Comparison of two numerical modelling approaches to a field experiment of unsaturated radon transport in a covered uranium mill tailings soil (Lavaugrasse, France).

Journal of Environmental Radioactivity xxx (2015) 1e12

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Comparison of two numerical modelling approaches to a field experiment of unsaturated radon transport in a covered uranium mill tailings soil (Lavaugrasse, France) ^di*, Je ro ^ me Guillevic Zakaria Saa Institut de Radioprotection et de Sûret e Nucl eaire (IRSN), PRP-DGE/SEDRAN/BRN, 31 Avenue de la Division Leclerc, Fontenay-aux-Roses, 92262, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 November 2014 Received in revised form 6 March 2015 Accepted 13 March 2015 Available online xxx

Uncertainties on the mathematical modelling of radon (222Rn) transport in an unsaturated covered uranium mill tailings (UMT) soil at field scale can have a great impact on the estimation of the average measured radon exhalation rate to the atmosphere at the landfill cover. These uncertainties are usually attributed to the numerical errors from numerical schemes dealing with soil layering, and to inadequate modelling of physical processes at the soil/plant/atmosphere interface and of the soil hydraulic and transport properties, as well as their parameterization. In this work, we demonstrate how to quantify these uncertainties by comparing simulation results from two different numerical models to experimental data of radon exhalation rate and activity concentration in the soil-gas measured in a covered UMT-soil near the landfill site Lavaugrasse (France). The first approach is based on the finite volume compositional (i.e., water, radon, air) transport model TOUGH2/EOS7Rn (Transport Of Unsaturated ^di et al., 2014), while the second one Groundwater and Heat version 2/Equation Of State 7 for Radon; Saa is based on the finite difference one-component (i.e., radon) transport model TRACI (Transport de RAdon e; Ferry et al., 2001). Transient simulations during six months of variable rainfall dans la Couche Insature and atmospheric air pressure showed that the model TRACI usually overestimates both measured radon exhalation rate and concentration. However, setting effective unsaturated pore diffusivities of water, radon and air components in soil-liquid and gas to their physical values in the model EOS7Rn, allowed us to enhance significantly the modelling of these experimental data. Since soil evaporation has been neglected, none of these two models was able to simulate the high radon peaks observed during the dry periods of summer. However, on average, the radon exhalation rate calculated by EOS7Rn was 34% less than that was calculated by TRACI, and much closer to the measured one for physically-based soil radon diffusion models. Unlike TRACI, EOS7Rn was able to simulate qualitatively seasonal variations of both radon exhalation and concentration. These results show that EOS7Rn produces less numerical errors than TRACI, and can be considered as a promising model for predicting radon transport in the landfill, if soil evaporation is modelled and its numerical inversion for parameter estimation is realized. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Uranium mill tailings Radon Diffusion Exhalation Modelling Uncertainty

1. Introduction Few modelling studies have been reported in the literature for simulating in-situ experiments of transient two-phase (watereair) flow and radon transport in covered uranium mill tailings soils at landfill sites. Data-model comparison is very complicated because of the need to characterize double porosity media (e.g.,

* Corresponding author. Tel.: þ33 158358898; fax: þ33 146290284. ^di). E-mail address: [email protected] (Z. Saa

macropores) and to construct the local history of climate, hydrology and bio-geo-chemistry of an UMT-landfill site. First transient simulations of unsaturated radon transport in UMT-landfill soils began with the works of Gee et al. (1984), Mayer et al. (1981), Mayer and Gee (1983), and Simmons and Gee (1981) who showed the importance of the long-term moisture content in multidimensional numerical simulations for predicting the longterm radon activity concentration in the soil-gas phase and exhalation from the long-term climatic history of the site. In their works, however, Richards' approximation for the two-phase flow problem has been considered and no data-model comparison has been made.

http://dx.doi.org/10.1016/j.jenvrad.2015.03.019 0265-931X/© 2015 Elsevier Ltd. All rights reserved.

^di, Z., Guillevic, J., Comparison of two numerical modelling approaches to a field experiment of unsaturated Please cite this article in press as: Saa radon transport in a covered uranium mill tailings soil (Lavaugrasse, France), Journal of Environmental Radioactivity (2015), http://dx.doi.org/ 10.1016/j.jenvrad.2015.03.019

^di, J. Guillevic / Journal of Environmental Radioactivity xxx (2015) 1e12 Z. Saa

2

The works of Ferry (2000) and Ferry et al. (2001, 2002) are ones among seldom studies on data-model comparison at transient field conditions. They carried out during four years (from December 1997 to September 2000) experiments of radon transport in two lysimeters, and in an artificial pond filled by covered and uncovered UMT materials to study the cover material (CM) effectiveness on radon mitigation at the surface. These experiments helped them to characterize both materials and to study radon transport in the covered-UMT of the Lavaugrasse landfill site. In their experiments climatic and soil conditions were monitored every half an hour to an hour. For simulating their experimental data, they used the onedimensional (1D) finite difference code TRACI. For the artificial pond experiment, although the shape and scale parameters of the UMT and CM hydraulic properties have been calibrated to account for CM-compaction and UMT-shrinkage (i.e., cracked UMT) during summer periods, TRACI simulations usually showed an overestimation of the transient measured radon exhalation rate at the surface of the covered and uncovered UMT materials. For the uncovered UMT-material experiment, the authors attributed the slight overestimation of measured radon exhalation rates during drainage of water after prolonged rainfall events to the hysteresis effect due to shrinkage and swelling of the UMT-material, which are not taken into account in the model. However, no sensitivity analysis has been performed to choose for the adequate mathematical model of radon diffusion in the unsaturated porous materials. It has been assumed that the well-known Rogers and Nielson (1991a) (RN) empirical formula is valid for these porous materials. ^di (2014), this formula can be However, as demonstrated by Saa unphysical to represent radon transport, especially in shallow subsurface environments. Moreover, there has been no comparison between measured and simulated transient radon activity concentration in the soil-gas for the model discrimination. Additionally, no numerical verification of the model TRACI has been made to conclude about its accuracy in dealing with transient radon transport in layered unsaturated porous materials. As shown in Ferry (2000), even for homogeneous soils, the numerical verification of the transient 1D two-phase flow and radon transport problems was not very convincing, since it was limited to a comparison between TRACI and numerical data from the literature. Other mechanisms like temperature, evaporation and dewing can also be of primary importance for improving the simulation of the radon exhalation rate at the covered UMT-material, but have been neglected in the TRACI-modelling approach. In this study, the artificial pond experiment carried out by Ferry et al. (2002) will serve as a valuable check of the accuracy of model and parameter uncertainty. We aim to demonstrate how the numerical modelling of this experiment can be enhanced when using ^di et al., 2014), with a finite volume numerical model, EOS7Rn (Saa the same hydraulic and radon source properties of the CM and UMT materials and their parameterization, as implemented in TRACI, but with a physically-based three-components diffusion model. 2. Materials and methods

