Poroelastic Model Research Articles

The Relationship Between the Optical Properties of Articular Cartilage and the Biomechanical Parameters of the Tissue.

This study investigates the relationship between the optical properties of articular cartilage with its biomechanical parameters. The absorption and reduced scattering coefficients of articular cartilage, and average maximum penetration depth, average maximum lateral spread, and average path length of photons were estimated by optical measurements and Monte Carlo simulation. The equilibrium and instantaneous moduli, and initial fibrillar network, strain-dependent fibrillar network, and nonfibrillar network moduli, and initial and deformation-dependent permeability of the tissue were estimated by multistep stress-relaxation measurement and fibril-reinforced poroelastic modeling. The relationship between the optical properties and biomechanical parameters was assessed using predictive regression modeling. A strong relationship was found between reduced scattering coefficients, averaged maximum penetration depth, averaged maximum lateral spread, and average path length of photons with equilibrium, instantaneous, and initial fibrillar network moduli. We attribute this relationship to the collagen fibers as the main contributor to the scattering and biomechanical properties of the tissue.

A Stokes–Dual–Porosity–Poroelasticity Model and Discontinuous Galerkin Method for the Coupled Free Flow and Dual Porosity Poroelastic Medium Problem

A Stokes–Dual–Porosity–Poroelasticity Model and Discontinuous Galerkin Method for the Coupled Free Flow and Dual Porosity Poroelastic Medium Problem

Biomechanics of Osseointegration of a Dental Implant in the Mandible Under Shock Wave Therapy: In Silico Study.

The most time-consuming aspect of dental prosthesis installation is the osseointegration of a metal implant with bone tissue. The acceleration of this process may be achieved through the use of extracorporeal shock wave therapy. The objective of this study is to investigate the conditions for osseointegration of the second premolar implant in the mandibular segment through the use of a poroelastic model implemented in the movable cellular automaton method. The mandibular segment under consideration includes a spongy tissue layer, 600 µm in thickness, covered with a cortical layer, 400 µm in thickness, and a gum layer, 400 µm in thickness. Furthermore, the periodontal layers of the roots of the first premolar and first molar were considered, while the implant of the second premolar was situated within a shell of specific tissue that corresponded to the phase of osseointegration. The model was subjected to both physiological loading and shock wave loading across the three main phases of osseointegration. The resulting fields of hydrostatic pressure and interstitial fluid pressure were then subjected to analysis in accordance with the mechanobiological principles. The results obtained have indicated that low-intensity shock wave therapy can accelerate and promote direct osseointegration: 0.05-0.15 mJ/mm2 in the first and second phases and less than 0.05 mJ/mm2 in the third phase. In comparison to physiological loads (when bone tissue regeneration conditions are observed only around the implant distal end), shock waves offer the primary advantage of creating conditions conducive to osseointegration along the entire surface of the implant simultaneously. This can significantly influence the rate of implant integration during the initial osteoinduction phase and, most crucially, during the longest final phase of bone remodeling.

Hydraulic permeability prediction from attenuation in an oil well using the squirt flow model

A practical methodology is presented for estimating the hydraulic permeability from the wave attenuation at sonic frequencies using the poroelastic squirt flow model associated with the mechanism that encompasses the interaction between solid and fluid in an oil well. The methodology consists of four stages: a) the petrophysical evaluation, b) the static rock physics modeling that includes its diagnostics, c) the estimation of wave attenuations using an inversion scheme to optimize the Z critical parameter from the squirt flow model, d) the correlation between attenuations and the Z parameter with hydraulic permeabilities obtained by conventional well logs and available core analysis. The correlations are the means to establish the predicted hydraulic permeabilities from sonic and ultrasonic data. The obtained results suggest that the Z parameter is low while attenuations are high when the medium presents high porosity and permeability. In the methodology, the inversion scheme is proposed to find the Z parameter, the velocity dispersion, and attenuations in terms of the inverse quality factors, respectively for P-wave (QP –1) and S-wave S (QS –1) using a simulated annealing technique. The results from the application of the methodology are validated with core data (water saturation, porosity, and permeability) and mineralogical analysis from thin sections by the point counting technique. This methodology promises a means for predicting the hydraulic permeability from sonic and ultrasonic velocities in a well.

