Effects of fracture intersections on seismic dispersion: theoretical predictions versus numerical simulations

The detection and characterisation of domains of intersecting fractures are important goals in several disciplines of current interest, including exploration and production of unconventional reservoirs, nuclear waste storage, CO₂ sequestration, and groundwater hydrology, among others. The objective of this study is to propose a theoretical framework for quantifying the effects of fracture intersections on the frequency‐dependent elastic properties of fluid‐saturated porous and fractured rocks. Three characteristic frequency regimes for fluid pressure communication are identified. In the low‐frequency limit, fractures are in full pressure communication with the embedding porous matrix and with other fractures. Conversely, in the high‐frequency limit, fractures are hydraulically isolated from the matrix and from other fractures. At intermediate frequencies, fractures are hydraulically isolated from the matrix porosity but can be in hydraulic communication with each other, depending on whether fracture sets are intersecting. For each frequency regime, the effective stiffness coefficients are derived using the linear‐slip theory and anisotropic Gassmann equations. Explicit mathematical expressions for the two characteristic frequencies that separate the three frequency regimes are also determined. Theoretical predictions are then applied to two synthetic 2D samples, each containing two orthogonal fracture sets: one with and another without intersections. The resulting stiffness coefficients, Thomsen‐style anisotropy parameters, and the transition frequencies show good agreement with corresponding numerical simulations. The theoretical results are applicable not only to 2D but also to 3D fracture systems and are amenable to being employed in inversion schemes designed to characterise fracture systems.     

How does water near clay mineral surfaces influence the rock physics of shales?

Clays and clay‐bearing rocks like shale are extremely water sensitive. This is partly due to the interaction between water and mineral surfaces, strengthened by the presence of nanometer‐size pores and related large specific surface areas. Molecular‐scale numerical simulations, using a discrete‐element model, show that shear rigidity can be associated with structurally ordered (bound or adsorbed) water near charged surfaces. Building on these and other molecular dynamics simulations plus nanoscale experiments from the literature, the water monolayer adjacent to hydrophilic solid surfaces appears to be characterised by shear stiffness and/or enhanced viscosity. In both cases, elastic wave propagation will be affected by the bound or adsorbed water. Using a simple rock physics model, bound water properties were adjusted to match laboratory measured P‐ and S‐wave velocities on pure water‐saturated kaolinite and smectite. To fit the measured stress sensitivity, particularly for kaolinite, the contribution from solid‐grain contact stiffness needs to be added. The model predicts, particularly for S‐waves, that viscoelastic bound water could be a source of dispersion in clay and clay‐rich rocks. The bound‐water‐based rock physics model is found to represent a lower bound to laboratory‐measured velocities obtained with shales of different mineralogy and porosity levels.     

Sedimentary and geochemical characterization of Middle–Late Miocene formations in the Neogene Tsugaru Basin,Japan by means of DTH27‐1 well sediment analysis

Middle–Late Miocene age siliceous formations outcropping along the northwestern side of Honshu Island are considered prospective source rocks for hydrocarbons. An analysis of geophysical, sedimentological, and geochemical properties is essential to evaluate the formations' source potential, and to understand the factors that determined the accumulation and preservation of organic matter. This study investigates the Middle–Late Miocene geological record of the Tsugaru back‐arc basin, located in the western part of Aomori prefecture, through an analysis of a 200 m long portion of a core from the DTH27‐1 well; this core is composed of the diatomaceous siltstones of the Akaishi Formation and the siliceous mudstones of the Odoji Formation. Sedimentological and geophysical characterization showed that the Akaishi Formation's diatomaceous siltstones are mostly massive and bioturbated, have low magnetic susceptibility, and demonstrate moderate natural radioactivity. Although the Odoji Formation's siliceous mudstones are massive, they have exceedingly low magnetic susceptibility and high natural radioactivity. Geochemical data from a Rock‐Eval Pyrolysis such as total organic carbon and generative potential (S1 + S2) revealed that, in the Tsugaru area, only the Odoji Formation is a likely prospective source rock for hydrocarbons. On the other hand, T_max values indicate that both the formations are thermally immature for generating hydrocarbons. The difference between the Akaishi and Odoji Formation in the sedimentological facies, in terms of the degree of bioturbation and the organic carbon content, indicates variations in lithological properties, such as porosity and grain size; moreover, this difference indicates a variation in the paleo‐oxygenation of bottom waters, with the transition from oxygen‐deficient conditions in the Middle Miocene to the more oxygenated conditions in the Late Miocene. Both the lithological and paleo‐environmental factors possibly influenced the organic richness in the two formations.     

