The study of elastic properties of fractured/cracked rocks has been an important subject of interest in seismology and geophysical exploration. Downhole logging provides a direct measurement of fractured rock properties in terms of elastic wave velocities and anisotropy. Most existing studies only provide qualitative descriptions of fracture properties as evidenced from the acquired measurements. To better utilize downhole measurements, this study provides a comprehensive theoretical analysis and develops an inversion technique to characterize fracture properties. Theoretical results for cracked rocks show that crack density, crack alignment direction, and crack filling materials are the three main fracture parameters that strongly affect the elastic wave properties of fractured rocks. Furthermore, a detailed analysis of the crack effects on elastic properties shows that the measured elastic moduli can be used to evaluate crack parameters of cracked rocks. We assume that cracks with any orientational distribution can be divided into two parts: horizontal and vertical. Based on the theoretical analysis, we develop an inversion method to estimate fracture parameters from well logs acquired in a vertical borehole. We assume a rock physics model for rocks that adds effective horizontal and vertical cracks that are filled with liquid in an isotropic background, the elastic and fluid properties of which are inverted from the measured logs. The inversion method enables the quantification of the directional crack density and crack-filling material when applied to field logging measurements acquired in fractured formations. Theoretically predicted fracture properties are validated with FMS (formation micro-resistivity scan) logging data and are consistent with interpretation results.

Analysis of the flow loss is important in the turbomachinery, the current analysis methods based on the cumulative loss such as the total pressure loss coefficient and the adiabatic efficiency, and the local loss method reflect the loss, can’ t quickly reflect the physical principles that leads the loss and its’ development. To solve this problem, the paper based on the first and second laws of thermodynamics, a local losses model about the compressor internal flow was estimated using the entropy gradient, give a dimensionless loss function parameter I , and was verified in a three-dimensional numerical simulation about Rotor67. The numerical results show that: the model can quickly capture the magnitude and location of loss, it also can reflect the loss source, when the dimensionless parameter , the area is considered as an high loss area, the local loss is expressed as I. If the parameter near the wall for negative value indicates that reflux occurred.