Benchmarking of coupled codes

Benchmarking of transport codes is an important activity which supports the credibility of the numerical simulations. It is essential for reactive transport codes describing complex geochemical interactions and/or radionuclide migration in the

vicinity of a nuclear waste repository or in laboratory experiments.

3.5.1 Reactive transport modelling of natural analogues

To cross-benchmark geochemical setups and reactive transport simulation approaches against experimental data, and other transport codes, the group is participating in the Grimsel LCS (Long Term Cement Studies) project. Within this project the Maqarin natural analogue is being investigated in terms of the long-term changes occurring in rocks in contact with a hyperalkaline solution. Several modelling teams have applied state-of-the-art geochemical models to re-appraise the earlier simulations of STEEFEL & LICHTNER (1998). In the approach taken here (in collaboration with H. Shao UFZ Leipzig) the geochemical setup for the rock mineralogy and the porewater was calibrated to match measurements from the Maqarin site (SHAO et al.,2012). The setup includes several clay and zeolite minerals, considers cation exchange processes, and a state-of-the-art model for cement phases. Similar to the earlier calculations of STEEFEL & LICHTNER

(1998), who used a much simpler geochemical model, pore clogging occurred after several hundred years at a distance of 5 - 10 mm from the surface in contact with the hyper alkaline solution. The cause of the pore clogging was a massive precipitation of ettringite and C-S-H minerals. Sensitivity studies performed by varying the intrinsic diffusion coefficient, the exponential factor in Archie's relation, and the mineral surface area available for dissolution and precipitation, showed that the dissolution of clay minerals controlled the availability of Al which was needed for ettringite and C-S-H phase precipitation. Thus, the initial amount of clay minerals and their dissolution rates controlled the spatial and temporal evolution of porosity changes. The simulations revealed that neither cation exchange processes, nor the formation of zeolite minerals, strongly influenced the geochemical evolution of the system.

3.5.2 OpenGeoSys consortium and co-operation with UFZ-Leipzig

Within the co-operation agreement between the Helmholtz Centre for Environmental Research (UFZ, Leipzig, Germany) and LES, the Richard’s flow module has been added into the OpenGeoSys-GEMS coupling. With this module it has become possible to simulate geochemical reactions in partially saturated media. Furthermore, the coupled OpenGeoSys-GEMS version was parallelized with a hybrid algorithm based on MPI and OMP threads. This enables a much more effective simulation of 2D/3D systems on current high performance computers.

In October 2012 the OpenGeoSys version 5.3.05 was published. This version contains the GEMS3K V3 source code which was published in October 2012 after several years of development under the LGPL license. On the 11^th October 2012 an OpenGeoSys community meeting took place in Leipzig where the new OpenGeoSys-GEMS version was presented. On the same day the OpenGeoSys steering board met in which Georg Kosakowski represented the LES. On the 12^th October 2012 the first meeting of a network of PhD students working in the field of reactive transport took place at the Division for Reactive Transport of the Helmholtz Centre Dresden-Rossendorf. PhD students from HZDR, UFZ and PSI presented their work. In particular, a strong exchange is expected in the framework of the PhD project on

“Reactive transport benchmark for coupled codes”

(PhD student Jenna Poonoosamy, started in October 2012).

3.5.3 Fluid-rock interaction modelling: Geo-thermal electrolyte solutions thermo-dynamic model and computational fitting framework development

In June 2012, PhD student Ferdinand Hingerl (GEOTHERM project supported by the Competence Center Environment and Sustainability, the Paul Scherrer Institut and the Swiss Ministry of Energy) successfully defended his PhD thesis at the ETH, Zürich. Within his PhD project, Ferdinand Hingerl developed an activity model for geothermal aqueous multi-electrolyte solutions rEUNIQUAC (revised Extended Universal QUAsi-Chemical activity model) and a stand-alone module for the GEMS-code,

GEMSFIT, which is a versatile computational tool for fitting thermodynamic models. The rEUNIQUAC has been applied to model the long-term permeability evolution of geothermal reservoirs.

The rEUNIQUAC activity model provides excess thermodynamic properties of aqueous binary solutions over a wide range of temperatures, from 298 to up to 573 K, and for concentrations up to 5 M (or saturation if the solubility is smaller than 5 M) under saturated water vapor conditions. Compared to the original EUNIQUAC, it implements a stricter treatment of long-range electrostatic interactions, an improved temperature dependence on the UNIQUAC parameters, and an empirical parameter for strongly associating electrolytes. The model is comparable to the standard Pitzer model in terms of accuracy, but requires less parameters and employs a simpler temperature dependence. In contrast to the Pitzer model, rEUNIQUAC does not require the addition of associated species, even in highly non-ideal systems containing complexing electrolytes.