Mechanical Characterization and Modeling of Large-Format Lithium-Ion Battery Cell Electrodes and Separators for Real Operating Scenarios

This study presents a novel application-oriented approach to the mechanical characterization and subsequent modeling of porous electrodes and separators in lithium-ion cells to gain a better understanding of their real mechanical operating behavior. An experimental study was conducted on the non-linear stiffness of LiNi0.8Co0.15Al0.05O2 and graphite electrodes as well as PE separators, harvested from large-format lithium-ion cells, using compression tests. The mechanical response of the components was determined for different operating conditions, including nominal stress levels, mechanical loading rates, and mechanical cycles. The presented work describes the test procedure, the experimental setup, and an objective evaluation method, allowing for a detailed summary of the observed mechanical behavior. A distinct nominal stress level and mechanical cycle dependency of the non-linear stiffnesses of the porous materials were found. However, no clear dependency on compression rate was observed. Based on the experimental data, a poroelastic mechanical model was utilized to predict the non-linear behavior of these porous materials under real mechanical operating scenarios with a normalized root-mean-squared error less than 5.5%. The results provide essential new insights into the mechanical behavior of porous electrodes and separators in lithium-ion cells under real operating conditions, enabling the accelerated development of high-performing and safe batteries for various applications.

Blood osmolytes such as sugar can drive brain fluid flows in a poroelastic model

The glymphatic system of fluid flow through brain tissue may clear amyloid-β during sleep and as such underlie the need for sleep. Dysfunctional glymphatic transport has been implicated in pathological conditions ranging from stroke and dementia to psychiatric illnesses. To date, the fastest observed in-vivo brain flows have been reported after the manipulation of blood osmotic pressures. Surprisingly, the brain seems to shrink while receiving more influx. Though influx of an incompressible fluid might expand the tissue, no physical theory for these observations has been proposed. We here present a minimal mathematical model of brain pressure, deformation, and fluid flows due to vascular osmotic pressures. The model is based on Darcy flow, linear poroelasticity theory and conservation of mass. We propose that a screened Poisson equation holds for interstitial pressure because vascular filtration corresponds to fluid divergence. The model resolves the apparent paradox of combined fluid influx with tissue shrinkage by showing that fluid absorption into the blood can drive both. In this model, small glucose concentration differences between plasma and brain can drive brain flow velocities observed in recent in-vivo assays. Osmosis may therefore drive brain fluid flow under physiological conditions and provide an explanation for the known correlations between diabetes and dementia.

A new multiphysics finite element method for a quasi-static poroelasticity model

In this paper, we propose a new multiphysics finite element method for a quasi-static poroelasticity model. Firstly, to overcome the displacement locking phenomenon and pressure oscillation, we reformulate the original model into a fluid-fluid coupling problem by introducing new variables-the generalized nonlocal Stokes equations and a diffusion equation, which is a completely new model. Then, we design a fully discrete multiphysics finite element method for the reformulated model-linear finite element pairs for the spatial variables (u,ξ,η) and backward Euler method for time discretization. And we prove that the proposed method is stable without any stabilized term and robust for many parameters and it has the optimal convergence order. Finally, we show some numerical tests to verify the theoretical results.

