /sfl. o
> v \
|._
g \.\
‘-“
2 M N
a .‘.wp\ \ (@)
h — O
&g"fim%—a.w. -—-__'_"'-O
0.04 0.06 0.08 0.40 0.12 044 0.16 0.8 0.20
. PORE ENTRANCE RADIUS (u)
Fig. 8. Porosity Distribution in Impregnated Graphite Bar 23 for Three Positions Within the Bar.
properties. The fluid measurements themselves thus remain as the most reliable means for de-
termining gas transport properties within a given MSRE bar.
Permeability Determinations
Basic Considerations. — Before proceeding to an examination of variations of the permeability
coefficient with position, it is instructive to again compare the untreated and impregnated speci-
mens. The decrease in permeability to helium at atmospheric pressure due to impregnation may
be defined by the ratio
K., . (untreated) 3.0x 107! em?/sec
- - 5.7x 10?, (10)
KHe (treated) 52.2x 10~° cm?/sec
in which the values presented in Table 1 have been employed. This ratio is less than the 10*
reduction which was cited in the description of materials, but it should be recalled that the
treated sample referred to in Table 1 must be regarded as a poorly impregnated graphite. Reduc-
tion factors which compare favorably with the value above will be encountered in a later portion
of this work. Of more importance is a comparison of the quantity
5 _ HeK (11)
which is a measure of the relative effect of free-molecule and hydrodynamic mechanisms on the
overall gas transport in that it denotes the normal fraction of the total resistance. At 1 atm
21
pressure, this quantity is found to be only 7% less than the hydrodynamic value of unity in the
case of the base stock, but for the impregnated material 5, -~ 0.40, a value which is 60% less
than the hyvdrodynamic result. ‘
This effect retains its importance even when we convert from helium and argon parameters to
corresponding values for typical fission products (e.g., xenon) at reactor conditions (2.36 atm |
and 936"K, as discussed about Table 6 in Report I). Here it is found that 0. is 91% less than ‘
the hvdrodynamic value. Furthermore, the overall coefficient is
p Pxox v Dxenme (1.45. 1071 (152~ 10-3)
as well as Ap
and that measured values of 4, L, and V remained constant during the experiment. The room tem-
perature and barometric pressure are recorded since the barometric pressure must be added to the
readings of the upstream-side pressure gages. Unless subatmospheric pressure measurements are
being performed, leaks and/or bleeds on the upstream side are of no consequence, since the
receiver system is connected to the stainless steel tubing. The incremental pressures are divided
by their respective incremental time intervals to obtain the flow rate.
In our particular experiments, once a set of permeability values had been determined, half of
the sample was machined away, and the permeability of the remaining portion was likewise in-
vestigated. These latter samples were identified by the letter b; thus specimen 5b refers to that
portion of specimen 5 which remained after the machining operation; Sa, on the other hand, des-
ignates the portion of specimen 5 which was removed by the machining process. The orientation
of sections a and b of a given sample relative to the center of the bar is also identified in Fig. 6.
Results. — The permeabilities of the samples to helium are displayed in Fig. 11. Each ex-
perimental value (or point) on this plot has been reduced by the intercept DHe of the correspond-
K
ing plot of K, vs < p> in order that all the experimental data may be conveniently shown on the
same plot. Although scatter in the experimental data is apparent, particularly so in the case of
specimen S, the relationship between permeability and sample position is unmistakable.
25
Table 4. Summary of CGB Graphite Flow Parameters at 23°C as a Function of Bar Position
. a z DHeK BO/TIHe
Specimen
(cm) (cm2 /sec) ((:m2 sec 1 atm_l)
x 104 x 1073
3 0.159% 7.97 12.6
2b 0.696 4.42 5.59
2 0.854 2.65 2.62
2a 1.014 1.89 1.71
b 0.696 4.32 4.89
4 0.854 2.89 3.32
4a 1.014 2.17 2.51
1b 1.550 1.15 1.12
1 1.709 0.644 0.555
la 1.870 0.447 0.369
5b 1.550 0.688 0.659
5 1.709 0.366 0.194
Sa 1.870 0.249 0.114
®Relative position in bar shown in Fig. 6; values for the a specimens calculated in accord-
ance with Eq. (14).
bMidpoint of half-specimen 3; see text.
The contribution of two sections, a and b, to the permeability of their composite can be shown
to be given by the expression
L
e
b
L;
i=1,...,5, (14)
K.
1
s
K
a
where L. = L_ + L, is the length of the ith composite (see Fig. 11) and K| is the permeability
coefficient of the whole sample 1. If the pressure across the pack is sufficiently small, all three
permeabilities may be referred to the same average pressure, ( p > Equation (14) therefore per-
mits us to calculate the permeability of the specimens a, which had been removed by the machin-
ing process. These results, in addition to the experimentally derived results, are summarized in
Table 4 in terms of the intercept D, . and slope B /5, of the corresponding K, vs plots.
If the center of a given sample is regarded as that point which is characteristic of the per-
meability of the sample as a whole, then the curves of Fig. 12 describe the variation of the viscous
and Knudsen coefficients with position within the MSRE moderator graphite bar. The vertical
““identical’’
lines associated with each point correspond to the spread in values of the two
samples which lie on either side of the center line. Consistent in this context is the assumption
that permeability characteristics of sample 3 are likewise representative of its halves, which are
positioned so that their midpoints correspond to a distance z = 0.159 cm from the center line of the
bar.
26
ORNL-OWG 66-12747R
o3 ] w03
7
/
Bo/ 7, VISCOUS-FLOW PARAMETER (cm2/sec-atm)
T
1
Dyyexs XNUDSEN DIFFUSION COEFFICIENT (cm?/sec)
4
I
/
i
|
|
1
mn
l—/"—i
¥
6!
o
|
|
;6 ; k a : i L
0 0.25 Q.50 Q75 1.0 1.25 1.50 .75 2.0
ZQ_, DISTANCE ALONG CENTERLINE (cm)
Fig. 12, Variation of the Viscous and Knudsen Flow Parameters Characteristic of Yarious Positions
Within Impregnated Graphite Bar 23.
The data shown in Fig. 12 clearly demonstrate the effect of impregnation on both the Knudsen
and the viscous flow parameters. In fact, it appears justifiable to represent this dependence in
fair approximation by a straight line of negative slope on a plot of log DjK Vs zZ.
In summary, we have demonstrated a rather gross inhomogeneity in flow characteristics of the
MSRE graphite as a result of impregnation and have indicated that the nonuniformity can be ap-
proximated by an exponential variation in the flow characterization parameters. We shall in-
vestigate the consequences of this variation on the migration characteristics of fission product
gases in the next part of this report.
