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Groundwater flow and radionuclide transport models for groundwater pathway analyses for ESS ESS-0051622

Name

Role/Title

Dmitri Bugai

Senior Consultant

Thomas Hjerpe

Senior Consultant, Facilia AB

Reviewer

Daniela Ene

Senior scientist, EHS division, ESS

Approver

Peter Jacobsson

Head of EHS division, ESS

Owner

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DOCUMENT REVISION HISTORY Revision Reason for and description of change

Author

Date

1

First issue

Dmitri Bugai

2016-02-05

1.1

Approved by Facilia

Rodolfo Avila, Facilia AB 2016-02-15

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TABLE OF CONTENT

PAGE

DOCUMENT REVISION HISTORY ....................................................................... 2 1.

GROUNDWATER FLOW MODEL .......................................................... 6

1.1.

Introduction ....................................................................................... 6

1.2.

Groundwater flow domain: physical dimensions, layering and numerical grid.............................................................................. 6

1.3.

Hydraulic parameters and boundary conditions ................................. 9

1.4.

Example of simulation results ........................................................... 12

2.

RADIONUCLIDE TRANSPORT MODEL ................................................ 14

2.1.

Introduction ..................................................................................... 14

2.2.

Conceptual transport model and its realization using Normalysa library for Ecolego 6 ........................................................ 15

2.3.

Mathematical model ........................................................................ 20

3.

REFERENCES ..................................................................................... 22

ANNEX 1. THE NORMALYSA MODEL FOR AQUIFER TRANSPORT .................... 24 A1.1. Model purpose ...................................................................................... 24 A1.2. Model applicability ................................................................................ 25 A1.3. Model components ............................................................................... 26 A1.4. Mathematical models for State variables .............................................. 41 A1.5. Mass balance equation for Media ......................................................... 45 ANNEX 2. THE NORMALYSA MODEL FOR AQUIFER MIXING ........................... 47 A2.1. Model purpose ...................................................................................... 47 A2.2. Model applicability ................................................................................ 48 A2.3. Model components ............................................................................... 49 A2.4. Mathematical models for State variables .............................................. 62 A2.5. Mass balance equation for Media ......................................................... 65 ANNEX 3. THE NORMALYSA MODEL FOR CONTAMINATED SOIL LAYER ......... 66 A3.1. Model purpose ...................................................................................... 66 Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015

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A3.2. Model applicability ................................................................................ 67 A3.3. Model components ............................................................................... 68 A3.4. Mathematical models for State variables .............................................. 80 A3.5. Mass balance equation for Media ......................................................... 82 ANNEX 4. THE NORMALYSA MODEL FOR A WELL ........................................... 83 A4.1. Model purpose ...................................................................................... 83 A4.2. Model applicability ................................................................................ 84 A4.3. Model components ............................................................................... 84 A4.4. Mathematical models for State variables .............................................. 86

LIST OF TABLES Table 1 .... Hydraulic parameter values for the 2D cross sectional groundwater flow model for the proton LINAC tunnel............................................................. 10

LIST OF FIGURES Figure 1... The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel (not to scale). ............................................... 7 Figure 2... The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel (Vertical exaggeration = 10). ........................ 8 Figure 3... The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel....................................................................... 8 Figure 4... Boundary conditions for the 2D cross sectional groundwater flow model for the proton LINAC tunnel (Vertical exaggeration = 10). ........................ 9 Figure 5... Scheme illustrating the water balance for the lower aquifer layer. .................... 11 Figure 6... Example simulation results for the 2D cross-section model for the proton LINAC tunnel (Vertical exaggeration = 10). Green arrow heads along the groundwater flow pathline corresponds to the travel time of 365 days. .............................................................................................................. 13 Figure 7... Conceptual model of radionuclide transport process to groundwater from the proton LINAC tunnel. ............................................................................ 17 Figure 8... Ecolego interaction matrix for the radionuclide transport model. ..................... 18

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Figure 9... Ecolego interaction matrix for the ‘Activated Soil Source Term’ subsystem. ........................................................................................................... 19

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1.

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GROUNDWATER FLOW MODEL

This section describes the groundwater flow model that is used in this project for simulating groundwater flow processes in the vicinity of the proton LINAC tunnel.

1.1.

Introduction

The groundwater flow model employs a 2D cross-sectional groundwater schematization of the flow from the tunnel to a well, which is briefly described in the assessment context report (Avila et al., 2015). The groundwater flow schematization, numerical implementation of the model and relevant hydraulic parameters will be presented in more detail in the following sections of this report. The numerical groundwater flow model is implemented using the MODFLOW computer code (McDonald and Harbaugh, 1983). MODFLOW is the USGS's finite-difference groundwater model1. Being extensively used, verified and validated over the last three decades in numerous industrial and research applications, MODFLOW is currently considered an international standard for simulating and predicting groundwater flow conditions (McDonald and Harbaugh, 2003). The MODPATH particle tracking postprocessing package for MODFLOW (Pollock, 1994) is used for groundwater flow net analyses. To facilitate input of parameters and visualization of MODFLOW simulation results the GUI pre-/post processing software Visual Modflow is used in this report (Guiger and Franz, 1996).

1.2.

Groundwater flow domain: physical dimensions, layering and numerical grid

A schematic groundwater flow domain for the 2D cross-sectional groundwater flow model is shown in Figure 1. This scheme is generally similar to the conceptual model in Figure 2-3 in (Huutoniemi and Nordlinder, 2014). The model assumes steady state groundwater flow regime. Dimensions and absolute elevation marks of different geological layers are based on information and data presented in (Huutoniemi and Nordlinder, 2014; Moller et al. 2013, Moller and Sundlof, 2013). A comparison of hydrogeological and hydraulic parameters of soil layers used in the ESS groundwater pathways assessment report ESS-0000025 (Huutoniemi and Nordlinder, 2014) and for groundwater transport analyses in the report ESSS-0005205 (Moller at al., 2013) was carried out by (Moller and Sundlof, 2013), and has shown that both studies used a generally consistent set of parameter values with relatively minor differences in hydraulic parameters.

1

http://water.usgs.gov/ogw/modflow/

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Based on data presented in (Huutoniemi and Nordlinder, 2014; Moller et al. 2013, Moller and Sundlof, 2013) the upper part of the soil profile at the site (including upper portion of the aquifer) is composed of relatively low permeability clay till material (hydraulic conductivity 10-8 – 10-6 m s-1), while the lower part of the aquifer is a sandy intermoraine sediment layer and underlying boundary fissured zone of bedrock is composed of a higher conductivity deposits (10-6 to 10-4 m s-1). Similarly to the schematization of (Huutoniemi and Nordlinder, 2014) we assume that this deeper higher permeability ‘sandy sediment’ layer has a combined thickness of 2 m (see Figure 1). The numerical grid of the MODFLOW 2D cross sectional model is shown in Figure 2. The horizontal (X axis) size of the flow domain is 350 m. The tunnel is situated in the interval from X= 45 m to X=50 m. The downstream (right hand side) boundary is set at 300 m distance from the tunnel (X=350 m). The upstream (left) boundary (X=0) is situated at 45 m distance from the tunnel. The size of the flow domain along the vertical coordinate (Z axis) is 11 m, which corresponds to interval from Z=70 m to Z=81 m. The lower layer (higher permeability “sand”) is situated in the range from Z=70 to 72 m. The upper aquifer layer (clay till) is situated in the range from Z=72 to 81 m. The numerical grid spacing in X direction (horizontal) ranges from 1 m to 0.5 m. A finer numerical grid was set in the close vicinity of the tunnel (see Figure 3). The numerical grid spacing in Z direction (vertical) was set to 0.5 m.

Figure 1

The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel (not to scale).

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Figure 2

The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel (Vertical exaggeration = 10).

Figure 3

The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel.

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1.3.

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Hydraulic parameters and boundary conditions

The boundary conditions for the groundwater flow model are illustrated in Figure 4. First order boundary conditions (prescribed hydraulic head values) were set for the lower aquifer unit. The boundary conditions at upstream (X1=0) and downstream (X2=350 m) boundaries were set based on the assumptions that the design value of the hydraulic head in the vicinity of the tunnel (Xt=50 m) is Ht=75 m (Moller et al. 2013, p.7) and that the horizontal hydraulic head gradient in the aquifer equals i=0.013 (Moller et al. 2013, p.13). Then the hydraulic head value at the upstream and downstream boundaries can be calculated as follows: Hk = Ht - (Xk-Xt)*i (k=1,2) Calculated values of the hydraulic head at corresponding boundaries are listed in Table 1. Table 1 lists also other hydraulic parameter values for the 2D cross sectional groundwater flow model (for the proton LINAC tunnel for the upper and lower aquifer layers), which were used to set up the model. These data are derived from the summary parameters tables presented in (Moller and Sundlof, 2013; Tables 4 and 5, p.9), and represent best guess parameter estimates based on the understanding of the site by the authors of this report. Sensitivity of the groundwater flow and radioactive contaminant transport model predictions to various parameter values and assumptions will be analysed at the next steps of this project.

Figure 4

Boundary conditions for the 2D cross sectional groundwater flow model for the proton LINAC tunnel (Vertical exaggeration = 10).

An important model parameter is the hydraulic conductivity value for the lower (higher permeability) aquifer unit. This parameter in previous analyses was treated as a highly uncertain parameter with the estimated range from 10-5 to 10-3 m/s in (Huutoniemi and Nordlinder, 2014), and from 10-6 to 10-4 m/s in (Moller et al. 2013).

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Table 1

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Hydraulic parameter values for the 2D cross sectional groundwater flow model for the proton LINAC tunnel.

Parameter

Unit

Value

Reference / Remark

Hydraulic head gradient in the lower unit

unitless

0.013

(Moller et al. 2013, p.13)

Infiltration recharge rate

m/y

0.1

(Moller et al. 2013, p.8-9)

Hydraulic head at upstream boundary (lower aquifer unit)

m

75.65

Calculated in this report

Hydraulic head at downstream boundary (lower aquifer unit)

m

71.10

Calculated in this report

Hydraulic conductivity

m/s

1.0E-7

(Moller and Sundlof , 2013, p.9)

Bulk density

kg/m3dw

2.0

(Moller and Sundlof , 2013, p.9)

Effective porosity, %

unitless

0.05

(Moller and Sundlof , 2013, p.9)

Hydraulic conductivity

m/s

5.0E-5

Calculated in this report from water balance; resulting value consistent with (Moller and Sundlof , 2013, p.9)

Bulk density

kg/m3dw

1.65

(Moller and Sundlof , 2013, p.9)

Effective porosity, %

unitless

0.2

(Moller and Sundlof , 2013, p.9)

Hydraulic parameters of the upper aquifer (“clay till”)

Hydraulic parameters of the lower aquifer (“sand”)

We have carried out simple balance calculations to constrain the hydraulic conductivity of the lower aquifer unit (Kf) based on known infiltration recharge rate to the lower aquifer (Infiltration_rate), the linear size of the watershed (Lw) and the hydraulic head gradient at the outflow boundary (i). Balance calculations are illustrated by the scheme in Figure 5.

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Figure 5

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Scheme illustrating the water balance for the lower aquifer layer.

The following balance equation has to be satisfied: Infiltration_rate * Lw = Haq * Kf *i Based on the above equation the hydraulic conductivity of the lower aquifer unit can be calculated as: 𝑲𝒇 =

𝑰𝒏𝒇𝒊𝒍𝒕𝒓𝒂𝒕𝒊𝒐𝒏_𝒓𝒂𝒕𝒆 × 𝑳𝒘 𝑯𝒂𝒒 × 𝒊

Assuming that the infiltration rate is 100 mm/y, the hydraulic head gradient is i=0.013, Haq=2 m, and the linear size of the watershed is some 350-450 m (Huutoniemi and Nordlinder, 2014; Moller et al. 2013), the hydraulic conductivity of the lower aquifer layer can be estimated at Kf = 4.4…5.5E-5 m/s. This estimate is consistent with the previously estimated range for this parameter in the cited above reports on the hydrogeology of the study site. The Kf value of 5.0E-5 m/s was used in this report as an initial ‘best guess estimate’ to set up the groundwater flow model.

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1.4.

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Example of simulation results

Example of groundwater simulation results using input parameter values listed in Table 1 are shown in Figure 6. The figure shows equipotential lines of the hydraulic head (blue lines) and also the groundwater pathline (green) for a particle placed near the basement of the proton LINAC tunnel (in the supposed zone of activated soil). Green arrow heads along the groundwater flow pathline corresponds to a travel time of 365 days. It can be seen that the flow direction in the upper clay till layer is nearly vertical while the flow in the lower sandy aquifer layer is sub-horizontal. For the considered groundwater pathline, the water travel time from the activated soil layer in clay till to the lower confined sand unit is estimated at 4 years, while the water travel time in the lower aquifer unit is estimated at ~ 3.25 years (from the aquifer area below the tunnel zone to the downstream boundary of flow domain where the water well is supposedly located). Based on the above data, the travel time of retarded species can be easily estimated. For example, if we assume that for Na-22,which is an important activation product of radiological concern with half-life of 2.6 y (Ene, 2015), the Kd for sand equals 1.3 l/kg (Huutoniemi and Nordlinder, 2014; Table 2-3 at p.10), the corresponding retardation factor is R=11.7 and the subsurface travel time of Na-22 to a well in the sand aquifer can be estimated at 38 years (~ 14 decay half-lives). This indicates that radiological impact from this radionuclide likely will be low; as a consequence of radioactive decay during transport. Systematic analyses of travel times for different activation products and sensitivity analyses of model predictions to various parameter values and assumptions will be carried out at the next steps of this project.

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Figure 6

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Example simulation results for the 2D cross-section model for the proton LINAC tunnel (Vertical exaggeration = 10). Green arrow heads along the groundwater flow pathline corresponds to the travel time of 365 days.

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2.

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RADIONUCLIDE TRANSPORT MODEL

This section of the report describes the radionuclide transport model for simulating radioactive contaminant transport processes from the proton LINAC tunnel to a water well.

2.1.

Introduction

The radionuclide transport model uses information on water fluxes and flow rates in the subsurface in the vicinity of the proton LINAC tunnel calculated by means of MODFLOW groundwater flow model described in the previous section of this report. The radionuclide transport model was developed using the Ecolego 6 software (Avila et al., 2005). Ecolego2 is a software package developed by Facilia AB for implementing deterministic and stochastic dynamic models described by first order ordinary differential equations. To implement the radionuclide transport model for the proton LINAC tunnel we used the NORMALYSA3 model library for Ecolego 6 developed in the frame of IAEA MODARIA4 (Modelling and Data for Radiological Impact Assessments) project WG-3 activities. The NORMALYSA software tool is designed for radiological safety assessment purposes, and it incorporates a library of generic models for Ecolego 6 organized in four different sub-sets: Source Term, Transport, Receptor and Dose Modules (e.g., models described in the IAEA SRS-19 report (IAEA, 2001)), as well a database of default model parameter values based on reputable sources (e.g., IAEA TRS-472 report (IAEA, 2010)). The NORMALYSA tool was extensively tested, verified and benchmarked in the frame of the IAEA MODARIA WG-3 activities, in particular by comparing it to RESRAD tool5 for a set of a test cases. A number of pre-programmed NORMALYSA source-term and groundwater transport models were used to model relevant elements of the LINAC tunnel radionuclide transport model. The schematization of radionuclide (activation product) transport process to groundwater from the proton LINAC tunnel, implementation of the transport model in Ecolego 6 using NORMALYSA library and relevant transport parameters will be presented in more detail in the following sections of this report.

2

http://ecolego.facilia.se/ecolego/ http://project.facilia.se/normalysa/software.html 4 http://www-ns.iaea.org/projects/modaria/ 5 https://web.evs.anl.gov/resrad/ 3

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2.2.

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Conceptual transport model and its realization using Normalysa library for Ecolego 6

Conceptual model The conceptual model of radionuclide (activation product) transport from the proton LINAC tunnel to the groundwater is shown in Figure 7. The model simulates the radionuclide transport processes from the contaminant source term (soil layer surrounding the tunnel containing activation products) in the aquifer cross section, and its structure is coherent with the MODFLOW model described in the previous section of this report. The source term of radioactivity, is a soil layer of about 1 m thickness surrounding the tunnel, which contains activation products (Huutoniemi and Nordlinder, 2014). The activated soil surrounding the tunnel is sub-divided within the model into several sublayers (see Figure 7): bottom layer, side layers, and top layer. The bottom soil layer can be situated in partially or fully water saturated soil conditions (the elevation of the bottom of the tunnel is 74.7 m (Moller and Sundlof, 2013), while the design value of hydraulic head in the vicinity of the tunnel is 75 m (Moller et al. 2013, p.7)). The side layers and top layer of soil are in unsaturated conditions. It is assumed that activation products can be leached from the soil layers in unsaturated conditions by infiltration of atmospheric precipitations. The radioactive contaminants leached from the unsaturated soil zone infiltrate to the saturated soil zone (the “bottom layer” of soil). The radionuclides are further mobilized from the “bottom layer” of soil (situated in the saturated zone) by the groundwater flow in the aquifer. The leaching rate is determined from groundwater flow modeling using the MODFLOW- based model of site. To simulate radionuclide leaching from the different soil layers described above we use the ‘Contaminated Soil Without Layer’ model from the ‘Sources’ library of NORMALYSA employing the soil leaching model described in (Baes and Sharp, 1983). This model assumes that all radionuclide inventories in the contaminated soil layer are in mobile (exchangeable) form, and that the radionuclide partitioning between the soil porous solution and soil matrix is described by the Kd model. The mathematical equations of the model will be presented below in Section 2.3. Radionuclides leached from contaminated soil zone surrounding the tunnel are first transported by groundwater flow in the relatively low permeability clay till layer towards the confined sand layer, situated in the bottom part of the aquifer (see Figure 7). Based on simulation of hydrogeological conditions, using the MODFLOW-based 2D cross-sectional groundwater flow model, the flow in the clay till layer occurs in vertical downward direction.

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To simulate the radionuclide transport in the clay till later we used the ‘Aquifer Transport’ module from the NORMALYSA library, which was appropriately configured to model this layer. This module simulates radionuclide transport along the flow path in the aquifer. It accounts for the advection, dispersion, radioactive decay and sorption process (using the Kd model). This module employs the ‘Transport’ block of Ecolego 6 to simulate contaminant migration in groundwater. Mathematical models and expressions for advective and dispersive transfer coefficients are presented in section 2.3. The radionuclide transport process in the confined sand layer were simulated using the ‘Aquifer Mixing’ and ‘Aquifer Transport’ modules from the NORMALYSA library, which were configured to model the sand aquifer unit. The ‘Aquifer mixing’ module simulates the aquifer zone within the confined sand layer immediately below the tunnel, where contaminated infiltration flux from the clay till layer mixes with the horizontal groundwater flow in the confined sand aquifer unit. The subsequent ‘Aquifer Transport’ module simulates the radionuclide transport by advection dispersion process towards a water well situated at a 300 m distance from the contaminant source, taking into account retardation due to sorption.. The radionuclide t concentration in well water is modeled using the ‘Well’ module from the ‘ ‘NORMALYSA’ library. The ‘Well’ module calculates radionuclide concentration in groundwater pumped by a water-well using a simple mixing model. It is assumed that some fraction of the well debit is formed by contaminated groundwater from the flow tube originating from the contamination source-term, while another part of well debit is formed by non-contaminated groundwater.

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Figure 7

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Conceptual model of radionuclide transport process to groundwater from the proton LINAC tunnel.

Realization of the radionuclide transport model in Ecolego 6 using NORMALYSA library The structure of radionuclide transport model in the format of Ecolego interaction matrix is shown in Figure 8. It shows the main sub-systems (sub-models) of the overall transport model and data exchanges between these sub-models.

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Figure 8

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Ecolego interaction matrix for the radionuclide transport model.

For the ‘Aquifer Transport (Clay till)’, ‘Aquifer Mixing’, ‘Aquifer Transport (Sand)’, and ‘Well’ sub-systems we used the corresponding modules from the NORMALYSA model library (see previous paragraph). Descriptions of the NORMALYSA modules are given in annexes to this report. Data exchanges between different modules take place in the form of radionuclide activity fluxes. The radioactivity flux, Activity_Flux, (Bq/y) is calculated in a general case using the following expression: Activity_Flux = Water_Flux * Cgw where Water_Flux (m3/y) is groundwater flux from the respective compartment, and Cgw (Bq/m3) is radionuclide concentration in out-flowing groundwater. Radionuclide concentration in groundwater is calculated within the corresponding sub-system in accordance with the mathematical groundwater transport model. Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 18 (86)

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Inflowing and out-flowing water flux values, for specific sub-regions of the groundwater flow model (e.g., for activated soil layers; clay till layer, confined sand layer), were calculated using the MODFLOW–based groundwater flow model. To calculate water budgets for specific sub-regions of the overall groundwater flow model the ZONEBUDGET subroutine (Harbaugh, 1990) for MODFLOW was used. The Ecolego interaction matrix for the ‘Activated Soil Source Term’ subs-system is shown in Figure 9. The activated soil layer surrounding the tunnel was sub-divided into two compartments – ‘Activated Soil – Bottom’ (layer) and ‘Activated Soil – Side’ layers. The inventory of radioactivity in the top layer directly above the tunnel (see Figure 7) is conservatively included to the ‘Activated Soil – Sides” compartment.

