153 6 Radionuclide Transport Processes and Modeling C. M. Vandecasteele CONTENTS 6.1 Introduction 154 6.2 Transport in the Atmosphere 155 6.2.1 Winds 155 6.2.2 Atmospheric Stability 156 6.2.3 The Gaussian Model 158 6.2.4 The Gaussian Model Applied to Radiological Dispersion Devices 162 6.2.5 Parameters of the Gaussian Model 163 6.2.6 Important Limitations of the Gaussian Model 163 6.2.7 Long-Range Dispersion Models 165 6.2.8 Plume Depletion 166 6.2.8.1 Radioactive Decay 167 6.2.8.2 Wet Deposition 167 6.2.8.3 Dry Deposition 167 6.3 Transfer in Terrestrial Food Chains 168 6.3.1 Direct Contamination of the Vegetation 169 6.3.1.1 Dry Deposition 169 6.3.1.2 Wet Deposition 170 6.3.1.3 Retention of Radionuclides Deposited on Vegetation 171 6.3.2 Indirect Contamination of Vegetation 172 6.3.2.1 Interaction of Radionuclides with Soil 172 6.3.2.2 Root Uptake 175 6.3.2.3 Radionuclide Retention in Soil 176 6.3.2.4 Translocation within Plants 177 6.3.3 Transfer to Animals 178 6.3.3.1 Contamination by Inhalation 178 6.3.3.2 Contamination by Ingestion 178 6.3.3.3 Distribution in the Animal 179 DK594X_book.fm Page 153 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC 154 Radionuclide Concentrations in Food and the Environment 6.3.3.4 Excretion 180 6.4 Transport in Aquatic Systems 181 6.4.1 Transport and Dispersion of Radioactivity in Aquatic Systems 182 6.4.1.1 Transport in Rivers 183 6.4.1.2 Transport in Lakes 185 6.4.1.3 Transport in the Marine Environment 186 6.4.1.4 Transport in Estuaries 189 6.4.2 Partition Between the Liquid and Solid Phases 191 6.4.3 Contamination of the Biocenose 192 6.5 Modeling the Transfer of Radionuclides 196 6.5.1 Model Roles and Uses 196 6.5.2 Model Building 196 6.5.2.1 Definition of the Relevant Scenario 197 6.5.2.2 Formulation of the Conceptual Model 197 6.5.2.3 Development of the Mathematical Model 198 6.5.2.4 Estimation of Parameter Values 198 6.5.2.5 Calculation of Model Predictions 199 6.5.3 Uncertainties and Errors Associated with Modeling 199 6.5.4 Model Validation 200 6.5.5 Model Types 200 6.5.5.1 Screening Models 201 6.5.5.2 Emergency Models 201 6.5.5.3 Generic Models 201 6.5.5.4 Experimental Models 201 6.5.5.5 Deterministic and Stochastic Models 202 6.5.5.6 Equilibrium and Dynamic Models 202 6.5.6 Uncertainty Analysis 202 6.5.7 Sensitivity Analysis 204 References 205 6.1 INTRODUCTION Nuclear electricity production generates large amounts of artificial radionuclides, which may be concentrated through reprocessing into radioactive wastes. The many applications of radioactivity in industry, medicine, and research make use of large quantities of artificial radioisotopes. Finally, some conventional industries (phosphate mills and oil extraction) concentrate naturally occurring radioactive materials (NORMs) in their residues. These activities are responsible for routine and accidental releases of radioactive elements into the environment. Radionuclides discharged into the atmosphere as gas, aerosols, or fine parti- cles are transported downwind, dispersed by atmospheric mixing phenomena, and progressively settled by deposition processes. During the passage of the radioactive plume, people are irradiated externally as well as internally by inha- lation. After the passage of the cloud, exposure of the population continues via DK594X_book.fm Page 154 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC Radionuclide Transport Processes and Modeling 155 three main pathways: external irradiation from the radionuclides deposited on the ground, inhalation of resuspended contaminated particles, and ingestion of con- taminated food products. When released into surface waters, radionuclides are partly removed from the water phase by adsorption on suspended solids and bottom sediments. As the radioactivity disperses, there is a continuing exchange between the liquid and solid phases. The contaminated sediments deposited on the banks of rivers, lakes, and coastal areas lead to external irradiation of people spending time at these sites. The residual activity in water exposes man internally through the ingestion of drinking water, aquatic food products, and terrestrial food products contami- nated by irrigation of vegetation and ingestion of water by livestock. Radioactivity may also contaminate soil due to lixiviation of waste heaps, shallow land burial, or geological disposal. It migrates slowly with soil water as soluble ions or organic complexes, interacting with the soil compounds in exchange reactions, and contaminates aquifers. 