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Benchmarking of reactive transport codes for 2D simulations with mineral dissolution–precipitation reactions and feedback on transport parameters

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Abstract

Porosity changes due to mineral dissolution–precipitation reactions in porous media and the resulting impact on transport parameters influence the evolution of natural geological environments or engineered underground barrier systems. In the absence of long-term experimental studies, reactive transport codes are used to evaluate the long-term evolution of engineered barrier systems and waste disposal in the deep underground. Examples for such problems are the long-term fate of CO2 in saline aquifers and mineral transformations that cause porosity changes at clay–concrete interfaces. For porosity clogging under a diffusive transport regime and for simple reaction networks, the accuracy of numerical codes can be verified against analytical solutions. For clogging problems with more complex chemical interactions and transport processes, numerical benchmarks are more suitable to assess model performance, the influence of thermodynamic data, and sensitivity to the reacting mineral phases. Such studies increase confidence in numerical model descriptions of more complex, engineered barrier systems. We propose a reactive transport benchmark, considering the advective–diffusive transport of solutes; the effect of liquid-phase density on liquid flow and advective transport; kinetically controlled dissolution–precipitation reactions causing porosity, permeability, and diffusivity changes; and the formation of a solid solution. We present and analyze the results of five participating reactive transport codes (i.e., CORE2D, MIN3P-THCm, OpenGeoSys-GEM, PFLOTRAN, and TOUGHREACT). In all cases, good agreement of the results was obtained.

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Acknowledgments

We thank Dr. Dmitrii Kulik, Dr. Eric Sonnenthal, and Dr. Victor Vinograd for their useful discussion. We thank the comments, corrections, and suggestions of the two anonymous reviewers who contributed to the improvement of the paper.

Funding

The first author gratefully acknowledges Nagra for funding her PhD thesis during most of the work presented in the manuscript was conducted. The contribution from the University of A Coruña was funded by the Spanish Ministry of Economy and Competitiveness (Grant number CGL2016-78281) with support from the FEDER funds. Jesús Fernández enjoyed a research contract from the FPI Program of the Spanish Ministry of Economy and Competitiveness.

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Appendices

Appendix A

Table 4 Equilibrium amount of solutes and phases (mol in 1 L of water) for boundary condition (BC) and initial condition (IC) for case 2
Table 5 Equilibrium amount of solutes and phases (mol in 1 L of water) for boundary condition (BC) and initial condition (IC) for case 3a
Table 6 Equilibrium amount of solutes and phases (mol in 1 L of water) for boundary condition (BC) and initial condition (IC) for case 3b
Table 7 Equilibrium amount of solutes and phases (mol in 1L of water) for boundary(BC) and initial conditions (IC) for case 4

Appendix B: Solid solution

Activities of the end-members of a solid solution in thermodynamic equilibrium are related to activities of aqueous ions by the following set of equations [80]:

$$ {\text{SO}}_{4}^{\mathrm{2-}}\mathrm{=}a_{\mathrm{S}{\text{rSO}}_{4}}K^{0}_{\mathrm{S}{\text{rSO}}_{4}}\mathrm{=}\gamma_{\mathrm{S}{\text{rSO}}_{4}}X_{\mathrm{S}{\text{rSO}}_{4}}K^{0}_{\mathrm{S}{\text{rSO}}_{4}} $$
(1)
$$ {\text{SO}}_{4}^{\mathrm{2-}}\mathrm{=}a_{\text{Ba}{\text{SO}}_{4}}K^{0}_{\text{Ba}{\text{SO}}_{4}}\mathrm{=}\gamma_{{\text{BaSO}}_{4}}X_{\text{Ba}{\text{SO}}_{4}}K^{0}_{\text{Ba}{\text{SO}}_{4}} $$
(2)

where ai, γi, and Xi are the activity, the activity coefficient, and the mole fraction of an end-member i, respectively. For a simple ideal solid solution, γi is equal to 1, such that the activity of an end-member is equal to its mole fraction

$$ a_{\text{BaS}\mathrm{O}_{4}}\mathrm{=}X_{\text{BaS}\mathrm{O}_{4}} $$
(3)
$$ a_{\text{SrS}\mathrm{O}_{4}}\mathrm{=}X_{\text{SrS}\mathrm{O}_{4}} $$
(4)

The solidus and solutus curves are derived from the following formula:

$$ \log\sum \prod \left( \text{solidus} \right)=\log\left( a_{\mathrm{S}{\text{rSO}}_{4}}K^{0}_{\mathrm{S}{\text{rSO}}_{4}}\mathrm{+}a_{\text{Ba}{\text{SO}}_{4}}K^{0}_{\text{Ba}{\text{SO}}_{4}} \right) $$
(5)
$$\begin{array}{@{}rcl@{}} &&\mathrm{log\sum \prod} \left( \text{solutus} \right)\\&&=\log\left( \frac{1}{x_{{\text{Ba}}^{\mathrm{2+}}} \left/ K^{0}_{\text{Ba}{\text{SO}}_{4}}\mathrm{+}x_{{\text{Sr}}^{\mathrm{2+}}}\right. \left/K^{0}_{\mathrm{S}{\text{rSO}}_{4}}\right.}\right) \end{array} $$
(6)

The solidus x-scale refers to the mole fraction of the end-members while the solutus x-scale is calculated as

$$ x_{{\text{Ba}}^{\mathrm{2+}}}\mathrm{=}\frac{a_{\text{BaS}\mathrm{O}_{4}}K^{0}_{\text{Ba}{\text{SO}}_{4}}}{\mathrm{\sum \prod} \left( \text{solidus} \right)} $$
(7)
$$ x_{{\text{Sr}}^{\mathrm{2+}}}\mathrm{= 1-}x_{{\text{Ba}}^{\mathrm{2+}}} $$
(8)

N.B.: in this section only (Appendix A), a refers to the activity different from a used in the manuscript which refers to surface area per volume of the mineral phase.

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Poonoosamy, J., Wanner, C., Alt Epping, P. et al. Benchmarking of reactive transport codes for 2D simulations with mineral dissolution–precipitation reactions and feedback on transport parameters. Comput Geosci 25, 1337–1358 (2021). https://doi.org/10.1007/s10596-018-9793-x

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