Recovery of Tritium in Room Air by Precious Metal Catalyst with Hydrophilic Substrate

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1 Journal of NUCLEAR SCIENCE and TECHNOLOGY, 25[4], pp. 383~394 (April 1988). 383 Recovery of Tritium in Room Air by Precious Metal Catalyst with Hydrophilic Substrate Kenzo MUNAKATA, Masabumi NISHIKAWA, Toshiharu TAKEISHI, Nobuo MITSUISHI and Mikio ENOEDAt Department of Nuclear Engineering, Faculty of Engineering, Kyushu University* Received June 19, 1987 Revised January 5, 1988 The catalytic oxidation and adsorption method is considered to be a potential and reliable measure to recover tritium released into room air in fusion power plants. The activity of )recious metal catalysts that are expected to be useful in recovery of tritium released into the -oom air is affected by moisture in the air, and tritium in the gas phase can be captured into :he catalyst substrate not only through adsorption but also through isotopic exchange reaction. The simulation study on tritium behavior in the catalyst bed was carried out quantitatively on :he basis of experimental results. It is confirmed by the simulation study that the installation A the preadsorption bed decreases water vapor before the gas is passed through the precious metal catalyst bed; this is an effective countermeasure against the deterioration of the catalytic )xidizing performance caused by moisture. It is also shown that large amounts of tritium :an be captured by the catalyst itself when the preadsorption bed is introduced. KEYWORDS: catalytic oxidation, exchange reaction, hydrophilic substrate, tritium, oxidizing performance, preadsorption bed, precious metal catalyst, tritium recovery, thermonuclear devices I. INTRODUCTION A system which recovers tritium released into the room air is required in a fusion power plant in order to prevent the release of tritium into the environment. The catalytic oxidation and adsorption method is considered to be the most potential and reliable measure to recover tritium released into the room air. As for catalysts, precious metal catalysts have been recommended because they can oxidize tritium efficiently at ambient temperature(1)~(3). However, it is found in the previous paper(4) that the oxidizing performance of precious metal catalyst is hindered by the water adsorbed on the catalyst substrate. A quantitative relationship between oxidation rate and amount of adsorbed water is obtained in this study. Behaviors of tritium in the precious metal catalyst bed is also studied by simulation considering oxidation of gaseous tritium, adsorption of tritiated water, isotopic exchange reaction between gaseous tritium and adsorbed or structural water of catalyst substrate, and isotopic exchange reaction between tritiated water in gas stream and adsorbed or structural water of catalyst. Hitherto, tritium capturing of catalyst through isotopic exchange reaction between tritiated water in gas stream and water in catalyst (adsorbed water and structural water of catalyst) has not been taken into account. The rate of exchange reaction and exchangeable capacity are reported by present authors(5)(6). An isotopic exchange reaction between gaseous tritium and water in catalyst is also considered to occur(7). Such a reaction is however negligible in the high oxygen level condition as reported elsewhere(8). * Hakozaki, Higashi-ku, Fukuoka 812. Present address: Japan Atomic Energy t Research Institute, Tokai-mura, Ibaraki-ken

