Mesoscopic Heterogeneities Research Articles

Predicting peak tensile stress in mesoscale concrete considering size effects: A data-physical hybrid-driven approach

The size effect and strength discreteness observed in concrete stem primarily from its mesoscopic heterogeneity. Despite this understanding, establishing a clear relationship between the macroscopic and mesoscopic mechanical behaviors remains a considerable challenge. While some advancements have been made in studying the size effect of concrete, particularly regarding the rate effect, there has been relatively less emphasis on addressing the influence of random meso-component distribution. To investigate the tensile behaviors of concrete across varying low strain rates (10−5 s−1∼10−1 s−1) and model sizes, a meso-model dataset was established comprising double edge notched concrete with mortar matrix, coarse aggregate, and interface transition zone. A convolutional neural network introducing physical parameters was implemented to capture the potential non-linear relationship of concrete from meso-structure, strain rate and model size to tensile peak stress. Subsequently, the data-driven solution for the “Static and Dynamic unified” Size Effect Law (SD-SEL) in concrete tensile strength was developed by deconstructing the back propagation (BP) neural network to enhance its rationality, followed by the verification of the proposed formula. The findings indicate that the Data-Physical Hybrid-Driven approach effectively analyzes the mechanical response of concrete without the need for complex mechanical derivations, offering a promising tool for studying the size effect of composite materials.

A numerical extension of White's theory of P-wave attenuation to non-isothermal poroelastic media.

Mesoscopic P-wave attenuation in layered, partially saturated thermo-poroelastic media is analyzed by combining the theories of Biot poroelasticity and Lord-Shulman thermoelasticity (BLS). The attenuation is quantified by estimating the quality factor Q. The mesoscopic attenuation effect, commonly referred to as wave-induced fluid flow (WIFF), is the process that converts fast compressional and shear waves into slow diffusive Biot waves at mesoscopic heterogeneities larger than the pore scale, but much smaller than the dominant wavelengths. This effect was first modeled in White's isothermal theory by quantifying the seismic response of a periodic sequence of planar porous layers that are alternately saturated with gas or water. This work presents a numerical extension of White's theory for the non-isothermal case in this type of sequence. For this purpose, an initial-boundary-value problem (IBVP) for the BLS wave propagation equations is solved using the finite element method, where the particle velocity field is recorded at uniformly distributed receivers. The quality factor is estimated using spectral-ratio and frequency-shift methods. The Q-estimates show that thermal effects influence the attenuation of the P-wave and the velocity dispersion compared to the isothermal case.

Laboratory experiments and theoretical study of pressure and fluid influences on acoustic response in tight rocks with pore microstructure

AbstractWave‐induced fluid flow is considered to be a major source of seismic attenuation and dispersion in porous rocks. From the physical description of partially saturated reservoirs, numerous analytical solutions based on upscaling homogenization theories have been employed to calculate equivalent frequency‐dependent poroelastic media. Nevertheless, dispersion and attenuation predictions are often not reasonably consistent with laboratory and field measurements in a broad frequency range, particularly due to influences of biphasic fluids and their distribution, presence of heterogeneities on various length scales, and pore microstructure. We investigate the role of pore microstructure on pressure and fluid saturation dependence of elastic velocities in tight sandstones. Previous work points out that differentiating the impacts of heterogeneities at various scales on dispersion within seismic exploration and sonic frequencies can be very difficult. In practice, this is because fluid‐related dispersion mechanisms are impossible to be independent. Thus, it is important for a theoretical and more quantitative analysis of the relative contribution of interrelated energy dissipation processes through a better understanding of combined influences due to the presence of microscopic and mesoscopic heterogeneities. Based on microscopic squirt flow and mesoscopic flow in a partially saturated medium, we develop a poroelastic model that allows evaluating the overall frequency‐dependent dispersion via considering a random distribution of fluid heterogeneities as well as the broadly distributed aspect ratio of compliant pores. Experimental validation of the model is accomplished via a comprehensive comparison of predictions with measurements of partially saturated velocities versus pressure and fluid for sandstones with specific pore microstructures.

