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Organic shales can split into laminae or thin layers due to their fissility and are usually characterized as transverse isotropic media. Understanding their elastic and anisotropic properties plays a significant role in geophysical modeling and imaging, reservoir geomechanics, and reservoir characterization. One can obtain their velocity anisotropy through laboratory and field measurements or rock-physics models. However, the measurements are scarce, and theoretical modeling of Thomsen’s anisotropy parameters generally requires extra inputs, which are sometimes difficult to obtain. We have compiled ultrasonic data from 159 self-sourced reservoir shale samples from the literature and our own measurements. Simple exponential models can capture the trends of the P- and S-wave anisotropy parameters [Formula: see text] and [Formula: see text] decreasing with the increasing vertical P- and S-wave velocities, with [Formula: see text] being above 0.84. The error in estimated anisotropy is small for high-velocity ([Formula: see text]) shales but relatively large for low-velocity ([Formula: see text]) shales. We analyze the influence of multiple geologic factors on the proposed anisotropy-velocity relationships. We observe that velocity anisotropy generally increases with clay content. In addition, mature shales (0.6 1.4). Overall, no single parameter dominates the source of velocity anisotropy, which is jointly affected by the coupled factors of clay content, organic matter, porosity, maturity level, and geologic history. The empirical model has the potential to offer a fast and straightforward method of predicting P- and S-wave anisotropy strength from vertical P- and S-wave velocities.

Understanding the linearly and nonlinearly elastic behaviors of tight reservoir rocks is crucial for numerous geophysical and geomechanical applications in hydrocarbon exploration and production, geologic repositories for greenhouse gases, and geothermal energy exploitation. We have performed a suite of triaxial load and unload cycling tests with increasing stress amplitudes on three tight sedimentary rocks to explore the evolution of their static mechanical properties (Young’s modulus and Poisson’s ratio). We intend to depict the transition from linear to nonlinear elasticity by combining static measurements with dynamic measurements. The experimental results suggest that static mechanical properties increase upon load stress cycling, but they decrease upon unload stress cycling. Upon the increasing-amplitude unload cycling, static mechanical properties gradually decrease from values approaching dynamic properties to values closer to static properties upon load cycling. By quadratically fitting the static mechanical properties as functions of the strain amplitude in the process of unload cycling, we define a characteristic strain amplitude of approximately 5 × 10−5 to distinguish the linearly elasticity-dominated and nonlinearly elasticity-dominated behaviors for three tight rocks. Such transitional behavior in tight sedimentary rocks can be microscopically explained by the gradual activation of friction-controlled sliding from the beginning of the cyclic stress unload. These observations provide direct experimental evidence of the transition from linear to nonlinear elasticity for tight sedimentary rocks during the laboratory static measurements, which will facilitate understanding of the dynamic-static parameter correlation and the modeling of rock deformations in geoscience or geoengineering applications.

Determining the crack initiation stress (Ci) for unconventional shale rocks is of critical importance in describing the entire failure process of unconventional shale reservoirs. We propose a new method to identify Ci values based on triaxial failure tests on four organic shale samples, attempting to improve the shortcomings of other methods. The new method is based on the relationship between crack development and strain energy evolution (SEE). Additionally, the proposed SEE method is compared with three widely used methods, including crack volumetric strain (CVS), moving point regression (MPR) and the lateral strain response (LSR), intending to examine the performance of different methods. The contrastive results indicate that the LSR method cannot determine Ci when the rock ruptures without volumetric dilatancy, which frequently occurs in the compression process of organic shales. Ci values obtained using the SEE method are consistent with those from the CVS and MPR methods. However, the proposed SEE method with a solid physical basis is more objective and stable than the CVS and MPR methods. The proposed method, from one aspect, compensates for the shortcomings of other methods when facing different failure modes in organic shales. From the other aspect, it provides a way to precisely determine Ci values for applications in wellbore stability evaluation and hydraulic fracturing design.

Sedimentary rocks are often heterogeneous porous media inherently containing complex distributions of heterogeneities (e.g., fluid patches and cracks). Understanding and modeling their frequency-dependent elastic and adsorption behaviors is of great interest for subsurface rock characterization from multiscale geophysical measurements. The physical parameter of dynamic volumetric strain (DVS) associated with wave-induced fluid flow is proposed to understand the common physics and connections behind known poroelastic models for modeling dispersion behaviors of heterogeneous rocks. We have derived the theoretical formulations of DVS for patchy saturated rock at the mesoscopic scale and cracked porous rock at microscopic grain scales, essentially embodying the wave-induced fluid-pressure relaxation process. By incorporating DVS into the classic Gassmann equation, a simple but practical “dynamic equivalent” modeling approach, the extended Gassmann equation, is developed to characterize the dispersion and attenuation of complex heterogeneous rocks at nonzero frequencies. Using the extended Gassmann equation, the effect of microscopic or mesoscopic heterogeneities with complex distributions on the wave dispersion and attenuation signatures can be captured. Our theoretical framework provides a simple and straightforward analytical methodology to calculate wave dispersion and attenuation in porous rocks with multiple sets of heterogeneities exhibiting complex characteristics. We also demonstrate that, with the appropriate consideration of multiple crack sets and complex fluid patches distribution, the modeling results can better interpret the experimental data sets of dispersion and attenuation for heterogeneous porous rocks.

Understanding the relationship between dynamic and static mechanical properties of organic-rich shales is crucial for successful in situ stress profile prediction and hydraulic fracturing stimulation in unconventional reservoirs. However, the relationship between dynamic and static properties remains ambiguous, considering the complex rock microstructure and subsurface stress environment. We have reported pseudotriaxial tests on a pair of outcrop Eagle Ford shale plugs, with the axial load applied perpendicular and parallel to bedding planes, to investigate the effects of intrinsic anisotropy and anisotropic stress on dynamic-static relationships. The bedding-parallel Young’s modulus is larger than the bedding-normal one dynamically and statically, whereas there exist complex relations among three static Poisson’s ratios, which are attributed to the intrinsic anisotropy induced by the lenticular texture and finely laminated alignment of kerogen. Along with a stress increment, static tests respond to superpositions of the elastic, viscoelastic, and nonelastic properties, whereas dynamic tests, with more than two orders of magnitude smaller strain amplitude, only reflect the elastic properties of rocks. As a result, the static properties characteristically exhibit more stress dependence than the dynamic properties. Moreover, the evolutions of static properties, especially two static Poisson’s ratios in the horizontal plug, are significantly influenced by the applied stress orientation with respect to the bedding plane. Lastly, we calculate four independent stiffnesses using the five static mechanical parameters with the assumption of transverse isotropy to compare with those calculated from ultrasonic velocities at different stress levels. Finally, when the deviatoric stress is approximately 20 MPa, static parameters derived from stress loading, unloading, and reloading almost intersect together. At this stress level, dynamic and static stiffnesses demonstrate a reasonable correlation with the fitting coefficient of approximately 1.4.

