Search

Geometric heterogeneities in tight reservoir rocks saturated with a fluid mixture may exhibit different scale distribution characteristics. Conventional models of rock physics based on poroelasticity, which usually consider single‐scale pore structure and fluid patches, are inadequate for describing elastic wave responses. A major challenge is to establish the relationship between the wave response at different spatial scales and frequencies. To address this problem, three sets of observational data over a wide frequency range were obtained from a tight oil reservoir in the Ordos Basin, China. Ultrasonic measurements were made on eight sandstone samples at partial oil‐water saturation at 0.55 MHz. Data from six borehole measurements and seismic profiles were acquired and analyzed at about 10 kHz and 30 Hz, respectively. Analysis of the cast thin sections shows that dissolution pores and microcracks generally develop, with fractal dimensions of the pores ranging from 2.45 to 2.67 for the samples with porosities between 5.1% and 10.2%. Compressional wave velocity and attenuation were estimated from the observed data. The results show that the velocity dispersion from seismic to ultrasonic frequencies is 10.02%, mostly occurring between sonic and ultrasonic frequencies. The attenuation is stronger at higher oil saturation. The relationships between velocity, attenuation, and wavelength were established and can be used for further forward modeling and seismic interpretation studies. A partial saturation model has been derived based on effective differential medium theory and a double double‐porosity model, assuming that the medium contains fractal cracks and fluid patches. The effects of scale and saturation on wave responses are prevalent. Modeling results consistent with observed data show that the radii of cracks and fluid patches range from 0.1 μm to 2.8 mm, affecting ultrasonic, acoustic, and seismic attenuation. The multiscale data and proposed model quantify the relationship between fracture and fluid distributions and attenuation and could be useful for upscaling to the reservoir scale. The study helps improve the understanding of seismic wave propagation in partially saturated rocks, which has potential applications in seismic exploration, hydrocarbon production in reservoirs, and CO2 sequestration in aquifers. Plain Language Summary: The physical properties of the rock and fluid can be inferred from the measured elastic wave responses and energy dissipation characteristics. However, the effects of heterogeneities of different sizes and at different frequencies can hinder studies to quantify wave responses in a partially saturated porous medium, which are usually based on laboratory measurements. A major problem is the difference between observed frequencies and scales: megahertz in the laboratory, 10 of kilohertz in the borehole scale, and hertz in the seismic exploration scale. In this work, the frequency‐ and saturation‐dependent compressional velocity and attenuation are investigated using three geophysical data sets from the same tight reservoirs. A strong velocity dispersion over the measured frequency range is observed. The stronger attenuation at partial saturation may be caused by the multiscale heterogeneities of the pore structure and fluid patch distribution. A fractal poroelasticity model is developed by gradually inserting inclusions of different sizes with compliant pores and liquid patches into a homogeneous host skeleton. The wave responses are significantly affected by scale distribution and saturation. The proposed model, verified by the measured data, can be useful in interpreting the anelasticity of tight heterogeneous reservoirs in a broadband range. Key Points: We investigate how fluid saturation affects wave attenuation and dispersion over a wide frequency range in tight sandstone layersA partial saturation model describes the fractal properties of the layersThe size of the cracks and fluid patches are determined by applying the fractal model to the multiscale data [ABSTRACT FROM AUTHOR]

