Operational Topic The results presented in this paper are from a 25-y mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.
Modeling of Transport Phenomena in Concrete Porous Media Ilija Plecas* Abstract: Two fundamental concerns must be addressed when attempting to isolate lowlevel waste in a disposal facility on land. The first concern is isolating the waste from water, or hydrologic isolation. The second is preventing movement of the radionuclides out of the disposal facility, or radionuclide migration. Particularly, we have investigated here the latter modified scenario. To assess the safety for disposal of radioactive wasteconcrete composition, the leakage of 60Co from a waste composite into a surrounding fluid has been studied. Leakage tests were carried out by the original method, developed at the Vincˇa Institute. Transport phenomena involved in the leaching of a radioactive material from a cement composite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source: an equation for diffusion coupled to a first-order equation, and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-y mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center. Health Phys. 106(Supplement 1):S30YS33; 2014 Key words: operational topics; waste disposal; waste management; waste, low-level
*Institute of Nuclear Sciences BVinca,[ University of Belgrade, P.O. BOX 522, 11001 Belgrade, Serbia. The author declares no conflicts of interest.
INTRODUCTION Cement and concrete are widely used in low-level waste management both as a means of solidifying waste and for containment of dry or liquid wastes. At present, there is also widespread interest in the use of near-surface concrete trench system for the disposal of radwaste materials. Typical concrete is a mixture of cement, sand, stone aggregate, and water in various proportions that together determine the structural properties and tightness of the poured material. Water content is one of the critical parameters and must be carefully controlled during purring and setting; to a large extent it will determine the porosity of the resulting material. Engineered barriers are features of the disposal system made or altered by humans during the construction, operation, and closure of a repository. Engineered barriers are intended to contribute to the overall performance of the disposal system by providing the level of containment required while the waste remains hazardous.
Ilija B. Ple(asˇ (19 June 1948, Belgrade) received the degree of B.Sc. Chemical Engineering Mr Sci and Ph.D. at the Faculty of Technology at the Belgrade University. He has been employed in the Radiation and Environmental Protection ˇ A’’ Institute of Nuclear Sciences since 1973 and constantly Laboratory in the ‘‘VINC engaged in research and design in the field of radioactive waste treatment, storing, and disposal, especially in the field of immobilization of radioactive waste by cement. Ilija B. Ple(asˇ has published more than 40 papers in International Journals and more than 100 papers on International Conferences and Symposia. Since 1992, Ilija B. Ple(asˇ has been Head of the Radiation and Environmental Protection Department in the ‘‘Vincˇa’’ Institute of Nuclear Sciences. Ilija B. Ple(asˇ has been ˇ A’’ Institute of Nuclear Science, Belgrade, Serbia (1999/ Acting director of ‘‘VINC 2001). Member of The Scientific Society of Serbia (2008Ypresent). His email is [email protected]
S30
In cases where the selected site or geological environment is not ideally suited for disposal, the repository can be heavily engineered so that, for meeting safety targets, reliance is placed primarily on the engineered barriers. Engineering trench systems provide three biological protection barriers: 1. Mortar for immobilizing the waste and filling the concrete containers (enable its penetration into all cavities of solid radioactive waste and thus fix it permanently; permit no leakage of radionuclidesV use of special cement or adsorbers and provide primary biological protection); 2. Concrete container (store and enable transport of low and intermediate level radioactive waste; provide secondary biological protection; provide safe keeping of radioactive waste for 300Y500 y); and 3. Concrete for filling trenches (provide tertiary biological protection and prevent leakage of radionuclides which have penetrated the second barrier). At the Vincˇa Institute of Nuclear Sciences, a promising composite for engineer trenches system, especially for concrete for filling trenches has been developed. A test for leakage measurements of radionuclides from concrete was
www.health-physics.com
Copyright © 2013 Health Physics Society. Unauthorized reproduction of this article is prohibited.
February 2014
The Radiation Safety Journal
Vol. 106, suppl 1 February 2014
reaction was considered. The initial and boundary conditions are:
Table 1. Composition and initial radioactivity. Formula Materials Cement (Portland), gr Sand, 0Y2 mm Aggregate, 2Y4 mm Aggregate, 4Y8 mm Water, mL Additives, mL Initial activity Ao (kBq) 60 Co
C1 405 840 518 422 190 4
studied using the above method (Morijama et al. 1977; Plecas et al. 1985, 1990, 1991, 2003; Plecas 2003aYc.
