Poroelastic Model Research Articles

A Double-Permeability Poroelasticity Model for Fluid Transport in a Biological Tissue

A Double-Permeability Poroelasticity Model for Fluid Transport in a Biological Tissue

Three-dimensional cleat scale modelling of gas transport processes in deformable fractured coal reservoirs

To understand the flow processes in naturally fractured coal reservoirs, a 3D numerical model for coupled gas flow, adsorption and deformation at the scale of coal cleat and matrix blocks is presented in this study. A discrete fracture matrix (DFM) modelling approach has been adopted where flow patterns in fractures and matrices are described separately and explicitly. Different from previous studies in which constant diffusion coefficient, equilibrium adsorption and lumped deformation of matrix and fracture are assumed, in this study, adsorbed gases are treated as an independent phase and the mass exchange process between free phase and adsorbed phase is described using the Langmuir kinetic model. Different gas transport mechanisms in a porous coal matrix are considered for both phase gas transport. Particularly, an equivalent poroelastic continuum model is applied to represent deformation of fracture-matrix system, in which impacts of fracture deformation on the bulk matrix-fracture deformation is accounted for. The hybrid dimensional elements have been employed to discretize the governing equations where fractures are discretized using lower-dimensional interface elements. The accuracy of developed model is validated against experimental results collected from literatures. The simulation results indicate that the gas diffusion process in coal matrices is pressure dependent, surface diffusion of adsorbed gas can contribute to the bulk gas diffusion in coal matrices. Individual cleat initially exhibits a slight opening, followed by significant closure due to adsorption-induced swelling. Ignoring the effect of fracture on bulk deformation, the aperture change is overestimated.

Toward temporal evolution of consolidation in fluid-saturated poroelastic media with various permeable conditions

Previous studies have revealed that consolidation is a time-dependent process and highly depends on the permeable properties of boundary as well as the loading modes. This work investigates the characteristics of temporal evolution during consolidation in fluid-saturated poroelastic media. After a revisit on Biot’s theory, a poroelastic model is established as a prototype that is widely existing in practice. Then, a solution strategy is proposed based on differential operator method and series expansions. The basic solutions are derived and consist of the kernel functions. The solutions in general situations are extended by these basic solutions. Especially, as one of the novelties, the impermeable and permeable boundaries with different loading modes are integrated into this framework. Several different loading distributions are considered, including time-constant periodic loading and uniform loading on the infinite and finite boundaries. Later, the solutions are verified by comparing with the results calculated by numerical method. Based on this, a series of numerical tests is performed to study consolidation behaviours of a poroelastic medium. Some insights to the characteristics of temporal evolution during consolidation are explored, where the influences of drainage effect, loading modes and material properties on this process are analysed.

Anisotropic Poroelastic Modelling of Depletion-Induced Pore Pressure Changes in Valhall Overburden

Stress and pore pressure changes due to depletion of or injection into a reservoir are key elements in stability analysis of overburden shales. However, the undrained pore pressure response in shales is often neglected but needs to be considered because of their low permeability. Due to the anisotropic nature of shales, the orientation of both rock and stresses should be considered. To account for misalignment of the medium and the stress tensor, we used anisotropic poroelasticity theory to derive an angle-dependent expression for the pore pressure changes in transversely isotropic media under true-triaxial stress conditions. We experimentally estimated poroelastic pore pressure parameters of a shale from the Lista formation at the Valhall field. We combined the experimental results with finite element modelling to estimate the pore pressure development in the Valhall overburden over a period of nearly 40 years. The results indicate non-negligible pore pressure changes several hundred meters above the reservoir, as well as significant differences between pore pressure and effective stress estimates obtained using isotropic and anisotropic pore pressure parameters. We formulate a simple model approximating the undrained pore pressure response in low permeable overburden. Our results suggest that in the proximity of the reservoir the amplitude of the undrained pore pressure changes may be comparable to effective stresses. Combined with the findings of joint analysis of locations of casing deformation and total and effective stresses, the results suggest that pore pressure modelling may become an important element of casing collapse and caprock failure risk analysis and mitigation.

