Fluid Pressure Gradient Research Articles

Incorporating cross-voxel exchange for the analysis of dynamic contrast-enhanced imaging data: pre-clinical results

Tumours exhibit abnormal interstitial structures and vasculature function often leading to impaired and heterogeneous drug delivery. The disproportionate spatial accumulation of a drug in the interstitium is determined by several microenvironmental properties (blood vessel distribution and permeability, gradients in the interstitial fluid pressure). Predictions of tumour perfusion are key determinants of drug delivery and responsiveness to therapy. Pharmacokinetic models allow for the quantification of tracer perfusion based on contrast enhancement measured with non-invasive imaging techniques. An advanced cross-voxel exchange model (CVXM) was recently developed to provide a comprehensive description of tracer extravasation as well as advection and diffusion based on cross-voxel tracer kinetics (Sinno et al 2021). Transport parameters were derived from DCE-MRI of twenty TS-415 human cervical carcinoma xenografts by using CVXM. Tracer velocity flows were measured at the tumour periphery (mean 1.78–5.82 μm.s−1) pushing the contrast outward towards normal tissue. These elevated velocity measures and extravasation rates explain the heterogeneous distribution of tracer across the tumour and its accumulation at the periphery. Significant values for diffusivity were deduced across the tumours (mean 152–499 μm2.s−1). CVXM resulted in generally smaller values for the extravasation parameter (mean 0.01–0.04 min−1) and extravascular extracellular volume fraction (mean 0.05–0.17) compared to the standard Tofts parameters, suggesting that Toft model underestimates the effects of inter-voxel exchange. The ratio of Tofts’ extravasation parameters over CVXM’s was significantly positively correlated to the cross-voxel diffusivity (P < 0.0001) and velocity (P = 0.0005). Tofts’ increased measurements were explained using Sinno et al (2021)’s theoretical work. Finally, a scan time of 15 min renders informative estimations of the transport parameters. However, a duration as low as 7.5 min is acceptable to recognize the spatial variation of transport parameters. The results demonstrate the potential of utilizing CVXM for determining metrics characterizing the exchange of tracer between the vasculature and the tumour tissue. Like for many earlier models, additional work is strongly recommended, in terms of validation, to develop more confidence in the results, motivating future laboratory work in this regard.

CONSIDERING PLEURAL FLUID GLUCOSE LEVELS COULD PREVENT UNNECESSARY PROCEDURES

CONSIDERING PLEURAL FLUID GLUCOSE LEVELS COULD PREVENT UNNECESSARY PROCEDURES

Mechanism and implications of shut-in induced earthquakes

Fluid pressurization rate is an important inducement to fracture slip. In order to characterize the fracture slip initiation and slip mode during fluid pressurization, a series of stepwise injection induced shear tests were carried out. Results show that fracture slip initiation depends on fluid pressure and roughness of fracture surface. Fluid pressurization rate, fluid pressure non– uniform distribution all affect fracture slip initiation. Reducing fluid pressurization rate seems cannot effectively avoid induced earthquake, but can delay the time and scale of induced earthquake, especially can alleviate induced earthquake after shut-in. Earthquake induced after shut-in may be caused by secondary damage of concave-convex body on fault surface under the action of fluctuating pressure generated from injection wells or underground water sources around fault. Furthermore, a new view is proposed that the change of fluid pressure gradient on fracture surface is an important complementary mechanism for shut-in induced earthquakes.

Electrokinetic effect provided by long oceanic waves coming on shore

Electrokinetic effect (EK) caused by long oceanic waves in porous water-saturated rocks of seabed and shore is examined theoretically. One possible reason for this effect is the motion of groundwater due to the volume deformation of porous rocks by oceanic waves coming on shore. The same mechanism is responsible for seismoelectric effect observed during seismic waves passage through ground-recording station. In this study, we examine another mechanism in which the wave-produced variable pressure on the seabed plays a role of a piston pushing seawater through the seabed rocks into sandy or porous rocks of the seashore thereby exciting the EK effect. To estimate this effect, we first consider a long gravity wave and then solve 2D‑problem on the pressure variations produced by this wave on the bottom. This solution is used to describe groundwater filtration in porous rocks subjected to the variable pressure of seawater. The EK current and telluric electric field in a porous medium are derivable through the pressure gradient of porous fluid. The amplitude of telluric electric field in a porous medium has been shown to decrease almost exponentially with distance from a shoreline. A penetration depth of the telluric field as a function of wave frequency in the range of 10‑100 mHz was analyzed. A role played by EK effect in the generation of ULF natural electromagnetic noise in coastal zone was discussed.

Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy

We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles in pressure-imposed rheology configuration, subject to a sudden change in shear rate or external pressure. Discrete element method simulations show that, depending on the flow parameters (particle and system size, initial volume fraction), the early stress response of the suspension may differ strongly from the prediction of the suspension balance model based on the steady-state rheology. We show that a two-phase model incorporating the Reynolds-like dilatancy law of Pailha &amp; Pouliquen (J. Fluid Mech., vol. 633, 2009, pp. 115–135), which prescribes the dilation rate of the suspension over a strain scale $\gamma _0$ , captures quantitatively the suspension dilation/compaction over the whole range of parameters investigated. Together with the Darcy flow induced by the pore pressure gradient during dilation or compaction, this Reynolds-like dilatancy implies that the early stress response of the suspension is non-local, with a non-local length scale $\ell$ that scales with the particle size and diverges algebraically at jamming. In regions affected by $\ell$ , the stress level is fixed, not by the steady-state rheology, but by the Darcy fluid pressure gradient resulting from the dilation/compaction rate. Our results extend the validity of the Reynolds-like dilatancy flow rule, initially proposed for jammed suspensions, to flowing suspension below the critical volume fraction at which the suspension jams, thereby providing a unified framework to describe dilation and shear-induced migration. They pave the way for understanding more complex unsteady flows of dense suspensions, such as impacts, transient avalanches or the impulsive response of shear-thickening suspensions.

Predicting In-Situ Physical Properties for Gas Condensates From Fluid Pressure Gradients

New hybrid EOS-PVT models have been developed for estimating in-situ fluid properties for retrograde gas condensate fluids. The hybrid models are based on tuned equation of state (EOS) properties for a globally distributed set of quality-controlled (QC) pressure-volume-temperature (PVT) analyses of gas condensates in which the condensate-to-gas ratio (CGR) ranges from ~5 to 350 bbl/MMscf and for which in-situ fluid densities range from ~0.2 to 0.6 g/cm3. The hybrid EOS-PVT models are based on the observation that in-situ fluid densities derived from measured fluid pressure gradients (FPG) are highly correlated with EOS-derived in-situ fluid densities obtained from tuned EOS models and QC PVT data. Using fluid density values calculated using in-situ FPG data, it is now possible to estimate a variety of gas condensate fluid properties such as viscosity, mole fraction of methane (XCH4), density, acoustic velocity, and adiabatic fluid moduli, the latter being a critical input for Gassmann fluid substitution models. The utility of the new hybrid EOS-PVT models lies in their ability to facilitate rapid evaluation of stranded gas resources without having to take a fluid sample for laboratory PVT analysis. Properly executed FPG data also have great utility as a reliable QC for laboratory-measured PVT properties. We present hybrid EOS-PVT models for CGR, viscosity, in-situ fluid density, and acoustic velocity for a broad suite of gas condensates. A significant contribution of this work is the development of a new fluid acoustic properties model that enables estimation of the adiabatic fluid modulus (Kad) for retrograde gas condensates. Using predictive models reported here for fluid density [ρ] and velocity [Vp], the adiabatic fluid modulus is easily calculated. The model reported for fluid velocity was validated with direct measurements of fluid acoustic velocity on a live sample, at in-situ conditions, from the HP/HT Shearwater Field in the Central North Sea (CNS).

New approach for filling simulations of dual-scale preforms used in the manufacturing of composites materials.

Some fibrous reinforcements used in the manufacturing of parts by Liquid Composite Molding (LCM) have a dual-scale nature, which supposes flow imbalances between the tows and channels at mesoscopic scale, which in turn, cause uncontrolled defects (voids, dry points, among others) and could considerably affect the global flow behavior during the filling of cavities at macroscopic scale. In the present work, a new approach to conduct filling simulations of dual-scale fibrous reinforcements at mesoscopic scale is proposed. This consists of prescribing a pressure gradient along the Representative Unitary Cell, and imposing Stokes-Darcy matching conditions between the tows and the channel sub-domains to determine the filling of the former ones. Contrarily to the traditional approach, where a uniform pressure is assumed for the channels and only the porous media fluid is modeled, the present one allows considering the fluid pressure gradient at channels (fluid motion), air compressibility and dissolution, flow-direction dependent capillary pressure, and vacuum pressure, as well as capturing several phenomena involved in the dynamic evolution of intra-tow voids, namely, compression, mobilization at constant volume and migration from tows towards channel. The velocity vectors and streamlines in the tows and channel subdomains, when these phenomena take place, are analyzed as well.

