An accurate analytical model for squirt flow in anisotropic porous rocks - Part 1: Classical geometry

Seismic wave propagation in porous rocks that are saturated with a liquid exhibits significant dispersion and attenuation due to fluid flow at the pore scale, so-called squirt flow. This phenomenon takes place in compliant flat pores such as microcracks and grain contacts that are connected to stiffer isometric pores. Accurate quantitative description is crucial for inverting rock and fluid properties from seismic attributes such as attenuation. Up to now, many analytical models for squirt flow were proposed based on simplified geometries of the pore space. These models were either not compared with a numerical solution or showed poor accuracy. We present a new analytical model for squirt flow which is validated against a three-dimensional numerical solution for a simple pore geometry that has been classically used to explain squirt flow; that is why we refer to it as classical geometry. The pore space is represented by a flat cylindrical (penny-shaped) pore whose curved edge is fully connected to a toroidal (stiff) pore. Compared with correct numerical solutions, our analytical model provides very accurate predictions for the attenuation and dispersion across the whole frequency range. This includes correct low- and high-frequency limits of the stiffness modulus, the characteristic frequency, and the shape of the dispersion and attenuation curves. In a companion paper (Part 2), we extend our analytical model to more complex pore geometries. We provide as supplementary material Matlab and symbolic Maple routines to reproduce our main results.

A New Anelasticity Model for Wave Propagation in Partially Saturated Rocks

Elastic wave propagation in partially saturated reservoir rocks induces fluid flow in multi-scale pore spaces, leading to wave anelasticity (velocity dispersion and attenuation). The propagation characteristics cannot be described by a single-scale flow-induced dissipation mechanism. To overcome this problem, we combine the White patchy-saturation theory and the squirt flow model to obtain a new anelasticity theory for wave propagation. We consider a tight sandstone Qingyang area, Ordos Basin, and perform ultrasonic measurements at partial saturation and different confining pressures, where the rock properties are obtained at full-gas saturation. The comparison between the experimental data and the theoretical results yields a fairly good agreement, indicating the efficacy of the new theory.

Experimental Assessment of the Transmission Performance of Step Index Polymer Optical Fibers Using a Green Laser Diode

Large-core polymer optical fiber (POF) links have limitations in capacity and reach due to the fibers’ high modal dispersion and attenuation. Most of these links use red laser diodes, even though the attenuation spectrum of poly(methyl methacrylate) (PMMA), the basic polymer used to manufacture these fibers, has a lower minimum in the green region. Therefore, we set out to explore the potential use of green light in transmission systems, comparing the performances of three step-index polymer optical fibers (SI-POFs) with different numerical apertures. We obtained measurements of intensity distribution, frequency response and bit error rate (BER), as functions of fiber length. We have also compared the fibers’ frequency responses with red and green light for a few selected lengths. Our results confirm that SI-POFs attenuate less in response to green light, which can increase their length. This advantage is partially counterbalanced by a slightly higher dispersion that limits the capacity of the high-aperture fibers, particularly at relatively short lengths. Our conclusions are critical to understanding SI-POF behavior and to designing thorough SI-POF models that can aid the design of POF-based links for different scenarios.

Characteristics of elastic wave dispersion and attenuation induced by microcracks in complex anisotropic media

The mechanism of dispersion and attenuation induced by fluid flow among pores and microcracks in rocks is an important research topic in geophysical domain. A generalised frequency-dependent fourth-rank tensor is proposed and derived herein by combining Sayers's discontinuity tensor formula and Gurevich's squirt flow model. Furthermore, a proposed method for establishing a cracked model with cracks embedded in a transversely isotropic (TI) background medium is developed. Based on the new formulation, we investigate the characteristics of dispersion, attenuation and azimuthal anisotropy of three commonly encountered vertical crack distributions, including aligned cracks, monoclinic cracks and cracks with partial random orientations. We validate the developed model by comparing its predictions with those of the classic anisotropic squirt flow model for an aligned crack. The numerical analyses indicate that the azimuth is independent of frequency when the maximum attenuation is observed for all three crack distributions. In a low-frequency range in the case of an anisotropic background, the attenuation of the qP-wave is inversely proportional to velocity, whereas the attenuation of the qSV-wave is proportional to velocity. In addition, the inherent anisotropy of the rock does not significantly affect the dispersion and attenuation owing to squirt flow. Finally, to investigate the applicability of the theory, we model laboratory data of a synthetic porous sandstone with aligned cracks. Overall, the models agree well with laboratory data. The complex characteristics determined through this study may be useful for the seismic characterisation of fractured reservoirs.

An Exact Expression for the Effective Bulk Modulus for Acoustic Wave Propagation in Cylindrical Patchy-Saturation Rocks

Hydrocarbon reservoirs often contain partially gas-saturated rocks that have attracted the attention of exploration geophysicists and geologists for many years. Wave-induced fluid flow (WIFF) is an effective mechanism to quantify seismic wave dispersion and attenuation in partially gas-saturated rocks. In this study, we focus on the local fluid flow induced by variations in fluids in different regions and present a new model that describes seismic wave propagation in partially gas-saturated rocks, namely, the cylindrical patchy-saturation model. Because the seismic wave velocity and attenuation oscillate at high frequencies, it is not ideal for studying dispersion and attenuation caused by WIFF. To avoid the high-frequency oscillation in the cylindrical patchy-saturated model, we use an approximation to the Newman function instead of the full Newman function to calculate the effective bulk modulus. We then calculate the P-wave velocity and attenuation of the proposed model and interpret the lab-measured data. The proposed model is an alternative patchy-saturation model that can explain the problem of high-frequency oscillation and low-frequency attenuation.