C2 415 580 516 676 195 4
C3 425 695 500 588 2,000 4 Per sample È60,0
C4 435 665 315 880 220 4
line and the diffusion coefficient De is given by:
De ¼
p 2 V2; m 2 4 S
ð3Þ
THEORETICAL METHODS Three methods are compared with respect to their applicability to experimental leaching data (Morijama et al. 1977; Matsuzuru et al. 1977). Method I: Diffusion equation based on a plane source model In this model the fraction f leached at time t(d)is:
pffiffiffiffiffiffiffiffiffiffi ~an 2 S De t n; pffiffiffiffi f ¼ ¼ Ao V p
ð1Þ
where San is the cumulative fraction leached of contaminant for each leaching period, Ao is the initial amount of contaminant in the sample, V is the volume of sample (cm3), S is the exposed surface area of the sample (cm2), tn the duration of leachant renewal period d, and De is the diffusion coefficient (cm2 dj1). The results may also be expressed by the cumulative fraction of the contaminant. Leach test results are plotted as the cumulative fraction of contaminant leached from the samples as a function of the square root of total leaching time: pffiffiffiffiffiffiffi ~an versus ~t n : Ao
Method II: Rate equation for coupled diffusion and simultaneous first-order reaction In this model, the rate equation is:
¯C ¼ De ð¯ 2 C=¯ X 2 Þ þ gðCÞ: ð4Þ ¯t Here, the special case where g(C) is directly proportional to the concentration C, i.e., a first-order
ð5Þ
t ¼ 0; xG0; C ¼ 0
ð6Þ
t 90; x ¼ 0; C ¼ 0:
ð7Þ
From this, the fraction leached from a specimen having a surface area S (cm2) and volume V (cm3) is: pffiffiffiffiffiffiffiffiffiffi pffiffiffiffi f ¼ ðS=V Þ De =k ½ðkt þ 1=2Þ erf kt
pffiffiffiffiffiffiffiffiffiffi þ kt=p expðjktÞ;
ð8Þ
where k is the rate constant of the first-order reaction and u
pffiffiffiffi 2 erf ðuÞ¼ð2= pÞ X exp ðjz Þdz: ð9Þ o Method III: Polynomial equation The orthogonal polynomial is one of the most useful empirical equations. Its general form is: n
yðxÞ ¼ ~ A i dðxÞ;
ð10Þ
i¼1
where Ai is the parameter to be determined, and Ci is a function of x. Here, Ei (x) is taken
ð2Þ
If the model is applicable a plot of SanAoj1 vs. Stnj1/2 is a straight Operational Radiation Safety
where m = (San/Ao) (1/¾St), is the slope of the straight line (dj1/2).
t ¼ 0; a9x90; C ¼ C 0
FIG. 1. The fraction of 60Co leached from cement composites as a function of the square root of leaching period (Method 1). www.health-physics.com
Copyright © 2013 Health Physics Society. Unauthorized reproduction of this article is prohibited.
S31
I. Plecas
Modeling of transport phenomena
as t i/2, and the leaching fraction is given by: n
f ¼ ~ Ai t i=2 :
ð11Þ
i¼1
To simplify the mathematical treatment, a fourth terms polynomial of the form: f ¼ Ao þ A1 t 1=2 þ A2 t þ A3 t 3=2 :
ð12Þ
was fitted to the leaching data. For this type of model, extrapolation to longer term leaching is not advisable since the arbitrary constants do not necessarily have any physical significance.
PREPARATION OF SAMPLE FOR LEACHING TEST More than 100 different formulations of concrete formulations were examined to optimize their mechanical and sorption properties. The concrete samples were prepared with a standard Portland cement PC-20-Z-45 MPa (Lafarge Factory, Trg Beocinske fabrike cementa 1; Beocin, South Backa, 21300 Serbia). The concrete composition was mixed with artificial radioactivity of cobalt 60Co, Ao = 55Y67 (kBq); the mixing time was about 10 min. The mixtures were cast into 50-mm-diameter cylindrical molds with a height of 50 mm, which were then sealed and cured for 28 d prior to the leaching experiments. Leaching of 60Co was studied using the method recommended by the IAEA (Hespe 1971). The duration of the leachant renewal period was 30 d. After each leaching period the radioactivity in the leachant was measured using an EG&GORTEC (100 Midland Road, Oak Ridge, TN 37830) Products Group spectrometry system (HPGe detector 50% relative efficiency) and software (Gamma Visionxx). In this paper, we discuss four representative formulations of concrete for filling trenches: C1, C2, C3, and C4. The composition and initial radioactivity A0 (Bq) per sample prepared for leakage test is shown in Table 1. S32
Figs. 1 and 2 present plots of f against t for leakage of 60Co from the four concrete samples for Methods I and Method III.