Investigating the stress state of a sample-standard column in forced-oscillation apparatus is critical to clearly quantify measurement credibility, offering insights into revealing intrinsic frequency-dependent elastic characteristics of a rock sample. To investigate the effects of the jointing condition, the location of strain gauges and device resonance on the stress state of a sample-standard column, we experiment with a typical forced-oscillation setup numerically and experimentally at frequencies of 2–800 Hz. Overall, the numerical model captures the primary features of the forced-oscillation device, which makes the simulated data fit well with the measured results. Meanwhile, based on the configuration of the sample-standard column with variable static friction in jointing contacts, the simulated results also indicate that mechanical contacts of the sample-standard-vibrator assembly lead to stress concentration, resulting in coordinate-dependent strains on both the sample and standard. Additionally, strain magnitude is also frequency-dependent, causing a relatively large measurement error on the elasticity of the sample at higher frequencies. Ultimately, numerical results not only optimize measurement workflow but also create a solid foundation for the interpretation of measured data.

The deformation and fracture of anisotropic shale rocks are of great interest to geoengineers concerned with assessing the stability of boreholes and underground excavations. However, some mechanic properties associated with anisotropic rock fracture remain ambiguous. We have purposely reported triaxial failure tests on two sets of transversely isotropic shale plugs (i.e., Marcellus and Eagle Ford shales) cutting parallel and perpendicular to the bedding planes. The experimental results suggest that the bedding planes give rise to considerable differences in the elastic properties, failure strength, and failure modes in the bedding-normal and bedding-parallel directions. In general, the static Young’s modulus is higher parallel to bedding than normal to bedding, whereas the static Poisson’s ratios measured from the vertical and horizontal shale plugs do not exhibit a certain relationship. The ratio between the bedding-parallel and bedding-normal failure strength is approximately 1.9 for Marcellus shales, whereas it is approximately 1.3 for Eagle Ford shales. At the failure point, the axial strains are appreciably larger than the radial strains. In contrast, the two orthogonal radial strains exhibit different characteristics in the bedding-normal and bedding-parallel directions, giving rise to complex failure modes. The extended cracks in the vertical plugs lead to fracturing in a shearing manner, with a single shear plane in the Eagle Ford shale and two conjugate shear planes in the Marcellus shale. In the horizontal plugs, the Eagle Ford shale exhibits shear banding in the bedding-normal direction and a combination of shear and extension in the bedding-normal direction. In contrast, the Marcellus shale exhibits three conjugated shear planes.

The static properties of subsurface rocks are needed for geomechanical applications, but the dynamic properties are usually more extensively available and can be acquired with much less effort. Therefore, it is important to know the relationships between the static and dynamic properties. Studying these relationships based on traditional triaxial testing yields confusing results, partly due to intrinsic deficiencies of the experimental setup and testing procedures. We have developed a new approach to study the relationship under hydrostatic stress conditions. The traditional ultrasonic velocity measurement system is sufficient for all of the testing, and it requires no application of the traditional strain gauge. During the pressure-dependent ultrasonic velocity measurements, the rock sample experiences static deformation when the pressure changes are in the order of megapascals. If the pore pressure is kept constant, the pore volume will vary with the confining pressure. The pore volume change can be monitored accurately by the pore pressure controlling pump, and it can be related to the volume strain of the rock for estimating the static bulk modulus of the rock sample. Based on the laboratory ultrasonic measurements available in the literature, we analyzed the effects of the differential pressure, clay content, crack density, and pore fluid on the relationship between the static and dynamic bulk moduli. From the analyses, we inferred that most of the laboratory-observed differences between the static and dynamic property may not exist for the reservoir rock under in situ conditions.

Understanding the differences between the static and dynamic elastic moduli of reservoir rocks is essential for the successful exploration and production of hydrocarbon reservoirs. However, the controlling factors on the dynamic-static discrepancy for sandstones remain ambiguous. Consequently, we have purposely selected three outcrop sandstone samples with large porosity contrast to investigate the effects of the stress state, magnitude, and load-unload history on the dynamic and static moduli through laboratory measurements. The results suggest that the dynamic moduli are systematically larger than the static moduli at almost any hydrostatic or deviatoric stress magnitude. In contrast, the static moduli are much more sensitive to the stress variations than the dynamic ones, leading to the decreasing dynamic-static difference upon hydrostatic loading and the increasing dynamic-static difference upon deviatoric loading. When the maximum stress in a cycle is initially reversed, the dynamic-static ratio tends to approach one, whatever the bulk modulus under hydrostatic pressure condition or the Young’s modulus under triaxial stress condition. Under the subsequent unloading process, the static bulk modulus is always higher than that derived during loading. However, the unloading static Young’s modulus is larger than the loading Young’s modulus only at a relatively high deviatoric stress magnitude greater than 30 MPa, while showing an opposite trend at a low-stress condition of less than 25 MPa. From the microstructural viewpoint, it is believed that the static tests accumulate the elastic, viscoelastic, and nonelastic properties within a certain stress or strain range. In contrast to the dynamic modulus, the static modulus exhibits greater sensitivity to the pressure or stress changes under hydrostatic and deviatoric stress conditions. The strong stress dependence makes it important to consider the in situ stress conditions when establishing dynamic-static modulus relations.