MPET2: a multi-network poroelastic and transport theory for predicting absorption of monoclonal antibodies delivered by subcutaneous injection

Subcutaneous injection of monoclonal antibodies (mAbs) has attracted much attention in the pharmaceutical industry. During the injection, the drug is delivered into the tissue producing strong fluid flow and tissue deformation. While data indicate that the drug is initially uptaken by the lymphatic system due to the large size of mAbs, many of the critical absorption processes that occur at the injection site remain poorly understood. Here, we propose the MPET2 approach, a multi-network poroelastic and transport model to predict the absorption of mAbs during and after subcutaneous injection. Our model is based on physical principles of tissue biomechanics and fluid dynamics. The subcutaneous tissue is modeled as a mixture of three compartments, i.e., interstitial tissue, blood vessels, and lymphatic vessels, with each compartment modeled as a porous medium. The proposed biomechanical model describes tissue deformation, fluid flow in each compartment, the fluid exchanges between compartments, the absorption of mAbs in blood vessels and lymphatic vessels, as well as the transport of mAbs in each compartment. We used our model to perform a high-fidelity simulation of an injection of mAbs in subcutaneous tissue and evaluated the long-term drug absorption. Our model results show good agreement with experimental data in depot clearance tests.

Poroelastic modelling reveals the cooperation between two mechanisms for albuminuria.

Albuminuria occurs when albumin leaks abnormally into the urine. Its mechanism remains unclear. A gel-compression hypothesis attributes the glomerular barrier to compression of the glomerular basement membrane (GBM) as a gel layer. Loss of podocyte foot processes would allow the gel layer to expand circumferentially, enlarge its pores and leak albumin into the urine. To test this hypothesis, we develop a poroelastic model of the GBM. It predicts GBM compression in healthy glomerulus and GBM expansion in the diseased state, essentially confirming the hypothesis. However, by itself, the gel compression and expansion mechanism fails to account for two features of albuminuria: the reduction in filtration flux and the thickening of the GBM. A second mechanism, the constriction of flow area at the slit diaphragm downstream of the GBM, must be included. The cooperation between the two mechanisms produces the amount of increase in GBM porosity expected in vivo in a mutant mouse model, and also captures the two in vivo features of reduced filtration flux and increased GBM thickness. Finally, the model supports the idea that in the healthy glomerulus, gel compression may help maintain a roughly constant filtration flux under varying filtration pressure.

Crossover from viscous fingering to fracturing in cohesive wet granular media: a photoporomechanics study.

We study fluid-induced deformation and fracture of cohesive granular media, and apply photoporomechanics to uncover the underpinning grain-scale mechanics. We fabricate photoelastic spherical particles of diameter d = 2 mm, and make a monolayer granular pack with tunable intergranular cohesion in a circular Hele-Shaw cell that is initially filled with viscous silicone oil. We inject water into the oil-filled photoelastic granular pack, varying the injection flow rate, defending-fluid viscosity, and intergranular cohesion. We find two different modes of fluid invasion: viscous fingering, and fracturing with leak-off of the injection fluid. We directly visualize the evolving effective stress field through the particles' photoelastic response, and discover a hoop effective stress region behind the water invasion front, where we observe tensile force chains in the circumferential direction. Outside the invasion front, we observe compressive force chains aligning in the radial direction. We conceptualize the system's behavior by means of a two-phase poroelastic continuum model. The model captures granular pack dilation and compaction with the boundary delineated by the invasion front, which explains the observed distinct alignments of the force chains. Finally, we rationalize the crossover from viscous fingering to fracturing by comparing the competing forces behind the process: viscous force from fluid injection that drives fractures, and intergranular cohesion and friction that resist fractures.