Research on the crack resistance of semi-flexible pavement mixture based on meso-heterogeneous model

Semi-Flexible Pavement (SFP) material, prepared by pouring cement-based grouting material into the voids of a porous asphalt mixture, has good load bearing capacity and excellent resistance to rutting. It is gaining increased applications in areas where permanent deformation of asphalt mixtures is a concern. When applied as the pavement surface course, the major distress observed in SFP is cracking. Currently, there is a lack of comprehensive understanding of the cracking mechanism of SFP. To improve such understanding, this study investigated the effects of fracture parameters of asphalt mortar and asphalt-aggregate interface on the crack resistance of SFP materials through laboratory experiments and numerical simulation using the finite element method. Firstly, a three-point bending test was performed on a beam SFP specimen. A multi-scale mesoscopic heterogeneity model was then established based on the mesoscopic structure of the specimen and calibrated and validated using the load-displacement curves and the cracking process features. With the validated model, the effects of different fracture parameters on the beam cracking process were investigated. It was found that the load-bearing capacity of SFP increased with the increase of the tensile strength of asphalt mortar and asphalt-aggregate interface in a certain range, while the crack propagation rate after crack initiation also increased. An increase in the fracture energy of asphalt mortar and asphalt-aggregate interface delayed the crack propagation rate, but with an attenuative effect with the increase of fracture energy. Based on the actual test conditions, the desirable range of key cracking parameters of SFP materials were recommended.

Mesoscopic chemical heterogeneities in laser powder bed fused CoCrMo and Ni mixed powders and their effect on the mechanical properties

Microstructural heterogeneity is a feature of common occurrence in alloys additively manufactured using techniques such as laser powder bed fusion (LPBF). Additionally, chemical heterogeneities can arise both at micro- and meso-scales, especially when powder mixtures are used. While such chemical heterogeneities are considered undesirable hitherto, recent studies show that they may be beneficial in tailoring for the desired mechanical property combinations. In this study, we fabricated a graded alloy coupon with the mixed powders of the CoCrMo alloy and elemental Ni and investigated the microstructural and mesoscopic chemical heterogeneities in it. Chemical heterogeneities, which are either rich in Ni or CoCrMo, were observed due to the incomplete mixing of the powders. Banded patterns, with alternating layers that are enriched with different chemical species, were also observed. Distinct stacking fault energies between these chemical heterogeneities result in distinct deformation mechanisms; while planar slip and strain-induced martensitic transformation occur in the CoCrMo-rich heterogeneities, homogenous deformation associated with the wavy slip occurs in the Ni-rich ones. Detailed mechanical property characterizations show that the microscale chemical segregation not only strengthens the matrix but also improves the work hardening ability of the bulk material through kinematic hardening mechanism. These findings substantiate the key design principles for exploiting chemical segregations that form during in situ alloying for simultaneous enhancement of the strength and ductility in AM alloys.

Stability analysis of jointed rock mass in large underground caverns based on multi-scale analysis method

Random defects at different scales are the crucial cause of damage evolution and cascade transfer in rocks. For a large-scale underground cavern, the rock mesoscopic heterogeneity and macroscopic random joints are inevitable factors of rock stability, which needs to be further studied. In this study, a multi-scale analysis method for the stability of jointed rock mass in large underground caverns is proposed. The statistical damage theory is used to describe the mesoscopic heterogeneous rock damage. Monte Carlo simulation and measured joint geometric information are combined to reconstruct the macroscopic random joint network of rock mass. The integrated analysis of mesoscopic heterogeneity of rock and the macroscopic response of random jointed rock mass is performed by Rock Failure Process Analysis (RFPA) system. The research shows that the existence of joint affects the failure mode of rock mass and strengthens the heterogeneity. The representative elementary volume (REV) of jointed rock mass and its equivalent mechanical parameters are determined and used in the stability analysis of a large-scale underground cavern project. Results show a good agreement with the in-situ monitoring deformation of surrounding rock mass, which verifies the effectiveness of the rock mass multi-scale analysis method.

A numerical assessment of local strain measurements on the attenuation and modulus dispersion in rocks with fluid heterogeneities