Developing a geomechanical model to predict breakdown pressure in a vertical borehole using failure analysis: a case study

Breakdown is an important process in geomechanics; a very complex process in hydraulic fracturing which has been the subject of extensive research in the literature. There exist several models in the literature for predicting the breakdown pressure. In this research, the breakdown pressure for hydraulic fracturing in a vertical borehole was modeled using 2D and 3D failure analysis. In the geomechanical model constructed in this case study, elastic moduli were obtained using petrophysical data as well as data extracted from core analysis. The in-situ stress state of the reservoir was obtained by poroelastic horizontal strain model and was then validated by field data. To test the accuracy of the horizontal strain model, several models were used to obtain the minimum horizontals stress. At the end, the induced principal stresses inside the borehole were modeled by Kirch Equations. Four failure criteria, namely Mohr–Coulomb, 2D Hoek–Brown, Hubbert-Willis and 3D Mogi-Coulomb were used to obtain the breakdown pressure for the target reservoir. Based on the prediction results of these failure criteria, it was obtained that 2D Hoek–Brown, Hubbert-Willis, and 3D Mogi-Coulomb criteria resulted in seemingly unrealistic breakdown pressures with respect to the minimum horizontal stress gradient. The Mohr–Coulomb criterion produced lower breakdown pressure gradients, yet closer to the minimum horizontal stress values, even though it neglects the effect of intermediate stress.

Manipulating crack formation in air-dried clay suspensions with tunable elasticity

Clay, the major ingredient of natural soils, is used as a rheological modifier while formulating paints and coatings. When subjected to desiccation, colloidal clay suspensions and clayey soils crack due to the accumulation of drying-induced stresses. Even when desiccation is suppressed, aqueous clay suspensions exhibit physical aging, with their elastic and viscous moduli increasing over time as the clay particles self-assemble into gel-like networks due to time-dependent inter-particle screened electrostatic interactions. The rate of evolution of the suspension structures and therefore of the mechanical moduli can be controlled by changing clay concentration or by incorporating additives. Since physical aging and desiccation should both contribute to the consolidation of drying clay suspensions, we manipulate the desiccation process via alterations of clay and additive concentrations. For a desiccating sample with an accelerated rate of aging, we observe faster consolidation into a semi-solid state and earlier onset of cracks. We estimate the crack onset time, tc, in direct visualization experiments and the elasticity of the drying sample layer, E, using microindentation in an atomic force microscope. We demonstrate that tc∝GcE, where Gc, the fracture energy, is estimated by fitting our experimental data to a linear poroelastic model that incorporates the Griffith's criterion for crack formation. Our work demonstrates that early crack onset is associated with lower sample ductility. The correlation between crack onset in a sample and its mechanical properties as uncovered here is potentially useful in preparing crack-resistant coatings and diverse clay structures.

Two-grid reduced-order method based on POD for a nonlinear poroelasticity model

In this paper, we consider a two-field nonlinear poroelasticity model, in which the unknown variables are the solid displacement and the pore pressure, and the permeability of the elastic material depends on the dilatation. A standard Galerkin method based on Picard iteration is presented. To reduce the computational costs, we develop the two-grid method, the reduced-order finite element (ROFE) method based on proper orthogonal decomposition (POD) technique, and a combination of the first two methods, i.e., the two-grid reduced-order finite element (TGROFE) method. The associated numerical error has four components due to the coarse triangulation discretization, fine triangulation discretization, time discretization, and eigenvalue truncation by POD. Numerical experiments show the accuracy and efficiency of these methods. To further illustrate the application of the POD technique to the quasi-static poroelasticity problem, we investigate two reduced-order mixed finite element methods, which avoid pressure oscillations and/or have locking-free property.

Poroelastic Response of a Fractured Rock to Hydrostatic Pressure Oscillations

AbstractPoroelastic coupling between fractures and the surrounding rock is important to numerous applications in geosciences. We measure the in‐situ fluid pressure and local strain response of a fractured carbonate sample to hydrostatic pressure oscillations. A linear poroelastic model that represents the rock sample is parameterized using X‐ray imaging and ultrasonic wave transmission measurements. The numerical solution, based on Biot's quasistatic equations, is consistent with the measured frequency dependent dispersion of the apparent bulk modulus of the background matrix and the in‐situ pore pressure response, which is caused by fluid pressure diffusion from the compliant fractures into the stiffer matrix. The observed fluid pressure diffusion is causally related to the numerically quantified intrinsic attenuation at seismic frequencies, which is a major contributor to the dissipation of seismic waves. Our analysis supports the use of a simple approximation of fractures as compliant and planar inclusions in numerical simulations based on linear poroelasticity.