The layer-induced seismic anisotropy of sedimentary strata is frequency-dependent. At the low-frequency limit, the effective anisotropic properties of the layered media can be estimated by the Backus averaging model. At the high-frequency limit, the apparent anisotropic properties of the layered media can be estimated by ray theory. First, we build a database of laboratory ultrasonic measurement on sedimentary rocks from the literature. The database includes ultrasonic velocity measurements on sandstones and carbonate rocks, and velocity-anisotropy measurements on shales. Then, we simulate the sedimentary strata by randomly selecting a certain number of rock samples and using their laboratory measurement results to parameterize each layer. For each realization of the sedimentary strata, we estimate the effective and apparent seismic anisotropy parameters using the Backus average and ray theory, respectively. We find that, relative to Backus averaging, ray theory usually underestimates the Thomsen parameters [Formula: see text] and [Formula: see text], and overestimates [Formula: see text]. For an effective layered medium consisting of isotropic sedimentary rocks, the differences are significant. These differences decrease when shales with intrinsic seismic anisotropy are included. For the same sedimentary strata, the seismic wave should perceive stronger seismic anisotropy than the ultrasonic wave.

Studying the empirical relations between seismic anisotropy parameters is important for the simplification and practical applications of seismic anisotropy. The elastic properties of mudrocks are often described by transverse isotropy. Knowing the elastic properties in the vertical and horizontal directions, a sole oblique anisotropy parameter determines the pattern of variation of the elastic properties of a transversely isotropic (TI) medium in all of the other directions. The oblique seismic anisotropy parameter [Formula: see text], which determines seismic reflection moveout behavior, is important in anisotropic seismic data processing and interpretation. Compared to the other anisotropy parameters, the oblique anisotropy parameter is more sensitive to the measurement error. Although, theoretically, only one oblique velocity is needed to determine the oblique anisotropy parameter, the uncertainty can be greatly reduced if multiple oblique velocities in different directions are measured. If a mudrock is not a perfect TI medium but it is expediently treated as one, then multiple oblique velocity measurements in different directions should lead to a more representative approximation of [Formula: see text] or [Formula: see text] because the directional bias can be reduced. Based on a data quality analysis of the laboratory seismic anisotropy measurement data from the literature, we found that there are strong correlations between the oblique anisotropy parameter and the principal anisotropy parameters when data points of more uncertainty are excluded. Examples of potential applications of these empirical relations are discussed.

Analyzing elastic and attenuation characteristics of heavy oil sand is critical for understanding and interpreting sonic and seismic data for their use in exploration and reservoir monitoring. The attenuation characteristic of oil sands is inherently complicated because of its loose frame, large porosity, and highly temperature-dependent viscosity of heavy oil. During thermal production, the attenuation of heavy oil sands undergoes significant changes due to the effects of pressure, temperature, and gas. Therefore, we have performed laboratory measurements of heavy oil sands under different physical conditions. By applying spectral-ratio method on the recorded wave signals, we are able to investigate the attenuation of the oil sands under different pressure and temperature conditions. For the measured sample, the [Formula: see text] decreases from 0.083 to 0.043 for a differential pressure increasing from 1.38 to 9.65 MPa. A peak of [Formula: see text] occurs at the middle temperature (approximately 60°C) for the wet sample, whereas the weakest [Formula: see text] occurs at the low temperature. Comparisons between the as-is (partially saturated) and wet (fully saturated) samples suggest that attenuation ([Formula: see text]) of the oil sands can be significantly affected by the presence of gas at a high temperature (greater than 60°C). In the end, the Havriliak-Negami model is used to capture the temperature-dependent attenuation characteristics of fully saturated oil sands. Although the measurements are conducted at ultrasonic frequency, the presented results indicate some implications for field-reservoir monitoring and also offer insights into applying attenuation attribute to characterize heavy oil reservoir during thermal production.

Characterizing the elastic signatures of overpressure of shale caused by the smectite-to-illite transition relies on a good understanding of this mechanism and is also necessary for pore-pressure prediction. Methods of pore-pressure prediction in shales that have undergone smectite-to-illite transition are mostly based on empirical fitting without a quantitative interpretation based on a micromechanism analysis. With upscaled wireline-logging data, two trends of smectite-to-illite transition are categorized by using the crossplot of sonic traveltime and density. Trend I associated with a fluid-expansion scenario exhibits a decrease of sonic velocity with little change in the bulk density, whereas trend II induced by a fluid-loss scenario contains an increase of density with little change in the sonic velocity. The fluid expansion typically gives rise to high-magnitude overpressure and tends to happen when the overlying formations have more shaly contents and low permeability. The fluid loss case tends to have relatively deeper overpressure onsets, and its overlying formations tend to have more sandy contents with relatively high permeability. We develop a modeling framework to capture the elastic and pore-pressure evolution characteristics in shale during the smectite-to-illite transition. With proper bulk volume models, the velocity, density, and pore pressure increase of shale can be computed in the fluid expansion, fluid loss, and a mixture of these two scenarios. After calibration with logging data, rock-physics modeling can quantitatively interpret the rock-property evolution characteristics within the smectite-to-illite transition zone.

The relationship between seismic velocity and porosity is one of the most important research topics in exploration geophysics. A strong correlation, if it exists, can be very useful for quantitative seismic interpretation of direct hydrocarbon indicators. The Voigt and Reuss bounds are often plotted alongside the data for quality control and interpretation. The relative position of the data within the bounds may supply important information regarding the pore shape, stress condition, lithology, and diagenesis of porous rocks. It is found that the Voigt bound and Reuss bound are actually special cases of the weighted power mean, with the power parameters being 1 and −1, respectively. The geometric mean is a special case of the power mean with the power parameter being zero. The power mean is a monotonic function of the power parameter. For the construction of a rock physics template, the region between the Voigt and Reuss bounds can be evenly divided by varying the power parameter between −1 and 1. The power mean can be a very useful tool for modeling the elastic properties of rocks. We have demonstrated the potential applications of the power mean in the studies of velocity-porosity relation, effective media, and pore fluids effect on seismic velocities.

Porosity measurement is an important step for petrophysical characterization of reservoir rocks, as porosity is essential for analysing elastic properties and estimating the capacity of rocks to hold hydrocarbon resources. Commonly used porosity measurement methods fail to work on heavy oil sands, because of the loose fragile sand frame and solid-like irreducible heavy oil. We develop three methods to measure the porosity of heavy oil sands, which are feasible and affordable in most laboratories. Method 1 involves calculating the bulk volume of the sample by measuring its physical dimensions directly. Method 2 uses calibrated sample weight and volume (after removing the protecting foil cover and metal clips).Method 3 first applies pressurizing on samples and then measures the weight and volume of the bare samples. The measurement results of the three methods are then compared and method 3 is determined as the most reliable, which is also verified by the porosity log. Finally, an analysis of the potential sources of errors associated with method 3 is performed.