2 384 J. Nucl. Sci, Technol., II. THEORY In the steady state condition, over all mass transfer coefficient of oxidation KF,ox can be expressed by the following equation : KF,ox=(Q/aVcat)exp(Cin/Cout), (1) where KF,ox: Over all mass transfer coefficient of oxidation (m/h) Q: Volumetric gas velocity (m3/h) Vcat: Volume of catalyst bed (m3) Cin: Concentration of hydrogen isotope in inlet gas (mol/m3) Cout : Concentration of hydrogen isotope in outlet gas (mol/md) a : Specific surface area of bed (m-1). The mass transfer of oxidation is considered to be dependent on the three major rate limiting steps. So that KF,ox is given by 1/KF,ox=1/kr+1/bks+1/kg, (2) where kr: Mass transfer coefficient of chemical reaction on precious metal (m/h) ks: Mass transfer coefficient due bto diffusional transfer of reactant in catalyst substrate (m/h) kg: Mass transfer coefficient due to transfer of reactant from bulk gas flow to surface of catalysts (m/h). The bks is larger than other mass transfer coefficients as stated previously(3), so that it can be negligible in estimating Kf,ox ; kg can be estimated by Carberry's equation(8) ; kr0 which is the kr in the dry condition was experimentally obtained and it was previously reported(3). kr0=8.82x109exp(-10,700/rt), (3) kr0,ht: kr0,h2=1:4, (4) where kr0,h2: kr in dry condition for H2 (m/h) kr0,ht: kr in dry condition for HT (m/h) T: Absolute temperature (K) R: Gas constant (cal/mol,k). The kr is affected by the adsorbed water on the catalyst substrate as previously reported"). The adsorbed water on the catalyst substrate is considered to hinder the reaction of hydrogen isotopes and oxygen on the precious metal, then kr could be expressed as follows(10) : kr=f(t,qad), (5) where qad: Amount of adsorbed water on catalyst substrate (mol/kg). As for the adsorption characteristics of water on the catalyst substrate as alumina, the modified Dubinin-Astakov model has been proposed as follows(7) : (6) where qad.oi: Amount of adsorbed water on substrate for i-th adsorption stage when A is O (mol/kg) Ei: Specific energy of adsorption for each adsorption stage (cal/mol) mi: Constant value for each adsorption stage A: Adsorption potential (cal/mol). The adsorption potential A is given by A=RTln(Ps/P), (7) where Ps: Saturated vapor pressure of water at temperature T (mmhg) P: Vapor pressure of water (mmhg). The catalyst substrate has adsorbed water and structural water which would present as the hydroxyle group as reported by Peri(11). If mixing of adsorbed water and structure water is assumed to proceed rapidly, the rate of exchange reaction between hydrogen isotopes of water vapor in the gas stream and hydrogen isotopes in the catalyst is given by the expression reported elsewherem where rex: Rate of exchange reaction (mol/m3,h) qnet,h2o Net concentration of water in catalyst (mol/kg) net,hto : Net concentration q of tritiated water in catalyst (mol/kg) CH2O : Water concentration in gas (8)(9) (10) phase (mol/m3) CHTO : Tritiated water concentration in gas phase (mol/m3) qad,h2o Concentration of adsorbed water in catalyst substrate (mol/kg) 62

3 Vol.25, No.4 (Apr. 1988) 385 qad,hto Concentration of tritiated water adsorbed in catalyst substrate (mol/kg) cat,h2o Concentration of structure water in catalyst substrate (mol/kg) qcat,hto Concentration of tritiated structure water in catalyst substrate (mol/kg) KF,ex: Mass transfer coefficient of exchange reaction (m/h). The mass transfer coefficient of exchange reaction is given by the present authors"' as KF,ex=118.8exp(-700/RT). (11) The exchange reaction between gaseous tritium and water in the catalyst should be also taken into account. It is however proved by our experiment that such an exchange reaction can be negligible in the high oxygen level condition as air(9). The amount of exchangeable structural water which was obtained by our experiment on Pt-alumina is mol/kg (cat)(5). Estimations are carried out by solving the following equations numerically : u(pch2/pz)+e(pch2/pt)+k-f,oxach2=0, (12) u(pcht/pz)+e(pcht/pt)+kf,oxacht=0, (13) u(pch2o/pz)+g(pqnet,h2o/pt) +e(pch2o/pt)-kf,oxach2=-0, (14) u(pchto/pz)+g(pqnet,hto/pt) (pchto/pt)-kf,oxacht=0, +e (15) et,h2o/pt)- KF,ada(CH2O+CHTO-C*)X2 g(pqn + KF,exaX1=0, (pqnet,hto/pt)-kf,ada(ch2o+chto-c*)x3 (16) g -KF,exaX1=0, (17) u(ptgas/pz)+e(ptgas/pt) where +4hw(Tgas- Troom)/(DCp,gas) hpa(tcat-tg)/cp +,gas=0, (18) Tcat/pt)-(CH2+CHT)KF,oxaH/Cp,cat g(p hpa(tcat-tgas)/cp,cat=0 + (19) X1=CHTO-(CH2O+CHTO)(qnet,HTO) /(qnet,h2o+qnet,hto) (20) (CH2O+CHTO -C*>=0) X2=CH2O/(CH2O+CHTO) (CH2O+CHTO-C*<0) X2=qnet,H2O/(qnet,H2O+qnat,HTO) (21) (CH20+ CHTO-C*>=0) X3=CHTO/(CH2O+CHTO), (CH2O+CHTO-C*<0) X3=qnet,HTO/(qnet,H2O+qnet,HTO) (22) and where z: Length in axial direction (m) t: Time (h) u: Superficial gas velocity (m/h) e : Void fraction of bed CH2: Hydrogen concentration in gas phase (mol/m3) CHT: Tritium concentration in gas phase (mol/m3) g : Packed density of bed (kg/m3) KF.ad: Mass transfer coefficient of adsorption (m/h) C* : Equilibrium concentration of water vapor in gas phase with amount of adsorbed water (mol/m3) Tgas: Gas temperature (K) Teat : Temperature of catalyst (K) Troom: Room temperature (K) hw: Heat transfer coefficient of outside wall of bed (cal/m2,h,k) D: Diameter of bed (m) Cp.gas: Heat capacity of gas (cal/kg,k) H: Reaction heat of oxidative reaction (cal/mol) hp: Heat transfer coefficient between gas and catalyst particle (cal/m2,h,k) Cp,cat: Heat capacity of catalyst (cal/kg,k). The one-dimensional model is used, so that the concentration distribution and temperature distribution are only considered in axial direction of catalyst bed, assuming the plug flow in the bed. The hw and hp can be estimated by empirical equations(12)(13). As to the mass transfer coefficient of water adsorption, the value reported by Koto et al. for alumina(14) is used in the simulation study. And the isotope effect in water adsorption is assumed to be negligible. III. EXPERIMENTAL The schematic diagram of apparatus is shown in Fig. 1 and experimental conditions are listed in Table 1. The temperature of bed is controlled with a constant temperature bath. The concentration of hydrogen isotopes is 63