V. THEORETICAL DESCRIPTION OF GASEOUS FISSION PRODUCT TRANSPORT
IN MSRE MODERATOR GRAPHITE
General Description of Diffusion with Sink Terms
In this section we derive the general equation for linear diffusive transport of a gaseous fis-
sion product in MSRE moderator graphite. To simplify the problem somewhat, however, we wish
first to carry over a result of Report I which had been discussed earlier, that is, that the Knudsen
mechanism dominates in describing the diffusive transport in CGB graphite (but not in the base
27
stock!). To a good approximation, we can therefore describe the flux ]j of any gaseous fission
product j by the relation
Ji= —DjK(dnj/dz) , (15)
where D].K is the Knudsen diffusion coefficient characteristic of component j and dnj./dz represents
the gradient of molecular density which causes transport.
If we consider the rate of accumulation of species j in a volume element A dz which is located
about the point z within the graphite, one readily obtains the expression
(16)
d
in which €, is the fraction of the bulk volume which is accessible to the gaseous species and )\j
is the decay constant of the fission product. [Burnup of component j can be handled by merely
redefining )‘j as (’\j)eff = )\j + chb, where & represents the neutron flux and o; is an appropriately
averaged capture cross section. We shall forgo this contingency, however.] It is important to
note the appearance of €, in every term except the diffusion term which contains D, . This is
frequently a point of confusion, and so we digress momentarily to elaborate on this subject. The
factor ¢, actually arises because we consider a volume element A dz of the graphite. In count-
ing up the number of j-type molecules, we must of course exclude that volume which is already
taken up by the graphite or is otherwise inaccessible to the j molecules. Thus, for example, the
total number of molecules of type j within the volume element is given by (¢, A dz)nj. In the
diffusion term, however, we have already provided for this contingency in our definition of DjK’
so its inclusion once again would be erroneous.
Equation (16) is easily recognized as a diffusion equation with a sink term. In order to ob-
tain an expression for the dependence of n; on position and time, the equation needs only to be
solved in a manner which is consistent with the appropriate initial and boundary conditions. This
can lead to quite complicated expressions in many cases, however, including those of interest
in this work. In a large number of applications, the problem is considerably simplified if only a
steady-state solution is sought, for under this condition
dnj/d!: 0, a7
and Eq. (16) reduces to the form
d
d—Z[DjK(dnj/dz)] —emnA; = 0. (18)
In the next sections we seek solutions of Eq. (18). Note also that we can write Eq. (18) for
every gaseous fission product j; no coupling terms arise (i.e., terms which contain the subscript
i for instance) by virtue of the Knudsen mechanism.
28
Steady-State Transport in Uniform Porous Media
Here we consider the transport of a gaseous fission product in a slab of a uniform graphite
which can only be penetrated at the surfaces z = —L and z = + L. Uniformity in this context
implies that Dj
x and £, are independent of position, so that Eq. (18) becomes
d*n fdz? — ep A /D, - 0. (19)
If the gas concentration is identical at the two surfaces, our choice of coordinate system
allows us to formulate the boundary conditions
n(=L)=nGL)=c,, (20a)
(a’nj/dz) =~ 0atz=20. (20b)
A second consequence of the choice of coordinates is that now only half of the problem, so to
speak, need be solved; the two halves are completely symmetrical. Some attention must be given
to algebraic signs, however, since Eq. (15) refers to diffusion in the + z direction. Diffusion into
the slab from the surface z = — L will therefore appear as a positive value of J;, but transport into
the slab from the surface z = + L, since it is obviously in the opposite direction, will be charac-
terized by a negative value of Jj'
The solution of Eq. (19), subject to the boundary conditions of Eq. (20), can be written in the
form
n,(z) = c, cosh (B;z)/cosh (B,L) , (21)
where
Bz (e A/D; 002 (22)
If we ignore the distinction between positive and negative values of ]r" the flux of component
j into the graphite is obtained by inserting Eq. (21) into Eq. (15) and evaluating the result at the
boundary. In this manner we obtain
J; = Cg(ét/\ijK)l/‘z tanh [(itr\j/DjK)l/QL] : (23)
Steady-State Transport in Nonuniform Porous Media (MSRE Graphite)
The situation involving a nonuniform medium likewise begins with Eq. (18), except that two
complications arise, The first of these is a dependence of the void fraction €, on position; but
in view of the data given earlier, in which only a 10% variation had been noted, we may, if we
wish, regard this parameter as effectively constant. The second complication, unfortunately,
cannot be dismissed as easily. This concerns the dependence of DjK on position, and, as we
have seen earlier, the dependence is quite marked. In fact, we had suggested the relation
29
_ —a;z 2
D,y (2)= D, (0) ™" 24)
to describe approximately the variation with position. The equation to which we seek a solution
is thus of the form
d
d—z[DjK(z) dnj(z)/dz] - )\jet(z) nj(z)= 0, (25)
where we have indicated those parameters which are functions of distance.
Unfortunately, Eq. (25) is not readily amenable to solution. One can concoct an iteration
technique by which the problem might be attacked, but such methods ordinarily yield series
solutions which may or may not converge rapidly. In the present case we can formally integrate
Eq. (25) twice and, with the aid of the boundary conditions discussed previously, obtain the
formal solution
3 L Et(z) z
n.(2)= cy — A, j; Dfl{(g{fg n,(2) dz} dz . (26)
The second approximation to nj(z) evolves from Eq. (26) by inserting a trial function for n].(z) in
the integral expression and performing the indicated operations. As a first approximation, we
can employ the result for the uniform case, Eq. (21), with Bj a constant, but the resultant form
of nj(z) in second approximation already takes on the appearance of a rather formidable com-
putational problem. In addition, although one builds up the solution from both ends simultaneously,
that is, from nj(O) and n].(L), there is no way in which one can test the convergence without
knowing the answer beforehand. This convergence can be painfully slow.
To gain some concept of the effect of nonuniformity on gaseous fission product transport, let
us therefore consider a situation in which the nonuniformity is discrete rather than continuous.
That is, let the transport characteristics of the medium be given by
D. =D, € ,=¢ EgzéL(regionl), (27a)
D. =D e —e. 0%z% 3 (rtegion 2), (27b)
27
where we have dropped the species subscript and the subscripts K and ¢ in favor of the numerical
subscripts which indicate the regions involved. (Note that we once again consider only half of
the medium. The entire medium is described by placing absolute value signs on & and L.)
It turns out that an exposition of this particular case provides considerable insight into the
problem athand. The physical situation under consideration comprises a slab of graphite (region
2) which is contacted on each of its two sides with another type of graphite. Insofar as gas
transport is concerned, both graphites are uniform, but each possesses different flow properties.
In line with our experimental results we shall eventually specify that D, > D .