Bitumen carbonate is an important source of bitumen, and knowledge of its properties needs to be improved. Owing to its high viscosity, most production methods of bitumen involve thermal techniques. Bitumen properties change tremendously during thermal production, which can inevitably affect the properties of bitumen carbonates. Moreover, the high pressure applied for steam injection can also impact the properties of bitumen carbonates. The variations of reservoir properties are indicators of a steam-affected zone, and thus they are significant for reservoir monitoring. To reveal the responses of bitumen carbonates under different pressure and temperature conditions, two bitumen carbonate samples are measured in the laboratory. We first develop a method that enables the estimation of porosity and bitumen saturation simultaneously. Then, the samples are exposed to various differential pressures, covering the in situ effective pressure range, to study the influence of pressure on velocities. Afterward, different temperatures are used to test the temperature sensitivity of the two samples. A histogram analysis of the velocity variations is also conducted to investigate the effects of distinct porosity and bitumen saturation. After washing off the bitumen, the clean samples are also measured and compared with the as-is samples, so as to check the impacts of bitumen on the carbonate samples. We have determined that porosity, bitumen saturation, pressure, and temperature can all have a noticeable influence on the velocities of bitumen carbonates. Although the research is in its initial stage, it can help improve our understanding of bitumen carbonates and also assist in monitoring the steam-affected zone during thermal production.

Sweet spots identification for unconventional shale reservoirs involves detection of organic-rich zones with abundant porosity. However, commonly used elastic attributes, such as P- and S-impedances, often show poor correlations with porosity and organic matter content separately and thus make the seismic characterization of sweet spots challenging. Based on an extensive analysis of worldwide laboratory database of core measurements, we find that P- and S-impedances exhibit much improved linear correlations with the sum of volume fraction of organic matter and porosity than the single parameter of organic matter volume fraction or porosity. Importantly, from the geological perspective, porosity in conjunction with organic matter content is also directly indicative of the total hydrocarbon content of shale resources plays. Consequently, we propose an effective reservoir parameter (ERP), the sum of volume fraction of organic matter and porosity, to bridge the gap between hydrocarbon accumulation and seismic measurements in organic shale reservoirs. ERP acts as the first-order factor in controlling the elastic properties as well as characterizing the hydrocarbon storage capacity of organic shale reservoirs. We also use rock physics modeling to demonstrate why there exists an improved linear correlation between elastic impedances and ERP. A case study in a shale gas reservoir illustrates that seismic-derived ERP can be effectively used to characterize the total gas content in place, which is also confirmed by the production well.

We extend the frequency- and angle-dependent poroelastic reflectivity to systematically analyse the characteristic of seismic waveforms for highly attenuating reservoir rocks. It is found that the mesoscopic fluid pressure diffusion can significantly affect the root-mean-square amplitude, frequency content, and phase signatures of seismic waveforms. We loosely group the seismic amplitude-versus-angle and -frequency characteristics into three classes under different geological circumstances: (i) for Class-I amplitude-versus-angle and -frequency, which corresponds to well-compacted reservoirs having Class-I amplitude-versus-offset characteristic, the root-mean-square amplitude at near offset is boosted at high frequency, whereas seismic energy at far offset is concentrated at low frequency; (ii) for Class-II amplitude-versus-angle and -frequency, which corresponds to moderately compacted reservoirs having Class-II amplitude-versus-offset characteristic, the weak seismic amplitude might exhibit a phase-reversal trend, hence distorting both the seismic waveform and energy distribution; (iii) for Class-III amplitude-versus-angle and -frequency, which corresponds to unconsolidated reservoir having Class-III amplitude-versus-offset characteristic, the mesoscopic fluid flow does not exercise an appreciable effect on the seismic waveforms, but there exists a non-negligible amplitude decay compared with the elastic seismic responses based on the Zoeppritz equation.

Three-dimensional poststack and prestack seismic inversion results such as P- and S-impedance are commonly used for reservoir characterization. However, the frequency bandwidth of surface-based reflection seismic surveys usually ranges from 10 to 70 Hz, and these surveys have limited vertical resolution. The frequency bandwidth of vertical seismic profiling (VSP) and crosswell data is much wider than that of surface reflection seismic data, and it can give a detailed illumination of the subsurface around the borehole. We test a joint inversion method that integrated surface reflection seismic, VSP, and crosswell data. To better constrain the inversion results, we further integrate a posteriori information on the reflectivity obtained from petrophysics data into the inversion procedure. The a posteriori distribution we use is a modified-Cauchy distribution obtained from the statistical analysis of petrophysics data. To demonstrate the effectiveness of our algorithm, we applied our inversion strategy to a 2D synthetic model and a real seismic data set, and an uncertainty assessment was also performed. The joint inversion method can detect the thin layers that surface seismic inversion fail to, demonstrating the higher resolution of the method.

Heavy oil reservoirs are important alternative energy resources to conventional oil and gas reservoirs. However, due to the high viscosity, most production methods of heavy oil reservoirs involve thermal production. Heavy oil reservoirs’ properties change dramatically during thermal production because the viscosity drops drastically with increasing temperature. Moreover, the velocity and density also decrease after steam injection, leading to a longer traveltime of seismic velocities and low impedance of the steam chamber zone. These changes of properties can act as indicators of the steam chamber and can be detected through the time-lapse inversion method. We first establish the rock-physics relationship between oil sands’ impedance and temperature on the basis of our previous laboratory work. Then, we perform the forward modeling of the heavy oil reservoir with the steam chamber to demonstrate the influence of steam injection on seismic profiles. Then, we develop a modified-Cauchy prior-distribution-based time-lapse inversion method and perform a 2D model test. The inversion method is then applied on the real field data, and the results are analyzed. By combining the inverted impedance and rock-physics relation between impedance and temperature, the temperature distribution map is obtained, which can work as an indicator of steam chamber. Finally, an empirical relation between impedance and velocity is established, and velocity is derived from the impedance.

