f E5h, N OAK RIDGE NATIONAEL operated by UNION CARBIDE CORPORATION for the U.5. ATOMIC ENERGY COMMISSION ORNL- TM~ 262 corvno. - 4 DATE - June 27, 1962 XENON DIFFUSION IN GRAPHITE: EFFECTS OF XENON ABSORPTION IN MOLTEN SALT REACTORS CONTAINING GRAPHITE G. M. Watson and R. B. Evans, IIT ABSTRACT Estimates have been made of the xenon poison fraction in a hypothetical molten salt reactor operating at steady-state conditions near those projected for the MSRE. The polson fraction was expressed as a function of the Xe-135 concen- tration in the molten salt fuel, the free gas space over the fuel, the pores of the unclad graphite contacting the fuel, and the corresponding volumes. Xenon transport rates were considered the various combinations of generation, burn-out, decay, removal via helium stripping, and diffusion into graphite. Particular attention was given to & discussion of the graphite porosity, permesbility, and xenon diffusion coefficient. These parameters govern the rate of xenon diffusion into the graphite moderator. The computations established that permeability and/or porosity reduction coupled with increased NOTICE This document contains information of o preliminary nature and was prepared primarily for internal use at the Ock Ridge National Laboratory. It is subject to revision or correction and therefore does not represent a final report. The information is not to be abstracted, reprinted or otherwise given public dis- semination without the approval of the ORNL patent branch, Legal and Infor- mation Control Department. stripping rates effectively decrease the xenon poison frac- tion and increase neutron economy. Within the range of graphites currently under consideration for the MSRE, in- creased stripping rates appear to be the most effective means of reducing the xenon poison fraction. At the circu- lation rates considered, it was found that neutron economy (with respect to xenon) could not be advanced through per- meability reduction alone. INTRODUCTION The possibility of employing unclad graphite in direct contact with the MSRE fuel leads to four contingencies, which must undergo continual and thorough examination, as conceptual designs approach specification form. These con- tingencies are: 1. Deposition of solid U0, arising from oxygen in- troduced via the graphite 2. Invasion of the graphite by the molten fuel 3. Variable reactivity resulting from a variable Xe-135 concentration in the graphite 4. High xenon poison fraction The first three items could result in erratic reactor operation; the last item is of importance from a standpoint of neutron economy. Research efforts, which are slanted to yield information applicable for evaluating these difficul- ties, involve: volatile impurity contents of graphites,l molten salt absorbability of graphitesz (also UF, to UOQ, conversion due to impurities), effects_of pore size distri- bution of graphites and we&ting agents~ and studies of gas transport in porous media. In addition to the third and fourth difficulties mentioned, it has been shown that Cs° for which Xe-135 is a precursor, is not compatible with graphite. The role o Cs° in gas cooled reactors has been discussed by Rosenthal and Cantor.’ A comparison of proposed methods for xenon control has been presented by Burch. More recent computations have been made by Spie&wak.9 The results of both studies are quite different with respect to xenon control and graphite requirements as the earlier work was based on high circula- tion rates and the presence of a large decay dome in series with the pump. These features have been eliminated in pres- ent designs which lead to increased driving forces for the xenon absorption by the graphite. The primary objective of this report was to extend the com- putations by Burch to lower ranges of removal rates to de- termine the feasibility of using low permeability graphites under the more recently projected conditions, In view of this