Figure 9

Ecolego interaction matrix for the ‘Activated Soil Source Term’ subsystem.

To simulate the activated soil compartments described above we use the ‘Contaminated Soil Layer’ model from the NORMALYSA library. A description of this module is given in the Annex 3 to this report.

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The production of activation elements within the soil layers surrounding the tunnel is modeled as Ecolego ‘Transfer’ blocks6,where the corresponding activity production rates (in Bq/y) are specified as parameters. It was assumed that activation element production rates within the specific soil layer (Qi) are proportional to the volume of this layer (Vi), so that the following equation holds: Qi = Qtotal * Vi /Vtotal Where Qtotal is the integral activation element production rate in activated soil in the vicinity of the proton LINAC tunnel, and Vtotal is the total volume of soil surrounding the tunnel, where activation process are taking place. Soil volume values for specific layers and total volume can be easily calculated based on the information on the assumed system geometry shown at Figure 1. The Qtotal values can be found, for example, in (Ene, 2010).

2.3.

Mathematical model

This sub-section of the report presents main mathematical expressions, which are used to model radionuclide transfers (fluxes) between different model compartments. Radioactivity source term To simulate radionuclide leaching from contaminated soil layer we use the soil leaching model described in (Baes and Sharp, 1983), which is commonly used in safety assessment analyses of radioactive waste repositories (IAEA, 2004a,b). The leaching rate from contaminated soil layer is defined by leaching (transfer) coefficient:

leach

w H w Rw Rw 1 K d ,w , w

,

where the following notation is used: - infiltration recharge (or flow) rate through the soil layer (m/y), w - water content in the soil layer (unitless), Hw - thickness of contaminated soil (waste) layer (m), Rw – sorption retardation coefficient in the soil layer (unitless), w – soil bulk density (kg/dm3), Kd,w – sorption distribution coefficient of soil(l/kg). Transfer coefficients for advective and dispersive transport The following well-known expressions were used to model advective-dispersive transport of radionuclides in the “distributed source” soil layer, unsaturated zone and aquifer (e.g., IAEA, 2004b, p.270). Advective transfer coefficient in the aquifer (ad,aq)

6

http://ecolego.facilia.se/ecolego/show/Transfer

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ad ,aq

V n dX Raq

aq Raq 1 K d ,aq

,

where the following notation is used: V – Darcy velocity (flow rate) in the aquifer (m/y), n – aquifer porosity (unitless), dX –size of compartment in the aquifer along the flow path (m), Raq – sorption retardation coefficient in the aquifer (unitless), aq –bulk density of the aquifer (kg/dm3), Kd,aq – sorption distribution coefficient of the aquifer (l/kg). Dispersive transfer coefficient in the aquifer (dis,aq)

dis ,aq

aq V n dX 2 Raq

,

Where aq – is dispersivity parameter for transport in the aquifer (m). Notations of other parameters are same as in previous formulas. Dispersivities (hydro-dispersion coefficients) An important parameter in the groundwater transport calculations is the ydrodynamic dispersion coefficient (D): D = V, Where V is the groundwater flow velocity (m/y), and is the dispersivity parameter (m). Measuring the dispersivity coefficient in-situ is a difficult experimental task, and the most practical approach is to use literature data for the parameter. It is known, that dispersivity is a scale-dependent parameter, which increases with increasing scale of the groundwater transport (Gelhar et al., 1992). A simple general approximation that is frequently used is that is set to the one-tenth of the scale of the problem (Walton, 1998; IAEA, 2004a): = 0.1 L, where L is groundwater travel distance (m). This formula is currently used in the NORMALYSA module library to define the default dispersivity values for aquifer transport modeling.

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REFERENCES

Avila, R., Broed, R., Pereira, A. (2005). ECOLEGO - A toolbox for radio ecological risk assessment, Proceedings of the International Conference on the Protection from the Effects of Ionizing Radiation’’, IAEA-CN-109/80. Stockholm: International Atomic Energy Agency. 229 - 232 Avila R., Hjerpe T., Windmark F., Ene D. (2015). Estimation of the Dose Factors for Updating the EES Environmental Impact Analysis Report. Assessment Context. Facilia AB. Baes, C.F.,III, and Sharp, R.D. (1983). A proposal for estimation of soil leaching and leaching constants in assessment models. J.Eviron. Qual., 12, 17-28 Bugai D., Avila R. (2015). NORMALYSA tool for Safety Assessment and Uranium Residues Management (Overview of IAEA MODARIA project WG-3 activities). Paper presented at the IAEA CGULS meeting, Dushabe, Tadjikistan, 1-5 June 2015, doi: 10.13140/RG.2.1.1393.0966 Ene D. (2010). Radioprotection studies for the ESS superconducting linear accelerator. Preliminary estimates. Ref. 1093060 v01.2010. Ene, D. (2015). ESS-0028551 Assessment of environmental consequences of the normal operations of ESS facility. Part #1 - Input data, Source Term, breakdown of radionuclides and related basic information. Gelhar, L.W., Welty, C., Rehfeldt, K.R. (1992). A Critical Review of Data on Field-Scale Dispersion in Aquifers, Water Resour. Res. 28 (7) 1955–1974. Guiger N., Franz T. (1996) User’s manual for Visual MOFLOW. Waterloo Hydrogeologic Inc. IAEA (2001). Generic Models for Use in Assessing the Impact of Discharges of Radioactive Substances to the Environment. Safety Report Series no.19, International Atomic Energy Agency, Vienna, 2001. IAEA (2004a). Safety Assessment Methodologies for Near Surface Disposal Facilities. Results of a co-ordinated research project Volume 1 Review and enhancement of safety assessment approaches and tools. International Atomic Energy Agency, Vienna. IAEA (2004b). Safety Assessment Methodologies for Near Surface Disposal Facilities. Results of a co-ordinated research project Volume 2 Test cases. International Atomic Energy Agency, Vienna. IAEA (2010). Handbook of Parameter Values for the Prediction of Radionuclide Transfer in Terrestrial and Freshwater Environments. Technical report Series no.472, International Atomic Energy Agency, Vienna, 2010.

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Harbaugh, A.W. (1990) A computer program for calculating sub-regional water budgets using results from the U.S. Geological Survey modular three-dimensional ground-water flow model: U.S. Geological Survey Open-File Report 90-392, 46 p. Huutoniemi T., Nordlinder T. (2014). Dose from activated soil in connection to a proton LINAC in Lund, Sweden. Report no. N-14/193, Studsvik Nuclear AB, 2014. Maul P., Robinson P., Broed R., Avila R. (2004) Further AMBER and Ecolego Intercomparisons SKI Report 2004:05 SSI Report 2004:01. Maul P., Robinson P., Avila R., Broed R., Pereira, A., Xu, S. (2003) AMBER and Ecolego Intercomparisons using Calculations from SR 97 SKI Report 2003:28’’, SSI report 2003:11 McDonald, M.G., Harbaugh, A.W. (1983). A modular three-dimensional finite-difference ground-water flow model. Open-File Report 83-875. U.S. Geological Survey. McDonald M.G.,Harbaugh, A.W. (2003). The History of MODFLOW. Ground Water 41 (2): 280–283. Moller H., Sundlof B., Alsterling H. (2013). GeoPM5 - Entire Site. Document ID ESS-0032672, G01 Tyrens AB, 2013 Moller H., Sundlof B. (2013). GeoPM6 – Radiation Protection Aspects. Document ID ESS0005023, G01-DT-DEFSGD Tyrens AB, 2013. Pollock, D.W. (1994) User's Guide for MODPATH/MODPATH-PLOT, Version 3: A particle tracking post-processing package for MODFLOW, the U.S. Geological Survey finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 94-464. Rensfeldt, V. (2014) The Normalysa tool. Paper presented at Symposium ores and radioactivity; Simposio minerios e radioatividade; Rio de Janeiro, RJ (Brazil); 18-20 August 2014; INIS-BR--14486 Walton, W.C. (1988). Practical Aspects of Groundwater Modelling, 3rd ed., National Water Well Association, Worthington, Ohio.

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ANNEX 1. THE NORMALYSA MODEL FOR AQUIFER TRANSPORT A1.1. Model purpose A1.1.1. Goal The goal of the ‘Aquifer’ module is to dynamically simulate the transport of radionuclides from the Source of radioactivity (e.g., ‘Tailings without Cover’, ‘Contaminated land’), which may be coupled with other modules simulating intermediate transfer such as ‘Unsaturated Zone’ and/or as ‘Aquifer Mixing’, within the groundwater aquifer towards receptor environment(s). The output of the ‘Aquifer’ module usually serves an input to the receptor module(s) (e.g., ‘Well’, or ‘Fresh Water Body’) (Figure 1).

Figure 1 – Overall model of the waste site system incorporating the Aquifer module

A1.1.2. Potential decision and regulatory framework(s) Coupled with the Source model (and possibly modules simulating intermediate transfers), the ‘Aquifer’ module can: provide an estimation of the time-dependent concentration of the targeted radionuclide(s) in aquifer pore water at a given distance from the source along the groundwater flow tube; provide an estimation of the time-dependent mass (activity) flux of the targeted radionuclide(s) in the aquifer cross-section at a given distance from the source along the groundwater flow tube.

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The output of the ‘Aquifer’ module usually serves an input to the receptor modules (‘Well’, or ‘Fresh Water Body’) (see Figure 1). These outputs can be used for evaluating the residence time of radioactive contaminant(s) in groundwater and the risk over time to exceed a given regulatory threshold for radioactive contaminant(s) in corresponding receptor compartments defined by the relevant regulations.

A1.2. Model applicability A1.2.1. Spatial scale and resolution The ‘Aquifer’ module is defined as a three-dimensional ‘groundwater flow tube’ system (i.e. defined by its cross-section area and length). The relevant spatial scale and resolution are governed by the homogeneity of the hydrogeological system under investigation (e.g. homogeneity with respect to hydraulic properties, geochemical properties, contamination levels, etc.). The ‘Aquifer’ module assumes that the system is homogeneous (laterally, longitudinally and vertically) with respect to its properties and parameters. For aquifer environments showing laterally significant variations in their properties, it is recommended to subdivide these latter in a sequence of homogeneous and independent flow zones (flow tubes). A1.2.2. Temporal scale and resolution There is no limitation for temporal scale (i.e. duration of the simulation). Processes and parameters included in the model of water dynamics in the aquifer (i.e., infiltration recharge rate, Darcy velocity) are relevant at yearly resolution. Therefore the ‘Aquifer’ module and coupled models are run at a yearly resolution.

A1.2.3. Steady-state vs dynamic processes The ‘Aquifer’ module simulates radionuclide transport processes within the hydrogeological environment dynamically, however: It is assumed that radionuclide transport in the aquifer occurs under the steady-state groundwater flow conditions;

The exchanges of radioactive contaminants between pore water and soil matrix are assumed to be at sorption equilibrium (i.e. sorption process are represented by a distribution coefficient Kd).

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A1.3. Model components A1.3.1. Media considered Definition: A ‘Medium’ is defined as an environmental or human compartment assumed to contain a given quantity of the radionuclide (chemical). The quantity of the radionuclide in the media is governed by loadings/losses (see A1.3.2 and A1.3.3) from/to other media and by radioactive decay. The ‘Aquifer’ module schematizes the groundwater aquifer (flow tube) system as a sequence of individual Transport Cells with a constant length. The model expressions operate total radionuclide inventories in each transport cell. Then radioactive contaminant concentrations in pore water and soil matrix can be calculated for each transport cell based on known cell inventory and equilibrium Kd-based sorption model describing radionuclide partitioning between the liquid and solid phases. The number and lateral size of cells is determined automatically based on specified accuracy requirements. The program generates the need number of cell compartments implicitly using Ecolego 6.0 ‘Transport’ block. The schematization and media considered are represented in Figure 2.

Figure 2 – Media considered in the Aquifer module

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A1.3.2. Loadings Definition: A ‘Loading’ is defined as the rate of release/input of the radionuclide of interest to the receiving system, here the ‘Aquifer’ system. The inputs of radioactive contaminant(s) into the ‘Aquifer’ system can have the following origins: Contaminants leached from the waste disposal facilities (such as uranium mill tailings facilities); Contaminants originating from contaminated topsoil layer due to leaching by atmospheric precipitations; Contaminants originating from direct application of liquid effluents on topsoil (e.g. direct application of sludge originating from sewage treatment plants, fertilizers, etc.); Contaminants originating from the surface water or groundwater systems through water used for irrigation purposes, etc.

The inputs of radioactive contaminant(s) into the ‘Aquifer’ system are needed to be defined by user in the coupled external Source model (possibly coupled with modules simulating intermediate transfers). In this case the outputs of the coupled Source module (or modules simulating intermediate transfers) are used as loading inputs for the ‘Aquifer’ model. The contaminant input is defined by specifying two parameters: radioactive contaminant activity concentration in the infiltrating (inflowing) water and inflow rate (Darcy velocity). The loading inputs are represented in Figure 3.

Figure 3 – Media considered + Loading inputs in the ‘Aquifer’model

A1.3.3. Losses Definition: A ‘Loss’ is defined as the rate of output of the radionuclide of interest from the receiving system, here the ‘Aquifer’system. The losses of radioactive contaminant(s) from the ‘Aquifer’ system are:

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Contaminant leaving the ‘Aquifer’ system towards Receptor environments (e.g., ‘Well’, ‘Lake’ or ‘River’ modules) or to the adjacent downstream zones of the hydrogeological system (e.g., consecutive ‘Aquifer’ module) by outflow (i.e., contaminant movement by advective outflow); Radioactive decay of contaminant in the Aquifer media.

The losses of contaminant(s) from the ‘Aquifer’ system are represented in Figure 4.

Figure 4 – Media considered + Loading inputs + Losses in the Aquifer model.

A1.3.4. Exchanges between model media Definition: An ‘Exchange’ is defined as the transfer of the radionuclide of interest between two media compartments of the system, here the Aquifer system. The potential exchanges of radioactive contaminant(s) between the media of the Aquifer model are: Advective transport of contaminants from Transport Cell i to Transport Cell i+1 (i.e. radioactive contaminant transport by advective water flow); Dispersive transport of radioactive contaminants from soil Transport Cell i to Transport Cell i+1 (and vice versa); The Aquifer model assumes that sorption equilibrium of radioactive contaminant(s) between pore water and soil matrix exists in each Transport Cell (described by Kd model). However, sorption/desorption is not modelled separately as an exchange process. Radioactive contaminant concentrations in pore water and soil matrix are calculated for each Transport Cell based on known layer inventory and equilibrium Kd sorption model using corresponding partitioning equation. The exchanges of radioactive contaminant(s) between model media are represented in Figure 5.

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Figure 5 - Media considered + Loading inputs + Losses + Exchanges in the Aquifer model.

A1.3.5. Potential coupled models ‘Coupled models’ are defined as models that can generate loadings to the investigated system (here the Aquifer system) or receive losses from the latter. The ‘Aquifer’ module can be coupled to other modules of the NORMALYSA library (see Figure 1). These latter can provide loading estimates or use losses from the Aquifer as input data: Coupled model Source Term models (‘Tailings without cover’, ‘Contaminated land’) ‘Unsaturated Zone’ ‘Aquifer mixing’ ‘Aquifer’

Can provide estimates of the following loading(s) Radioactive contaminant concentration in infiltrating water; infiltration rate Radioactive contaminant concentration in infiltrating water; infiltration rate Radioactive contaminant concentration in infiltrating water; Darcy velocity Radioactive contaminant concentration in infiltrating water; Darcy velocity

‘Well’ ‘Fresh Water Body’

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Can use the following losses from the Aquifer as input data

Radioactive contaminant concentration in outflow water; Darcy velocity Radioactive contaminant concentration in outflow water; Darcy velocity Radioactive contaminant concentration in outflow water; Darcy velocity

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A1.3.6. Forcing variables A ‘Forcing variable’ is defined as an external or exogenous (from outside the model framework) factor that influences the state variables calculated within the model. Such variables include, for example, climatic or environmental conditions (temperature, wind flow, etc.). For running the Aquifer module, the following forcing variables must be informed for calculating the loading inputs: Forcing variable

Abbreviation and unit

Purpose

Concentration of the radioactive contaminant in water infiltrating (inflowing) to the aquifer Darcy velocity within the Aquifer

c_water_pore_in (Bq m-3)

Is used to calculate the input activity flux through infiltration (inflow) of contaminated ground water

u_Darcy (m.y-1)

Is used to calculate the input activity flux through infiltration infiltration (inflow) of contaminated ground water

The forcing variables (with indication of the processes they are involved in) are represented in Figure6.

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Can be calculated if the ‘Aquifer’ model is coupled to the … ‘Source Term’, ‘Unsaturated Zone’, ‘Aquifer Mixing’ ‘Aquifer Mixing’

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Figure 6- Media considered + Loading inputs + Losses + Exchanges + Forcing variables in the Aquifer model.

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A1.3.7. Parameters A ‘Parameter’ is defined as a term in the model that is fixed during a model run or simulation but can be changed in different runs as a method for conducting sensitivity analysis or to achieve calibration goals. For running the Aquifer model, the following parameters must be informed:

Site-specific parameters: Name

Abbreviation and unit

Purpose

Aquifer (flow tube) cross-section area perpendicular to flow direction

area_flow_tube (m2)

It defines the geometry of groundwater system (flow tube).

the

modelled

Length of the aquifer (flow tube)

length_flow_tube (m)

It defines the geometry of groundwater system (flow tube)

the

modelled

Used for calculating the following state variable(s) It is used for converting the total activity in the system into concentrations in media, in particular to pore water concentration in outflow water(c_water_pore_out) It is used to calculate activity flux from the aquifer (Flux_out) Length of discretized transport cell (dz)

Soil physico-chemical properties: Name

Dry density of aquifer soil Porosity of soil in the aquifer

Abbreviation and unit rho_aquifer (kg.m-3) porosity_aquifer (m3.m-3)

Purpose It is used for calculating the Retardation factor in the Aquifer It is used to calculate: transfer coefficient by advection, retardation factor, radionuclide concentration in pore water, etc.

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Used for calculating the following state variable(s) Retardation factor in the aquifer soil (Ret_aquifer) Radionuclide concentration in pore water out flowing from the aquifer (c_water_pore_out) Retardation factor in the aquifer (Ret_aquifer)

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Initial contamination of groundwater in the aquifer by radionuclides

Sorption distribution coefficient

Initial contamination inventories discretized transport cells

in

Abbreviation and unit Kd_aquifer (m3.kg-1)

Purpose

Used for calculating the following state variable(s)

The exchanges of contaminants between pore water and soil matrix are assumed to be at equilibrium and represented by a distribution coefficient at equilibrium Kd_aquifer

Retardation factor in the aquifer soil (Ret_aquifer)

Parameters related to radioactive decay: Name

Radionuclide half life

It is used for calculating the initial condition for radionuclide transport calculations in the aquifer

Parameters related to partition between phases: Name

c0_gw_aquifer (Bq m-3)

Abbreviation and unit halfLife (year)

Purpose

Used for calculating the following state variable(s)

Is used to account for radioactive decay of contaminants

Radionuclide inventories in discretized transport cell compartments and concentrations in media

Parameters controlling spatial resolution and accuracy of numerical solution of transport equation: Name

Abbreviation and unit

Minimum number of transport cells in Aquifer model

N_min

Maximum number of transport cells in Aquifer model

N_max

Purpose Sets a minimum number of transport cells in aquifer model (default value is 5). It is not recommended to change this value Sets a maximum number of transport cells in Aquifer model (default value is 100). Actual number is calculated by the model. Setting larger N_max may improve accuracy, but may increase the

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Used for calculating the following state variable(s) Length of discretized transport cell (dz)

Length of discretized transport cell (dz)

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Parameter controlling accuracy of approximation of dispersion flux

Dispersion_accuracy

needed computational resources This parameter controls the numerical dispersion when solving transport equation. Recommended value is 0.1-0.2. Smaller values may improve accuracy, but may increase the needed computational resources

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Used to calculate the number of Length of discretized transport cell (N_transp)

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A1.3.8. Intermediate State variables An ‘Intermediate State variable’ is defined as a dependent variable calculated within the model. Some State variables are fixed during a model run or simulation because they are calculated only from parameters. Some others are time-dependent because they are calculated from parameters, but also from time-dependent forcing variables. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes. For running the Aquifer model, the following state variables are calculated for the following purposes.

