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Modelling the dispersion and attenuation of seismic waves in partially saturated rocks is important for quantitative interpretation of seismic data. To observe the partial saturation effects on modulus and attenuation, three sandstone samples with different porosities were used in the laboratory experiment. The samples were measured by ultrasonic testing system under different water saturation using drainage process. The experimental results show that the bulk modulus more rapidly increased at higher saturations (>80 per cent), and attenuation peaks could be observed. Then we develop a new partial saturation model based on Chapman's theory and poroelastic theory. The new model is consistent with the Gassmann equation when the water saturation is 0 or 100 per cent. By analysing the characteristic frequency, the new model can be concluded in the form of a standard linear solid model. A comparison of the new model with the White model and the measured data is conducted. The results show that the model performed well at predicting the effective bulk modulus and attenuation of the rock with different water saturation. Finally, we discussed the impact of frequency, fluids and pore structures on the new model. The results reveal that the new model will be helpful in discussing partial saturation in rocks. [ABSTRACT FROM AUTHOR]

Frequency-dependent anisotropy can be used for detection and evaluation of fractured reservoirs. In this study, three numerical models of fractured reservoirs are designed to study the frequency dependence of amplitude variation with azimuth (AVAZ). Here, two factors, which can make the AVAZ responses frequency dependent, are taken into consideration, the fluid flow and the tuning effect. Model I is used for the analysis of frequency-dependent AVAZ induced only by the fluid flow. Model II is used to study frequency-dependent AVAZ induced only by the tuning effect. For Model III, these two factors are in the presence at the same time. In this study, the fluid flow is simulated by Chapman's multi-scale rock physics model, and the azimuthal seismic gathers are generated by propagating matrix method. Spectral decomposition is implemented based on the smoothed pseudo Wigner-Ville distribution, so that the frequency dependence for the AVAZ gathers can be discussed. It is demonstrated that both the fluid flow and the tuning effect can cause significant frequency-dependent AVAZ, and the frequency-dependent AVAZ is helpful for fluid identification and anisotropic thin bed detection. Besides, for both factors, the incident angle can influence the frequency-dependent AVAZ responses, accordingly azimuthal seismic gathers with large incident angles are necessary for field data application. [ABSTRACT FROM AUTHOR]

Fractures usually spread over various scales and strongly influence velocity and anisotropy. We investigate elastic velocity and anisotropy in rocks with fractures of different sizes. Based on synthetic rocks with controlled fracture geometries, we create a set of rocks with fracture diameter of 2, 3 and 4 mm and the fracture thickness is 0.06 mm. P‐ and S‐wave velocities are measured at 0.1 MHz, while the rocks are saturated with water and air. For a fixed measurement frequency (0.1 MHz), velocities are higher in rocks with larger fractures, while anisotropy is higher in rocks with smaller fractures, even for the same fracture density. These phenomena are associated with the wave‐induced fluid flow process. Some novel effective medium theories are adopted to calibrate with the laboratory data and analyse the anisotropy affected by the fluid flow mechanism and fracture size. The results of our study demonstrate the significant effects of fracture scale on wave responses by effective medium theories in different ways. We suggest that these scale effects should be of considerable concern in some disciplines (e.g. shear wave splitting in earth's crust and hydraulic fracture monitoring with microseismic data). Considering the scale effects of fractures, the accuracy during these investigations would be improved. [ABSTRACT FROM AUTHOR]

Study of the Krauklis wave in fractured media reveals the potential for characterizing fracture geometry. In this paper, a finite element scheme is proposed to simulate the Krauklis wave in fractures with different geometries. The influence of fracture geometry on the propagation properties of the Krauklis waves is evaluated. Here, fracture geometry refers to the fracture shape, width, and length. First, a series of numerical models containing a single water-filled fracture is set up, in which the fracture shape can be an ellipse or rectangle, its width varies from 5 to 10 mm, and its length varies from 2 to 3 m. The proposed finite element scheme is applied to simulate Krauklis waves. From these simulation results, the Krauklis wave signals inside the fractures are extracted, and a velocity estimation method is developed and implemented to estimate the average velocity within the finite length fractures. For comparison, the theoretical velocity is solved from a dispersion equation, in which the fracture is assumed to be an infinite thin fluid layer. It is shown that the rectangular fractures generate stronger amplitude and higher velocity waves than the elliptical ones. The amplitude varies along the fracture and can be significantly affected by the fracture geometry. Furthermore, the velocity increases with the fracture width, whereas the fracture length does not affect the velocity for both elliptical and rectangular fractures. These effects indicate that Kraulklis waves are rich in information about fracture geometry, and this is valuable when applied to the quantitative characterization of fractures. [ABSTRACT FROM AUTHOR]