objective, considerable discussions of the graphite parameters of interest are presented. BASIC CONSIDERATIONS Xenon Poison Fraction Maximum Poison Fraction A maximum poison fraction indicates a low level of neutron economy, and a relatively high rate of Cs® produc- tion within the graphite. Since the maximum fraction ap- pears as a limiting value for many of the curves presented, a brief discussion of maximum poisoning follows. The maximum poison fraction is the product of three factors: the ratio of Xe-135 burn-out to total Xe-135 loss, i.e., ($p0)/($,0 + Axe)s the moles of Xe-135 formed per fission, and the ratio of neutrons causing fission to the total number absorbed by U-233. Thus, O 2.21 P.F. | = [_,,.._;..E___.,.._% (6.2:10™%) g ) - (1) ax. ¢cc + RXe .5 This expression is based on the assumption that all the Xe-135 which does not decay 1is burned out in. the reactor core. Since Ay, is the decay constant, (sec)™, the power level contribution is contained in the Xe-135 destruction constant ¢eo, (sec)~l. To show the effects of Xe-135 re-~ moval by stripping and Xe-135 absorption by graphite, one must employ a destruction ratio which is more complex than that appearing in Eq. 1. Poison Fraction with Removal Rates The complete destruction ratio may be developed by con- sidering a steady-state Xe-135 mass balance and the total neutron captures by Xe-135, Let: np be the diffusion rate of Xe-135 into the graphite, fis be the removal rate at the primary pump, nj, be the Xe-135 dissolved in 211 the salt, and nyp,. be the amount of Xe-135 dissolved in the core salt. The poilson fraction is given by $e0 on —————— « N P.F. (%) = (éc Le ¥ ¢.0 + xe D ) (5.48) (2) écOnLc + kX@nL + nS + nD The variables, n;, DLcs and ng can be expressed in terms of reactor parameters through the use of the noble gas solu- bility relationship, that is, n, = Cg (KPRT)VL, (3a) nj, = C, (KpRT)VLc, (3b) A, = C, (KpRT}QS, (3¢) where V and Qg are volume and volumetric strip rate, re- spectively, and C, is the gas phase xenon concentration in equilibrium with the dissolved concentration, nL/VL. The Henry's law constant is given by Kp. Typical plotslo?ll’lz of Kp versus temperature for various mixtures are shown in Fig. 1. Only one stripping term, ng or Qg, appears in Eq. 2 as current plans for the MSRE call for one free gas space at the primary pump bowl. The bowl will be swept with helium and will see Xenon-saturated salt at a rate equivalent to Qg, which is (0.04) (circulating pump rate). A rough sketch salt-atm) [ o Xenon Solubility Constant (molie Xe/cc NaF-BeF, x\x\\\\\ N (57-43) \ \. - LiF-BeF, \\\\\\\\ - (64-36) \ (x10 11 - 5 - ORNL~L.i-Dwg. 56196 o Tnelgssified emperature, C 800 750 700 650 600 550 500 { | | K i | N I i I { ¥ I 1 Ets\ ‘\\\\\\\\\ NaF-ZrF, -UF, NN (50-46-4) L X X ™~ Proportion in mole % «5 10, Fig, 0 10.5 11.0 1 \ N 1.5 12.0 1 Reciprocal Temperature, (°K)-! 1. Molten S8alt Mixtures AN 2.5 13. Xenon Solubility Constants for Various of the pump configuration is presented as Fig. 2. Use of Eq. 2 and Eq. 3 implies the assumptions that (a) Henry's law holds (equilibrium is maintained between the dissolved gas, the gases entering the pump bowl, and the graphite- salt interface); also that (b) diffusion rates across films and through the salt are negligible as compared to the rates of absorption by graphite and removal at the pump. Hypothetical Reactor Conditions The following reactor conditions and related para- metric values were utilized to carry out the poison fraction computations. Xe-~135 decay constant, AXe’ = 2,11 x 10“5 sec™! . Xe-135 destruction constant, ¢_0ge, = 7.4 x 107° sec™ . Average reactor temperature, T, = 936°9K. Gas constant, R, = 82.05 cm®-atm/mole-°K. Xe solubility constant, Ky =3 % 107% moles Xe/cm® salt-atm. Total salt volume, Vi, = 66.5 ft3= 1.88 x 10% cm®. Le’ 20 ft° = 5,66 x 10°cm3. Salt circulation rate (reactor pump rate), Qp, = 2.67 ft?