单裂缝不同传播方向Krauklis波振幅变化的实验研究

裂缝广泛分布于地壳岩石中并具有多尺度的特点,研究地震波在裂缝介质中的传播规律具有重要的科学意义和应用价值.含流体的裂缝中传播的Krauklis波(也曾被称为慢流体波、裂缝波、斯通利导波等)近年来逐渐成为地球物理学界的研究热点之一.本研究利用地震物理模型技术研究横波在单裂缝样品中传播时随传播方向变化的响应特征,在实验室用环氧树脂为基质构建模型样品,一个为不含裂缝的参考样品,一个为含直径30 mm、厚度0.2 mm的薄币状单裂缝的模型,利用0.5 MHz换能器测试了横波在模型中传播时透射信号的特征.实验结果显示在单裂缝样品中透射横波发生了波形的畸变和振幅降低,振幅谱显示透射信号的主频明显降低,在初至横波之后为具有一定能量的尾波.对尾波进行时频分析,发现在方位角较小时尾波能量较弱而方位角较大时尾波能量较强,尾波中信号的主频在0.1 MHz左右,与前人理论和实验研究结果一致.     

Acoustic and petrophysical properties of mechanically compacted overconsolidated sands: Part 2 – Rock physics modelling and applications

Part one of this paper reported results from experimental compaction measurements of unconsolidated natural sand samples with different mineralogical compositions and textures. The experimental setup was designed with several cycles of stress loading and unloading applied to the samples. The setup was aimed to simulate a stress condition where sediments underwent episodes of compaction, uplift and erosion. P-wave and S-wave velocities and corresponding petrophysical (porosity and density) properties were reported. In this second part of the paper, rock physics modelling utilizing existing rock physics models to evaluate the model validity for measured data from part one were presented. The results show that a friable sand model, which was established for normally compacted sediments is also capable of describing overconsolidated sediments. The velocity–porosity data plotted along the friable sand lines not only describe sorting deterioration, as has been traditionally explained by other studies, but also variations in pre-consolidation stress or degree of stress release. The deviation of the overconsolidated sands away from the normal compaction trend on the V_P/V_S and acoustic impedance space shows that various stress paths can be predicted on this domain when utilizing rock physics templates. Fluid saturation sensitivity is found to be lower in overconsolidated sands compared to normally consolidated sands. The sensitivity decreases with increasing pre-consolidation stress. This means detectability for four-dimensional fluid saturation changes can be affected if sediments were pre-stressed and unloaded. Well log data from the Barents Sea show similar patterns to the experimental sand data. The findings allow the development of better rock physics diagnostics of unloaded sediments, and the understanding of expected 4D seismic response during time-lapse seismic monitoring of uplifted basins. The studied outcomes also reveal an insight into the friable sand model that its diagnostic value is not only for describing sorting microtextures, but also pre-consolidation stress history. The outcome extends the model application for pre-consolidation stress estimation, for any unconsolidated sands experiencing similar unloading stress conditions to this study.     