4 386 J. Nucl. Sci. Technol., judging from the experimental data, so that these catalysts are mainly discussed in this study. Fig. 1 Flow sheet of experimental apparatus Table 1 Experimental condition IV. RESULTS AND DISCUSSION Figure 2 shows the relationship between vapor pressure and kr/kr0 on Pt-alumina in the steady state condition at various catalyst temperature, where kr0 means kr in the dry gas condition. It can be seen from this figure that kr is smaller in the case of higher water vapor pressure, and relationships between vapor pressure and kr/kr0 are different for different catalyst temperature. The reaction on the precious metal is considered to be hindered by the water adsorbed on the catalyst substrate as mentioned above. The amount of adsorbed water can be given as a function of adsorption potential A according to Dubbinin-Astakov model, so that there would be a proper correlation between A and kr/kr0. The relationship between A and kr/kr0 shown in Fig. 3(a) suggests an adequate correlation. The adsorption characteristics of Pt-alumina is given as the following equation based on the modified Dubinin-Astakov model, which was reported elsewhere(15). qad=0.994exp(-a/3,200)+1.95 exp(-a/667) +3.56exp(-A/154) (mol/kg). (23) In the same condition, the amount of adsorbed water on the catalyst is 1/3 of that on the alumina substrate without the precious metal particle(15). The relationship between kr and the amount of adsorbed water is given by determined with a gas chromatograph. The tritium level is traced with an ionization chamber. The mass transfer coefficients can be estimated by Eq. (1) or (2). Argon or N2 is used as the carrier gas. The catalyst is heated at 300dc for 2 h in the dry gas stream before measurements. The Pt-alumina, Pd-alumina, Pt- MS-5A and Pt-SDB are used in the experiment. Among such catalysts, Pt-alumina or Pt-MS-5A is considered to be recommendable for use as the catalyst of emergency clean-up system (q.e<1.2) (9ad>=1.2) kr/kr0=-0.39qad3+0.6qad2-0.85qad+1 kr/kr0,=exp(-2.76qad+1.27) (24) Figure 3(b) shows the relationship between A and kr/kr0 on two kinds of catalysts. The oxidizing performance of Pt-SDB which has a hydrohobic substrate is also deteriorated in the humid condition. The Pd-alumina has a similar tendency to Pt-alumina on the relationship between A and kr/kr0. 64

5 Vol.25, No.4 (Apr. 1988) 387 Fig. 2 Relationship between kr/kr0 and water vapor pressure Fig. 3(a), (b) Relationship between kr/kr0 and adsorption potential for Pt-alumina and various catalysts 65