/sec = 7.56 x 10¢cm® /sec. (0.04)(7.56 x 10%) 3.02 x 10° cm3/sec. Xenon concentration in salt entering bowl = np/Vy; at exit = 0. Total salt volume in the core, V Salt circulation rate through pump bowl, st i When these values are combined with Eq. 2a and Eq. 3, one obtains /N 5.29-10~% + 4.26°10 2<§E> PF (%) = G. 1.88-10-% + 0.174r + (fin . (2b) The by=-pass or recycle rate, 0,04 OQp, has been replaced by (in Eq. 2b) to show the effect of stripping in subse- quent computations. -7 - ORNL-LR-Dwg. S6197 Unclassified Drive Helium + KRéenon Helium Liguid Level o Ol Recycle “'fi\ A L eI e . - S (:::::jmwt::;;:ZD galt Bowl Out Impellier Upper Shell Salt In Fig. 2 Schematic Diagram of Primary Circulating Pump The only factor remaining to be discussed is n /co, which introduces the contributions of the rate of xenon diffusion into the pores of the graphite-moderator blocks. P@rtinentlgraphite dimensions, as presently envisioned for the MSRE, are tabulated below: total graphite volume - 77 ft?, total number of blocks - 565, exposed area per block - 545 in.?, 3.08-10° in.2? ~ 2¢10° cm?. and total exposed area A cross-sectional sketch of the blocks may be found on Fig. 3. Xenon Diffusion in Graphite Permeability and Diffusion Coefficients It should be clear, at this point, that low permeability, high density graphites are most applicable for advanced molten salt reactors. This statement is made in view of the problems associated with graphites as outlined in the Introduction. The discussion here will center on graphites with ?ermeability coefficients ranging from 1°10~° to 1107 cm?/sec. Gaseous diffusion rates within such materials are governed by wall collisions - not by intermolecular collisions. The xenon rates should not be influenced by the presence of other gases, (e.g., helium) in the same passages. When these conditions exist, each gas possesses its own dif- fusion coefficient, D, which is closely approximated by the permeability coefficient, K. The definitions of the coefficients may be obtained from the steady-state equations: fif RT = KXe and nD RT = DXe where fif is the forced flow rate, Pye 1s partial pressure, and L is the length of graphite. Essentially, the above argument implies that the gas does not differentiate between AP, (3) = i AP (4) - 9 - ORNL~LR-Dwg. 56198 Unclassified 1 ! .f’ ‘\ r’ h i i i ) | T e T T T T T ~ | m; / ZHR uZ”R ‘ !mm___'m___‘ s T \ j\ // N tY < 2 ] Fig., 3 Tentative Cross-~Section of MSRE Moderator Blocks - 10 - P and Py, in small passa%es. An equation applicable to all porous media 1is given by 4,15 4 3 where B, and K, are_characteristics of the medium, p is the gas viscosity, and Vv is the mean thermal velocity or _ /8RT\z v =) (6) M Py is the mean pressure of the flowing gas. When Bo is large, viscous flow controls. K=B, m4+ 2KV, (5) L Also, 1.5 D -p_ Yo (EW\ : (7) He-Xe °p \T,/ When B, — 0, Knudsen flow prevails. Then, D, ~ =2k ¥ (8) xe “ Ke 3KV . By Eq. 6 and Eq. 8, o T = He RN N The pf%nts under discussion are reflected in the following data: D, Apparent Diffusion K, Permeability Type Graphite Coefficient, cm2/sec Coefficient, cm?/sec Helium Argon Helium Argon AGOT (National 7.2 x 10™% 2.3 x 10~ 1.6 x 10° 1.2 x 10° Carbon Company) CEY Coated Pipe 1.3 x 10~ 0.4 x 10-° 7.6 x 105 2.6 x 10~° (National Carbon Company) * Data referred to 25°9C and 1 atm. It may be noted that the K/D ratio for the permeable graphite is 400; whereas that for the low permeability graphite is 6. This tends to verify the approximation indicated at Eq. 8. For materials with a K lower than that of CEY graphite, K/D should approach unjty. Another point of interest involves the ratio (My/Myx.)z = 3.16. Both K and D for CEY graphite appear to follow this relationship (Eq. 9). DxXe at 936°K is estimated to be 3.86-10"%cm?