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Shale gas reservoirs have a large amount of resources, a wide range of burial, and great development potential. In order to evaluate the elastic properties of the shale, elastic wave velocity and anisotropy measurements of Longmaxi shale samples were carried out in the laboratory. Combined with the results of back scattering scanning electron microscopy (SEM) and digital mineral composition tests, the relationship between the anisotropy and the mineral components of the shale samples is discussed. It is found that the clay and kerogen combination distributed with an inorganic mineral background is the main cause of anisotropy. Then, the elastic properties of the organic-rich shale are analyzed with the anisotropic differential equivalent medium model (DEM). The clay and kerogen combination is established with kerogen as the background medium and clay mineral as the additive phase. The bond transformation is used to rotate the combination so that its directional arrangement is consistent with the real sedimentary situation of the stratum. Then, the clay and kerogen combination is added to the inorganic mineral matrix, with the organic and inorganic pores added to characterize the anisotropy of the shale to the greatest extent. It is found that the error between the wave velocity results calculated from the model and measured in the laboratory is less than 10%, which means the model is reliable. Finally, the effects of the microcracks and aspect ratio, kerogen content, and maturity on the elastic and anisotropic properties of shale rocks are simulated and analyzed with this model. The degree of anisotropy increases with the decrease in the pore aspect ratio and the increase in the microcracks content. The greater the kerogen content and maturity, the greater the anisotropy of rock. This study is of great significance for predicting the “sweet spot” of shale gas and optimizing hydraulic fracturing layers.

Rapid-prototyping plays a critical role in the design of antennas and related planar circuits for wireless communications, especially as we embrace the 5G/6G protocols going forward into the future. While there are a number of software modules commercially available for such rapid prototyping, often they are found to be not as reliable as desired, especially when they are based on approximate equivalent circuit models for various circuit components comprising the antenna system. Consequently, it becomes necessary to resort to the use of more sophisticated simulation techniques, based on full-wave solvers that are numerically rigorous, albeit computer-intensive. Furthermore, optimizing the dimensions of antennas and circuits to enhance the performance of the system is frequently desired, and this often exacerbates the problem since the simulation must be run a large number of times to achieve the performance goal—an optimized design. Consequently, it is highly desirable to develop accurate yet efficient techniques, both in terms of memory requirements and runtimes, to expedite the design process as much as possible. This is especially true when the antenna utilizes metamaterials and metasurfaces for their performance enhancement, as is often the case in modern designs. The purpose of this paper is to present strategies that address the bottlenecks encountered in the generation of Green’s Functions for layered media, especially in the millimeter wave frequency range where the dimensions of the antennas and the platforms upon which they are mounted can be several wavelengths in size. The paper is divided into two parts. Part-I covers the topics of construction of layered medium Green’s Function for millimeter wavelengths; the Equivalent Medium Approach (EMA) which obviates the need to construct Green’s Function for certain geometries; and the T-matrix approach for hybridizing the finite methods with the Method of Moments(MoM). In Part-II of this paper, we go on to discuss three other strategies for performance enhancement of CEM techniques: the Characteristic Basis Function Method (CBFM); mesh truncation for finite methods by using a new form of the Perfectly Matched Layer (PML); and GPU acceleration of MoM as well as FDTD (Finite Difference Time Domain) algorithms. The common theme between the two parts is the “performance enhancement” of CEM (Computational Electromagnetics) techniques, which provides the synergistic link between the two parts.

Seismic anisotropy can help to extract azimuthal information for predicting crack alignment, but the accurate evaluation of cracked reservoir requires knowledge of degree of crack development, which is achieved through determining the crack density from seismic or VSP data. In this research we study the dependence of seismic anisotropy on crack density, using synthetic rocks with controlled crack geometries. A set of four synthetic rocks containing different crack densities is used in laboratory measurements. The crack thickness is 0.06 mm and the crack diameter is 3 mm in all the cracked rocks, while the crack densities are 0.00, 0.0243, 0.0486, and 0.0729. P and S wave velocities are measured by an ultrasonic investigation system at 0.5 MHz while the rocks are saturated with water. The measurements show the impact of crack density on the P and S wave velocities. Our results are compared to the theoretical prediction of Chapman (J App Geophys 54:191–202, 2003 ) and Hudson (Geophys J R Astron Soc 64:133–150, 1981 ). The comparison shows that measured velocities and theoretical results are in good quantitative agreement in all three cracked rocks, although Chapman’s model fits the experimental results better. The measured anisotropy of the P and S wave in the four synthetic rocks shows that seismic anisotropy is directly proportional to increasing crack density, as predicted by several theoretical models. The laboratory measurements indicate that it would be effective to use seismic anisotropy to determine the crack density and estimate the intensity of crack density in seismology and seismic exploration.