Акустическое и деформационное исследование раскрытия трещины гидроразрыва в пороупругом модельном материале

Акустическое и деформационное исследование раскрытия трещины гидроразрыва в пороупругом модельном материале

Frequency-dependent P-wave anelasticity due to multiscale (fractal) heterogeneities in rocks

Understanding the effect that multiscale heterogeneities have on the wave responses of rocks at different frequencies is essential in the interpretation of seismic data. In fact, the behaviors of ultrasonic and seismic waves differ because the experiments involve different spatial scales. Then, a solution is to apply a theory that establishes a relation between the wave properties at different frequency bands considering a size range of heterogeneities. To investigate this problem, we have measured the compressional wave (P-wave) anelasticity (velocity and attenuation) of tight reservoir rocks at ultrasonic, sonic and seismic frequencies. The wave behavior as a function of porosity or clay content shows a consistent trend. With increasing confining pressure, the effect of porosity on attenuation decreases, while that of clay content gradually becomes important. To interpret the data, we propose a double-fractal poroelasticity model by incorporating the self-similarity characteristics of cracks and clay minerals. The comparison between the experimental data and model results reveals the fractality of the clay inclusions and cracks, with radii range of [10−6, 10−1.5] m and [10−6, 10−3.1] m, respectively, which is responsible for the anelastic behavior of the waves on a wide frequency band.

Modeling large-volume subcutaneous injection of monoclonal antibodies with anisotropic porohyperelastic models and data-driven tissue layer geometries

Subcutaneous injection of therapeutic monoclonal antibodies (mAbs) has become one of the fastest-growing fields in the pharmaceutical industry. The transport and mechanical processes behind large volume injections are poorly understood. Here, we leverage a large-deformation poroelastic model to study high-dose, high-speed subcutaneous injection. We account for the anisotropy of subcutaneous tissue using of a fibril-reinforced porohyperelastic model. We also incorporate the multi-layer structure of the skin tissue, generating data-driven geometrical models of the tissue layers using histological data. We analyze the impact of handheld autoinjectors on the injection dynamics for different patient forces. Our simulations show the importance of considering the large deformation approach to model large injection volumes. This work opens opportunities to better understand the mechanics and transport processes that occur in large-volume subcutaneous injections of mAbs.

Multiphysics finite element method for a nonlinear poroelasticity model with finite strain

Multiphysics finite element method for a nonlinear poroelasticity model with finite strain

Associations of human femoral condyle cartilage structure and composition with viscoelastic and constituent-specific material properties at different stages of osteoarthritis

The relationships between structure and function in human knee femoral cartilage are not well-known at different stages of osteoarthritis. Thus, our aim was to characterize the depth-dependent composition and structure (proteoglycan content, collagen network organization and collagen content) of normal and osteoarthritic human femoral condyle cartilage (n = 47) and relate them to their viscoelastic and constituent-specific mechanical properties that are obtained through dynamic sinusoidal testing and fibril-reinforced poroelastic material modeling of stress-relaxation testing, respectively. We characterized the proteoglycan content using digital densitometry, collagen network organization (orientation angle and anisotropy) using polarized light microscopy and collagen content using Fourier transform infrared spectroscopy. In the superficial cartilage (0–10 % of thickness), the collagen network disorganization and proteoglycan loss were associated with the smaller initial fibril network modulus - a parameter representing the pretension of the collagen network. Furthermore, the proteoglycan loss was associated with the greater strain-dependent fibril network modulus - a measure of nonlinear mechanical behavior. The proteoglycan loss was also associated with greater cartilage viscosity at a low loading frequency (0.005 Hz), while the collagen network disorganization was associated with greater cartilage viscosity at a high loading frequency (1 Hz). Our results suggest that proteoglycan loss and collagen network disorganization reduce the pretension of the collagen network while proteoglycan degradation also increases the nonlinear mechanical behavior of the collagen network. Further, the results also highlight that proteoglycan loss and collagen disorganization increase the viscosity of femoral cartilage, but their contribution to increased viscosity occurs in completely different loading frequencies.