State variables related to discretization of the Aquifer soil profile in sub-layers:

State variable n° 1

Name

Abbreviation and unit

Purpose

Process followed for calculating the state variable

Length of discretized transport cell

dz (m)

The total aquifer system (flow tube) is subdivided into a set of transport cells for subsequent radioactive contaminant transport calculations

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2

Initial estimate of the number of transport cells

N_transp0

The number of transport cells is calculated taking into account accuracy criteria for numerical solution of advection-dispersion equation

3

Final estimate of the number of transport cells

N_transp

The final number of transport cells is adjusted taking into account N_transp0 and maximum allowed number N_max

State variable n° 5

State variables related to radioactive contaminant transport in soil: Name

Abbreviation and unit

Purpose

Process followed for calculating the state variable

Dispersivity

dispersivity_aq (m)

Dispersivity parameter for transport in the Aquifer (calculated from the linear scale of the transport problem)

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4

Retardation factor

Ret_aquifer (-)

5

Mass transfer by infiltration to the 1-st Aquifer transport cell

Infiltration

6

Mass transfer coefficient by advective transport

advection_aquifer

The contaminant is partly sorbed on the soil matrix, only the dissolved phase is assumed to move along the soil profile, resulting in a retardation. The Retardation factor accounts for the adsorption of contaminants on the soil matrix and is included in the advection-dispersion transfers within the soil profile. It is assumed that mass transport to the 1-st transport cell in the aquifer is determined by flux of infiltration water with specified concentration of contaminant(s)

This mass transfer coefficient is used to calculate fluxes of contaminants between adjacent transport cells in the aquifer by advective transport

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7

Mass transfer coefficient by dispersive transport (forward)

dispersion_aq_for ward

This mass transfer coefficient is used to calculate fluxes of contaminants between adjacent transport cells by dispersive (based on Fickian law) transport (forward direction; that is from cell i to cell i+1)

8

Mass transfer coefficient by dispersive transport (backwards)

dispersion_aq_bac k

This mass transfer coefficient is used to calculate fluxes of contaminants between adjacent transport cells by dispersive (based on Fickian law) transport (backward direction; that is from cell i to cell i-1)

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Same as for the mass transfer coefficient dispersion_aq_forward

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A1.3.9. Regulatory State variables A ‘Regulatory State variable’ is defined as a dependent variable calculated within the model. It is generally time-dependent because it is calculated from parameters, but also from time-dependent forcing variables and loadings. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes.

The following ‘regulatory state variables’ are calculated according to the flow charts presented in Figure :

State variable n° 9

Name Radioactive contaminant concentration in the porous

Abbreviation and unit c_water_pore_out

solutions out-flowing from the Aquifer (flow tube) 10

Radioactive contaminant flux from the Aquifer (integral over aquifer cross-section)

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Flux_out

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Figure 7 - Flow chart of key process for calculating the ‘regulatory state variables’

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A1.4. Mathematical models for State variables The objective of this section is to present the mathematical models used for calculating each of the State variables conceptually listed in A1.3.8. The understanding of these models is a prerequisite for understanding the mass balance equations presented in section A1.5. In the following tables, the following symbols were adopted:

A1.4.1. State variables related to discretization of the Aquifer soil profile in sub-layers Length of transport cell dz The data process for calculating the State variable ’dz’’ is reminded here:

The ‘dz’ State variable is calculated as follows:

(1)

dz

Length flow _ tube N transp

Initial estimate of the number of transport cells The data process for calculating the State variable’N_transp0’ is reminded here:

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The ‘N_transp0’ State variable is calculated as follows:

(2)

N transp0

lengthflow _ tube max N min , 2 dispersion dispersivi ty accuracy aq

here [ ] stays for the ‘whole part of a decimal number +1’.

Final estimate of the number of transport cells The data process for calculating the State variable’N_transp’ is reminded here:

The ‘N_transp’ State variable is calculated as follows:

(3)

N transp min( N transp 0 , N max )

A1.4.2. State variables related to radioactive contaminant transport in soil: Dispersivity The data process for calculating the State variable dispersivity_aq is reminded here:

The ‘dispersivity_aq’ State variable is calculated as follows: (4)

dispersivityaq 0.1 lengthflow _ tube

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Retardation factor The data process for calculating the State variable Ret_uns_zone is reminded here:

The ‘Ret_aquifer’ State variable is calculated as follows:

(5)

Retaquifer 1.0

rhoaquifer porosityaquifer

Kd aquifer

Mass transfer by infiltration to the first Aquifer cell The data process for calculating the State variable ‘Infiltration’ is reminded here:

The ‘Infiltration’ State variable is calculated as follows: (6)

Infiltration cwater _ pore _ in u Darcy area flow _ tube

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Mass transfer coefficient by advective transport The data process for calculating the State variable ‘advection_aquifer’ is reminded here:

The ‘advection_aquifer’ State variable is calculated as follows:

(7)

advectionaquifer

u Darcy porosityaquifer dz Retaquifer

Mass transfer coefficient by dispersive transport (forward) The data process for calculating the State variable dispersion_aq_forward is reminded here:

The ‘dispersion_aq_forward’ State variable is calculated as follows:

(8)

dispersionaq _ forward

dispersivityaq u Darcy porosityaquifer Retaquifer dz 2

Mass transfer coefficient by dispersive transport (backward) The data process and the formula for calculation for the mass transfer coefficient by dispersive transport (backwards) ‘dispersion_aq_back’ is the same as for the State variable ‘dispersion_aq_forward’.

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A1.4.3. Regulatory state variables Radioactive contaminant concentration in the porous solutions out-flowing from the Aquifer (flow tube) The ‘c_water_pore_out’ State variable is dynamically calculated as follows:

(9)

ñwater _ pore _ out

Transport _ CellNtransp

1

area flow _ tube dz

porosityaquifer Ret aquifer

Radioactive contaminant flux from the Aquifer (integral over aquifer cross-section) The ‘Flux_out’ State variable is dynamically calculated as follows: (10)

Fluxout u Darcy area flow _ tube cwater _ pore _ out

A1.5. Mass balance equation for Media The Media, loadings, losses and exchanges that govern the mass balance models for each medium are shown at Figures 5 and 7.

A1.5.1. The ‘Transp_Cell_1’ Media The mass balance model for the Transp_Cell_1 (‘1-st Aquifer Transport Cell’) media is given by:

dTransp _ Cell1 ln(2) .Transp _ Cell1 Infiltration dt half _ Life . dispersionaq _ forward Transp _ Cell1 dispersionaq _ back Transp _ Cell2 advectionaquifer Transp _ Cell1

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A1.5.2. The ‘Transp_Cell_i’ Media The mass balance model for the ‘Transp_Cell_i’ (Aquifer Transport Cell i) media is given by: dTransp _ Celli ln( 2) .Transp _ Celli advectionaquifer Transp _ Celli 1 advectionaquifer Transp _ Celli dt half _ Life . dispersionaq _ forward Transp _ Celli dispersionaq _ back Transp _ Celli dispersionaq _ back Transp _ Celli 1 dispersionaq _ forward Transp _ Celli 1

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ANNEX 2. THE NORMALYSA MODEL FOR AQUIFER MIXING A2.1. Model purpose A2.1.1. Goal The goal of the ‘Aquifer Mixing’ module is to dynamically simulate transport of radioactive contaminants from the Source of radioactivity (e.g., ‘Tailings without Cover’, ‘Contaminated land’), which may be coupled with other modules simulating intermediate transfer such as ‘Unsaturated Zone’) within the groundwater aquifer immediately below the contaminated site. The output of the ‘Aquifer’ module usually serves an input to the ‘Aquifer’ module simulating radionuclide transport in groundwater towards receptor module(s) (e.g., ‘Well’ or ‘Fresh Water Body’) (Figure 1.).

Figure 1 – Overall model of the waste site system incorporating the ‘Aquifer Mixing’ module

A2.1.2. Potential decision and regulatory framework(s) Coupled with the Source model (and possibly modules simulating intermediate transfers), the ‘Aquifer Module’ module can:

provide an estimation of the time-dependent concentration of the targeted radionuclide(s) in aquifer pore water below the contaminated site; provide an estimation of the time-dependent mass (activity) flux of the targeted radionuclide(s) in the aquifer from the contaminated site. The output of the ‘Aquifer Mixing’ module usually serves an input to the ‘Aquifer’ module simulating radionuclide transport in groundwater towards the receptor modules (‘Well’, or ‘Fresh Water Body’) (see Figure 1). These outputs can be used for evaluating the residence time of radioactive contaminant(s) in groundwater and the risk over time to exceed a given regulatory threshold for radioactive contaminant(s) in corresponding receptor compartments defined by the relevant regulations. Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 47 (86)

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A2.2. Model applicability A2.2.1. Spatial scale and resolution The ‘Aquifer Mixing’ module is defined as a 3-dimensional compartment within the aquifer (i.e. defined by its length, width and height). The relevant spatial scale and resolution are governed by the geometry of the source and features of the hydrogeological system under investigation. The ‘Aquifer Mixing’ module assumes that the modelled aquifer compartment is homogeneous (laterally, longitudinally and vertically) with respect to its properties and parameters. A2.2.2.Temporal scale and resolution There is no limitation for temporal scale (i.e. duration of the simulation). Processes and parameters included in the model of water dynamics in the aquifer (i.e., infiltration recharge rate, Darcy velocity) are relevant at yearly resolution. Therefore the ‘Aquifer Mixing’ module and coupled models are run at a yearly resolution.

A2.2.3.Steady-state vs dynamic processes The ‘Aquifer Mixing’ module simulates radionuclide transfer processes within the hydrogeological environment dynamically, however: It is assumed that radionuclide transport in the aquifer occurs under the steady-state groundwater flow conditions;

the exchanges of radioactive contaminants between pore water and soil matrix are assumed to be at sorption equilibrium (i.e. sorption process are represented by a distribution coefficient Kd).

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A2.3. Model components A2.3.1. Media considered Definition: A ‘Medium’ is defined as an environmental or human compartment assumed to contain a given quantity of the radionuclide (chemical). The quantity of the radionuclide in the media is governed by loadings/losses (see A2.3.2 and A2.3.3) from/to other media and by radioactive decay. The ‘Aquifer Mixing’ module schematizes the groundwater aquifer immediately below the contaminated site as a single compartment. The model expressions operate total radionuclide inventories in this compartment. Then radioactive contaminant concentrations in pore water and soil matrix can be calculated based on known inventory of compartment and equilibrium Kd-based sorption model describing radionuclide partitioning between the liquid and solid phases. The schematization and media considered are represented in Figure 2.

Figure 2 – Media considered in the ‘Aquifer Mixing’ module

A2.3.2. Loadings Definition: A ‘Loading’ is defined as the rate of release/input of the radionuclide of interest to the receiving system, here the ‘Aquifer’ system. The inputs of radioactive contaminant(s) into the ‘Aquifer Mixing’ compartment can have the following origins: Contaminants leached from the waste disposal facilities (such as uranium mill tailings facilities); Contaminants originating from contaminated topsoil layer due to leaching by atmospheric precipitations; Contaminants originating from direct application of liquid effluents on topsoil (e.g. direct application of sludge originating from sewage treatment plants, fertilizers, etc.); Contaminants entering the modelled aquifer compartment by lateral inflow from the upstream aquifer zone. Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 49 (86)

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The inputs of radioactive contaminant(s) into the ‘Aquifer Mixing’ system by infiltration mechanism are needed to be defined by user in the coupled external Source model (possibly coupled with modules simulating intermediate transfers). In this case the outputs of the coupled Source module (or modules simulating intermediate transfers) are used as loading inputs for the ‘Aquifer mixing’ model. The contaminant input is defined by specifying two parameters: radioactive contaminant activity concentration in the infiltrating water and infiltration rate. The loading inputs are represented in Figure 3.

Figure 3 – Media considered + Loading inputs in the ‘Aquifer Mixing’module.

A2.3.3. Losses Definition: A ‘Loss’ is defined as the rate of output of the radionuclide of interest from the receiving system, here the ‘Aquifer Mixing’ compartment. The losses of radioactive contaminant(s) from the ‘Aquifer Mixing’ compartment are: Contaminant leaving the ‘Aquifer Mixing’ system towards adjacent downstream zones of the hydrogeological system (e.g., consecutive ‘Aquifer’ module) by outflow (i.e., contaminant movement by advective outflow); Radioactive decay of contaminant in the aquifer media. The losses of contaminant(s) from the ‘Aquifer Mixing’ compartment are represented in Figure 4.

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Figure 4 – Media considered + Loading inputs + Losses in the ‘Aquifer Mixing’ model.

A2.3.4. Exchanges between model media Definition: An ‘Exchange’ is defined as the transfer of the radionuclide of interest between two media compartments of the system, here the Aquifer system. The Aquifer model assumes that a sorption equilibrium of radioactive contaminant(s) between pore water and soil matrix exists (described by Kd model). However sorption/desorption is not modelled separately as an exchange process. Radioactive contaminant concentrations in pore water and soil matrix are calculated for each Transport Cell based on known layer inventory and equilibrium Kd sorption model using corresponding partitioning equation. The exchanges of radioactive contaminant(s) between model media are represented in Figure 5.

Figure 5 - Media considered + Loading inputs + Losses + Exchanges in the ‘Aquifer Mixing’ model.

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A2.3.5. Potential coupled models ‘Coupled models’ are defined as models that can generate loadings to the investigated system (here the ‘Aquifer Mixing’ compartment) or receive losses from the latter. The ‘Aquifer Mixing’ module can be coupled to other modules of the NORMALYSA library (see Figure 1). These latter can provide loading estimates or use losses from the ‘Aquifer Mixing’ compartment as input data: Coupled model Source Term models (‘Tailings without cover’, ‘Contaminated land’) ‘Unsaturated Zone’

Can provide estimates of the following loading(s) Radioactive contaminant concentration in infiltrating water; infiltration rate

Can use the following losses from the Aquifer as input data

Radioactive contaminant concentration in infiltrating water; infiltration rate

‘Aquifer’

Radioactive contaminant concentration in outflow water; Darcy velocity Radioactive contaminant concentration in outflow water; Darcy velocity Radioactive contaminant concentration in outflow water; Darcy velocity

‘Well’ ‘Fresh Water Body’

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A2.3.6. Forcing variables A ‘Forcing variable’ is defined as an external or exogenous (from outside the model framework) factor that influences the state variables calculated within the model. Such variables include, for example, climatic or environmental conditions (temperature, wind flow, etc.). For running the ‘Aquifer Mixing’ module, the following forcing variables must be informed for calculating the loading inputs: Forcing variable

Abbreviation and unit

Purpose

Concentration of the radioactive contaminant in water infiltrating to the aquifer Infiltration rate to the aquifer

c_ infiltration_aquifer (Bq m-3)

Is used to calculate the input activity flux through infiltration (inflow) of contaminated ground water

rate_infiltration (m.y-1)

Concentration of the radioactive contaminant in groundwater inflowing to the aquifer from upstream direction Darcy velocity in the aquifer

c_water_pore_in (Bq m-3)

Is used to calculate the input activity flux through infiltration of contaminated pore water Is used to calculate the input activity flux through inflow of contaminated groundwater from upstream direction

u_Darcy (m.y-1)

Is used to calculate the input activity flux through inflow of contaminated groundwater from upstream direction

The forcing variables (with indication of the processes they are involved in) are represented in Figure 6.

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Can be calculated if the ‘Aquifer’ model is coupled to the … Source Term models, ‘Unsaturated Zone’ Source Term models, ‘Unsaturated Zone’

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Figure 6- Media considered + Loading inputs + Losses + Exchanges + Forcing variables in the ‘Aquifer Mixing’ module.

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A2.3.7. Parameters A ‘Parameter’ is defined as a term in the model that is fixed during a model run or simulation but can be changed in different runs as a method for conducting sensitivity analysis or to achieve calibration goals. For running the ‘Aquifer Mixing’ module, the following parameters must be informed:

Site-specific parameters: Name

Abbreviation and unit

Purpose

Surface of the contamination source (waste site), which is situated on top of the ‘Aquifer Mixing’ compartment

Area_source (m2)

It defines the geometry hydrogeological system

Length of the aquifer compartment

length_waste_site (m)

Thickness of the aquifer "mixing zone" below the waste site

h_mixing (m)

It defines the geometry of the modelled groundwater system It defines the geometry of the modelled “aquifer mixing” compartment, where vertical infiltration flux from the contaminated site mixes with the lateral groundwater flow in the aquifer

of

the

modelled

Used for calculating the following state variable(s) It is used for converting the total activity in the system into concentrations in media, in particular to pore water concentration in outflow water(c_water_pore_out) It is used also to calculate activity input to the modelled system (Infiltration) It is used to calculate average width of the contaminated site (from its area) It is used to calculate cross-sectional area of the aquifer (area_flow_tube)

Soil physico-chemical properties: Name

Dry density of aquifer soil Porosity of soil in the aquifer

Abbreviation and unit rho_aquifer (kg.m-3) porosity_aquifer

Purpose It is used for calculating the Retardation factor in the aquifer It is used to calculate: transfer coefficient by

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Used for calculating the following state variable(s) Retardation factor in the aquifer soil (Ret_aquifer) Radionuclide concentration in pore water

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Initial contamination of groundwater in the aquifer by radionuclides

advection, retardation factor, concentration in pore water, etc.

c0_gw_aquifer (Bq m-3)

It is used for calculating the initial condition for radionuclide transfers calculations in the aquifer

radionuclide

out flowing from the aquifer (c_water_pore_out) Retardation factor in the aquifer (Ret_aquifer) Initial contamination inventories in the modelled aquifer compartment

Parameters related to partition between phases: Name

Sorption distribution coefficient

(m-3.m-3)

Abbreviation and unit Kd_aquifer (m3.kg-1)

Purpose

Used for calculating the following state variable(s)

The exchanges of contaminants between pore water and soil matrix are assumed to be at equilibrium and represented by a distribution coefficient at equilibrium Kd_aquifer

Retardation factor in the aquifer soil (Ret_aquifer)

Parameters related to radioactive decay: Name

Radionuclide half life

Abbreviation and unit halfLife (year)

Purpose

Used for calculating the following state variable(s)

Is used to account for radioactive decay of contaminants

Radionuclide inventories in discretized transport cell compartments and concentrations in media

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A2.3.8. Intermediate State variables An ‘Intermediate State variable’ is defined as a dependent variable calculated within the model. Some State variables are fixed during a model run or simulation because they are calculated only from parameters. Some others are time-dependent because they are calculated from parameters, but also from time-dependent forcing variables. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes. For running the Aquifer model, the following state variables are calculated for the following purposes.

State variable n° 1

State variables related to geometry of the aquifer compartment: Name

Width

of

contaminated (source

site of

contaminant infiltration

to

the

Abbreviation and unit

Purpose

Process followed for calculating the state variable

width_waste_site (m)

Defines geometrical characteristics of the ‘Aquifer Mixing’ compartment, which are further used in mass/activity calculations for the compartment

aquifer)

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Cross-sectional

area

of the aquifer (flow

area_flow_tube (m2)

Used to calculate integral mass/activity fluxes in the aquifer

tube)

State variable n° 3

State variables related to radioactive contaminant transport in soil: Name

Abbreviation and unit

Purpose

Process followed for calculating the state variable

Retardation factor

Ret_aquifer (-)

The contaminant is partly sorbed on the soil matrix, only the dissolved phase is assumed to move along the soil profile, resulting in a retardation. The Retardation factor accounts for the adsorption of contaminants on the soil matrix and is included in the advection-dispersion transfers within the soil profile.

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4

Mass transfer by infiltration (vertical) to the ‘Aquifer Mixing’ compartment

Infiltration

Vertical mass (activity) transport to the ‘Aquifer Mixing’ compartment is determined by flux of infiltration water with specified concentration of contaminant(s)

5

Mass transfer by inflow (horizontal) to the ‘Aquifer Mixing’ compartment

Inflow

Horizontal mass (activity) transport to the ‘Aquifer Mixing’ compartment is determined by inflow flux of groundwater with specified concentration of contaminant(s)

6

Mass transfer coefficient by advective transport (outflow from compartment)

advection_gw_out

This mass transfer coefficient is used to calculate fluxes of contaminants out of compartment by advective transport

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A2.3.9. Regulatory State variables An ‘Regulatory State variable’ is defined as a dependent variable calculated within the model. It is generally time-dependent because it is calculated from parameters, but also from time-dependent forcing variables and loadings. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes.

The following ‘regulatory state variables’ are calculated according to the flow charts presented in Figure :

State variable n° 6

Name Radioactive contaminant concentration in the porous

Abbreviation and unit c_water_pore_out

solutions out-flowing from the Aquifer (flow tube) 7

Radioactive contaminant flux from the Aquifer (integral over aquifer cross-section)

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Flux_flow_tube

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Figure 7 - Flow chart of key process for calculating the ‘regulatory state variables’ Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 61 (86)

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A2.4. Mathematical models for State variables The objective of this section is to present the mathematical models used for calculating each of the State variables conceptually listed in A2.3.8. The understanding of these models is a prerequisite for understanding the mass balance equations presented in Chapter A2.5. In the following tables, the following symbols were adopted:

A2.4.1. State variables related to geometry of the aquifer compartment: Width of contaminated site The data process for calculating the State variable ‘width_waste_site’ is reminded here:

The ‘width_waste_site’ State variable is calculated as follows:

(1)

widthwaste _ site

areasource lengthwaste _ site

Cross-sectional area of the aquifer The data process for calculating the State variable ‘area_flow_tube’ is reminded here:

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The ‘area_flow_tube’ State variable is calculated as follows: (2)

area flow _ tube hmixing widthwaste _ site

A2.4.2. State variables related to radioactive contaminant transport in soil: Retardation factor The data process for calculating the State variable Ret_uns_zone is reminded here:

The ‘Ret_aquifer’ State variable is calculated as follows:

(3)

Retaquifer 1.0

rhoaquifer porosityaquifer

Kd aquifer

Mass transfer by vertical infiltration to ‘Aquifer Mixing’ cell The data process for calculating the State variable ‘Infiltration’ is reminded here:

The ‘Infiltration’ State variable is calculated as follows: (4)

Infiltration cinf iltration u Darcy area flow _ tube

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Mass transfer by horizontal inflow to ‘Aquifer Mixing’ cell The data process for calculating the State variable ‘Inflow’ is reminded here:

The ‘Inflow’ State variable is calculated as follows:

Inflow cipore _ water _ in u Darcy area flow _ tube

(5)

Mass transfer coefficient by advective transport The data process for calculating the State variable ‘advection_gw_out’ is reminded here:

The ‘advection_gw_out’ State variable is calculated as follows:

(6)

advectionaquifer

uDarcy porosityaquifer lengthwaste _ site Retaquifer

A2.4.3. Regulatory state variables Radioactive contaminant concentration in the porous solutions out-flowing from the Aquifer (flow tube) The ‘c_water_pore_out’ State variable is dynamically calculated as follows:

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ñwater _ pore _ out

Aquifer _ Mixing 1 area flow _ tube lengthwaste _ site porosityaquifer Ret aquifer

Radioactive contaminant flux from the Aquifer (integral over aquifer cross-section) The ‘Flux_out’ State variable is dynamically calculated as follows: (8)

Flux flow _ tube u Darcy area flow _ tube cwater _ pore _ out

A2.5. Mass balance equation for Media The Media, loadings, losses and exchanges that govern the mass balance models for each medium are shown at Figures 5 and 7.