A Mori-Tanaka scheme-based model for gas-water two-phase cracked rocks and its application

Microporous structure and pore fluid are two important components of poroelastic rocks that influence the variation of rock modulus. Cracks are special microstructures that are more likely to be compressed during wave propagation than stiff pores, resulting in squirt flow. In addition, the distribution of different fluids, such as water and gas, may be characterized by patchy saturation and generate fluid pressure gradients. By combining the Mori-Tanaka scheme and these two local fluid flows, a new rock physics model for gas-water two-phase cracked rocks is developed. Among effective medium models, the Mori–Tanaka model is of superiority in describing non-dilute-inclusion rocks and has an explicit expression. It is used to provide a reasonable variable range of the rock modulus. First, it is re-derived by assuming that the pore structure contains cracks and stiff pores. Then, the pore fluid pressures are investigated by considering the effects of squirt flow and patchy saturation simultaneously. The proposed model agrees well with the boundary models and is consistent with the variation of the experimental and well-logging data. With the new model, the joint effect of two different local fluid flows on rock moduli with frequency can be analyzed in detail.

Crustal Electrical Structure and Deep Metallogenic Potential in Northern Wuyi Area (South China), based on Magnetotelluric Data

AbstractThe northern Wuyi area, which is located in the northern Wuyi metallogenic belt, has superior mineralization conditions. The Pingxiang–Guangfeng–Jiangshan–Shaoxing fault (PSF) extends across the whole region regardless of whether or how the PSF relates to the near‐surface mineralization. We carried out an MT survey in the region and obtained a reliable 2D model of the crustal electrical structure to a depth of 30 km. In the resistivity model, we inferred that a continuous high conductivity belt that ranges from the shallow to deep crust is a part of the PSF. Then, we estimated the fluid content and pressure gradient to identify the deep sources of fluid as well as its pattern of motion pattern. Finally, we proposed a model for the deep metallogenic migration processes that combines geological data, fluid content data, pressure gradient data, and the subsurface resistivity model. The model analysis showed that the Jiangnan orogenic belt and the Cathaysia block formed the PSF during the process of com. The deep fluid migrated upward through the PSF to the shallow crust. Therefore, we believe that the PSF is an ore‐forming fluid migration channel and that it laid the material basis for large‐scale mineralization in the shallow crust.

The effects of gravity and compression on interstitial fluid transport in the lower limb

Edema in the limbs can arise from pathologies such as elevated capillary pressures due to failure of venous valves, elevated capillary permeability from local inflammation, and insufficient fluid clearance by the lymphatic system. The most common treatments include elevation of the limb, compression wraps and manual lymphatic drainage therapy. To better understand these clinical situations, we have developed a comprehensive model of the solid and fluid mechanics of a lower limb that includes the effects of gravity. The local fluid balance in the interstitial space includes a source from the capillaries, a sink due to lymphatic clearance, and movement through the interstitial space due to both gravity and gradients in interstitial fluid pressure (IFP). From dimensional analysis and numerical solutions of the governing equations we have identified several parameter groups that determine the essential length and time scales involved. We find that gravity can have dramatic effects on the fluid balance in the limb with the possibility that a positive feedback loop can develop that facilitates chronic edema. This process involves localized tissue swelling which increases the hydraulic conductivity, thus allowing the movement of interstitial fluid vertically throughout the limb due to gravity and causing further swelling. The presence of a compression wrap can interrupt this feedback loop. We find that only by modeling the complex interplay between the solid and fluid mechanics can we adequately investigate edema development and treatment in a gravity dependent limb.