Discontinuous curvilinear collocated grid combined with nonuniform time step Runge-Kutta scheme for poroelastic finite-difference modeling

For poroelastic media, the existence of a slow P-wave mode, next to the standard fast P and S waves, hinders efficient numerical implementations to propagate poroelastic waves through arbitrary seismic models. The slow P-wave speed can be an order of magnitude smaller than the fast P-wave speed. Hence, a stable and accurate simulation that can capture the slow P wave requires a fine grid and a small time step, which increases the overall computation cost greatly. To decrease the computation cost, we propose a poroelastic finite-difference simulation method that combines a discontinuous curvilinear collocated-grid method with a nonuniform time step Runge-Kutta (NUTS-RK) scheme. The fine grid and small time step are only used for areas near interfaces, where the contribution of the slow P wave is nonnegligible. The NUTS-RK scheme is derived from a Taylor expansion and it can circumvent the need for interpolations or extrapolations otherwise required by communications between different time levels. The accuracy and efficiency of the proposed method are verified by numerical tests. Compared with the curvilinear collocated-grid finite-difference method that uses a globally uniform space grid as well as a uniform time step, the proposed method requires fewer computing resources and can reduce the computing time greatly.

Minimum design requirements for a poroelastic mimic of articular cartilage

The exceptional functional performance of articular cartilage (load-bearing and lubrication) is attributed to its poroelastic structure and resulting interstitial fluid pressure. Despite this, there remains no engineered cartilage repair material capable of achieving physiologically relevant poroelasticity. In this work we develop in silico models to guide the design approach for poroelastic mimics of articular cartilage. We implement the constitutive models in FEBio, a PDE solver for multiphasic mechanics problems in biological and soft materials. We investigate the influence of strain rate, boundary conditions at the contact interface, and fiber modulus on the reaction force and load sharing between the solid and fluid phases. The results agree with the existing literature that when fibers are incorporated the fraction of load supported by fluid pressure is greatly amplified and increases with the fiber modulus. This result demonstrates that a stiff fibrous phase is a primary design requirement for poroelastic mimics of articular cartilage. The poroelastic model is fit to experimental stress-relaxation data from bovine and porcine cartilage to determine if sufficient design constraints have been identified. In addition, we fit experimental data from FiHy™, an engineered material which is claimed to be poroelastic. The fiber-reinforced poroelastic model was able to capture the primary physics of these materials and demonstrates that FiHy™ is beginning to approach a cartilage-like poroelastic response. We also develop a fiber-reinforced poroelastic model with a bonded interface (rigid contact) to fit stress relaxation data from an osteochondral explant and FiHy™ + bone substitute. The model fit quality is similar for both the chondral and osteochondral configurations and clearly captures the first order physics. Based on this, we propose that physiological poroelastic mimics of articular cartilage should be developed under a fiber-reinforced poroelastic framework.

Backflow modeling in nanofluid infusion and analysis of its effects on heat induced damage during magnetic hyperthermia