Seismic wave propagation is affected by wave‐induced local fluid flow between stiff pores and multiscale fractures. To investigate this phenomenon, forced vibration (1–100 Hz) and ultrasonic (106 Hz) measurements are performed on two tight sandstones with complex pore geometry in dry and water‐saturated scenarios. Porosity, permeability, and ultrasonic velocities were also measured at different differential pressures. The results indicate that the nonlinear behavior of these properties is strongly influenced by the presence of cracks, and the correlations between the permeability/ultrasonic velocities and porosity are different. A wave propagation model is then developed in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium to describe the wave anelasticity in a wide frequency band at different pressures. As a result, the model provides good agreement with the measured P‐wave velocity dispersion, and the pore aspect ratio spectrum and crack radii are determined. We then compare the estimated crack radii and pore size distributions from nuclear magnetic resonance spectroscopy. Published data of a tight sandstone and a low porosity sandstone in the frequency range (2–200, 106) and (1–3,000) Hz at different differential pressures are also analyzed to validate the model. The aspect ratios, volume fractions, and radii of pores/cracks are used to describe the measured permeability. The present work can provide new insights into the geophysical properties of reservoir rocks with complex pore geometry. Plain Language Summary: Multiscale cracks exert an important influence on the dispersion and attenuation of broadband acoustic waves. To better understand the underlying mechanism, we measured frequency‐dependent elastic moduli and pressure‐dependent porosity, permeability, and ultrasonic wave velocities of two tight sandstones. These data show that velocity dispersion is observable in water‐saturated rock and that permeability and ultrasonic velocities are differentially correlated with porosity. A proposed wave propagation model, in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium, successfully describes the experimental data and other published data on tight sandstone and low‐porosity sandstone, and aspect ratios, volume fractions, and radii of pores/cracks are determined. Key Points: We propose a model to investigate the effect of multiscale cracks on seismic waves in tight sandstonesThe pore aspect ratio and crack‐radius spectra are estimated at different differential pressuresThe permeability is obtained according to the pore geometry [ABSTRACT FROM AUTHOR]

The elastic properties of rocks depend on the mineral constituents, pore structure, saturating fluids, and stress (loading) conditions. To study these properties, we measured ultrasonic P‐ and S‐wave velocities as a function of the differential (confining minus pore) pressure and propose an unrelaxed double‐porosity acoustoelasticity model, which generalizes the single‐porosity one. The new approach includes the effects of crack closure, based on the David‐Zimmerman model, and the squirt‐flow mechanism, based on the Gurevich model. When cracks are open at low differential pressures, their properties dominate the wave velocity variations, followed by the squirt‐flow mechanism. Then, a transition occurs, where cracks partially close, and the squirt‐flow effect vanishes. At high pressures, cracks close and acoustoelasticity effects prevail. This behavior is observed in sedimentary rocks, whereas in granites, which have a low crack content, the acoustoelastic effect is dominant at all pressures. Plain Language Summary: It is well known that physical properties of rocks are important factors affecting the elastic wave velocities. However, how these properties affect the velocity‐pressure relations are not well understood. We conducted laboratory experiments and observed that the variation of wave velocities is related to crack closure, squirt flow and acoustoelasticity effects. To study the combined effects of these mechanisms, we propose an unrelaxed double‐porosity acoustoelasticity model. The theoretical results compared with the experimental data shows that, in sedimentary rocks, the crack properties dominate the pressure‐dependent velocities, followed by the squirt‐flow mechanism at low differential pressures. At high pressures, cracks approach full closure and the acoustoelasticity effect is the most significant. For low porosity granites, the acoustoelasticity effect dominates at all pressures. Key Points: We measure elastic wave velocities in saturated rocks, to analyze the effects of crack closure, squirt flow and acoustoelasticityTo this purpose, we develop an unrelaxed double‐porosity acoustoelasticity modelCrack closure dominates, followed by the squirt‐flow mechanism at low differential pressures, while acoustoelasticity effects are important at high differential pressures. In granites, the last effect prevails [ABSTRACT FROM AUTHOR]