SUMMARY The forced oscillation method is widely used to investigate intrinsic seismic wave dispersion and attenuation in rock samples by measuring their dynamic stress–strain response. However, using strain gauges to locally measure the strains on samples surfaces can result in errors in determining the attenuation and moduli of rocks with mesoscopic scale heterogeneities. In this study, we developed a 3-D numerical model based on Biot's poroelastic theory to investigate the effect of strain gauge location, number and size on attenuation and dispersion in response to wave-induced fluid flow. Our results show that increasing the strain gauge length, number, and size can reduce the error between local and bulk responses. In a homogeneous and isotropic rock with a quasi-fractal fluid heterogeneity at 12 per cent gas saturation, the relative error between local and bulk responses stays below 6 per cent when the strain gauge length surpasses 8.6 times the correlation length. As the gas saturation becomes larger, the ratio minimally changes non-monotonically, initially increasing and then decreasing. We also used the Monte Carlo method to demonstrate that local laboratory measurements can approximate the reservoir-scale response with a minimum relative error of 1.5 per cent as the sample number increases. Our findings provide guidance for (i) interpreting local low-frequency measurements in terms of bulk properties of rock and (ii) upscaling lab measurements to reservoir-scale properties.

Formation Mechanism of a Heterogeneous Network in Epoxy Resins

In general, the network structure formed in epoxy resins is heterogeneous, and its extent is dependent on the curing temperature. Based on Fourier-transform infrared spectroscopy in conjunction with coarse-grained molecular dynamics simulations, we herein discuss the origin of mesoscopic heterogeneity in an epoxy resin composed of a typical epoxy base and diamine hardener, which react with each other in two steps. The rate balance of the first and second step reactions, which led to chain extension and branching, respectively, depended on the curing temperature; at a higher temperature, the second-step reaction became faster. Since the reaction proceeded more slowly at lower temperatures, a homogeneous domain was formed as unreacted substances were incorporated into the network. At higher temperatures, on the other hand, the reaction proceeded rapidly before unreacted substances were incorporated into the network, leaving isolated small fragments and nanoscale voids or free spaces in the domain. We also found that an actively reacting domain with a length scale of several tens of nanometers was formed even at a conversion lower than the gel point, regardless of the curing temperature. The connection of domains was also key to better understanding the temperature dependence of the hierarchical heterogeneity. The final network was found to be denser and more homogeneous at a lower temperature, while heterogeneous with many free spaces at a higher temperature. Our molecular picture of the network formation drawn by combining experimental and simulation techniques advances our current understanding of the heterogeneity formed in epoxy resins.

Polymorphic Uncertain Structural Analysis: Challenges in Data‐Driven Inelasticity

AbstractThis contribution addresses polymorphic uncertainty quantification within structural analysis of reinforced concrete structures composed of heterogeneous concrete and reinforcement (e.g. steel bars or carbon fibres). The macroscopic material behaviour of concrete is strongly dependent on the mesoscopic heterogeneities, which are considered by multiscale modelling. The heterogeneous mesoscopic material behaviour is characterized by representative volume elements (RVE) and the transition of scales is carried out by utilizing numerical homogenization methods.The concept of data‐driven computational mechanics enables material model free finite element analyses directly based on material data sets, overcoming the necessity of assumptions in material modelling. This approach mainly consists in assigning a stress‐strain state, which leads to a minimum of an objective function and fulfils equilibrium as well as compatibility constraints of every integration point. Inelastic material behaviour is taken into account through the definition of local data sets containing only data set states which are consistent with respect to the past local history . The realistic modelling of structures requires the consideration of data uncertainty. Generalized polymorphic uncertainty models are utilized in order to take variability, imprecision, inaccuracy and incompleteness of material data into account by combining aleatoric and epistemic uncertainty models.In this contribution, a computationally efficient approach for the consideration of data sets containing uncertain stress‐strain states within data‐driven analysis based on information reduction measurements is presented. Due to generalization, the approach is applicable to various aleatoric, epistemic and polymorphic uncertainty models. The identification of admissible local data sets for taking inelastic material behaviour into account within data‐driven analysis is realized by an energy based history parametrization which is extended to uncertain data. An approach for the efficient selection of these local data sets is presented and challenges in data‐driven inelasticity, particularly in the use case of polymorphic uncertain analyses of concrete structures, are pointed out.