Radiation effect on unsteady MHD mixed convection of kerosene oil-based CNT nanofluid using finite element analysis

This work conducts a numerical analysis of thermal radiation with a semicircular heater on the middle part of the bottom wall and a sliding lid on the top in a square enclosure. Magnetohydrodynamic (MHD) unsteady mixed convection for kerosene oil-based CNT nanofluid is studied. The finite element-based Galerkin residual technique is used to obtain nonlinear dimensionless governing equations. The thermal conductivity and dynamic viscosity models incorporate nanoparticle Brownian motion. Simulations were conducted for Reynolds number = 100, Hartmann number = 10, Richardson number = 1, and particle concentration = 0.05. The effects of fluid velocity magnitude, pressure gradient, temperature gradient magnitude, average temperature, bulk temperature, drag force of the sliding lid, and Nusselt number of the semicircular heater were investigated for different radiation parameters and dimensionless time. Results showed that increasing radiation intensity and dimensionless time improves fluid velocity, pressure gradient, and temperature gradient but decreases the heat transfer rate of the semicircular heater. Furthermore, the drag force of the moving lid is likewise found to be substantially dependent on the radiation parameter as well as dimensionless time. It is worth noted that after a while, the considered parameter exhibits consistent behavior.

Mathematical simulation of the calendering process for non-Newtonian polymers

This paper mathematically studies calendering with a tangent hyperbolic model to simulate non-Newtonian polymers. The constitutive equations based on Lubrication Approximation Theory (LAT) are first non-dimensionalized and then simplified. The simplified equations describing the flow inside the calender are solved (a) analytically using the perturbation method and (b) numerically using MatLab built-in routine “BVP4c” method. The first case obtains an analytical expression for velocity, pressure gradient, and final sheet thickness with the help of the perturbation method, while BVP4c and Runge-Kutta methods are used to calculate the velocity, pressure, pressure gradient, and mechanical quantities numerically. The power-law index and Weissenberg number influence on pressure, pressure gradient, and velocity profiles of fluid being calendered are shown with graphs. The pressure inside the calender decreases as the power-law index and Weissenberg number increase. The force function and final sheet thickness decreases as the power-law index and Weissenberg number increases.

Multilayer microfluidic platform for the study of luminal, transmural, and interstitial flow

Efficient delivery of oxygen and nutrients to tissues requires an intricate balance of blood, lymphatic, and interstitial fluid pressures (IFPs), and gradients in fluid pressure drive the flow of blood, lymph, and interstitial fluid through tissues. While specific fluid mechanical stimuli, such as wall shear stress, have been shown to modulate cellular signaling pathways along with gene and protein expression patterns, an understanding of the key signals imparted by flowing fluid and how these signals are integrated across multiple cells and cell types in native tissues is incomplete due to limitations with current assays. Here, we introduce a multi-layer microfluidic platform (MμLTI-Flow) that enables the culture of engineered blood and lymphatic microvessels and independent control of blood, lymphatic, and IFPs. Using optical microscopy methods to measure fluid velocity for applied input pressures, we demonstrate varying rates of interstitial fluid flow as a function of blood, lymphatic, and interstitial pressure, consistent with computational fluid dynamics (CFD) models. The resulting microfluidic and computational platforms will provide for analysis of key fluid mechanical parameters and cellular mechanisms that contribute to diseases in which fluid imbalances play a role in progression, including lymphedema and solid cancer.

Tidal modulation of seismicity at the Coso geothermal field

Studying the seismicity triggering response of fault systems to periodic stress fluctuations can improve our understanding of earthquake nucleation, rupture failure processes, and local stress states. Geothermal fields are well known to be susceptible to triggering, as the injection and extraction activities change the local stress and fluid flow conditions. Here, we examine the modulation of earthquakes by Earth tides within California's Coso geothermal field (CGF) and its vicinity. To maximize our resolution to detect modulation of small earthquakes, we take advantage of the new Quake Template Matching catalog in southern California, which has nearly twice as many events in the Coso region as the standard catalog and is complete down to about magnitude 0.3. We observe strong tidal triggering of earthquakes within the CGF, even though the fluctuations of tidal stresses are small (∼2 kPa). The tidally-triggered earthquakes tend to occur near the time of maximum tensile tidal stress. The signal is strongest near the edges of the zone of new production wells, suggesting fluid pressure gradients encourages triggering at tidal periods.