30
The mathematical treatment of the problem!® proceeds in a manner similar to that for com-
pletely uniform media, except that two similar solutions of a second-order differential equation
are involved and are now subject to the four boundary conditions
n (L)~ cg,, (282)
n (@) =n,&), (28b)
D (dn,/dz)= D,(dn,/dz)atz =& , (28¢)
and
(dn,/dz)=0atz- 0. (28d)
The solution of the equations is straightforward but tedious. After much manipulation one
obtains the mathematical expressions
n (z) ) Y3, cosh (8,a) cosh [[31(2 —aN+ B sinh (3,a) sinh [Bl(z —a))
cs vB,cosh (B,a)cosh[B (L — 3N B, sinh (8,3) sinh [, (L —7)] (29a)
n,() vB, cosh (8,2)
c, yB,cosh (B,a) cosh B (L — &)~ B, sinh (B,a) siah (B (L — 0 (295)
in which
B, - (e A/DDV?, (3009
B,= (s, A/D)HV?, (308)
and
V=5 (30¢)
Beta values for several isotopes are listed in Table 5. The values of D which are required
in the calculation were derived from the extreme outer D value (4 x 107> cm?/sec) for bar
23, as shown in Fig. 12, and were converted to refer to the particular isotope at reactor tempera-
ture,
Although we found it mathematically expedient to position the origin of the coordinate system
at the center of the slab, this system is awkward from an applied point of view, particularly since
penetration profiles of fission products universally refer to the surface of the graphite as the
origin. To convert to this system, which we hereafter denote the ‘‘y-coordinate system,’’ we
merely employ the transformations y = L — zanda=L — &.
154, S. Carslaw and J. C. Jeager, Conduction of Heat in Solids, 2d ed., pp. 1536—-57, Oxford University
Press, New York, 1959,
31
Table 5. Characterization Parameters for Transport of Krypton and Xenon Isotopes
in MSRE Moderator Graphite at 936°K
Fisston tl/z A D, Ba
Product (sec) (sec_l) (cmz/sec) (cm™ 1)
) 92Ky 3.0 2.31 x 1071 1.5% 103 39.2
89K (Sr) 192.0 3.61x 1073 1.5%x 10™3 4.91
141xe(Ce) 1.7 4.08 x 1071 1.2 x 10™° 58.31
140% e (Ba) 16.0 4.33x 102 1.2x 1075 19.00
135%e 32,940 4.4%107° P 1.2x 1075 0.61
€7The fractional void volume €, was taken as 0.10.
PHere A includes the burnup term o, in which the cross section is averaged over the MSRE neutron
spectrum. The factor ¢ = (1.18 x 106 x 10—24 cm2) (1.95x 1013 cm—2 sec—1)= 2.3 x 10—-5 sec—1. The
decay constant itself is 2.1 x 10—5 sec—1,
The parameter a might therefore be regarded as a **
skin thickness,’’ especially when D, >> D,
which protects the inner core of the graphite. We shall now consider four special cases involv-
ing Egs. (29). It is assumed throughout, of course, that slab geometry is representative of the
moderator configuration for the particular A involved.
The first example involves the case in which a = L/2, BQL =1=p8,L/4,D,= 16D, and
€, = ¢,. The resulting concentration profile is described by curve 1 in Fig. 13. At first glance
the sudden change in slope at y/L = 0.5, that is, at y = a, appears unnatural. However, this be-
havior is well known; it occurs whenever the diffusion resistance is abruptly altered. This is
due to the boundary condition Eq. (28¢), which prohibits an accumulation of molecules at the
boundary, since this would violate the steady-state condition.
Curve 2 of Fig. 13 represents a half slab which is infinite in extent where the boundary be-
tween regions 1 and 2 is situated at a finite length a = L./2, where the distance L is given by
B,L=1=p3 L/4. As in the previous case, D, = 16D and £, = ;. (Note that in this case L
is not half the thickness of the sample. We have retained this symbol in order that all of the
curves might be plotted on the same scale.)
The remaining two curves concern a homogeneous rather than a composite medium. Curve 3
reptesents the case SL = 4, in which L is half the thickness of the specimen. The solution cor-
responding to curve 3 is given by Eq. (21), which becomes, after transformation to the y-coor-
dinate system,
n(y) = Cy cosh [B(L — y)l/cosh (BL) . (3D
- The steady-state flux for this case is given by Eq. (23):
J= cg(el‘)\D)l/2 tanh (BL) .
32
ORNL-DWG 68- 7T410R
.00
0.80 AN
0.60 \
0.40
0.20
o \
: \
0.10 E \ |
0.08 \ \\ —=3
\ AN
Q.06 \ \ 3
NN
NN
XN
y/ L
Fig. 13. Generalized Plot of Fission Product Profiles as Described by the Steady-State Diffusion Equa- .
tions. Curves | and 2 represent composite media joined ata = L/2, with y =1, B2L =1= [3][4/4, and D, = 16D
Curves 3 and 4 are plots for homogeneous media with BL: 4, Theparameter L represents half the thick-
1
ness of the sample for curves 1 and 3, whereas the thickness of the samples corresponding to curves 2 and
4 is infinite in extent. [n these cases the parameter L is defined by BzL: 1= B]L/Ai for curve 2 and by
BL: 4 for curve 4,
Curve 4 is the analog of curve 2 for the homogeneous case. Here we again define a length L,
given by SL = 4, for convenience in plotting, but note that the sample is actually infinite in ex-
tent. The mathematical expression for this situation can be easily obtained from Eq. (31) simply
by allowing L to approach infinity. The result is
n(y)=c4 exp (=fy), (32)
and for the flux,
]:cg(et)\D)l/Q . (33)
An examination and comparison of the equations for each of the cases investigated shows
that, whereas the effect of < A remains the same for both the slope of the concentration profiles
and the flux expressions, the role of the Knudsen diffusion coefficient is toward a reversal. This -
can be seen quite clearly from a consideration of the uniform infinite-half-thickness case. By
Eq. (32), the slope of the concentration profile at the surface (y = 0) is given by
33
dn/dy = —c (e, A/D)' 2
thus an increase in D reduces the slope. From Eq. (33), however, we see that an increase in D
yields an increase in the flux J. This reversal is mitigated somewhat for the bounded cases.
For example, Eq. (31) yields
dn/dy = ——cg(@\/D)l/2 tanh [(eA/D)'/?L] ,
whereas
J = c4(eAD)!/? tanh [(eA/D)! /2L .
For small values of the argument, we can write tanh u = u, so the two equations are given ap-
proximately by
dn/dy = —cgE/\L/D , J= cge/\L .
In this instance the slope varies inversely as the Knudsen diffusion coefficient, but J is in-
variant to this parameter.