The scale of the fractures can vary, making the seismic velocity and anisotropy substantially scale dependent. Two mechanisms of the scale-dependent phenomenon may be considered: scattering and wave-induced fluid flow. In this study, we measure the scale-dependent velocity and anisotropy effects through laboratory experiments on porous and non-porous artificial rocks containing aligned fractures. This allows us to isolate the effects of these two mechanisms for the first time, yielding some insights into the scale-dependent phenomenon. For short-wavelength waves, scattering dominates with less wave-induced fluid flow effects. For intermediate- and long-wavelength waves, the P-wave is strongly scale dependent mainly due to wave-induced fluid flow mechanism, and the slow shear-wave is also strongly scale dependent but due to both scattering and wave-induced fluid flow. However, the fast shear-wave is almost scale independent. Moreover, a multi-scale equivalent medium theory can model the P-wave propagation accurately. [ABSTRACT FROM AUTHOR]

Fractures are widely distributed within the Earth's crust and have a substantial influence on wave propagation. Although many studies have been conducted on fracture characterization based on seismic anisotropic attributes, natural horizontal fractures and hydraulic fracture networks have yet to be characterized. Here, we investigate the influence of the fracture orientation and saturation on the Vp/Vs ratio via laboratory observations and theoretical modeling. Then, we discuss the feasibility of using the Vp/Vs ratio to predict natural horizontal fractures and evaluate hydraulic fracture networks. Our study demonstrates that an abnormally low Vp/Vs ratio, together with a lack of shear wave splitting, could be used to predict horizontal fractures. Fracture network development that results from hydraulic fracturing stimulation is associated with a much higher Vp/Vs ratio and no shear wave splitting; these two characteristics could be used to estimate fracture development and evaluate hydraulic fracturing stimulation. [ABSTRACT FROM AUTHOR]

Rock physics experimental research on fractured media always uses synthetic samples with fractures, but most previous work has used samples of very different material and structure from natural rocks. This study has used a new construction method to build samples with controlled fractures, which have a more realistic mineral compensation and pore structure, similar to natural rocks. A set of samples with different fracture densities was built, and the P and S wave velocities were measured with 0.5 MHz transducers. The measured data were compared with Hudson model predicted results in order to calibrate the theoretical model. P and S wave anisotropies were compared and results demonstrate the accuracy of theoretical prediction of P and S wave velocities and anisotropies influenced by fracture density and fluids. Shear wave splitting shows a strong relationship to fracture density, and the SWS (%) is with around 100 times fracture density. [ABSTRACT FROM AUTHOR]

Clays play important roles in velocity anisotropy. Unlike brittle minerals, e.g., quartz, ductile clays are commonly more easily affected by mechanical compaction. Hence, clays tend to have a platy structure that might introduce significant velocity anisotropy. Cracks developed in clay-rich shales also have substantial influences on the shale elastic anisotropy and hydraulic stimulation. However, crack developments are sometimes unknown, and the effects of clays and cracks are ambiguous due to the complexity of shale properties. In this study, we construct artificial clay-rich shale samples which contain 40% clays by weight (kaolinite, smectite, and illite, respectively). The artificial shale samples are cored into shale-90 samples (along the bedding-parallel direction) and shale-0 samples (along the bedding-normal direction), and the P- wave and S- wave velocities are measured as the axis pressure (P a) increases from 15 MPa to 50 MPa, while the confining pressure (P c) remains at 15 MPa. We evaluate the slopes of the fitting line of velocity versus pressure, and estimate the crack density. We analyze the velocity anisotropy effect from clays and cracks based on laboratory experiments. Clays with an apparent platy grain structure (e.g., illite) introduce higher anisotropy, indicating that velocity anisotropy is dependent on the clay lamination structure. The comparison suggests that the mineralogy effects are the dominant factors in the anisotropy of clay-rich artificial shale samples, and the microcrack effects further enhance the velocity anisotropy. • The velocity anisotropy is strongly affected by the platy grain shape of clay minerals. • Clay minerals with laminated structures (e.g., illite) introduce higher anisotropy. • The mineralogy effects are the dominant factors affecting the anisotropy of the clay-rich artificial shales. [ABSTRACT FROM AUTHOR]

