Review of measurement methods
*Counting time associated with detection limit
Typical radioecological models (at equilibrium): terrestrial environment
Traditional assessments of the radioecological impact of tritium in terrestrial ecosystems rely on the concept of specific activity formulated in terms of tritium concentration in water rather than the ratio of tritium activity to the hydrogen mass in a given compartment. Concentration of OBT is expressed in terms of equivalent radioactivity in water of the dry material (i.e., the quantity of water produced after complete combustion of the dry material).
Initially, it is possible to use a weighting factor for tritium concentration in the air to estimate the concentration in tritiated water of the root layer of a soil subject to a dry and moist deposit originating in the atmospheric plume according to the following equation (IAEA, 2010):
1 This parameter is difficult to estimate, and depends on a large number of local factors. The geometric average calculated from local data is 0.23, but a slightly greater value is used as a reference due to the uncertainty involved. A value of 0.5 appears conservative, even if values around 1 are plausible. The data suggests that southern and humid regions may have higher values. Values based on local measures should be used as much as possible (IAEA, 2010).
In the case of prolonged exposure where tritium concentrations of water vapour from air and water of the soil root layer are approximately constant over a long period of time, the concentration of tritiated water in plants is estimated using the following equation, which explicitly considers contributions from the atmosphere (via diffusion through foliar stomata) and roots (via transpiration) (Murphy, 1984):
The previous equation using relative humidity rates applies specifically to plant leaves, which draw most tritium from the air. The equation is conservative for fruits, roots and tubers, which draw most of their tritium from the soil, which is less contaminated than the humidity of the air in the case of an atmospheric discharge.
Proportion of water in terrestrial plants (in L/kg wet weight)
Concentration of organic tritium in plants is estimated using the following formula (IAEA, 2010):
2 The values of this parameter should be determined empirically in stationary conditions. The most reliable estimates are from controlled laboratory experiments, where the plant is exposed to an HTO concentration that is kept constant or subject to continuous monitoring. Values obtained in these experiments are all less than 1, with a geometric mean of 0.54 and a geometric standard deviation of 1.16 for the crops considered (maize, barley and alfalfa). In the absence of other information, a value of 0.54 is applied by default to all types of plants.
Water equivalent factors for terrestrial plants (L/kg dry weight)3
3 The “water equivalent” factor is difficult to measure but can be reliably calculated using the hydrogen content of proteins, lipids and carbohydrates (7%, 12% and 6.2%, respectively) and the fractions of proteins, lipids and carbohydrates in the dry matter in the plant (IAEA, 2010). Values calculated in this manner vary little across different plant categories.
Animals can ingest tritium in the form of HTO in food and drinking water and in the form of OBT found in the organic fraction of their food. Inhalation and cutaneous absorption are also possible pathways for uptake of HTO to the animal. Exchangeable organic tritium and HTO quickly return to equilibrium with the water in the animal’s body. The major part of HTO taken in by the animal remains in the form of HTO, with a small fraction converted into OBT. In contrast, approximately half the tritium taken in by the animal in the form of OBT is converted into HTO, with the other half remaining in organic form (IAEA, 2010).
Tritium concentrations in products of animal origin can be estimated using a metabolic model (Galeriu et al., 2007) according to which the principal output variable is the ratio RCpa of the concentration in the animal product to the concentration in ingested food and drinking water and inhaled air. Distinct concentration ratios were determined for uptake of HTO and OBT by the animal. Total tritium concentrations (HTO+OBT) in the product of animal origin are determined using the following equations (IAEA, 2010):
RCfHTO is the sum of HTO concentrations transferred to the animal via food, drinking water and respiration (including cutaneous absorption), weighted by relative contributions from each uptake to the total water uptake. In general, inhalation represents approximately 2-5% of total water take in by the animal, and metabolic water approximately 10%. The fraction of water from food depends on the animal’s diet and should be defined by the user.
RCfOBT is a weighted average that includes uncontaminated as well as contaminated food, since local sources of supply represent only a fraction of an animal’s diet in today’s industrialised agriculture.
Concentration ratios for various animal products in temperate climates are presented in the two tables below. For each product, the best estimate of concentration ratio is defined in regard to the animal weight and the production and uptake levels given in the table. The value intervals were calculated taking into account the variability of animal weight, and production and food level. The highest values are conservatives and should be used for animals raised in a cold climate or having high fat content in their products.
Concentration ratio for HTO uptakes
Concentration ratio for OBT uptakes
OBT concentration in the animal product may then be estimated by multiplying total concentration by fOBT, total fraction of tritium in the form of OBT in the animal product; HTO concentration in the animal product is then calculated by multiplying total concentration by (1- fOBT).
The effect of food processing is quantified by a transfer factor, also called a retention factor. This factor gives the fraction of radionuclide remaining in the product after processing.
Food processing transfer factor (Bq/kg wet weight of product processed by Bq/kg wet weight of raw product)
Common radioecological models: fresh water
Water and sediment
Modelling physical processes of tritium transfer in freshwater hydrosystems takes into account tritium dispersion, described by the classical laws of hydrodynamics as with other radionuclides using numerical models of variable complexity. Direct anthropogenic input, i.e., discharge of liquid effluent in an aquatic environment, constitutes input data for dispersion of tritium. Regarding other inputs, occurring mainly via the watershed, little work has been done on transfer functions for tritium.