6.2 TRANSPORT IN THE ATMOSPHERE The atmosphere is the first important path for the dispersion of radioactive pollutants in the environment. Its lower layer, which extends to a height of about 15 km at the equator and 10 km in the polar regions, constitutes the common receptor of routine industrial gaseous discharges and accidental atmospheric releases. This layer, called the troposphere, is a turbulent zone, saturated in water vapor and constantly mixed by winds generated by the heat balance at the Earth’s surface. 6.2.1 W INDS Winds are the driving force for the transport of airborne pollutants. They deter- mine the direction of the plume of pollutants and the speed at which these pollutants are transported downwind. Winds are caused by the interaction of the forces created by the pressure gradients between anticyclones and depressions and the Coriolis forces generated by the Earth’s rotation. When equilibrium is reached between these forces, air masses move parallel to the isobars. In the Northern Hemisphere, the flow is clockwise around high pressure areas and counterclockwise around depressions. Closer to the Earth’s surface, however, below 650 m, the shearing forces of contact with the ground modify wind direction and speed. These friction effects can cause the wind to change direction by about 30 degrees (outward around anticyclones and inward around high pressure areas) between altitude (650 m) and the surface. The forces exerted by the roughness of the ground surface due to natural (mountains, hills, valleys, forests) and man-made (buildings and cities) obstacles can change wind trajectories and speed. Variations in wind speed and direction (along the vertical axis) creates turbulence, which increases the disper- sion of airborne pollutants. DK594X_book.fm Page 155 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC 156 Radionuclide Concentrations in Food and the Environment 6.2.2 A TMOSPHERIC S TABILITY Another key parameter influencing the dispersion of airborne contaminants is the stability of the atmosphere, which is determined by the vertical temperature profile of the atmosphere relative to the adiabatic lapse rate, that is, the temperature decrease that a small air parcel undergoes when rising. As pressure decreases with height, rising air masses expand and hence cool down. Considering small air volumes as adiabatic systems (i.e., thermodynamically isolated and not exchanging energy or heat with their environment), the temperature of a rising air bubble decreases at a rate of 9.8˚C/km until it becomes water saturated (i.e., when water vapor starts to condense). This rate is known as the dry adiabatic lapse rate. As soon as the air bubble becomes saturated, further rise, and hence cooling, provoke condensation, which causes its temperature to decrease at a reduced rate of 6.5˚C/km (termed the saturated or moist adiabatic lapse rate) because the temperature decrease due to expansion is partially compensated for by the recovery of the latent vaporization heat released by condensation of water vapor. Thus, comparing the actual altitudinal air temperature gradient with the dry or saturated adiabatic lapse rate (Figure 6.1), the atmosphere is • Neutral if the actual temperature gradient in the atmosphere is equal to the adiabatic lapse rate, • Stable if its temperature gradient is higher than the adiabatic lapse rate, possibly positive (inversion), and • Unstable when its temperature gradient is lower than the adiabatic lapse rate. FIGURE 6.1 Illustration of the stability conditions of the atmosphere. The dotted arrows represent the behavior of an adiabatic air parcel. Height T° stable unstable neutral DK594X_book.fm Page 156 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC Radionuclide Transport Processes and Modeling 157 The vertical temperature profile in the lower troposphere is directly influence by •The thermal fluxes to (insolation in the day time) and from (infrared radiation during the night) the Earth’s surface, •The heat capacity of the Earth’s surface (soil or water), •The thermal conductivity between the Earth’s surface and the lower air layer in contact, and •The degree of mixing by winds. Based on experimental observations, Pasquill [1,2] proposed an empirical categorization of the stability of the atmosphere in six classes from A (very unstable) to F (stable), which are based on a few easily observable weather parameters such as wind speed at 10 m and sunshine intensity in the daytime, and wind speed and cloud cover during the night (Table 6.1). Later, a class G was added for very stable atmospheric conditions. The Pasquill stability classi- fication is still used internationally in atmospheric dispersion modeling. Using more or less comparable approaches, that is, combining synoptic data (wind velocity, solar radiation, solar angle, cloudiness), vertical