CO2 saturation estimates at Sleipner (North Sea) from seismic tomography and rock physics inversion

CO₂ saturations are estimated at Sleipner using a two-step imaging workflow. The workflow combines seismic tomography (full-waveform inversion) and rock physics inversion and is applied to a two-dimensional seismic line located near the injection point at Sleipner. We use baseline data (1994 vintage, before CO₂ injection) and monitor data that was acquired after 12 years of CO₂ injection (2008 vintage). P-wave velocity models are generated using the Full waveform inversion technology and then, we invert selected rock physics parameters using an rock physics inversion methodology. Full waveform inversion provides high-resolution P-wave velocity models both for baseline and monitor data. The physical relations between rock physics properties and acoustic wave velocities in the Utsira unconsolidated sandstone (reservoir formation) are defined using a dynamic rock physics model based on well-known Biot–Gassmann theories. For data prior to injection, rock frame properties (porosity, bulk and shear dry moduli) are estimated using rock physics inversion that allows deriving physically consistent properties with related uncertainty. We show that the uncertainty related to limited input data (only P-wave velocity) is not an issue because the mean values of parameters are correct. These rock frame properties are then used as a priori constraint in the monitor case. For monitor data, the Full waveform inversion results show nicely resolved thin layers of CO₂–brine saturated sandstones under intra-reservoir shale layers. The CO₂ saturation estimation is carried out by plugging an effective fluid phase in the rock physics model. Calculating the effective fluid bulk modulus of the brine–CO₂ mixture (using Brie equation in our study) is shown to be the key factor to link P-wave velocity to CO₂ saturation. The inversion tests are done with several values of Brie/patchiness exponent and show that the CO₂ saturation estimates are varying between 0.30 and 0.90 depending on the rock physics model and the location in the reservoir. The uncertainty in CO₂ saturation estimation is usually lower than 0.20. When the patchiness exponent is considered as unknown, the inversion is less constrained and we end up with values of exponent varying between 5 and 20 and up to 33 in specific reservoir areas. These estimations tend to show that the CO₂–brine mixing is between uniform and patchy mixing and variable throughout the reservoir.     

A semi-empirical approach to model pressure dependence of elastic moduli in granular media accounting for variations of coordination-number and Poisson-ratio

The effective medium theory based on the Hertz–Mindlin contact law is the most popular theory to relate dynamic elastic moduli (or elastic velocities) and confining pressure in dry granular media. However, many experimental results proved that the effective medium theory predicts pressure trends lower than experimental ones and over-predicts the shear modulus. To mitigate these mispredictions, several evolutions of the effective medium theory have been presented in the literature. Among these, the model named modified grain contact theory is an empirical approach in which three parametric curves are included in the effective medium theory model. Fitting the parameters of these curves permits to adjust the pressure trends of the Poisson ratio and the bulk modulus. In this paper, we present two variations of the modified grain contact theory model. First, we propose a minor modification in the fitting function for the porosity dependence of the calibration parameters that accounts for non-linearity in the vicinity of the critical porosity. Second, we propose a major modification that reduces the three-step modified grain contact theory model to a two-step model, by skipping the calibration parameter–porosity fit in the model and directly modelling the calibration parameter–pressure relation. In addition to an increased simplicity (the fitting parameters are reduced from 10 to 6), avoiding the porosity fit permits us to apply the model to laboratory data that are not provided with accurate porosity measurements. For this second model, we also estimate the uncertainty of the fitting parameters and the elastic velocities. We tested this model on dry core measurements from literature and we verified that it returns elastic velocity trends as good as the original modified grain contact theory model with a reduced number of fitting parameters. Possible developments of the new model to add predictive power are also discussed.     

A triple porosity scheme for fluid/solid substitution: theory and experiment

Quantifying the effects of pore-filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid-octadecane-saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so-called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.     

Rock fall hazard control along a section of railway based on quantified risk

Rock falls represent a large percentage of landslide-related hazards reported by Canadian railways in mountainous terrain. A 54.7?km-long section of railway through the Canadian Cordillera is examined that experiences, on average, 18 rock falls each year. An approach for rock fall hazard management is developed based on quantified risk. The approach focuses on defining railway operation procedures (freight train operations and track maintenance) that comply with quantified risks. Weather-based criteria that define periods when rock falls are more likely to occur along the study area are examined. These criteria are used herein to reduce exposure to rock falls and reduce their consequences. Several freight train operation strategies are proposed that comply with a tolerable level of risk adopted in this study for illustrative purposes. The approach provides a simple, flexible and practical strategy for railway operations that can be regularly adopted by the operators, and that is based on a more comprehensive assessment of quantified risk.