Induced magnetic field and thermal regulation of synovial fluid flow through irregular surfaces with first-order slip and gold nanoparticles

ABSTRACT The current computational exploration develops a poroelastic model of the knee cartilage to elevate its temperature under cyclic sinusoidal loading. A contributing factor to the rise in temperature is this tissue’s viscous dissipation, which converts some of the mechanical energy supplied into heat. The manipulation of cartilage temperature is mostly reliant on the movement of synovial fluid inside the space between joints and within the permeable cartilage. We developed the region flow model in the presence of induced magnetic fields and gold nanoparticles, which enhanced the efficiency of joint lubrication by boosting the load-carrying capacity. We dealt with the problem for two different models. Model 1 assumes that viscosity is exponentially dependent on concentration. The shear thinning index in Model 2 is regarded as a concentration-dependent variable. We introduce these models for a complex wavy surface, where the first-order slip effect occurs. We modified the governing problem by assuming a long wavelength and a low Reynolds number. We followed up with a computational analysis utilizing the Rung–Kutta–Merson approach with Newton iteration in a shooting and matching strategy. We have conducted detailed comparisons between Model 1 and Model 2. The graphical findings have been shown for the distributions of velocity, temperature, and nanoparticle concentration. Additionally, the pressure gradients, streamlines, and axially generated magnetic fields have also been included. These results are presented for numerous physical parameters. The mechanics of trapping are thoroughly examined through the use of streamlines.

Dam impoundment near active faults in areas with high seismic potential: Case studies from Bisri and Mseilha dams, Lebanon

Reservoir induced seismicity is caused by stress changes due to the impoundment of water behind dams. In seismically active areas, the presence of critically located active faults makes the impoundment of water behind dams a seismic safety risk. Dam projects in Lebanon have become a soaring example of complacency and negligence that has overlooked the concerns for seismic safety raised over the projects and their high potential of inducing seismicity. In this paper, we use 2D and 3D fully coupled poroelastic modeling to assess the risk of dam impoundment on seismogenic faults located near dam sites in Lebanon. The coulomb failure stresses are calculated along the faults, and their variations are observed in relation to changes in pore pressures and normal stresses. In addition, the expected maximum earthquake magnitudes are computed along those faults. Our results show a high risk for reservoir induced seismicity on faults that are either underneath the reservoir or hydraulically connected to a fault beneath the reservoir. Consequently, the studied dams would present a serious hazard of induced seismicity in time where the region is already at high risk of destructive earthquakes after the catastrophic seismic events that struck Turkey and Syria on 6 February 2023 on the Eastern Anatolian Fault, which is connected to the Dead Sea Transform Fault that passes through Lebanon.

The impact of effective fractured rock mass properties on development of flow channeling in enhanced geothermal systems

Controlling the distribution of working fluid in an Enhanced Geothermal System (EGS) is crucial to prevent early thermal breakthrough and sustain the initial heat drainage area. Over time, working fluid flow may localize to a small area if fracture permeability increases non-uniformly, and efforts are not made to control the flow distribution. This scenario can potentially lead to mechanical reopening of hydraulic fractures, flow channeling, and thermal short-circuiting. However, current models neglect the nonlinear and inelastic deformation of fractured rock masses on EGS coupled thermo-mechanical response. The objective of this work is to estimate and predict the likelihood of thermal short-circuiting by flow-channeling in an EGS reservoir composed of rock and compliant natural fractures. We utilize three dimensional numerical solutions with reservoir properties based on effective medium theory of fractured rocks to achieve this objective. The results show that presence of natural fractures considerably changes the EGS response to thermal destressing, compared to linear poroelastic models. Flow channeling and short-circuiting, resulting in early thermal breakthrough, are more likely to occur in sparsely fractured reservoirs with stiff and strong natural fractures. Conversely, short-circuiting is unlikely in densely fractured reservoirs where thermal strains are absorbed by natural fracture opening and shear sliding rather than by rock matrix contraction. Estimation of natural fracture density is crucial in long-term forecasting and prediction of EGS power output. Accurate fracture characterization could decisively impact the fate of a project.