temperature gra- dient, horizontal fluctuation of the wind direction, and ground surface roughness, alternative classifications have been proposed by McElroy [3], McElroy and Pooler [4], Klug [5], Bultynck et al. [6], Vogt [7], and Doury [8], which can be more or less correlated (Table 6.2). The stability of the atmosphere determines the pattern of the plume (Figure 6.2). The “looping” pattern occurs when the atmosphere is unstable, that is, when the temperature gradient of the atmosphere is very negative (superadiabatic). This situation creates whirling air motions that cause the plume to strike the ground repeatedly along its trajectory. Such conditions (very unstable atmosphere) are achieved by strong sunshine and weak winds because they require a warm up of the soil. The “coning” pattern occurs when the atmosphere is neutral or when the gradient is only slightly superadiabatic (weakly unstable). This situation is TABLE 6.1 Stability Classes Related to Meteorological Conditions [1] Wind Speed at 10 m (m/sec) In the Daytime; Sunshine During the Night: Cloudiness Strong Moderate Slight > 3/8 ≤ 3/8 <2 2–3 3–5 5–6 >6 A A–B B C C A–B B B–C C–D D B C C D D — E D D D — F E D D DK594X_book.fm Page 157 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC 158 Radionuclide Concentrations in Food and the Environment the one that is the most faithfully represented by the Gaussian model (see Section 6.2.3). The “fanning” pattern occurs in a stable or very stable atmosphere, when the gradient is less negative than the adiabatic lapse rate, or even positive. 6.2.3 T HE G AUSSIAN M ODEL The Gaussian model is an empirical model providing an analytical solution to the transport and diffusion equations representing short duration (puffs) or con- tinuous (plumes) releases of atmospheric pollutants. It was developed in the early 1960s by Pasquill [1] and Gifford [9], based on a theoretical description of eddy diffusion in the atmosphere proposed by Sutton [10]. But despite, and also because of its relative simplicity and because it can be run with limited, readily obtainable meteorological information, it is still widely used today. TABLE 6.2 Rough Correspondence of the Stability Classes Between Different Classification Systems Pasquill [1] A B C D E F G McElroy [3] McElroy and Pooler [4] B 2 B 1 CD Bultynck et al. [6]E6E5E4E3–E2E2–E1E1 Doury [8]DNDF FIGURE 6.2 Typical pollutant dispersion patterns in unstable, neutral, and stable atmo- spheres. The dotted line on the left graphs represent the air temperature profile as the adiabatic lapse rate. Looping Coning T° T° h h h unstable stable neutral DK594X_book.fm Page 158 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC Radionuclide Transport Processes and Modeling 159 The Gaussian model is based on the assumption that diffusion of airborne pollutants can be equated to a probabilistic phenomenon, which can be described by a Gaussian equation. In other words, the concentration profiles in the plane perpendicular to the wind axis (plume model) as well as on the wind axis (puff model) adopt Gaussian patterns (Figure 6.3). Therefore the maximum of concen- tration is centered on the plume axis. The diffusion intensities are expressed by the values taken by the standard deviations, which increase progressively with the distance from the source. In theory, the model applies only for sites with very simple topography (flat lands, without obstacles or discontinuities) and rather homogeneous meteorolog- ical conditions during the release and on the puff or plume travel path. Concen- trations observed at some distance from the release point can have extreme fluctuations, depending on variations in wind direction and turbulence, therefore the model provides only average concentrations. In the case of a puff release, the concentration ( C ( x , y , z , t ) ) at a given point ( x , y , z ) and a given time ( t ) can be estimated by the following mathematical expression: C ( x , y , z , t ) = (6.1) FIGURE 6.3 Coordinate system for dispersion calculations (after Turner [56]). z y x h H (x,0,0) (x,y,0) (x,y,z) (0,0,0) QxutyzH xyz xy () exp () () 2 1 2 3 2 2 2 2 2 2 πσσσ σσσ − − ++ − zz 2                   DK594X_book.fm Page 159 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC 160 Radionuclide Concentrations in Food and the Environment where Q = total quantity of pollutants released at the stack (in kg or Bq), σ i = standard deviations of the Gaussian distribution, representing the diffusion intensities of the pollutants, along each of the three axes x , y , and z (per m), u – = mean wind velocity at the level of the effective release height H (in m/sec), H = the so-called effective release