Luminal flow actuation generates coupled shear and strain in a microvessel-on-chip

In the microvasculature, blood flow-derived forces are key regulators of vascular structure and function. Consequently, the development of hydrogel-based microvessel-on-chip systems that strive to mimic the in vivo cellular organization and mechanical environment has received great attention in recent years. However, despite intensive efforts, current microvessel-on-chip systems suffer from several limitations, most notably failure to produce physiologically relevant wall strain levels. In this study, a novel microvessel-on-chip based on the templating technique and using luminal flow actuation to generate physiologically relevant levels of wall shear stress and circumferential stretch is presented. Normal forces induced by the luminal pressure compress the surrounding soft collagen hydrogel, dilate the channel, and create large circumferential strain. The fluid pressure gradient in the system drives flow forward and generates realistic pulsatile wall shear stresses. Rigorous characterization of the system reveals the crucial role played by the poroelastic behavior of the hydrogel in determining the magnitudes of the wall shear stress and strain. The experimental measurements are combined with an analytical model of flow in both the lumen and the porous hydrogel to provide an exceptionally versatile user manual for an application-based choice of parameters in microvessels-on-chip. This unique strategy of flow actuation adds a dimension to the capabilities of microvessel-on-chip systems and provides a more general framework for improving hydrogel-based in vitro engineered platforms.

Interpretation of Recent Unrest Events (Bradyseism) at Campi Flegrei, Napoli (Italy): Comparison of Models Based on Cyclical Hydrothermal Events versus Shallow Magmatic Intrusive Events

Several recent models that have been put forth to explain bradyseism at Campi Flegrei (CF), Italy, are discussed. Data obtained during long-term monitoring of the CF volcanic district has led to the development of a model based on lithological-structural and stratigraphic features that produce anisotropic and heterogeneous permeability features showing large variations both horizontally and vertically; these data are inconsistent with a model in which bradyseism is driven exclusively by shallow magmatic intrusions. CF bradyseism events are driven by cyclical magmatic-hydrothermal activity. Bradyseism events are characterized by cyclical, constant invariant signals repeating over time, such as area deformation along with a spatially well-defined seismogenic volume. These similarities have been defined as “bradyseism signatures” that allow us to relate the bradyseism with impending eruption precursors. Bradyseism is governed by an impermeable shallow layer (B-layer), which is the cap of an anticlinal geological structure culminating at Pozzuoli, where maximum uplift is recorded. This B-layer acts as a throttling valve between the upper aquifer and the deeper hydrothermal system that experiences short (1-102 yr) timescale fluctuations between lithostatic/hydrostatic pressure. The hydrothermal system also communicates episodically with a cooling and quasi-steady-state long timescale (103-104 yr) magmatic system enclosed by an impermeable carapace (A layer). Connectivity between hydrostatic and lithostatic reservoirs is episodically turned on and off causing alternatively subsidence (when the systems are connected) or uplift (when the systems are disconnected), depending on whether permeability by fractures is established or not. Earthquake swarms are the manifestation of hydrofracturing which allows fluid expansion; this same process promotes silica precipitation that seals cracks and serves to isolate the two reservoirs. Faults and fractures promote outgassing and reduce the vertical uplift rate depending on fluid pressure gradients and spatial and temporal variations in the permeability field. The miniuplift episodes also show “bradyseism signatures” and are well explained in the context of the short timescale process.

Strike-slip faulting on Titan: Modeling tidal stresses and shear failure conditions due to pore fluid interactions

Expressions of strike-slip faulting are well documented on multiple ocean worlds (e.g., Europa, Enceladus, and Ganymede) and the motion along these faults is thought to be driven by variations in diurnal tidal stresses. Titan exhibits a complex and dynamic geology with a varied surface morphology developed from fluvial, aeolian, and possible cryovolcanic and tectonic activity. However, observational data are currently limited and no clear strike-slip indicators have been identified so far. Nevertheless, the inferred presence of a porous ice layer saturated with liquid hydrocarbons in Titan's shallow subsurface provides a unique environment for studying zones of frictional weakness, shear heating, and the promotion of cryovolcanism. This study examines Titan's ability to host shear deformation mechanisms, including considerations for how the presence of near-surface liquid hydrocarbons and the crustal porosity of ice significantly reduce the resistance to shear failure of strike-slip faults in flexed areas under maximum diurnal tidal stresses. We conduct a sensitivity analysis of Titan's shear failure tendencies, given optimal failure conditions that may exist due to pore fluid interactions, and we examine the possibility for strike-slip tectonics guided by Coulomb failure laws and tidal stress mechanisms. Using the SatStress tidal stress model for a Titan-appropriate rheology, we compute the diurnal tidal stress tensor and resolve shear and normal stresses onto a suite of fault orientations. We adopt plausible coefficients of friction and include the effect of a hydrostatic pore fluid pressure gradient for Titan. At shallow fault depths (< 1 km) and for optimally oriented faults, this exploratory model suggests shear failure is achievable under diurnal tidal stress conditions subject to such pore fluid pressures, especially in the polar regions. Our results suggest that under these conditions, shear failure is not only possible, but may be an active deformation mechanism on the surface and in the subsurface of Titan, and could potentially serve as a pathway for the exchange of surface and subsurface materials through shear heating mechanisms. Moreover, the inference of conditions supporting strike-slip tectonism on Titan could have important implications for future Dragonfly observations and for future studies directed at better understanding the structural development of the surfaces of icy moons.