Preparatory to our discussions in later sections of this work, we wish to mention that very
little interest has been given to the steady-state diffusion of gaseous fission products with long
half-lives, '3°Xe excepted. Most current attention has focused on easily identified, immobile
daughters of short-lived precursors. For these isotopes the total penetrations are much smaller
than the overall thickness of the specimens employed, so that the homogeneous infinite-half-slab
model should be reasonably representative of the experimental conditions. We shall therefore
restrict ourselves only to Eqs. (32) and (33) for the remainder of this work. In this connection,
it is advantageous to point out that Eq. (32) is a universal function in terms of the reduced
parameters n/cg and By. In other words, we should be able to fit all the experimental data on a
single curve, regardless of the value of the Knudsen diffusion coefficient or isotope. The isotope
135Xe, however, should display rather deep penetration. This invalidates the use of a uniform
infinite-half-slab geometry and possibly even linear diffusion. For this isotope a radial, rather
than a linear, flow model might be mote appropriate. With these thoughts in mind, we now con-
sider studies of pertinence to this work.
VI. RELATEDSTUDIES
Early Investigations
Before discussing current studies of fission product migration in MSRE graphite, it seems ap-
propriate to review some of the pioneering researches of molten-salt breeder systems as con-
ducted by members of the Reactor Chemistry Division and allied divisions during the period 1958
to 1961. One might regard this period as a sort of interim between the completion of conceptual
design studies and the initial stages of specifying and producing the MSRE components. As
34
viewed now, the early supporting researches that had particular application to fission product
problems involved xenon adsorption on graphite,?® noble-gas solubility in molten salts,!’
18 9
chromium migration in container alloys,'® alloy-salt compatibility tests,!? and considerations of ‘
neutron losses resulting from !*%Xe sorption as influenced by moderator graphite characteristics.?°
17 received the most research atten- .
Of all these activities, the noble-gas solubility studies
tion because it was not at all clear at the outset of the molten-salt reactor program research how
a ‘““spongy’’ moderator material like graphite might behave in direct contact with the salt and fis-
sion gases. It was therefore presumed that most of the !?°Xe would reside in the core in the form
of small quantities of dissolved gases. It turned out that the quantity of xenon dissolved in
molten LiF—BeF2 mixtures would be indeed small and that the degree of solubility would de-
crease as the salt temperature increased. The solubility behavior here was thus quite different
from that exhibited by either CO, in water or HF in fluoride salts, where bicarbonates or bi-
fluorides are formed. In all the systems studied, Henry’s law was followed, and Arrhenius plots
permitted a computation of the enthalpy of solution. A simple model relating the free energy of
solution to that required to overcome the salt surface tension associated with the formation
of a hole (wherein the gas might reside) gave a good description of the solution mechanism
and permitted order of magnitude estimates of the solubility constants.
Investigations of the diffusivity of chromium'® and nickel-base alloys were initiated because
thermal convection loops indicated marked transfer of the chromium alloy constituent from hot to
cold zones. Surprisingly enough, metallographic examination of the exposed alloys and CrF,
concentrations in the salt suggested that the rate of transfer was controlled by the rate at which
chromium could move up to or away from the salt-metal interface; such transfer might be induced
via reversible redox reactions relative to the UF./UF, ratio in the salt.18? Moreover, an over-
all chromium leaching (not just a transfer) could be induced by the presence of HF, NiF_, or
27
FeF intrace quantities.'®¢
Experimentally derived diffusion coefficients, coupled with the
limited amount of equilibrium data available at that time, along with some reasonable guesses,
permitted one to conclude that corrosion would be minimal unless appreciable amounts of NiF,
or HF were present, particularly if the alloy employed were INOR-8 (now called Hastelloy N).
YoM, C. Cannon et al., Nucl. Sci. Eng. 12, 4 (1962),
17(3) G. M. Watson et al., J. Chem. Eng. Data 7, 285 {1962); (b} M. Blander et al., J. Phys. Chem. 63,
1164 (1959); (c) W. R. Grimes et al.., J. Phys. Chem. 62, 862 (1938).
18(:’3) R. B. Evans Il et al.. Self-Diffusion of Chromium in Nickel-Base Alloys, ORNL-2982 (January
1961}, (b) W. R. Grimes et al., ‘*Radio-Tracer Techniques in the Study of Corrosion by Molten Fluorides,”’
Radioisotopes in Physical Sciences and Industry, vol. 3, p. 559, IAEA, Vienna, Austria, 1962; (¢) J. H.
deVan and R. B. Evans III, ‘“Corrosion Behavior of Reactor Materials in Fluoride Salt Mixtures,”” Corrosion
of Reactor Materials, p. 557, IAEA, Vienna, Austria, 1962,
19The first report of this work, authorized for limited external distribution, was prepared by R. J. -
Sheil, R. B. Evans IIl, and G. M. Watson, Molten Salt—Graphite Compatibility Test. Results of Physical
and Chemical Measurements, ORNL-CF-59-8-133 (August 1959). Most of the results were later presented
with additional data in a report by R. B. Schulze et al., INOR-8—Graphite—~Fused Salt Compatibility Test,
ORNL-3124 (June 1961), -
2OThe results were initially issued for internal distribution by G. M, Watson and R. B. Evans III,
Xenon Diffusion in Graphite: Effects of Xenon Absorption in Molten Salt Reactors Containing Graphite,
ORNL-CF-61-2-59 (February 1961). The report has since been released for external distribution as ORNL-
TM-262 (1964).
35
In addition to the static and thermal-convection-loop corrosion studies described above, a
long-term pump-loop experiment!® was begun on May 9, 1958, and terminated on May 20, 1959.
The average experimental temperature was 650°C, and the salt was LiF-BeF,-UF, (62-37-1
mole %). The objectives were to test salt-alloy-graphite compatibility, with emphasis on the
corrosion of the alloy and behavior of the graphite. As anticipated from earlier results and
thermodynamic calculations, almost negligible amounts of alloy corrosion and/or carburization
occurred. The condition of the 1.91-g/cm? graphite attracted considerable interest, however, for
only trace amounts of saltinvaded the graphite matrices; in fact, 82% of the samples suffered a
minute weight loss, indicating a tolerable degree of erosion. Obviously salt did not adhere to the
graphite surfaces. Wet analyses gave some idea as to the amount of beryllium and uranium in the
graphite. The mode of their invasion was somewhat complicated by the fact that the as-received
graphite possessed cracks and fractures, a ubiquitous feature of high-density, low-permeability
graphite. Since a flush salt (no uranium) treatment may have filled these cracks initially, it was
not surprising that the U/Be ratio in the graphite was lower than that of the pumped salt, which
contained ~ 1 mole % UF,.
Finally, we review the short-term !3%Xe poisoning studies and associated out-of-pile experi-
ments where water was used as a make-believe molten salt. This work?? entailed a very simple
parametric study carried out with an outdated manual computerized system, a 12-in. slide rule,
The study was based on an optimistic first assumption that the pump-bow! stripper would operate
at 100% efficiency. This was done in an effort to compensate for the pessimistic second assump-
tion that no resistance film would be present to help guard against transfer of the xenon poison
from the salt to the graphite. Since it was realized that the graphite specifications would not
be written specifically to ensure a low gas permeability or porosity (low fluid permeabilities were
specified, however), the results were expressed in terms of a bypass or recycle ratio r and the
combination Dxe)\)’{e, where D, _ is the effective diffusion coefficient of xenon relative to the
graphite and
)\;{e = [ef(f\Xe + gbo_){e)/l)l'(e]l/z "
Thus A’ is equivalent to 3 as defined by Eq. (22), in which the burnup term ¢ ¢ is included.
