Flow and Transport Model

The multi-species reactive transport model TBC (Schafer et al., 1998) was used for the simulation of both experiments. The model column was discretised into 19 elements, each of 0.02 m length. The temporal discretisation was 0.01 d. The high temporal resolution was necessary to fulfill the stability and accuracy criteria required by the numerical model. 

TBC employs a finite-difference approach for both flow and transport modelling. 

The bormdary conditions for the flow model were a fixed potential boundary at the column inflow and a prescribed flux bormdary condition at the outflow side. For the transport modelling a time-variant fixed concentration boundary at the inflow of the column was assumed. The concentrations values at the inflow boundaries were taken from the measurements at the column inlet. 

There were no independent measurements for the determination of the effective porosity and the dispersivity of the medium. However, as the residence time of the solutes in the column (approx. 4-5 hours) was much smaller than the time intervals between the concentration measurements (at least 2 days), the solute movement inside the column could not be resolved and hence effective porosity and dispersivity values were of minor importance for the comparison of model results and observations. A value of 15 % was assumed for the effective porosity and 0.01 m for the dispersivity. These are reasonable assumptions for small scale transport in porous media. 

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Unlike groundwater flow and transport models, thermodynamic models, in principal, do not need any calibration. However, considering surface-controlled or kinetically controlled reaction models might be subject to calibration. 

Zhu C. (2000) Estimate of recharge from radiocarbon dating of groundwater and numerical flow and transport modeling. Water Resour. Res. 36, 2607-2620. 

Siegel M. D. and Erickson K. E. (1986) Geochemical sensitivity analysis for performance assessment of HEW repositories effects of speciation and matrix diffusion. Proceedings of the Symposium on Groundwater Flow and Transport Modeling for Performance Assessment of Deep Geologic Disposal of Radioactive Waste A Critical Evaluation of the State of the Art. Sandia National Eaboratories, Albuquerque, NM, pp. 465-488. 

SESOIL Unsaturated zone SESOIL is a one-dimensional, finite difference flow and transport model. The model estimates the rate of vertical solute transport and transformation from the land surface to the water table. 

CHEMFLO Unsaturated zone CHEMFLO is a one-dimensional flow and transport model designed to simulate the movement of water and chemicals into and through soils. 

The more recent development of sophisticated ground-water flow and transport modeling software and the availability of powerful computers allow a much more detailed modeling of the tracer evolution in ground-water systems. Consequently, applications of tracer data in conjunction with multi-dimensional flow and transport models began to show up in the 1990s (Reilly et al. 1994 Szabo et al. 1996 Sheets et al. 

Tracers were collected over several thousand hours and breakthrough curves analysed by different flow and transport models. The tracer breakthrough curves for the non-sorbing tracers can be used to obtain information on the mean residence time and on the spread in residence time. The latter is commonly called dispersion. The mean residence time can be used to assess the volume of flowpath if one assumes that the flow rate of all the collected water has the same residence time as that obtained by the tracer. Further, assuming that all the water has flown through one fracture, Feature A, the aperture of Feature A, can be determined. This was found to be about 3 mm. This is much larger than expected or reasonable. Typical fracture apertures are on the order of 0.1 mm. 

Shestakov V.M., Kuvaev A.A., Lekhov A.V., Pozdniakov S.P., Rybalchenko A.I., Zubkov A.V., Davis P.A., Kalinina E.A. 2002. Flow and transport modeling of liquid radioactive waste injection using data from Siberian Chemical Plan Injection Site. Environmental Geology. 42(2-3) pp.214-221... 

You L, Liu H. A two-phase flow and transport model for PEM fuel cells. J Power... 

In Russia, the flow and transport models are well developed and commonly used for engineering purpose. These models calculate hydrology and hydrodynamic conditions (flow, velocity, surface runoff), movement of water quality constituents. The problems of eutrophication are well studied for lakes and impoundments [4] [5] [6] [7] [8]. 

In a study of natural flux of trichloroethylene (TCE) from the subsurface reported by Tillman et al. (2003), surface flux measurements made by a flux chamber were compared with flux simulations using a transient, one-dimensional gas-flow and transport model incorporating the effects of gas phase diffusion,... 

You, L. and H. Liu, A Two-Phase Flow and Transport Model for the Cathode of PEM Fuel Cells, International Journal of Heat and Mass Transfer, Vol. 45, 2002, pp. 1177-22S7. 

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