Laboratory experiments on partially saturated rocks show that seismic attenuation can be significant. The main mechanism, wave‐induced local fluid flow (WILFF), is affected by the spatial fluid distribution, especially in conditions of patchy saturation at different spatial scales. We propose a theory to obtain the seismic properties of partially saturated rocks based on fractal (self‐similar) patches, leading to an effective frequency‐dependent fluid modulus. The model combines the differential effective medium and Biot‐Rayleigh theories, where the patches are inclusions incrementally added, such that the effective fluid calculated in the current addition serves as host fluid in the next one. The analysis shows that adding identical inclusions in one or several steps produces nearly the same results, but the seismic properties depend on the scale range (radius) of the inclusions, fractal dimension Df of the self‐similar distribution, parameter θ $\theta $ of the exponential distribution, mean radius r0 and variance σr2 ${\sigma }_{r}^{2}$ of the Gaussian distribution. Forced‐oscillation experiments were performed on a limestone sample under partial water‐saturation conditions at seismic frequencies (2–500 Hz), to obtain the velocity dispersion and extensional attenuation. The proposed theory provided a reasonable description of these experimental data as well as other published measurements on tight carbonate and Berea sandstone. Plain Language Summary: Seismic wave velocity dispersion and attenuation in partially saturated rock are affected by the size of the fluid patches, and their fractal dimension. To study this phenomenon, we have developed a wave propagation theory, in which the final partially saturated material is incrementally constructed by adding inclusions in size order into a homogenous frame saturated by a host fluid. We analyze the effects of wave‐induced local fluid flow due to the multi‐scale fluid heterogeneities on wave attributes. The broadband wave anelasticity predicted by the model is strongly affected by the scale range of the heterogeneities and their fractal dimension. The theory was compared with experimental data measured on different rock specimens and the fluid distribution characteristics at different saturations were estimated. Key Points: We present a wave propagation theory for partially saturated rocks with a fractal (self‐similar) distribution of fluid patchesWe analyzed the effects of wave‐induced local fluid flow on seismic attributes due to multi‐scale fluid heterogeneitiesWe estimated variations of the fluid distribution characteristics in partially‐saturated rock samples by tying the data to the low frequency measurements [ABSTRACT FROM AUTHOR]

The exploration and exploitation of shale oil is an important aspect in the oil industry. Seismic properties and well‐log data are essential to establish wave‐propagation models. Specifically, the description of wave dispersion and attenuation under complex geological conditions needs proper lithological and petrophysical information. This complex physical mechanism has to be considered if a traditional modeling approach is adopted. In this sense, machine learning (ML) techniques provide new possibilities for this purpose. We compare two deep‐neural‐network (DNN)‐based wave propagation models. In the first (pure data‐driven), a DNN is trained to connect seismic attributes, such as wave velocities, to multivariate functions of rock‐physics properties. By training DNNs with different initial parameters, the uncertainty of the proposed method can be quantified. The second method assumes the form of the wave equations. Then, the elastic constants of the constitutive relations are predicted by DNNs. The resulting dynamical equations describe the dispersion and attenuation and wavefield simulations can be performed to obtain more information. On the basis of a test, the two kinds of wave‐propagation models yield acceptable estimations of the seismic properties, with the second approach showing a broader application because the DNN is trained without S wave data. The methodologies illustrate that the new wave‐propagation model based on ML has high precision and can be general in terms of rheological description. Plain Language Summary: We develop a model to estimate the underground conditions, based on two machine‐learning techniques by using measurement data as input. The first uses pure data‐driven surrogate models, while the second is based on the classical wave propagation model in fluid‐saturated porous medium proposed by Biot, where deep neural networks predict the elastic coefficients so that the theoretical seismic properties match the actual measurements. The two models are tested on the basis of data from five wells located in a shale‐oil reservoir area. Compared with the pure data‐driven model, the wave‐equation method may be used to predict more reservoir properties. Key Points: Machine‐learning methods are proposed to drive wave propagation based on seismic dataOptimal prediction results of seismic attributes are obtained by feeding rock‐physics properties into the trained modelsThe proposed method has the potential to obtain additional physical quantities and shows a broad application prospect [ABSTRACT FROM AUTHOR]