As had been anticipated, a knowledge of the solubility of xenon in the molten salt proved to
be invaluable in performing the necessary calculations. Furthermore, it was clearly pointed out
that ¢, and D play equal roles in determining the overall behavior and that unless the value
€Dy, were very low, approximately 10~ 7, the sparging and stripping rates would have to be
quite high and efficient.
135X e Migration in the MSRE
The '3°Xe poisoning investigations were reactivated in 1963, about two years after con-
struction of the MSRE began. The major portion of this work was performed by R. J. Kedl of the
Reactor Division, although several others participated in and contributed to these efforts. The
36
significant advances which resulted from the investigations under discussion involved a con-
sideration of transient conditions, that is, cases in which the accumulation term dnj/dt of
Eq. (16) is nonzero; refinements of the older studies to provide for bubbles which circulated with
the molten salt;?!
and diffusion of the xenon through the salt itself,
To evaluate the mass transfer coefficients which were employed to describe the xenon-salt
diffusion in both the core and the pump bowl stripper regions, a series of #°Kr addition-stripping
experiments were performed during the barren salt flushing procedures which signaled the startup
of the MSRE operations. One of the more important conclusions regarding these investigations
was the finding that diffusion through the salt primarily controlled the !'3°Xe characteristics of
the reactor.??
Esentially the same conclusion could have been inferred from our first reported?? D . values
for MSRE graphite (viz., 1.32 x 10~% cm?/sec) and the previous demonstration?® that unless
D, . were considerably less than 107* cm’/sec, little or no absorption resistance could be ex-
pected on the part of the graphite in the absence of xenon-salt diffusion (which were called
“film effects’’) and/or very high and efficient stripping rates.
Repeat computations verified Kedl’s results, not only for the MSRE but for the MSBR (breeder
reactor) as well.?* In the latter design the salt is to be in turbulent flow; this condition will
lessen the effective diffusion path (film) of the xenon through the salt.
Graphite Surveillance Specimen Results
The recent emphasis which has been placed upon mass transfer in the salt constitutes a
major justification for the expenditure of much of the effort to be described in the succeeding
portions of this report. Most of the work has several features in common: short-lived isotopes
were involved, concentration profiles were quite steep, and the penetration data were laboriously
garnered using mechanical sectioning and counting techniques.
If short-lived isotopes are involved, one can in principle evaluate the surface concentration
Cg of a given gaseous fission product from the time-corrected count data. A comparison of this
value with that obtained in the bulk salt thus yields an additional check on film effectiveness.??>
Our interests, however, are concerned with the behavior within the graphite. As we had seen
earlier, each of the mathematical relationships which we had developed in this connection could
2IR. J. Kedl and J. R. Engel, ‘“Circulating Bubbles (in the MSRE),”’ pp. 2224 in MSR Program
Semiann. Progr. Rept. Aug. 31, 1966, ORNL-4037 (January 1967).
27R. J. Kedl and A. Houtzeel, Development of a Mode! for Computing 135xe Migration in the MSRE,
ORNL-4069 (June 1967),
23 .
A. P. Malinauskas, J. L. Rutherford, and R. B. Evans III, Gas Transport in MSBR Moderator Graphite.
I. Review of Theory and Counterdiffusion Experiments, ORNL-4148 (September 1967).
24C. F. Baes, Jr., and R. B. Evans III, ‘““Xenon Diffusion and Possible Formation of Cesium Carbide
in an MSBR,’’ pp. 158-65 in MSR Program Semiann. Progr. Rept. Aug. 31. 1966, ORNL-4037 (January
1967).
R, J. Kedl, A Mode! for Computing the Migration of Very Short-Lived Noble Gases into MSRE
Graphite, ORNL-TM-1810 (July 1967).
37
ORNL-DWG 68-6481R
2 9/32 in.
T
VHS
KIRSLIS
DD N
\\\;
7%
e
" ste
K
503
/aamSanY
L0001 T ieY
o
&
55
e
S
e
KIRSLIS
K5
LS
TR
bovetetel
I
066010
(o) (&)
Fig. 14. Location of MSRE Graphite Specimens Employed by Kirslis and Co-Workers. Positions referred
to are: (a) locations in original unmachined bar 635 as they relate to machined bars and associated perme-
ability specimens; (b) locations in surveillance-specimen bundles which are inserted in the MSRE core.
Regions A comprise graphite specimens; regions B comprise cross sections of Hastelloy N (INOR-8) tensile
specimens; region C locates a flux monitor,
be expressed in terms of n/cg, and since Cg 1S by definition of steady-state conditions a con-
stant, an absolute value of the surface concentration is unnecessary for our purposes. In like
manner, film effects (i.e., diffusion through the salt) should not alter the behavior in the
graphite.
In essence, our primary concern here is to ascertain whether or not we could have obtained
the same information regarding the concentration profiles through out-of-pile (and out-of-hot-cell)
experiments. As a corollary, we should also be able to determine whether or not the pores at the
graphite surface have been plugged with liquid or solid, or whether the graphite itself has become
more permeable under reactor conditions. Our intent should in no way be construed as a demon-
stration that the in-pile studies were performed inefficiently; the efforts of Kirslis and co-workers,
as an example, embrace several important facets of the overall problem of fission product trans-
port, whereas our involvement concerns only gaseous fission product migration in the graphite.
The present review is thus restricted as described above.
Of pertinence to this work are the first graphite surveillance specimen data, which were pub-
lished by Kirslis?® in 1966. Location of the sample with respect to position within the original
unmachined graphite bar 635 and within the reactor package is shown in Fig. 14,
265 5. Kirslis, “‘Fission Product Behavior in the MSRE,”’ pp. 16591 in MSR Program Semiann. Progr.
Rept. Aug. 31, 1966, ORNL-4037 (January 1967).
38
The rectangular samples utilized by Kirslis were exposed in the MSRE for 7800 Mwhr at
temperatures ranging about 650°C. After withdrawal from the MSRE, the specimens were sectjoned
in a rather ingenious manner to obtain the time-corrected concentration profile data which have
been partially reproduced in Table 6.
