[1] The finite element method is used to solve Biot's equations of consolidation in the displacement-pressure (u − p) formulation. We compute one-dimensional (1-D) and two-dimensional (2-D) numerical quasi-static creep tests with poroelastic media exhibiting mesoscopic-scale heterogeneities to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations. The P wave modulus is used to calculate the frequency-dependent attenuation (i.e., inverse of quality factor) and phase velocity of the medium. Attenuation and velocity dispersion are due to fluid flow induced by pressure differences between regions of different compressibilities, e.g., regions (or patches) saturated with different fluids (i.e., so-called patchy saturation). Comparison of our numerical results with analytical solutions demonstrates the accuracy and stability of the algorithm for a wide range of frequencies (six orders of magnitude). The algorithm employs variable time stepping and an unstructured mesh which make it efficient and accurate for 2-D simulations in media with heterogeneities of arbitrary geometries (e.g., curved shapes). We further numerically calculate the quality factor and phase velocity for 1-D layered patchy saturated porous media exhibiting random distributions of patch sizes. We show that the numerical results for the random distributions can be approximated using a volume average of White's analytical solution and the proposed averaging method is, therefore, suitable for a fast and transparent prediction of both quality factor and phase velocity. Application of our results to frequency-dependent reflection coefficients of hydrocarbon reservoirs indicates that attenuation due to wave-induced flow can increase the reflection coefficient at low frequencies, as is observed at some reservoirs.Citation: Quintal, B., H. Steeb, M. Frehner, and S. M. Schmalholz (2011), Quasi-static finite element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media,

Biot’s equations of poroelasticity were solved to study the effects of fracture connectivity on S-wave attenuation caused by wave-induced fluid flow at the mesoscopic scale. The methodology was based on numerical quasistatic pure-shear experiments performed on models of water-saturated rocks containing pairs of either connected or unconnected fractures of variable inclination. Each model corresponded to a representative elementary volume of a periodic medium. Inertial terms were neglected, and hence, the observed attenuation was entirely due to wave-induced fluid flow at the mesoscopic scale. We found that when fractures are not connected, fluid flow in the embedding matrix governs S-wave attenuation, whereas fluid flow through highly permeable fractures, from one fracture into the other one, may dominate when fractures are connected. Each of these energy-dissipation phenomena has a distinct characteristic frequency, with the S-wave attenuation peak associated with flow through connected fractures occurring at higher frequencies than that associated with flow in the embedding matrix. Exploring a range of geometric arrangements of either connected or unconnected fractures at different inclinations, we also observed that the magnitude of S-wave attenuation at both characteristic frequencies shows a strong dependence on fracture inclination. For comparison, we performed quasistatic uniaxial compressibility tests to compute P-wave attenuation in the same models. We found that the attenuation patterns of S-waves tend to differ fundamentally from those of P-waves with respect to fracture inclination. The attenuation characteristics of P- and S-waves in fractured media are thus, largely complementary. With respect to fracture connectivity, we observed that S-wave attenuation tends to follow a specific pattern, indeed, more consistently than that of the P-waves. Our results point to the promising perspective of combining estimates of attenuation of P- and S-waves to infer information on fracture connectivity as well as on the effective permeability of fractured media.

A sample of Bentheim sandstone was characterized using high‐resolution three‐dimensional X‐ray microscopy at two different confining pressures of 1 MPa and 20 MPa. The two recordings can be directly compared with each other because the same sample volume was imaged in either case. After image processing, a porosity reduction from 21.92% to 21.76% can be deduced from the segmented data. With voxel‐based numerical simulation techniques, we determined apparent hydraulic transport properties and effective elastic properties. These results were compared with laboratory measurements using reference samples. Laboratory and computed volumes, as well as hydraulic transport properties, agree fairly well. To achieve a reasonable agreement for the effective elastic properties, we define pressure‐dependent grain contact zones in addition to mineral phases in the digital rock images. From that, we derive a specific digital rock physics template resulting in a very good agreement between laboratory data and simulations. The digital rock physics template aims to contribute to a more standardized approach of X‐ray computed tomography data analysis as a tool to determine and predict elastic rock properties.

Experimental data for foams lead to different values of the elastic moduli depending on the performed test, i.e. compression and tension tests give a different set of parameters than shear and bending tests. This may be explained by the size effect, which depends on the microstructure of the foams. Thus, in this paper, the behaviour of foams is investigated on the basis of both microscopic and macroscopic mechanical models. The microscopic approach is based on a lattice beam model. The solution of this model shows that the boundary-layer effect is strongly local but allows for the explanation of the size effect. Furthermore, the size effect can be included in the macroscopic continuum model by application of a Cosserat formulation. The extended continuum model allows for the independent fit of material parameters to different load cases, i.e. to compression and shear. The solution of the macroscopic Cosserat model permits a relation of the internal length-scale to the average cell size of the microstructure.

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In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface‐coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi‐static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi‐static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex‐valued, frequency‐dependent stress and strain fields. An energy‐based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy‐based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P‐wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi‐static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations.

Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 μm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids’ topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.

Nature will always be an endless source of bioinspiration for man‐made smart materials and multifunctional devices. Impressively, even cutoff leaves from resurrection plants can autonomously and reproducibly change their shape upon humidity changes, which goes along with total recovery of their mechanical properties after being completely dried. In this work, simple bilayers are presented as autonomously moving, humidity‐triggered bending actuators. The bilayers—showing reproducible bending behavior with reversible kinematics and multiway behavior—are studied in terms of their mechanical behavior upon humidity changes. The active layer consists of a highly conducting polymer film based on poly(3,4‐ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) with poly(dimethylsiloxane) (PDMS) as passive layer. The response to humidity is explored with dynamic mechanical thermal analysis and quartz crystal microbalance measurements. Introduction of a composite beam model allows to predict the curvature of the actuators with input from the rheological measurements. It is clearly demonstrated that volumetric strain and Young's modulus, both heavily influenced by the water uptake, dominate the bending behavior and therefore the curvature of the actuators. This loop of rheological characterization coupled with an analytical model allows to predict curvatures of in principle any complex geometry and material combination for moving parts in soft robotics.