/sec, zs based on the Dj cited and Eg. 9. Porosity I1f one considers two graphites with equal permeability coefficients and unequal porosities, it is apparent that the specimen with the highest porosity value will contain the largest amount of gas at equilibrium saturation and during steady flow. Low porosity graphites have a low absorption capacity with respect to gaseous fission products. Thus, a discussion of porosity is pertinent. Two definitions of porosity are often employed in dis- cussions of gaseous flow through graphites. One is the total porosity, which is based on a comparison of the measured density and a theoretical density (2.26 gm/cc). The other is the effective porosity or open porosity as measured by helium cbsorption. The total value is greater than the ef- fective value, which indicates the presence of completely closed voids. The effective value is of primary importance regarding the Xe-135 problem, Another point of interest involves the relationship be- tween the porosity and permeability of graphites. From the standpoint of graphite fabrication, porosity reduction is not a necessary condition for permeability reduction; how- ever, the former is a sufficient condition for the iatter. It is possible to partially plug the channels within a graph- ite without markedly decreasing the porosity; on the other hand, a treatment which reduces the porosity of a graphite will reduce the permeability coefficient. One may generalize thus: graphites having low porosity values also have low permea- bility coefficients. The degree to which this generalization hoids is illustrated by nominal permeability-porosity values, which are tabulated below. - 12 - Helium Effective Permeability Graphite Vendor Grade or Type Porosity, € Coefficient, K Notes (%) (em? /sec) National Carbon AGOT 22 2 X 100 a Speer Carbon Moderator No. 1 17 7 X 10'1 a Unknown Experimental 17 3 x 1074 b National Carbon CEY (coated pipe) 11 5 x 107 a National Carbon CEY 5 4 x 107° c Hawker Siddeley HS-143-9 1 4 x 1077 c Raytheon Pyrolytic 0.02 3 x 107° c a. ORNL Data™' b. Data from HutcheanlS ¢. General Atomic Datal8 From a2 standpoint of product improvement, the data suggest that treatments to reduce permeability would be far more successful than efforts to reduce porosity. Pore Diffusion Equation When consideration is given to a gas-cooled reactor which utilizes coated particles or pyrolytic-graphite coated fuel elements, the primary problem involves fission product release and resultant coolant stream contamination. The rate controlling step (slowest step) of release is, to a large degree, dependent on surface and lattice diffusion mechanisms, as the fissioning process occurs in the solid state within a ceramic shell or matrix. This philosophy is reversed when consideration is given to a moiten salt reactor. In this case, the fission process takes place in the liquid and one is concerned with the fastest mode of xanon absorption as a gas - not as a nuclide recoiled into a lattice. Lattice and surface diffusion of xenon are of secondary importance in molten-salt reactors._ The equation most applicable is the pore diffusion equation, 2?2 2 N 8C Dye V' C = € (¢ 05, + KXQ)C + €5 - (10) The symbol C, mole/cc, represents free gas concentration - in this case Xe-~135; t, sec, represents time. All other symbols have been defined. The porosity term, €, appears, since xXenon can accumulate or deplete (also burn-out or decay) only within the pores of the graphite. It may be recalled that Dy, 1s re- ferred to the external graphite geometry and to steady-state flow which do not depend on porosity. Transient Solutions.