In this work we attempt to correlate the experimental data by considering the homogeneous
case involving a semi-infinite slab; the corresponding mathematical expression is given by Eq. (32):
Table 6. Selected Penetration Results for Daughters of Short-Lived Fission Products That
Ditfused into CGB Graphite® as Noble Gases
141Xe 140Xe SQKI_
y, Average
Penetration Cou?ts By A Counlts 1 By n(y)/c Counlts . By n( ‘e,
(cm) (dis min™ " g— %) € {(dis min™ " g~ ") (dis min™ ~ g~ )
x 1072 % 107 x 1010 % 1010
VH5 (Wide Face — Surface Sample)®
0.00 23.0°¢ 0.00 1.00 15.0¢ 0.00 1.00 12.0¢ 0.00 1.00
0.79 8.6 0.83 0.37 10.4 0.36 0.69 11.9 0.14 0.99
2.59 1.6 1.2 0.11 5.7 0.45 0.48
4.86 0.19 5.1 0.008 2.0 2.2 0.13 .2 0.85 0.52
6.82 0.72 3.1 0.048 4.0 1.19 0.33
10.11 0.04 10.7¢ 0.002¢ 0.17 4.6 0.011 1.5 1.76 0.13
VHS5 (Side Face — Surface Sample)
0.00 23.0°¢ 0.00 1.00 0.95°¢ 0.00 1.00
1.45 5.0 1.50 0.22 0.49 0.66 0.52
4.41 0.21 4.60 0.009 0.14 2.00¢ 0.0229
Y2 (Wide Face — Interior Sc|mple))b
0.00 62.0¢ 0.00 1.00 15.0° 0.00 1.00 16.0° 0.00 1.00
0.76 31.7 0.64 0.51 14.4 0.25 0.96 12.8 0.11 0.80
2.71 6.5 2.3 0.10 6.6 0.88 0.44 11.0 0.38 0.69
4.84 . 4.1 0.023 2.8 1.6 0.18 7.6 0.67 0.48
6.67 0.73 5.69 0.0129 1.6 2.2 0.11 7.1 0.93 0.44
8.44 0.97 2.7 0.065 4.6 1.2 0.28
10.37 0.76 3.4 0.051 4.3 1.4 0.27
Y2 (Side Face — Interior Sample)
0.00 100.0° 0.00 1.00 22.0¢ 0.00 1.00
0.98 33.8 0.82 0.34 14.1 0.32 0.64
3.23 7.7 1.0 0.35
5.21 2.5 4.4 0.025 3.9 1.7 0.18
6.36 3.0 2.1 0.14
7.79 0.84 6.69 0.0089 1.5 2.5 0.069
“Moderator bar 635; data reported by Kirslis. 2®
bBar position; see Fig. 14.
“Extrapolated value from count vs penetration data.
9Not plotted in Fig. 15.
39
n.(y)c, - exp (=) .
This relationship obviously describes a universal function in terms of the reduced parameters
nj(y)/cg and B}.y; hence a plot of In nj(y) vs In y should be superposable on a plot of In X vs In
. Y, where
X = nj(}/)/cg s
Y = [31:" ’
simply by translating the axes distances corresponding to — In Cy and In [3]. respectively. Hence
concentration profile data, provided they can be described by the universal relationship, yield
values of /Hj and Dj directly.
A generalized plot of the data listed in Table 6 is given in Fig. 15; the values of Bj and Dj
which appear in the figure have been determined as outlined above, A comparison of the Dj re-
sults for the interior and the surface specimen suggests that the variation of diffusion coefficient
ORNL-DWG 6§8-6480
5 | T
INTERIOR SPECIMEN
! ! MASS 105xD; 4107'x B
> ) | NO.j (ecm%/sec) (em)™ |
v 14 5.7 8.4
® {40 4.0 3.3
ko | A 89 19 a4
o o —
il <% ‘ _ —
» “ I — - -
D
s
. “&
0.2 o
A\‘{o
FRACTION OF SURFACE CONCENTRATION, n. (y}/cg
oX -9
.
0.05 [+~
0.02 - -
SURFACE SPECIMEN
MASS 10°xD; 107'x §;
00l — NOj (em%sec) (em)™ |
— v 14 3.7 105 —
___© 140 24 4.5 . - —
0.005 '7 A 89 ‘_2 ,.? —
% ——— —
| .
0.002 :
- 0 i 2 3 4 5
REDUCED PENETRATION, B; y
. Fig. 15. Generalized Profiles for Short-Lived Noble-Gas Fission Products in Specimens from Bar 635.
Profiles are based on concentrations of immobile daughters of the noble-gas precursors. The interior speci-
men corresponds to Y2 in Fig. 14; the exterior, to YVH5. Row data were compiled by Kirslis et al.; correlated
values appear in Toble 6.
40
with position is not as pronounced as one might expect on the basis of the bar 23 data. However,
the variation should not be as large, since the surveillance specimens were much larger than
our permeability samples.
The degree with which Eq. (32) describes the experimental data is nothing less than amazing
and is perhaps the best indication we have of the care with which a most difficult experimental
investigation had been conducted. On the other hand, a thought which had disturbed us right at
the beginning of our studies appears to be forcefully verified by comparing D . for the interior
specimen of bar 635 with the corresponding value for bar 23 [cf. Eq. (12) of this work]. For bar
635, D, =5x 10~ % ¢cm?/sec, whereas for bar 23, Dy.=1x 104 cm?/sec. At this point it
seems as though we have selected the most nonrepresentative moderator bar for our gas trans-
port studies! (Additional interpretations of Kirslis’ data appear in a more recent report.?7)
ORR Molten-Salt In-Pile Loop 2
As a complement to the MSRE graphite surveillance program, an in-pile loop experiment was
28a
conducted by Compere and co-workers in the Oak Ridge Research Reactor. This experiment
was described as Molten-Salt In-Pile Loop 2. In many ways it was similar to a previous out-of-
pile loop experiment described earlier.!?
Location of the graphite employed, relative to the original unmachined bar 159 from which it
was taken, is shown in Fig. 16 along with a soft x-ray photograph of the specimen after experi-
mentation. Details regarding the experiment are best obtained by consulting the original descrip-
tion; 2% for our purposes, it is pertinent only to note that the molten salt was made to flow through
the eight holes which were drilled through the graphite.
It is evident from the x-ray photograph in Fig. 16 that the specimen possessed several cracks
which were invaded by the salt. The penetration data which were reported, however, were cor-
285 although the results represent average values
rected for uranium intrusion in these cracks,
for eight holes.
Previous experience with fission fragment gamma counting techniques prompted us to select
140%e as representative of a typical gaseous fission product, since its activity peak resides at
a rather high energy. Although this is a good choice from the standpoint of gamma counting
technique, one must also bear in mind the possibility of migration of the !'*°Ba daughter under
the temperature conditions of about 650°C of this experiment. Nonetheless, we selected !4%Xe
for correlation purposes.