Bitumen is a very important hydrocarbon resource, which exists in enormous amounts all over the world. Bitumen sands and bitumen carbonates have large percentages of bitumen content. However, the differences in lithology, porosity, and bitumen content cause them to have distinct properties, which can further lead to different production methods. Therefore, it is significant to study the different properties between bitumen sands and bitumen carbonates, so as to further analyze the factors causing the differences and to provide guidance for production. To study the basic properties of the bitumen rocks, we have developed a method to measure the rock samples’ true porosity, which can estimate the porosity even for “as is” samples. The method involves injecting water and can provide relatively accurate estimation of the porosity. Then, we compared the porosities and bitumen content of the bitumen sands and bitumen carbonates from the same area. Due to different rock formation mechanisms, mineral composition, and compaction, bitumen sands and bitumen carbonates show different porosity and bitumen saturation. Based on the differences in porosity and bitumen content, the responses of the bitumen sands and bitumen carbonates under different pressure and temperature conditions are also compared and analyzed. The bitumen sands are more sensitive to pressure and temperature than are the bitumen carbonates, owing to the larger porosities and higher bitumen content. Bitumen carbonates show distinct behaviors from bitumen sands — the velocities drop faster at the high temperature range. In the end, the waveforms of the signals of the bitumen sands and bitumen carbonates are also compared, and the attenuation is calculated. Bitumen sands and bitumen carbonates display stronger attenuation in the middle temperature range, which is related to the bitumen properties. Comparatively stronger attenuation occurs in bitumen sands because of its loose frame and higher bitumen content.

We have investigated the elastic properties of heavy oil sands influenced by the multiphase properties of heavy oil itself and the solid matrix with regard to temperature, pressure, and microstructure. To separately identify the role of the heavy oil and solid matrix under specific conditions, we have designed and performed special ultrasonic measurements for the heavy oil and heavy oil-saturated solids artificial samples. The measured data indicate that the viscosity of heavy oil reaches [Formula: see text] at the temperature of glass point, leading the heavy oil to act as a part of a solid frame of the heavy oil sand sample. The heavy oil is likely movable pore fluid accordingly once its viscosity dramatically drops to approximately [Formula: see text] at the temperature of liquid point. The viscosity-induced elastic modulus of heavy oil in turn makes the elastic properties of heavy oil-saturated grain solid sample to be temperature dependent. In addition, the rock physics model suggests that the microstructure of heavy oil sand is transitional; consequently, the solid Gassmann equation underestimates the measured velocities at the low temperature range of the quasisolid phase of heavy oil, whereas overestimates when the temperature exceeds the liquid point. The heavy oil sand sample has a higher modulus and approaches the upper bound due to the stiffer heavy oil itself acting as a rock frame as the temperature decreases. In contrary, heavy oil sand displays a lower modulus and approaches the lower bound when the heavy oil becomes softer as the temperature goes up.

We have made various experimental investigations on rock-physics properties of the halite salt coming from a salt dome in the U.S. Gulf Coast Basin. The effect of crystal defects and intercrystal cracks on the P-wave velocity of the halite salt sample can be mitigated after high-pressure annealing. The temperature effect on seismic velocities of halite salt is dominant relative to the stress effect. Azimuthal anisotropy is not observed on the halite salt samples. We have observed that the velocity variations in different directions were mostly caused by the crystal-scale heterogeneity. For the salt structures primarily made of creep-deformed halite, the effect of seismic velocity anisotropy might be negligible for seismic exploration. No significant dispersion of seismic velocities was observed from the low-frequency measurement. Our measurements supply basic information for seismic velocity model building that may help to improve seismic imaging of salt structures.

The conventional porosity measurement is not adequate to precisely measure “as-is” porosity of heavy oil sand samples due to its irregular sample shape, pore-filling viscous fluids, and especially difficult storage without losing mass. From a practical laboratory point of view, a confined porosity measurement strategy is specifically introduced to measure the as-is porosity of heavy oil sand sample. This overall strategy primarily consists of two parts. First of all, as-is porosity is estimated by using the assumed parameters (grain density, fluid density, and fluids saturation) and measured bulk density that is calculated from the Archimedes principle, which not only keeps the sample intact, but also is advantageous for minimizing mass loss and external covers. Furthermore, by extracting the pore fluids (heavy oil, water, and possibly gas) from the original sample, the assumed indispensable parameters are precisely measured; more importantly, a group of porosity data can be calculated by applying directly measured grain volume data and bulk volume data. Based on the measured data and error analysis, we have concluded that the porosity calculated from these directly measured data set gives us a low porosity bound whereas as-is porosity estimated from the Archimedes principle indicates the upper bound.

Heavy oil reservoirs are important alternative energy resources to conventional oil and gas reservoirs. However, due to the high viscosity of heavy oil, much production of heavy oil reservoirs involves injecting steam, and determining the temperature distribution is significant for production. To do this, time-lapse inversion is commonly used to derive the change of the oil sand properties during steam injection, and rock-physics models are used to link the properties and temperature. Many people have done research on simulating variations of the oil sand properties with temperature; however, the previous models fail to adequately represent our experimental data, and they overestimate their values. The errors between previous models’ predictions and measurements are quite large, especially at low temperatures. To study the oil sand properties, we first measured eight oil sand samples including five presteam samples and three poststeam samples, and we experimentally quantified the pressure sensitivity of velocity, the temperature sensitivity of velocity, and the corresponding [Formula: see text] ratios. Then we developed a new model, introducing a frame damage parameter and a solid oil proportion parameter. This model integrates the solid oil into the sand frame, and it incorporates the temperature-dependent frame damage to characterize the frame moduli variations with increasing temperature. The solid-Gassmann equation was then applied to saturate the sands’ frame with heavy oil. Our simulation results determined that the errors at low temperature and high temperature were both compensated, and the new model fitted better than previous models over the whole measurement temperature range. The modeling was also extended to the thermal production temperature range, and the phase transition of water was considered, which provided a useful indicator of the steam.