6 388 J. Nucl. Sci. Technol., Figure 4(a) shows the change of tritium species level in the outlet gas of Pt-alumina bed when the N2 gas which includes HT of 6 mci/m3, H2 of 360 ppm and O2 of 25,000 ppm is passed through the catalyst bed. Though two chemical forms (gaseous tritium and tritiated water) are expected in the outlet gas of the catalyst bed, only tritiated water is detected in the outlet gas because almost all tritium is oxidized in the catalyst bed of which operating condition is shown in Fig. 4(a). It is seen from this figure that almost all oxidized tritium is captured in the catalyst bed in earlier time and that the tritium level in the outlet gas is increasing gradually because of increase of tritiated water ratio in the catalyst due to proceeding of adsorption and exchange reaction. The solid line in this figure shows the change of estimated tritium level in the outlet gas, which is calculated by using Eqs. (12)~ (22). The estimated curve agrees fairly well with the experimental result, considering temperature change of +-10dc from the set value in the case shown in this figure. This figure also shows that 7.7 mci of tritium is captured by about 1 g of Pt-alumina catalyst in the conditions of this experiment. Figure 4(b) shows the change of tritium level in the outlet gas when a N2, gas with H2O of 9,800 ppm and O2 of 15,000 ppm is passed through the catalyst bed after the experiment shown in Fig. 4(a) is performed. The total amount of recovered tritium estimated from the curve in Fig. 4(b) is 7.4 mci, so that Fig. 4(a) Change of tritium level in outlet gas of catalyst bed Fig. 4(b) Change of released tritium level from catalyst bed by humid gas 66

7 Vol.25, No.4 (Apr. 1988) 389 it is proved that the captured tritium in the catalyst bed is recovered by applying the exchange reaction using water, though drying with hot gas stream can release only adsorbed water as stated elsewhere(5). Figure 5 shows the tritiated water amount captured by the catalysts. Tcat,ad, Tcat,ex and T cat,total mean amount of tritium in water adsorbed on the catalyst substrate, amount of tritium captured by the catalyst substrate through exchange reaction and total amount of tritium that the catalyst captures, respectively. Measurements are carried out as follows. An inert gas which contains some amount of tritium, hydrogen and oxygen of the order of 104 ppm is passed through the catalyst bed until the tritium level in the outlet gas reaches the inlet level of tritium. Then the adsorbed tritiated water is recovered from the catalyst bed by passing a hot inert gas containing no water vapor. After the drying procedure, tritium captured into the structural water is extracted by passing an inert gas which contains some amount of water vapor or hydrogen. During both of procedures, the tritium level in the outlet gas is traced with an ionization chamber and the total amounts of recovered tritium in both procedures are estimated from the obtained curves. The experimentally obtained values and the estimated values from adsorption performance and amount of structural water presented in the previous paper(5) are compared. It is seen from this figure that there is a good agreement between the experimental value and the estimated value. Simulations of tritium behavior in the catalyst bed of the emergency clean-up system are carried out by a numerical calculation method. Conditions of estimation are listed in Table 2. An air that contains I-IT of 1 ppm, some amount of H2 and some amount of water vapor is assumed to pass the catalyst bed. Hydrogen is added in order to know the effect of enhancement on the oxidation rate by the reaction heat of hydrogen. As to the room air, it is assumed that the temperature is 20dc and the humidity is 70% (16,000 ppm). A condition in which the inlet water vapor is 50 ppm is based on an assumption that the room air is passed through a preadsorption bed to remove the water vapor before the air is passed through the catalyst bed. This preadsorption concept is proposed as the countermeasure against the deterioration of oxidizing performance of catalyst by adsorbed water(4). Table 2 Conditions of calculation Fig. 5 Amount of tritium captured as adsorbed water or structural water into catalyst A change of temperature distribution curve in the catalyst bed at various time is shown in Fig. 6 when the air which contains H2 of 5,000 ppm and H2O of 16,000 ppm is assumed to pass the catalyst bed. The temperature distribution in the catalyst bed changes largely in about 20 min. And after that, the change of temperature distribution is small except at the inlet side of catalyst bed. The change of temperature distribution in the inlet side is responsible for increase of adsorbed water which deteriorates the oxidizing performance of catalyst. The broken line shows the temperature distribution after 300min in the case 67

