(A-2)Appendix A
Two-Compartment Environmental Transport Model for Tritium
The physical and chemical properties of HTO include its complete miscibility in water, the absence of any known sequestering tendencies (i.e., no preferential uptake of HTO by organisms or other components of the environment), the similarity of its properties (such as diffusion coefficient and vapor pressure) to water, and the observed uniform distribution of HTO among the aqueous phases of all interacting compartments in field studies that have approximated steady-state conditions [Murphy, 1984, 1993]. These properties imply that the fate and transport tendencies of HTO are best predicted by modeling it as having infinite affinity for the water phase of any compartment and relatively negligible affinity for other phases, such as the organic phase of biota or mineral phase of soil.
We use a two-compartment model to estimate the steady-state distribution of tritiated water between air and soil media that would result from continuous HTO emissions to the atmosphere (air compartment) from the NTLF. Using the principle of mass conservation, the model provides an algorithm for predicting steady-state HTO-specific activities (concentrations) in the soil and air compartments.
On a local scale, the transfer of HTO from air to the land surface occurs mainly by precipitation with a minor role played by diffusional vapor exchange [NCRP, 1979]. On a global scale, the tritium concentration in air is relatively uniform and, on average higher than that in soil, so that the reverse of the local-scale case appears to hold.
The deposition of HTO from air to ground does not necessarily represent a definitive loss from the air compartment since deposited HTO can re-emerge back into the air compartment via evapotranspiration or simple evaporation. Only HTO that finds its way deep into the ground (well below the root zone) represents a true air compartment loss.
When HTO enters soil, it follows the same transport processes as H
2O [Murphy, 1993]. Thus, important transport mechanisms in the terrestrial environment include bulk flow (due to gradient of hydraulic head), and flow due to vapor gradient, temperature gradient, and HTO concentration gradient. The environmental half-life of tritium in soil is generally longer than in other components of the ecological system, and this relatively longer compartment half-life extends the residence time of tritium in vegetation rooted in that soil. High-water-use plants may affect the movement of a tritium pulse in soil. The observed environmental half-life of tritium in soil appears to be made up of two components—a shorter one reflecting the bulk movement of water and a longer one reflecting tritium retained in more stationary water, such as chemically bound water [Koranda and Martin, 1973].Under steady-state conditions, the concentration of tritium in surface waters would be the same as that in the water-phase of the atmosphere. When the source of tritium is air and the residence-time of the surface water body is long relative to the half-life of tritium—which is the case for the oceans, the Great Lakes, San Francisco Bay, etc.—the HTO concentration in the surface water is lower than that in atmospheric water on average. However, near the top of a surface water column a steady-state concentration is likely to exist. HTO concentrations in aquatic organisms closely follow those in the water [Murphy, 1993].
Plants take up HTO from water vapor in air through plant respiration and from water in soil through transpiration [Koranda and Martin, 1973]. For plants grown in tritium-free soil, the tritium concentration in plant leaves is on the order of 0.3 to 0.7 times the tritium concentration in atmospheric water [Murphy, 1993]. Some of the tritiated water taken into plant tissues can be converted to organically-bound tritium (OBT), which has a longer residence time in plants than molecular water. Photosynthesis is the primary process by which HTO is converted to OBT in plants. However, a very low fraction of tritium moving through the plant is transformed to OBT. Thus, Murphy [1993] has noted that OBT in plants can be neglected as a sink for Tritium. Nevertheless, the effective residence time of tritium in plants may be affected by even small amounts of OBT.
As discussed in Section A.1.4, tritium activity in the terrestrial biota compartment is readily inferred once the soil and air activities are known. Thus, the activity in the biota compartment need not be predicted explicitly. Adding a biota compartment would require the quantification of inputs such as the uptake rate from soil into plants, but there is insufficient information for this quantification.
Because the current application of the model does not include estimating exposure through the food ingestion pathway, the biota concentrations are not required for our purposes. Biota need only be considered inasmuch as it affects the ultimate steady state HTO inventories in air and soil water (soil water affects runoff concentration, which will be subject to dermal contact). In addition, the fraction of land covered by surface water is minimal, allowing the surface water compartment to be neglected for the purposes of the fate and transport modeling (streams are considered in the dose assessment). Thus, a two compartment model is sufficient.
The premises of our modeling approach are that HTO will distribute itself primarily in the aqueous phase of a compartment, that non-aqueous tritium (i.e., OBT) in any compartment can be accounted for by increasing the effective residence time and that under equilibrium conditions water-phase tritium activities in each compartment will be equal.
For convenience, we call the water-phase HTO-specific activity in compartment i, the "aquivalence," which will be denoted AQ
i. In a closed system that is in equilibrium, the aquivalences of all compartments are the same. Similar terminology has been used in modeling the fate and transport of inorganic and organic chemical species [Mackay and Diamond, 1989; Diamond et al., 1992; McKone, 1993].We propose here a model for a system that has achieved steady state in terms of mass exchange by balancing gains and losses. However, in terms of chemical thermodynamics the system is not assumed to be at equilibrium. The simultaneous balancing of gains and losses for both soil and air compartments allows non-equilibrium aquivalences of the two compartments to be calculated. The bulk compartment's specific activity is easily calculated once its aquivalence is quantified. Because only the aqueous phase of a compartment is allowed to hold HTO, both the total compartments inventory and water-phase inventory of tritium are the same. The bulk specific activity (i.e., inventory normalized by the aqueous as well as non-aqueous phase volumes) of compartment i, is calculated as a function of its volumetric water content, denoted Ø
i, and its aquivalence (AQi) as:C
i = Øi ´ AQi (A-1)where C
i denotes compartment i's bulk specific activity, and the other terms are as defined above.Thus, the bulk specific activities of HTO in adjacent compartments may differ even under equilibrium conditions, since the two compartments may differ in their volumetric water contents. Under equilibrium conditions compartment i's capacity for holding HTO is effectively dictated by its volumetric water content, Ø
i.The volumetric fraction of water in air is calculated based on the observed relative humidity (RH—expressed as the fraction of saturation) at LBNL, and the saturation vapor pressure. The saturated vapor pressure (VP
sat) in Pascals (Pa) is calculated as a function of temperature by using the following Antoine equation [Weast et al., 1986]. (A-2)
where T is the ambient absolute air temperature in kelvins. Using VPsat , we calculate the volume fraction of water in air, Øa, as
(A-3)
where R is the universal gas constant, 8.314 Pa-m3/mol-°K; MWH2O is the molecular weight of water, 18 g/mol; and rH2O is the density of water, 106 g/m3.