A2.5.1. The ‘Aquifer_Mixing’ Compartment The mass balance model for the ‘Aquifer_Mixing’ (AM) compartment is given by: dAM ln( 2) . AM Inflow Infiltration advectiongw _ out AM dt half _ Life

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ANNEX 3. THE NORMALYSA MODEL FOR CONTAMINATED SOIL LAYER A3.1. Model purpose A3.1.1. Goal The goal of the ‘Contaminated Soil layer’ module is to dynamically simulate the source term of radioactive contaminants for modelling subsequent radionuclide transport in the subsurface environment such as the unsaturated zone of soil and / or saturated transport in the aquifer. The output of the ‘Contaminated Soil layer’ module usually serves an input to the unsaturated zone and\or aquifer transport modules (‘Unsaturated Zone’, ‘Aquifer Mixing’ and/or ‘Aquifer’) (Figure 1).

Figure 1 – Overall model of the waste site system incorporating the ‘Contaminated Soil Layer’ module

A3.1.2. Potential decision and regulatory framework(s) The ‘Contaminated Soil Layer’ module can:

provide an estimation of the time-dependent concentration of the targeted radionuclide(s) in soil pore water and in soil matrix in contaminated (top) soil layer ; provide an estimation of the time-dependent mass (activity) flux of the targeted radionuclide(s) from the contaminated (top) soil layer. These outputs can be used for evaluating the residence time of radioactive contaminant(s) in soil and subsurface environment (coupled with other modules) and the risk over time to exceed a given regulatory threshold for radioactive contaminant(s) defined by the relevant regulations. The output of the ‘Contaminated Soil Layer’ module can also serve an input to the unsaturated zone and aquifer transport modules (‘Unsaturated Zone’, ‘Aquifer Mixing’ and/or ‘Aquifer’). Coupled Source term and transport modules can be used for evaluating radioactive Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 66 (86)

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contaminant concentrations in relevant Receptor compartments (e.g., ‘Well’ or ‘Fresh Water Body’) (see Figure 1). .

A3.2. Model applicability A3.2.1. Spatial scale and resolution The ‘Contaminated Soil Layer’ module is defined as a 3 dimensional system (i.e. defined by its surface area and depth). The relevant spatial scale and resolution are governed by the homogeneity of the soil system under investigation (e.g. homogeneity with respect to hydraulic properties, geochemical properties, contamination levels, etc.). The typical vertical dimension can vary from several tens of centimetres to several meters. The ‘Contaminated Soil layer’ model assumes that the system is homogeneous (laterally, longitudinally and vertically) with respect to its properties and parameters. For soil zones showing significant relative lateral variations in their properties, it is recommended to subdivide these latter in adjacent homogeneous and independent zones. Soil profiles showing significant variation of soil properties in vertical direction can be represented by a sequence of interconnected ‘Contaminated Soil Layer’ modules. A3.2.2.Temporal scale and resolution There is no limitation for temporal scale (i.e. duration of the simulation). Processes and parameters included in the model water dynamics in soil (i.e., infiltration recharge rate) are relevant at yearly resolution. Therefore the ‘Contaminated Soil Layer’ module and coupled models are run at a yearly resolution.

A3.2.3.Steady-state vs dynamic processes The ‘Contaminated Soil Layer’ module simulates radionuclide transport processes in soil profile dynamically, however: It is assumed that radionuclide leaching in from soil layer occurs under the steadystate moisture infiltration conditions (infiltration rate is constant in time);

the exchanges of radioactive contaminants between pore water and soil matrix are assumed to be at sorption equilibrium (i.e. sorption process are represented by a distribution coefficient Kd).

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A3.3. Model components A3.3.1. Media considered Definition: A ‘Medium’ is defined as an environmental or human compartment assumed to contain a given quantity of the radionuclide (chemical). The quantity of the radionuclide in the media is governed by loadings/losses (see A2.3.2 and A2.3.3) from/to other media and by radioactive decay. The ‘Contaminated Soil Layer’ module schematizes the contaminated soil as a single compartment. The model expressions operate total radionuclide inventories in this compartment. Then radioactive contaminant concentrations in pore water and soil matrix can be calculated based on known inventory of compartment and equilibrium Kd-based sorption model describing radionuclide partitioning between the liquid and solid phases. The schematization and media considered are represented in Figure 2.

Figure 2 – Media considered in the ‘Contaminated Soil Layer’ model

A3.3.2. Loadings Definition: A ‘Loading’ is defined as the rate of release/input of the radionuclide of interest to the receiving system, here the ‘Contaminated Soil Layer’’ system. The inputs of radioactive contaminant(s) into the ‘Contaminated Soil Layer’ system can have the following origins: Contaminant originating from direct application of liquid effluents on topsoil (e.g. direct application of sludge originating from sewage treatment plants, fertilizers, etc);

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Contaminant originating from the surface water or groundwater systems through water used for irrigation purposes, etc. Contaminant leaching from the upper contaminated topsoil layers, etc.

The inputs of radioactive contaminant(s) into the ‘Contaminated Soil Layer’ system are needed to be defined by user in the coupled external Source model. In this case the outputs of the coupled Source models are used as loading inputs for the ‘Contaminated Soil Layer’ model. The contaminant input is defined by specifying two parameters: radioactive contaminant activity concentration in the infiltrating water and infiltration rate. The loading inputs are represented in Figure 3

Figure 3 – Media considered + Loading inputs in the ‘Contaminated Soil Layer’model

A3.3.3. Losses Definition: A ‘Loss’ is defined as the rate of output of the radionuclide of interest from the receiving system, here the ‘Contaminated Soil Layer’ compartment. The losses of radioactive contaminant(s) from the ‘Contaminated Soil Layer’ system are: Contaminant leaving the ‘Contaminated Soil Layer’ system towards deeper soil zones of the hydrogeological system (unsaturated soil and/or groundwater aquifer) by vertical exfiltration (contaminant movement by advective outflow); Radioactive decay of contaminant in the Soil media. The losses of contaminant(s) from the ‘Contaminated Soil Layer’ system are shown in Figure 4.

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Figure 4 – Media considered + Loading inputs + Losses in the ‘Contaminated Soil Layer’ model.

A3.3.4. Exchanges between model media Definition: An ‘Exchange’ is defined as the transfer of the radionuclide of interest between two media compartments of the system, here the ‘Contaminated Soil Layer’ system. The ‘Contaminated Soil Layer’ model assumes that a sorption equilibrium of radioactive contaminant(s) between pore water and soil matrix exists in each soil layer (described by Kd model). However sorption/desorption is not modelled separately as an exchange process. Radioactive contaminant concentrations in pore water and soil matrix are calculated for the soil layer based on known layer inventory and equilibrium Kd sorption model using corresponding partitioning equation. The exchanges of radioactive contaminant(s) between model media are represented in 5.

Figure 5 - Media considered + Loading inputs + Losses + Exchanges in the Contaminated Soil Layer’ model. Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 70 (86)

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A3.3.5. Potential coupled models ‘Coupled models’ are defined as models that can generate loadings to the investigated system (here the ‘Contaminated Soil Layer’ system) or receive losses from the latter. The ‘Contaminated Soil Layer’ model can be coupled to other models of the NORMALYSA library (see Figure 1). These latter can or use losses from the Unsaturated Zone as input data (or provide loading estimates): Coupled model

Can provide estimates of the following loading(s)

‘Unsaturated Zone’ ‘Aquifer’ ‘Aquifer mixing’ Source Term models (‘Tailings without cover’, one other ‘Contaminated Soil Layer’)

Radioactive contaminant concentration in infiltrating water; infiltration rate

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Can use the following losses from the Aquifer as input data Radioactive contaminant concentration in infiltrating water; infiltration rate Radioactive contaminant concentration in outflow water; infiltration rate Radioactive contaminant concentration in outflow water; infiltration rate Radioactive contaminant concentration in outflow water; infiltration rate

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A3.3.6. Forcing variables

A ‘Forcing variable’ is defined as an external or exogenous (from outside the model framework) factor that influences the state variables calculated within the model. Such variables include, for example, climatic or environmental conditions (temperature, wind flow, etc.). For running the ‘Contaminated Soil Layer’ model, the following forcing variables must be informed for calculating the loading inputs: Forcing variable

Abbreviation and unit

Purpose

Concentration of the radioactive contaminant in infiltration water

c_infiltration (Bq m-3)

Is used to calculate the input activity flux through infiltration of contaminated pore water

Infiltration rate to soil layer

Rate_infiltration (m.y-1)

Is used to calculate the input activity flux through infiltration of contaminated pore water

The forcing variables (with indication of the processes they are involved in) are represented in Figure 6.

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Can be calculated if the ‘Contaminated Soil Layer’ model is coupled to the … Source Term models (‘Tailings without cover’, one other ‘Contaminated Soil Layer’) Source Term models (‘Tailings without cover’, one other ‘Contaminated Soil Layer’)

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Figure 6 - Media considered + Loading inputs + Losses + Exchanges + Forcing variables in the ‘Contaminated Soil Layer’ model.

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A3.3.7. Parameters A ‘Parameter’ is defined as a term in the model that is fixed during a model run or simulation but can be changed in different runs as a method for conducting sensitivity analysis or to achieve calibration goals. For running the ‘Contaminated Soil Layer’ module, the following parameters must be informed:

Site-specific parameters: Name

Abbreviation and unit

Purpose

Surface of the contaminated soil zone under investigation

Area_source (m2)

It defines the geometry of the modelled soil system.

Thickness of the modelled soil profile

Thickness_waste (m)

It defines the geometry of the modelled soil system. More specifically it defines the thickness of soil layer from where the contaminant leaching occurs

Used for calculating the following state variable(s) It is used for converting the total activity in the system into concentrations in media, in particular to pore water concentration in outflow water(c_water_pore_out) It is used to calculate activity flux from the soil layer (Flux_out) Leache rate (transfer coefficient) from soil layer (Leaching)

Soil physico-chemical properties: Name

Dry density of soil Soil water content

Abbreviation and unit rho_waste (kg.m-3) Moisture_waste 3 .m-3)

(m-

Purpose It is used for calculating the Retardation factor in the soil layer It is used to calculate: transfer coefficient by leaching, retardation factor, radionuclide concentration in pore water, etc.

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Used for calculating the following state variable(s) Retardation factor in the soil layer (R_waste) Radionuclide concentration in pore water out flowing from the soil layer (c_water_pore_out)

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Initial contamination of the soil layer by radionuclides

It is used for calculating the initial condition for radionuclide leaching source term in soil

Parameters related to partition between phases: Name

Sorption distribution coefficient

c_waste (Bq kg-1)

Retardation factor in soilsoil (R_waste) Leache rate (transfer coefficient) from soil layer (Leaching) Initial contamination inventory in soil layer

Abbreviation and unit Kd_waste (m3.kg-1)

Purpose The exchanges of contaminants between pore water and soil matrix are assumed to be at equilibrium and represented by a distribution coefficient at equilibrium Kd_waste

Used for calculating the following state variable(s) Retardation factor in soil (R_waste)

Parameters related to radioactive decay: Name

Radionuclide half life

Abbreviation and unit halfLife (year)

Purpose

Used for calculating the following state variable(s)

Is used to account for radioactive decay of contaminants

Radionuclide inventories in discretized soil layer compartments and concentrations in media

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A3.3.8. Intermediate State variables An ‘Intermediate State variable’ is defined as a dependent variable calculated within the model. Some State variables are fixed during a model run or simulation because they are calculated only from parameters. Some others are time-dependent because they are calculated from parameters, but also from time-dependent forcing variables. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes. For running the Contaminated Soil Layer model, the following state variables are calculated for the following purposes.

State variable n° 1

State variables related to radioactive contaminant transport in soil: Name

Abbreviation and unit

Purpose

Process followed for calculating the state variable

Retardation factor

R_waste (-)

The contaminant is partly sorbed on the soil matrix, only the dissolved phase is assumed to move along the soil profile, resulting in a retardation. The Retardation factor accounts for the adsorption of contaminants on the soil matrix and is included in the advection-dispersion transfers within the soil profile.

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2

Mass

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transfer

by

Infiltration

It is assumed that mass transport to the soil layer is determined by flux of infiltration water with specified concentration of contaminant(s)

Leaching

This mass transfer coefficient is used to calculate the external flux of contaminants from soil layers by advective flow with infiltration water

infiltration to the soil layer

3

Mass

transfer

coefficient leaching

by (advective

flow)

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A3.3.9. Regulatory State variables An ‘Regulatory State variable’ is defined as a dependent variable calculated within the model. It is generally time-dependent because it is calculated from parameters, but also from time-dependent forcing variables and loadings. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes.

The following ‘regulatory state variables’ are calculated according to the flow charts presented in Figure :

State variable n° 4

Name Radioactive contaminant concentration in the porous

Abbreviation and unit c_water_pore_out

solutions out-flowing from the soil layer 5

Radioactive contaminant flux from the soil layer (integral over surface area of soil)

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Flux_out

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A3.4. Mathematical models for State variables The objective of this section is to present the mathematical models used for calculating each of the State variables conceptually listed in A3.3.8. The understanding of these models is a prerequisite for understanding the mass balance equations presented in Chapter A3.5. In the following tables, the following symbols were adopted:

A3.4.1. State variables related to radioactive contaminant transport in soil: Retardation factor The data process for calculating the State variable R_waste is reminded here:

The ‘R_waste’ State variable is calculated as follows:

(1)

Rwaste 1.0

rhowaste Kd waste moisturewaste

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Mass transfer by infiltration to the soil layer The data process for calculating the State variable ‘Infiltration’ is reminded here:

The ‘Infiltration’ State variable is calculated as follows: (2)

Infiltration cinf iltrationn rateinfiltrati on areasource

Mass transfer coefficient by leaching The data process for calculating the State variable ‘Leaching’ is reminded here:

The ‘Leaching’ State variable is calculated as follows:

(3)

leaching

rateinfiltrati on moisturewastee Thicknesswaste Rwaste

Radioactive contaminant concentration in the porous solutions out-flowing from the soil layer The ‘c_water_pore_out’ State variable is dynamically calculated as follows:

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C water _ pore _ out

(4)

Activitysource 1 areasource Thicknesswaste moisturewaste Rwaste

Radioactive contaminant flux from the soil layer (integral over surface area of soil) The ‘Flux_out’ State variable is dynamically calculated as follows: (5)

Fluxout rateinf iltration areasource cwater _ pore _ out

A3.5. Mass balance equation for Media The Media, loadings, losses and exchanges that govern the mass balance models for each medium are shown at Figures 5 and 7.

A3.5.1. The ‘Activity_source’ Media The mass balance model for the ‘Activity_source’ (activity inventory in the soil layer) media is given by: dActivitysource ln(2) . ActivitySource Infiltration Leaching Activitysource dt half _ Life

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ANNEX 4. THE NORMALYSA MODEL FOR A WELL A4.1. Model purpose A4.1.1. Goal This module calculates radionuclide concentrations in groundwater pumped by a water well. It is assumed that some fraction of the well debit is formed by contaminated groundwater from the flow tube originating from the waste site, while the other part of well debit is formed by "background" groundwater hence it is linked to ‘Aquifer’ transport module and to a receptor.

Figure 1. Conceptual model for the well

A4.1.2. Potential decision and regulatory framework(s) Coupled with the transport model (and possibly modules simulating intermediate transfers), the ‘Well’ module can: 1. time-dependent concentration of radionuclide(s) in well water. The outputs can be used for evaluating the risk to exceed a given regulatory norm for environmental risk. 2. time-dependent concentration of radionuclide(s) in bottom sediments. In connection with the model dose model for example Human_ing, the well model is able to provide an estimation of the time-dependent concentration of RN in drinking water. This output can be used for evaluating the risk to exceed a given regulatory limit for human health. The output of the ‘Well’ module usually serves an input to other receptor modules where water is use for irrigation or for drinking water for human or animals (e.g. garden plot ), see Figure 1.

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The Well model can be coupled with dose models where the outputs of the well model (radionuclide concentrations in the well water) are used as input to derive doses to members of the public through ingestion of water and various foodstuff.

A4.2. Model applicability A4.2.1. Temporal scale and resolution There is no limitation for temporal scale (i.e. duration of the simulation).

A4.3. Model components A4.3.1. Loadings Definition: A ‘Loading’ is defined as the rate of release/input of radionuclide to the receiving system, here the Well system. The inputs of radioactive contaminant(s) into the ‘Well’ system can have the following origins: Radionuclides coming from the contaminated groundwater flow tube system (e.g. aquifer) A4.3.2. Losses

Definition: A ‘Loss’ is defined as the rate of output of RN from the receiving system, here the well system. The losses of radioactive contaminant(s) from the ‘Well’ system are:

Radionuclide decay. Radionuclides leaving the ‘Well’ system towards Receptor environments biosphere objects where well water is being directly used or for irrigation (e.g. garden plot).

Figure 2 - Loading inputs (inward arrows) + Losses (outwards arrows) in the Well model

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A4.3.3. Potential coupled models Coupled models are defined as models that can generate loadings to the investigated system (here the Well system) or receive losses from the latter. The Well model can be coupled to other models of the Normalysa library. The latter can provide loading estimates or use losses from the Well as input data: Coupled model

Can provide estimates of the following loading(s) Radioactive contaminant concentration in outflow water coming into the well

‘Aquifer’

Can use the following losses from the well as input data

Radioactive contaminant concentration in outflow water

‘Garden plot’

A4.3.4. Parameters A Parameter is defined as a fixed term in the model that during a simulation but can be changed in different runs as a method for conducting sensitivity analysis or to achieve calibration goals. For running the Well model, the following parameters must be informed: Site-specific parameters: Name

Abbreviation and Unit

Purpose

Used for calculating the following state variable(s)

Radionuclide concentration in background groundwater

c_gw_background (Bq/m3)

Represents the radionuclide concentration in background

Radionuclide concentration in well water (c_water)

groundwater forming the remaining fraction of the well debit and is used to determine the radionuclide concentration in well water

Radionuclide concentration in the water coming from the aquifer

c_water_pore_out (Bq/m3)

Represents the radionuclide

Radionuclide concentration

concentration in the aquifer

in well water (c_water)

(flow tube) groundwater flowing into the well

Fraction of

f_debit_flowtube (-)

groundwater coming to the well from the flow tube

Represents the fraction of groundwater coming to the well from the flow tube and used to determine the radionuclide concentration in well water

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Radionuclide concentration in well water (c_water)

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A4.3.5. Regulatory State variables A ‘Regulatory State variable’ is defined as a dependent variable calculated within the model. It is generally time-dependent because it is calculated from parameters, but also from time-dependent forcing variables and loadings. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes.

State variable n°

Name

Abbreviation and unit

1

Radionuclide concentration in well water

c_water (Bq/m3 )

A4.4. Mathematical models for State variables The objective of this section is to present the mathematical models used for calculating each of the State variables conceptually listed in A4.3.5.. In the following diagrams, the following symbols were adopted:

A4.4.1. Regulatory State variables Concentration in water The data process for calculating the State variable c_water of the lake is reminded here:

The equation for calculating the radionuclide concentration in the wellwater, c_water, is (𝟏) 𝑐𝑤𝑎𝑡𝑒𝑟 = 𝑓𝑑𝑒𝑏𝑖𝑡,𝑓𝑙𝑜𝑤𝑡𝑢𝑏𝑒 × 𝑐𝑤𝑎𝑡𝑒𝑟,𝑝𝑜𝑟𝑒,𝑜𝑢𝑡 + (1.0 − 𝑓𝑑𝑒𝑏𝑖𝑡,𝑓𝑙𝑜𝑤𝑡𝑢𝑏𝑒) × 𝑐𝑔𝑤,𝑏𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛𝑑

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Groundwater flow and radionuclide transport models for groundwater pathway analyses for ESS ESS-0051622

Name

Role/Title

Dmitri Bugai

Senior Consultant

Thomas Hjerpe

Senior Consultant, Facilia AB

Reviewer

Daniela Ene

Senior scientist, EHS division, ESS

Approver

Peter Jacobsson

Head of EHS division, ESS

Owner

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DOCUMENT REVISION HISTORY Revision Reason for and description of change

Author

Date

1

First issue

Dmitri Bugai

2016-02-05

1.1

Approved by Facilia

Rodolfo Avila, Facilia AB 2016-02-15

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TABLE OF CONTENT

PAGE

DOCUMENT REVISION HISTORY ....................................................................... 2 1.