Exchange models have been presented to describe exchanges with the atmosphere and interstitial water in sediment (IRSN, 2009).
Exchange with the atmosphere. It occurs primarily through two mechanisms: exchange between tritiated water in the river system and tritiated water vapour from the atmosphere, and input from precipitation.
Input from precipitation is expressed by the product of rain intensity and tritium concentration in rainwater. This gives:
Exchange between tritiated water in a hydrosystem and tritiated water vapour in the atmosphere is essentially related to the processes of diffusion, evaporation and condensation at the interface of these two environments. While some few studies consider the relevance of these mechanisms by identifying correlations between tritium radioactivity in the atmosphere close to river systems contaminated by tritium discharge, this exchange remains largely undocumented and is rarely treated in transfer models. Exchange by diffusion applies at all times but is more or less weighted depending on the conditions for humidity saturation in the air layers in contact with the river system surface: 1) undersaturation, 2) saturation and 3) oversaturation.
For undersaturation conditions (es>ea), exchange is primarily due to evaporation from the water surface and occurs primarily from the hydrosystem to the atmosphere. Modelling may then be based on the product of the evaporation flow from the alluvial aquifer and the radioactivity of tritium in the water in the hydrosystem:
The evaporation flow from a water surface depends on temperature, atmospheric pressure, wind speed and the difference between vapour pressure and saturation vapour pressure. The Rohwer formula is frequently used:
At saturation (es = ea), the water flow balance between the atmosphere and the river system is zero. Tritium exchange occurs primarily through diffusion depending on the gradient in tritium concentrations in river water and in water vapour in the atmosphere.
For oversaturation conditions (es<ea), mechanisms for transfer from the atmosphere to the river system (condensation of water vapour in the air, interception of water droplets on the surface of the river system) can play a dominant role. In addition to flow from diffusion, modelling should also take into account kinetics of water droplet formation and the speed of deposit onto the surface.
Summary of the existing processes depending on saturation conditions:
Exchange with interstitial water in sediment. Even though water flow to sediment can, in certain cases, constitute the principal source of hydrosystem contamination (Bolsunovsky and Bondareva, 2003), it is processed using transfer models that are primarily concerned with the specific or surface activity of dry sediment. Sediment is however composed of water and solid particles and the specific activity of this mix is not zero as soon as tritium is found in the interstitial water. Therefore:
Variations of [HTO]its depend primarily on two types of mechanisms: interstitial diffusion at the interface of the water column and sediment (diffusive exchange), and exchange with the alluvial aquifer.
Subject to the nature of the soil (porous, fractured, impermeable, etc.) and flow conditions due to pressure gradients and permeability of the environment, exchange with the alluvial aquifer are complicated to model. For this reason, they are generally considered empirically and occasionally on the basis of tritium measurement.
For diffusive exchange, vits depends on the exchange speeds of the river system (vhds) and sediment (vsed) at their interface:
vhds can be deduced with several equations. The following relationship will serve as an example (Higashino et al., 2004):
vsed corresponds to the ratio of Dsed, the diffusion coefficient of the superficial sediment layer, to hsed, the thickness of the layer (between several mm and several cm).
Dsed (m2/s) is the molecular diffusion coefficient for the superficial sediment layer. It may be related to n, the porosity of this layer (Shultz and Zabel, 2000).
Free tritium. The principle of complete equilibrium in terms of specific activity, corresponding to rapidly reaching equilibrium between tritiated water (HTO) of the surrounding aquatic environment and the tissue free water tritium (TFWT), was primarily applied to fish according to the following formula (IAEA, 2010):
This approach may be considered as valid for all aquatic organisms.
Organic tritium. Uptake as organic forms of free tritium in the tissue water of exposed organisms is the result of various processes, including photosynthesis and growth. Considering these phenomena is indispensable for correct modelling of tritium transfer to living organisms. This approach has notably been applied by Myamoto et al. (1995), which represent organisms as a sum of two compartments, one corresponding to TFWT, which exchanges with the outside environment, and the other to OBT, formed from TFWT. Two types of modelling with the equilibrium corresponding to this situation are presented below (IRSN, 2009).
Supposing steady conditions, organisms are immerged in an environment with constant HTO activity. It is thus reasonable to suppose for biological synthesis of OBT from free tritium in water that OBT activity in the combustion water of these organisms is identical to HTO activity in their environment, corrected by a factor expressing this equilibrium.
The first approach is usually application of an equivalent concentration factor, expressing reaching equilibrium of OBT content in the organism in relation to HTO activity in the environment using the equation:
The second approach consists of applying a partition factor to HTO concentration in the water. This factor takes into account the presence of exchangeable hydrogen in the combustion water and isotopic discrimination in body-water exchange. With these assumptions, activity of OBT formed from HTO is estimated in fresh fish using the following equation (IRSN, 2009):
Comment. Several sources offer dynamic modelling of transfer of free and organic tritium. The models specifically take into account transfer to primary producers (phytoplankton) and fish. An IRSN report on tritium gives an overview of these models (IRSN, 2009).
Dose conversion coefficients (DCCs), expressed in wet weight
nd*: DCC non determinable due to distance
nd*: DCC non determinable due to the distance to sediment or the protection provided by it
nd*: DCC non determinable due to the distance to sediment or the protection provided by it