Dispersion analysis of crack-waves in an artificial subsurface fracture using two crack models

The authors investigated crack-wave dispersions in an artificial subsurface fracture both experimentally and numerically using a wavelet analysis and two crack models. Crack-waves are seismic modes that propagate along a fracture. The dispersion characteristics of crack-waves depend on the geometry and physical properties of a fracture. The authors measured crack-waves at an artificial subsurface fracture in Higashi-Hachimantai Hot Dry Rock model field, Japan. This subsurface fracture is at a depth of about 370 m. During a measurement, they injected water into the fracture and changed the interface conditions of the fracture. A wavelet analysis provided the dispersion of the arrival times of crack-waves. The crack-waves showed positive velocity dispersion; i.e., low frequency components arrived later. As wellhead pressure increased due to water injection, the dispersion characteristics changed. A low-velocity-layer (LVL) model and a crack-stiffness model were examined to explain crack-wave dispersion. In the LVL model, rock layers with a low velocity surround a fluid layer. There is no contact between the LVLs. On the other hand, the crack-stiffness model considers crack stiffness due to contact between asperities on fracture surfaces. The arrival-time curves calculated by the crack-stiffness model showed a good fit to the measured values. As wellhead pressure increased, crack stiffness decreased and thickness of a fluid layer increased. In contrast, the LVL model did not adequately duplicate the measured dat

Machine learning for the subsurface characterization at core, well, and reservoir scales

The development of machine learning techniques and the digitization of the subsurface geophysical/petrophysical measurements provides a new opportunity for the industries focusing on exploration and extraction of subsurface earth resources, such as oil, gas, coal, geothermal energy, mining, and sequestration. With more data and more computation power, the traditional methods for subsurface characterization and engineering that are adopted by these industries can be automized and improved. New phenomenon can be discovered, and new understandings may be acquired from the analysis of big data. The studies conducted in this dissertation explore the possibility of applying machine learning to improve the characterization of geological materials and geomaterials. Accurate characterization of subsurface hydrocarbon reservoirs is essential for economical oil and gas reservoir development. The characterization of reservoir formation requires the integration interpretation of data from different sources. Large-scale seismic measurements, intermediate-scale well logging measurements, and small-scale core sample measurements help engineers understand the characteristics of the hydrocarbon reservoirs. Seismic data acquisition is expensive and core samples are sparse and have limited volume. Consequently, well log acquisition provides essential information that improves seismic analysis and core analysis. However, the well logging data may be missing due to financial or operational challenges or may be contaminated due to complex downhole environment. At the near-wellbore scale, I solve the data constraint problem in the reservoir characterization by applying machine learning models to generate synthetic sonic traveltime and NMR logs that are crucial for geomechanical and pore-scale characterization, respectively. At the core scale, I solve the problems in fracture characterization by processing the multipoint sonic wave propagation measurements using machine learning to characterize the dispersion, orientation, and distribution of cracks embedded in material. At reservoir scale, I utilize reinforcement learning models to achieve automatic history matching by using a fast-marching-based reservoir simulator to estimate reservoir permeability that controls pressure transient response of the well. The application of machine learning provides new insights into traditional subsurface characterization techniques. First, by applying shallow and deep machine learning models, sonic logs and NMR T2 logs can be acquired from other easy-to-acquire well logs with high accuracy. Second, the development of the sonic wave propagation simulator enables the characterization of crack-bearing materials with the simple wavefront arrival times. Third, the combination of reinforcement learning algorithms and encapsulated reservoir simulation provides a possible solution for automatic history matching

Seismic characterization of naturally fractured reservoirs

Many hydrocarbon reservoirs have sufficient porosity but low permeability (for example, tight gas sands and coal beds). However, such reservoirs are often naturally fractured. The fracture patterns in these reservoirs can control flow and transport properties, and therefore, play an important role in drilling production wells. On the scale of seismic wavelengths, closely spaced parallel fractures behave like an anisotropic media, which precludes the response of individual fractures in the seismic data. There are a number of fracture parameters which are needed to fully characterize a fractured reservoir. However, seismic data may reveal only certain fracture parameters and those are fracture orientation, crack density and fracture infill. Most of the widely used fracture characterization methods such as Swave splitting analysis or amplitude vs. offset and azimuth (AVOA) analysis fail to render desired results in laterally varying media. I have conducted a systematic study of the response of fractured reservoirs with laterally varying elastic and fracture properties, and I have developed a scheme to invert for the fracture parameters. I have implemented a 3D finite-difference method to generate multicomponent synthetic seismic data in general anisotropic media. I applied the finite-difference algorithm in both Standard and Rotated Staggered grids. Standard Staggered grid is used for media having symmetry up to orthorhombic (isotropic, transversely isotropic, and orthorhombic), whereas Rotated Staggered grid is implemented for monoclinic and triclinic media. I have also developed an efficient and accurate ray-bending algorithm to compute seismic traveltimes in 3D anisotropic media. AVOA analysis is equivalent to the first-order Born approximation. However, AVOA analysis can be applied only in a laterally uniform medium, whereas the Born-approximation does not pose any restriction on the subsurface structure. I have developed an inversion scheme based on a ray-Born approximation to invert for the fracture parameters. Best results are achieved when both vertical and horizontal components of the seismic data are inverted simultaneously. I have also developed an efficient positivity constraint which forbids the inverted fracture parameters to be negative in value. I have implemented the inversion scheme in the frequency domain and I show, using various numerical examples, that all frequency samples up to the Nyquist are not required to achieve desired inversion results.Geological Science

Simulating Shear Wave Propagation in Two-Dimensional Fractured Heterogeneous Media by Coupling Boundary Element and Finite Difference Methods

A hybrid method to model the shear wave (SH) scattering from 2D fractures embedded in a heterogeneous medium is developed by coupling Boundary Element Method (BEM) and Finite Different Method (FDM) in the frequency domain. FDM is used to propagate an SH wave from a source through heterogeneities to localized homogeneous domains where fractures are embedded within artificial boundaries. According to Huygens’ Principle, the boundary points can be regarded as “secondary” point sources and their values are determined by FDM. Given the incident fields from these point sources, BEM is applied to model scatterings from fractures and propagate them back to the artificial boundaries. FDM then takes the boundaries as secondary sources and continues propagating the scattered field into the heterogeneous medium. The hybrid method utilizes both the advantage of BEM and FDM. A numerical iterative scheme is also presented to account for the multiple scattering between different sets of fractures. The results calculated from this hybrid method with pure BEM method are first compared to show the accuracy of the hybrid approach and the iterative scheme. This method is then applied to calculate the wave scattered from fractures embedded in complex media