The data of interest appeared as a cumulative (integral) plot, wherein the ordinate values
were referred to the percentage of total isotope within the loop. To cast the data into a form
27S. S. Krislis and F. F. Blankenship, ‘‘Fission Product Behavior in the MSRE,”’ pp. 116—35 in
MSR Program Semiann. Progr. Rept. Aug. 31. 1967, ORNL-4191 (December 1967),
28(6) E. L. Compere ef al.. ‘“‘Molten-Salt Irradiation Experiments,’ pp. 22-31 in Reactor Chem. Div.
Ann. Progr. Rept. Dec. 31. 1967, ORNL-4229 (March 1968); ‘‘Molten Salt Convection Loop in the ORR,”’
pp. 176—-95 in MSR Program Semiann. Progr. Rept. Aug. 31, 1967, ORNL-4191 (December 1967); (b) private
communication, March 1968.
41
(o) b)
Fig. 16. Location of Graphite Regions Exposed to Fissioning Molten Salt in ORR Convection-Loop
Experiments. Regions studied are adjacent to the small holes. Positions are referred to: (a) locations
with respect to unmachined bar 159 and associated permeability specimens, (b) various salt-filled cracks
revealed by salt x-ray radiographs.
amenable to the use of Eq. (32), it was necessary to invert the plot, extrapolate to zero penetra-
tion, reduce the ordinate values, and finally graphically differentiate to acquire the appropriate
information., Our efforts are displayed in Fig. 17. Except for the small deviations beyond about
0.04 cm, it appears that Eq. (32) once again describes the data accurately. Once again, how-
ever, D, _ for this specimen is considerably lower than the value for bar 23.
Reconciliation of Flow and In-Pil e Results
We have demonstrated in the two previous sections the possibility of accurately describing
in-pile transport of gaseous fission products in the MSRE. We have been unable to show, how-
ever, an ability to predict the behavior. As the situation now stands, either our mathematical
model is essentially correct but requires a diffusion coefficient which is about a hundredfold
smaller than the measured value or the diffusion coefficients of the moderator bars which were
employed in the in-pile experiments (bars 159 and 635) are about a hundred times smaller than
42
ORNL-DWG 68-6479
]
MASS 10®xD; 40'xpB;
' 0 NO. | (cm%/sec) (cm)~!
’ 140 3.4 3.7
0.8
> \
s
> \
5 0.6
<1
o \
e8]
o
T \
“ 0.4
<
'S
o \
o}
w
w
O
3
= N
b \‘
coe T~
\h\
\-...
0.4
0 1 2 3 4 5 {(x40~2)
PENETRATION, y, (cm)
Fig. 17. Penetration Profile for MOXe Diffusion Normal to Circular Areas in Bar 159 Curve is based
on smoothed-corrected estimotes made by Compere et al.
bar 23. To resolve this question we thus sought to measure the permeabilities of samples re-
moved from bars 159 and 635. In each case two specimens were removed, one from the position
designated la in Figs. 6 and 14, that is, a surface specimen, and an interior sample, as desig-
nated by position 3. The permeability results are presented in Table 7 along with corresponding
values for bars 23 and 788.
If we focus on the interior specimen (position 3), it is immediately obvious that the diffusion
coefficients of the graphites employed in the in-pile experiments are indeed about a hundred
times less than bar 23. In fact, the four specimens show about a thousandfold variation in dif-
fusion coefficient, with bar 23 being the most porous. Furthermore, comparison of position la
specimens with the corresponding interior samples indicates bar 23 to also be most nonuniform
with respect to gas transport.
A comparison of the diffusion coefficient values obtained from the permeability data and those
derived from the in-pile experiments for moderator bar 635 is given in Table 8. The agreement
is nothing less than amazing in view of the difficulties in obtaining the in-pile data and possible
normal variations in the actual diffusion coefficients of the permeability and the in-pile speci-
mens even though they were obtained from the same source. In summary, we have demonstrated
43
Table 7. Selected CGB Graphite Flow Parameters as Determined from Helium Permeability Data at 23°C*®
Position? la Position? 3
- |
Moderator c d c d |
Bar No DHeK BO’/UHe DHeK BO’/nHe (DHe K)S/(DHeK)la |
(cm?‘/sec) (cm2 sec ! atm_l) (sz/sec) (cm2 sec " Latm™ 1)
« 1078 w1077 «10™° 107
788 0.28 0.06 3.09 0.27 11.0
159 2.41 1.16 15.8 8.88 6.56
635 3.13 2.05 11.4 9.33 3.64
23 44 .7 36.9 797.0 1260.0 17.8
FA1l of the specimens have bulk densities in the range 1.85 to 1.86 g;"’cm3.
bSee Figs. 6 and 14.
“Intercept of helium permeability vs average pressure plot.
IThe modified viscous flow coefficient. Stope of K vs < p> plot.
Experiments with Moderator Bar 635 Specimens
Table 8. Comparison of Fission Product Migration Results Based on Permeability and Grinding
|
\
|
|
D:‘K’ Predicted Fission Fragment Coefficient (CmQ/SeC)
Fission Decay Position? la Position® 3
- F ¢ Constant
ragmen (sec_l) By Flow Concentration By Flow Concentration
Experiments? Profiles € Experiments Profiles
% 1072 % 107° x 107° x107° x 1078
80
Kr 0.36 1.17 1.2 4.26 1.9
140%e 4.33 0.93 2.1 3.40 4.0
R & 40.8 0.93 3.7 3.39 5.7
“See Figs. 6 and 14.
bComputed from values in Table 7 assuming a reactor temperature of 02 2°K (1200°F).
“Data from ref. 26; see Fig. 15.
that a relatively uncomplicated mathematical model can be employed to quantitatively predict
the behavior of short-lived gaseous fission products in MSRE moderator graphite,
VII. DISCUSSION
One of the unfortunate situations which arises in presenting the experimental data as we have
* done, without adding the ‘‘color,”” so to speak, is that the reader often receives the impression
that the experimental aspects proceeded smoothly and in a straightforward fashion. This was
not the case in the present study. The sample employed by Compere et al., as illustrated in
44
Fig. 16, is typical of the bulk of the moderator graphite. In other words, the material as a whole
contains innumerable fractures and cracks. Except for the specimens taken from bars 23 and 635,
the occurrence of these defects made the selection of appropriate samples for gas transport
measurements a most trying experience.
Short-Range MSRE Considerations
The intercomparison of the gas transport characteristics of the four moderator bars which has
been given in Table 7 rather lucidly points out the folly in applying such data indiscriminately.
This is particularly important when penetration data are of interest, since the diffusion coefficient
appears in the exponential term. Part of the divergence in the transport characteristics arises
from the fact that each of the moderator bars from which the samples were taken represents a
different fabrication batch. To some extent, then, the differences reflect the manufacturer’s
ability to economically reproduce the fabrication conditions. However, care must also be taken
in applying the results even to graphites of the same manufacture lot. As shown in Table 9, the
Knudsen diffusion coefficients for helium which were determined for two bars of the same fabrica-
tion batch also show a fair degree of variability. In discussing gaseous fission product migra-
tion, as for example in connection with the graphite surveillance specimen program, we therefore
cannot stress sufficiently the importance of determining the gas transport characteristics of the
surveillance samples prior to their in-pile use.