The fractal texture (or fabric) of porous media, which supports fluid flow at different scales, is the main cause of wave anelasticity (dispersion and attenuation) on a wide range of frequencies. To model this phenomenon, we develop a theory of wave propagation in a fluid saturated infinituple‐porosity media containing inclusions at multiple scales, based on the differential effective medium (DEM) theory of solid composites and Biot‐Rayleigh theory for double‐porosity media. The dynamical equations are derived from first principles, that is, based on the strain (potential), kinetic, and dissipation energies, leading to generalized stiffness and density coefficients. The scale of the inclusions can be characterized by different distributions. The theory shows that the anelasticity depends on the size (radius) of the inclusions, parameter θ (exponential distribution), mean radius r0 and variance σr2 (Gaussian distribution) and the fractal dimension Df (self‐similar distribution). When Df = 2, θ = 1 and σr2 = 4, the three distributions give the same P‐wave velocities and attenuation, since each added inclusion phase has nearly the same volume fraction. For the modeling results, the range of anelasticity of Df = 2.99/θ = 1/σr2 = 4 is broader than that of Df < 2.99/θ < 1/σr2 < 4. To confirm the validity of the model, we compare the results with laboratory measurements on tight sandstone and carbonate samples in the range 1 Hz–1 kHz, Fox Hill sandstone (5 Hz–800 kHz) and field measurements of marine sediments (50 Hz–400 kHz). This comparison shows that the model successfully describes the observed anelasticity. Key Points: We develop a theory of wave propagation in infinituple‐porosity media based on multiple‐scale inclusionsWe consider different distributions of the size of the inclusions aimed to model the anelasticityThe model provides a reasonable explanation of broadband laboratory and field data [ABSTRACT FROM AUTHOR]

There is recent experimental evidence that the effective pressure coefficient for pore volume exceeds unity in limestones with dual porosity structure. Within the realm of linear poroelastcity, this means that the unjacketed pore modulus is negative. This would be a rather unusual rock behavior since it implies that the pore volume increases for a positive pressure increment during hydrostatic compression. Generally, any deviation of the unjacketed pore modulus from strictly positive mineral bulk modulus means that the deformation is inhomogeneous. We critically examine these observations by attempting to reconcile them with the poroelastic constitutive equations of micro‐inhomogeneous rocks that encompass inhomogeneous deformations. Consistency checks among measured poroelastic constants reveal that the measurement accuracy of pore volume changes concurring with the deformation experiments is not as high as desired. However, assigning moderate variations to the measured pore volume changes either due to random or systematic measurement errors, we show that the experimental observations are indeed reconcilable with the constitutive poroelastic equations. Hence, the negative unjacketed pore modulus observed is deemed plausible though overestimated. Within the poroelasticity framework for micro‐inhomogeneous rocks, a negative unjacketed pore modulus is the result of a partial localization of elastic strain energy in the fluid space. This in turn could be caused by dissolved calcite particles that block thin pore throats and thus generate temporary fluid pressure compartmentalization. A far‐reaching consequence of a negative unjacketed pore modulus is that description of the undrained bulk modulus in rocks with dual porosity structure is more complicated than previously thought. Key Points: Critical examination of recently reported laboratory measurements reveals a negative unjacketed pore modulus in micro‐inhomogeneous rockThis unusual rock behavior is reconcilable with the theory of poroelasticity of micro‐inhomogeneous rocksMicro‐inhomogeneity in mono‐mineralic rocks is due to variability of pore sizes [ABSTRACT FROM AUTHOR]

Understanding the effect of temperature on physical properties of rocks is important to develop deep oil, gas, and geothermal resources. Velocity‐porosity relations are essential ingredients for a seismic rock physics model. However, relatively little effort has thus far been made to capture the temperature effect on velocity‐porosity relations. To overcome this limitation, we develop a double‐porosity model based on Biot's theory. This model is complemented with the Batzle‐Wang empirical equations for the pressure and temperature dependence of the pore fluid, as well as the David‐Zimmerman model to quantify temperature‐dependent microcrack density. The combined model is tested on carbonate and hyaloclastite samples, for which the variation of ultrasonic P‐wave velocity with temperature has been measured in the laboratory. Comparison of the predicted P‐wave velocity with the measured velocity shows that the proposed model is capable of quantitatively describing the rock velocity‐temperature and velocity‐porosity relations. We found that, for our rock samples, the temperature‐dependent change of microcrack porosity was not the dominant factor affecting the velocity‐porosity relation and that the temperature‐dependent fluid properties had a greater effect. The proposed model also predicts that the velocity dispersion and the attenuation peak of P‐waves in carbonate rock samples become less pronounced with increasing temperature. Key Points: We develop a temperature‐dependent double‐porosity model for analyzing joint effects of pore fluid and microcracks on rock anelasticityModeling experimental data shows that temperature‐dependence of fluids dominates velocity‐temperature relations in rocksFor different pore fluids, there is a characteristic trend of velocity‐porosity at different temperatures [ABSTRACT FROM AUTHOR]