Based on a textural analysis, the CM and UMT layers were characterized as loamy sand and sandy silt soils, respectively. Their hydraulic properties, i.e. their water retention curve and effective unsaturated permeability, were determined from their fine texture and calibration of the two-phase flow problem to measured soil water saturation and capillary pressure. Characterization of the radon source properties of both materials, i.e. determination of their radium activity concentration and emanation coefficient, was carried out by laboratory methods. The first property was measured by g-spectrometry, with a relative measurement uncertainty close to 7 and 25% for CM and UMT-soils, respectively. The radon emanation coefficient was measured by an accumulation technique in 10 dry samples of the CM-soil, whereas that of the UMT was measured by different measurement techniques in dry and wet conditions (Ferry, 2000). The relative measurement uncertainty was close to 20%. Continuous observations of water flow and radon transport in the experimental devices were carried out in situ. Capillary pressures were measured with tensiometers (Jetfill, soilmoisture Corp., USA) at different depths in the UMT- and CM-layers, with a relative measurement error less than 1%. The moisture content in the CMlayer was deduced from permittivity measurements by dielectric probes (HMS 9000, SDEC, France). The probe calibration can result in an absolute error equal to 0.02 m3 m3. Radon concentration in the gas phase of the UMT and CM was measured by a probe using a solid state silicon detector placed in a specially designed measurement chamber (head of BARASOL; Algade, France). The relative uncertainty on the measured radon activity concentration is about 10%. It accounts for measurements errors due to count rate and probe calibration. A data logger monitored all of these measurements every 30 min. Radon flux densities were measured every three hours using an automated accumulation chamber containing an AlphaGUARD (Genitron Instruments, Germany). The detection limit of this apparatus is 10 mBq m2 s1, whereas the relative error is between 20 and 40% for the range of values measured in this experiment. Meteorological data were recorded every half an hour and included rainfall, atmospheric air pressure and temperature, relative air humidity, wind speed and sunshine. 2.2. The mathematical models 2.2.1. TRACI This numerical model (Ferry, 2000; Ferry et al., 2002) uses a fully implicit finite difference numerical method to solve the isothermal 1D-vertical mass conserving equations of the twophase (watereair) Darcy-flow and radon Fick-transport problems. TRACI calculates capillary pressure and moisture content profiles in a soil subject to meteorological conditions, radon concentration in the soil gas-phase and the radon flux at the surface, in relation to time. The two-phase flow problem is formulated by the two following equations governing flow of liquid and gas phases in the soil pores in terms of their respective matric head potentials, hl (m) and hg (m), as dependent variables:

2.1. The experimental pond set-up The small artificial pond (Ferry et al., 2002), with dimensions of 14 m 15 m and height of 1.8 m, is representative of the Lavaugrasse site and was designed to reproduce a UMT disposal facility on a small scale and to study the cover material effectiveness. The radon exhalation rate at the surface was first studied at the surface of a 0.8 m layer of the UMT. A 1 m layer of the cover material, compacted every 0.6 m, was then placed on top of the first layer to study its effect on radon exhalation coming from the UMT.

Cl

vhg vhl vt vt

¼ Ks

v vhl krl 1 vz vz

(1)

! rgo vhg vhg vhl ml v rg krg þ r g Cl ¼ Ks fð1 Sl Þ r g Cl ho vt vt mg vz vz (2) with



hg ¼

Pg Po rl g

(3a)

P Po hl ¼ l rl g ho ¼

(3b)

(3c)

Pc hc ¼ hg hl ¼ rl g

Cl ¼ f

rl g ml

(3d)

(3e)

dSl dhc

(3f)

where Pl and Pg are the liquid and gas-phase pressures (Pa), respectively; Sl is the soil liquid saturation (e); Pc ¼ Pl Pg is the capillary pressure (Pa), a function of Sl (i.e., Pc ðSl Þ), known as the soil water retention curve; Po is a reference pressure (1 bar ¼ 1 105 Pa); the variable hy (y≡l; g; o; c) expresses the matric head potential (m); rl and rg are the liquid and gas densities (kg.m3), respectively; rgo is the gas density at the reference pressure (1.25 kg m3); f is the total soil porosity (e); Cl is the specific water capacity (m1); krl ðSl Þ and krg ðSl Þ are the relative unsaturated permeability of the soil to liquid and gas (e), respectively; ml and mg are the dynamic viscosity of the liquid and gas phase (Pa.s), respectively; Ks is the saturated hydraulic conductivity of the soil (m s1); kp is the scaling parameter of the relative permeability, called also the soil intrinsic permeability (m2); g is the gravitational acceleration constant (9.81 m s2); z is the vertical coordinate positively oriented downward (m); and t is time (s). Eqs. (1) and (2) assume that i) the soil is rigid and isotropic; ii) the liquid density is constant and the gas is ideal; iii) the effect of gravity on the gas-phase flow is ignored; and iv) there is no source or sink term for liquid and gas phases. For given initial hydric profile, liquid and gas pressure or flux boundary conditions, and soil hydraulic properties (i.e., characterization of the relationships Pc ðSl Þ, krl ðSl Þ and krg ðSl Þ), Eqs. (1) and (2) are solved for hb and Sb (b ≡ l, g) (with Sg ¼ 1 Sl ), and thus for the Darcy velocity vb (m s1) for each fluid phase b as follows:

vb ¼ kp

krb vPb ub rb g b≡l; g mb vz

(4)

where ul ¼ 1 and ug ¼ 0, according to the hypotheses for the development of Eqs. (1) and (2), respectively. Follows, then, the solution of the radon transport problem by solving the following equation governing the radon activity concentration in the soil-gas phase CgRn (Bq.m3) as a dependent variable:

v

ðRnÞ Rg Cg

vt

! ðRnÞ

¼

v h ðRnÞ i vCg Dg RN vz vz 226

þ lErd Cs

v

ðRnÞ vg Cg

vz

ðRnÞ

lRg Cg

Ra

(5) with

RN

ðRnÞ ðRnÞ t0 tg ðSl Þ RN dg ¼ f 1 Sl þ Sl KOst

ðRnÞ ðRnÞ Rg ¼ f 1 Sl þ Sl KOst þ rd Kdg ðSl Þ

(6a)

(6b)