Development of acoustic impedance tube system using 3D printing and finite element analysis

This study aims to demonstrate and provide a practical guide on correctly designing, fabricating, and verifying the acoustic impedance tube system. Many parts required to build this tube system were uniquely designed and 3D printed, such as the driver case, specimen holder, microphone holder, etc. In addition, this acoustic tube is designed to meet three functions: standard sound absorption measurement, in-situ measurement, and microphone mismatch measurement. Various types of specimens are tested to verify the accuracy of the measurement and how it compares to the poroelastic theoretical models and FEM models. To estimate the poroelastic parameters, measurement and FEM models were used to run the optimization process. The validation study shows good agreement in all three cases: measurement, the poroelastic model, and the FEM model.

Characterization and estimation of the acoustical and elastic parameters in stone wool samples

Mineral wool is widely used in acoustic applications. The properties of glass wool have been broadly investigated, thus resulting in a good knowledge of its structure and parameters. This information is used to describe mineral wool in general. Nevertheless, other types, such as stone wool, involve a different production process and therefore have a different fibre structure. e.g. stone wool is not transversally isotropic as glass wool. These differences can have important effects depending on the use of the material; therefore, assuming the same parameter values for both materials may lead to inaccurate results in simulations and calculations. Currently there are few studies that characterize both the acoustic and elastic properties of stone wool. This contribution reports on the characterization of two stone wool samples with different densities (~70 kg/m3 and ~140 kg/m3). The characterization aimed at obtaining the parameters that are required for the description of the propagation of sound in the material through the Biot poroelastic model, i.e. the acoustic and elastic parameters. The obtained knowledge enables the adequate modelling of the investigated poroelastic materials in different configurations by numerical methods such as finite elements and the transfer matrix method.

Acoustics response of granular porous material: experiment and modeling

Granular porous materials such as activated carbon have drawn increasing attention due to their good sound absorption performance at low frequency. However, some unique acoustical behaviors have been observed during sound absorption measurements of granular porous materials in impedance tubes: e.g., circumferential edge-constraint effects, level-dependent absorption behavior, and time-dependent absorption behavior. In order to explain these observations, a 1-dimensional poro-elastic model was first applied to describe the sound propagation in granules stacked in a cylindrical sample holder, as in a standing wave tube. Then this model was extended to a 2-dimensional finite difference (2DFD) model with depth-dependent stiffness of the granule stack considered by combining Janssen's model and Hertzian contact theory. The 2DFD model was validated with the measurements of the granular porous materials, and it was found that the 2DFD model is a powerful tool to analyze the acoustic response of granular porous material, thus providing a means of characterizing the granular materials. In the present work, the above-mentioned experimental observations and the 2DFD model are introduced, and the experiment results are analyzed with the 2DFD model. Finally some future work on granular porous materials is introduced.

Very‐Near‐Field Coseismic Fault Pressure Drop and Delayed Postseismic Cross‐Fault Flow Induced by Fault Damage From the 2018 M6.3 Hualien, Taiwan Earthquake

