4. METHOD OF SOLUTION
4.1 The Physical System
A simplistic description of the physical simulated by SYVAC is given below.
Low and intermediate level radioactive waste is stored in a repository or "vault". For shallow disposals, the "vault" is an engineered trench at depths of 20-30mm; for deep disposals a modified mine or purpose built structure at depths of 150-300m. Over a long period of time, groundwater penetrates the vault structure and the canisters containing the waste corrode. The radionuclides migrate in the groundwater flow through the vault structure into the ground - the "geosphere" - surrounding the vault.
The processes are represented in the code by a set of modules known as the Vault submodel.
The radionuclides from the vault migrate through the geosphere to the surface and into the "biosphere" where they become accessible to man, through drinking water, crops etc. The migration takes place through the groundwater flows in aquifer structure for both the shallow and deep disposal sites; for the shallow sites, the radionuclides can also migrate directly to the surface and, where appropriate, this latter process is simulated in SYVAC as part of the Vault submodel.
The process of migration through the Geosphere (with the exception noted above for the shallow site direct path) is represented in the code by the set of modules known as the Geosphere submodel.
The Vault and Geosphere submodels are controlled within the program by the Executive, a set of management modules. Generally, the Executive modules are concerned with data handling and data input/output to the submodels. The Vault and Geosphere submodels are principally concerned with the numerical calculations needed to simulate radionuclide migration from the vault through the geosphere into the biosphere.
The final output from the Geosphere submodel is in the form of a radionuclide flux over time. To estimate the subsequent radiological risk to man from this flux, the SYVAC program applies a series of dose conversion factors (these are different for each nuclide). The dose rate is calculated by multiplying the nuclide flux by the dose conversion factors, and applies to maximally exposed individuals.
These dose conversion factors are supplied to SYVAC as input data, in the form of biosphere data files. The files are currently produced from a structurally separate biosphere model called ECOS.
4.2 Probabilistic Parameter Sampling in Syvac
The previous section has briefly described the simulation of radionuclide migration carried out by the Vault and Geosphere submodels. This simulation requires data to describe the physical structure and transport characteristics of the vault and geosphere.
The necessary data is supplied to SYVAC in the form of parameters that represent hydraulic conductivities, diffusion coefficients, porosities etc for the vault and geosphere. Thirteen basic vault parameters are used to model deep disposal sites, and fifteen for shallow disposals. For both types of site, an additional six parameters are needed for each geological layer modelled in the geosphere.
The values of some of the parameters are not precisely known, and will vary over the timescale of the transport to the biosphere. SYVAC allows for this with a probabilistic approach; the parameter values are sampled from distributions chosen to cover the expected range of values that may be encountred during the post-closure phase of a vault. For each parameter, SYVAC allows the user to select one of five distributions: constant, uniform, log uniform, normal and log normal. Usually, for each parameter, the user will select the distribution that best fits the observed parameter values.
The calculation of risk to man requires knowledge of both the dose from a particular run, and the probability of that run.
Clearly, the dose to man calculated for a particular simulation run will depend on the parameter values chosen for that run. The probability of a particular run - i.e. the probability of choosing a particular set of parameter values - also depends on the parameter value chosen, and can be calculated from the parameter distributions selected by the user when setting up the input data.
The probabilistic nature of these calculations means that to obtain statistically valid estimates of risk (etc), SYVAC must be run a large number of times with different parameter values. The user chooses the number of runs when setting up the input data. The user also chooses the type of sampling used to select the parameter values for each run. SYVAC stores the results of each run for later analysis.
Two different sampling methods can be chosen for SYVAC; Random Sampling and Deterministic Generator Sampling. Random Sampling chooses values (randomly) from the entire range of the distribution chosen for each parameter. Deterministic Generator sampling selects one of 11 possible (discrete) sample points for each parameter for a run; the method of sampling is such that all eleven points are chosen in the course of 11 consecutive runs. The eleven points span the range of the distribution chosen for each parameter.
4.3 Run Acceptance Level
The calculations performed in the Vault and Geosphere submodels use most of the CPU time needed for a run. Consequently, to avoid unnecessary calculations, the program carries out a screening procedure to eliminate runs (i.e. sets of parameter values) that will produce no dose or are physically unrealistic. After the sampled parameter values have been generated, each SYVAC run is classified as being one of four run acceptance levels. The interpretation of run levels is as follows:
Level 0 : No dose expected within the time of study.
Level 1 : A non-zero dose expected. This is an accepted run. The actual dose of course may turn out to be zero.
Level 2 : Physically unreal data. An infeasible combination of sampled parameters has been selected.