ðRnÞ

Po rl g

Ks ¼ kp

h i ðRnÞ Dg

3

where KOst is the dimensionless Ostwald coefficient (e); rd is the ðRnÞ soil dry bulk density (kg.m3); Kdg is the radon surface adsorption coefficient (m3 kg1); l is the radioactive decay of the radon ðRnÞ (2.1 106 s1); ½Dg RN is the average bulk diffusion coefficient of radon in an unsaturated soil (m2 s1), with the subscript RN refers to the Rogers and Nielson (1991a) model for radon diffusion; t0 tg is the dimensionless unsaturated soil tortuosity factor which includes a porous medium dependent factor t0 and a coefficient tg that ðRnÞ depends on the water saturation; dg is the diffusion coefficient of 2 1 radon in free air (m s ); E is the radon emanation coefficient of 226 Ra the soil (e); and Cs is the radium activity of the soil solid matrix (Bq kg1). Eq. (5) assumes that i) radon diffusion in the solid phase is negligible; ii) Henry's law governs the balance between the radon dissolved in the liquid and radon in the gas phase; iii) radon adsorption onto solid surfaces is instantaneous and reversible; iv) radon advection in the liquid phase is low (i.e., vl ¼ 0); and v) radium is almost in the solid matrix. ðRnÞ Once Eq. (5) is solved for Cg given initial radon concentration profile, radon concentration or flux boundary conditions, and soil radon emanation,226diffusion and adsorption properties (i.e., charRa ðRnÞ acterization of Cs and the relationships EðSl Þ, Dg ðSl Þ and ðRnÞ Kdg ðSl Þ), the radon flux density in the gas phase (Bq m2 s1) is calculated according to Fick's law, as follows: ðRnÞ

Fg

i h ðRnÞ ¼ Dg

ðRnÞ

vCg RN vz

ðRnÞ

þ vg Cg

(7)

For a given time step, the solution procedure consists first of ðRnÞ solving Eqs. (1) and (2) for Pl and Pg before solving Eq. (5) for Cg although the three equations are linked via the unknown variable Sl . Solving Eq. (5) independently from Eqs. (1) and (2) for the same time step can lead to significant numerical errors. Hydraulic properties of the soils, i.e. determination of their continuous relationships Pc ðSl Þ, krl ðSl Þ and krg ðSl Þ, are necessary in order to solve Eqs. (1) and (2). The first two properties were modelled by the well-known van Genuchten-Mualem (VG-M) relationships (Mualem, 1976; van Genuchten, 1980), whereas the third property was modelled by Parker et al. (1987) relationship, as follows:

" 1=ð1mVG Þ #mVG Sl Slr Pc Sle ¼ ¼ 1þ Pco ¼ rw g=aVG Sls Slr Pco

krl ðSl Þ ¼

h mVG i2 kl ðSl Þ 1=2 1=m ¼ Sle 1 1 Sle VG kp

krg ðSl Þ ¼

2mVG kg ðSl Þ 1=m ¼ ð1 Sle Þ1=2 1 Sle VG kp

(8)

(9)

(10)

where Sle is the effective soil water saturation (e); subscripts r and s refer to residual and full water saturation; mVG is a dimensionless shape parameter, which is soil texture-dependent; Pco is a scaling pressure parameter (Pa) inversely proportional to the well-known VG-parameter aVG (m1); kl ðSl Þ and kg ðSl Þ are the effective unsaturated permeability of the soil to water and air (m2), respectively. Both aVG and kp are soil structure-dependent parameters. To solve Eq. (5), the three relationships EðSl Þ, ½t0 tg ðSl ÞRN , and ðRnÞ Kdg ðSl Þ were modelled using the well-known Nielson et al.



4

(1982) and Rogers and Nielson (1991a, 1991b) formulas, respectively, as follows:

( E¼

t0 tg

. . Ew Sl S*l þ Ea 1 Sl S*l

if Sl S*l

Ew

elsewhere

RN

ðRnÞ

Kdg

¼ f exp 6fSl 6ðSl Þ14f

ðRnÞ

¼ Kdgo expðbSl Þ

(11)

(12)

4

(14)

t0 tg t0 tg

MQ

¼ f Sg

(15)

7=3 ¼ f1=3 Sg

(16)

ðRnÞ

ðRnÞ

The input parameters dg and KOst are considered constant for a given temperature since of isothermal conditions.

2.2.2. TOUGH2/EOS7Rn ^di et al., 2014) is based The fluid property module EOS7Rn (Saa on the TOUGH2 software capabilities (Pruess et al., 1999) which can handle finite volume numerical problems of non-isothermal, twophase (liquid and gas), five-component (water, brine, radon, tracer, and air) flow and transport in three-dimensional porous and fractured media. The basic mass- and energy balance equations solved by TOUGH2/EOS7Rn can be written in the general form:

d dt

Z Vn

MðkÞ dVn ¼

Z Gn

F ðkÞ $ndGn þ

ðkÞ

k ¼ 1; …; NK

(18)

(19) ðkÞ

where the subscript b refers to the phase gas (g) or liquid (l); Db is the bulk diffusion coefficient of component k in soil fluid phase b ðkÞ (m2 s1); db is the diffusion coefficient of component k in free fluid ðkÞ phase b (m2 s1); and Xb is the mass fraction of component k in phase b (e). By assuming that the transport is 1D, convection and diffusion in liquid phase negligible, the gas phase density rg is constant with space coordinates, and concentration can be written ðkÞ ðkÞ as Cg ¼ rg Xg , Eq. (18) simplifies readily to Eq. (7). For the radon component (k ¼ 3 ¼ Rn), the terms M ðRnÞ and qðRnÞ are given by:

MðRnÞ ¼ f

X b¼g;l

ðRnÞ

Sb rb Xb

ðRnÞ ðRnÞ Xg

þ rd rg Kdg

qðRnÞ ¼ lM ðRnÞ þ uEðSl Þ

226

BU

ðkÞ

with

u ¼ Cs

ðkÞ

rb Xb vb Db rb VXb

(20)

(21)

with

with:

X

ðkÞ ðkÞ Db ¼ fSb t0 tb db

where Ew and Ea are the emanation coefficients at saturation and at dryness (e); S*l is the minimum water saturation on the plateau of ðRnÞ the emanationewater saturation curve; Kdgo is the adsorption coefficient at dryness (m3 kg1); and b is a dimensionless correlation constant, generally lying between 10 and 15 but can be significantly higher. Recently, other bulk diffusion coefficient or tortuosity models have been implemented in the code TRACI to allow more choices and comparison to other codes and experimental data, namely those of Buckingham (1904) (BU) and Millington and Quirk (1961) (MQ):

4≡BU or MQ

F ðkÞ ¼

b¼g;l

(13)

h i ðRnÞ ðRnÞ Dg ¼ fð1 Sl Þ t0 tg 4 dg

The total flux term F ðkÞ is assumed to result from advection and diffusion. It is given, according to Darcy's (Eq. (4)) and Fick's (Eq. (7)) laws, by:

Z

qðkÞ dVn

(17)

Vn

The integration is over an arbitrary subdomain Vn (m3) of the flow system under study, which is bounded by the closed surface Gn (m2); the quantity M appearing in the accumulation term represents mass or energy per volume (i.e. kg m3 or J m3), with k ¼ 1; …; NK (NK ¼ 5) labeling the mass components (water, brine, radon, tracer, air), and k ¼ NK þ 1 the heat “component”; F denotes mass or heat flux vector (kg m2 s1 or J m2 s1); q denotes sinks and sources (kg m3 s1 or J m3 s1); n is a normal vector on surface element Gn , pointing inward into Vn . Vectors in Eq. (17) are written in bold.

