Problem 2-Thermal and Tracer Diffusion (EOS7R/rdif7)

This problem is prepared to illustrate thermal and tracer diffusion. It was originally present in TOUGH3/EOS7R user manual (rdif7). There are in fact two independent flow problems in two separate 1-D grid systems, each with 1 $m^2$ cross sectional area and 2 m long, divided into 20 grid blocks of 0.1 m length.

The “A-grid” (element name starting with "A") is initialized in single phase liquid conditions with default parameters of P = $10^5 Pa$, T = 8 ˚C, and zero mass fractions for brine, Rn1, Rn2, and air. Boundary conditions provided by block “ina 1” with a very large volume are (P, Xb, XRn1, XRn2, X, T) = ( $10^5, 10^{-3}, 10^{-7}, 10^{-8}, 10^{-6}$, 9 ˚C). The radionuclide tracers are stable (half-life of $10^{50}$ seconds). Rn1 with an inverse Henry’s constant of $10^5 Pa^{-1}$ has low volatility, while Rn2 is a volatile species with the same inverse Henry’s constant as air, $10^{-10} Pa^{-1}$. Diffusivities specified in data block DIFFU override parameters in block SELEC; all diffusivities are specified as -1.e-6 so that, for all components, mass diffusion occurs with saturation and tortuosity-independent effective diffusivities of $10^{-6} m^2/s$. In addition to mass diffusion, there is also thermal diffusion due to the different temperature at the boundary. Thermal diffusivity is $d_{th}=\lambda/ \rho C$ ≈ 2.5/(2500x1000) = $10^{-6} m^2/s$, equal to component diffusivities. Porosity was chosen to be small, $\phi=10^{-4}$, so that fluid contributions to formation specific heat are small. This parametrization allows a direct comparison between changes for mass fractions and temperatures. The “B-grid” (element name starting with "B") is initialized in single-phase gas conditions at the same pressure of $10^{5} Pa$, but at a temperature of 125 ˚C, and also with zero mass fractions of all components other than water. Different non-zero mass fractions for the various components are specified in block “ina 2” with a very large volume at the boundary of the B-grid.

Advective effects are suppressed because the medium was assigned zero permeability. Accordingly, the only active processes are mass diffusion of the various components, and thermal diffusion in the A-grid. Note that mass fractions for all components are always calculated in both aqueous and gas phases, regardless of phase composition of the fluid. Under the specified conditions, the diffusive profiles are expected to be the same for all components, the only difference being different normalization, because of the different absolute magnitude of the concentration step at the boundary. The liquid phase mass fraction profiles for brine, Rn1, and Rn2 in the A-grid are seen to be in excellent agreement with each other, as well as with the temperature profile from heat conduction. The gas phase radionuclide mass fractions listed for the A-grid are obtained from phase partitioning according to Henry’s law locally; there is no mass inventory associated with these because gas phase saturations are zero. The simulation results for tracer masses fraction in gas phase are different to the corresponding results from TOUGH3/EOS7R. This is caused by using different HC for air solubility calculation. TOUGH4 uses temperature dependent HC, but TOUGH3 uses constant HC. If set IE(402)=1, similar results will be obtained.

In the single-phase gas conditions in the B-grid, it is the gas phase mass fractions which are to be compared; for all components they agree very well among each other, as well as with the diffusion profile calculated for the same diffusivities in the single-phase liquid conditions in the A-grid.

The simulation input and output files are present below.

Input files: Infile_rdif7.zip

Output files: output_rdif7.zip