Benchmark Calculations with COMSOL of the Transport of Radionuclides through Clay and Bentonite Barriers in a Geological Repository

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1 Excerpt rom the Proceedings o the COMSOL Conerence 2009 Milan Benchmark Calculations with COMSOL o the Transport o Radionuclides through Clay and Bentonite Barriers in a Geological Repository Manuel Lorenzo Sentís *1, Felix Altorer 1, Martin Herort 1, Andreas Jakob 2, Georg Kosakowski 2, Sven Friedel 3 1 Swiss Federal Nuclear Saety Inspectorate (ENSI) 2 Paul Scherrer Institute (PSI) 3 COMSOL Multiphysics GmbH *Corresponding author: ENSI, Disposal and Saety Analyses Section (TISA), CH-5232 Villigen-ENSI, Switzerland, manuel.sentis@ensi.ch Abstract: A benchmark study was carried out by the Swiss Nuclear Saety Inspectorate (ENSI) in collaboration with the Laboratory or Waste Management (LES) o the Paul Scherrer Institute (PSI) in order to evaluate the capabilities o the program COMSOL or the calculation o the transport o radionuclides through clay and bentonite barriers in a geological repository or radioactive waste. In this study results o our dierent codes were compared. The results o the transport calculations or a selection o key radionuclides are shown in this paper. The good agreement o the results obtained with the dierent codes is a veriication o COMSOL as modeling tool or a geological repository o radioactive waste in a clay ormation. Keywords: Geological repository, radioactive waste, saety assessment, benchmark, porous medium. 1. Introduction The Swiss Nuclear Saety Inspectorate ENSI is the regulatory authority or nuclear saety and radiation protection in nuclear acilities in Switzerland. It also supervises the preparations or the disposal o radioactive waste, which includes the review o saety assessments or geological repositories or all types o radioactive waste submitted by the Swiss implementer Nagra. The sectoral plan or the selection o appropriate sites or geological repositories or all kind o nuclear waste (spent uel, vitriied high-level and long-lived intermediate-level waste as well as or low-level waste) in Switzerland started in 2008 and will last about ten years. ENSI examines and evaluates the proposals put orward by the implementer Nagra rom the point o view o saety. In order to perorm independent saety analysis calculations and thus to review the saety assessments o the implementer Nagra, ENSI decided to use the program COMSOL [1,2] in particular the Earth Science Module. To gain conidence in the quality o the results o the saety analysis, especially since the program must provide results or very long timescales, it is general practice to perorm a veriication o the code. This is done typically by perorming benchmark analyses in which the results o dierent codes are compared to each other. With this objective a benchmark study was undertaken in collaboration with PSI, in which the results o our dierent codes were compared, namely PICNIC, FRAC3DVS, COMSOL (Version 3.4) and Tough2-EOS9nT [3,4]. PICNIC calculations were published by Nagra [5] or a conceptual model o a geological repository within a easibility study (project Opalinus Clay ). The results were reproduced by PSI [6] with help o FRAC3DVS and an independently developed COMSOL model as well as by ENSI with COMSOL and Tough2-EOS9nT [7,8]. For the easibility study a potential site located in the geological ormation Opalinus Clay in northern Switzerland was selected by Nagra. 2. Conceptual Model To estimate the release o radionuclides to the biosphere, the complex system o caverns and tunnels was simpliied into a one-dimensional (PICNIC) or into a two-dimensional (COMSOL, FRAC3DVS, Tough2-EOS9nT) conceptual model as shown in Figure 1. As a irst simpliication the horizontal distances between the can-