Ra

rd

MRn NAv

103

(22)

where MRn is the molecular weight of radon (222 g mol1); NAv is Avogadro's number (6.0221367 1023 mol-1); and u is a constant (kg m3 s1), defined as the total mass of radon produced per unit time in a unit soil volume from radioactive decay of radium; it is reduced by the value of E to accounting for the net production of radon released to the pore space according to the emanation process. A partition phase of radon between liquid and gas phase is assumed according to Henry's law: ðRnÞ ðRnÞ xl

PRn ¼ KH

(23)

where PRn is the partial pressure of Rn (Pa); xRn is the mole fraction l ðRnÞ of the dissolved Rn in the aqueous phase (e); and KH is the Henry's law coefficient (Pa), a dimensional form of the dimenðRnÞ sionless Ostwald coefficient KOst . For the other components (water, brine, tracer, and air), equation for M ðkÞ (k ¼ 1; 2; 4; 5) is similar to that used for radon (Eq. (20)), except that the second term in the right hand side of Eq. (20) is cancelled (no adsorption), and qðkÞ ¼ 0 (k ¼ 1; 2; 4; 5) in Eq. (21) (no sink or source term). Similarly, the heat accumulation term in the two-phase (liquidegas) system is:

MðNKþ1Þ ¼ rd CS T þ f

X b¼g;l

Sb rb ub

(24)

where CS is the specific heat of the soil (J kg1 C1); T is the soil temperature ( C); and ub is specific internal energy of phase b (J kg1). Heat flux includes conductive (Fourier's law) and convective components:



5

Table 1 Initial and boundary conditions applied to the 1D two-layered CM/UMT column for the two numerical experiments #1 and #2. Numerical experiment #

Top boundary condition (surface)

Bottom boundary condition (1.8 m)

Initial condition (INCON)

1

Gas: constant air pressure of 900 mbara Water: zero flux Radon: zero concentration Gas: time-variable atmospheric air pressure (Fig. 1) Water: flux applied by rainfall intensity (Fig. 1) Radon: zero concentration

Gas: constant air pressure of 900 mbar Water: suction of 400 mbar Radon: zero concentration Gas: time-variable atmospheric air pressure (Fig. 1) Water: suction of 400 mbar Radon: zero concentration

Gas: constant air pressure of 974 mbar Waterb: saturation profile after drainage Radonb: concentration profile after drainage idem #1

2

a b

1 mbar ¼ 100 Pa. Calculated by TRACI after a long time-period of water drainage from a saturated soil column.

F ðNKþ1Þ ¼ lT VT þ

X b¼g;l

Hb rb vb

(25)

where lT is the thermal conductivity of the soil (W m1 C1); and Hb is specific enthalpy in phase b (J kg1). Radiative heat transfer according to the StefaneBoltzmann law can also be modeled. Hypotheses behind development of Eq. (5) in the model TRACI are similar to those used for developing the radon transport equation in the model EOS7Rn (Eq. (17) for k ¼ 3 ¼ Rn associated to Eqs. (18)e(23)). Radon convection and diffusion are modelled using Darcy's and Fick's laws (Eq. (18)), adsorption is assumed linear (Eq. (20)), radon decay and emanation are considered as sink and source terms, respectively (Eq. (21)), and solubility in the soil is modelled using the Henry's law (Eq. (23)). However, for the two-phase (watereair) flow problem, Eq. (17) for k ¼ 1; 5 in EOS7Rn is more general than Eqs. (1) and (2) used in TRACI. EOS7Rn assumes that water and air can be as two gaseous components, which can dissolve and diffuse in liquid or gas phases, rather than the main liquid and gas phases, which is physically more realistic. The fact that the heat transfer and brine transport problems can be solved in EOS7Rn, it is possible to modelling water vapor transport in the soil, and studying the effects of temperature and/or water salinity on ^di et al., radon adsorption, diffusion, emanation and solubility (Saa 2014).

The space-discretization of the mass-conservation equations of each component k (Eq. (17)) is carried out using the Integral Finite Difference Method (Oldenburg and Pruess, 1995; Pruess et al., 1999). This numerical discretization method is more conservative than the finite difference method used in TRACI, especially when solving three-dimensional problems. The numerical discretization ^di et al., 2014) in Eq. (21) is the in time of the emanation term (Saa same for the decay term as used by Oldenburg and Pruess (1995), but with a different variable time-weighting parameter to represent either Crank-Nicolson or the fully implicit scheme. Phase appearance and disappearance are well dealt with by EOS7Rn rather than by TRACI. Six primary variables have to be solved for a given single-phase (liquid or gas) condition such as pressure, mass fractions of brine, radon, tracer and air in the single-phase, and temperature; whereas for unsaturated conditions, the six primary variables to be solved for are gas pressure, mass fractions of brine, radon and tracer in liquid phase, gas-phase saturation, and temperature. For a given time-step, all the non-linear equations are solved simultaneously using the NewtoneRaphson iteration method. In addition to the implementation of the model TRACIequations in the model EOS7Rn, such as Eqs. (8)e(16) for representing soil hydraulic properties and main physical properties of radon transport in soils, other equations for modelling these properties have been implemented in EOS7Rn to help studying the uncertainty on the model equations and their parameters. 3. Results and discussions Before comparing the results from both numerical models (i.e., TRACI and EOS7Rn) to experimental data from the experimental

Table 2 Parameters values of the physical, hydrodynamic and radon source properties for the CM and UMT materials (Ferry, 2000; Ferry et al., 2002).

Fig. 1. Rainfall and atmospheric air pressure data considered at the surface boundary of the CM/UMT column in the numerical experiment #2. Data were recorded every hour, from March 15th to April 15th, at the weather station located in the site Lavaugrasse.