• Simulate the backflow behavior for nanofluid infusion inside bio-tissue under a geometric nonlinear model. • Investigate the bio-tissue deformation and its effect on the change of material property during nanofluid infusion. • Investigate the interstitial pressure and the local stress distribution inside bio-tissue due to the nanofluid infusion. • Effect of backflow on treatment temperature distribution and heat induced damage for malignant tissue. Although targeted magnetic hyperthermia has been proven to be an effective tumor ablation technique, its use in clinical applications is still scarce particularly due to the difficulty in imposing a desired nanofluid distribution in the therapeutic area. In addition to the inherent difficulty of imposing a distribution with few injection shots, during the nanofluid infusion, the tissue deformation can cause the nanofluid deviation from the targeted injection area and the backflow along the needle can deliver the injected nanofluid to the outer surface of the tissue. Both phenomena can result in an irregular distribution for nanofluid inside bio-tissue. This study develops a poroelastic model considering geometrically nonlinear behavior in order to evaluate the effect of syringe needle size and infusion rate on the backflow. A 26 gauge needle for syringe is used as a typical example to further investigate the nanofluid transport and the change of solid matrix material properties under different infusion rates after comparing the infusion results for several sizes of needle. Finally, the resulting nanofluid concentration distribution obtained with the proposed model is used to simulate the temperature distribution and the cancerous cell damage. The results demonstrate that the infusion pressure and its resulting tissue deformation are the fundamental reasons for obtaining an irregular solution distribution. Tissue deformation induces the increase of porosity and permeability for biomaterials around the tip, and enhances the fluidity of nanofluids inside the tissue. The results also indicate that the increase in backflow length can improve the uniformity of the nanofluid distribution after diffusion and, consequently, the treatment effect. However, it also increases the risk of MNP leakage from the targeted area to the tumor surface, so it is important to keep the backflow rate limited during the injection process.

Study of Locking Compression Plate Through Biodegradable Implant

Orthopaedic implant biomechanics research is booming, especially in bone fixation. Fixation involves securing a plate to a broken bone. The femur fractured mostly. Long bone fractures can be difficult to cure despite technological and medical breakthroughs. This study analyses the performance and optimal screw arrangement for biodegradable locking compression plate. This study compares biodegradable bone plate materials to identify the best (Iron, Zinc and Magnesium). SolidWorks models fracture repair plates and fixes them in a normal walking condition to a mid-ship fracture. Further, finite element analysis was performed on models with homogeneous and isotropic bone and plate. Simulation was done using COMSOL programme and screws. Idealized poroelastic 3D FE femoral model with 5 mm fracture gap and plate-screw design. We saw stress and displacement. The minimal von Mises stress and deformation for 6 screws. Under pure zinc and magnesium load, the highest von Mises stress was 7.94 MPa and the maximum deformation was 0.08 mm, proving that iron was the best material. Based on finite element analysis, the LCP can offer mechanical stability for comminuted fractures, fixing the bone block and promoting bone healing.

Numerical investigation of salt-frost damage of pervious concrete at the scale of a few aggregates

In this study, we aim to gain insight into the damage mechanisms of pervious concrete subject to frost attacks in the presence of salt. We perform numerical simulations using a poroelastic model on system geometries representing pervious concrete at the scale of one or a few aggregates: (1) one aggregate coated with cement paste, (2) one aggregated coated with a cracked layer of cement paste, and (3) two aggregates coated and bonded with cement paste. The numerical simulations indicate that the damage is more likely to occur at the contact between aggregates. Furthermore, we observe significant shear stress at the vicinity of the paste/aggregate interface. We undertake a thorough parametric study to evaluate the impact of various boundary conditions, initial conditions, and materials parameters on the stresses generated during one or several freeze–thaw cycles. The insights can provide guidelines to design pervious concretes with enhanced freeze–thaw durability.

A two-level multiphysics finite element method for a nonlinear poroelasticity model

In this paper, we propose a two-level multiphysics finite element method for a nonlinear poroelasticity model. To clearly reveal the multiphysics processes and overcome the “locking phenomenon”, we reformulate the original fluid-solid coupled problem into a fluid-fluid coupled problem–a generalized nonlinear Stokes problem coupled with a diffusion problem. To reduce the cost of computation, we propose two fully discrete coupling and decoupling two-level multiphysics finite element methods and use the backward Euler method for time variable of the reformulated nonlinear poroelasticity model. In computation, the generalized nonlinear poroelasticity (Stokes in Algorithm 2) problem is solved by using the Newton iterative method on a coarse mesh, then a linearized poroelasticity problem is solved on a fine mesh by using the solution of the coarse mesh. Then, we give the stability analysis and error estimates of the proposed methods. Finally, we show some numerical examples to verify the theoretical results–overcoming “locking phenomenon” and reducing the computational cost. • It is the first time to propose a two-level multiphysics finite element method for the nonlinear poroelasticity model. • The optimal order error estimate of the proposed two-level method is given. • To reduce the cost of computation, a poroelasticity problem is solved by using the Newton method on a coarse mesh.