RESULTS
fIII ðC1 Þ¼7; 2 10j8þ5:75 10j5 t1=2 þ5; 4 10j8 t þ 9; 7 10j12 t3=2 fIII ðC2 Þ¼5; 3 10j8þ6:6 10j5 t1=2
Experimental data show the fractions of 60Co leached from concrete composite as a function of the square root of the leaching period. The linear relation between f and t is not observed throughout the test period. From the application of Method I to the leaching data we obtained:
f I ðC1 Þ¼ 2;1 f I ðC2 Þ¼ 3;5 f I ðC3 Þ¼ 4;0 f I ðC4 Þ¼ 5;4
Using the least squares procedure, Method III yielded:
10j5 10j5 10j5 10j5
t1=2 þ7;3 t1=2 þ5;5 t1=2 þ6;0 t1=2 þ6;5
10j9 10j9 10j9 10j9
The diffusion coefficients predicted by Method I are: DI ðC1 Þ ¼ 5;3 10j6 ð cm2 = dÞ DI ðC2 Þ ¼ 5;5 10j6 ð cm2 = dÞ DI ðC3 Þ ¼ 6;0 10j6 ð cm2 = dÞ DI ðC4 Þ ¼ 7;6 10j6 ð cm2 = dÞ Method II was applied to the leakage data to obtain the unknown parameters De and k. From this we obtained: DII ðC1 Þ ¼ 4;50 10j6 ð cm2 = dÞ DII ðC2 Þ ¼ 5;20 10j6 ð cm2 = dÞ DII ðC3 Þ ¼ 5;36 10j6 ð cm2 = dÞ DII ðC4 Þ ¼ 6;90 10j6 ð cm2 = dÞ
þ6; 7 10j8 t þ 9; 4 10j12 t3=2
fIII ðC3 Þ¼4; 5 10j8þ7:4 10j5 t1=2 þ6; 5 10j8 t þ 9; 7 10j12 t3=2 fIII ðC4 Þ¼3; 4 10j8þ7:1 10j5 t1=2 þ9; 8 10j8 t þ 9; 4 10j12 t3=2
DISCUSSION AND CONCLUSION The results are presented in Figs. 1 and 2 and show the fraction of 60Co leached from cement composites as a function of the square root of the leaching period. In the data for cement composite as a matrix, the linearity between f and t(d) is not always obtained throughout the period tested as seen in Fig. 1. However, there are two different stages of linearity between f and t2, before and after a leaching time of about 10 d. The slope of the linear relation for the early stage is larger than for the latter one. This change in the leaching rate may be associated with the fact that, as the leaching time elapsed, the diffusion rate
FIG. 2. The fraction of 60Co leached from cement composites as a function of the square root of leaching period (Method 2). www.health-physics.com
Copyright © 2013 Health Physics Society. Unauthorized reproduction of this article is prohibited.
February 2014
The Radiation Safety Journal
would gradually slow down as the diffusion path becomes longer. Method I cannot describe the whole leaching process, but it is very convenient to simulate leaching over a long period because of its simplicity. Despite the complex numerical treatment required, the fit obtained using Method II is no better than that obtained using Method I. Method III provides the best approximation over the whole leaching period. In many cases, however, the leaching mechanisms are unknown and, therefore, it is convenient to use polynomial approximation (Epimakov and Oleinik 2000). Finally, the results presented in this paper will define the design of our future engineered trenches disposal system for radioactive waste. The radiological and physicchemical performance assessment of the disposal facility can provide
Operational Radiation Safety
Vol. 106, suppl 1 February 2014
a key input into the choice of barrier. The conclusion was that disposal option in near-surface would be effective for a long term period of time and would very effective in preventing water intrusion and retarding radionuclide release even over a long term of period. AcknowledgmentsVWork supported by the Ministry of Science and Technology of the Republic of Serbia (Project No III 43009).