The elastic properties are crucial rock physics properties in the exploration and reserve evaluation of hydrate reservoirs. However, accurately describing the evolution of these properties is a complex task due to the influence of numerous factors, such as particle properties, matrix components, sediments framework, and the distribution of natural gas hydrates within the pores. Existing empirical models often exhibit limitations in adequately capturing the effect of these factors, hindering a comprehensive understanding of the elastic behavior of hydrate-bearing sediments. In this study, the digital rock method was applied to analyze the impact of four factors, which include porosity, particle size, clay components, and the hydrate distribution morphology, on the elastic properties of sediments. The applicability of three theoretical models, namely the time-averaging equation, cementation theory, and three-phase Biot equation, in characterizing the effects of these factors was evaluated. Finally, the numerical simulation results were used to offer a comprehensive characterization of the range of variation in sediment elastic properties under each category of influencing factors. The results indicate that the applicability of the uncemented-sand model is dependent on the initial porosity of the sample, while the cemented-sand model is not a reliable predictor of the shear modulus. On the other hand, the simplified three-phase Biot equation exhibits good coverage of the simulated data at hydrate saturations exceeding 30%. Moreover, the distribution of hydrates can be effectively determined by adjusting the model parameters. The findings from this study contribute to a better understanding of the impact of these factors on sediment elastic properties and have important implications for the exploration and assessment of hydrate reservoirs. • The elastic properties of hydrate-bearing sediments under various influencing factors is simulated based on digital rock method. • The applicability of three rock physics models was evaluated. • The relationship between electrical and elastic properties of hydrate-bearing sediments was further investigated. [ABSTRACT FROM AUTHOR]

Permeability is a critical factor in evaluating the fluid flow capacity and production performance of natural gas hydrate reservoirs. The similarity of electrical conduction and hydraulic flow makes it possible to predict reservoir permeability using electrical data. Clarifying the relationship between the permeability and resistivity of sediments with different hydrate growth habits contributes to the efficient exploration and development of natural gas hydrate resources. In this work, normalized permeability and the resistivity index models for grain-coating (GC) and pore-filling (PF) hydrates are developed based on the fractal geometry theory, forming a new relationship between normalized permeability and resistivity index. The empirical exponent is determined by fractal dimension. Meanwhile, we selected five sets of 3-D computed tomography (CT) images of quartz sand with different particle sizes, GC and PF hydrate digital rocks are constructed using random simulation methods. The numerical simulation of permeability and resistivity index is carried out, based on the pore microstructure images, the box counting method was used to calculate the fractal dimension and analyse the relationship between pore space and transport paths. Furthermore, the pore radius, throat radius and pore connection number are extracted through the pore network method to study the evolution of pore space. The results show that the tortuosity fractal dimension is a critical parameter in the relationship between normalized permeability and resistivity index. The proposed analytical expressions are validated by laboratory and well log data, and the exponent ranges cover existing hydrate permeability–resistivity index data. The models provide the possibility to predict the normalized permeability of hydrate reservoirs based on electrical data alone. [ABSTRACT FROM AUTHOR]