Effect of fluid pressure gradient on the factor of safety in rock stability analysis

Inappropriate assessment of rock stability may result in anthropogenic geohazards during underground space development and energy extraction. To reasonably estimate the factor of safety (FOS) for rock stability, it is critical to address uncertainties involved in the estimation. Fluid pressure gradient is of great concern in the estimation of the FOS. We carried out laboratory experiment and numerical modeling to reproduce fluid pressure gradient on a smooth fracture in granite. We compared the FOS derived from a nearly uniform fluid pressure gradient and that from a significantly non-linear fluid pressure gradient and found that the non-linear gradient of fluid pressure may amplify the FOS value. We also conducted a theoretical analysis to compare the FOS values for uniform, linear, and non-linear fluid pressure gradients. The results revealed that a considerable gradient and a pronounced non-linearity of fluid pressure are likely to cause premature failure of a rock fracture. Moreover, the upper bound of the FOS with a non-linear fluid pressure gradient depends on the initial FOS for a rock fracture without fluid pressurization. These findings are conducive to interpreting rock instability due to fluid pressurization and developing a more robust FOS estimation method.

A study of ellipsoidal and spherical particle flow, clogging and unclogging dynamics

To study ellipsoidal and spherical particle flow, clogging behavior and unclogging dynamics, a series of numerical simulations were carried out using our validated 3-D coupled computational fluid dynamics–discrete element method (CFD–DEM) model. For the first time, the strength of clogging arches is assessed in terms of fluid pressure gradient, which can effectively break up the clog. The main findings are as follows. In a clogged assembly, only when the flushing fluid reaches the unclogging pressure gradient, the ellipsoidal and spherical particles can flow in a continuous state. For the ellipsoids and spheres with the same equivalent volume, the unclogging pressure gradient of an ellipsoidal assembly is 11.8 times higher than that of a spherical assembly. Clogging arches at the outlet show the highest strength when the longitudinal orientations of the ellipsoids are perpendicular to the outlet plane. In contrast, the formed arch has the lowest stability when the longitudinal orientations of the ellipsoids are in the same direction as the long side of the outlet, as shown in the graphical abstract. The unclogging pressure gradient of the former case is 1.9 times greater than that of the latter case. The granular arches observed in our 3-D model are categorized as complex 3-D backbone arches. In the flowing region, particles rotate nearly perpendicular to the outlet plane, especially those approaching the outlet. Moreover, triangular stagnant zones are formed on both sides of the bottom of the rectangular box. The model presented here offers a great promise for future investigation of various granular systems at the particle scale.

Digital rock physics applied to squirt flow

We have developed a workflow for computing the seismic-wave moduli dispersion and attenuation due to squirt flow in a numerical model derived from a micro X-ray computed tomography image of cracked (through thermal treatment) Carrara marble sample. To generate the numerical model, the image is processed, segmented, and meshed. The finite-element method is adopted to solve the linearized, quasistatic Navier-Stokes equations describing laminar flow of a compressible viscous fluid inside the cracks coupled with the quasistatic Lamé-Navier equations for the solid phase. We compute the effective P- and S-wave moduli in the three Cartesian directions for a model in dry conditions (saturated with air) and for a smaller model fully saturated with glycerin and having either drained or undrained boundary conditions. For the model saturated with glycerin, the results indicate significant and frequency-dependent P- and S-wave attenuation and the corresponding dispersion caused by squirt flow. Squirt flow occurs in response to fluid pressure gradients induced in the cracks by the imposed deformations. Our digital rock-physics workflow can be used to interpret laboratory measurements of attenuation using images of the rock sample.