Modeling the Effect of Multiscale Heterogeneities on Wave Attenuation and Velocity Dispersion

Wave attenuation and velocity dispersion are of great significance to fluid evaluation in fluid-saturated rocks. Inspired by the double-porosity and cracked porous elastic wave theory, we develop a multi-scale heterogeneities elastic wave theory to better describe the attenuation characteristics caused by wave-induced fluid flow at various scales in saturated rocks. First, we introduce penny-shaped and narrow-shaped coupled cracks into double-porosity model. The potential energy function is given by the stress-strain relationship. The kinetic energy function and dissipation function are derived based on the generalized Biot theory. Next, we derive the multi-scale wave equations through the Lagrange equation and obtain three compressional waves and one shear wave. According to the novel wave equations, we work out the phase velocity and inverse quality factor in double-porosity and cracked media based on plane-wave analysis. The numerical simulation results show that there are four attenuation peaks in the whole frequency band, corresponding to mesoscopic fluid flow, two kinds of squirt flow and Biot flow respectively. Then, we investigate the effect of poroelastic parameters on wave propagation. It is found that porosity, inclusion size, crack aspect ratio and other parameters significantly affect the dispersion and attenuation. Finally, we compare experimental data and theoretical prediction. Moreover, the new elastic wave theory can degenerate into classical Biot’s theory, double porosity theory and pore-crack theory under certain conditions, which demonstrates the consistency of this method. The proposed theory can better predict and simulate the wave propagation by incorporating the effects of microscopic, mesoscopic, and macroscopic heterogeneities.

A physical modelling study of waveform amplification effects of reservoir heterogeneity on time‐lapse seismic attribute analysis

AbstractHydrocarbon depletion causes fluid saturation and pressure changes, resulting in perturbations in reservoir elasticities and, hence, observable time‐lapse (or 4D) seismic responses. Using controlled physical modelling experiments, we aim to evaluate reservoir heterogeneities‐related scattering effects on seismic signatures and assess pore‐fluid substitution impacts on the 4D seismic attributes. Physical modelling experiments reveal that wave propagations in heterogeneous rocks produce substantially magnified 4D attribute differences related to fluid replacements, contrary to seismic features in homogeneous rocks. In particular, reflected waveforms from the gas‐filled scenario exhibit more apparent discontinuities and amplitude variations than water‐ and oil‐saturated scenarios in the heterogeneous regions. It is interesting to see that fluid substitution‐induced 4D seismic differences are observable within the weakly heterogeneous region but significantly strong within the highly heterogeneous region. Although it is expected that substituting oil with water produces weak perturbations in reservoir elasticities, the 4D difference observations between time‐varying records are apparent. This implies that in addition to reservoir heterogeneities‐induced amplifying effects, 4D seismic anomalies are also caused by pore‐fluid changes. Due to mesoscopic rock heterogeneities, seismic responses are complicated, and 4D difference estimates will be amplified strongly and, thus, unable to quantify variations in fluid saturation appropriately. This implies that obvious difference volumes in the underburden regions do not necessarily correspond to significant variations in pore‐fluid. Subsequently, two end‐member rock physics models were applied to predict the widest range of velocity variations and pore‐fluid behaviours. Although mesoscopic heterogeneities cause varying degrees of difficulties for hydrocarbon detection, the deformed waveform‐induced seismic attribute anomalies, which are often greatly amplified, may be beneficial for more accurately identifying reservoir fluids and monitoring their minor variations in practice.

Impact of the plastic deformation microstructure in metals on the kinetics of recrystallization: A phase-field study

The sensitivity of recrystallization kinetics in metals to the heterogeneity of microstructure and deformation history is a widely accepted experimental fact. However, most of the available recrystallization models employ either a mean field approach or use grain-averaged parameters, and thus neglecting the mesoscopic heterogeneity induced by prior deformation. In the present study, we investigate the impact of deformation-induced dislocation (subgrain) structure on the kinetics of recrystallization in metals using the phase-field approach. The primary focus here is upon the role of dislocation cell boundaries. The free energy formulation of the phase-field model accounts for the heterogeneity of the microstructure by assigning localized energy to the resulting dislocation microstructure realizations generated from experimental data. These microstructure realizations are created using the universal scaling laws for the spacing and the misorientation angles of both the geometrically necessary and incidental dislocation boundaries. The resulting free energy is used into an Allen-Cahn based model of recrystallization kinetics, which are solved using the finite element method. The solutions thus obtained shed light on the critical role of the spatial heterogeneity of deformation in the non-smooth growth of recrystallization nuclei and on the final grain structure. The results showed that, in agreement with experiment, the morphology of recrystallization front exhibits protrusions and retrusions. By resolving the subgrain structure, the presented algorithm paves the way for developing predictive kinetic models that fully account for the deformed state of recrystallizing metals.