The primary resonance responses of high-performance nanocomposite materials used in spacecraft components in complex electromagnetic field environments were investigated. Simultaneously considering the interfacial effect, agglomeration effect, and percolation threshold, a theoretical model that can predict Young’s modulus and electrical conductivity of graphene nanocomposites is developed by the effective medium theory (EMT), shear lag theory, and the Mori-Tanaka method. The magnetoelastic vibration equation for an axially moving graphene nanocomposite current-carrying beam was derived via the Hamilton principle. The amplitude-frequency response equations were obtained for different external loading conditions. The study reveals the significant role of graphene concentration, external force, and magnetic field on the system’s primary resonance, highlighting how electromagnetic forces play a critical role similar to external excitation forces. It is shown that the increase in graphene content could lead the system from period-doubling motion into chaotic behavior. Moreover, an enhanced magnetic field strength may lower the minimum graphene concentration needed for period-doubling motion. This work provides new insights into controlling nonlinear vibrations of such systems through applied electromagnetic fields, emphasizing the importance of designing multifunctional nanocomposites in multi-physics coupled environments. The concentration of graphene filler would significantly affect the primary resonance and bifurcation and chaos behaviors of the system.

Taking the carbonate of the Majiagou Formation in the Ordos Basin as an example, this paper introduces a method for predicting the S‐wave velocity of carbonate based on rock physics modeling. By analyzing the samples in the study area, we can find that the carbonate reservoirs in the study area have the following characteristics: (1) The lithology of the Majiagou Formation in the Ordos Basin is relatively complex, mainly composed of dolomite, lime dolomite, dolomitic limestone, gypsum, and gypsum‐bearing dolomite. The pore types include intergranular pores formed by dolomitization, intergranular dissolution pores formed by dissolution, and fractures. (2) Due to the diverse types and complex distribution of rock‐forming minerals, there are always some rock samples whose matrix modulus is beyond the upper or lower limits. Those were calculated using the Voigt–Reuss–Hill (VRH) average method. (3) The pore structure of carbonate is very complex due to diagenesis. Based on the influence of pore shape characteristics on rock elastic parameters, pore shapes are divided into three types using the pore aspect ratio. Among them, the aspect ratio of intergranular pores is the largest, while that of the fracture pores is the smallest, and the aspect ratio of intergranular dissolved pores falls between the two. Therefore, the accuracy of predicting S‐wave velocity in this area based on traditional rock physics modeling methods is low. In this paper, we will introduce a new model that is aimed at improving the traditional rock physics model. The first improvement is based on a variable matrix modulus, which can be used for matrix modeling to mitigate the influence of uneven mineral distribution. The second enhancement involves quantitatively characterizing the impact of different pore aspect ratios on the S‐wave velocity of carbonate rocks, using a porous differential equivalent medium (DEM) model.

The detection and extraction of weak signals are crucial in various engineering and scientific fields, yet current acoustic sensing technologies are restricted by fundamental pressure detection methods. This paper proposes gradient-equivalent medium-coupled metamaterials (GEMCMs) utilizing strong wave compression and an equivalent medium mechanism to capture weak signals in complex environments and enhance target acoustic signals. Overcoming shape and impedance mismatch limitations of traditional gradient structures, GEMCMs significantly improve control performance. Experimental and numerical simulations indicate that GEMCMs can effectively enhance specific frequency components in acoustic signals, outperforming traditional gradient structures. This enhancement of specific frequency components relies on the resonance effect of the unit cell structure. By introducing acoustic resonance within a spatially wound acoustic channel, a significant amplification of weak acoustic signals is achieved. This provides a new research direction for acoustic wave manipulation and enhancement, and holds significant importance in fields such as mechanical fault diagnosis and medical diagnostics.