-- Having written Eqg. 10, it is con- venient to touch on methods of employing this relationship for the determination of the ¢ and X (and D) of low permeability graphites. The destruction term becomes zero, since noble gases other than Xe-135 are employed in the experiments. Eq. 10 takes the form: 2 :xf = ¢ %% n (10b) The solution of Eqg. 10b, P(x,t), which involves K and €, is used to obtain (8P/8X)yx fixeq; this is multiplied by -D-A and in- tegrated with respect to time. The P(t) thus obtained is uti- iized to correlate pressure build-up data for specimens of known geometry. When P(t) varies with time, the build-up is in- fluenced by X and e; when AP(t) /At is constant, P(t) depends on K alone. One obtains K through the steady-state data -~ then employs this value and the transient data to obtain e.18,22 1p many cases, the transient period is brief due to the material and specimen geometry employed; thus ¢ must be measured via gas absorption methods or estimated via the gross density measurements. - 14 - Steady~State Solutions.-- The form of Eq. 10 applicable to the poison fraction expression (Eq. 2b) is Dy, V% (C) = € (§ 09, + Axe)C . (10¢) A rigorous solution for the graphite blocks (see Fig. 3) would be cumbersome in that two variables related to geometry would be present. In lieu of the rigorous solution, there are two solutions of Eq. 10c (representing simpler geometries) that yield convenient rate expressions. These equations should closely approximate the rigorous equation within certain ranges of D and ¢. For very low values of D and ¢, the solution corresponding to a semi-infinite geometry is applicable, i.e., C =D_e , (1l1ia) which leads to the rate expression: fiD/Co = fiDXel , (12a) where 1 A= [(E)(qfico‘xe + Ay )/ (D)]2 cm™ , and X = penetration distance, cm. Cylindrical geometry is applicable for nearly all values of D and € since the back-pressure of xenon in the center of the graphite blocks is taken into account. The corresponding equations are: 1, (Ar) and I, (Ar) Plots corresponding to Eq. 11 and Eq. 12 are shown on Fig. 4a and Fig. 4b, respectively. The curves indicate that the concentra- tion profiles and rates for the two geometries merge as values of D decrease. Based on the profiles at low values of D (Fig. 4a) - 15 - ORNL~LR-Dwg. 56199 Unclassified | Cylindrical Sclution _— Legend: -~ —— Semi~-infinite Soluticn e = 10.52% 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Penetration Distance, ¢cm Fig. 4a. Computed Concentration Proiiles for Xe-135 in Various Graphites with MSRE Moderator Geometry fiXe cm 20 T l —" " sec " Co " Legend: ‘//,/” —~—— Cylindrical P A/”/”’/’ 15 b L L = —— Seml—lnflnlggf’ e — ~ ~ 7~ 10 < ] ’//b//ICondiiions / e = 10.52% . 5 / DA = 3.16 x 10"3])":’f cn/sec // A= 2x 106 cm® / t O | - -6 0 2 4 6 8 10(x1077) Xenon Diffusion Coefficient cm®/sec Fig. 4b. Steady State Diffusion Rates - 16 - it was concluded that most of the xenon is near the surface in promising cases; thus the external area of the cylinders was taken as the external area of the blocks (2 x 10%cm?). The equivalent cylinder radius was taken as 3,603 cm. Geometry ef- fects with respect to poison fraction computations are pursued in the section to follow. RESULTS AND DISCUSSION OF XENON POISON FRACTION COMPUTATIONS Equivalent Graphite Geometry The poison fraction was computed utilizing both diffusion rate expressions (Eq. 12a and Eq. 12b) under assumed recycle values of 4 and 100%. The curves arising from the cylindrical case are shown as solid lines on Fig. 5; those arising from the semi~infinite case are shown as dotted lines on Fig. 5. Although the curves are plotted with DA as the independent variable, it was necessary to specify a fixed value of porosity to define the cylindrical values. This was required since np/ce is proportional to the product of D-A and the ratio of modified Bessel functions; D*A is proportional to (De)z. The arguments of the Bessel functions are proportional to (e/D)=. A convenient ¢hoice for ¢ was 10,52%, yhich fixed DA at 3.16°1072.