2 - 2 - isters in a tunnel are conservatively neglected. Although the geological repository consists o a series o tunnels, based on symmetry arguments o the geometrical coniguration it is only necessary to consider one tunnel in the study. The interactions between neighboring tunnels are considered by setting no-low conditions at the two vertical boundaries. The vertical dimensions are deined based on the location o the nearest aquier. Ater the above-mentioned considerations the conceptual model or the benchmark study is simpliied as shown in the Figure 1 [6,9]. solubility limits were conservatively neglected in these calculations. The purpose o this paper is to show the numerical estimation by dierent codes o the radionuclide mass low on the top and bottom boundary o the model. This is obtained by integrating the mass lux over the top and bottom boundaries. These mass lows are used within the biosphere model to obtain the eective dosis to the population. 3. Mathematical Model To study the transport o dierent nuclides through the dierent barriers o the geological repository the program COMSOL Multiphysics and in particular the Earth Science Module was used. The study concentrated on some critical radionuclides that show only small retention in the dierent barriers o the geological repository: I-129, Ca-41, Cl-36, Se-79 and C-14. The Model is based on the ollowing three equations [1]: Mass conservation o water ( φ s ρ ) + ( φ s ρ v) = Q (1) Figure 1. Conceptual model or the simulations [6]. The radionuclides are conined in the canister until the corrosion o the steel canister allows them to be released into the bentonite backill. The thickness o the canister wall is about 1 cm. Based on a steel corrosion rate o 1μm/a it is assumed in the calculations perormed in this paper that the radionuclides start being released rom the canister ater years. Aterwards the radionuclides are transported through the low-permeable bentonite and clay barriers based on advective and mainly diusive processes. Due to the small values o the Darcy velocities, the dispersive transport o radionuclides was not considered in the calculations. The bentonite backill and the Opalinus Clay, assumed to be completely saturated, were modeled as saturated homogeneous porous media without ractures. The sorption coeicients o the radionuclides in the clay and bentonite layers are considered, with ρ [kg m -3 ] or the density o water, v [m/s] the average velocity o the low in the porous medium, s [-] the saturation o the medium, φ [-] the porosity o the medium and Q [kg m -3 s -1 ] a source term or the low o water. Darcy s law or the mass lux o water j = ρ φ v = ρ Kφ ϕ (2) with K [m/s] or the hydraulic conductivity and φ [m] or the hydraulic potential. The equation (1) is simpliied with the elimination o the time derivative (stationary low) and o the source term or water. Furthermore the medium considered in this report is ully saturated and that means: s = 1 (3)

3 - 3 - Taking into account these considerations and equation (2), equation (1) becomes: ρ Kφ Δϕ = 0 (4) Mass conservation o the radionuclides or transport equation ( φ c) + ( ρ tcs ) + [ φ D c + φvc] = R + R + s Q (5) with ρ t [kg m -3 ] or the bulk density, c [kg m -3 ] the concentration o the nuclide in the liquid phase and c s [-] (the dimensions are mass o adsorbed contaminant per dry unit weight o solid) the concentration o the nuclide in the solid phase, D [m 2 /s] the hydrodynamic dispersion tensor, which is given by the ollowing expression: viv j D ij = ( α L α T ) + α T v δ ij + D (6) p v where α L and α T are the longitudinal and transverse dispersivity and D p is the pore diusion coeicient related to the molecular diusion coeicient D 0 in water through a orm actor : D p = (7) D 0 α L and α T are considered equal to zero (dispersion term negligible in comparison to the diusion term) or the calculations in this document and then the dispersion tensor reduces to D p. R [kg m -3 s -1 ] and R s [kg m -3 s -1 ] are the terms or the reactions (sum over the dierent reactions, or example chemical reactions, radioactive decay) o the nuclides in water and in the solid phase. For the calculations shown in this document only radioactive decay was considered and the two terms reduce to: R = λ c (8) Rs = λ c s (9) with λ [s -1 ] or the decay constant o the considered radionuclide. For the calculations shown in this document c s is related to c through a linear isotherm with a sorption coeicient K d [m 3 /kg]: c = s Kd c (10) The last term Q [kg m -3 s -1 ] in equation (5) represents the solute added per unit volume o soil and per unit time. The release o the nuclides rom the canister is implemented in COMSOL as a boundary condition at the canister boundary. Thereore the term Q is neglected in (5). Ater all these considerations the equation (5) becomes: c [ φ + ρ g K s ] + [ φd p c + uc] = [ φ+ ρ cλ (11) g K s ] The Darcy velocity u is deined as the product: u = φ ν (12) and it is oten reerred to as speciic discharge. The hydraulic boundary conditions are ixed potentials o 0 m at the top and 80 m at the bottom (boundaries A and B in Figure 1), that corresponds to a hydraulic gradient o 1 m/m. On the let and right part o the boundary (boundaries C and D in Figure 1) a no-low boundary or both, low and transport was deined. As consequence o the corrosion o the waste container the nuclides are released rom the boundary E. The volume between E and F was deined in order to implement a source term in the codetough2- EOS9nT. In COMSOL this bentonite volume does not play an active role since the release rates rom the canister are implemented as boundary conditions. The values o the release rate originally in a tabular ormat are implemented into COMSOL by means o an interpolation unction. As initial condition or the hydraulic potential a linear variation rom the bottom to the top o the domain was set (upward low). The initial pressure in the bentonite illing is Pa. The low and the transport model are symmetric with respect to a vertical line passing through the centre o the canister and thereore only the right part was considered in the calculations. This reduces the time needed or the solution. However, the computational time was not a critical aspect in the simulations because this time was o the order o some minutes or each nuclide with COMSOL as well as with Tough2-EOS9nT. The values o all parameters mentioned in this document are listed in table 1 in the appendix.

