# Experimental Study of Dissolution Kinetics of K-feldspar as a Function of Crystal Structure Anisotropy under Hydrothermal Conditions

M. Pollet-Villard, D. Daval, P. Ackerer, D. Saldi, K.G. Knauss, B. Wild, B. Fritz

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## To cite this version:

M. Pollet-Villard, D. Daval, P. Ackerer, D. Saldi, K.G. Knauss, et al. Experimental Study of Dissolution Kinetics of K-feldspar as a Function of Crystal Structure Anisotropy under Hydrothermal Conditions. Procedia Earth and Planetary Science, 2017, 17, pp.165-168. 10.1016/j.proeps.2016.12.042. hal-02105902

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Submitted on 27 Sep 2021

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15th Water-Rock Interaction International Symposium, WRI-15

Experimental study of dissolution kinetics of K-feldspar as a
function of crystal structure anisotropy under hydrothermal
conditions

M. Pollet-Villard<sup>a</sup>, D. Daval<sup>a,b</sup>, P. Ackerer<sup>a</sup>, G. D. Saldi<sup>b,c</sup>, K. G. Knauss<sup>b</sup>, B. Wild<sup>a</sup> and B. Fritz<sup>a*</sup>

<sup>a</sup> Laboratoire d'Hydrologie et de Géochimie de Strasbourg, Université de Strasbourg/EOST, Strasbourg, France

<sup>b</sup> Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

<sup>c</sup> Géosciences Environnement Toulouse - CNRS - Université de Toulouse, 31400 Toulouse, France

Abstract

We present the results of an experimental study of the effect of anisotropy on the kinetics of K-Feldspar dissolution under hydrothermal conditions as encountered in the Soultz-sous-Forêts enhanced geothermal system. We try to quantify the impact of K-feldspar anisotropy on dissolution rates in order to develop a more comprehensive model of the evolution of the reactive surface of silicate minerals in order to propose alternate kinetic rate laws to be implemented into water-rock interaction models and reactive transport codes. Our results evidence a relation between K-spar dissolution rate and the Gibbs free energy of reaction (ΔG<sub>r</sub>) which clearly differs from the transition state theory usually implemented into geochemical codes: it depends on the crystallographic orientation of K-spar mineral with significant differences between the different crystal faces. As for the far-from-equilibrium dissolution rate, this result highlights that using a unique theoretical rate law to describe dissolution rate as a function of ΔG<sub>r</sub> remains highly questionable. These results are very important for our challenge of understanding and modelling the dissolution mechanisms and they evidence that the dissolution anisotropy plays a fundamental role in these mechanisms.©

© 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of WRI-15

Keywords: experimental study; dissolution kinetics; anisotropy; K-feldspar; hydrothermal conditions;

<footnote>* Corresponding author. Tel.: 33 (0) 3 68 85 04 12; fax: 33 (0) 3 68 85 04 02.</footnote>

<footnote>E-mail address: bfritz@unistra.fr</footnote>
# 1. Introduction

The kinetic data for dissolution rate laws are key-parameters in the development of water-rock interaction numerical models. Highly concerned by these interactions, feldspar minerals are part of the most abundant minerals in the Earth crust. Predicting their long term evolution dissolution represents a critical issue for several geological and engineering concerns. For example, in the context of the Soultz-sous-Forêts enhanced geothermal system (Alsace, France), the pumping of the hot water and the exploitation of heat at surface may provoke a partial re-equilibration of the aqueous fluid composition, and re-injection of cooled water at depth may favor the dissolution of the main rock-forming minerals of the reservoir (such as K-feldspar) while promoting the precipitation of secondary phases¹. The relative intensities of primary mineral leaching and secondary phase formation may significantly affect the porosity and the permeability of the reservoir, thereby influencing its hydraulic performance and the efficiency of the geothermal site.

To determine the long term evolution of fluid/rock interactions in natural environments, the common strategy consists in investigating experimentally the influence of different parameters (pH, temperature, concentration of cations, deviation from equilibrium...) on dissolution rates in conditions in which dissolution is relatively fast (high temperature, far-from equilibrium conditions...) to be measured. Resulting kinetic rate laws are implemented in geochemical codes which are ultimately used to make an extrapolation to field conditions. With this method, five orders of magnitude are sometimes reported between laboratory-based silicate weathering rates and those measured in field².

In actual reactive transport codes, the evolution of surface area is related to the amount of dissolving mineral through a shrinking core model. The dissolution is considered as to be isotropic. However, recent studies suggest that some faces could dissolve up to 1,000 times faster than others³. Besides, etch pitting is responsible for the development of micro-facets less energetic (i.e. less reactive) during long-term dissolution (Fig. 1 and e.g.⁴). These results cast doubt of the relevance of a surface model based on shrinking spheres

<figure><img src="image_3.png" /><figcaption>Fig. 1: Schematic evolution of (a) crystal morphology and (b) surface topography over time. While the most reactive faces tend to vanish over time at the grain scale, an opposite trend may take place at the µm-scale on each face. Depending on the prevailing mechanism, one can expect either an apparent increase or a decrease of mineral reactivity over time.</figcaption></figure>

The aim of this study is to quantify the impact of K-feldspar anisotropy on dissolution rates in order to develop a more comprehensive model of the evolution of the reactive surface of silicate minerals. Our global objective is to propose alternate kinetic rate laws which could in turn be implemented into reactive transport codes and ultimately improve the predictive ability of hydro-geochemical simulations.