Acoustic sensing systems play a critical role in identifying and determining weak sound sources in various fields. In many fault warning and environmental monitoring processes, sound-based sensing techniques are highly valued for their information-rich and non-contact advantages. However, noise signals from the environment reduce the signal-to-noise ratio (SNR) of conventional acoustic sensing systems. Therefore, we proposed novel nonlinear gradient-coiling metamaterials (NGCMs) to sense weak effective signals from complex environments using the strong wave compression effect coupled with the equivalent medium mechanism. Theoretical derivations and finite element simulations of NGCMs were executed to verify the properties of the designed metamaterials. Compared with nonlinear gradient acoustic metamaterials (Nonlinear-GAMs) without coiling structures, NGCMs exhibit far superior performance in terms of acoustic enhancement, and the structures capture lower frequencies and possess a wider angle acoustic response. Additionally, experiments were constructed and conducted using set Gaussian pulse and harmonic acoustic signals as emission sources to simulate real application scenarios. It is unanimously shown that NGCMs have unique advantages and broad application prospects in the application of weak acoustic signal sensing, enhancement and localization.

Natural gas hydrate saturation (NGHS) in reservoirs is one of the critical parameters for evaluating natural gas hydrate resource reserves. Current widely-accepted evaluation methods developed for evaluating conventional natural gas saturation in reservoirs, to some extents, are not sufficient enough to obtain accurate predicted results. In light of the equivalent medium theory, the natural gas hydrate is regarded as the fluid (Mode A) when NGHS is relatively low, while it is regarded as the rock matrix (Mode B) when NGHS is high. Two mathematical model are then developed for evaluating NGHS at Mode A and B. Experimental verification shows that R 2 of the predicted results based upon the proposed model is 0.968, and the average absolute relative error percentage is 8.90%. The error of the predicted results gradually decreases with increasing NGHS, whereas increases with increasing confining pressure. In addition, the proposed model has been applied to the 142.9–147.7 m well section of Well DK-1 in the permafrost region, Qilian Mountains. The results show that the error of the predicted results is less than 13.92%, with its average error being 10.51%. The predicted value gradually increases with its error decreasing as the depth continues to increase, which is consistent with the change behavior of measured data. NGHS evaluation method proposed in this paper fully considers the occurrence form of natural gas hydrate in reservoirs. The model parameters are easy to determine and the predicted results are reliable. Highlights A new evaluation method of natural gas hydrate saturation is developed The prediction error shows that R 2  = 0.968 and AAREP = 8.90% compared with test data The predicted results of field application match the measured values well

The study of fractures in the subsurface is very important in unconventional reservoirs since they are the main conduits for hydrocarbon flow. For this reason, a variety of equivalent medium theories have been proposed for the estimation of fracture and fluid properties within reservoir rocks. Recently, the Galvin model has been put forward to model the frequency-dependent elastic moduli in fractured porous rocks and has been widely used to research seismic wave propagation in fractured rocks. We experimentally investigated the feasibility of applying the Galvin model in fractured tight stones. For this proposal, three artificial fractured tight sandstone samples with the same background porosity (11.7% ± 1.2%) but different fracture densities of 0.00, 0.0312, and 0.0624 were manufactured. The fracture thickness was 0.06 mm and the fracture diameter was 3 mm in all the fractured samples. Ultrasonic P- and S-wave velocities were measured at 0.5 MHz in a laboratory setting in dry and water-saturated conditions in directions at 0°, 45°, and 90° to the fracture normal. The results were compared with theoretical predictions of the Galvin model. The comparison showed that model predictions significantly underestimated P- and S- wave velocities as well as P-wave anisotropy in water-saturated conditions, but overestimated P-wave anisotropy in dry conditions. By analyzing the differences between the measured results and theoretical predictions, we modified the Galvin model by adding the squirt flow mechanism to it and used the Thomsen model to obtain the elastic moduli in high- and low-frequency limits. The modified model predictions showed good fits with the measured results. To the best of our knowledge, this is the first study to validate and calibrate the frequency-dependent equivalent medium theories in tight fractured rocks experimentally.

Metasurface-based antennas have received considerable recent attention in recent years because they are not only useful for designing new antennas, but for improving the performance of legacy designs as well. However, systematically designing these antennas is challenging because the antennas are usually multiscale in nature and they typically require a long time when simulated by using commercial solvers. In this work, we present a new approach for analyzing antennas that utilize Metasurfaces (MTSs) and Metamaterial (MTMs). The proposed method departs from the widely used technique based on an anisotropic impedance representation of the surface and relies on an equivalent medium approach instead. The principal advantage of the proposed approach is that such an equivalent medium representation can be conveniently inserted directly in commercial EM solvers, circumventing the need to develop special numerical EM simulation codes to handle metasurfaces. Several illustrative examples are presented in the paper to demonstrate the efficacy of the present approach when simulating MTS- and MTMbased antennas.