Level 3 : The data is outside the validated range of one of the submodels and there is an expectation of a high dose. Note that the Vault and Geosphere submodel calculations are only performed for accepted (level 1) runs.
To arrive at the classification for a particular run a series of tests (of different levels of severity) is performed. Each test checks whether a sampled parameter value or value calculated from several parameters is within a specified range.
4.4 Executive Control
The Executive is the framework that controls the simulation program as a whole, and specifically calls the Vault and Geosphere submodels.
The functions performed by the Executive are:
(i) Input and validation of user defined data.
(ii) Generation of sampled values for data defined by probability distributions.
(iii) Verification and classification of each complete set of sampled data.
(iv) Invocation and control of the submodels which represent the stages of the nuclide transportation process.
(v) Generation of reports and other output.
(vi) Case study control.
4.5 Vault Submodel
The Vault submodel simulates the release of radionuclides from non heat-producing radioactive waste placed within an engineered vault in either deep or shallow land disposal facilities. The model includes representations of the waste matrix, waste canister, vault liner, the vault backfill material and the region of host rock around the vault disturbed during construction.
This submodel consists of a hydrogeological model, representing the groundwater flow through the different engineered barriers, and a radionuclide migration model. In the hydrogeological model,the different structural features of the vault are represented by a series of compartments. The hydrogeological model uses an electrical resistance analogy to represent flow within each of these compartments.
The migration model includes the processes of solubility-limited or mass-limited leaching of radionuclides from the waste matrix, linear equilibrium sorption of radionuclides onto the barrier materials, radioactive chain decay, dispersion and advection. Migration of radionuclides in groundwaters is predicted using a numerical solution to the transport equation. The leaching of radionuclides from the waste matrix is simulated using a diffusion model and gives the source term for the transport equation. In solving the transport equation, the radionuclide concentration at the vault/geosphere interface is taken to be zero.
4.6 Geosphere Submodel
The Geosphere submodel is a 1-dimensional model that deals with the migration of radionuclides from the vault to the biosphere through the geosphere. This is through the calculation of a response function for each geosphere layer. The response function describes the output from each geosphere layer at a given time for unit input to the geosphere layer at a start time The convolution of this response function with the time-varying input to the layer gives the total output from the geosphere layer at any time. Up to five distinct layers can be modelled. This submodel includes the effects of linear equilibrium sorption (for porous or fractured media), linear dispersion and chain decay. Up to 8 member chains can be considered. A semi-finite analytical Laplace transform solution technique is used to solve the geosphere partial differential transport equation.
4.7 Biosphere Model - ECOS
The biosphere code ECOS calculates the rate of accumulation of committed effective dose equivalent (dose) arising from the flux of radionuclides entering the biosphere. Dose to a maximally exposed individual and collective dose are calculated deterministically.
ECOS is an equilibrium-type compartmental model. The contents of parent and daughter radionuclides at equilibrium in nine activity reservoirs are computed by solving a set of linear simultaneous equations which represent the equilibrium solution of a general differential equation description.
The transfer processes modelled are: percolation and leaching in soils, erosion by wind and water, irrigation, cropping, water phase and sediment phase transport, sedimentation and resuspension in aquatic environments, equilibrium radionuclide sorption and radioactive decay. The dose pathways to man modelled are: drinking water, foodstuffs, external exposure and inhalation. Consumption of aquatic foodstuffs, terrestrial crops and animal products are included. For both drinking water and foodstuff pathways, intakes by man are reduced if the contaminated suply is insufficient to meet total annual needs. The model database includes parameters (e.g. foodchain parameters and sorption coefficients) for 53 radionuclides.
ECOS can be used in two different ways. It can be used in isolation, in order to investigate the relation between dose and biosphere state and in order to identify biosphere scenarios that should be considered in radiological assessment. It can also be used, as part of the overall SYVAC simulation, to produce dose conversion factors that are applied to the activity flux from the geosphere in order to estimate dose to man.
4.8 Nuclide Chemistry
Chemical processes are incorporated in the Vault and Geosphere submodels, not in a separate chemistry submodel.
Chemical parameters are obtained from expert judgement, basic research and site data, together with the use of more detailed models to examine scenarios and hence estimate ranges of values. At present, probability distributions are obtained judgementally for most cases.
The detailed models include simulation of the near-field, which provides direct input to SYVAC in the form of limiting solubilities, and coupled geochemical transport programs which are intended to provide verification for SYVAC runs. The principal programs used are based on ion-association models and solve for mass balance and mass action iteratively using a form of the Newton-Raphson technique and/or a continued fraction approach.