The volumetric water fraction of the soil compartment is determined directly from field data (See Table 6).
The steady-state equations describing gains and losses in the two compartments are used to solve for the steady-state inventory in each compartment. Equations A-4 and A-5, which are the same as Equations 4-1 and 4-2, express gains and losses for the air and soil compartments, respectively.
S + T
sa Ns = La Na , (air) (A-4)and
T
as Na = Ls Ns , (surface soil) (A-5)where N represents a compartment HTO inventory (a compartment's bulk inventory and its water-phase inventory are equivalent) and the T
ij (i, j = a or s) are transfer rate constants, with units of day-1, that express fraction per unit time of the inventory of compartment i that is transferred to compartment j. The compartment abbreviations are a for air, and s for surface soil. The product of an N term and a T term is the rate of change of inventory in Bq/d. Li Ni represents all losses from compartment i, Bq/d. The term S in Equation A-4 represents the rate of HTO input (i.e., the NTLF's HTO emission rate) into the air compartment, Bq/d. Transfer-rate constants are functions of landscape characteristics and environmental mass transfer rates.In terms of aquivalence the balance in Bq/d is expressed as a loss from a compartment i and transfer to a compartment j in the form
loss = Area
´ vij ´ Øik ´ AQi = Tij Ni , (A-6)where Area in m
2 is that across which mass exchange occurs, vij is the advection velocity from i to j at the exchange boundary, and Øik is the volumetric moisture content of the moving phase k from i to j, (in this analysis the moving phase is always water, e.g., recharge or runoff, and therefore Øik, is generally equal to Øwater and AQi represents the aquivalence of compartment i. Compartment inventory Ni is calculated using Equation A-1 and the compartment volume.N
i = Øi AQi Vi (A-7)Combining Equations A-6 and A-7 and rearranging terms yields the following for T
ij,
, (A-8)
where Vi is the compartment volume, di is the compartment depth or height, and Øi is the volumetric fraction of water in compartment, i. This is the general approach used in the paragraphs that follow to obtain the transfer rate constants.
In the box model used for air, the inventory N
a, in Bq, is described by solving Equations A-4 and A-5. La is the sum of all loss-rate constants from the air compartment.L
a = Tas + Tao + l (A-9)L
a Na is the sum of all losses from the air compartment, in Bq/d. The rate constant Tas accounts for rain-water washout from air to surface soil.
(A-10)
The air compartment mixing depth is analogous to the mixing height parameter used in Gaussian plume modeling. For the NTLF analysis this parameter depends on the box-model volume used in the analysis. For the Zone 1 risk characterization, the mixing depth is roughly 15 m (see Site Characteristics subsection below). In Equation A-10, Øwater describes the scavenging factor for rain drops passing through air.
The factor Tao on a box model accounts for atmospheric dispersion that is applied to the natural bowl in which the NTLF is located. According to Benarie [1980], the long-term average pollutant concentration in a region bordered by a box model with volume Va and pollution source, S in Bq/d, is given by
, (A-11)
where c is a unitless proportionality constant, Area is the area of the model region, and vw is the long-term average wind speed in m/d. This implies that the inverse of the rate constant, Tao, is the convective residence time and is given by the expression, c da/vw, where da is the atmospheric mixing height. Based on a model for area sources developed by Turner [1970], the constant c can be estimated as 4.3 /da. Making the appropriate substitutions gives the following expression for the convective loss-rate constant in the air compartment:
. (A-12)
Equation 5 describes the mass balance for the soil compartment inventory, Ns, in Bq of HTO. Ls is the sum of soil compartment transfer-rate constants:
Ls = Tsa + Trecharge + Trunoff + l , (A-13)
where Tsa is the soil-to-air transfer rate primarily representing evapotranspiration processes, Trecharge and Trunoff are the rate constants for recharge losses to ground water and runoff losses to outside the unit, respectively; and l is the radioactive decay rate. Rate constants are in units of day–1. These loss-rate constants are given by
, (A-14)
, (A-15)
, (A-16)
recharge = rain – evapotrans – runoff . (A-17)
The parameter recharge is the yearly average ground-water recharge at the site, in m/d; rain is the yearly average rainfall, in m/d; evapotrans is the yearly average evapotranspiration, in m/d; and runoff is the yearly average runoff; in m/d.
Equations A-4 and A-5 represent a system of two equations, with two unknowns, and can be solved to determine the steady-state inventories, N
i, of contaminant in the soil and air compartments. This solution yields the following relationships,
(A-18)
(A-19)
These solutions are used to determine the inventory of tritium in the air, soil, and runoff from the site.