REFERENCES Epimakov VN, Oleinik MS. Ecological danger of cementing products of mineralized liquid radioactive waste concentrates. Ecological Chem 9:116Y120; 2000. Hespe ED. Leach testing of immobilized radioactive waste. Solids Atomic Energy Rev 9:195Y207; 1971. Matsuzuru HI, Moriyama NO, Wadachi YA, Ito AK. Leaching behavior of 137Cs in cementVwaste composites. Health Phys 32:529Y534; 1977. Morijama NO, Dojiri D, Matsuzuru SH. Leaching of Cs from the ion-exchange resin incorporated in polyethylene
or cement composite. Health Phys 33: 549Y552; 1977. Plecas IL, Mihajlovic Lj, Kostadinovic AN. Optimization of concrete containers composition in radioactive waste technology. Radioactive Waste Management Nucl Fuel Cycle 6:161Y175; 1985. Plecas IL, Drljaca JA, Peric AL, Kostadinovic AN, Glodic SN. Radionuclide migration through porous nuclear waste forms. Radioactive Waste Management Nucl Fuel Cycle 14:195Y205; 1990. Plecas IL, Peric AL, Kostadinovic AN, Drljaca JA. Determination of retardation factors of 137Cs in migration process in concrete. J Radioanalytical Nucl Chem 154:121Y131; 1991. Plecas IL, Pavlovic RA, Pavlovic SN. Leaching of 60Co and 137Cs from spent ion exchange resins in cement-bentonite clay matrix. Bull Mater Sci 26:699Y701; 2003. Plecas IL. Immobilization of 137Cs and 60 Co in concrete matrix. Annals Nucl Energy 30/18:1899Y1903; 2003a. Plecas IL. Leaching of 137Cs from spent ion exchange resins in cementVBentonite Clay Matrix. Acta Chem Slovenica 50/3: 593Y596; 2003b. Plecas IL. Comparison of mathematical interpretation in radioactive waste leaching studies. J Radioanalytical Nucl Chem 258:435Y437; 2003c.
www.health-physics.com
Copyright © 2013 Health Physics Society. Unauthorized reproduction of this article is prohibited.
S33
Modeling of Transport Phenomena in Concrete Porous Media Ilija Plecas* Abstract: Two fundamental concerns must be addressed when attempting to isolate lowlevel waste in a disposal facility on land. The first concern is isolating the waste from water, or hydrologic isolation. The second is preventing movement of the radionuclides out of the disposal facility, or radionuclide migration. Particularly, we have investigated here the latter modified scenario. To assess the safety for disposal of radioactive wasteconcrete composition, the leakage of 60Co from a waste composite into a surrounding fluid has been studied. Leakage tests were carried out by the original method, developed at the Vincˇa Institute. Transport phenomena involved in the leaching of a radioactive material from a cement composite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source: an equation for diffusion coupled to a first-order equation, and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-y mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center. Health Phys. 106(Supplement 1):S30YS33; 2014 Key words: operational topics; waste disposal; waste management; waste, low-level
*Institute of Nuclear Sciences BVinca,[ University of Belgrade, P.O. BOX 522, 11001 Belgrade, Serbia. The author declares no conflicts of interest.
INTRODUCTION Cement and concrete are widely used in low-level waste management both as a means of solidifying waste and for containment of dry or liquid wastes. At present, there is also widespread interest in the use of near-surface concrete trench system for the disposal of radwaste materials. Typical concrete is a mixture of cement, sand, stone aggregate, and water in various proportions that together determine the structural properties and tightness of the poured material. Water content is one of the critical parameters and must be carefully controlled during purring and setting; to a large extent it will determine the porosity of the resulting material. Engineered barriers are features of the disposal system made or altered by humans during the construction, operation, and closure of a repository. Engineered barriers are intended to contribute to the overall performance of the disposal system by providing the level of containment required while the waste remains hazardous.
