Page 54 - Machine Learning for Subsurface Characterization

40 Machine learning for subsurface characterization

1 Introduction
Fractures influence the transport and mechanical properties of materials. Fracture
characterization is essential for producing from unconventional hydrocarbon
reservoirs, deep mineral resources, and subsurface geothermal energy
resources. Fractures are mechanical discontinuities that influence the bulk and
shear moduli. Consequently, compressional and shear wave propagations can
be used for fracture characterization. When the dimensions of fractures are
orders of magnitude smaller than the wavelength, an effective medium
approach is valid, wherein the elastic constants can be expressed as a function
of the fracture density/intensity [1, 2, 3]. Requirements for the validity of
effective medium approach are not met in laboratory-based fracture
characterization studies because the fracture dimensions are comparable with
wavelength of ultrasonic waves used for various laboratory measurements.
Significant gaps still exist in fracture characterization using compressional and
shear wave propagations due to heterogeneity of mechanical properties and
complexity of fracture geometry in a fractured material.
Experiments have shown that the displacement discontinuity model can
capture many of the frequency-dependent and saturation-dependent effects of
fracture on a sonic wave propagating through a fractured material. The
displacement discontinuity theory predicts that amplitude variation at a given
frequency depends on the fracture stiffness [4, 5, 6], which is defined as the
ratio between the stress and the magnitude of displacement discontinuity
produced by the fracture. A fractured zone in a material will have a lower
fracture stiffness compared with an intact zone. A schematic representation
of the displacement discontinuity model and the effect of fracture stiffness
on the amplitude of a transmitted sonic wave is shown in Fig. 2.1. A fracture
is modeled as a zero-width zone between two elastic half spaces, having

FIG. 2.1 Schematic representation of the displacement discontinuity model, where a fracture is
represented as zero-width boundary between two elastic media and the compressional and shear
stiffness of the fracture depends on the extent of fracture-induced geomechanical alteration.