- 4-4. Results A two-step approach with COMSOL version 3.4 was used to solve the above-mentioned equations.

4 Results A two-step approach with COMSOL version 3.4 was used to solve the above-mentioned equations. In a irst step the stationary water low equation (4) (Darcy s law model) is solved and the velocity obtained is used as input or the second step, in which the transport equation (11) is solved (solute transport model). Integration coupling variables were deined on the top and bottom part o the domain in order to integrate the lux o each nuclide over these boundaries. The results o the simulations are shown in the igures 2-6 and were represented with the help o Tecplot [10].They represent the sum o the integrated mass lux over the top and bottom boundaries. The red points represent the values o the source term used in the calculations. The maxima o the mass low values and the times o these maxima are summarized in Table 2 or the dierent codes and or the dierent radionuclides. The results or Ca-41 are shown in Figure 2. Two intervals can be distinguished, the one beore the peak and the one ater the peak. In the interval beore the peak Tough2-EOS9nT and Frac3dvs limits the maximal and minimal mass lows respectively. Figure 2. Geosphere release rates or Ca-41. The dierent approach to the interpolation o the source term by the dierent codes and also the ast decrease o the source term at about years explain the dierences in the rising edge o the mass low or the dierent codes. The dierences in the irst part o the breakthrough curve relect also the one-dimensional approach o Picnic in comparison with the other codes and the dierent time steps o the simulations. Ater the peak the agreement among the results or the dierent codes is excellent. Figure 3 shows the results or the non-sorbing radionuclide C-14 (organic). Figure 3. Geosphere release rates or C-14. Ca-41 and C-14 have the same values or the diusion constant and or the eective porosity. The dierences are the data o the source term, which are about times larger or C-14; the hal lie, which is about 100 times longer or Ca- 41; and the sorption coeicient K d, which is zero or C-14. Due to zero sorption o C-14, the peak or C-14 is reached earlier than the one or Ca-41 and the peak concentration is about 100 times higher or C-14 than or Ca-41. At a irst glance a peak concentration or C times higher would have been expected but the hal lie, the sorption coeicient and the aster decline o the source term or C-14 compensate the larger values o the source term. A higher peak value is observed or C-14 rom the calculations perormed with Picnic in comparison with the other codes. Namely mol/a or Picnic and about ( ) 10-8 mol/a or the other codes as it can be seen in Table 2 in the Appendix. Picnic is a one-dimensional computer code and thereore neglects the diusive low in the transverse direction, that explains the higher values o the release rates.

1 10 6 years, that explains the width o the breakthrough curve reaching rom 10 5 to 10 7 years.

5 - 5 - Figure 4 shows the results o the simulations or Se-79, which has a zero sorption coeicient in both Opalinus clay and bentonite. The agreement between the dierent results is good, only Picnic shows a small dierence to the results o the other codes. The hal lie o Se-79 is years, that explains the width o the breakthrough curve reaching rom 10 5 to 10 7 years. The weak decline o the breakthrough curve or long times in comparison with C-14 and Ca-41 is caused by the same decline o the source term. Figure 5. Geosphere release rates or Cl-36. Finally, Figure 6 shows the results o the calculations or the radionuclide I-129, which migrates through the clay layers as an anion and it is thereore weakly retained by the negatively charged clay layers. Figure 4. Geosphere release rates or Se-79. Figure 5 shows the breakthrough curve or Cl- 36. The only dierences between the input o Cl- 36 and that o Se-79 are the hal lie, which is one order o magnitude larger or Se-79 and the details o the source term. The source term has higher values or Cl-36 but the decrease is also aster. The aster decrease and the lower hal lie explain that the breakthrough curve extends over a broader range on the time-axis. The higher values o the peak relect the larger values o the source term or Cl-36 at the beginning. Figure 6. Geosphere release rates or I-129. I-129 has the longest hal lie o all considered radionuclides namely years. That together with the slow decrease and the high values o the source term explains that the solute breakthrough curve extends over a very long range o time values even beyond 10 7 years. The retardation eect as result o the sorption coeicient o I-129 is partially compensated by the high values o its source term, what in turn explains also the higher values o the peak or I- 129 in comparison with Se-79 and Cl-36.