height; that is, the actual height of the stack incremented by an extra height representing the buoyancy effect (due to initial ejection speed or higher temperature of the gases released at the stack compared to that of the air) (in m). For a continuous release (plume), the concentration ( C ( x , y , z ) ) at a given point ( x , y , z ) is estimated using a similar expression, where the quantity of pollutants released is replaced by the quotient of the mean emission flux Φ (in kg/sec or Bq/sec) divided by the average wind speed – u (in m/sec). In this case, the diffusion along the y -axis (wind axis), that is, the path of the plume, is neglected because one may suppose that downstream diffusion is compensated for by upstream back-diffusion: C ( x , y , z ) =(6.2) When the puff or the plume strikes the ground, total reflection is assumed (i.e., deposition on the ground is not included at this stage). Mathematically this is achieved by considering a virtual source identical to the actual one, but sym- metrical relative to the ground surface (Figure 6.4). The pollutant concentrations in air, beyond the contact point, are the sum of the direct contribution from the source and that resulting from the pollutants reflection on the ground. The equations become (6.3) for a puff release and for a plume release. Φ u yzH yz yz 2 1 2 2 2 2 2 πσ σ σσ exp () − + −                   . C Qxuty xyz xyz xy (,,) () exp () = − − + 2 1 2 3 2 2 2 2 πσσσ σσ 22 2 2 1 2                   × − −     exp ()zH z σ   + − +                 exp ()1 2 2 2 zH z σ C u y xyz yz y (,,) exp exp= −         × − Φ 2 1 2 1 2 2 2 πσ σ σ (() exp ()zH zH zz −       + − +            2 2 2 2 1 2 σσ      (6.4) DK594X_book.fm Page 160 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC Radionuclide Transport Processes and Modeling 161 Similar constructions can be made to cope with temperature inversions (Figure 6.5), through which the penetration of pollutants is not supposed to happen. For example, when the inversion is higher than the effective release, a virtual source of emission must be created at a height corresponding to the height of the inversion plus the difference between the inversion height and the effective release height. FIGURE 6.4 Schema for coping with the total reflection of the plume on the ground surface. FIGURE 6.5 Example of situations when a temperature inversion is observed below or above the release point. z y x -H H Lofting Trapping T° T° h h DK594X_book.fm Page 161 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC 162 Radionuclide Concentrations in Food and the Environment 6.2.4 T HE G AUSSIAN M ODEL A PPLIED TO R ADIOLOGICAL D ISPERSION D EVICES To cope with recent public and political concerns, the Gaussian model was also adapted (Figure 6.6) to provide a tool to assess the consequences of the dispersion of radioactive material by conventional explosives as a consequence of terrorist actions (“dirty bombs”). Such an application has been developed by the University of California, Lawrence Livermore National Laboratory [11]. Based on the power of the explosion, related to the amount of explosive material expressed in weight equivalent of TNT (in kg), the Hotspot model calculates the height (in meters) of the cloud top (93 × w 0.25 ) and the cloud radius ( r = 0.2 × height of the cloud top). The model then assumes an initial distribution of the dispersed radioactive material between five initial puffs positioned on top of each other at different heights from the ground level up to 0.8 times the cloud top and attributes to each of them a fraction of the total source term (Table 6.3). With each puff are associated two virtual point sources located at a height corresponding to that of the puff and at an upwind distance, d y and d z , such that σ y and σ z at the vertical of the explosion epicenter ( x = 0), for the prevalent atmospheric stability class, are equal to one-tenth of the cloud top. For each individual puff, a Gaussian model calculates the concentrations at any point of coordinates ( x , y , z ), taking into account possible reflections of the pollutants on the ground or at the level of an inversion. The expected value is the sum of the five individual contributions. FIGURE 6.6 Gaussian model adapted to cope with the dispersion of radioactivity after the explosion of a radiologic dispersion device (RDD). The picture illustrates the coordi- nate system for two of the five fractions of the total plume considered by the model. Redrawn from Hotspot 49 [11]. X Y Z d y d z H4 eff H2 eff H0 eff DK594X_book.fm Page 162 Tuesday, June 6, 2006 9:53 AM © 2007 by Taylor & Francis Group, LLC [...]