8 390 J. Nucl. Sci. Technol., where the inlet air contains H2 of 1,000 ppm. When the inlet H2 level is less than 100 ppm, the catalyst bed temperature is almost same as the inlet gas temperature. Accordingly, in order to raise the catalyst bed temperature to give a proper oxidation rate of tritium in the room air containing water vapor, hydrogen of several thousands ppm should be added in the inlet air. Then more than 20,000 ppm water vapor with tritiated water that must be taken away from the gas stream is produced. of catalytic oxidizing performance and HT cannot be oxidized efficiently as shown later. In the case of 5,000 ppm H2 swamping, the part where less water is adsorbed is remained because of bed temperature rising by the reaction heat. The amount of adsorbed water is only 1/100~1/1,000 and deterioration of oxidizing rate does not occur in the case where inlet water level is so low as 50 ppm. Fig. 6 Change of temperature distribution in catalyst bed Figures 7 and 8 show the change of distribution curve of water amount adsorbed on the catalyst substrate. It is seen from Fig. 7 that the amount of adsorbed water increases rapidly in the case where the inlet water vapor level is high and the inlet hydrogen level is less than 1,000 ppm. This causes the deterioration Fig. 7 Change of amount of adsorbed water in catalyst bed Fig. 8 Change of water amount in catalyst bed when water vapor in inlet gas is small Figure 9 shows the change of a decontamination factor of HT at oxidation in various cases, where the decontamination factor at oxidation is given by the expression as, K=CHT,in/CHT,out, (25) where CHT,in : HT concentration in inlet gas CUT,out HT concentration in outlet gas. It is seen from curves (1), (2), (5) and (7) that K decreases rapidly when an air which contains water vapor whose level corresponds to the relative humidity of 70% at ambient temperature is passed through the catalyst bed. The K is however kept as the large value because of temperature rising by the reaction heat of hydrogen as shown in curve (3), in the case where the air contains H2 of 5,000 ppm. In the case where the inlet H2O level is as low as 50 ppm, no change of K is seen as shown in the curves (4), (6) and (8), because the amount of adsorbed water on the catalyst substrate is small. 68

9 Vol.25, No.4 (Apr. 1988) 391 Fig. 9 Change of decontamination factor at oxidation of HT The amount of tritiated water captured in the catalyst bed is compared in Fig. 10, where the broken line corresponds to the total HT amount introduced to the catalyst bed. Almost all tritium introduced as HT can be captured in the catalyst bed by adsorption and isotopic exchange reaction when the inlet water vapor level is lowered as shown in curve (1), though the ratio of tritium captured in the catalyst bed is largely decreased as shown in curves (2) and (3) when the inlet water level is high or when the inlet H2 level is high. This is because a large amount of diluted tritiated water is made. Fig. 10 Amount of captured tritiated water in catalyst bed Figure 11(a)~(d) shows the change of tritium species level in the outlet air of catalyst bed. As for tritium species, HTO and HT are contained in the outlet gas. The broken line shows the inlet HT level. The difference between concentration of tritium in the inlet gas and that in the outlet gas corresponds to tritium captured in the catalyst bed. It is seen from Fig. 11(a), (b) that outlet HT level increases rapidly in the case where the inlet water vapor level is high (16,000 ppm) and the inlet H2 is not so large (100 or 1,000 ppm). It is however seen from Fig. 11(c) that almost all HT can be oxidized in the case where the inlet H2 level is 5,000 ppm, in spite of high water vapor level in the inlet air. This is responsible for rising of catalyst temperature by the reaction heat of hydrogen and oxygen. In these cases as shown in Fig. 11(a)~(c), total tritium level in the outlet gas exceeds the inlet tritium level after several tens of minutes. This is due to release of tritium which is captured through exchange reaction or adsorption in earlier time when oxidation rate of tritium is large. It is seen from Fig. 11(d) that almost all tritium can be oxidized and that almost all tritium oxidized can be captured in the catalyst bed in the case where a preadsorption bed is assumed to be installed to take away water vapor at the upper course 69

10 392 J. Nucl. Sci. Technol., Fig. 11(a)~(d) Change of tritium species level in outlet gas of the catalyst bed. The amount of tritium captured is obtained as the product of the specific activity of tritium in the gas stream by the total amount of adsorbed water and structural water. As stated in the previous paper(5), the amount of structural water is not affected by temperature or vapor pressure in the range used in this experiment. Therefore, the amount of tritium that can be captured in the catalyst bed is largely increased when the preadsorption bed concept is applied. Figure 12 shows the simulation results comparing the effect of catalyst bed volume by changing the bed length Z. It can be seen from this figure that the two times larger catalyst bed can capture almost all tritium which comes into the catalyst bed for about 500 h under the condition when preadsorption bed is installed. It is proved by results of parametric study that the installation of preadsorption bed is an effective measure to keep a good oxidizing 70