An illustrative theory is developed to analyze the acoustic wave propagation characteristics in the porous media with anisotropic permeability. We focus here on the role of fracture permeability in the unconsolidated porous media, looking in particular at the compressional P -wave phase velocity and attenuation. Two fluid pressure equilibration characteristic time factors are defined, which are corresponding to crack–pore system and crack–crack system, respectively. The theoretical results show that the dispersion and attenuation characteristics of acoustic wave are affected by porous matrix and fracture permeability simultaneously. Due to the fluid exchange that takes place between fractures and pores dominantly, the influence of the fracture connectivity on the wave propagation is very weak when the permeability of background medium is relatively high. However, correlation between wave propagation and fracture permeability is significant when the matrix permeability at a low level. A second attenuation peak occurs for the fluid flow within fractures in high-frequency region for more and more higher fracture permeability. The exact analytical solutions that are compared to numerical forward modeling of wave propagation in fractured media allow us to verify the correctness of the new model. If there exists another approach for obtaining the connectivity information of background media, we can use this model to analyze qualitatively the permeability of fractures or afford an indicator of in-situ permeability changes in a oil reservoir, for example, fracturing operations. [ABSTRACT FROM AUTHOR]

For many geophysical problems it is important to understand the influence of clay on the elastic behaviour of the rocks. However, this is difficult to measure because the complex petrophysical characteristics of tight sandstones make it challenging to control the clay parameters in natural samples. In this study, we synthesized nine tight sandstones with different clay types and content. Ultrasonic measurements and theoretical simulations were then used to analyse the influence of clay on the elastic modulus of brine saturated samples. We found that the shear modulus of smectite-rich samples decreased drastically after saturation, while the decrease observed in kaolinite-rich samples was relatively low. We propose that the reduction in surface energy caused by surface-particle clay hydration is a common mechanism that leads to shear softening in both kaolinite-rich and smectite-rich samples. However, the contact deformation caused by cation hydration of smectite is the primary mechanism leading to greater shear softening of tight sandstones containing smectite. Although the differential Kuster–Toksöz model is based on idealized pore shapes, a dual-porosity scheme can be used to explain and simulate the shear softening of artificial clay-rich tight sandstones. [ABSTRACT FROM AUTHOR]

The seismoelectric method is a modification of conventional seismic measurements which involves the conversion of an incident poroelastic wave to an electromagnetic signal that can be measured at the surface or down a borehole. This technique has the potential to probe the physical properties of the rocks at depth. The problem is that we currently know very little about the parameters which control seismoelectric conversion and their dependence on frequency and permeability, which limits the development of the seismoelectric method. The seismoelectric coupling coefficient indicates the strength of seismoelectric conversion. In our study, we focus on the effects of the reservoir permeability, porosity and frequency on the seismoelectric coupling coefficient through both experimental and numerical modellings. An experimental apparatus was designed to record the seismoelectric signals induced in water-saturated samples in the frequency range from 1 to 500 kHz. The apparatus was used to measure seismoelectric coupling coefficient as a function of porosity and permeability. The results were interpreted using a microcapillary model for the porous medium to describe the seismoelectric coupling. The relationship between seismoelectric coupling coefficients and the permeability and porosity of samples were also examined theoretically. The combined experimental measurements and theoretical analysis of the seismoelectric conversion has allowed us to ascertain the effect of increasing porosity and permeability on the seismoelectric coefficient. We found a general agreement between the theoretical curves and the test data, indicating that seismoelectric conversion is enhanced by increases in porosity over a range of different frequencies. However, seismoelectric conversion has a complex relationship with rock permeability, which changes with frequency. For the low-permeability rock samples (0–100 × 10−15 m2), seismoelectric coupling strengthens with the increase of permeability logarithmically in the low-frequency range (0–10 kHz); in the high-frequency range (10–500 kHz), the seismoelectric coupling is at first enhanced, with small increases of permeability leading to small increases in size in electric coupling. However, continued increases of permeability then lead to a slight decrease in size and image conversion again. For the high-permeability rock samples (300 × 10−15–2200 × 10−15 m2), the seismoelectric conversion shows the same variation trend with low-permeability samples in low-frequency range; but it monotonically decreases with permeability in the high-frequency range. The experimental and theoretical results also indicate that seismoelectric conversion seems to be more sensitive to the changes of low-permeability samples. This observation suggests that seismic conversion may have advantages in characterizing low permeability reservoirs such as tight gas and tight oil and shale gas reservoirs. [ABSTRACT FROM AUTHOR]

