Three‐Dimensional Phase‐Field Investigation of Pore Space Cementation and Permeability in Quartz Sandstone

Abstract

The present work investigates the dynamics of quartz precipitation from supersaturated formation fluids in granular media, analogous to sandstones, using a multiphase‐field model. First, we derive a two‐dimensional (2‐D) Wulff shape of quartz from the three‐dimensional (3‐D) geometry and simulate the unitaxial growth of quartz in geological fractures in 2‐D in order to examine the role of misorientation and crystal c to a axis ratios (c/a) in the formation of quartz bridge structures that are extensively observed in nature. Based on this sensitivity analysis and the previously reported experiments, we choose a realistic value of c/a to computationally mimic the 3‐D anisotropic sealing of pore space in sandstone. The simulated microstructures exhibit similarities related to crystal morphologies and remaining pore space with those observed in natural samples. Further, the phase‐field simulations successfully capture the effect of grain size on (I) development of euhedral form and (II) sealing kinetics of cementation, consistent with experiments. Moreover, the initially imposed normal distribution of pore sizes evolves eventually to a lognormal pattern exhibiting a bimodal behavior in the intermediate stages. Furthermore, computational fluid dynamics analysis is performed in order to derive the temporal evolution of permeability in numerically cemented microstructures. The obtained permeability‐porosity relationships are coherent with previous findings. Finally, we highlight the capabilities of the present modeling approach in simulating 3‐D reactive flow during progressive sealing in porous rocks based on innovative postprocessing analyses and advanced visualization techniques.

Quartz Cementation in Polycrystalline Sandstone: Insights From Phase‐Field Simulations

“…We adapt the multiphase-field model of Wendler et al (2016) who simulated the epitaxial growth of quartz veins under the experimental conditions of Okamoto et al (2010) and Okamoto and Sekine (2011). The model equations are recapitulated for two purposes: (I) to enhance the readability and comprehensibility while highlighting the advantages of this model over the previous one (Prajapati et al, 2018b) and (II) to elaborate the methodology of determining the parameter set for temperature and pressure close to reservoir conditions, following the approach proposed by Wendler et al (2016). The Helmholtz free energy of the system is formulated as…”

“…These cements form in optical continuity with the grains and inherit their crystallographic orientations. Natural textures of quartz cement growing anisotropically in porous sandstones composed of monocrystalline quartz grains were successfully modeled by Prajapati et al (2018b). However, depending on the source area, many quartzarenites also contain polycrystalline detrital quartz grains consisting of several subdomains of quartz crystals (or "subgrains").…”

“…In the past decade, the phase-field method has established itself as a viable alternative for simulating mineral growth in 2-D and 3-D (Ankit et al, 2013;Ankit, Urai, et al, 2015;Ankit, Selzer, et al, 2015;Prajapati et al, 2017Prajapati et al, , 2018aPrajapati et al, , 2018bWendler et al, 2011Wendler et al, , 2016. In contrast to the aforementioned front tracking models that were based on the sharp interface approach, the phase-field models describe interfaces as diffuse regions.…”

“…The increasing utility of these models is due to the fact that they do not require explicit tracking of interfaces, making it a robust and computationally efficient methodology in treating a broad range of moving boundary problems (see review articles Chen, 2002;Moelans et al, 2008;Nestler & Choudhury, 2011;Qin & Bhadeshia, 2010). Prajapati et al (2018b) analyzed the impact of cementation on the relationships between different rock properties (i.e., porosity, permeability, grain sizes, and pore size statistics) in grain packs composing of monocrystalline spherical grains. However, the model suffered from three main limitations.…”

“…To account for the abovementioned tendencies, an anisotropy in the growth kinetics is required. Third, a simple interpolation of the inverse mobilities (i.e., ss and sl in Prajapati et al, 2018b) of the solid-solid and solid-liquid interfaces was employed. This interpolation creates an artificial pinning of the triple junctions (shared between the solid-solid-liquid phases) when the inverse mobilities differ by orders of magnitude.…”