Ilija B. Ple(asˇ (19 June 1948, Belgrade) received the degree of B.Sc. Chemical Engineering Mr Sci and Ph.D. at the Faculty of Technology at the Belgrade University. He has been employed in the Radiation and Environmental Protection ˇ A’’ Institute of Nuclear Sciences since 1973 and constantly Laboratory in the ‘‘VINC engaged in research and design in the field of radioactive waste treatment, storing, and disposal, especially in the field of immobilization of radioactive waste by cement. Ilija B. Ple(asˇ has published more than 40 papers in International Journals and more than 100 papers on International Conferences and Symposia. Since 1992, Ilija B. Ple(asˇ has been Head of the Radiation and Environmental Protection Department in the ‘‘Vincˇa’’ Institute of Nuclear Sciences. Ilija B. Ple(asˇ has been ˇ A’’ Institute of Nuclear Science, Belgrade, Serbia (1999/ Acting director of ‘‘VINC 2001). Member of The Scientific Society of Serbia (2008Ypresent). His email is [email protected]
S30
In cases where the selected site or geological environment is not ideally suited for disposal, the repository can be heavily engineered so that, for meeting safety targets, reliance is placed primarily on the engineered barriers. Engineering trench systems provide three biological protection barriers: 1. Mortar for immobilizing the waste and filling the concrete containers (enable its penetration into all cavities of solid radioactive waste and thus fix it permanently; permit no leakage of radionuclidesV use of special cement or adsorbers and provide primary biological protection); 2. Concrete container (store and enable transport of low and intermediate level radioactive waste; provide secondary biological protection; provide safe keeping of radioactive waste for 300Y500 y); and 3. Concrete for filling trenches (provide tertiary biological protection and prevent leakage of radionuclides which have penetrated the second barrier). At the Vincˇa Institute of Nuclear Sciences, a promising composite for engineer trenches system, especially for concrete for filling trenches has been developed. A test for leakage measurements of radionuclides from concrete was
www.health-physics.com
Copyright © 2013 Health Physics Society. Unauthorized reproduction of this article is prohibited.
February 2014
The Radiation Safety Journal
Vol. 106, suppl 1 February 2014
reaction was considered. The initial and boundary conditions are:
Table 1. Composition and initial radioactivity. Formula Materials Cement (Portland), gr Sand, 0Y2 mm Aggregate, 2Y4 mm Aggregate, 4Y8 mm Water, mL Additives, mL Initial activity Ao (kBq) 60 Co
C1 405 840 518 422 190 4
studied using the above method (Morijama et al. 1977; Plecas et al. 1985, 1990, 1991, 2003; Plecas 2003aYc.
C2 415 580 516 676 195 4
C3 425 695 500 588 2,000 4 Per sample È60,0
C4 435 665 315 880 220 4
line and the diffusion coefficient De is given by:
De ¼
p 2 V2; m 2 4 S
ð3Þ
THEORETICAL METHODS Three methods are compared with respect to their applicability to experimental leaching data (Morijama et al. 1977; Matsuzuru et al. 1977). Method I: Diffusion equation based on a plane source model In this model the fraction f leached at time t(d)is:
pffiffiffiffiffiffiffiffiffiffi ~an 2 S De t n; pffiffiffiffi f ¼ ¼ Ao V p
ð1Þ
where San is the cumulative fraction leached of contaminant for each leaching period, Ao is the initial amount of contaminant in the sample, V is the volume of sample (cm3), S is the exposed surface area of the sample (cm2), tn the duration of leachant renewal period d, and De is the diffusion coefficient (cm2 dj1). The results may also be expressed by the cumulative fraction of the contaminant. Leach test results are plotted as the cumulative fraction of contaminant leached from the samples as a function of the square root of total leaching time: pffiffiffiffiffiffiffi ~an versus ~t n : Ao
Method II: Rate equation for coupled diffusion and simultaneous first-order reaction In this model, the rate equation is:
¯C ¼ De ð¯ 2 C=¯ X 2 Þ þ gðCÞ: ð4Þ ¯t Here, the special case where g(C) is directly proportional to the concentration C, i.e., a first-order
ð5Þ
t ¼ 0; xG0; C ¼ 0
ð6Þ
t 90; x ¼ 0; C ¼ 0:
ð7Þ
From this, the fraction leached from a specimen having a surface area S (cm2) and volume V (cm3) is: pffiffiffiffiffiffiffiffiffiffi pffiffiffiffi f ¼ ðS=V Þ De =k ½ðkt þ 1=2Þ erf kt
pffiffiffiffiffiffiffiffiffiffi þ kt=p expðjktÞ;
ð8Þ
where k is the rate constant of the first-order reaction and u
pffiffiffiffi 2 erf ðuÞ¼ð2= pÞ X exp ðjz Þdz: ð9Þ o Method III: Polynomial equation The orthogonal polynomial is one of the most useful empirical equations. Its general form is: n
yðxÞ ¼ ~ A i dðxÞ;
ð10Þ
i¼1
where Ai is the parameter to be determined, and Ci is a function of x. Here, Ei (x) is taken
ð2Þ
If the model is applicable a plot of SanAoj1 vs. Stnj1/2 is a straight Operational Radiation Safety
where m = (San/Ao) (1/¾St), is the slope of the straight line (dj1/2).