# 2. Method

To investigate the effect of crystallographic orientation of K-spar dissolution kinetics, single-crystals of K-spar were oriented using electron back-scattered diffraction (EBSD), cut, polished, and the starting topography was measured using vertical scanning interferometry (VSI). Our experimental protocol consisted in dissolving such crystals in an apparatus which allows for the creation of a non-wetted, unreacted reference surface (Fig. 2a). After alteration in a mixed-flow reactor (Fig. 2b) at 180°C in a synthetic alkaline solution, the surface retreat was
determined using VSI, which allows for a direct measurement of the face-specific dissolution rate (Fig. 2c). Measurements were carried out under a large range of Gibbs free energy ($\Delta G_f$) in order to determine, for each face, the evolution of the dissolution rate with the deviation from equilibrium.

# 3. Results and Discussion

## 3.1. Far from equilibrium dissolution rate

A typical result of dissolution experiments monitored with the surface retreat is shown in Fig. 2a. This figure represents the evolution of surface retreats for three different faces ((001), (101) and (111)) as a function of time. Since the surface retreat increases linearly with time, the dissolution rate is constant over time for each face. Besides, we see that the dissolution rate of the (001) face is ten times slower than the two other faces. This is an example of a non-negligible dissolution anisotropy.

Current geochemical codes use a single dissolution rate value to describe mineral dissolution kinetic. Our results give rise to the question of the meaning and the relevance of this value. Indeed, if the dissolution rate depends on the crystallographic orientations of the mineral, it seems to be unreasonable to use a single, isotropic dissolution rate constant in models.

<figure><img src="image_4.png" /><figcaption>Fig. 2: Face-specific measurements of K-spar dissolution rate. (a) Oriented K-spar crystal mounted on a Ti-jig as designed by 3. Pressure was applied via a screw on a Viton disk, creating a non-wetted reference area. (b) The crystal was subsequently altered in a mixed-flow reactor at 180°C, in a synthetic alkaline solution. (c) After reaction, the K-spar crystal was recovered and the nanotopography of the surface (here, face (111)) was monitored using VSI. The measurement of the surface retreat allows for the determination of the dissolution rate of the mineral.</figcaption></figure>

## 3.2. Relation between the dissolution rate and the Gibbs free energy of the reaction

In several geothermal systems, fluid-rock interactions occur at conditions which can be referred to as 'close-to-equilibrium conditions', in a Gibbs free energy range where the relations between dissolution rate and chemical
affinity are poorly known and unreachable through conventional approaches based on the measurement of the concentrations of cations released during dissolution (because the concentration of cations released during the course of dissolution is negligible compared to the electrolyte background concentration). Such measurements are made possible using our protocol described in Fig. 2, allowing us to propose a relation between K-spar dissolution rate and the Gibbs free energy for the 6 different crystallographic orientations studied

Our results evidence that the relation between K-spar dissolution rate and $\Delta G_r$ differs from the transition state theory currently implemented into geochemical codes. In addition, this relation depends on the crystallographic orientation of K-spar mineral (Fig. 3). As for the far-from-equilibrium dissolution rate, this result highlights that using a unique theoretical rate law to describe dissolution rate as a function of $\Delta G_r$ remains highly questionable.

<figure><img src="image_5.png" /><figcaption>Fig. 3: Surface retreat monitored as a function of time with VSI during an experiment carried out at pH 8.9 at 180°C ($\Delta G_r$) = -60 kJ.mol⁻¹). A ten-fold factor between the dissolution rate of the slowest and fastest faces can be seen, attesting to the anisotropic nature of K-spar dissolution.</figcaption></figure>

## 4. Conclusion

The dissolution anisotropy at the crystal habit scale as well as the complex evolution of the surface topography are at odds with the shrinking core model implemented in most of geochemical codes. In addition, the relation between the dissolution rate and $\Delta G_r$ for a mineral seems to depend on crystallographic orientations expressed in the mineral morphology. These results challenge our understanding of dissolution mechanisms and evidence that the dissolution anisotropy plays a fundamental role in these mechanisms. Our challenge now is to see how to include this new knowledge in the modelling approach of dissolution processes in water-rock interaction models.

## References

1. Fritz, B., Jacquot, E., Jacquemont, B., Baldeyrou-Bailly, A., Rosener, M., Vidal, O. Geochemical modelling of fluid-rock interactions in the context of the Soultz-sous-Forets geothermal system. *Cr Geosci* 2010; **342**, 653-667.

2. White, A. F. and Brantley, S. L., The effect of time on the weathering of silicate minerals: why do weathering rates differ in the laboratory and field? 2003; *Chem Geol* **202**, 479-506.

3. Daval, D., Hellmann, R., Saldi, G. D., Wirth, R., Knauss, K. G. Linking nm-scale measurements of the anisotropy of silicate surface reactivity to macroscopic dissolution rate laws: New insights based on diopside. *Geochimica et Cosmochimica Acta* 2013; **107**, 121-134.

4. Smith, M.E., Knauss, K.G., Higgins, S.R. Effects of crystal orientation on the dissolution of calcite by chemical and microscopic analysis. *Chemical Geology* 2013; **360-361**, 10-21.