GROUNDWATER FLOW MODEL .......................................................... 6

1.1.

Introduction ....................................................................................... 6

1.2.

Groundwater flow domain: physical dimensions, layering and numerical grid.............................................................................. 6

1.3.

Hydraulic parameters and boundary conditions ................................. 9

1.4.

Example of simulation results ........................................................... 12

2.

RADIONUCLIDE TRANSPORT MODEL ................................................ 14

2.1.

Introduction ..................................................................................... 14

2.2.

Conceptual transport model and its realization using Normalysa library for Ecolego 6 ........................................................ 15

2.3.

Mathematical model ........................................................................ 20

3.

REFERENCES ..................................................................................... 22

ANNEX 1. THE NORMALYSA MODEL FOR AQUIFER TRANSPORT .................... 24 A1.1. Model purpose ...................................................................................... 24 A1.2. Model applicability ................................................................................ 25 A1.3. Model components ............................................................................... 26 A1.4. Mathematical models for State variables .............................................. 41 A1.5. Mass balance equation for Media ......................................................... 45 ANNEX 2. THE NORMALYSA MODEL FOR AQUIFER MIXING ........................... 47 A2.1. Model purpose ...................................................................................... 47 A2.2. Model applicability ................................................................................ 48 A2.3. Model components ............................................................................... 49 A2.4. Mathematical models for State variables .............................................. 62 A2.5. Mass balance equation for Media ......................................................... 65 ANNEX 3. THE NORMALYSA MODEL FOR CONTAMINATED SOIL LAYER ......... 66 A3.1. Model purpose ...................................................................................... 66 Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015

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A3.2. Model applicability ................................................................................ 67 A3.3. Model components ............................................................................... 68 A3.4. Mathematical models for State variables .............................................. 80 A3.5. Mass balance equation for Media ......................................................... 82 ANNEX 4. THE NORMALYSA MODEL FOR A WELL ........................................... 83 A4.1. Model purpose ...................................................................................... 83 A4.2. Model applicability ................................................................................ 84 A4.3. Model components ............................................................................... 84 A4.4. Mathematical models for State variables .............................................. 86

LIST OF TABLES Table 1 .... Hydraulic parameter values for the 2D cross sectional groundwater flow model for the proton LINAC tunnel............................................................. 10

LIST OF FIGURES Figure 1... The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel (not to scale). ............................................... 7 Figure 2... The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel (Vertical exaggeration = 10). ........................ 8 Figure 3... The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel....................................................................... 8 Figure 4... Boundary conditions for the 2D cross sectional groundwater flow model for the proton LINAC tunnel (Vertical exaggeration = 10). ........................ 9 Figure 5... Scheme illustrating the water balance for the lower aquifer layer. .................... 11 Figure 6... Example simulation results for the 2D cross-section model for the proton LINAC tunnel (Vertical exaggeration = 10). Green arrow heads along the groundwater flow pathline corresponds to the travel time of 365 days. .............................................................................................................. 13 Figure 7... Conceptual model of radionuclide transport process to groundwater from the proton LINAC tunnel. ............................................................................ 17 Figure 8... Ecolego interaction matrix for the radionuclide transport model. ..................... 18

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Figure 9... Ecolego interaction matrix for the ‘Activated Soil Source Term’ subsystem. ........................................................................................................... 19

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1.

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GROUNDWATER FLOW MODEL

This section describes the groundwater flow model that is used in this project for simulating groundwater flow processes in the vicinity of the proton LINAC tunnel.

1.1.

Introduction

The groundwater flow model employs a 2D cross-sectional groundwater schematization of the flow from the tunnel to a well, which is briefly described in the assessment context report (Avila et al., 2015). The groundwater flow schematization, numerical implementation of the model and relevant hydraulic parameters will be presented in more detail in the following sections of this report. The numerical groundwater flow model is implemented using the MODFLOW computer code (McDonald and Harbaugh, 1983). MODFLOW is the USGS's finite-difference groundwater model1. Being extensively used, verified and validated over the last three decades in numerous industrial and research applications, MODFLOW is currently considered an international standard for simulating and predicting groundwater flow conditions (McDonald and Harbaugh, 2003). The MODPATH particle tracking postprocessing package for MODFLOW (Pollock, 1994) is used for groundwater flow net analyses. To facilitate input of parameters and visualization of MODFLOW simulation results the GUI pre-/post processing software Visual Modflow is used in this report (Guiger and Franz, 1996).

1.2.

Groundwater flow domain: physical dimensions, layering and numerical grid

A schematic groundwater flow domain for the 2D cross-sectional groundwater flow model is shown in Figure 1. This scheme is generally similar to the conceptual model in Figure 2-3 in (Huutoniemi and Nordlinder, 2014). The model assumes steady state groundwater flow regime. Dimensions and absolute elevation marks of different geological layers are based on information and data presented in (Huutoniemi and Nordlinder, 2014; Moller et al. 2013, Moller and Sundlof, 2013). A comparison of hydrogeological and hydraulic parameters of soil layers used in the ESS groundwater pathways assessment report ESS-0000025 (Huutoniemi and Nordlinder, 2014) and for groundwater transport analyses in the report ESSS-0005205 (Moller at al., 2013) was carried out by (Moller and Sundlof, 2013), and has shown that both studies used a generally consistent set of parameter values with relatively minor differences in hydraulic parameters.

1

http://water.usgs.gov/ogw/modflow/

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Based on data presented in (Huutoniemi and Nordlinder, 2014; Moller et al. 2013, Moller and Sundlof, 2013) the upper part of the soil profile at the site (including upper portion of the aquifer) is composed of relatively low permeability clay till material (hydraulic conductivity 10-8 – 10-6 m s-1), while the lower part of the aquifer is a sandy intermoraine sediment layer and underlying boundary fissured zone of bedrock is composed of a higher conductivity deposits (10-6 to 10-4 m s-1). Similarly to the schematization of (Huutoniemi and Nordlinder, 2014) we assume that this deeper higher permeability ‘sandy sediment’ layer has a combined thickness of 2 m (see Figure 1). The numerical grid of the MODFLOW 2D cross sectional model is shown in Figure 2. The horizontal (X axis) size of the flow domain is 350 m. The tunnel is situated in the interval from X= 45 m to X=50 m. The downstream (right hand side) boundary is set at 300 m distance from the tunnel (X=350 m). The upstream (left) boundary (X=0) is situated at 45 m distance from the tunnel. The size of the flow domain along the vertical coordinate (Z axis) is 11 m, which corresponds to interval from Z=70 m to Z=81 m. The lower layer (higher permeability “sand”) is situated in the range from Z=70 to 72 m. The upper aquifer layer (clay till) is situated in the range from Z=72 to 81 m. The numerical grid spacing in X direction (horizontal) ranges from 1 m to 0.5 m. A finer numerical grid was set in the close vicinity of the tunnel (see Figure 3). The numerical grid spacing in Z direction (vertical) was set to 0.5 m.

Figure 1

The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel (not to scale).

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Figure 2

The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel (Vertical exaggeration = 10).

Figure 3

The conceptual scheme of the 2D cross-sectional groundwater flow model for the proton LINAC tunnel.

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1.3.

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Hydraulic parameters and boundary conditions

The boundary conditions for the groundwater flow model are illustrated in Figure 4. First order boundary conditions (prescribed hydraulic head values) were set for the lower aquifer unit. The boundary conditions at upstream (X1=0) and downstream (X2=350 m) boundaries were set based on the assumptions that the design value of the hydraulic head in the vicinity of the tunnel (Xt=50 m) is Ht=75 m (Moller et al. 2013, p.7) and that the horizontal hydraulic head gradient in the aquifer equals i=0.013 (Moller et al. 2013, p.13). Then the hydraulic head value at the upstream and downstream boundaries can be calculated as follows: Hk = Ht - (Xk-Xt)*i (k=1,2) Calculated values of the hydraulic head at corresponding boundaries are listed in Table 1. Table 1 lists also other hydraulic parameter values for the 2D cross sectional groundwater flow model (for the proton LINAC tunnel for the upper and lower aquifer layers), which were used to set up the model. These data are derived from the summary parameters tables presented in (Moller and Sundlof, 2013; Tables 4 and 5, p.9), and represent best guess parameter estimates based on the understanding of the site by the authors of this report. Sensitivity of the groundwater flow and radioactive contaminant transport model predictions to various parameter values and assumptions will be analysed at the next steps of this project.

Figure 4

Boundary conditions for the 2D cross sectional groundwater flow model for the proton LINAC tunnel (Vertical exaggeration = 10).

An important model parameter is the hydraulic conductivity value for the lower (higher permeability) aquifer unit. This parameter in previous analyses was treated as a highly uncertain parameter with the estimated range from 10-5 to 10-3 m/s in (Huutoniemi and Nordlinder, 2014), and from 10-6 to 10-4 m/s in (Moller et al. 2013).

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Table 1

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Hydraulic parameter values for the 2D cross sectional groundwater flow model for the proton LINAC tunnel.

Parameter

Unit

Value

Reference / Remark

Hydraulic head gradient in the lower unit

unitless

0.013

(Moller et al. 2013, p.13)

Infiltration recharge rate

m/y

0.1

(Moller et al. 2013, p.8-9)

Hydraulic head at upstream boundary (lower aquifer unit)

m

75.65

Calculated in this report

Hydraulic head at downstream boundary (lower aquifer unit)

m

71.10

Calculated in this report

Hydraulic conductivity

m/s

1.0E-7

(Moller and Sundlof , 2013, p.9)

Bulk density

kg/m3dw

2.0

(Moller and Sundlof , 2013, p.9)

Effective porosity, %

unitless

0.05

(Moller and Sundlof , 2013, p.9)

Hydraulic conductivity

m/s

5.0E-5

Calculated in this report from water balance; resulting value consistent with (Moller and Sundlof , 2013, p.9)

Bulk density

kg/m3dw

1.65

(Moller and Sundlof , 2013, p.9)

Effective porosity, %

unitless

0.2

(Moller and Sundlof , 2013, p.9)

Hydraulic parameters of the upper aquifer (“clay till”)

Hydraulic parameters of the lower aquifer (“sand”)

We have carried out simple balance calculations to constrain the hydraulic conductivity of the lower aquifer unit (Kf) based on known infiltration recharge rate to the lower aquifer (Infiltration_rate), the linear size of the watershed (Lw) and the hydraulic head gradient at the outflow boundary (i). Balance calculations are illustrated by the scheme in Figure 5.

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Figure 5

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Scheme illustrating the water balance for the lower aquifer layer.

The following balance equation has to be satisfied: Infiltration_rate * Lw = Haq * Kf *i Based on the above equation the hydraulic conductivity of the lower aquifer unit can be calculated as: 𝑲𝒇 =

𝑰𝒏𝒇𝒊𝒍𝒕𝒓𝒂𝒕𝒊𝒐𝒏_𝒓𝒂𝒕𝒆 × 𝑳𝒘 𝑯𝒂𝒒 × 𝒊

Assuming that the infiltration rate is 100 mm/y, the hydraulic head gradient is i=0.013, Haq=2 m, and the linear size of the watershed is some 350-450 m (Huutoniemi and Nordlinder, 2014; Moller et al. 2013), the hydraulic conductivity of the lower aquifer layer can be estimated at Kf = 4.4…5.5E-5 m/s. This estimate is consistent with the previously estimated range for this parameter in the cited above reports on the hydrogeology of the study site. The Kf value of 5.0E-5 m/s was used in this report as an initial ‘best guess estimate’ to set up the groundwater flow model.

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1.4.

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Example of simulation results

Example of groundwater simulation results using input parameter values listed in Table 1 are shown in Figure 6. The figure shows equipotential lines of the hydraulic head (blue lines) and also the groundwater pathline (green) for a particle placed near the basement of the proton LINAC tunnel (in the supposed zone of activated soil). Green arrow heads along the groundwater flow pathline corresponds to a travel time of 365 days. It can be seen that the flow direction in the upper clay till layer is nearly vertical while the flow in the lower sandy aquifer layer is sub-horizontal. For the considered groundwater pathline, the water travel time from the activated soil layer in clay till to the lower confined sand unit is estimated at 4 years, while the water travel time in the lower aquifer unit is estimated at ~ 3.25 years (from the aquifer area below the tunnel zone to the downstream boundary of flow domain where the water well is supposedly located). Based on the above data, the travel time of retarded species can be easily estimated. For example, if we assume that for Na-22,which is an important activation product of radiological concern with half-life of 2.6 y (Ene, 2015), the Kd for sand equals 1.3 l/kg (Huutoniemi and Nordlinder, 2014; Table 2-3 at p.10), the corresponding retardation factor is R=11.7 and the subsurface travel time of Na-22 to a well in the sand aquifer can be estimated at 38 years (~ 14 decay half-lives). This indicates that radiological impact from this radionuclide likely will be low; as a consequence of radioactive decay during transport. Systematic analyses of travel times for different activation products and sensitivity analyses of model predictions to various parameter values and assumptions will be carried out at the next steps of this project.

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Figure 6

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Example simulation results for the 2D cross-section model for the proton LINAC tunnel (Vertical exaggeration = 10). Green arrow heads along the groundwater flow pathline corresponds to the travel time of 365 days.

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RADIONUCLIDE TRANSPORT MODEL

This section of the report describes the radionuclide transport model for simulating radioactive contaminant transport processes from the proton LINAC tunnel to a water well.

2.1.

Introduction

The radionuclide transport model uses information on water fluxes and flow rates in the subsurface in the vicinity of the proton LINAC tunnel calculated by means of MODFLOW groundwater flow model described in the previous section of this report. The radionuclide transport model was developed using the Ecolego 6 software (Avila et al., 2005). Ecolego2 is a software package developed by Facilia AB for implementing deterministic and stochastic dynamic models described by first order ordinary differential equations. To implement the radionuclide transport model for the proton LINAC tunnel we used the NORMALYSA3 model library for Ecolego 6 developed in the frame of IAEA MODARIA4 (Modelling and Data for Radiological Impact Assessments) project WG-3 activities. The NORMALYSA software tool is designed for radiological safety assessment purposes, and it incorporates a library of generic models for Ecolego 6 organized in four different sub-sets: Source Term, Transport, Receptor and Dose Modules (e.g., models described in the IAEA SRS-19 report (IAEA, 2001)), as well a database of default model parameter values based on reputable sources (e.g., IAEA TRS-472 report (IAEA, 2010)). The NORMALYSA tool was extensively tested, verified and benchmarked in the frame of the IAEA MODARIA WG-3 activities, in particular by comparing it to RESRAD tool5 for a set of a test cases. A number of pre-programmed NORMALYSA source-term and groundwater transport models were used to model relevant elements of the LINAC tunnel radionuclide transport model. The schematization of radionuclide (activation product) transport process to groundwater from the proton LINAC tunnel, implementation of the transport model in Ecolego 6 using NORMALYSA library and relevant transport parameters will be presented in more detail in the following sections of this report.

2

http://ecolego.facilia.se/ecolego/ http://project.facilia.se/normalysa/software.html 4 http://www-ns.iaea.org/projects/modaria/ 5 https://web.evs.anl.gov/resrad/ 3

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2.2.

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Conceptual transport model and its realization using Normalysa library for Ecolego 6

Conceptual model The conceptual model of radionuclide (activation product) transport from the proton LINAC tunnel to the groundwater is shown in Figure 7. The model simulates the radionuclide transport processes from the contaminant source term (soil layer surrounding the tunnel containing activation products) in the aquifer cross section, and its structure is coherent with the MODFLOW model described in the previous section of this report. The source term of radioactivity, is a soil layer of about 1 m thickness surrounding the tunnel, which contains activation products (Huutoniemi and Nordlinder, 2014). The activated soil surrounding the tunnel is sub-divided within the model into several sublayers (see Figure 7): bottom layer, side layers, and top layer. The bottom soil layer can be situated in partially or fully water saturated soil conditions (the elevation of the bottom of the tunnel is 74.7 m (Moller and Sundlof, 2013), while the design value of hydraulic head in the vicinity of the tunnel is 75 m (Moller et al. 2013, p.7)). The side layers and top layer of soil are in unsaturated conditions. It is assumed that activation products can be leached from the soil layers in unsaturated conditions by infiltration of atmospheric precipitations. The radioactive contaminants leached from the unsaturated soil zone infiltrate to the saturated soil zone (the “bottom layer” of soil). The radionuclides are further mobilized from the “bottom layer” of soil (situated in the saturated zone) by the groundwater flow in the aquifer. The leaching rate is determined from groundwater flow modeling using the MODFLOW- based model of site. To simulate radionuclide leaching from the different soil layers described above we use the ‘Contaminated Soil Without Layer’ model from the ‘Sources’ library of NORMALYSA employing the soil leaching model described in (Baes and Sharp, 1983). This model assumes that all radionuclide inventories in the contaminated soil layer are in mobile (exchangeable) form, and that the radionuclide partitioning between the soil porous solution and soil matrix is described by the Kd model. The mathematical equations of the model will be presented below in Section 2.3. Radionuclides leached from contaminated soil zone surrounding the tunnel are first transported by groundwater flow in the relatively low permeability clay till layer towards the confined sand layer, situated in the bottom part of the aquifer (see Figure 7). Based on simulation of hydrogeological conditions, using the MODFLOW-based 2D cross-sectional groundwater flow model, the flow in the clay till layer occurs in vertical downward direction.

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To simulate the radionuclide transport in the clay till later we used the ‘Aquifer Transport’ module from the NORMALYSA library, which was appropriately configured to model this layer. This module simulates radionuclide transport along the flow path in the aquifer. It accounts for the advection, dispersion, radioactive decay and sorption process (using the Kd model). This module employs the ‘Transport’ block of Ecolego 6 to simulate contaminant migration in groundwater. Mathematical models and expressions for advective and dispersive transfer coefficients are presented in section 2.3. The radionuclide transport process in the confined sand layer were simulated using the ‘Aquifer Mixing’ and ‘Aquifer Transport’ modules from the NORMALYSA library, which were configured to model the sand aquifer unit. The ‘Aquifer mixing’ module simulates the aquifer zone within the confined sand layer immediately below the tunnel, where contaminated infiltration flux from the clay till layer mixes with the horizontal groundwater flow in the confined sand aquifer unit. The subsequent ‘Aquifer Transport’ module simulates the radionuclide transport by advection dispersion process towards a water well situated at a 300 m distance from the contaminant source, taking into account retardation due to sorption.. The radionuclide t concentration in well water is modeled using the ‘Well’ module from the ‘ ‘NORMALYSA’ library. The ‘Well’ module calculates radionuclide concentration in groundwater pumped by a water-well using a simple mixing model. It is assumed that some fraction of the well debit is formed by contaminated groundwater from the flow tube originating from the contamination source-term, while another part of well debit is formed by non-contaminated groundwater.

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Figure 7

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Conceptual model of radionuclide transport process to groundwater from the proton LINAC tunnel.

Realization of the radionuclide transport model in Ecolego 6 using NORMALYSA library The structure of radionuclide transport model in the format of Ecolego interaction matrix is shown in Figure 8. It shows the main sub-systems (sub-models) of the overall transport model and data exchanges between these sub-models.

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Figure 8

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Ecolego interaction matrix for the radionuclide transport model.

For the ‘Aquifer Transport (Clay till)’, ‘Aquifer Mixing’, ‘Aquifer Transport (Sand)’, and ‘Well’ sub-systems we used the corresponding modules from the NORMALYSA model library (see previous paragraph). Descriptions of the NORMALYSA modules are given in annexes to this report. Data exchanges between different modules take place in the form of radionuclide activity fluxes. The radioactivity flux, Activity_Flux, (Bq/y) is calculated in a general case using the following expression: Activity_Flux = Water_Flux * Cgw where Water_Flux (m3/y) is groundwater flux from the respective compartment, and Cgw (Bq/m3) is radionuclide concentration in out-flowing groundwater. Radionuclide concentration in groundwater is calculated within the corresponding sub-system in accordance with the mathematical groundwater transport model. Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 18 (86)

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Inflowing and out-flowing water flux values, for specific sub-regions of the groundwater flow model (e.g., for activated soil layers; clay till layer, confined sand layer), were calculated using the MODFLOW–based groundwater flow model. To calculate water budgets for specific sub-regions of the overall groundwater flow model the ZONEBUDGET subroutine (Harbaugh, 1990) for MODFLOW was used. The Ecolego interaction matrix for the ‘Activated Soil Source Term’ subs-system is shown in Figure 9. The activated soil layer surrounding the tunnel was sub-divided into two compartments – ‘Activated Soil – Bottom’ (layer) and ‘Activated Soil – Side’ layers. The inventory of radioactivity in the top layer directly above the tunnel (see Figure 7) is conservatively included to the ‘Activated Soil – Sides” compartment.