Fractures often play an important role in controlling the fluid flow in hydrocarbon reservoirs. When the seismic wave propagates through media containing fracture corridors, significant scattering dispersion and attenuation can occur. In this work, we study the P -wave dispersion and attenuation due to the scattering caused by 2-D fluid-saturated aligned fractures with finite thickness, which are embedded in an isotropic elastic background medium. Using the Foldy approximation and the representation theorem, the P -wave dispersion and attenuation are related to the displacement discontinuities across the fractures. These fracture displacement discontinuities are obtained from the boundary conditions and the P -wave dispersion and attenuation can thus be calculated. A numerical example shows that the fracture thickness has significant influence on the dispersion and attenuation, especially in the low-frequency regime when the fracture size is smaller than the seismic wavelength. The effects of the fluid bulk modulus are also significant, which are opposite to those of the fracture thickness. However, the effect of the fluid viscosity is found to be negligible for the studied configurations. To validate the proposed model, the theoretical predictions are compared with ultrasonic measurements on fractured samples. The comparison shows overall good agreement between theory and experiment. This work reveals the important influence of fracture thickness and saturating fluid properties on the P -wave scattering dispersion and attenuation. Hence, it shows a potential to extract these parameters from seismic data. [ABSTRACT FROM AUTHOR]

Natural porous media have extremely complex pore structures, which greatly affect the material properties. However, it remains a challenge to characterize the pore structure complexity accurately. Fractal geometry is one of the effective tools for this task, which allows for quantitative analysis. In this paper, a new method is proposed for evaluating the pore structure complexity of digital rock models by using the relative value of box-counting fractal dimension. The proposed method transforms the judgment criterion from the comparison of the absolute value to the comparison of the relative value in the fractal dimension by establishing an intermediate fractal reference model. Firstly, the digital core model with progressively changing porosity and pore structure is reconstructed using a numerical modeling means, and three kinds of fractal dimensions of the model are estimated by the box-counting algorithm. Meanwhile, the relationship curve between fractal dimension and porosity is employed as the fractal reference model. Then, the fractal dimensions of the study samples and the reference model are mapped to the same coordinate system. By comparing their relative positional relationship, the pore structure complexity of samples is effectively evaluated and classified. Finally, CT samples are taken as a concrete example to illustrate the application of the proposed method. The correctness and availability of this method are verified through the comprehensive analysis of digital images, pore structure, porosity, and permeability. The constructed method provides a reference for a more accurate evaluation and classification of the complexity of pore space in digital rock physics. • A new method for evaluating the pore structure complexity of digital rocks is proposed. • The degree and law of the influence of porosity and pore structure on the fractal dimension are analyzed. • The interface fractal dimension is an effective parameter in evaluating the pore structure complexity. [ABSTRACT FROM AUTHOR]

Clays are among the main mineral components of shales and play a significant role in mechanical properties and anisotropy. However, it is difficult to quantify the impact of clay minerals on the mechanical properties of rocks because of the complex influence factors. In this study, we construct two artificial clay-rich shale samples containing kaolinite and smectite, respectively, and prepare one natural sample to study the static and dynamic responses of dry samples containing different types of clay during confining loading and unloading. The physical and mechanical properties of shales can be greatly affected by the type of clay minerals due to their structural difference. The kaolinite-rich sample exhibits higher porosity and permeability than those in smectite-rich sample. Both the static and dynamic linear compressibility of our samples generally decrease with confining pressure and display obvious anisotropy. The static compressibilities are larger than dynamic compressibility during loading; however, static compressibilities are not always larger than their equivalent dynamic compressibilities due to the elastically response of samples during early unloading stage. The damage parameters based on the existence of crack-like pores are used to explain the observed nonlinear elastic behavior, and the hysteresis in elastic properties can partly explain the difference in damage parameters between loading and unloading. • Artificial and natural shale samples are prepared to study the static and dynamic linear compressibility. • The mineralogy effects are the main factor affecting the physical and mechanical properties of artificial shales. • The stress dependent elastic behavior and microcracks effects has been explained by a theoretical model. [ABSTRACT FROM AUTHOR]