t ¼ 0; a9x90; C ¼ C 0
FIG. 1. The fraction of 60Co leached from cement composites as a function of the square root of leaching period (Method 1). www.health-physics.com
Copyright © 2013 Health Physics Society. Unauthorized reproduction of this article is prohibited.
S31
I. Plecas
Modeling of transport phenomena
as t i/2, and the leaching fraction is given by: n
f ¼ ~ Ai t i=2 :
ð11Þ
i¼1
To simplify the mathematical treatment, a fourth terms polynomial of the form: f ¼ Ao þ A1 t 1=2 þ A2 t þ A3 t 3=2 :
ð12Þ
was fitted to the leaching data. For this type of model, extrapolation to longer term leaching is not advisable since the arbitrary constants do not necessarily have any physical significance.
PREPARATION OF SAMPLE FOR LEACHING TEST More than 100 different formulations of concrete formulations were examined to optimize their mechanical and sorption properties. The concrete samples were prepared with a standard Portland cement PC-20-Z-45 MPa (Lafarge Factory, Trg Beocinske fabrike cementa 1; Beocin, South Backa, 21300 Serbia). The concrete composition was mixed with artificial radioactivity of cobalt 60Co, Ao = 55Y67 (kBq); the mixing time was about 10 min. The mixtures were cast into 50-mm-diameter cylindrical molds with a height of 50 mm, which were then sealed and cured for 28 d prior to the leaching experiments. Leaching of 60Co was studied using the method recommended by the IAEA (Hespe 1971). The duration of the leachant renewal period was 30 d. After each leaching period the radioactivity in the leachant was measured using an EG&GORTEC (100 Midland Road, Oak Ridge, TN 37830) Products Group spectrometry system (HPGe detector 50% relative efficiency) and software (Gamma Visionxx). In this paper, we discuss four representative formulations of concrete for filling trenches: C1, C2, C3, and C4. The composition and initial radioactivity A0 (Bq) per sample prepared for leakage test is shown in Table 1. S32
Figs. 1 and 2 present plots of f against t for leakage of 60Co from the four concrete samples for Methods I and Method III.
RESULTS
fIII ðC1 Þ¼7; 2 10j8þ5:75 10j5 t1=2 þ5; 4 10j8 t þ 9; 7 10j12 t3=2 fIII ðC2 Þ¼5; 3 10j8þ6:6 10j5 t1=2
Experimental data show the fractions of 60Co leached from concrete composite as a function of the square root of the leaching period. The linear relation between f and t is not observed throughout the test period. From the application of Method I to the leaching data we obtained:
f I ðC1 Þ¼ 2;1 f I ðC2 Þ¼ 3;5 f I ðC3 Þ¼ 4;0 f I ðC4 Þ¼ 5;4
Using the least squares procedure, Method III yielded:
10j5 10j5 10j5 10j5
t1=2 þ7;3 t1=2 þ5;5 t1=2 þ6;0 t1=2 þ6;5
10j9 10j9 10j9 10j9
The diffusion coefficients predicted by Method I are: DI ðC1 Þ ¼ 5;3 10j6 ð cm2 = dÞ DI ðC2 Þ ¼ 5;5 10j6 ð cm2 = dÞ DI ðC3 Þ ¼ 6;0 10j6 ð cm2 = dÞ DI ðC4 Þ ¼ 7;6 10j6 ð cm2 = dÞ Method II was applied to the leakage data to obtain the unknown parameters De and k. From this we obtained: DII ðC1 Þ ¼ 4;50 10j6 ð cm2 = dÞ DII ðC2 Þ ¼ 5;20 10j6 ð cm2 = dÞ DII ðC3 Þ ¼ 5;36 10j6 ð cm2 = dÞ DII ðC4 Þ ¼ 6;90 10j6 ð cm2 = dÞ
þ6; 7 10j8 t þ 9; 4 10j12 t3=2
fIII ðC3 Þ¼4; 5 10j8þ7:4 10j5 t1=2 þ6; 5 10j8 t þ 9; 7 10j12 t3=2 fIII ðC4 Þ¼3; 4 10j8þ7:1 10j5 t1=2 þ9; 8 10j8 t þ 9; 4 10j12 t3=2
DISCUSSION AND CONCLUSION The results are presented in Figs. 1 and 2 and show the fraction of 60Co leached from cement composites as a function of the square root of the leaching period. In the data for cement composite as a matrix, the linearity between f and t(d) is not always obtained throughout the period tested as seen in Fig. 1. However, there are two different stages of linearity between f and t2, before and after a leaching time of about 10 d. The slope of the linear relation for the early stage is larger than for the latter one. This change in the leaching rate may be associated with the fact that, as the leaching time elapsed, the diffusion rate
FIG. 2. The fraction of 60Co leached from cement composites as a function of the square root of leaching period (Method 2). www.health-physics.com
Copyright © 2013 Health Physics Society. Unauthorized reproduction of this article is prohibited.