Figure 9

Ecolego interaction matrix for the ‘Activated Soil Source Term’ subsystem.

To simulate the activated soil compartments described above we use the ‘Contaminated Soil Layer’ model from the NORMALYSA library. A description of this module is given in the Annex 3 to this report.

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The production of activation elements within the soil layers surrounding the tunnel is modeled as Ecolego ‘Transfer’ blocks6,where the corresponding activity production rates (in Bq/y) are specified as parameters. It was assumed that activation element production rates within the specific soil layer (Qi) are proportional to the volume of this layer (Vi), so that the following equation holds: Qi = Qtotal * Vi /Vtotal Where Qtotal is the integral activation element production rate in activated soil in the vicinity of the proton LINAC tunnel, and Vtotal is the total volume of soil surrounding the tunnel, where activation process are taking place. Soil volume values for specific layers and total volume can be easily calculated based on the information on the assumed system geometry shown at Figure 1. The Qtotal values can be found, for example, in (Ene, 2010).

2.3.

Mathematical model

This sub-section of the report presents main mathematical expressions, which are used to model radionuclide transfers (fluxes) between different model compartments. Radioactivity source term To simulate radionuclide leaching from contaminated soil layer we use the soil leaching model described in (Baes and Sharp, 1983), which is commonly used in safety assessment analyses of radioactive waste repositories (IAEA, 2004a,b). The leaching rate from contaminated soil layer is defined by leaching (transfer) coefficient:

leach

w H w Rw Rw 1 K d ,w , w

,

where the following notation is used: - infiltration recharge (or flow) rate through the soil layer (m/y), w - water content in the soil layer (unitless), Hw - thickness of contaminated soil (waste) layer (m), Rw – sorption retardation coefficient in the soil layer (unitless), w – soil bulk density (kg/dm3), Kd,w – sorption distribution coefficient of soil(l/kg). Transfer coefficients for advective and dispersive transport The following well-known expressions were used to model advective-dispersive transport of radionuclides in the “distributed source” soil layer, unsaturated zone and aquifer (e.g., IAEA, 2004b, p.270). Advective transfer coefficient in the aquifer (ad,aq)

6

http://ecolego.facilia.se/ecolego/show/Transfer

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ad ,aq

V n dX Raq

aq Raq 1 K d ,aq

,

where the following notation is used: V – Darcy velocity (flow rate) in the aquifer (m/y), n – aquifer porosity (unitless), dX –size of compartment in the aquifer along the flow path (m), Raq – sorption retardation coefficient in the aquifer (unitless), aq –bulk density of the aquifer (kg/dm3), Kd,aq – sorption distribution coefficient of the aquifer (l/kg). Dispersive transfer coefficient in the aquifer (dis,aq)

dis ,aq

aq V n dX 2 Raq

,

Where aq – is dispersivity parameter for transport in the aquifer (m). Notations of other parameters are same as in previous formulas. Dispersivities (hydro-dispersion coefficients) An important parameter in the groundwater transport calculations is the ydrodynamic dispersion coefficient (D): D = V, Where V is the groundwater flow velocity (m/y), and is the dispersivity parameter (m). Measuring the dispersivity coefficient in-situ is a difficult experimental task, and the most practical approach is to use literature data for the parameter. It is known, that dispersivity is a scale-dependent parameter, which increases with increasing scale of the groundwater transport (Gelhar et al., 1992). A simple general approximation that is frequently used is that is set to the one-tenth of the scale of the problem (Walton, 1998; IAEA, 2004a): = 0.1 L, where L is groundwater travel distance (m). This formula is currently used in the NORMALYSA module library to define the default dispersivity values for aquifer transport modeling.

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3.

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REFERENCES

Avila, R., Broed, R., Pereira, A. (2005). ECOLEGO - A toolbox for radio ecological risk assessment, Proceedings of the International Conference on the Protection from the Effects of Ionizing Radiation’’, IAEA-CN-109/80. Stockholm: International Atomic Energy Agency. 229 - 232 Avila R., Hjerpe T., Windmark F., Ene D. (2015). Estimation of the Dose Factors for Updating the EES Environmental Impact Analysis Report. Assessment Context. Facilia AB. Baes, C.F.,III, and Sharp, R.D. (1983). A proposal for estimation of soil leaching and leaching constants in assessment models. J.Eviron. Qual., 12, 17-28 Bugai D., Avila R. (2015). NORMALYSA tool for Safety Assessment and Uranium Residues Management (Overview of IAEA MODARIA project WG-3 activities). Paper presented at the IAEA CGULS meeting, Dushabe, Tadjikistan, 1-5 June 2015, doi: 10.13140/RG.2.1.1393.0966 Ene D. (2010). Radioprotection studies for the ESS superconducting linear accelerator. Preliminary estimates. Ref. 1093060 v01.2010. Ene, D. (2015). ESS-0028551 Assessment of environmental consequences of the normal operations of ESS facility. Part #1 - Input data, Source Term, breakdown of radionuclides and related basic information. Gelhar, L.W., Welty, C., Rehfeldt, K.R. (1992). A Critical Review of Data on Field-Scale Dispersion in Aquifers, Water Resour. Res. 28 (7) 1955–1974. Guiger N., Franz T. (1996) User’s manual for Visual MOFLOW. Waterloo Hydrogeologic Inc. IAEA (2001). Generic Models for Use in Assessing the Impact of Discharges of Radioactive Substances to the Environment. Safety Report Series no.19, International Atomic Energy Agency, Vienna, 2001. IAEA (2004a). Safety Assessment Methodologies for Near Surface Disposal Facilities. Results of a co-ordinated research project Volume 1 Review and enhancement of safety assessment approaches and tools. International Atomic Energy Agency, Vienna. IAEA (2004b). Safety Assessment Methodologies for Near Surface Disposal Facilities. Results of a co-ordinated research project Volume 2 Test cases. International Atomic Energy Agency, Vienna. IAEA (2010). Handbook of Parameter Values for the Prediction of Radionuclide Transfer in Terrestrial and Freshwater Environments. Technical report Series no.472, International Atomic Energy Agency, Vienna, 2010.

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Harbaugh, A.W. (1990) A computer program for calculating sub-regional water budgets using results from the U.S. Geological Survey modular three-dimensional ground-water flow model: U.S. Geological Survey Open-File Report 90-392, 46 p. Huutoniemi T., Nordlinder T. (2014). Dose from activated soil in connection to a proton LINAC in Lund, Sweden. Report no. N-14/193, Studsvik Nuclear AB, 2014. Maul P., Robinson P., Broed R., Avila R. (2004) Further AMBER and Ecolego Intercomparisons SKI Report 2004:05 SSI Report 2004:01. Maul P., Robinson P., Avila R., Broed R., Pereira, A., Xu, S. (2003) AMBER and Ecolego Intercomparisons using Calculations from SR 97 SKI Report 2003:28’’, SSI report 2003:11 McDonald, M.G., Harbaugh, A.W. (1983). A modular three-dimensional finite-difference ground-water flow model. Open-File Report 83-875. U.S. Geological Survey. McDonald M.G.,Harbaugh, A.W. (2003). The History of MODFLOW. Ground Water 41 (2): 280–283. Moller H., Sundlof B., Alsterling H. (2013). GeoPM5 - Entire Site. Document ID ESS-0032672, G01 Tyrens AB, 2013 Moller H., Sundlof B. (2013). GeoPM6 – Radiation Protection Aspects. Document ID ESS0005023, G01-DT-DEFSGD Tyrens AB, 2013. Pollock, D.W. (1994) User's Guide for MODPATH/MODPATH-PLOT, Version 3: A particle tracking post-processing package for MODFLOW, the U.S. Geological Survey finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 94-464. Rensfeldt, V. (2014) The Normalysa tool. Paper presented at Symposium ores and radioactivity; Simposio minerios e radioatividade; Rio de Janeiro, RJ (Brazil); 18-20 August 2014; INIS-BR--14486 Walton, W.C. (1988). Practical Aspects of Groundwater Modelling, 3rd ed., National Water Well Association, Worthington, Ohio.

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ANNEX 1. THE NORMALYSA MODEL FOR AQUIFER TRANSPORT A1.1. Model purpose A1.1.1. Goal The goal of the ‘Aquifer’ module is to dynamically simulate the transport of radionuclides from the Source of radioactivity (e.g., ‘Tailings without Cover’, ‘Contaminated land’), which may be coupled with other modules simulating intermediate transfer such as ‘Unsaturated Zone’ and/or as ‘Aquifer Mixing’, within the groundwater aquifer towards receptor environment(s). The output of the ‘Aquifer’ module usually serves an input to the receptor module(s) (e.g., ‘Well’, or ‘Fresh Water Body’) (Figure 1).

Figure 1 – Overall model of the waste site system incorporating the Aquifer module

A1.1.2. Potential decision and regulatory framework(s) Coupled with the Source model (and possibly modules simulating intermediate transfers), the ‘Aquifer’ module can: provide an estimation of the time-dependent concentration of the targeted radionuclide(s) in aquifer pore water at a given distance from the source along the groundwater flow tube; provide an estimation of the time-dependent mass (activity) flux of the targeted radionuclide(s) in the aquifer cross-section at a given distance from the source along the groundwater flow tube.

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The output of the ‘Aquifer’ module usually serves an input to the receptor modules (‘Well’, or ‘Fresh Water Body’) (see Figure 1). These outputs can be used for evaluating the residence time of radioactive contaminant(s) in groundwater and the risk over time to exceed a given regulatory threshold for radioactive contaminant(s) in corresponding receptor compartments defined by the relevant regulations.

A1.2. Model applicability A1.2.1. Spatial scale and resolution The ‘Aquifer’ module is defined as a three-dimensional ‘groundwater flow tube’ system (i.e. defined by its cross-section area and length). The relevant spatial scale and resolution are governed by the homogeneity of the hydrogeological system under investigation (e.g. homogeneity with respect to hydraulic properties, geochemical properties, contamination levels, etc.). The ‘Aquifer’ module assumes that the system is homogeneous (laterally, longitudinally and vertically) with respect to its properties and parameters. For aquifer environments showing laterally significant variations in their properties, it is recommended to subdivide these latter in a sequence of homogeneous and independent flow zones (flow tubes). A1.2.2. Temporal scale and resolution There is no limitation for temporal scale (i.e. duration of the simulation). Processes and parameters included in the model of water dynamics in the aquifer (i.e., infiltration recharge rate, Darcy velocity) are relevant at yearly resolution. Therefore the ‘Aquifer’ module and coupled models are run at a yearly resolution.

A1.2.3. Steady-state vs dynamic processes The ‘Aquifer’ module simulates radionuclide transport processes within the hydrogeological environment dynamically, however: It is assumed that radionuclide transport in the aquifer occurs under the steady-state groundwater flow conditions;

The exchanges of radioactive contaminants between pore water and soil matrix are assumed to be at sorption equilibrium (i.e. sorption process are represented by a distribution coefficient Kd).

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A1.3. Model components A1.3.1. Media considered Definition: A ‘Medium’ is defined as an environmental or human compartment assumed to contain a given quantity of the radionuclide (chemical). The quantity of the radionuclide in the media is governed by loadings/losses (see A1.3.2 and A1.3.3) from/to other media and by radioactive decay. The ‘Aquifer’ module schematizes the groundwater aquifer (flow tube) system as a sequence of individual Transport Cells with a constant length. The model expressions operate total radionuclide inventories in each transport cell. Then radioactive contaminant concentrations in pore water and soil matrix can be calculated for each transport cell based on known cell inventory and equilibrium Kd-based sorption model describing radionuclide partitioning between the liquid and solid phases. The number and lateral size of cells is determined automatically based on specified accuracy requirements. The program generates the need number of cell compartments implicitly using Ecolego 6.0 ‘Transport’ block. The schematization and media considered are represented in Figure 2.

Figure 2 – Media considered in the Aquifer module

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A1.3.2. Loadings Definition: A ‘Loading’ is defined as the rate of release/input of the radionuclide of interest to the receiving system, here the ‘Aquifer’ system. The inputs of radioactive contaminant(s) into the ‘Aquifer’ system can have the following origins: Contaminants leached from the waste disposal facilities (such as uranium mill tailings facilities); Contaminants originating from contaminated topsoil layer due to leaching by atmospheric precipitations; Contaminants originating from direct application of liquid effluents on topsoil (e.g. direct application of sludge originating from sewage treatment plants, fertilizers, etc.); Contaminants originating from the surface water or groundwater systems through water used for irrigation purposes, etc.

The inputs of radioactive contaminant(s) into the ‘Aquifer’ system are needed to be defined by user in the coupled external Source model (possibly coupled with modules simulating intermediate transfers). In this case the outputs of the coupled Source module (or modules simulating intermediate transfers) are used as loading inputs for the ‘Aquifer’ model. The contaminant input is defined by specifying two parameters: radioactive contaminant activity concentration in the infiltrating (inflowing) water and inflow rate (Darcy velocity). The loading inputs are represented in Figure 3.

Figure 3 – Media considered + Loading inputs in the ‘Aquifer’model

A1.3.3. Losses Definition: A ‘Loss’ is defined as the rate of output of the radionuclide of interest from the receiving system, here the ‘Aquifer’system. The losses of radioactive contaminant(s) from the ‘Aquifer’ system are:

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Contaminant leaving the ‘Aquifer’ system towards Receptor environments (e.g., ‘Well’, ‘Lake’ or ‘River’ modules) or to the adjacent downstream zones of the hydrogeological system (e.g., consecutive ‘Aquifer’ module) by outflow (i.e., contaminant movement by advective outflow); Radioactive decay of contaminant in the Aquifer media.

The losses of contaminant(s) from the ‘Aquifer’ system are represented in Figure 4.

Figure 4 – Media considered + Loading inputs + Losses in the Aquifer model.

A1.3.4. Exchanges between model media Definition: An ‘Exchange’ is defined as the transfer of the radionuclide of interest between two media compartments of the system, here the Aquifer system. The potential exchanges of radioactive contaminant(s) between the media of the Aquifer model are: Advective transport of contaminants from Transport Cell i to Transport Cell i+1 (i.e. radioactive contaminant transport by advective water flow); Dispersive transport of radioactive contaminants from soil Transport Cell i to Transport Cell i+1 (and vice versa); The Aquifer model assumes that sorption equilibrium of radioactive contaminant(s) between pore water and soil matrix exists in each Transport Cell (described by Kd model). However, sorption/desorption is not modelled separately as an exchange process. Radioactive contaminant concentrations in pore water and soil matrix are calculated for each Transport Cell based on known layer inventory and equilibrium Kd sorption model using corresponding partitioning equation. The exchanges of radioactive contaminant(s) between model media are represented in Figure 5.

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Figure 5 - Media considered + Loading inputs + Losses + Exchanges in the Aquifer model.

A1.3.5. Potential coupled models ‘Coupled models’ are defined as models that can generate loadings to the investigated system (here the Aquifer system) or receive losses from the latter. The ‘Aquifer’ module can be coupled to other modules of the NORMALYSA library (see Figure 1). These latter can provide loading estimates or use losses from the Aquifer as input data: Coupled model Source Term models (‘Tailings without cover’, ‘Contaminated land’) ‘Unsaturated Zone’ ‘Aquifer mixing’ ‘Aquifer’

Can provide estimates of the following loading(s) Radioactive contaminant concentration in infiltrating water; infiltration rate Radioactive contaminant concentration in infiltrating water; infiltration rate Radioactive contaminant concentration in infiltrating water; Darcy velocity Radioactive contaminant concentration in infiltrating water; Darcy velocity

‘Well’ ‘Fresh Water Body’

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Can use the following losses from the Aquifer as input data

Radioactive contaminant concentration in outflow water; Darcy velocity Radioactive contaminant concentration in outflow water; Darcy velocity Radioactive contaminant concentration in outflow water; Darcy velocity

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A1.3.6. Forcing variables A ‘Forcing variable’ is defined as an external or exogenous (from outside the model framework) factor that influences the state variables calculated within the model. Such variables include, for example, climatic or environmental conditions (temperature, wind flow, etc.). For running the Aquifer module, the following forcing variables must be informed for calculating the loading inputs: Forcing variable

Abbreviation and unit

Purpose

Concentration of the radioactive contaminant in water infiltrating (inflowing) to the aquifer Darcy velocity within the Aquifer

c_water_pore_in (Bq m-3)

Is used to calculate the input activity flux through infiltration (inflow) of contaminated ground water

u_Darcy (m.y-1)

Is used to calculate the input activity flux through infiltration infiltration (inflow) of contaminated ground water

The forcing variables (with indication of the processes they are involved in) are represented in Figure6.

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Can be calculated if the ‘Aquifer’ model is coupled to the … ‘Source Term’, ‘Unsaturated Zone’, ‘Aquifer Mixing’ ‘Aquifer Mixing’

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Figure 6- Media considered + Loading inputs + Losses + Exchanges + Forcing variables in the Aquifer model.

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A1.3.7. Parameters A ‘Parameter’ is defined as a term in the model that is fixed during a model run or simulation but can be changed in different runs as a method for conducting sensitivity analysis or to achieve calibration goals. For running the Aquifer model, the following parameters must be informed:

Site-specific parameters: Name

Abbreviation and unit

Purpose

Aquifer (flow tube) cross-section area perpendicular to flow direction

area_flow_tube (m2)

It defines the geometry of groundwater system (flow tube).

the

modelled

Length of the aquifer (flow tube)

length_flow_tube (m)

It defines the geometry of groundwater system (flow tube)

the

modelled

Used for calculating the following state variable(s) It is used for converting the total activity in the system into concentrations in media, in particular to pore water concentration in outflow water(c_water_pore_out) It is used to calculate activity flux from the aquifer (Flux_out) Length of discretized transport cell (dz)

Soil physico-chemical properties: Name

Dry density of aquifer soil Porosity of soil in the aquifer

Abbreviation and unit rho_aquifer (kg.m-3) porosity_aquifer (m3.m-3)

Purpose It is used for calculating the Retardation factor in the Aquifer It is used to calculate: transfer coefficient by advection, retardation factor, radionuclide concentration in pore water, etc.

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Used for calculating the following state variable(s) Retardation factor in the aquifer soil (Ret_aquifer) Radionuclide concentration in pore water out flowing from the aquifer (c_water_pore_out) Retardation factor in the aquifer (Ret_aquifer)

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Initial contamination of groundwater in the aquifer by radionuclides

Sorption distribution coefficient

Initial contamination inventories discretized transport cells

in

Abbreviation and unit Kd_aquifer (m3.kg-1)

Purpose

Used for calculating the following state variable(s)

The exchanges of contaminants between pore water and soil matrix are assumed to be at equilibrium and represented by a distribution coefficient at equilibrium Kd_aquifer

Retardation factor in the aquifer soil (Ret_aquifer)

Parameters related to radioactive decay: Name

Radionuclide half life

It is used for calculating the initial condition for radionuclide transport calculations in the aquifer

Parameters related to partition between phases: Name

c0_gw_aquifer (Bq m-3)

Abbreviation and unit halfLife (year)

Purpose

Used for calculating the following state variable(s)

Is used to account for radioactive decay of contaminants

Radionuclide inventories in discretized transport cell compartments and concentrations in media

Parameters controlling spatial resolution and accuracy of numerical solution of transport equation: Name

Abbreviation and unit

Minimum number of transport cells in Aquifer model

N_min

Maximum number of transport cells in Aquifer model

N_max

Purpose Sets a minimum number of transport cells in aquifer model (default value is 5). It is not recommended to change this value Sets a maximum number of transport cells in Aquifer model (default value is 100). Actual number is calculated by the model. Setting larger N_max may improve accuracy, but may increase the

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Used for calculating the following state variable(s) Length of discretized transport cell (dz)

Length of discretized transport cell (dz)

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Parameter controlling accuracy of approximation of dispersion flux

Dispersion_accuracy

needed computational resources This parameter controls the numerical dispersion when solving transport equation. Recommended value is 0.1-0.2. Smaller values may improve accuracy, but may increase the needed computational resources

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Used to calculate the number of Length of discretized transport cell (N_transp)

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A1.3.8. Intermediate State variables An ‘Intermediate State variable’ is defined as a dependent variable calculated within the model. Some State variables are fixed during a model run or simulation because they are calculated only from parameters. Some others are time-dependent because they are calculated from parameters, but also from time-dependent forcing variables. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes. For running the Aquifer model, the following state variables are calculated for the following purposes.