... termed rainout The contamination of plants by sprinkling irrigation is similar to wet deposition The interception efficiency of the vegetation depends on the size of the droplets and the amount of rainfall, as well as on changes in radionuclide concentrations in the rainwater as a function of the length of the rainfall period The foliar surfaces are able to retain a certain quantity of water and the excess... Diarrhea changes the permeability of the intestine and hence the flux of mineral elements through the intestinal barrier 6. 3.3.3 Distribution in the Animal Radionuclides absorbed in the GI tract are transported by blood and distributed into the various organs and animal products The distribution varies according to the physiological status of the animal as well as the nature and chemical form of the pollutant... parameters, the initial capacity (ai) and the half-life (λi) After oral dosing, the first compartment can generally be related to the radioactivity present in the GI tract; other compartments of increasing half-lives represent fractions of radionuclides retained in the body in decreasingly accessible forms and having increasing turnover rates Excretion rates vary with the chemical properties of the radioelement... uptake, The ionic concentration in the water solution, which depends on the quality and quantity of soil colloids (clay minerals and organic matter) and varies over the course of the growing season according to the weather (e.g., rainfall increasing the soil moisture) and agricultural practices (fertilization, liming, manure), The pH and Eh, which affect the solubility of some elements (precipitation and. .. stratification disappears and the two layers are mixed 6. 4.1.3 Transport in the Marine Environment The initial dispersion of radionuclides discharged into the marine environment from coastal nuclear installations or from rivers is mainly in uenced by the hydrodynamic conditions prevailing at the entrance point, which rule the transport of pollutants by advection and turbulent diffusion Advection is induced by high... low-temperature sink to transform the heat they produce into electricity For that reason, they are installed along seashores or on the banks of rivers that maintain a minimum water flow, allowing the evacuation of residual heat while limiting the increase of the river water temperature downstream from the discharge point Other industries associated with the nuclear fuel cycle (enrichment or reprocessing... FIGURE 6. 9 Main pathways for radionuclides to man in continental agricultural food chains © 2007 by Taylor & Francis Group, LLC DK594X_book.fm Page 169 Tuesday, June 6, 20 06 9:53 AM Radionuclide Transport Processes and Modeling 169 on the ground, inhalation of resuspended contaminated particles, and ingestion of contaminated food products 6. 3.1 DIRECT CONTAMINATION OF THE VEGETATION Direct contamination... limited area defined as a single compartment, close to the discharge point, which constitutes the interface between the source and the other (regional) compartments The local model describes the fate of the radionuclides in this box and allows calculation of the radionuclide content associated with sediments, suspended solids, and water From there, the contamination levels in the various biological compartments... 9:53 AM 188 Radionuclide Concentrations in Food and the Environment [ ]l,t = Q (1 − e − Λe × t ) Λ e ∗ Vl (6. 34) where Vl is the total volume of the compartment (in m3) When equilibrium is reached (t → ∞), the total activity and radionuclide concentration in the water compartment are given by the relations Q Λe (6. 35) Q Λ e ∗ Vl (6. 36) Al,eq = and [ ]l,eq = The radioactivity (Qlr) leaving the local... Q , (6. 30) p m j j =1 i k k =1 where [ ]i = activity concentration of the radionuclide in specific river compartments, that is, in water ([ ]w, in Bq/l) or in sediments ([ ]s, in Bq/l); a further distinction can be made between bottom sediments and suspended solids and inorganic and organic fractions, vi = mean velocity between the discharge and the sampling point of the radionuclide fraction in compartment . 163 6. 2.7 Long-Range Dispersion Models 165 6. 2.8 Plume Depletion 166 6. 2.8.1 Radioactive Decay 167 6. 2.8.2 Wet Deposition 167 6. 2.8.3 Dry Deposition 167 6. 3 Transfer in Terrestrial Food Chains. Contamination of the Biocenose 192 6. 5 Modeling the Transfer of Radionuclides 1 96 6.5.1 Model Roles and Uses 1 96 6.5.2 Model Building 1 96 6.5.2.1 Definition of the Relevant Scenario 197 6. 5.2.2. Transport in Rivers 183 6. 4.1.2 Transport in Lakes 185 6. 4.1.3 Transport in the Marine Environment 1 86 6.4.1.4 Transport in Estuaries 189 6. 4.2 Partition Between the Liquid and Solid Phases 191 6. 4.3