Although there is no assumption of pore geometry in derivation of Gassmann’s equation, the pore geometry is in close relation with hygroscopic water content and pore fluid communication between the micropores and the macropores. The hygroscopic water content in common reservoir rocks is small, and its effect on elastic properties is ignored in the Gassmann theory. However, the volume of hygroscopic water can be significant in shaly rocks or rocks made of fine particles; therefore, its effect on the elastic properties may be important. If the pore fluids in microspores cannot reach pressure equilibrium with the macropore system, assumption of the Gassmann theory is violated. Therefore, due to pore structure complexity, there may be a significant part of the pore fluids that do not satisfy the assumption of the Gassmann theory. We recommend that this part of pore fluids be accounted for within the solid rock frame and effective porosity be used in Gassmann’s equation for fluid substitution. Integrated study of ultrasonic laboratory measurement data, petrographic data, mercury injection capillary pressure data, and nuclear magnetic resonance T2 data confirms rationality of using effective porosity for Gassmann fluid substitution. The effective porosity for Gassmann’s equation should be frequency dependent. Knowing the pore geometry, if an empirical correlation between frequency and the threshold pore-throat radius or nuclear magnetic resonance T2 could be set up, Gassmann’s equation can be applicable to data measured at different frequencies. Without information of the pore geometry, the irreducible water saturation can be used to estimate the effective porosity.

Based on the theory of anisotropic elasticity and observation of static mechanic measurement of transversely isotropic hydrocarbon source rocks or rock-like materials, we reasoned that one of the three principal Poisson’s ratios of transversely isotropic hydrocarbon source rocks should always be greater than the other two and they should be generally positive. From these relations, we derived tight physical constraints on c13, Thomsen parameter δ, and anellipticity parameter η. Some of the published data from laboratory velocity anisotropy measurement are lying outside of the constraints. We analysed that they are primarily caused by substantial uncertainty associated with the oblique velocity measurement. These physical constraints will be useful for our understanding of Thomsen parameter δ, data quality checking, and predicting δ from measurements perpendicular and parallel to the symmetrical axis of transversely isotropic medium. The physical constraints should also have potential application in anisotropic seismic data processing.

Elastic interactions between pores and cracks reflect how they are organized or spatially distributed in porous rocks. The principle goal of this paper is to understand and characterize the effect of elastic interactions on the effective elastic properties. We perform finite element modelling to quantitatively study how the spatial arrangement of inclusions affects stress distribution and the resulting overall elasticity. It is found that the stress field can be significantly altered by elastic interactions. Compared with a non-interacting situation, stress shielding considerably stiffens the effective media, while stress amplification appreciably reduces the effective elasticity. We also demonstrate that the T-matrix approach, which takes into account the ellipsoid distribution of pores or cracks, can successfully characterize the competing effects between stress shielding and stress amplification. Numerical results suggest that, when the concentrations of cracks increase beyond the dilute limit, the single parameter crack density is not sufficient to characterize the contribution of the cracks to the effective elasticity. In order to obtain more reliable and accurate predictions for the effective elastic responses and seismic anisotropies, the spatial distribution of pores and cracks should be included. Additionally, such elastic interaction effects are also dependent on both the pore shapes and the fluid infill.

Based on poroelasticity analysis, we developed a new concept of frequency-dependent dynamic fluid modulus (DFM) to understand the velocity dispersion and wave attenuation due to wave-induced fluid flow. Conventional applications of Gassmann’s equation require a complete homogeneity inside the porous media (or equivalently, at zero frequency) and closed boundary condition. We first analyzed the fluid effect on the bulk modulus in homogeneous porous media with a nonclosed condition. The partial drainage of pore fluid causes additional pore volume change under applied stress. An incoming fluid flow stiffens the porous system, and an outgoing flow softens it. Such a phenomenon can still be effectively formulated as a closed system with Gassmann’s equation, by introducing a DFM, which adds a flow term into the original fluid modulus. We further proved that in heterogeneous porous media, the wave-induced internal fluid flow caused additional bulk volume deformation. It equals the amount of the fluid flow from a soft phase to a stiff phase times the difference of Skempton coefficients between the two phases. Again, with a frequency-dependent complex number DFM, the use of Gassmann’s equation can be extended into heterogeneous porous media at nonzero frequencies to fully characterize its viscoelastic behavior on rock’s bulk modulus. We evaluated three examples to show how to model the P-wave attenuation and velocity dispersion in porous media due to microscopic and mesoscopic scale heterogeneities, as well as in the presence of multiple sets of heterogeneities. Finally, we demonstrated that the DFM can be conveniently and deterministically inverted from the measured lab data. The inverted results can be used to identify the possible mechanisms behind the observed wave attenuation and velocity dispersion, and they were good indicators of the degree and distribution of heterogeneities inside the rocks.

We have investigated the impact of wave-induced fluid flow, including Biot flow and mesoscopic flow, on the signatures of seismic reflectivity in heterogeneous reservoir rocks. We have incorporated the dynamic poroelastic responses of mesoscopic flow into the classical Biot theory. The resulting effective Biot media could capture the characteristics of velocity dispersion and wave attenuation in heterogeneous poroelastic media. On the basis of this effective Biot media, an approach was developed to compute the poroelastic reflection at arbitrary angles and frequencies from the boundary of two heterogeneous porous media. The computed poroelastic reflections not only depended on the elastic properties’ contrast and incident angle, but also relied on the fluid mobility and observational frequency. For a typical sand-shale reflector, with the given rock and fluid properties, we found that the effect of mesoscopic flow causes P-wave reflection amplitude variations with the frequency being as high as 40% and a maximum phase shift as high as 16° at the seismic exploration frequency band. In addition, it was found that the amplitude variation with offset intercept and the gradient at the poroelastic interface were impacted by the mesoscopic flow and had a decreasing trend with frequency. Therefore, ignoring the impact of mesoscopic flow could possibly lead to uncertainty in seismic imaging as well as quantitative interpretation of reservoir properties. In comparison, the Biot flow-induced seismic dispersion effect, which occured at a very high-frequency range, was almost negligible.

Dispersion and attenuation are important attributes of seismic data that can provide important information about reservoir rock lithology, pore fluid type, and pore structure. Based on Cheng’s pore-aspect-ratio spectrum inversion methodology, we related the closure and deformation of soft pores to the measured pressure-dependent porosity data. With this additional constraint, the inverted pore-aspect-ratio spectrum and concentrations are more realistic. The complex pore structure controls two important intrinsic dispersion and attenuation mechanisms: Biot flow and squirt flow. We modified and extended Tang’s unified velocity dispersion and attenuation model and made it applicable to poroelastic media with a complex pore structure under the undrained condition. The inverted pore-aspect-ratio spectra from pressure-dependent ultrasonic velocity measurements were put into the modified Tang’s model to predict velocity dispersion and attenuation in full frequency range at various differential pressure conditions.