Mesoscopic attenuation mechanism in VTI seismic anisotropy

In this work, the effect of mesoscopic heterogeneity in the attenuation and scattering of waves propagating in poroelastic media is studied analytically and numerically. In case of heterogeneity size lower than the dominant wavelength, the medium composed of interbedded poroelastic layers of different lithology or by layers saturated with different fluids behaves as a homogeneous VTI medium. We developed frequency dependent expressions to estimate attenuation and phase velocity in such media. The results indicate that the behavior of the slow and fast compression waves depend on the frequency and direction of propagation. When an wave propagates parallel to the symmetry axis, attenuation of the rapid P wave becomes highest while the attenuation of the slow P wave becomes lowest. The behavior of the acoustic waves confirms that the slow P wave responds to the fluid flow associated with heterogeneities that generate pressure gradients on the borders that separate poroelastic media. The wave propagating in all directions manifests the mesoscopic mechanism at low frequency and the Biot's one at high ones. The dominant mechanism depends on the path of propagation and the degree of heterogeneity of the poroelastic compound.

Numerical investigation on effect of randomized mesoscopic heterogeneity in stochastically located arbitrary shaped aggregates in impact response of reinforced concrete

A numerical methodology is endeavoured to infuse the inherent heterogeneity of reinforced concrete (RC) when subjected to low-velocity impact loading contrary to the existing practice of homogenized model. Coarse aggregates are inserted as a form of inclusion with varying shape, material properties and arranged randomly across the volume. Weibull statistics has been used to quantify the random variation of material properties. A suitable damage plasticity model is used with mapped inelastic and cracking behaviour for a given grade of concrete. After validating the present model with experimental evidences in literature, the plastic work done and the energy dissipation are investigated. It was observed that the plastic work accumulation at supports loses its symmetric pattern, particularly at time-instant of maximum deformation, when present formulation of heterogeneity is considered. This significantly affects the damage accumulation and nucleation of cracks during the impact event as observed in the global failure patterns across sections at different longitudinal locations.

Nanoscale Sub-Compartmentalization of the Dendritic Spine Compartment.

Compartmentalization of the membrane is essential for cells to perform highly specific tasks and spatially constrained biochemical functions in topographically defined areas. These membrane lateral heterogeneities range from nanoscopic dimensions, often involving only a few molecular constituents, to micron-sized mesoscopic domains resulting from the coalescence of nanodomains. Short-lived domains lasting for a few milliseconds coexist with more stable platforms lasting from minutes to days. This panoply of lateral domains subserves the great variety of demands of cell physiology, particularly high for those implicated in signaling. The dendritic spine, a subcellular structure of neurons at the receiving (postsynaptic) end of central nervous system excitatory synapses, exploits this compartmentalization principle. In its most frequent adult morphology, the mushroom-shaped spine harbors neurotransmitter receptors, enzymes, and scaffolding proteins tightly packed in a volume of a few femtoliters. In addition to constituting a mesoscopic lateral heterogeneity of the dendritic arborization, the dendritic spine postsynaptic membrane is further compartmentalized into spatially delimited nanodomains that execute separate functions in the synapse. This review discusses the functional relevance of compartmentalization and nanodomain organization in synaptic transmission and plasticity and exemplifies the importance of this parcelization in various neurotransmitter signaling systems operating at dendritic spines, using two fast ligand-gated ionotropic receptors, the nicotinic acetylcholine receptor and the glutamatergic receptor, and a second-messenger G-protein coupled receptor, the cannabinoid receptor, as paradigmatic examples.

Influence of loading rate on failure property of concrete twin fibers pull-out test

Under the premise of considering the mesoscopic heterogeneity of each phase material, we use the dynamic finite element analysis software RFPA^3D-dynamics to establish a three-dimensional dynamic numerical model of concrete twin fibers pull-out test and study the effect of different loading rates on fracture performance of concrete twin fibers pull-out specimens. Based on the elastic damage constitutive relation of mesoscopic elements, the failure diagram of the whole process, distribution curve of interfacial shear stress, acoustic emission (AE) histogram, accumulative AE curves and AE energy analysis of each specimen have been obtained. The results show that the fracture process of concrete twin fibers pull-out specimens under different loading rates goes through the following stages: elastic stage, elastic-plastic damage stage, interface debonding stage and steel fiber pull-out stage. The higher the loading rate, the faster the crack propagation and the interfacial shear stress transmission, and the higher the cumulative acoustic emission counts and the total acoustic emission energy.

