Model approaches: Fits and transport simulations

This study aimed to mechanistically describe surface charge, surface complexation, cation exchange, and precipitation reactions for long-term safety relevant elements at different mineral-water interfaces (muscovite, orthoclase, quartz, cf. Richter (2015) and Britz (2018)). Therefore, surface charge models and surface complexation models were developed to derive surface complexation parameters (SCPs) from titration and batch experiments, respectively, for each considered mineral phase via inverse modelling. SCPs comprise protolysis constants (pK-values), surface site densities (SSDs), specific surface site areas (SSAs), and surface complexation constants (logK-values) as well as model-inherent parameters such as capacities and co- and counterion association coefficients (basis Stern model). The diffuse double layer model, the basic Stern model, and a non electrostatic model are used to assess whether one model can be preferred over another. Futhermore, the 1-pK as well as the 2-pK model approaches are applied. Inverse fitting is realized via the combination of the geochemical speciation code PHREEQC (Parkhurst and Appelo, 1999) with the parameter estimation code UCODE (Poeter et al., 2005). Fig. 1 illusrates the coupling of PHREEQC and UCODE which shows how the inverse modelling procedure is implemented.

For Eu(III), SCPs determined form surface charge mesaurements and sorption experiments where then used in reactive transport models to predict Eu migration under different geochemical conditions in order to qualify the estiamted Eu SCPs for transport simulations. For reactive transport simulations SCPs from titration and batch experiments are applied as fixed parameter values; transport behavior of Eu is simulated (foreward); no adaptation of SCPs is allowed. Transport parameters such as dispersivities, diffusion coefficient, etc. are estimated with STANMOD (Simunek et al., 1999) using Br tracer breakthroug curves. In Britz (2018) detailed information is provieded concerning mineral titration, Eu batch, and Eu column experiments as well as fitting and simulation approaches. A brief summary of selected resutls may also be obtained here (under construction):

 

Fig.1: Flowchart of PHREEQC application in combination with UCODE for parameter estimation (after Britz (2011)). Data files: .dat – database, .pqi – PHREEQC input file, .pqo – PHREEQC output file, P.out – PHREEQC output file in UCODE routine, .tpl – template file for UCODE routine, .instructions – UCODE instruction file to extract fitted data from UCODE selected output file (.txt), .obs – observations for UCODE routine, .in – definition of UCODE processes and iteration procedures, P.in – PHREEQC input file in UCODE routine, .#out – UCODE output file, .bat – PHREEQC and UCODE batch files.

 

References:

Britz, S.: Sorption studies of Eu3+ on muscovite and orthoclase, Diploma thesis. Gesellschaft für Anlagen- und Reaktorsicherheit mbH, TU Braunschweig, (2011) 100 p.

Britz, S.: Europium sorption experiments with muscovite, orthoclase, and quartz: Modeling of surface complexation and reactive transport, PhD thesis, DOI 10.24355/dbbs.084-201806051207-0, GRS Braunschweig, Theodor-Heuss-Sr. 4, Abt. 401, 38122 Braunschweig (2018).

Parkhurst, D.L., and Appelo, C.A.J.: User’s guide to PHREEQC (Version 2) - A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations: U.S. Geological Survey Water-Resources Investigations Report 99-4259, (1999) 312 p.

Richter, C., 2015. Sorption of environmentally relevant radionuclides (U(VI), Np(V)) and lanthanides (Nd(III)) on feldspar and mica. Ph.D thesis, Technical University Dresden.

Simunek, J., van Genuchten, M. Th., Sejna, M., Toride, N., Leij, F. J.: The STANMOD computer software for evaluating solute transport in porous media using analytical solutions of convection-dispersion equation, U. S. Salinity laboratory, Agricultural Research Service, U. S. Department of Agriculture, Riverside, California, (1999) 20 p..

Poeter, E.P., Hill, M.C., Banta E.R., Mehl, S., Christensen, S.: UCODE_2005 and Six Other Computer Codes for Universal Sensitivity Analysis, Calibration, and Uncertainty Evaluation, U.S Geological Survey, Techniques and Methods 6-A11, (2005) 299 p.