6 - 6 - Small variations in the results obtained with the codes can be explained by dierences in the conceptualization and because o dierent numerical methods implemented in the codes. Picnic uses a one-dimensional approximation or the transport in the geosphere, while the other codes use a two-dimensional approximation. Besides, Tough2-EOS9nT uses the integral inite dierence method whereas Picnic and Comsol use the inite element method and Frac3dvs uses both the inite volume and inite dierence methods. For all the radionuclides considered in these calculations the results o COMSOL are always in between the results o all the other codes. As a general conclusion, Picnic tends to overestimate the peak o the mass low when compared with the results o the other codes. Such a trend can be explained based on the onedimensionality o Picnic. Tough2-EOS9nT overestimates in comparison with the other codes the mass low at rising edge o the breakthrough curves. The reason or that is not yet clear but presumably it is due to the dierent interpolation techniques o the tabular data o the source term. Such an interpolation can be made in many dierent ways, or example as a linear interpolation between two consecutive points or in terms o a step unction in each interval. 6. Conclusions and Outlook The good agreement between the results o the transport o the radionuclides C-14, Ca-41, Cl- 36, Se-79, I-129 can be considered as a successul veriication test o COMSOL as a simulation tool or the saety analysis about a nuclear waste geological repository in an homogeneous rock like clay. Moreover, COMSOL is a very userriendly code that can be used to obtain a quick assessment o a conceptual model or a geological repository to gain insight in how the simulated system works. 7. Reerences 1. COMSOL, Earth Science Module (Comsol Multiphysics 3.3), Comsol AB, COMSOL, Comsol Multiphysics 3.3, User's Guide, Pruess K., Oldenburg C., Moridis G., Tough2 User's Guide, version 2.0, Moridis G.J., Wu Y., Pruess K., EOS9nT, A Tough2 module or the simulation o water low and solute/colloid transport in the subsuraces, Nagra NTB 02-05, Project Opalinus Clay Saety Report Demonstration o Disposal easibility or spent uel; vitriied high-level waste and long-lived intermediate level waste (Entsorgungsnachweis), Kosakowski G., Time-dependent Flow and Transport Calculations or Project Opalinus Clay (Entsorgungsnachweis), PSI-Report 04-10, Sentis M.L., Altorer F., Herort M., Benchmarkberechnungen ür die Simulation der Ausbreitung ausgewählter Nuklide innerhalb von Bentonit- und Opalinustonschichten mit den Rechenprogrammen Tough2-EOS9nT und COMSOL, ENSI-AN-6877, Sentis M.L., Altorer F., Kosakowski G., Benchmark calculations with Tough2-EOS9nT o the transport o radionuclides through clay and bentonite barriers in a geological repository. Proceedings o Tough Symposium Nagra NTB 02-03, Projekt Opalinuston Synthese der geowissenschatlichen Untersuchungsergebnisse - Entsorgungsnachweis ür abgebrannte Brennelemente, verglaste hochaktive sowie langlebige mittelaktive Abälle Tecplot 360, User's Guide. Tecplot, Inc ENSI will use COMSOL in combination with other hydrogeological and transport codes to evaluate the calculations o the implementer Nagra within the sectoral plan in Switzerland that started in In this ramework the code will be tested to be used as a tool or the evaluation o ractured systems and or radionuclide decay chains.

7 Appendix Table 1. Material parameters or the dierent radionuclides used in this benchmark study, (Nagra, NTB 02-06) and (Kosakowski, 2004). Parameter Unit Ca-41 C org -14 Cl-36 I-129 Se-79 Molecular diusion coeicient D 0 m 2 a Decay constant λ a Hal lie T ½ a Bentonite Unit Ca-41 C org -14 Cl-36 I-129 Se-79 Eective porosity φ t Eective diusion coeicient D e m 2 s Distribution coeicient or sorption K s m 3 kg Tortuosity τ Opalinus Clay Unit Ca-41 C org -14 Cl-36 I-129 Se-79 Eective porosity φ t Eective diusion coeicient D e m 2 s Distribution coeicient or sorption K s m 3 kg Tortuosity τ Table 2. Comparison o the maximum values o the release rates or the dierent codes. Nuclide Frac3dvs Picnic Comsol Tough2-EOS9nT Ca C org Se Cl I

Numerical Simulations of Radionuclide Transport through Clay and Confining Units in a Geological Repository using COMSOL

Numerical Simulations of Radionuclide Transport through Clay and Confining Units in a Geological Repository using COMSOL J. Hansmann *1, M. L. Sentis 1, C. Belardinelli 2, B. J. Graupner 1, M. Hugi 1 and