Digital rock physics in four dimensions: simulating cementation and its effect on seismic velocity

Porosity exerts a strong control on the mechanical and hydraulic properties of rocks, but can often only be imaged indirectly from the surface using geophysical measurements, such as seismic velocity. Understanding and quantifying the relationship between seismic velocity and porosity is therefore a fundamental goal of many rock physics models. Simulating the geological processes that control porosity to generate digital rocks, and numerically modelling wave propagation to estimate their elastic properties, allows for flexible and rapid calibration of velocity-porosity trends. Here, the initial deposition of two digital carbonate sediments are simulated: grainstone (near spherical grains) and coquina (anisotropic shell fragments). The gradual precipitation of cement is then simulated, resulting in a suite of 3-D volumes of varying porosity with otherwise constant and known mineral and grain phases. These models are then used as input to a 3-D acoustic staggered-grid finite difference simulation of wavefield propagation, from which we estimate bulk seismic velocity and calculate the estimated bulk modulus. The resulting bulk modulus varies systematically with respect to porosity within the physical limits imposed by the Hashin Shtrikman bounds. The samples exhibit anisotropy in the measured velocity consistent with structural anisotropy due to the settling of elongate grains under gravity. We use the resulting bulk velocity-porosity trends to test competing rock physics models, including one that accounts for varying effective pore-aspect ratio with porosity. The results validate the hypothesis that there is a power-law relationship between effective pore aspect ratio and porosity. This relationship is consistent with similar results obtained from a suite of natural carbonate grainstones examined in the laboratory. The results show the optimal rock physics model to be relatively insensitive to the degree of anisotropy in the fabric of the starting material, and may now be used with more confidence to link observed changes in effective pore aspect ratio to changes in porosity due to a range of geological processes, for example fracturing, dissolution and compaction, where other process-based models are available.