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Radionuclide Migration


Mathematical Modeling of Radionuclide Migration in the Subsurface Hydrosphere

Tech Area / Field

  • ENV-MRA/Modelling and Risk Assessment/Environment
  • ENV-WPC/Water Pollution and Control/Environment

3 Approved without Funding

Registration date

Leading Institute
VNIIEF, Russia, N. Novgorod reg., Sarov

Supporting institutes

  • Russian State Hydrometeorological University, Russia, St Petersburg


  • SRK Consulting (UK) Ltd, UK, Cardiff

Project summary

The development of effective modeling methods for radionuclide migration (transport) processes in groundwater is an urgent problem at present time. First, the nuclear power station designing requires estimating the spread of radionuclides due to off-design conditions and accidents. Second, underground storage facilities are currently considered to be the most environmentally safe method for long-term disposition of radioactive waste. Crystalline rocks (Sweden), tuffs (USA), salt domes (Germany), and clay thicknesses (Switzerland, France, Spain, Belgium) are proposed as possible geological structures for such storage facilities. To construct an underground storage facility, it is necessary to substantiate that its operation is environmentally safe. Third, there are many areas all over the world, where groundwater, soils and rocks are contaminated with radioactive materials. The assessment of consequences of the contamination spread beyond the contaminated areas and the development of an optimum remediation strategy are impossible without the development of effective numerical models.

The proposed project objective is to develop effective modeling methods for the radionuclide transport processes in groundwater and develop a software system to allow predicting the radioactive contamination spread with regard to the mass transport with convection and dispersion, mass exchange processes in double-porosity media, radioactive material decay, physico-chemical interactions in the “water-rock” system (dissolution and deposition of minerals, sorption mechanism with surface complexation, ion exchange, generation of colloids, isotope exchange). Special attention will be paid to the migration of solutions of a varying density caused by variations in the concentration of salts and temperature variations.

The project proposes a complex approach to solving the problem of interest. The project core is the development of a mathematical model based on

  • non-linear Darcy and Fick law generalization, when modeling the flow and mass transport processes in a porous medium with solutions of a varying density;
  • consideration of the temperature-dependence of the rock and solution properties, when calculating the natural convection in a seamy-porous medium;
  • computational methods for balances and kinetics of physico-chemical interactions in the “water-rock” system.

The physico-mathematical model to be developed will be implemented within NIMFA software earlier developed within the ISTC Projects #714 and #1565. This would allow focusing on the development and implementation of the physico-mathematical model proper and reducing efforts for the development of service programs.

To achieve the project goal, it is necessary to effectively resolve a number of fundamental and application problems:

  • compilation of a list of main schemes for hydrological conditions and identification of a type set of entities to be described mathematically;
  • compilation of a list of main geological, physical, and physico-chemical factors determining the specifics of the processes of interest;
  • derivation of macroscopic relations to describe the non-isothermal flow and mass transport processes in the presence of density and concentration gradients;
  • construction of grid schemes to solve the convection-diffusion equations describing the radioactive contaminant transport by a fluid flow and providing a high accuracy of long-term prediction results;
  • development of numerical methods to solve nonlinear coupled problems of different-density flow and heat-and-mass transport;
  • development of algorithms to implement the developed methods for numerical simulation of the heat-and-mass transport by flow of chemically reactive solutions in seamy-porous media, development of a code and integration of this code within NIMFA software;
  • numerical experiments for verification of the developed mathematical models basing on the data from open sources;
  • validation and demonstration tests for the problem of radioactive contamination distribution for various hypothetic scenarios of radionuclide getting into the subsurface hydrosphere.

Resolution of the problems above will allow developing and implementing a mathematical model of heat and mass transport during the flow process of radioactive solutions in the geological environment. Such model will allow predicting long-term environmental risks associated with possible escape of radioactive materials from the place of underground burial of liquid radioactive waste, developing effective remediation strategies for the radionuclide-contamination areas, and estimating a potential impact of enterprises belonging to the nuclear industry complex on groundwater, both in the normal mode of operation of these enterprises and under emergency conditions. The lines of further possible developments include the following:
  • environmental expertise for projects of radioactive waste disposal in geological formations;
  • the development of a general theory of different-density non-isothermal flow in heterogeneous porous media;
  • the development of high-performance simulation systems oriented to massively parallel computers.

Leading experts on nonlinear flow problems will be the given project collaborators. Such collaboration implies joint meetings and workshops; consulting on the problems associated with compilation of the list of main geological, physical and physico-chemical factors that complicate the modeling of the processes of interest, selection and verification of models describing the sorption processes and derivation of macroscopic constitutive relations for the non-isothermal flow and mass transport in the presence of density and temperature gradients.

The RFNC-VNIIEF and RGGMU scientists and specialists having a great experience in developing mathematical models of the mechanics of porous media, qualitative analysis of nonlinear flow problems with closing relations taking into consideration both static (hysteresis) and dynamic (relaxation) memory effects, solving the coupled nonlinear heat and mass transport problems, and developing advanced iteration methods, including multiple-grid methods, will be involved in the project activity.


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