The stand-alone computational module GEMSFIT is the first open-source implementation of a generic thermodynamic fitting tool coupled to a chemical equilibrium solver which uses the direct Gibbs energy minimization approach. GEMSFIT provides the most common tools for statistical analysis which allows a thorough evaluation of the fitted parameters, and it has a generic interface to a PostgreSQL database to access measurement data. Results from parameter regression, as well as from statistical analysis, can be visualized and directly printed to various graphical formats. Usage of the code is facilitated by a graphical user interface which assists in setting up GEMSFIT input files. Using GEMSFIT, an internally consistent set of rEUNIQUAC parameters has been created for the binary electrolyte systems NaCl-H₂O, KCl-H₂O, CaCl₂-H₂O, MgCl₂ -H2O, HCl-H2O, NaOH-H2O, KOH-H2O, Na2SO4 -H2O, K2SO4-H2O and MgSO4-H2O. The fitted parameters cover temperatures up to 573 K and a maximum concentration of 5 M. Furthermore, Ferdinand Hingerl has successfully fitted anhydrite solubility in a NaCl-H2O solution from 373 to 573 K (Fig. 3.9), which demonstrates that rEUNIQUAC has the potential to be applied to mixed-electrolyte solutions, even if they contain highly complexing solutes.

Recent benchmarking studies performed by ANDRE

et al. (2006) demonstrated that slight differences in activity coefficients, thermodynamic equilibrium constants and kinetic models can result in significant differences in the predicted mineral assemblages.

Motivated by these discrepancies, Ferdinand Hingerl has investigated thermodynamic activity models (e.g.

Pitzer, rEUNIQUAC) and associated computational fitting frameworks suitable for the description of fluid-rock interactions in Enhanced Geothermal Systems.

Fig. 3.9: Predicted and measured solubilities of anhydrite in the system NaCl-CaSO₄ at 373 K, P_sat (from HINGERL, 2013).

3.6 References

ANDRÉ, L., SPYCHER, N., YU, T., PRUESS, K., VUATAZ,F.-D.(2006)

Comparing FRACHEM and TOUGHREACT for reactive transport modeling of brine-rock interactions in Enhanced Geothermal Systems (EGS).

Proceedings of the 31^st Workshop on Geothermal Reservoir Engineering, Stanford University, 350–

358.

BERNER,U.,KULIK,D.A.,KOSAKOWSKI,G. (2012) Influence of a low-pH cement liner on the near-field of a repository for spent fuel and high-level radioactive waste. Phys. Chem. Earth, submitted.

CHURAKOV,S.V.&GIMMI,TH. (2011)

Up-scaling of molecular diffusion coefficients in clays: a two-step approach. J. Phys. Chem. C 115, 6703-6714.

HINGERL,F. (2013)

Geothermal electrolyte solutions: thermodynamic model and computational fitting framework development. Thesis, ETH Zürich, (in prep.).

HUMMEL,W. (2009)

Ionic strength corrections and estimation of SIT ion interaction coefficients. PSI Technical Report TM-44-09-01.

KOSAKOWSKI,G.,BERNER,U. (2012)

The evolution of clay rock/cement interfaces in a cementitious repository for low and intermediate level radioactive waste. Phys. Chem. Earth, submitted.

PARDAL, X., BRUNET, F., CHARPENTIER, T., POCHARD,I.,NONAT,A. (2012)

27Al and ²⁹Si solid-state NMR characterization of calcium-aluminosilicate-hydrate. Inorg. Chem. 51, 1827-1836.

PFINGSTEN, W., BRADBURY, M.H., BAEYENS, B.

(2011)

The influence of Fe(II) competition on the sorption and migration of Ni(II) in MX-80 bentonite. Appl.

Geochem. 26, 1414-1422.

SHAO, H., KOSAKOWSKI, G., BERNER, U., KULIK, D.A.,MÄDER,U.K.,KOLDITZ,O. (2012)

Reactive transport modeling of the clogging process at Maqarin natural analogue site. Phys. Chem. Earth, submitted.

STEEFEL,C.,LICHTNER,P. (1998)

Multicomponent reactive transport in discrete fractures - II: Infiltration of hyperalkaline groundwater at Maqarin, Jordan, a natural analogue site. J. Hydrology 209(1-4), 200–224.

TAYLOR,H.F.W. (1993)

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Based. Mater. 1, 38–46.

THOENEN,T.(2012)

SIT database for NaCl solutions. Priv. comm.

VAN LOON, L.R., SOLER, J.M., MUELLER, W., BRADBURY,M.H. (2004)

Anisotropic diffusion in layered argillaceous rocks: A case study with Opalinus clay. Environ. Sci. Technol.

38, 5721-5728.

YU, P., KIRKPATRICK, R.J., POE, B., MCMILLAN, P.F.,CONG,X.D. (1999)

Structure of calcium silicate hydrate (C-S-H): Near-, mid-, and far-infrared spectroscopy. J. Am. Ceram.

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