Two other facets in connection with the MSRE concern our assumption of the temperature
independence of the internal geometry of the graphite and alteration of this geometry as a result
of the neutron flux. The agreement between the results derived from flow measurements and
those obtained from the profile data presented in Table 8 suggests that both effects are quite
small for the MSRE operating conditions.
Table 9. Comparison of Knudsen Diffusion Coefficients for He lium at 23°C for
CGB Specimens Within Given Lots
Fabrication Moderator DHeK (cm?'/SEC)
Batch Bar Position la Position 3
x 10~° x 10~°
10 788 0.28 3.1
608 5.23 1.23
3 159 2.41 15.8
615 5,61 170
8 635 3.13 11.4
107 15.4 288
12 23 44,7 797
628 9,37 335
45
Some attention has been given to the effect of temperature on the pores of the graphite.
Napier and Spencer,??
as an example, have demonstrated that the porosity of the graphite in-
creases with temperature. On the other hand, Hutcheon®? found no temperature dependence of
the graphite on permeability, within experimental error. More recently, these studies have been
extended by Hawtin and Dawson®! to gaseous diffusion through graphite. These workers also
find no temperature dependence of the graphite on gas transport over the temperature range 20 to
600°C. Apparently the porosity increase does not significantly affect the ‘‘through-pores’’;
that is, although -, increases with temperature, <" does not. As reactor operation temperatures
rise, however, this aspect should be reinvestigated.
In like manner, we are unaware of any definitive work which has been performed regarding the
effects of neutron damage on the gas transport characteristics of moderator graphite. Studies of
this problem should also be considered.
Features Relative to MSBR Application
The MSBR imposes far more stringent conditions on the migration of fission productsinto
the graphite to achieve prolonged, successful operation than those required for the MSRE. As
an example, it has been estimated that a permeability of less than 10~®% cm?/sec is required in
order to maintain the xenon concentration in the core at the desired level.?? (It is obvious that a
permeability value of 1078 cm?/sec again permits us to describe gas transport through the graphite
in terms of the Knudsen diffusion coefficient alone.) Since the MSRE graphite is typically
characterized by a value of 107°% cm?/sec at the surface, additional reduction is clearly required.
Although a hundredfold reduction of the Knudsen coefficient is still probably attainable by
liquid hydrocarbon impregnation, but with considerable difficulty, attention has recently focused
3 To date, the most promis-
on sealing or gas impregnation methods to effect the desired value.?
ing technique involves the decomposition of a low-molecular-weight gaseous hydrocarbon in the
pores of the graphite. Reduction of the permeability in this manner is visually demonstrated in
Fig. 18. A graphite specimen which was subjected to permeability reduction by gas impregnation
was then sectioned, and mercury was injected into one of the sections under an applied pressure
of 1000 psig. Figure 18 is a radiograph of this section; the portion of the sample whose pores
have been filled with mercury is now opaque to x rays and thus appears as the light section.
Conversely, that section where permeability reduction has been effected retains its transparency
to the x rays. Furthermore, it is possible to use the radiographic technique to ascertain the
2B A. Napier and D. H. T. Spencer, Nature 218, 948 (1968).
SOJ. M. Hutcheon, B. Longstaff, and R. K. Warner, ‘“The Flow of Gases Through a Fine Pore Graphite,”’
Industrial Carbon and Graphite. pp. 239-70, Soc. of Chem. Ind., London, 1957.
31P. Hawtin, R. W. Dawson, and ]. Roberts, Trans. Inst. Chem. Engrs. {in press). We are indebted to
P. Hawtin for making the paper available to us prior to its publication.
3Ip R, Kasten et al.. Graphite Behavior and Its Effects on MSBR Performance. ORNL-TM-2136,
chap. 3 (in press).
PR.L. Beatty and D. V. Kiplinger, ‘‘Gas Impregnation of Graphite with Carbon,’” MSR Program Semiann.
Progr. Rept. Aug. 31, 1968, ORNL.-4344.
46
Y -88804
Fig. 18. Effectiveness of a Gas Impregnation Technique for Graphite Permeability Reduction as
Evidenced by a Radiographic Method Employing Mercury Penetration. The light section, which is opaque
to the x rays, has been penetrated by the mercury. The graphite surface where permeability reduction has
been effected remains translucent to the radiation.
nature of the impregnated region by exposing the sample to x rays after mercury injection under
successively increasing applied pressures. Results obtained in this way indicate that the sealed
area is highly nonuniform; the sealing technique is most effective at the surface and decreases in
effectiveness as one proceeds inward.?3
The gas impregnation technique has been successfully employed to reduce helium permeabilities
of about 102 cm?/sec to 10~ 1% cm?/sec. Samples obtained in this manner are currently being in-
vestigated from the standpoint of radiation stability; experiments have already been conducted to
demonstrate that the gas-impregnated specimens retain their permeability characteristics even after
3000°C heat treatments.3?
The maximum depth of gas impregnation effectiveness, as illustrated in Fig. 18, is about 15
mils; over this distance the permeability increases from about 10~ '° c¢m?/sec or better to about
10~2 cm?/sec; so it is apparent that the model for gaseous fission product transport for the case
of a uniform porous medium is certainly not applicable to the impregnated area, although it can
be employed to describe profile data for the interior region.
47
Except for the inferences which were made in discussing the in-pile fission product migra-
tion studies, we know of no definitive work which has been performed regarding the effect of
> radiation-induced dimensional changes on the gas transport properties of the material. Since the
MSBR graphite will be exposed to rather high neutron fluxes, and particularly in view of the
- desired extent of gas impenetrability, we believe investigations of this nature are of prime im-
portance. In like manner, again because of the stringent permeability requirements, we strongly
suggest that the possible temperature dependence of €’/q” be reinvestigated.
Useful Approximations in Describing Gas Transport Through Porous Media
Throughout this report we have utilized pore size distribution data in only a qualitative
sense; most of the discussion of a quantitative nature has relied upon the permeability and
counterdiffusion data. Although all three sets of data have mote or less been considered as
independent of one another, an intercomparison of sorts is possible, provided we are willing to
make a few approximations. In a similar manner, this intercomparison may be employed to ob-
tain approximate values of one parameter from another.
The entire argument involves a grouping which was introduced in Report I, namely,
i “mTm9m
GRS WL
q.
T,
1/2
: . : . . . — 1/2 7 ;
in which r_ is the equivalent radius of the mth pore of equivalent length [ = g L in terms
of the length L of the graphite. If we assume at this point that the average of a product or quotient
is equal to the product or quotient of the average values, then the equation takes the approximate
form
£’