Laboratory physical models play an important role in understanding rock properties and wave propagation, both theoretically and at the field scale. In some cases, 3D-printing technology can be adopted to construct complex rock models faster, more inexpensively, and with more specific features than previous model-building techniques. In this study, we use 3D-printed rock models to assist in understanding the effects of various fluids (air, water, engine oil, crude oil, and glycerol) on the models’ elastic properties. We first used a 3D-printed, 1-in. cube-shaped layered model. This model was created with a 6% primary porosity and a bulk density of 0.98 g/cc with VTI anisotropy. We next employed a similar cube but with horizontal inclusions embedded in the layered background, which contributed to its total 24% porosity (including primary porosity). For air to liquid saturation, P-velocities increased for all liquids in both models, with the highest increase being with glycerol (57%) and an approximately 45% increase for other fluids in the inclusion model. For the inclusion model (dry and saturated), we observed a greater difference between two orthogonally polarized S-wave velocities (Vs1 and Vs2) than between two P-wave velocities (VP0 and VP90). We attribute this to the S2-wave (polarized normal to both the layering and the plane of horizontal inclusions), which appears more sensitive to horizontal inclusions than the P-wave. For the inclusion model, Thomsen’s P-wave anisotropic parameter (ɛ) decreased from 26% for the air case to 4% for the water-saturated cube and to 1% for glycerol saturation. The small difference between the bulk modulus of the frame and the pore fluid significantly reduces the velocity anisotropy of the medium, making it almost isotropic. We compared our experimental results with theory and found that predictions using Schoenberg’s linear slip theory combined with Gassmann’s anisotropic equation were closer to actual measurements than Hudson’s isotropic calculations. This work provides insights into the usefulness of 3D-printed models to understand elastic rock properties and wave propagation under various fluid saturations.
A viscoelastic Eshelby inclusion model and analysis of the Cell-in-Gel system
