Narrow Results

Relative permeability (RP) plays a critical role in fluid flow and transport in fracture systems, with considerable advances in theoretical and computational methods over the last few decades. Nevertheless, there is no standard procedure for measuring RP in fractures, and the essential controls on RP in rough fractures are not yet definitive. In this study, we developed a theoretical model to investigate the RP in inclined rough fractures under stress dependence based on fractal theory. The topography of the rough fracture surfaces is well addressed by fractal theory and lubrication theory, and thin bending theory is used to characterize permeability evolution characteristics of fractures under stress conditions. The model accounts for multiple key factors, including the microstructure of the rough fractures (e.g. the fractal dimension, the area ratio, the length ratio, and the maximum and minimum base radii), rock lithology (e.g. elastic modulus and Poisson’s ratio), gravity and effective stress. The predicted results agree well with the available experimental data. It is inferred that the effect of gravity on RP decreases as pressure gradient increases. In general, the theoretical fractal model reveals the coupled flow-deformation mechanisms in fractures, and tends to improve the efficacy of reservoir development strategies. With this new analytical solution, it can help to reduce the uncertainty in flow through fractures and obtain data with high accuracy.

In this paper, we discussed the longitudinal harmonic waves reflection from a solid elastic half-space with electromagnetic and gravity fields influence, considering a fractional order via fractional exponential function method. The clarifications are required for the reflection amplitudes ratios (i.e. the ratios between the reflected waves amplitude and the incident waves amplitude). The results obtained were calculated analytically and displayed by graphs to show the physical meaning of the phenomenon. A comparison has been made between the fractional and integer derivatives. The results of this paper demonstrate the rigor and effectiveness of the considered fractional technique.

Maximum residue limits (MRLs) on pesticides and veterinary drugs in plant and animal products are established to promote food safety and animal and plant health. In practice, however, they are often accused of creating unnecessary trade barriers. The controversy is more prominent when a given MRL is stricter than the corresponding international standard developed by Codex. Using the score indices constructed by Li and Beghin (2012), we empirically assess the implications of stringency in MRLs in plant and animal products, relative to Codex levels, for Canadian and US trade performance. We find little evidence that US imports are influenced by domestic stringency or those imposed by its trading partners. However, US exports are negatively affected by stringency in destination markets. Canada’s stringent MRLs facilitate its exports of plant and animal products and these exports do not seem to be impeded by MRL stringency in destination markets. Canada’s imports do not appear to be systematically influenced by either its own or its trading partners’ MRL stringency. We draw implications for the potential harmonization of MRLs between the two countries.