We mapped probabilities of lithology and fluid based on seismic and well observations in a heterogeneous carbonate reservoir of the Sichuan Basin, southwest China, thus characterizing the reservoir complexity and identifying the potential sweet spot. Rock physical analysis showed that the presence of a vuggy-fracture porosity system combined with the fluids’ effect complicate the elastic responses of heterogeneous carbonates. This also gives physical insight into how the elastic properties of different lithofluid classes can be distinguished. With the application of Bayesian linearized amplitude variation with offset inversion, we found that the posterior distribution of P- and S-wave velocities were reliably extracted, whereas the inverted density tended to show high uncertainty due to a lack of wide angle data in the migrated seismic gathers. Finally, a Bayesian approach was implemented to propagate uncertainty from prestack seismic data to lithofluid classes in an integrated framework. The gas-carbonate predictions with high posterior probabilities were consistent with well observations at the well location and the present geological continuity. The probability distributions for the anhydrite, limestone, and dolostone were essential to understand the reservoir architecture and delineate the reservoir heterogeneities. We also ascertained that the uncertainty of lithofacies prediction is determined by the uncertainty of seismic inversion as well as the uncertainty of the link between lithofacies to their corresponding elastic responses.

Ultrasonic velocities were measured on a stack of synthetic material (plexiglass), at low (90/120 kHz, long wavelength range) and high (480 kHz, short wavelength range) frequencies. Plates were pressed together with uniaxial normal stress. These measurements were repeated under different uniaxial pressures for two cases: 1Without circular rubber inclusions between synthetic fractures and 2With circular rubber inclusions between fractures. Calculation of anisotropy parameters and also normal and shear interface (fracture) compliances using linear calculus show reasonable variations. Anisotropy and compliances decreases as overburden pressure increases suggesting that anisotropy is caused by compliances. At higher frequencies, synthetic fractures seem to be stiffer than at lower frequencies. For the long and short wavelength ranges, similar variations were observed for anisotropy parameters and fracture compliances. VS measurements in different directions show that for the case without rubber inclusions there is a good approximation of VTI medium whereas for the case with inclusions there is a significant difference between VS travelling in directions parallel and perpendicular to the plates.

Hydrate-bearing sands and shallow nodular hydrate are potential energy resources and geohazards, and they both need to be better understood and identified. Therefore, it is useful to develop methodologies for modeling and simulating elastic constants of these hydrate-bearing sediments. A gas-hydrate rock-physics model based on the effective medium theory was successfully applied to dry rock, water-saturated rock, and hydrate-bearing rock. The model was used to investigate the seismic interpretation capability of hydrate-bearing sediments in the Gulf of Mexico by computing elastic constants, also known as seismic attributes, in terms of seismic interpretation, including the normal incident reflectivity (NI), Poisson’s ratio (PR), P-wave velocity ([Formula: see text]), S-wave velocity ([Formula: see text]), and density. The study of the model was concerned with the formation of gas hydrate, and, therefore, hydrate-bearing sediments were divided into hydrate-bearing sands, hydrate-bearing sands with free gas in the pore space, and shallow nodular hydrate. Although relations of hydrate saturation versus [Formula: see text] and [Formula: see text] are different between structures I and II gas hydrates, highly concentrated hydrate-bearing sands may be interpreted on poststack seismic amplitude sections because of the high NI present. The computations of elastic constant implied that hydrate-bearing sands with free gas could be detected with the crossplot of NI and PR from prestack amplitude analysis, and density may be a good hydrate indicator for shallow nodular hydrate, if it can be accurately estimated by seismic methods.

This paper discusses and addresses two questions in carbonate reservoir characterization: how to characterize pore‐type distribution quantitatively from well observations and seismic data based on geologic understanding of the reservoir and what geological implications stand behind the pore‐type distribution in carbonate reservoirs. To answer these questions, three geophysical pore types (reference pores, stiff pores and cracks) are defined to represent the average elastic effective properties of complex pore structures. The variability of elastic properties in carbonates can be quantified using a rock physics scheme associated with different volume fractions of geophysical pore types. We also explore the likely geological processes in carbonates based on the proposed rock physics template. The pore‐type inversion result from well log data fits well with the pore geometry revealed by a FMI log and core information. Furthermore, the S‐wave prediction based on the pore‐type inversion result also shows better agreement than the Greensberg‐Castagna relationship, suggesting the potential of this rock physics scheme to characterize the porosity heterogeneity in carbonate reservoirs. We also apply an inversion technique to quantitatively map the geophysical pore‐type distribution from a 2D seismic data set in a carbonate reservoir offshore Brazil. The spatial distributions of the geophysical pore type contain clues about the geological history that overprinted these rocks. Therefore, we analyse how the likely geological processes redistribute pore space of the reservoir rock from the initial depositional porosity and in turn how they impact the reservoir quality.

P-wave seismic reflection data, with variable offset and azimuth, acquired over a fractured reservoir can theoretically be inverted for the effective compliance of the fractures. The total effective compliance of a fractured rock, which is described using second- and fourth-rank fracture tensors, can be represented as background compliance plus additional compliance due to fractures. Assuming monoclinic or orthotropic symmetry (which take into account layering and multiple fracture sets), the components of the effective second- and fourth-rank fracture compliance tensors can be used as attributes related to the characteristics of the fractured medium. Synthetic tests indicate that using a priori knowledge of the properties of the unfractured medium, the inversion can be effective on noisy data, with S/N on the order of 2. Monte Carlo simulation was used to test the effect of uncertainties in the a priori information about elastic properties of unfractured rock. Two cases were considered with Wide Azimuth (WAZ) and Narrow Azimuth (NAZ) reflection data and assuming that the fractures have rotationally invariant shear compliance. The relative errors in determination of the components of the fourth-rank tensor are substantially larger compared to the second-rank tensor, under the same assumptions. Elastic properties of background media, consisting in horizontal layers without fractures, do not cause azimuthal changes in the reflection coefficient variation with offset. Thus, due to the different nature of these properties compared to fracture tensor components (which cause azimuthal anomalies), simultaneous inversion for background isotropic properties and fracture tensor components requires additional constraints. Singular value decomposition (SVD) and resolution matrix analysis can be used to predict fracture inversion efficacy before acquiring data. Therefore, they can be used to determine the optimal seismic survey design for inversion of fracture parameters. However, results of synthetic inversion in some cases are not consistent with resolution matrix results and resolution matrix results are reliable only after one can see a consistent and robust behaviour in inversion of synthetics with different noise levels.