Layer

CM

UMT

Thickness (m) Porosity, f (e) Dry bulk density, rd (kg m3) Residual liquid saturation, Slr (e) Full liquid saturation, Sls (e) Intrinsic permeability, kp (1012 m2) VG-M pressure scale parameter, aVG (m1) VG-M shape parameter, mVG (e) 226 Ra Radium-226 mass activity, Cs (kBq kg1) Emanation coefficient at dryness, Ea (e) Emanation coefficient at saturation, Ew (e) Minimum water saturation on the plateau of the emanation-water saturation relationship (Eq. (11)), S*l (e)

1 0.39 (0.07) 1520 (120) 0.1282 (0.08) 1 1.2257 (1.8242) 3.4674 (3.7524) 0.4246 (0.212) 4.7 (0.3) 0.23 (0.05) 0.23 (0.05) e

0.8 0.4 (0.10) 1370 (250) 0.15 (0.1375) 1 0.4086a 1.122 (1.886) 0.1667a 60 (15) 0.05 (0.01) 0.32 (0.06) 0.15

a Calibrated against experimental data to account for the clayey nature and cracking of the UMT.



6

Table 3 The numerical conditions used to solve for EOS7Rn and TRACI solutions.

Space vertical increment (m) Initial time step (s) Minimum time step (s) Maximum time step (s) Time step reduction factor in case of convergence failure (e) Maximum number of Newtonian iterations (e) Convergence criterion for relative error (e) Upstream weighting factor (e) Automatic time step control (e) Interface mobility and permeability weighting scheme (e) Interface liquid and gas diffusivities weighting scheme (e) a b c d e f

TOUGH2/EOS7Rn

TRACI

0.05 0.1 e 1800a 4 8 1.0E-5 1 4b UW, HWc HWe

0.05 1800 1800 1800 1 20 0.01 e e ed ef

Must be less than 0.01 times half-life time of radon, i.e., 3.3 103 s (Oldenburg and Pruess, 1995). Time step size is doubled if convergence occurs within 4 NewtoneRaphson iterations. Mobility upstream weighted (UW); permeability harmonic weighted (HW). Interface mobility affected to the mobility of the grid block (element) above the interface e No interface permeability required. Separate harmonic weighting (HW) of gas and liquid phase diffusivities. Interface diffusivity affected to the diffusivity of the grid block (element) above the interface.

pond, we will first compare between the numerical solutions obtained from each numerical model for some specific initial and boundary conditions. This can help us to draw some conclusions about differences between the models conceptualizations (i.e., oneand three-component diffusion for TRACI and EOS7Rn, respectively) and numerical schemes used to solve for the two-phase flow and radon transport problems formulated by each model (i.e., finite difference and finite volume schemes, for TRACI and EOS7Rn, respectively).

To allow this numerical comparison, the pond was assumed as a 1D-vertical two-layered soil column, with 1 m thickness of the CMlayer over 0.8 m thickness of the UMT-layer. Two numerical experiments were applied to the soil column using different initial and boundary conditions (Table 1). The first one (experiment #1) corresponds to water drainage from the column with a constant air pressure (900 mbar) during one year, while the second one

(experiment #2) corresponds to alternate water infiltration and drainage by considering variable rainfall and atmospheric air pressure during a one month-period (from March 15th to April 15th 2000) at the soil surface (Fig. 1). Rainfall conditions are such that ponding depth could not occur at the surface of the CM-layer. In both numerical experiments the lower boundary (depth 1.8 m) has been assumed at a constant negative pressure of 400 mbar (40000 Pa). Parameters values of hydraulic properties (i.e., parameters of Eqs. (8)e(10)) and radon source properties (i.e., parameters of Eqs. (5), (11) and (22)) of the CM and UMT materials are those obtained by Ferry (2000) and Ferry et al. (2002), and which are also shown in Table 2. Methods of the characterization of these properties are summarized in sub-section 2.1. Adsorption and hysteresis have been neglected. Isothermal conditions were assumed at 25 C. Therefore, the ðRnÞ binary diffusion coefficient of radon in free air dg (Eqs. (6a) and 5 2 1 (14)) was taken equal to 1.1 10 m s in both models, whereas ðRnÞ the Ostwald coefficient KOst (Eqs. (6a) and (6b)) was taken equal to

Fig. 2. Soil water saturation profiles after one year (365 days) of water drainage from the CM/UMT column, calculated from their initial state (INCON) by using EOS7Rn and TRACI for the numerical experiment #1.

Fig. 3. Time-variations of the water saturation at soil depth 0.025 m during one year of water drainage from the CM/UMT column, calculated by using EOS7Rn and TRACI for the numerical experiment #1.

3.1. The numerical comparison TRACI vs EOS7Rn



Fig. 4. Time-variations of the radon exhalation rate at the surface of the cover material during one year of water drainage from the CM/UMT column, calculated by using EOS7Rn and TRACI with the two diffusion models MQ and RN for the numerical experiment #1.

0.2263 in the model TRACI. In EOS7Rn, the binary diffusion coefðRnÞ ficient of radon in free liquid dl (Eq. (19)) was taken to 9 2 1 1.0 10 m s , whereas values of the binary diffusion coefficient of water vapor and air in free liquid and gas phases were assumed identical to those of radon diffusion in free water and air, respectively. Values of Henry's law coefficient for air and radon with ðairÞ ðRnÞ respect to liquid water (i.e., KH and KH in Eq. (23)) were taken 10 equal to 1.0 10 Pa (Default value) and 0.6068 109 Pa (equivðRnÞ alent to KOst ¼ 0.2263), respectively.

Fig. 5. Profiles of radon activity concentration in the soil-gas phase after one year of water drainage from the CM/UMT column, calculated from their initial state (INCON) by using EOS7Rn and TRACI with the two diffusion models MQ and RN for the numerical experiment #1.

7

Fig. 6. Soil water saturation profiles after 31 days of water infiltration and drainage, calculated from their initial state (INCON) by using EOS7Rn and TRACI for the numerical experiment #2.

Simulations were run by using the numerical conditions given in Table 3. These include the numerical parameters such as vertical space meshing (or increments), time stepping, and convergence criteria; and the numerical approximations for inter-nodal (or interface) mobility, permeability, and diffusivity. The CrankNicolson time-weighting scheme for decay and emanation terms has been chosen for EOS7Rn-simulations, whereas a fully implicit time discretization scheme has been chosen for TRACI simulations. Both RN and MQ formulations for radon diffusion in the unsaturated two-layered soil column were considered for the comparison. 3.1.1. The water drainage numerical experiment (experiment #1) For the two-phase flow problem, a good agreement is found between the two numerical water saturation profiles (Fig. 2) at the

Fig. 7. Time-variations of the water saturation at soil depth 0.025 m during 31 days of water infiltration and drainage, calculated by using EOS7Rn and TRACI for the numerical experiment #2.