AbstractEarthquakes can produce rock damage, poroelastic deformation, and ground shaking that modify fault zone hydrogeologic properties. Coseismic and postseismic hydrologic response to the ruptured fault can serve as constraints on hydrogeologic property changes. Here, we document fluid pressure responses to the 2018 M6.3 Hualien, Taiwan earthquake and model the postseismic fault zone hydrology inferred from very‐near‐fault data. Two groundwater wells located ∼180–250 m from the fault damage zone experienced 10–15 m of groundwater level decline followed by a prolonged (>6 months) recovery. Poroelastic models indicate that strain dilation in the fault's hanging wall can produce water level reductions of several meters. However, the model cannot explain groundwater level change in the footwall nor the delayed postseismic recovery, suggesting fault zone damage played a primary role in both the coseismic and postseismic water level reductions. Fluid flow models incorporating the effects of coseismic fault damage on the temporal evolution of hydrologic fault properties show enhanced hydraulic anisotropy after the earthquake. The best‐fit models show that while both vertical hydraulic conductivity and specific storage likely increased within the fault zone, the horizontal hydraulic conductivity is low, suggesting the fault zone behaves as a hydraulic barrier to cross‐fault flow with modeled diffusivities as low as ∼10−3 m2/s. High‐fidelity hydrologic measurements in the very‐near‐field of fault zones (e.g., within a few hundred meters) may be a useful tool to constrain the spatial and temporal evolution of fault zone properties before, during, and after rupture.

Mathematical Models for Ultrasound Elastography: Recent Advances to Improve Accuracy and Clinical Utility.

Changes in biomechanical properties such as elasticity modulus, viscosity, and poroelastic features are linked to the health status of biological tissues. Ultrasound elastography is a non-invasive imaging tool that quantitatively maps these biomechanical characteristics for diagnostic and treatment monitoring purposes. Mathematical models are essential in ultrasound elastography as they convert the raw data obtained from tissue displacement caused by ultrasound waves into the images observed by clinicians. This article reviews the available mathematical frameworks of continuum mechanics for extracting the biomechanical characteristics of biological tissues in ultrasound elastography. Continuum-mechanics-based approaches such as classical viscoelasticity, elasticity, and poroelasticity models, as well as nonlocal continuum-based models, are described. The accuracy of ultrasound elastography can be increased with the recent advancements in continuum modelling techniques including hyperelasticity, biphasic theory, nonlocal viscoelasticity, inversion-based elasticity, and incorporating scale effects. However, the time taken to convert the data into clinical images increases with more complex models, and this is a major challenge for expanding the clinical utility of ultrasound elastography. As we strive to provide the most accurate imaging for patients, further research is needed to refine mathematical models for incorporation into the clinical workflow.

Sand Production Prediction and Management Using a One-Dimensional Geomechanical Model: A Case Study in NahrUmr Formation, Subba Oil Field

Sand production in sandstone reservoirs is a complex problem for oil and gas companies. This problem can damage downhole equipment and surface production facilities. This paper presents a sand production case and quantifies sand risks for the NahrUmr formation located in Subbaoilfied.The risk of sanding or rock failure is commonly observed during production phases as well as drilling operations. A (1D) mechanical earth model was created using wireline log data and core data for estimating the formations mechanical properties.The extrapolation method is utilized for vertical stress prediction, whereas pore pressure and static Young’s modulus were calculated using Slowness Eaton method and John Fuller correlation respectively. The poro-elastic model was used to determine horizontal principal stresses and hydrocarbon intervals susceptible to sand production issues.The purpose of this study was achieved using Tech-Log software. Sand onset intervals are firstly predicted as an open hole using ten methods: Loading factor (LF), Critical drawdown pressure (CDDP), B-index, schlumberger (Sc), Elastic combination index (Ec-index), Interval Transit-Time (DTc), Total porosity method (PHIT), unconfined compressive strength (UCS), Shear modulus to bulk compressibility ratio (G/Cb), and shear failure method. Approximately ten methods refer to the same intervals that can produce sand. Secondly, sand depths were predicted by representing the well according to what actually existed as a cased hole by calculating the critical drawdown pressure (CDDP), which is calculated at various depletion rates (0%, 15%, 25%, and 35%) in order to measure the effect of reservoir pressure depletion on sand production. The results show that as the rock strength is increased, the amount of sand-free drawdown and depletion becomes larger. Also, a single-depth analysis was conducted for problem intervals, indicatg a sandwillproducefromdepth of 2527.7 m under certain conditions. Therefore, it is necessary to install sand control equipment in this well.