11 Vol.25, No.4 (Apr. 1988) 393 Fig. 12 Comparison of tritiated water concentration in outlet gas when catalyst bed volume is changed performance of catalyst, and it is also shown that tritium can be captured in the catalyst bed when a preadsorption bed is introduced. The preadsorption bed would act as the filter for the oil mist which gives hindrance effect on the catalyst. In the case where larger amounts of hydrogen than several thousands ppm is added, the good oxidizing performance of tritium can be maintained in spite of large amounts of water vapor in the process gas. In such a case, tritiated water contained in the outlet gas of the catalyst bed would be recovered by passing the gas through the adsorption bed after cooling. In the case where the inlet gas of catalyst bed contains H2O of 16,000 ppm, H2 of 5,000 ppm and HT of 1 ppm, the outlet gas of the catalyst bed contains H2O of 21,000 ppm and HTO of 1 ppm after saturation of tritium in the catalyst bed. If the adsorption bed with MS-5A is used at the 20dc, HTO which can be adsorbed on 1 g of MS-5A is only 1x10-5 g in spite of that the water adsorption capacity of MS-5A is estimated to be 0.2 g/g (adsorbent) in this condition(14), because the ratio of HTO concentration to H2O concentration in the gas stream is so low as 5x10-5. In the case where the preadsorption bed is assumed to be installed as shown in Fig. 11(d) and 12, the ratio of HT concentration to the total concentration of H2 and H2O in gas phase is 1 X 10-2 at the inlet of catalyst bed. If an air which contains HTO of 1 ppm and H2O of 100 ppm is passed through the Pt-alumina catalyst bed, 1 g of catalyst can capture HTO of 2.7x10-4g by the exchange reaction, even when the amount of HTO adsorbed on the catalyst is ignored. Comparison of these two cases implies that the catalyst having an alumina substrate can capture larger amounts of tritium than the adsorbent as MS-5A when the preadsorption bed is installed. The catalyst having an MS-5A substrate can also capture tritium as MS-5A can adsorb more water than alumina though it has less amount of structural water than Pt-alumina(5). In addition, it has been reported that KF,ex is larger than KF,ad(5)(14). Accordingly the adsorption bed may not be needed if the preadsorption bed is installed and proper amount of catalyst is adopted. V. CONCLUSION The oxidizing performance of tritium by the precious metal catalyst is deteriorated in the humid condition, and a correlation between the oxidation rate and the amount of adsorbed water on the catalyst substrate is proposed. It is confirmed by the simulation study that the installation of preadsorption bed to reduce the water vapor before the air comes into the catalyst bed is the effective countermeasure against the deterioration of catalytic oxidizing performance by the adsorbed water on the 71

12 394 J. Nucl. Sci. Technol., catalyst substrate. And it is also shown that almost all tritium can be captured as the structural water or adsorbed water in the catalyst bed when the preadsorption bed is introduced because high T/H ratio is obtained by removing most water vapor at the preadsorption bed. Hydrogen swamping of more 5,000 ppm is effective to keep the oxidation rate of tritium in the humid air though diluted tritiated water is made. REFERENCES (1) SHERWOOD, A. E.: CONF , 24th Conf. on Remote Systems Tech., Am. Nucl. Soc., Washington, DC, (2) BIXEL, J.C., KERSHNER, C. J.: Proc. 2nd Envir. Prot. Conf., WASH-1332, (1974). (3) NISHIKAWA, M., at al.: J. Nucl. Mater., 135, 1 (1983). (4) NISHIKAWA, M., et al.: J. Nucl. Sci. Technol., 22[11], 922 (1985). (5) NISHIKAWA, M., et al.: JAERI-M , (1987). (6) NISHIKAWA, M., at al.: Preprint 1987 Fall Mtg. of AESJ, Sapporo, K19, (1987). (7) ENOEDA, M., at al.: J. Nucl. Sci. Technol., 23[12], 1083 (1986). (8) NISHIKAWA, M., et al.: Preprint 1987 Annu. Mtg. of AESJ, Nagoya, K36, (1987). (9) CARBERRY, J. J.: AIChE J., 6, 460 (1960). (10) DUBININ, M. M.: "Adsorption and Desorption Phenomena", (1972), Academic Press, NY. (11) PERI, J.B. : J. Phys. Chem., 69, 211 (1968). (12) RANZ, W.E.: Chem. Eng. Prog., 116, 248 (1952). (13) MCADAMS, W. H. : Heat Transmission, 177, 172 (1954). (14) KOTO, K., ENOEDA, M., NISHIKAWA, M.: in preparation; partly reported by ENOEDA, M. in M. Eng. Thesis, Kyushu Univ., (1984). (15 ) NISHIKAWA, M., ENOEDA, M., KOTO, K.: Preprint 1983 Annu. Mtg. of AESJ, E54, (1983). 72