8


between two grid blocks of the mesh, and consequently on the diffusive radon flux densities. Differences in interface pore gas velocities calculated between the two numerical codes during transient times were not substantial (Sa^ adi, 2011), and could not explain these discrepancies. Small differences were found between convective radon flux densities at interfaces. Note, however, the big difference between radon exhalation rates which can reach a maximum of 3.0 Bq m2 s1 when using different formulations for the unsaturated radon diffusion (i.e., RN and MQ), whatever the numerical solution used (TRACI or EOS7Rn). Because of the small discrepancies found between radon exhalation rates calculated near the equilibrium state, for a given radon diffusion model, small discrepancies are calculated between radon activity concentration profiles at time 365 days (Fig. 5). The small deviations from the initial conditions (INCON) in the case of the RNformulation are obvious, since the initial radon activity concentration profile has been calculated by TRACI using the same formulation (RN) for radon diffusion (Table 1). Calculated radon activity concentration profiles for both MQ and RN formulations are in accordance with the radon exhalation rates calculated. The smaller the radon exhalation rate, the greater the radon activity concentration profile and vice versa. Fig. 8. Profiles of radon activity concentration in the soil-gas after 31 days of water infiltration and drainage, calculated from their initial state (INCON) by using EOS7Rn and TRACI with the two diffusion models MQ and RN for the numerical experiment #2.

final simulation-time 365 days. The water saturation profile simulated by ESO7Rn slightly overestimates the one calculated by TRACI, as it can also be seen in Fig. 3 during transient times near the soil surface at depth 0.025 m (first grid block or element in the mesh). For the radon transport problem, the radon exhalation rate calculated by TRACI overestimates the one calculated by EOS7Rn during the whole simulation period (Fig. 4). Discrepancies can reach a maximum of 1.3 Bq m2 s1 at transient times whatever the unsaturated diffusion (or tortuosity) model used (MQ or RN). As ^di (2011, 2013), these discrepancies are essentially shown by Saa attributed to the small differences in depth soil water saturation between the two codes during transient states, which can have a great impact on the values of the interface diffusion coefficient

Fig. 9. Time-variations of the radon exhalation rate at the surface of the cover material during 31 days of water infiltration and drainage, calculated by using EOS7Rn and TRACI with the diffusion models MQ and RN for the numerical experiment #2.

3.1.2. The water infiltration and drainage numerical experiment (experiment #2) For the two-phase flow problem, only near the soil surface in the CM-layer that a good agreement is found between TRACI and EOS7Rn simulated water saturation profiles after 31 days (Fig. 6). Time-variations of water saturation at depth 0.025 m (Fig. 7) calculated by both numerical codes confirm results shown for water saturation profiles near the soil surface. However, high discrepancies are found near the interface and in the UMT-layer. TRACI simulates water drainage, whereas EOS7Rn simulates an accumulation or retention of the infiltrated water in the UMT-layer. These discrepancies between water saturation profiles explain well differences between radon activity concentration profiles (Fig. 8) and radon exhalation rates (Fig. 9) calculated by both codes for the example of the MQ-diffusion model. The greater the water

Fig. 10. Rainfall and atmospheric air pressure data considered for the simulation of pond experiment. Data were recorded every half an hour from 1st June to 30th November 1999 at the weather station located in the site Lavaugrasse.



9

Table 4 Values of binary diffusion coefficients of gas components (water vapor, radon and air) in liquid and gas phases as well as their corresponding Henry's law (or Ostwald) coefficients with respect to liquid water for the average air temperature of 15 C, at atmospheric air pressure.

Component

T ¼ 15 C

Binary diffusion coefficient (m2 s1)

Henry's law coefficient (109 Pa)

Phase

Liquid (water)

Gas (air)

Liquid (water)

Water vapor Radon Air

1.92E-09 1.25E-09 1.59E-09

2.35E-05 1.03E-05 1.94E-05

e 0.441 8.231

Ostwald coefficient (e)

e 0.3016 e

saturation, the greater the radon activity concentration in the soil gas, the smaller the radon exhalation rate, and vice versa. As discussed in the numerical experiment #1, even smaller differences in soil water saturation can have a great impact on the simulation results of radon transport in the soil profile. The substantial difference between water saturation profiles can be explained by the different numerical approximations used by each code for solving the interface boundary (Table 3) between two constraining porous materials (i.e., CM/UMT interface) during the infiltration process ^di, 2011, 2013). (Saa The model discrimination is difficult to solve for this numerical experiment, since neither analytical nor semi-analytical solutions exist that can solve for the mathematical problem of the transient two-phase flow and radon transport in a 1D two-layered

unsaturated soil column, subjected to heterogeneous initial conditions and time-variable boundary conditions (Table 1). In addition, other numerical trials showed that, under gravity effects on the air-phase flow, the radon exhalation rate calculated using EOS7Rn is reduced by approximately 60 and 66%, for the numerical experiments #1 and #2, respectively, without greatly affecting the calculation of the water saturation profile. Numerical analysis of this mathematical problem is very complicated and difficult to solve, and needs a detailed numerical study, which is beyond the scope of this paper. Now, the question is what is the best numerical model which can predict the radon exhalation rate at the surface of a covered UMT-soil? The only way to answer to this question is to compare both numerical solutions (i.e., TRACI and EOS7Rn) to data from the

Fig. 11. Time-variations of measured and calculated radon activity concentrations at depth 0.25 m. Calculations are made using TRACI and EOS7Rn with the three models of radon diffusion in the unsaturated pond: Rogers and Nielson (1991a) (RN), Buckingham (1904) (BU), and Millington and Quirk (1961) (MQ).

Fig. 12. Time-variations of measured and calculated radon activity concentrations at depth 0.5 m. Calculations are made using TRACI and EOS7Rn with the three models of radon diffusion in the unsaturated pond: Rogers and Nielson (1991a) (RN), Buckingham (1904) (BU), and Millington and Quirk (1961) (MQ).


10


experiment of radon transport in the two-layered pond, which is the subject of the next paragraph. 3.2. Model discrimination: TRACI vs EOS7RN vs pond experiment

free liquid and gas phase, and Henry's law (or Ostwald) coefficient for water vapor, radon and air (Table 4) were input to their measured values, or calculated using suitable empirical relation^di et al., 2014) in the code EOS7Rn for this average air ships (Saa temperature and average atmospheric air pressure (986.84 mbar). Simulations were run for the same time-weighting schemes and numerical conditions shown in Table 3, as discussed in subsection 3.1 for the numerical comparison between TRACI and EOS7Rn solutions. However, here, a sensitivity analysis is performed by testing different unsaturated radon diffusion coefficient models, i.e., RN, BU, and MQ. Effects of radon adsorption, hysteresis, evaporation, dewing, and UMT-shrinkage were considered negligible.