State variables related to discretization of the Aquifer soil profile in sub-layers:

State variable n° 1

Name

Abbreviation and unit

Purpose

Process followed for calculating the state variable

Length of discretized transport cell

dz (m)

The total aquifer system (flow tube) is subdivided into a set of transport cells for subsequent radioactive contaminant transport calculations

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2

Initial estimate of the number of transport cells

N_transp0

The number of transport cells is calculated taking into account accuracy criteria for numerical solution of advection-dispersion equation

3

Final estimate of the number of transport cells

N_transp

The final number of transport cells is adjusted taking into account N_transp0 and maximum allowed number N_max

State variable n° 5

State variables related to radioactive contaminant transport in soil: Name

Abbreviation and unit

Purpose

Process followed for calculating the state variable

Dispersivity

dispersivity_aq (m)

Dispersivity parameter for transport in the Aquifer (calculated from the linear scale of the transport problem)

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4

Retardation factor

Ret_aquifer (-)

5

Mass transfer by infiltration to the 1-st Aquifer transport cell

Infiltration

6

Mass transfer coefficient by advective transport

advection_aquifer

The contaminant is partly sorbed on the soil matrix, only the dissolved phase is assumed to move along the soil profile, resulting in a retardation. The Retardation factor accounts for the adsorption of contaminants on the soil matrix and is included in the advection-dispersion transfers within the soil profile. It is assumed that mass transport to the 1-st transport cell in the aquifer is determined by flux of infiltration water with specified concentration of contaminant(s)

This mass transfer coefficient is used to calculate fluxes of contaminants between adjacent transport cells in the aquifer by advective transport

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7

Mass transfer coefficient by dispersive transport (forward)

dispersion_aq_for ward

This mass transfer coefficient is used to calculate fluxes of contaminants between adjacent transport cells by dispersive (based on Fickian law) transport (forward direction; that is from cell i to cell i+1)

8

Mass transfer coefficient by dispersive transport (backwards)

dispersion_aq_bac k

This mass transfer coefficient is used to calculate fluxes of contaminants between adjacent transport cells by dispersive (based on Fickian law) transport (backward direction; that is from cell i to cell i-1)

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Same as for the mass transfer coefficient dispersion_aq_forward

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A1.3.9. Regulatory State variables A ‘Regulatory State variable’ is defined as a dependent variable calculated within the model. It is generally time-dependent because it is calculated from parameters, but also from time-dependent forcing variables and loadings. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes.

The following ‘regulatory state variables’ are calculated according to the flow charts presented in Figure :

State variable n° 9

Name Radioactive contaminant concentration in the porous

Abbreviation and unit c_water_pore_out

solutions out-flowing from the Aquifer (flow tube) 10

Radioactive contaminant flux from the Aquifer (integral over aquifer cross-section)

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Flux_out

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Figure 7 - Flow chart of key process for calculating the ‘regulatory state variables’

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A1.4. Mathematical models for State variables The objective of this section is to present the mathematical models used for calculating each of the State variables conceptually listed in A1.3.8. The understanding of these models is a prerequisite for understanding the mass balance equations presented in section A1.5. In the following tables, the following symbols were adopted:

A1.4.1. State variables related to discretization of the Aquifer soil profile in sub-layers Length of transport cell dz The data process for calculating the State variable ’dz’’ is reminded here:

The ‘dz’ State variable is calculated as follows:

(1)

dz

Length flow _ tube N transp

Initial estimate of the number of transport cells The data process for calculating the State variable’N_transp0’ is reminded here:

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The ‘N_transp0’ State variable is calculated as follows:

(2)

N transp0

lengthflow _ tube max N min , 2 dispersion dispersivi ty accuracy aq

here [ ] stays for the ‘whole part of a decimal number +1’.

Final estimate of the number of transport cells The data process for calculating the State variable’N_transp’ is reminded here:

The ‘N_transp’ State variable is calculated as follows:

(3)

N transp min( N transp 0 , N max )

A1.4.2. State variables related to radioactive contaminant transport in soil: Dispersivity The data process for calculating the State variable dispersivity_aq is reminded here:

The ‘dispersivity_aq’ State variable is calculated as follows: (4)

dispersivityaq 0.1 lengthflow _ tube

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Retardation factor The data process for calculating the State variable Ret_uns_zone is reminded here:

The ‘Ret_aquifer’ State variable is calculated as follows:

(5)

Retaquifer 1.0

rhoaquifer porosityaquifer

Kd aquifer

Mass transfer by infiltration to the first Aquifer cell The data process for calculating the State variable ‘Infiltration’ is reminded here:

The ‘Infiltration’ State variable is calculated as follows: (6)

Infiltration cwater _ pore _ in u Darcy area flow _ tube

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Mass transfer coefficient by advective transport The data process for calculating the State variable ‘advection_aquifer’ is reminded here:

The ‘advection_aquifer’ State variable is calculated as follows:

(7)

advectionaquifer

u Darcy porosityaquifer dz Retaquifer

Mass transfer coefficient by dispersive transport (forward) The data process for calculating the State variable dispersion_aq_forward is reminded here:

The ‘dispersion_aq_forward’ State variable is calculated as follows:

(8)

dispersionaq _ forward

dispersivityaq u Darcy porosityaquifer Retaquifer dz 2

Mass transfer coefficient by dispersive transport (backward) The data process and the formula for calculation for the mass transfer coefficient by dispersive transport (backwards) ‘dispersion_aq_back’ is the same as for the State variable ‘dispersion_aq_forward’.

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A1.4.3. Regulatory state variables Radioactive contaminant concentration in the porous solutions out-flowing from the Aquifer (flow tube) The ‘c_water_pore_out’ State variable is dynamically calculated as follows:

(9)

ñwater _ pore _ out

Transport _ CellNtransp

1

area flow _ tube dz

porosityaquifer Ret aquifer

Radioactive contaminant flux from the Aquifer (integral over aquifer cross-section) The ‘Flux_out’ State variable is dynamically calculated as follows: (10)

Fluxout u Darcy area flow _ tube cwater _ pore _ out

A1.5. Mass balance equation for Media The Media, loadings, losses and exchanges that govern the mass balance models for each medium are shown at Figures 5 and 7.

A1.5.1. The ‘Transp_Cell_1’ Media The mass balance model for the Transp_Cell_1 (‘1-st Aquifer Transport Cell’) media is given by:

dTransp _ Cell1 ln(2) .Transp _ Cell1 Infiltration dt half _ Life . dispersionaq _ forward Transp _ Cell1 dispersionaq _ back Transp _ Cell2 advectionaquifer Transp _ Cell1

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A1.5.2. The ‘Transp_Cell_i’ Media The mass balance model for the ‘Transp_Cell_i’ (Aquifer Transport Cell i) media is given by: dTransp _ Celli ln( 2) .Transp _ Celli advectionaquifer Transp _ Celli 1 advectionaquifer Transp _ Celli dt half _ Life . dispersionaq _ forward Transp _ Celli dispersionaq _ back Transp _ Celli dispersionaq _ back Transp _ Celli 1 dispersionaq _ forward Transp _ Celli 1

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ANNEX 2. THE NORMALYSA MODEL FOR AQUIFER MIXING A2.1. Model purpose A2.1.1. Goal The goal of the ‘Aquifer Mixing’ module is to dynamically simulate transport of radioactive contaminants from the Source of radioactivity (e.g., ‘Tailings without Cover’, ‘Contaminated land’), which may be coupled with other modules simulating intermediate transfer such as ‘Unsaturated Zone’) within the groundwater aquifer immediately below the contaminated site. The output of the ‘Aquifer’ module usually serves an input to the ‘Aquifer’ module simulating radionuclide transport in groundwater towards receptor module(s) (e.g., ‘Well’ or ‘Fresh Water Body’) (Figure 1.).

Figure 1 – Overall model of the waste site system incorporating the ‘Aquifer Mixing’ module

A2.1.2. Potential decision and regulatory framework(s) Coupled with the Source model (and possibly modules simulating intermediate transfers), the ‘Aquifer Module’ module can:

provide an estimation of the time-dependent concentration of the targeted radionuclide(s) in aquifer pore water below the contaminated site; provide an estimation of the time-dependent mass (activity) flux of the targeted radionuclide(s) in the aquifer from the contaminated site. The output of the ‘Aquifer Mixing’ module usually serves an input to the ‘Aquifer’ module simulating radionuclide transport in groundwater towards the receptor modules (‘Well’, or ‘Fresh Water Body’) (see Figure 1). These outputs can be used for evaluating the residence time of radioactive contaminant(s) in groundwater and the risk over time to exceed a given regulatory threshold for radioactive contaminant(s) in corresponding receptor compartments defined by the relevant regulations. Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 47 (86)

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A2.2. Model applicability A2.2.1. Spatial scale and resolution The ‘Aquifer Mixing’ module is defined as a 3-dimensional compartment within the aquifer (i.e. defined by its length, width and height). The relevant spatial scale and resolution are governed by the geometry of the source and features of the hydrogeological system under investigation. The ‘Aquifer Mixing’ module assumes that the modelled aquifer compartment is homogeneous (laterally, longitudinally and vertically) with respect to its properties and parameters. A2.2.2.Temporal scale and resolution There is no limitation for temporal scale (i.e. duration of the simulation). Processes and parameters included in the model of water dynamics in the aquifer (i.e., infiltration recharge rate, Darcy velocity) are relevant at yearly resolution. Therefore the ‘Aquifer Mixing’ module and coupled models are run at a yearly resolution.

A2.2.3.Steady-state vs dynamic processes The ‘Aquifer Mixing’ module simulates radionuclide transfer processes within the hydrogeological environment dynamically, however: It is assumed that radionuclide transport in the aquifer occurs under the steady-state groundwater flow conditions;

the exchanges of radioactive contaminants between pore water and soil matrix are assumed to be at sorption equilibrium (i.e. sorption process are represented by a distribution coefficient Kd).

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A2.3. Model components A2.3.1. Media considered Definition: A ‘Medium’ is defined as an environmental or human compartment assumed to contain a given quantity of the radionuclide (chemical). The quantity of the radionuclide in the media is governed by loadings/losses (see A2.3.2 and A2.3.3) from/to other media and by radioactive decay. The ‘Aquifer Mixing’ module schematizes the groundwater aquifer immediately below the contaminated site as a single compartment. The model expressions operate total radionuclide inventories in this compartment. Then radioactive contaminant concentrations in pore water and soil matrix can be calculated based on known inventory of compartment and equilibrium Kd-based sorption model describing radionuclide partitioning between the liquid and solid phases. The schematization and media considered are represented in Figure 2.

Figure 2 – Media considered in the ‘Aquifer Mixing’ module

A2.3.2. Loadings Definition: A ‘Loading’ is defined as the rate of release/input of the radionuclide of interest to the receiving system, here the ‘Aquifer’ system. The inputs of radioactive contaminant(s) into the ‘Aquifer Mixing’ compartment can have the following origins: Contaminants leached from the waste disposal facilities (such as uranium mill tailings facilities); Contaminants originating from contaminated topsoil layer due to leaching by atmospheric precipitations; Contaminants originating from direct application of liquid effluents on topsoil (e.g. direct application of sludge originating from sewage treatment plants, fertilizers, etc.); Contaminants entering the modelled aquifer compartment by lateral inflow from the upstream aquifer zone. Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 49 (86)

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The inputs of radioactive contaminant(s) into the ‘Aquifer Mixing’ system by infiltration mechanism are needed to be defined by user in the coupled external Source model (possibly coupled with modules simulating intermediate transfers). In this case the outputs of the coupled Source module (or modules simulating intermediate transfers) are used as loading inputs for the ‘Aquifer mixing’ model. The contaminant input is defined by specifying two parameters: radioactive contaminant activity concentration in the infiltrating water and infiltration rate. The loading inputs are represented in Figure 3.

Figure 3 – Media considered + Loading inputs in the ‘Aquifer Mixing’module.

A2.3.3. Losses Definition: A ‘Loss’ is defined as the rate of output of the radionuclide of interest from the receiving system, here the ‘Aquifer Mixing’ compartment. The losses of radioactive contaminant(s) from the ‘Aquifer Mixing’ compartment are: Contaminant leaving the ‘Aquifer Mixing’ system towards adjacent downstream zones of the hydrogeological system (e.g., consecutive ‘Aquifer’ module) by outflow (i.e., contaminant movement by advective outflow); Radioactive decay of contaminant in the aquifer media. The losses of contaminant(s) from the ‘Aquifer Mixing’ compartment are represented in Figure 4.

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Figure 4 – Media considered + Loading inputs + Losses in the ‘Aquifer Mixing’ model.

A2.3.4. Exchanges between model media Definition: An ‘Exchange’ is defined as the transfer of the radionuclide of interest between two media compartments of the system, here the Aquifer system. The Aquifer model assumes that a sorption equilibrium of radioactive contaminant(s) between pore water and soil matrix exists (described by Kd model). However sorption/desorption is not modelled separately as an exchange process. Radioactive contaminant concentrations in pore water and soil matrix are calculated for each Transport Cell based on known layer inventory and equilibrium Kd sorption model using corresponding partitioning equation. The exchanges of radioactive contaminant(s) between model media are represented in Figure 5.

Figure 5 - Media considered + Loading inputs + Losses + Exchanges in the ‘Aquifer Mixing’ model.

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A2.3.5. Potential coupled models ‘Coupled models’ are defined as models that can generate loadings to the investigated system (here the ‘Aquifer Mixing’ compartment) or receive losses from the latter. The ‘Aquifer Mixing’ module can be coupled to other modules of the NORMALYSA library (see Figure 1). These latter can provide loading estimates or use losses from the ‘Aquifer Mixing’ compartment as input data: Coupled model Source Term models (‘Tailings without cover’, ‘Contaminated land’) ‘Unsaturated Zone’

Can provide estimates of the following loading(s) Radioactive contaminant concentration in infiltrating water; infiltration rate

Can use the following losses from the Aquifer as input data

Radioactive contaminant concentration in infiltrating water; infiltration rate

‘Aquifer’

Radioactive contaminant concentration in outflow water; Darcy velocity Radioactive contaminant concentration in outflow water; Darcy velocity Radioactive contaminant concentration in outflow water; Darcy velocity

‘Well’ ‘Fresh Water Body’

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A2.3.6. Forcing variables A ‘Forcing variable’ is defined as an external or exogenous (from outside the model framework) factor that influences the state variables calculated within the model. Such variables include, for example, climatic or environmental conditions (temperature, wind flow, etc.). For running the ‘Aquifer Mixing’ module, the following forcing variables must be informed for calculating the loading inputs: Forcing variable

Abbreviation and unit

Purpose

Concentration of the radioactive contaminant in water infiltrating to the aquifer Infiltration rate to the aquifer

c_ infiltration_aquifer (Bq m-3)

Is used to calculate the input activity flux through infiltration (inflow) of contaminated ground water

rate_infiltration (m.y-1)

Concentration of the radioactive contaminant in groundwater inflowing to the aquifer from upstream direction Darcy velocity in the aquifer

c_water_pore_in (Bq m-3)

Is used to calculate the input activity flux through infiltration of contaminated pore water Is used to calculate the input activity flux through inflow of contaminated groundwater from upstream direction

u_Darcy (m.y-1)

Is used to calculate the input activity flux through inflow of contaminated groundwater from upstream direction

The forcing variables (with indication of the processes they are involved in) are represented in Figure 6.

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Can be calculated if the ‘Aquifer’ model is coupled to the … Source Term models, ‘Unsaturated Zone’ Source Term models, ‘Unsaturated Zone’

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Figure 6- Media considered + Loading inputs + Losses + Exchanges + Forcing variables in the ‘Aquifer Mixing’ module.

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A2.3.7. Parameters A ‘Parameter’ is defined as a term in the model that is fixed during a model run or simulation but can be changed in different runs as a method for conducting sensitivity analysis or to achieve calibration goals. For running the ‘Aquifer Mixing’ module, the following parameters must be informed:

Site-specific parameters: Name

Abbreviation and unit

Purpose

Surface of the contamination source (waste site), which is situated on top of the ‘Aquifer Mixing’ compartment

Area_source (m2)

It defines the geometry hydrogeological system

Length of the aquifer compartment

length_waste_site (m)

Thickness of the aquifer "mixing zone" below the waste site

h_mixing (m)

It defines the geometry of the modelled groundwater system It defines the geometry of the modelled “aquifer mixing” compartment, where vertical infiltration flux from the contaminated site mixes with the lateral groundwater flow in the aquifer

of

the

modelled

Used for calculating the following state variable(s) It is used for converting the total activity in the system into concentrations in media, in particular to pore water concentration in outflow water(c_water_pore_out) It is used also to calculate activity input to the modelled system (Infiltration) It is used to calculate average width of the contaminated site (from its area) It is used to calculate cross-sectional area of the aquifer (area_flow_tube)

Soil physico-chemical properties: Name

Dry density of aquifer soil Porosity of soil in the aquifer

Abbreviation and unit rho_aquifer (kg.m-3) porosity_aquifer

Purpose It is used for calculating the Retardation factor in the aquifer It is used to calculate: transfer coefficient by

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Used for calculating the following state variable(s) Retardation factor in the aquifer soil (Ret_aquifer) Radionuclide concentration in pore water

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Initial contamination of groundwater in the aquifer by radionuclides

advection, retardation factor, concentration in pore water, etc.

c0_gw_aquifer (Bq m-3)

It is used for calculating the initial condition for radionuclide transfers calculations in the aquifer

radionuclide

out flowing from the aquifer (c_water_pore_out) Retardation factor in the aquifer (Ret_aquifer) Initial contamination inventories in the modelled aquifer compartment

Parameters related to partition between phases: Name

Sorption distribution coefficient

(m-3.m-3)

Abbreviation and unit Kd_aquifer (m3.kg-1)

Purpose

Used for calculating the following state variable(s)

The exchanges of contaminants between pore water and soil matrix are assumed to be at equilibrium and represented by a distribution coefficient at equilibrium Kd_aquifer

Retardation factor in the aquifer soil (Ret_aquifer)

Parameters related to radioactive decay: Name

Radionuclide half life

Abbreviation and unit halfLife (year)

Purpose

Used for calculating the following state variable(s)

Is used to account for radioactive decay of contaminants

Radionuclide inventories in discretized transport cell compartments and concentrations in media

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A2.3.8. Intermediate State variables An ‘Intermediate State variable’ is defined as a dependent variable calculated within the model. Some State variables are fixed during a model run or simulation because they are calculated only from parameters. Some others are time-dependent because they are calculated from parameters, but also from time-dependent forcing variables. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes. For running the Aquifer model, the following state variables are calculated for the following purposes.

State variable n° 1

State variables related to geometry of the aquifer compartment: Name

Width

of

contaminated (source

site of

contaminant infiltration

to

the

Abbreviation and unit

Purpose

Process followed for calculating the state variable

width_waste_site (m)

Defines geometrical characteristics of the ‘Aquifer Mixing’ compartment, which are further used in mass/activity calculations for the compartment

aquifer)

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Cross-sectional

area

of the aquifer (flow

area_flow_tube (m2)

Used to calculate integral mass/activity fluxes in the aquifer

tube)

State variable n° 3

State variables related to radioactive contaminant transport in soil: Name

Abbreviation and unit

Purpose

Process followed for calculating the state variable

Retardation factor

Ret_aquifer (-)

The contaminant is partly sorbed on the soil matrix, only the dissolved phase is assumed to move along the soil profile, resulting in a retardation. The Retardation factor accounts for the adsorption of contaminants on the soil matrix and is included in the advection-dispersion transfers within the soil profile.

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4

Mass transfer by infiltration (vertical) to the ‘Aquifer Mixing’ compartment

Infiltration

Vertical mass (activity) transport to the ‘Aquifer Mixing’ compartment is determined by flux of infiltration water with specified concentration of contaminant(s)

5

Mass transfer by inflow (horizontal) to the ‘Aquifer Mixing’ compartment

Inflow

Horizontal mass (activity) transport to the ‘Aquifer Mixing’ compartment is determined by inflow flux of groundwater with specified concentration of contaminant(s)

6

Mass transfer coefficient by advective transport (outflow from compartment)

advection_gw_out

This mass transfer coefficient is used to calculate fluxes of contaminants out of compartment by advective transport

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A2.3.9. Regulatory State variables An ‘Regulatory State variable’ is defined as a dependent variable calculated within the model. It is generally time-dependent because it is calculated from parameters, but also from time-dependent forcing variables and loadings. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes.

The following ‘regulatory state variables’ are calculated according to the flow charts presented in Figure :

State variable n° 6

Name Radioactive contaminant concentration in the porous

Abbreviation and unit c_water_pore_out

solutions out-flowing from the Aquifer (flow tube) 7

Radioactive contaminant flux from the Aquifer (integral over aquifer cross-section)

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Flux_flow_tube

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A2.4. Mathematical models for State variables The objective of this section is to present the mathematical models used for calculating each of the State variables conceptually listed in A2.3.8. The understanding of these models is a prerequisite for understanding the mass balance equations presented in Chapter A2.5. In the following tables, the following symbols were adopted:

A2.4.1. State variables related to geometry of the aquifer compartment: Width of contaminated site The data process for calculating the State variable ‘width_waste_site’ is reminded here:

The ‘width_waste_site’ State variable is calculated as follows:

(1)

widthwaste _ site

areasource lengthwaste _ site

Cross-sectional area of the aquifer The data process for calculating the State variable ‘area_flow_tube’ is reminded here:

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The ‘area_flow_tube’ State variable is calculated as follows: (2)

area flow _ tube hmixing widthwaste _ site

A2.4.2. State variables related to radioactive contaminant transport in soil: Retardation factor The data process for calculating the State variable Ret_uns_zone is reminded here:

The ‘Ret_aquifer’ State variable is calculated as follows:

(3)

Retaquifer 1.0

rhoaquifer porosityaquifer

Kd aquifer

Mass transfer by vertical infiltration to ‘Aquifer Mixing’ cell The data process for calculating the State variable ‘Infiltration’ is reminded here:

The ‘Infiltration’ State variable is calculated as follows: (4)

Infiltration cinf iltration u Darcy area flow _ tube

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Mass transfer by horizontal inflow to ‘Aquifer Mixing’ cell The data process for calculating the State variable ‘Inflow’ is reminded here:

The ‘Inflow’ State variable is calculated as follows:

Inflow cipore _ water _ in u Darcy area flow _ tube

(5)

Mass transfer coefficient by advective transport The data process for calculating the State variable ‘advection_gw_out’ is reminded here:

The ‘advection_gw_out’ State variable is calculated as follows:

(6)

advectionaquifer

uDarcy porosityaquifer lengthwaste _ site Retaquifer

A2.4.3. Regulatory state variables Radioactive contaminant concentration in the porous solutions out-flowing from the Aquifer (flow tube) The ‘c_water_pore_out’ State variable is dynamically calculated as follows:

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(7)

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ñwater _ pore _ out

Aquifer _ Mixing 1 area flow _ tube lengthwaste _ site porosityaquifer Ret aquifer

Radioactive contaminant flux from the Aquifer (integral over aquifer cross-section) The ‘Flux_out’ State variable is dynamically calculated as follows: (8)

Flux flow _ tube u Darcy area flow _ tube cwater _ pore _ out

A2.5. Mass balance equation for Media The Media, loadings, losses and exchanges that govern the mass balance models for each medium are shown at Figures 5 and 7.