(D)> and A as 3,16-10"3-(D)~2, The curves of Fig. 5 show that the semi-infinite solution is adequate for all values of R~r or x if DA < approximately 1 x 10-5 cm/sec or D is less than 1 x 10~®> cm2/sec. The curves also show the effects of the back pressure at high values of DA which are introduced by the cylindrical solution. Both curves for the semi-infinite case approach the maximum poison fraction; whereas, the curves derived from the cylindrical case approach a constant value arising from a saturation effect which depends only on the relative rate of Xe-135 production and removal at the pump. Percent Xenon Poison-~Fraction, - 17 - ORNL~LR-Dwg. 55200 Unclassified Legend: ——— Cylindrical Solution — —— Semi~infinite Solution e = 10.52% . DA = (D x 10™°)2, cm/sec i r = { PR S M#_’,"‘ " // ////#/ % ~ * ~ T = 4% // 7~ Y // r = 100% / / / {/ / /‘f’/ /’/ / Vv / ¢ // )¢/ A / // ‘ | 6 1 2 4 6 1 2 4 6 1 2 4 (x10-%) (x1075) (x10~%) DA, cm/sec Fig. 5. Effect of Geometry on Computed Poison Fractions Effect of Porosity As pointed out previously, there is a slight trend be- tween porosity and permeability, in that large decreases in permeability (or diffusibility) are often accompanied by slight decreaseg in porosity. The diffusion rate is propor- tional to (D:e)z at low values of D. Within this region, which is the region of interest, the effects of varying e¢ are the same as those of varying D. Curves showing the ef- fects of varying ¢ are presented on Fig. 6. Improved Graphites Versus Removal Rates A family of poison fraction curves as a function of re- cycle rate, r, and DA (actually Dz since ¢ is fixed) is shown on Fig. 7. The estimated DA for CEY* graphite js [ (9.51:10-5 sec-1)(6.9°107%)(3.9°10"% cm2/sec)]z or 5:10-% cm/sec, and that for AGOT* graphite is 6°107% cm/sec. These grades represent the best, and perhaps the worst, grades of non-pyrolytic graphites which are commercially available in large quantities at the present time. Within the region of 6°10-*% cm/sec5:10"% cm?/sec the curves of Fig. 7. indicate that increasing the recycle rate (i.e., the stripping or re- moval rate) is the most effective means of reducing the poison fraction. For example, at DA of 1:10"°® cm/sec increasing the recycle rate from 4 to 10 percent will reduce the poison frac- tion from 4.1% to 3.85%. To achieve the same reduction while holding the rate at 4%, one must obtain a graphite with a DX of 3.5-10~¢ cm/sec. This corresponds to a reduction in D from 1-10-° cm2/sec to 1.2°10-% cm2/sec. In other words, doubling the recycle rate is equivalent to decreasing the permeability of the graphite by a factor of 7. With graphites similar to AGOT, poison fraction reduction can be achieved only through increased recycle rates, * CEY and AGOT are National Carbon Company products. Percent Xenon Poison Fraction, ORNL~LR-Dwz. 56201 Unclassified Condition: 6 : D=2 x 10 cmz/sec \ | \ \ Fig. 6. 6 10 20 €, Porosity, % Effect of Porosity on Xenon Poison Fraction Percent Xenon Poison Fraction, - 20 - ORNL-~LR-Dwg. 56202 Unclassified Conditions: e = 10.52% L DA = (D x 10"5)2 cm/sec o ! ! | “"é Kge = 1 T 107 cEy AGOT 5 ; Y y 4 --—"""-—_'*w r = 0070 M—MM:WW r = 2// /// i //’/j.=“§// 4///////’//// . ///f 4 = 10 /// 3 r L % // u : r = 20 // / - //f r =‘%O ////f/ 2 / / / / A // / / / / / / //// r = 100% e A ’ | 1 / A / / < VLY r///////////////// ,/’/// - 1 //M”'/ o —F—] 1 2 4 6 1 2 4 6 1 2 4 6 1 (x10-7) (x10-%) (x10-5) x10-%) DA, cm/sec Fig. 7. Xenon Poison Fraction at Various Values of Recycle Rates and Diffusion Coefficients - 21 - In view of the relative importance of Xe-135 removal at the pump, a series of curves were prepared (see Fig. 8), which show the effect of increasing the circulation rate while holding the recycle rate constant. An increase in the circulation rate has the same effect as increasing the recycle rate. This would also be true for any additional stripping devices in the reactor. The curves of Fig. 7 clearly demonstrate that decreasing DA from 6-107* cm/sec (AGOT graphite) to 5-107% cm/sec (CEY graphite) offers no advantages with respect to Xe-135 poisoning particularly when the recycle rate (r) is 4%. Proceeding further down the 4% curve, one finds that the Xe poison fraction is 3.4% (max. 4.15%) for a graphite with a Kyge = 1:107°% cm?