Based on a large quantity of laboratory ultrasonic measurement data of sedimentary rocks and using Monte Carlo simulation and Backus averaging, we have analyzed the layering effects on seismic anisotropy more realistically than in previous studies. The layering effects are studied for different types of rocks under different saturation conditions. If the sedimentary strata consist of only isotropic sedimentary layers and are brine-saturated, the [Formula: see text] value for the effective transversely isotropic (TI) medium is usually negative. The [Formula: see text] value will increase noticeably and can be mostly positive if the sedimentary strata are gas bearing. Based on simulation results, [Formula: see text] can be determined by other TI elastic constants for a layered medium consisting of isotropic layers. Therefore, [Formula: see text] can be predicted from the other Thomsen parameters with confidence. The theoretical expression of [Formula: see text] for an effective TI medium consisting of isotropic sedimentary rocks can be simplified with excellent accuracy into a neat form. The anisotropic properties of the interbedding system of shales and isotropic sedimentary rocks are primarily influenced by the intrinsic anisotropy of shales. There are moderate to strong correlations among the Thomson anisotropy parameters.

The gas hydrate petroleum system at the 2009 Gulf of Mexico Gas Hydrate Joint Industry Project Leg II (JIP Leg II) Green Canyon 955 (GC955) site shows a complex seismic amplitude and waveform response of highly negative and positive amplitudes with continuous and discontinuous character within inferred gas-hydrate- and gas-bearing sand reservoirs. Logging-while-drilling (LWD) data obtained during JIP Leg II and conventional 3-D seismic data allowed for the identification of thick highly concentrated hydrate layers by integrating rock physics modeling, amplitude and thin layer analysis, and spectral decomposition. Rock physics modeling with constraints from three JIP LWD holes allowed for the analysis of variations in acoustic amplitude characteristics as a product of hydrate saturation, gas saturation, and reservoir thickness. Using the well log-derived acoustic models, thick highly concentrated gas hydrate with and without underlying free gas accumulations have been identified. These results suggest that thick highly concentrated gas-hydrate-bearing sand units (with thicknesses greater than half of the seismic tuning thickness and gas hydrate saturations greater than 50%) underlain by gas can be differentiated from sands containing only gas, but thin gas-hydrate-bearing sand units with low gas hydrate concentrations (with thicknesses less than half of the seismic tuning thickness and gas hydrate saturations less than 50%) are difficult to identify from post-stack seismic amplitude data alone. Within GC955, we have identified six zones with seismic amplitude anomalies interpreted as being caused by gas hydrate deposits with variable lateral extent, thickness and saturation, and in some cases overlying free-gas-bearing intervals. Synthetic seismic images produced from well-log- and model-derived velocity and density distributions mimic similar reflection characteristics in the corresponding field seismic data.

Gas hydrate can be interpreted from seismic data through observation of bottom simulating reflector (BSR). It is a challenge to interpret gas hydrate without BSR. Three-dimensional qualitative and quantitative seismic interpretations were used to characterize gas hydrate distribution and concentration in the eastern Green Canyon area of the Gulf of Mexico, where BSR is absent. The combination of qualitative and quantitative interpretation reduces ambiguities in the estimation and identification of gas hydrate. Sandy deposition and faults are qualitatively interpreted from amplitude data. The 3D acoustic impedance volume was interpreted in terms of high P-impedance hydrate zones and low P-impedance free gas zones. Gas hydrate saturation derived from P-impedance is estimated by a rock physics transform. We interpreted gas hydrate in the sand-prone sediments with a maximum saturation of approximately 50% of the pore space. Sheet-like and some bright spot gas hydrate accumulations are interpreted. The interpretation of sheet-like gas hydrate within sand-prone sediments around faults suggests that fluid moves into the sand zones laterally by conduits. Variations in depths of interpreted gas hydrate zones imply nonequilibrium conditions. Low P-impedance free gas zones within high P-impedance gas hydrate zones imply possible coexistence of hydrate and free gas within the hydrate stability zone. We propose that gas hydrate distribution and concentration are associated with structures, buried sedimentary bodies, sources of gas, and fluid flux.

Studies on how the velocity of [Formula: see text] is affected by temperature and pressure are important for understanding seismic properties of fluid and rock systems with a [Formula: see text] component. We carried out laboratory experiments to investigate velocity of [Formula: see text] in temperatures ranging from [Formula: see text] and pressures ranging from [Formula: see text], in which [Formula: see text] is in a liquid phase. The results show that under the above conditions, in general, the velocity of [Formula: see text] increases as pressure increases and temperature decreases. Near the critical point ([Formula: see text] and [Formula: see text]), the velocity of [Formula: see text] reaches a minimum and has a complicated behavior with temperature and pressure conditions due to the [Formula: see text] transition between gas and liquid phases. We also developed preliminary empirical models to calculate the velocity of [Formula: see text] based on newly measured data.

The velocity and attenuation anisotropy of dry and oil-saturated shale were measured at laboratory ultrasonic frequency by using the transmission technique. Our purpose is to find the variation rules of wave velocity and attenuation in different directions as a function of effective pressure in dry and oil-saturated situations, and those intrinsic factors that result in such anisotropy. Using x-ray diffraction techniques and a scanning electron microscope, the causative factors for the velocity anisotropy are found to be mainly due to the alignment of clay mineral and microcracks. The attenuation of P- and S-waves also shows apparent directional dependence, but different from that of velocities. Attenuation anisotropy can be interpreted in terms of grain and pore geometry. For dry shale samples, the dominant attenuation mechanism is phase hysteresis due to static friction. On one hand, the Biot flow plays a key role in causing wave attenuation for the P-wave propagating parallel to bedding for fluid-saturated samples. On the other hand, the fluid-related attenuation is mainly attributed to the mechanisms of squirt flow for the P-wave propagating vertical to bedding.