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

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.