February 2014
The Radiation Safety Journal
would gradually slow down as the diffusion path becomes longer. Method I cannot describe the whole leaching process, but it is very convenient to simulate leaching over a long period because of its simplicity. Despite the complex numerical treatment required, the fit obtained using Method II is no better than that obtained using Method I. Method III provides the best approximation over the whole leaching period. In many cases, however, the leaching mechanisms are unknown and, therefore, it is convenient to use polynomial approximation (Epimakov and Oleinik 2000). Finally, the results presented in this paper will define the design of our future engineered trenches disposal system for radioactive waste. The radiological and physicchemical performance assessment of the disposal facility can provide
Operational Radiation Safety
Vol. 106, suppl 1 February 2014
a key input into the choice of barrier. The conclusion was that disposal option in near-surface would be effective for a long term period of time and would very effective in preventing water intrusion and retarding radionuclide release even over a long term of period. AcknowledgmentsVWork supported by the Ministry of Science and Technology of the Republic of Serbia (Project No III 43009).
REFERENCES Epimakov VN, Oleinik MS. Ecological danger of cementing products of mineralized liquid radioactive waste concentrates. Ecological Chem 9:116Y120; 2000. Hespe ED. Leach testing of immobilized radioactive waste. Solids Atomic Energy Rev 9:195Y207; 1971. Matsuzuru HI, Moriyama NO, Wadachi YA, Ito AK. Leaching behavior of 137Cs in cementVwaste composites. Health Phys 32:529Y534; 1977. Morijama NO, Dojiri D, Matsuzuru SH. Leaching of Cs from the ion-exchange resin incorporated in polyethylene
or cement composite. Health Phys 33: 549Y552; 1977. Plecas IL, Mihajlovic Lj, Kostadinovic AN. Optimization of concrete containers composition in radioactive waste technology. Radioactive Waste Management Nucl Fuel Cycle 6:161Y175; 1985. Plecas IL, Drljaca JA, Peric AL, Kostadinovic AN, Glodic SN. Radionuclide migration through porous nuclear waste forms. Radioactive Waste Management Nucl Fuel Cycle 14:195Y205; 1990. Plecas IL, Peric AL, Kostadinovic AN, Drljaca JA. Determination of retardation factors of 137Cs in migration process in concrete. J Radioanalytical Nucl Chem 154:121Y131; 1991. Plecas IL, Pavlovic RA, Pavlovic SN. Leaching of 60Co and 137Cs from spent ion exchange resins in cement-bentonite clay matrix. Bull Mater Sci 26:699Y701; 2003. Plecas IL. Immobilization of 137Cs and 60 Co in concrete matrix. Annals Nucl Energy 30/18:1899Y1903; 2003a. Plecas IL. Leaching of 137Cs from spent ion exchange resins in cementVBentonite Clay Matrix. Acta Chem Slovenica 50/3: 593Y596; 2003b. Plecas IL. Comparison of mathematical interpretation in radioactive waste leaching studies. J Radioanalytical Nucl Chem 258:435Y437; 2003c.
www.health-physics.com
Copyright © 2013 Health Physics Society. Unauthorized reproduction of this article is prohibited.
S33
