RESUMO
Many effective medium theories are designed to describe the macroscopic properties of a medium (the rock, or reservoir in this case) in terms of the properties of its constituents (the background matrix of the rock and the inclusions, for our scenario). A very well known effective medium theory is the Eshelby-Cheng model, which was studied by us in previous work, being tested for the case where the background medium was weakly-anisotropic and porous. The analysis was done testing elastic velocities and Thomsen parameters - as a function of crack density for fixed values of aspect ratio - predicted by the model with data acquired from synthetic rock samples. In this work, we aim to complete the analysis of the Eshelby-Cheng model capabilities when applied to rocks with porous and vertical transversely isotropic (VTI) backgrounds, testing the model for the elastic velocities as functions of aspect ratio - for fixed values of crack density - against experimental data. The data used to test the model were obtained from 17 synthetic rock samples, one uncracked and 16 cracked, the latter divided into four groups of four samples each, each group with cracks having the same aspect ratio, but with the samples having different crack densities. In these samples, ultrasonic pulse transmission measurements were performed to obtain the experimental velocities used to test the model. As was not possible to acquire data for velocity as a function of aspect ratio for fixed values of crack density, we performed interpolations of the experimental data to estimate these velocities. Eshelby-Cheng model effective velocities and Thomsen parameters were calculated using three formulations proposed for the crack porosity: one proposed by Thomsen, the second one proposed in our previous work (which depends only on the crack density) and the third one proposed in this work (which depends on the crack porosity and the aspect ratio, just like Thomsen's proposal). The comparisons between elastic velocities and Thomsen parameters - as function of crack aspect ratio, for fixed values of crack density - predicted by the model and estimated from the data via interpolation showed that the third formulation produced better fittings (lower root-mean-square errors) between model and experimental data for all ranges of aspect ratio and crack density.
RESUMO
The study of fractures in subsurface is very important since they are, in some cases, the main conduits for hydrocarbon flow in a reservoir. There are many ways to study the behavior of seismic waves in different fracturing conditions, including the use of physical modeling. This method allows, among other approaches, the analysis of the behavior of seismic wave properties in complex fractured media, such as media with orthorhombic symmetry. In this work we performed ultrasonic measurements on fractured physical models with orthorhombic symmetry from which we analyzed the behavior of elastic velocities and anisotropy parameters for different number of fractures. The presented results show the efficiency of the construction methodology used in the study by presenting P- and S- wave velocity values consistent with the theory for an orthorhombic medium. It was observed that for the direction perpendicular to the fracture system the values of P and S-wave velocities were the smallest for each model, and that the velocities decreased as the number of fractures increased in all models. Furthermore, most of the ∊ and γ values show a decreasing behavior as a function of the decreasing number of cracks, being the trend curves of ∊ linear and most of the trend curves of γ quadratic. Additionally, all the ∊ parameters presented a high correlation with the γ parameters for a small number of fractures, lower than 5.