In this subsection our data-model comparison is limited to meteorological and measured radon data available from 1st June to 30th November 1999 when the 0.8 m thickness of the UMT-layer in the pond was only covered by the non-compacted 0.5 m thickness of the CM-soil. Therefore, only measurements of the radon exhalation rate at the surface of the pond and radon activity concentration in the soil-gas at depths 0.25 and 0.5 m are considered in our comparison. Methods of measurements as well as uncertainties on these measurements are summarized in subsection 2.1. The pond was assumed as a 1D two-layered soil column (CM/ UMT) of 1.3 m in length instead of 1.8 m. Atmospheric air pressure and rainfall data, recorded every half an hour at the meteorological station of Lavaugrasse site during this 6-month period (Fig. 10), were considered at the surface boundary condition. The bottom boundary was assumed at constant capillary pressure (400 mbar). Parameters of the equations describing soil hydraulic (Eqs. (8)e(10)) and radon source properties (Eqs. (5), (11), and (22)) are the same given in Table 2. However, isothermal conditions were assumed at the average atmospheric air temperature for the six months period (i.e., 15 C). Therefore, the diffusion coefficient in

3.2.1. Simulation of the measured deptheradon activity concentration As shown in Fig. 11 small differences between radon activity concentrations are calculated by TRACI at depth 0.25 m for the three diffusion models. Whatever the diffusion model used, TRACI overestimates the radon activity measured at this depth. This overestimation confirms results shown in Fig. 8 (case of MQdiffusion model) where we observe that radon activity concentration in the CM-layer simulated by TRACI is higher than that simulated by EOS7Rn. If we exclude the time-period of radon measurements from 15th to 30th September, we see that EOS7Rn improved markedly the simulation of the measured concentrations in both magnitude and time. Neither TRACI nor EOS7Rn was able to

Fig. 13. Time-variations of measured and calculated radon exhalation rates at the surface of the cover material. Calculations are made using TRACI with the three models of radon diffusion in the unsaturated pond: Rogers and Nielson (1991a) (RN), Buckingham (1904) (BU), and Millington and Quirk (1961) (MQ).

Fig. 14. Time-variations of measured and calculated radon exhalation rates at the surface of the cover material. Calculations are made using EOS7Rn with the three models of radon diffusion in the unsaturated pond: Rogers and Nielson (1991a) (RN), Buckingham (1904) (BU), and Millington and Quirk (1961) (MQ).



11

Table 5 Measured and calculated monthly and six-monthly averaged radon exhalation rates at the surface of the cover material. Calculations are made using TRACI and EOS7Rn with the diffusion models MQ and RN. Diffusion model

Radon exhalation rate (Bq m2 s1) TOUGH2\EOS7Rn

TRACI

MQ

1st June e 30th November June July August September October November

RN

Measured

MQ

RN

Mean

SD

Error

Mean

SD

Error

Mean

SD

Error

Mean

SD

Error

Mean

SD

3.42 4.23 3.69 2.58 4.11 3.24 2.70

2.33 1.99 1.61 1.58 2.99 2.72 2.22

0.65 0.95 3.01 0.85 0.10 0.83 0.40

1.82 2.28 2.31 1.53 1.70 1.82 1.26

0.50 0.35 0.42 0.37 0.30 0.25 0.21

2.25 2.90 4.39 1.90 2.51 0.60 1.04

10.04 10.85 10.89 9.50 10.10 9.85 8.98

1.76 1.43 1.55 1.59 1.76 1.57 1.76

5.99 5.67 4.19 6.07 5.89 7.43 6.68

10.62 11.32 11.34 10.16 10.67 10.46 9.71

1.50 1.21 1.33 1.36 1.53 1.31 1.52

6.57 6.14 4.64 6.73 6.45 8.04 7.42

4.07 5.18 6.70 3.43 4.21 2.42 2.30

4.02 3.75 5.40 2.21 4.53 1.85 1.99

simulate peaks of radon activity concentration measured at this depth during this excluded time-period. This can be explained by the failure to account for dew formation in both numerical models. Similar results were obtained for depth 0.5 m (Fig. 12). Little difference was observed between radon activity concentrations calculated by EOS7Rn for the physically-based diffusion models (i.e., BU and MQ), whereas a high underestimation of the measured radon activity concentration was observed for the diffusion model RN. 3.2.2. Simulation of the measured radon exhalation rate For any diffusion model used, neither TRACI nor EOS7Rn was able to simulate peaks of high radon exhalation rates measured during the highest evaporative demand periods of summer (Figs. 13 and 14). For the MQ-diffusion model, EOS7Rn shows a best estimation of low measured radon exhalation rates, as well as prediction of their abrupt changes in time as a result of rainfall and barometric air pressure fluctuations at the surface of the CM-layer (Fig. 14). However, TRACI usually overestimates the measured radon exhalation rates at a nearly constant value in time (Fig. 13), whatever the diffusion model used, and confirms results shown in Fig. 9. For the MQ-diffusion model, less discrepancy is found between mean monthly and six-monthly measured and EOS7Rn-calculated radon exhalation rates (Table 5). The six-monthly averaged radon exhalation rate calculated by EOS7Rn (3.42 ± 2.33 Bq m2 s1) is 34% less than that is calculated by TRACI and much closer to the measured one (4.07 ± 4.02 Bq m2 s1). Failure to account for soil evaporation in EOS7Rn explains the high underestimation of the average measured radon exhalation rate during July. The high underestimation of the average measured radon exhalation rate (Fig. 14) when using the RN-diffusion model in EOS7Rn confirms its nonsuitable use for shallow subsurface environments (Sa^ adi, 2014). 4. Conclusion Comparison of TRACI and EOS7Rn simulation results to the same field radon transport experiment revealed that EOS7Rn is more sensitive to the radon diffusion model chosen and can best simulate transient radon concentration and exhalation rate for physicallybased diffusion models. However, both numerical models fail to simulate the radon exhalation rate during the highest evaporative demand periods. Work is underway for implementing processes at the soil-plant-atmosphere interface in TOUGH2/EOS7Rn, as suggested by soil-vegetation-atmosphere transfer models (e.g., Braud et al., 1995), so as to account for actual soil evaporation and evapotranspiration for bare and cultivated soils, respectively. Moreover, the numerical inversion of EOS7Rn by using iTOUGH2 (Finsterle, 2004) at this stage of data model-comparison became a

necessity in order to avoid time-consuming by hand calibration and validation methods.