We have performed ultrasonic measurements on tight siltstone samples to obtain the P wave coda and intrinsic attenuations using a single isotropic scattering model and the spectral ratio method. The results indicate that attenuation is predominantly caused by scattering. Intrinsic attenuation increases with gas saturation and permeability and decreases with grain size, whereas coda attenuation is stronger under partial saturation conditions and increases with grain size. Porosity and mineral composition do not have significant effects on attenuation. The triple‐porosity and scattering models are used to simulate the intrinsic and scattering attenuations, respectively. The results show that the intrinsic attenuation is predominately caused by wave‐induced fluid flow between microcracks/micropores and intergranular pores. The model incorporating the scattering effects of microcracks underestimates the scattering loss in the coda, which may thus be better explained by heterogeneities in the clustering structure of grains. Key Points: Coda and intrinsic attenuations in siltstones are estimated with a single isotropic scattering model and the spectral ratio methodUltrasonic P wave coda attenuation in oil‐water partially saturated siltstones is stronger than that at the full saturationsCoda and intrinsic attenuations depend on permeability, grain size, and skewness but generally do not depend on mineral content [ABSTRACT FROM AUTHOR]

We develop a numerical algorithm for simulation of wave propagation in linear nonisothermal poroelastic media, based on Biot theory and a generalized Fourier law of heat transport in analogy with Maxwell model of viscoelasticity. A plane wave analysis indicates the presence of the classical P and S waves and two slow waves, namely, the Biot and the thermal slow modes of propagation, which present diffusive behavior under certain conditions, depending on viscosity, frequency, and the thermoelastic constants. The wavefield is computed with a direct meshing method using the Fourier differential operator to calculate the spatial derivatives. We propose two alternative time‐stepping algorithms, namely, a first‐order explicit Crank‐Nicolson method and a second‐order splitting method. The Fourier differential operator provides spectral accuracy in the calculation of the spatial derivatives. Modeling the thermal diffusive mode is relevant for high‐temperature high‐pressure fields and since it leads to mesoscopic attenuation by mode conversion of the fast waves to the thermal waves. Key Points: The differential equations of dynamic thermoporoelasticity are solved with a direct grid methodThe solver is based on the Fourier pseudospectral method to compute the spatial derivativesThe simulation reveals the behavior of four wave modes, namely, the fast P, slow P, S, and the thermal wave-diffusion field [ABSTRACT FROM AUTHOR]

Permeability is an important rock property in exploration geophysics. Darcy's law assumes a steady‐state regime and constant permeability. However, recent studies showed that the effects of fluid viscosity and pore geometry on permeability cannot be neglected. The periodic variation of pore fluid pressure gradient due to elastic wave propagation induces the oscillated fluid flow. We consider a Maxwell fluid in a 3‐D pore network subject to harmonic oscillations. The network is based on the Voronoi method, which provides a realistic connectivity. The permeability of polyethylene oxide and cetylpyridinium chloride and sodium salicylate solution have been simulated. The results show that permeability is constant at frequencies less than several kHz and rapidly decreases to extremely low values as frequency tends to infinite. In addition, we find that fluid mainly flows in sparse‐large pore networks at low frequencies and in dense‐small pore networks at high frequencies. The Maxwell fluid shows significant permeability peaks related to the mean coordination number, indicating that there exists an optimal network connectivity at which fluid flow is maximum. These results have been central to understand how fluid flows in natural reservoir rocks. The permeability variations versus frequency, fluid rheology, and pore connectivity provide key information of reservoir fluid properties and pore network structure. The results indicate that it is questionable whether Darcy static permeability can be applied at high frequencies. Key Points: We study how fluid rheology and pore connectivity affect the permeability of pore networksFluid rheology has a significant effect on permeability; peaks are observed on permeability‐frequency curves for a Maxwell fluidPore‐network connectivity plays a key role, since the pore radius and mean coordination number lead to permeability variations for the same porosity [ABSTRACT FROM AUTHOR]