Phase‐field modeling of epitaxial growth of polycrystalline quartz veins in hydrothermal experiments

Abstract

Mineral precipitation in an open fracture plays a crucial role in the evolution of fracture permeability in rocks, and the microstructural development and precipitation rates are closely linked to fluid composition, the kind of host rock as well as temperature and pressure. In this study, we develop a continuum thermodynamic model to understand polycrystalline growth of quartz aggregates from the rock surface. The adapted multiphase‐field model takes into consideration both the absolute growth rate as a function of the driving force of the reaction (free energy differences between solid and liquid phases), and the equilibrium crystal shape (Wulff shape). In addition, we realize the anisotropic shape of the quartz crystal by introducing relative growth rates of the facets. The missing parameters of the model, including surface energy and relative growth rates, are determined by detailed analysis of the crystal shapes and crystallographic orientation of polycrystalline quartz aggregates in veins synthesized in previous hydrothermal experiments. The growth simulations were carried out for a single crystal and for grain aggregates from a rock surface. The single crystal simulation reveals the importance of crystal facetting on the growth rate; for example, growth velocity in the c‐axis direction drops by a factor of ~9 when the faceting is complete. The textures produced by the polycrystal simulations are similar to those observed in the hydrothermal experiments, including the number of surviving grains and crystallographic preferred orientations as a function of the distance from the rock wall. Our model and the methods to define its parameters provide a basis for further investigation of fracture sealing under varying conditions.

Modeling fracture cementation processes in calcite limestone: a phase-field study

“…While the recent numerical works (e.g., Ankit et al 2015a, b;Wendler et al 2016) advocate the potential of the phase-field approach in addressing quartz mineral growth in sandstones, the present study in addition to our previous work (Prajapati et al 2017) serves as a basis for new calcite cementation models for carbonate rocks based on sound thermodynamic principles. The present study complements the works of Bons (2001) and Hilgers et al (2001) (who used front-tracking technique) and adds to them.…”

“…The model has been previously applied to address the growth of minerals such as potash alum (Ankit et al 2013), quartz (Ankit et al 2013(Ankit et al , 2015aWendler et al 2016), and calcite (Prajapati et al 2017). Therefore, for the sake of completeness, we briefly reiterate the model equations.…”

“…In contrast with the traditional front-tracking methods (see Urai et al 1991;Bons 2001;Hilgers et al 2001;Nollet et al 2005), the phase-field approach does not require explicit tracking of the interfaces as the motion of interfaces is inherently captured in the governing equations. This property makes it a computationally efficient and robust approach for the treatment of moving boundary problems such as cement growth in open fractures or porous rocks, even in three dimensions (e.g., Ankit et al 2013Ankit et al , 2015aWendler et al 2016;Prajapati et al 2017).…”

Petroleum reservoir quality prediction: overview and contrasting approaches from sandstone and carbonate communities

“…Such models are enticing because they have the potential to predict textures and morphologies that may be compared directly with data from natural samples and laboratory experiments and because they serve as a more rigorous basis for predicting a wide range of rock properties compared with the model types discussed above. To date, most grain/pore scale simulation studies either have involved imposing a predefined diagenetic state as a means to rigorously simulate the impact of diagenetic alteration on bulk rock properties (Bakke & Øren 1997;Øren & Bakke 2002Øren & Bakke , 2003Øren et al 2007;Jin et al 2012;Mousavi & Bryant 2013;Prodanovic et al 2013;van der Land et al 2013;Hosa & Wood 2017) or consider a subset of the diagenetic processes that affect reservoir quality (Abe & Mair 2005;Lander et al 2008a;Marketos & Bolton 2009;Gale et al 2010;Cheung et al 2013;Ankit et al 2015;Lander & Laubach 2015;Wendler et al 2016). Although the promise of models of this class is enormous, considerable work is needed to develop comprehensive modelling approaches that are capable of making accurate pre-drill predictions.…”

Integrated Research as Key to the Development of a Sustainable Geothermal Energy Technology

“…[31,33,34] Wendler et al showed that PFMs were able to reproduceh ydrothermal quartz growth experiments ( Figure 6I). [20] Hence, such models provide new insights into various sealings tructures andc orresponding flow paths.T of ate,P FMs have only been used to simulate pure sealing processes on micro-to millimeter scales.H owever, under reservoir conditions,t here should be an interaction of precipitation and dissolution processes, as shown in core-scale reactive percolation experiments under high pressure-temperature conditions with CO 2 -rich brines. [28] Because reactive transport in fractures dependso na vailable response surfaces,m echanically induced fracture geometries are crucial.…”