References Braud, I., Dantas-Antonino, A.C., Vauclin, M., Thony, J.L., Ruelle, P., 1995. A simple soil-plant-atmosphere transfer model (SiSPAT) development and field verification. J. Hydrol. 166, 213e250. Buckingham, E., 1904. Contributions to Our Knowledge of the Aeration of Soils. Report USDA, Bureau of Soil Bull. No. 25. U.S. Government Printing Office, Washington, DC. , M.-C., 2002. Evaluation of the effect of a cover Ferry, C., Richon, P., Beneito, A., Robe layer on radon exhalation from uranium mill tailings: transient radon flux analysis. J. Environ. Radioact. 63 (1), 49e64. , M.-C., 2001. Radon exhalation from uranium Ferry, C., Richon, P., Beneito, A., Robe mill tailings: experimental validation of a 1-D model. J. Environ. Radioact. 54 (1), 99e108. Ferry, C., 2000. La migration du radon 222 dans un sol. Application aux stockages sidus issus de traitement des minerais d'uranium. Ph.D. Dissertation. Paris des re XI (Orsay) University, Paris, 173pp. Finsterle, S., 2004. Multiphase inverse modeling: review and iTOUGH2 applications. Vadose Zone J. 3 (3), 747e762. Gee, G.W., Nielson, K.K., Rogers, V.C., 1984. Predicting Long-term Moisture Contents of Earthen Covers at Uranium Mill Tailings Sites. DOE/UMT-D220 (PNL-5047) report. Pacific Northwest Laboratory, Richland, Washington, 54pp. Mayer, D.W., Gee, G.W., 1983. Multidimensional Simulation of Radon Diffusion through Earthen Covers. DOE/UMT-0212 (PNL-4458) report. Pacific Northwest Laboratory, Richland, Washington, 23pp þ Appendices. Mayer, D.W., Oster, C.A., Nelson, R.W., Gee, G.W., 1981. Radon Diffusion Multilayer Earthen Covers: Models and Simulations. DOE/UMT-0204 (PNL-3989) report. Pacific Northwest Laboratory, Richland, Washington, 55pp. Millington, R.J., Quirk, J.M., 1961. Permeability of porous solids. Trans. Faraday Soc. 57 (7), 1200e1207. Mualem, Y., 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12 (3), 513e521. Nielson, K.K., Rogers, V.C., Mauch, M.L., Hartley, J.N., Freeman, H.D., 1982. Radon emanation characteristics of uranium mill tailings. In: Uranium Mill Tailings Management-V. Colorado State University, Fort Collins, pp. 335e368. Oldenburg, C., Pruess, K., 1995. EOS7R: Radionuclide Transport for TOUGH2. Report LBL-34868. Lawrence Berkeley National Laboratory, Berkeley, California, USA, 54pp. Parker, J.C., Lenhard, R.J., Kuppusamy, T., 1987. A parametric model for constitutive properties governing multiphase flow in porous media. Water Resour. Res. 23 (4), 618e624. Pruess, K., Oldenburg, C., Moridis, G.J., 1999. TOUGH2 User's Guide, Version 2.0. Report LBNL-43134. Lawrence Berkeley National Laboratory, Berkeley, California, USA, 197pp. Rogers, V.C., Nielson, K.K., 1991a. Correlations for predicting air permeabilities and 222 Rn diffusion coefficients of soils. Health Phys. 61 (2), 225e230. Rogers, V.C., Nielson, K.K., 1991b. Multiphase radon generation and transport in porous materials. Health Phys. 60 (6), 807e815. ^di, Z., Gay, D., Guillevic, J., Ame on, R., 2014. EOS7RndA New TOUGH2 module for Saa simulating radon emanation and transport in the subsurface. Comput. Geosci. 65, 72e83. ^di, Z., 2014. On the air-filled effective porosity parameter of Rogers and Nielson's Saa (1991) bulk radon diffusion coefficient in unsaturated soils. Health Phys. 106 (5), 598e607. ^di, Z., 2013. Numerical verification and experimental validation of the Saa TOUGH2/EOS7Rn module for non-isothermal radon transport in two-phase lisation Mathe matique et Sciporous and fractured media. In: MoMaS (Mode entifique) Multiphase Abstracts 2013, Oral Communication, Seminar Days.


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Institut des Hautes Etudes Scientifiques IHES. Bures-sur-Yvette, France, 7-9 October, 2013. ^di, Z., 2011. Adaptation de TOUGH2 a la mode lisation de l'e manation et de Saa s. De veloppement du nouveau transport du radon dans les sols non-sature Nucle aire module TOUGH2/EOS7Rn. Institut de Radioprotection et de Sûrete (IRSN). PRP-DGE/SEDRAN/BRN, Technical Report, 90pp. þ Appendices, December 2011.

Simmons, C.S., Gee, G.W., 1981. Simulation of Water Flow and Retention in Soil Layers Overlying Uranium Mill Tailings. DOE/UMT-0203 (PNL-3877). Pacific Northwest Laboratory, Richland, Washington, 78pp. þ Appendices. van Genuchten, M.Th, 1980. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892e898.


Attenuation of radon flux from uranium mill tailings by consolidation.

Radon emanation from backfilled mill tailings in underground uranium mine.

Ecological aspects of microorganisms inhabiting uranium mill tailings.

Uranium in vitro bioassay action level used to screen workers for chronic inhalation intakes of uranium mill tailings.

Radionuclides distribution, properties, and microbial diversity of soils in uranium mill tailings from southeastern China.

Comparison of unsaturated flow and solute transport through waste rock at two experimental scales using temporal moments and numerical modeling.

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Dynamics of soil water evaporation during soil drying: laboratory experiment and numerical analysis.

A comparison of two approaches to sciatic nerve block.

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Vertical transport and plant uptake of nanoparticles in a soil mesocosm experiment.

Field comparison of several commercially available radon detectors.

Splitting failure in side walls of a large-scale underground cavern group: a numerical modelling and a field study.

TRANSPORT AND FATE OF AMMONIUM AND ITS IMPACT ON URANIUM AND OTHER TRACE ELEMENTS AT A FORMER URANIUM MILL TAILING SITE.

Characterization of long-lived radioactive dust in uranium mill operations.

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A comparison of two collapsing methods in different approaches.

Sensitivity Analysis and Validation for Numerical Simulation of Water Infiltration into Unsaturated Soil.

A replicated climate change field experiment reveals rapid evolutionary response in an ecologically important soil invertebrate.

Uranium and radon in private bedrock well water in Maine: geospatial analysis at two scales.

Indirect Reciprocity; A Field Experiment.

A Two-Dimensional Numerical Investigation of Transport of Malaria-Infected Red Blood Cells in Stenotic Microchannels.