/sec (DA = 1.4°10"%). An increase in r from 4 to 8% (at this D) yields a poison fraction of 2.8%. Addition of a separate stripping section would be required at this point, as r = 8% represents %he minimum pump efficiency (92%) which can be tolerated.z When one considers the combined effects of a Kge = 1°107° cm?/sec graphite and the presence of a stripping section comparable to a 50% recycle rate, it is apparent that the poison fraction would be 1%. Adequate stripping coupled with the utilization of low permeability graphites affords an effective combination for reducing Xe-135 poisoning. On the other hand, it is evident that the Xe-135 poison problem cannot be solved through graphite improvement alone. Another aspect of Xe~135 poisoning, which is not related to neutron economy, involves intermittent operation of the reactor.%44 A shut-down and fuel-drainage operation would allow the graphite to de-saturate with respect to Xe-135. Resumption of operation with the same fuel could result in a special control problem (before the xenon content of the graphite reached normal levels). This problem arises since fractional removal of dissolved UF, is difficult to accomplish. Thus, low Xe~135 concentrations in the reactor prior to shutdown would be desirable. This might suggest further justification for ade- quate stripping and permeability reduction. Diffusion in Liquid-Graphite Systems Comparison of experiments, wherein helium and argon were allowed to interdiffuse through a dry CEY graphite specimen - then interdiffuse with the specimen surrounded by a liquid phase Xenon Poison Fraction, Percent Wh - 22 - ORNL-LR-Dwg. 56203 Unclassified { Conditions: e = 10.52% r = 10% N N 2 X lg:imifi/sec D = 2 X\lo"? \\ 5 10 15 20 25 30 Pump Rate, ft’/sec Fig. 8. Effect of Pump Rate on Xenon Poison Fraction - 23 - (water on the argon side) reveal that the rates are decreased when the liquid phase 1is present. This was to be expected as the specimen face was water-wet and 1% of the effective porosity was occupied by water, although the water diffusion rate was below the limit of detection. The argon and helium data, which are referred to two atmospheres total pressure (on each side of the specimen) and ZSOC, are shown below: Type D, Apparent Diffusion Coefficients cm’/sec Experiment Helium Argon (x 10”6) (x 10'5) dry 10.5 3.4 with water 2.2 1.9 Based on the argon data (which are analogous to xenon and krypton), the rate of xenon absorption with liqujd at zero flow rate would be decreased by a factor of (1.9/3.4)Z as compared to the dry case. Films induced by liquid flow and resistance resulting from higher liquid saturations of the porous material would decrease the value of the ratio shown. - 24 - CONCLUSIONS Experimental data have verified that the diffusion coeffi- cient and the permeability coefficient of a given gas- graphite system approach equality when the coefficients of the systems under consideration are very low, i.e., approx- imately 1-1077 cm?/sec. The effective porosity, as well as the diffusion coefficient for a given graphite, influences the steady-state rate at which xenon is absorbed by graphite under conditions of burn-out. Low porosity and transport coefficients (diffu- sion and permeability) lead to low Xe-135 absorption rates. Low porosity graphites generally possess low transport coef- ficients; however, low porosity values are not necessary indicia for low values of the transport coefficients. For an approximate geometry for diffusion equations in- volving the graphite moderator, one may utilize the semi- infinite case when Dgxe<1:107° cm?/sec., At higher D values, the cylindrical case appears to be most suitable. O0f all the Xe-~135 control variables studied, the rate at which xenon is removed from the reactor appears to be of primary importance. Adequate stripping coupled with graphite permeability {(and porosity) reduction affords an effective combination for de- creasing the xenon poison fraction. 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