Hydro-mechanical response of Opalinus Clay in the CO2 long-term periodic injection experiment (CO2LPIE) at the Mont Terri rock laboratory

Guaranteeing the sealing capacity of caprocks becomes paramount as CO2 storage scales up to the gigaton scale. A significant number of laboratory experiments have been performed with samples of intact rock, showing that low-permeability and high-entry pressure caprocks have excellent sealing capacities to contain CO2 deep underground. However, discontinuities, such as bedding planes, fractures and faults, affect the rock properties at the field scale, being at the same time challenging to monitor in industrial-scale applications. To bridge these two spatial scales, Underground Research Laboratories (URLs) provide a perfect setting to investigate the field-scale sealing capacity of caprocks under a well-monitored environment. In particular, the CO2 Long-term Periodic Injection Experiment (CO2LPIE) at the Mont Terri rock laboratory, Switzerland, aims at quantifying the advance of CO2 in Opalinus Clay, an anisotropic clay-rich rock with bedding planes dipping 45° at the experiment location. To assist in the design of CO2LPIE and have an initial estimate of the system response, we perform plane-strain coupled Hydro-Mechanical simulations using a linear transversely isotropic poroelastic model of periodic CO2 injection for 20 years. Simulation results show that pore pressure changes and the resulting stress variations are controlled by the anisotropic behavior of the material, producing a preferential advance along the bedding planes. CO2 cannot penetrate into Opalinus Clay due to the strong capillary effects in the nanoscale pores, but advances dissolved into the resident brine. We find that the pore pressure oscillations imposed at the injection well are attenuated within tens of cm, requiring a close location of the monitoring boreholes with respect to the injection interval to observe the periodic signal.Article highlightsUnderground rock laboratory experiments permit examining the caprock sealing capacity at a representative scale for CO2 storage;We perform coupled transverse isotropic hydro-mechanical simulations to gain insight on the response of shaly rock to CO2 periodic injection;Simulation results assist in the design of the injection amplitude and period and monitoring of the long-term periodic CO2 injection experiment.

Modelling of pore pressure evolution in a compressional tectonic setting: The Kuqa Depression, Tarim Basin, northwestern China

The Kuqa Depression is part of a Mesozoic-Cenozoic foreland basin located at the northern margin of the Tarim Basin. High fluid overpressures were reported in the Mesozoic section related to both the complex tectonic evolution and the sealing by the salt-bearing sequence within the Paleogene Kumugeliemu Group. The role of structural evolution and compressional shortening in the generation of overpressures is poorly understood and requires a model-based understanding of the basin structure for different time steps. Structurally restored geometries based on a present-day geological section interpreted from a 2D seismic line, has been used as input for a basin and petroleum system model to simulate pore pressure history through geological time. In this simulation, we demonstrate structural dependencies of pore pressure development, and examine the impact of disequilibrium compaction, tectonic compression, opening and closing of faults over time, as well as folding on overpressure evolution. The poroelastic model is used to quantitatively evaluate the contribution of horizontal shortening due to tectonic compression on overpressure. We found that the pressure increase caused by 12.5% shortening can account for a maximum of more than 60% of overpressure, depending on lithology and deformation strength. We also simulated the effect of salt content within the seal layer on overpressure and found that the increase in salt has promoted the onset time and magnitude of overpressure in the underlying strata, which favors porosity preservation. A heat flow sensitivity analysis was performed, suggesting that the pressure increase caused by extremely high heat flow is rather low.