A2.5.1. The ‘Aquifer_Mixing’ Compartment The mass balance model for the ‘Aquifer_Mixing’ (AM) compartment is given by: dAM ln( 2) . AM Inflow Infiltration advectiongw _ out AM dt half _ Life

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ANNEX 3. THE NORMALYSA MODEL FOR CONTAMINATED SOIL LAYER A3.1. Model purpose A3.1.1. Goal The goal of the ‘Contaminated Soil layer’ module is to dynamically simulate the source term of radioactive contaminants for modelling subsequent radionuclide transport in the subsurface environment such as the unsaturated zone of soil and / or saturated transport in the aquifer. The output of the ‘Contaminated Soil layer’ module usually serves an input to the unsaturated zone and\or aquifer transport modules (‘Unsaturated Zone’, ‘Aquifer Mixing’ and/or ‘Aquifer’) (Figure 1).

Figure 1 – Overall model of the waste site system incorporating the ‘Contaminated Soil Layer’ module

A3.1.2. Potential decision and regulatory framework(s) The ‘Contaminated Soil Layer’ module can:

provide an estimation of the time-dependent concentration of the targeted radionuclide(s) in soil pore water and in soil matrix in contaminated (top) soil layer ; provide an estimation of the time-dependent mass (activity) flux of the targeted radionuclide(s) from the contaminated (top) soil layer. These outputs can be used for evaluating the residence time of radioactive contaminant(s) in soil and subsurface environment (coupled with other modules) and the risk over time to exceed a given regulatory threshold for radioactive contaminant(s) defined by the relevant regulations. The output of the ‘Contaminated Soil Layer’ module can also serve an input to the unsaturated zone and aquifer transport modules (‘Unsaturated Zone’, ‘Aquifer Mixing’ and/or ‘Aquifer’). Coupled Source term and transport modules can be used for evaluating radioactive Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 66 (86)

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contaminant concentrations in relevant Receptor compartments (e.g., ‘Well’ or ‘Fresh Water Body’) (see Figure 1). .

A3.2. Model applicability A3.2.1. Spatial scale and resolution The ‘Contaminated Soil Layer’ module is defined as a 3 dimensional system (i.e. defined by its surface area and depth). The relevant spatial scale and resolution are governed by the homogeneity of the soil system under investigation (e.g. homogeneity with respect to hydraulic properties, geochemical properties, contamination levels, etc.). The typical vertical dimension can vary from several tens of centimetres to several meters. The ‘Contaminated Soil layer’ model assumes that the system is homogeneous (laterally, longitudinally and vertically) with respect to its properties and parameters. For soil zones showing significant relative lateral variations in their properties, it is recommended to subdivide these latter in adjacent homogeneous and independent zones. Soil profiles showing significant variation of soil properties in vertical direction can be represented by a sequence of interconnected ‘Contaminated Soil Layer’ modules. A3.2.2.Temporal scale and resolution There is no limitation for temporal scale (i.e. duration of the simulation). Processes and parameters included in the model water dynamics in soil (i.e., infiltration recharge rate) are relevant at yearly resolution. Therefore the ‘Contaminated Soil Layer’ module and coupled models are run at a yearly resolution.

A3.2.3.Steady-state vs dynamic processes The ‘Contaminated Soil Layer’ module simulates radionuclide transport processes in soil profile dynamically, however: It is assumed that radionuclide leaching in from soil layer occurs under the steadystate moisture infiltration conditions (infiltration rate is constant in time);

the exchanges of radioactive contaminants between pore water and soil matrix are assumed to be at sorption equilibrium (i.e. sorption process are represented by a distribution coefficient Kd).

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A3.3. Model components A3.3.1. Media considered Definition: A ‘Medium’ is defined as an environmental or human compartment assumed to contain a given quantity of the radionuclide (chemical). The quantity of the radionuclide in the media is governed by loadings/losses (see A2.3.2 and A2.3.3) from/to other media and by radioactive decay. The ‘Contaminated Soil Layer’ module schematizes the contaminated soil as a single compartment. The model expressions operate total radionuclide inventories in this compartment. Then radioactive contaminant concentrations in pore water and soil matrix can be calculated based on known inventory of compartment and equilibrium Kd-based sorption model describing radionuclide partitioning between the liquid and solid phases. The schematization and media considered are represented in Figure 2.

Figure 2 – Media considered in the ‘Contaminated Soil Layer’ model

A3.3.2. Loadings Definition: A ‘Loading’ is defined as the rate of release/input of the radionuclide of interest to the receiving system, here the ‘Contaminated Soil Layer’’ system. The inputs of radioactive contaminant(s) into the ‘Contaminated Soil Layer’ system can have the following origins: Contaminant originating from direct application of liquid effluents on topsoil (e.g. direct application of sludge originating from sewage treatment plants, fertilizers, etc);

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Contaminant originating from the surface water or groundwater systems through water used for irrigation purposes, etc. Contaminant leaching from the upper contaminated topsoil layers, etc.

The inputs of radioactive contaminant(s) into the ‘Contaminated Soil Layer’ system are needed to be defined by user in the coupled external Source model. In this case the outputs of the coupled Source models are used as loading inputs for the ‘Contaminated Soil Layer’ model. The contaminant input is defined by specifying two parameters: radioactive contaminant activity concentration in the infiltrating water and infiltration rate. The loading inputs are represented in Figure 3

Figure 3 – Media considered + Loading inputs in the ‘Contaminated Soil Layer’model

A3.3.3. Losses Definition: A ‘Loss’ is defined as the rate of output of the radionuclide of interest from the receiving system, here the ‘Contaminated Soil Layer’ compartment. The losses of radioactive contaminant(s) from the ‘Contaminated Soil Layer’ system are: Contaminant leaving the ‘Contaminated Soil Layer’ system towards deeper soil zones of the hydrogeological system (unsaturated soil and/or groundwater aquifer) by vertical exfiltration (contaminant movement by advective outflow); Radioactive decay of contaminant in the Soil media. The losses of contaminant(s) from the ‘Contaminated Soil Layer’ system are shown in Figure 4.

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Figure 4 – Media considered + Loading inputs + Losses in the ‘Contaminated Soil Layer’ model.

A3.3.4. Exchanges between model media Definition: An ‘Exchange’ is defined as the transfer of the radionuclide of interest between two media compartments of the system, here the ‘Contaminated Soil Layer’ system. The ‘Contaminated Soil Layer’ model assumes that a sorption equilibrium of radioactive contaminant(s) between pore water and soil matrix exists in each soil layer (described by Kd model). However sorption/desorption is not modelled separately as an exchange process. Radioactive contaminant concentrations in pore water and soil matrix are calculated for the soil layer based on known layer inventory and equilibrium Kd sorption model using corresponding partitioning equation. The exchanges of radioactive contaminant(s) between model media are represented in 5.

Figure 5 - Media considered + Loading inputs + Losses + Exchanges in the Contaminated Soil Layer’ model. Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 70 (86)

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A3.3.5. Potential coupled models ‘Coupled models’ are defined as models that can generate loadings to the investigated system (here the ‘Contaminated Soil Layer’ system) or receive losses from the latter. The ‘Contaminated Soil Layer’ model can be coupled to other models of the NORMALYSA library (see Figure 1). These latter can or use losses from the Unsaturated Zone as input data (or provide loading estimates): Coupled model

Can provide estimates of the following loading(s)

‘Unsaturated Zone’ ‘Aquifer’ ‘Aquifer mixing’ Source Term models (‘Tailings without cover’, one other ‘Contaminated Soil Layer’)

Radioactive contaminant concentration in infiltrating water; infiltration rate

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Can use the following losses from the Aquifer as input data Radioactive contaminant concentration in infiltrating water; infiltration rate Radioactive contaminant concentration in outflow water; infiltration rate Radioactive contaminant concentration in outflow water; infiltration rate Radioactive contaminant concentration in outflow water; infiltration rate

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A3.3.6. Forcing variables

A ‘Forcing variable’ is defined as an external or exogenous (from outside the model framework) factor that influences the state variables calculated within the model. Such variables include, for example, climatic or environmental conditions (temperature, wind flow, etc.). For running the ‘Contaminated Soil Layer’ model, the following forcing variables must be informed for calculating the loading inputs: Forcing variable

Abbreviation and unit

Purpose

Concentration of the radioactive contaminant in infiltration water

c_infiltration (Bq m-3)

Is used to calculate the input activity flux through infiltration of contaminated pore water

Infiltration rate to soil layer

Rate_infiltration (m.y-1)

Is used to calculate the input activity flux through infiltration of contaminated pore water

The forcing variables (with indication of the processes they are involved in) are represented in Figure 6.

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Can be calculated if the ‘Contaminated Soil Layer’ model is coupled to the … Source Term models (‘Tailings without cover’, one other ‘Contaminated Soil Layer’) Source Term models (‘Tailings without cover’, one other ‘Contaminated Soil Layer’)

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Figure 6 - Media considered + Loading inputs + Losses + Exchanges + Forcing variables in the ‘Contaminated Soil Layer’ model.

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A3.3.7. Parameters A ‘Parameter’ is defined as a term in the model that is fixed during a model run or simulation but can be changed in different runs as a method for conducting sensitivity analysis or to achieve calibration goals. For running the ‘Contaminated Soil Layer’ module, the following parameters must be informed:

Site-specific parameters: Name

Abbreviation and unit

Purpose

Surface of the contaminated soil zone under investigation

Area_source (m2)

It defines the geometry of the modelled soil system.

Thickness of the modelled soil profile

Thickness_waste (m)

It defines the geometry of the modelled soil system. More specifically it defines the thickness of soil layer from where the contaminant leaching occurs

Used for calculating the following state variable(s) It is used for converting the total activity in the system into concentrations in media, in particular to pore water concentration in outflow water(c_water_pore_out) It is used to calculate activity flux from the soil layer (Flux_out) Leache rate (transfer coefficient) from soil layer (Leaching)

Soil physico-chemical properties: Name

Dry density of soil Soil water content

Abbreviation and unit rho_waste (kg.m-3) Moisture_waste 3 .m-3)

(m-

Purpose It is used for calculating the Retardation factor in the soil layer It is used to calculate: transfer coefficient by leaching, retardation factor, radionuclide concentration in pore water, etc.

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Used for calculating the following state variable(s) Retardation factor in the soil layer (R_waste) Radionuclide concentration in pore water out flowing from the soil layer (c_water_pore_out)

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Initial contamination of the soil layer by radionuclides

It is used for calculating the initial condition for radionuclide leaching source term in soil

Parameters related to partition between phases: Name

Sorption distribution coefficient

c_waste (Bq kg-1)

Retardation factor in soilsoil (R_waste) Leache rate (transfer coefficient) from soil layer (Leaching) Initial contamination inventory in soil layer

Abbreviation and unit Kd_waste (m3.kg-1)

Purpose The exchanges of contaminants between pore water and soil matrix are assumed to be at equilibrium and represented by a distribution coefficient at equilibrium Kd_waste

Used for calculating the following state variable(s) Retardation factor in soil (R_waste)

Parameters related to radioactive decay: Name

Radionuclide half life

Abbreviation and unit halfLife (year)

Purpose

Used for calculating the following state variable(s)

Is used to account for radioactive decay of contaminants

Radionuclide inventories in discretized soil layer compartments and concentrations in media

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A3.3.8. Intermediate State variables An ‘Intermediate State variable’ is defined as a dependent variable calculated within the model. Some State variables are fixed during a model run or simulation because they are calculated only from parameters. Some others are time-dependent because they are calculated from parameters, but also from time-dependent forcing variables. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes. For running the Contaminated Soil Layer model, the following state variables are calculated for the following purposes.

State variable n° 1

State variables related to radioactive contaminant transport in soil: Name

Abbreviation and unit

Purpose

Process followed for calculating the state variable

Retardation factor

R_waste (-)

The contaminant is partly sorbed on the soil matrix, only the dissolved phase is assumed to move along the soil profile, resulting in a retardation. The Retardation factor accounts for the adsorption of contaminants on the soil matrix and is included in the advection-dispersion transfers within the soil profile.

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2

Mass

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transfer

by

Infiltration

It is assumed that mass transport to the soil layer is determined by flux of infiltration water with specified concentration of contaminant(s)

Leaching

This mass transfer coefficient is used to calculate the external flux of contaminants from soil layers by advective flow with infiltration water

infiltration to the soil layer

3

Mass

transfer

coefficient leaching

by (advective

flow)

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A3.3.9. Regulatory State variables An ‘Regulatory State variable’ is defined as a dependent variable calculated within the model. It is generally time-dependent because it is calculated from parameters, but also from time-dependent forcing variables and loadings. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes.

The following ‘regulatory state variables’ are calculated according to the flow charts presented in Figure :

State variable n° 4

Name Radioactive contaminant concentration in the porous

Abbreviation and unit c_water_pore_out

solutions out-flowing from the soil layer 5

Radioactive contaminant flux from the soil layer (integral over surface area of soil)

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Flux_out

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Figure 7 - Flow chart of key process for calculating the ‘regulatory state variables’ Chess Controlled Core Word Rev: 2 Template Active Date: 18 Sep 2015 79 (86)

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A3.4. Mathematical models for State variables The objective of this section is to present the mathematical models used for calculating each of the State variables conceptually listed in A3.3.8. The understanding of these models is a prerequisite for understanding the mass balance equations presented in Chapter A3.5. In the following tables, the following symbols were adopted:

A3.4.1. State variables related to radioactive contaminant transport in soil: Retardation factor The data process for calculating the State variable R_waste is reminded here:

The ‘R_waste’ State variable is calculated as follows:

(1)

Rwaste 1.0

rhowaste Kd waste moisturewaste

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Mass transfer by infiltration to the soil layer The data process for calculating the State variable ‘Infiltration’ is reminded here:

The ‘Infiltration’ State variable is calculated as follows: (2)

Infiltration cinf iltrationn rateinfiltrati on areasource

Mass transfer coefficient by leaching The data process for calculating the State variable ‘Leaching’ is reminded here:

The ‘Leaching’ State variable is calculated as follows:

(3)

leaching

rateinfiltrati on moisturewastee Thicknesswaste Rwaste

Radioactive contaminant concentration in the porous solutions out-flowing from the soil layer The ‘c_water_pore_out’ State variable is dynamically calculated as follows:

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C water _ pore _ out

(4)

Activitysource 1 areasource Thicknesswaste moisturewaste Rwaste

Radioactive contaminant flux from the soil layer (integral over surface area of soil) The ‘Flux_out’ State variable is dynamically calculated as follows: (5)

Fluxout rateinf iltration areasource cwater _ pore _ out

A3.5. Mass balance equation for Media The Media, loadings, losses and exchanges that govern the mass balance models for each medium are shown at Figures 5 and 7.

A3.5.1. The ‘Activity_source’ Media The mass balance model for the ‘Activity_source’ (activity inventory in the soil layer) media is given by: dActivitysource ln(2) . ActivitySource Infiltration Leaching Activitysource dt half _ Life

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ANNEX 4. THE NORMALYSA MODEL FOR A WELL A4.1. Model purpose A4.1.1. Goal This module calculates radionuclide concentrations in groundwater pumped by a water well. It is assumed that some fraction of the well debit is formed by contaminated groundwater from the flow tube originating from the waste site, while the other part of well debit is formed by "background" groundwater hence it is linked to ‘Aquifer’ transport module and to a receptor.

Figure 1. Conceptual model for the well

A4.1.2. Potential decision and regulatory framework(s) Coupled with the transport model (and possibly modules simulating intermediate transfers), the ‘Well’ module can: 1. time-dependent concentration of radionuclide(s) in well water. The outputs can be used for evaluating the risk to exceed a given regulatory norm for environmental risk. 2. time-dependent concentration of radionuclide(s) in bottom sediments. In connection with the model dose model for example Human_ing, the well model is able to provide an estimation of the time-dependent concentration of RN in drinking water. This output can be used for evaluating the risk to exceed a given regulatory limit for human health. The output of the ‘Well’ module usually serves an input to other receptor modules where water is use for irrigation or for drinking water for human or animals (e.g. garden plot ), see Figure 1.

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The Well model can be coupled with dose models where the outputs of the well model (radionuclide concentrations in the well water) are used as input to derive doses to members of the public through ingestion of water and various foodstuff.

A4.2. Model applicability A4.2.1. Temporal scale and resolution There is no limitation for temporal scale (i.e. duration of the simulation).

A4.3. Model components A4.3.1. Loadings Definition: A ‘Loading’ is defined as the rate of release/input of radionuclide to the receiving system, here the Well system. The inputs of radioactive contaminant(s) into the ‘Well’ system can have the following origins: Radionuclides coming from the contaminated groundwater flow tube system (e.g. aquifer) A4.3.2. Losses

Definition: A ‘Loss’ is defined as the rate of output of RN from the receiving system, here the well system. The losses of radioactive contaminant(s) from the ‘Well’ system are:

Radionuclide decay. Radionuclides leaving the ‘Well’ system towards Receptor environments biosphere objects where well water is being directly used or for irrigation (e.g. garden plot).

Figure 2 - Loading inputs (inward arrows) + Losses (outwards arrows) in the Well model

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A4.3.3. Potential coupled models Coupled models are defined as models that can generate loadings to the investigated system (here the Well system) or receive losses from the latter. The Well model can be coupled to other models of the Normalysa library. The latter can provide loading estimates or use losses from the Well as input data: Coupled model

Can provide estimates of the following loading(s) Radioactive contaminant concentration in outflow water coming into the well

‘Aquifer’

Can use the following losses from the well as input data

Radioactive contaminant concentration in outflow water

‘Garden plot’

A4.3.4. Parameters A Parameter is defined as a fixed term in the model that during a simulation but can be changed in different runs as a method for conducting sensitivity analysis or to achieve calibration goals. For running the Well model, the following parameters must be informed: Site-specific parameters: Name

Abbreviation and Unit

Purpose

Used for calculating the following state variable(s)

Radionuclide concentration in background groundwater

c_gw_background (Bq/m3)

Represents the radionuclide concentration in background

Radionuclide concentration in well water (c_water)

groundwater forming the remaining fraction of the well debit and is used to determine the radionuclide concentration in well water

Radionuclide concentration in the water coming from the aquifer

c_water_pore_out (Bq/m3)

Represents the radionuclide

Radionuclide concentration

concentration in the aquifer

in well water (c_water)

(flow tube) groundwater flowing into the well

Fraction of

f_debit_flowtube (-)

groundwater coming to the well from the flow tube

Represents the fraction of groundwater coming to the well from the flow tube and used to determine the radionuclide concentration in well water

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Radionuclide concentration in well water (c_water)

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A4.3.5. Regulatory State variables A ‘Regulatory State variable’ is defined as a dependent variable calculated within the model. It is generally time-dependent because it is calculated from parameters, but also from time-dependent forcing variables and loadings. We distinguish ‘Intermediate State variables’ and ‘Regulatory State variables’. The first ones are generally not used by decision-makers for regulatory purposes but can be used as performance indicators of the model that change over the simulation. The second ones can be used by decision-makers for regulatory purposes.

State variable n°

Name

Abbreviation and unit

1

Radionuclide concentration in well water

c_water (Bq/m3 )

A4.4. Mathematical models for State variables The objective of this section is to present the mathematical models used for calculating each of the State variables conceptually listed in A4.3.5.. In the following diagrams, the following symbols were adopted:

A4.4.1. Regulatory State variables Concentration in water The data process for calculating the State variable c_water of the lake is reminded here:

The equation for calculating the radionuclide concentration in the wellwater, c_water, is (𝟏) 𝑐𝑤𝑎𝑡𝑒𝑟 = 𝑓𝑑𝑒𝑏𝑖𝑡,𝑓𝑙𝑜𝑤𝑡𝑢𝑏𝑒 × 𝑐𝑤𝑎𝑡𝑒𝑟,𝑝𝑜𝑟𝑒,𝑜𝑢𝑡 + (1.0 − 𝑓𝑑𝑒𝑏𝑖𝑡,𝑓𝑙𝑜𝑤𝑡𝑢𝑏𝑒) × 𝑐𝑔𝑤,𝑏𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛𝑑

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