Numerical investigation of mining-induced strata disturbances using a discontinuous deformation and displacement coupling method

Strata movement and ground subsidence caused by mining have a significant influence on the safety and stability of the goaf. By taking the mesoscopic heterogeneity of rock masses into account, the discontinuous deformation and displacement (DDD) method was applied to simulate the whole failure process of overlying strata after coal mining under different advancing distances of the working face. The results show that key strata would not be broken when the working face was advanced by 30 m. When the advancing distance increased to 50 m, the first key stratum was broken; when it went up to 70 m, both the first and the second key strata were broken and collapsed successively. Moreover, the bed separation of strata had become particularly obvious and a three-zone phenomenon—including collapsed zone, fractured zone, and continuous deformation zone—presented throughout the whole rock mass when the distance rose to 90 m. As the working face is advanced by increasing distances, there are increases in the ranges of deformation, disturbance, and damage in the overlying strata, as well as surface settlement. Meanwhile, the gradual collapse process of the strata is further analyzed in terms of the background-stress evolution; i.e., stress accumulation, stress shadow, and stress transference. Furthermore, it has been proven that the DDD method is an effective approach to reproduce the whole process of strata collapse and macro instability from small deformation, crack initiation, and propagation to block translation, rotation, and contact, which is crucial for predicting strata movement and surface subsidence.

Numerical simulation and modeling of a poroelastic media for detection and discrimination of geo-fluids using finite difference method

Seismic numerical modeling technique provide most suitable way for the simulation of wave propagation through subsurface rocks and play an essential role in seismic interpretation, seismic inversion and in evaluating and designing a seismic survey. In order to delineate subsurface more precisely, different approaches are proposed for numerical modeling in which the solutions of Biot’s poroelastic equation are given by using reflectivity, finite element and finite difference algorithms. In current study, a finite difference forward modeling method is proposed to quantify the variation in wave properties during its propagation in a poroelastic media exhibiting mesoscopic heterogeneity due to the existence of three phase fluids. The Biot’s poroelastic wave equations are resolved and a generalized finite difference technique in time domain (FDTD) is used to examine seismic responses in a poroelastic media saturated with three phase fluids. So that the ability to detect geo-fluids through forward modeling technique can be improved. The accuracy of the simulation will lay a good foundation for the follow up work and will enhance our understandings about wave propagation through multi-phase poroelastic media and will also assist in detection and discrimination between fluids of different nature. Also, the proposed approach is of great significance for imaging and prediction of subsurface structures and distribution of fluids.

Analysis of the frequency dependence characteristics of wave attenuation and velocity dispersion using a poroelastic model with mesoscopic and microscopic heterogeneities

ABSTRACTSeismic waves passing through partially saturated porous rocks produce pressure gradients in the fluid phase, and, hence, the resulting fluid flow is accompanied by various length scales. The major mechanism responsible for seismic attenuation and dispersion is arguably known as wave‐induced fluid flow between inhomogeneities of microscopic, mesoscopic and macroscopic scales. Previous studies have revealed that differentiating the influence of heterogeneities at various scales on wave attenuation within seismic exploration and sonic frequencies, nevertheless, is very difficult. This is because wave attenuation mechanisms due to different heterogeneities are practically impossible to be unrelated. Therefore, it is important for a more quantitative interpretation of the relative contribution of inter‐dependent energy loss mechanisms through improved understanding of the combined influences associated to the microscopic squirt flow and mesoscopic fluid flow. We introduce a scaled poroelastic model to evaluate frequency‐dependent attenuation and velocity dispersion characteristics by considering the combined presence of microscopic and mesoscopic heterogeneities. To do so, the capillarity effects are incorporated into the poroelastic model with random distributions of the sizes of mesoscopic‐scale heterogeneities. A range of pertinent scenarios are calculated, and the acoustic properties indicate wave attenuation decreases whereas the phase velocity increases corresponding to additional capillary forces. Meanwhile, numerical results of the proposed model were compared with experimental measurements of a tight sandstone to examine its validity. Results of numerical simulations suggest that seismic reflections produce more complicated signatures in the presence of an interbedded structure of a reservoir exhibiting velocity dispersion. Therefore, the proposed procedure can help in assessing the sensitivities of frequency‐dependent seismic signatures to reservoir fluid mobility and patch heterogeneities.

Extended Gassmann equation with dynamic volumetric strain: Modeling wave dispersion and attenuation of heterogeneous porous rocks

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.