Poroelastic Model Research Articles

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.

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.

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.

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.

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.

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.

Separating Injection‐Driven and Earthquake‐Driven Induced Seismicity by Combining a Fully Coupled Poroelastic Model With Interpretable Machine Learning

Separating Injection‐Driven and Earthquake‐Driven Induced Seismicity by Combining a Fully Coupled Poroelastic Model With Interpretable Machine Learning

Nonlinear Tissue Permeability Drives Tissue Pressure and Injection Distribution: A Computational Investigation of Subcutaneous Injections.

There is a significant opportunity to expand the understanding of subcutaneous injection mechanics with an aim to increase injectable volume while controlling tissue strain and associated subject pain. Computational modeling can evaluate the mechanics of subcutaneous injections as a supplement to experimental, animal and clinical studies. The objectives of this study are to (1) develop a computational model for subcutaneous injection in tissue, (2) investigate the influence anisotropic tissue permeability has on bolus formation, and (3) explore the effects that injection flow rate and viscosity have on injection flow and tissue strain. Poroelastic models with subsurface flow were implemented in finite element software (COMSOL, ABAQUS). Pore pressure and injectate distribution showed excellent agreement with experimental results when evaluated at multiple injection rates (20 ml/hr, 120 ml/hr and 360 ml/hr). Including the anisotropy of tissue permeability causes the injectate to preferentially spread horizontally, similar to experimentally observed bolus distributions. Cases are presented to provide additional insight into injection mechanics, including variations on the delivery rate, the injection volume, viscosity and the thickness of the subcutaneous layer. The results support the use of computational modeling as a valid tool for understanding tissue strains and injectate distributions for large volume injections.

Inertial flow-induced fluid pressurization enhances the reactivation of rate-and-state faults

We reveal that inertial flow can introduce additional pressure perturbations which accelerate the instability of critically stressed faults. We integrate a poroelastic spring-slider model with rate-and-state friction (RSF), a nonlinear flow model characterized by the improved Izbash equation, and a universal visco-inertial permeability model. The effect of inertial flow depends on the fracture network properties, proximity to faults, and injection parameters. Significant inertial flow results in higher pressure magnitudes and pressurization rates, causing notable differences in predictions between linear and nonlinear flow models, as well as aging and slip laws. The impact of inertial flow is particularly pronounced within a specific permeability range and is enhanced by high-rate injections. The fault reactivation is delayed due to fault strengthening with RSF in response to increased pressurization rates. Conversely, the presence of inertial flow enhances fault reactivation and promotes unstable slip behaviors. Furthermore, the results demonstrate that cyclic injection increases the critical stiffness of faults without an adequate release of pore pressure in each cycle. The time interval of the cyclic injection is prolonged as inertial flow generates higher pressure levels. This study highlights the importance of inertial flow in the stability analysis of critically stressed faults.

Implication of fast shear wave azimuth and critically stressed fractures in a coalbed methane reservoir

The orientation of the fractures and stresses within coal seams plays a critical role in gas production from coalbed methane reservoirs. In this study, we used resistivity images and sonic logs to investigate these parameters, aiming to (1) establish the relationship between fracture orientations and the polarization angles of fast shear waves and (2) detect active fractures in the coal seam. Shear waves in anisotropic formations are split into fast and slow components, with Alford’s rotation method used to determine the polarization angles of the fast shear wave. We found that the fast shear wave aligns with the direction of higher fracture intensity. Subsequently, we incorporated the poroelastic strain model to estimate the vertical ([Formula: see text]), maximum horizontal ([Formula: see text]), and minimum horizontal ([Formula: see text]) stresses in the wellbore. These stress magnitudes aided in identifying the faulting regime and were corroborated by vertical opening mode fractures. Validation of [Formula: see text] and [Formula: see text] involved comparisons with the breakout width in image logs and the closure pressure observed during hydraulic fracturing treatments. Applying Mohr’s Coulomb criteria, the stress model discerned the state of the fractures, transforming the stress magnitudes into shear and effective normal stress on each fracture plane. Our observations indicated that the identified fractures existed in a noncritically stressed condition, suggesting a lack of interconnectivity among them. These findings correspond to the absence of gas production to date, providing insights into the dynamics of fractures and their impact on production behavior.

Revealing Detailed Cartilage Function Through Nanoparticle Diffusion Imaging: A Computed Tomography & Finite Element Study

The ability of articular cartilage to withstand significant mechanical stresses during activities, such as walking or running, relies on its distinctive structure. Integrating detailed tissue properties into subject-specific biomechanical models is challenging due to the complexity of analyzing these characteristics. This limitation compromises the accuracy of models in replicating cartilage function and impacts predictive capabilities. To address this, methods revealing cartilage function at the constituent-specific level are essential. In this study, we demonstrated that computational modeling derived individual constituent-specific biomechanical properties could be predicted by a novel nanoparticle contrast-enhanced computer tomography (CECT) method. We imaged articular cartilage samples collected from the equine stifle joint (n = 60) using contrast-enhanced micro-computed tomography (µCECT) to determine contrast agents’ intake within the samples, and compared those to cartilage functional properties, derived from a fibril-reinforced poroelastic finite element model. Two distinct imaging techniques were investigated: conventional energy-integrating µCECT employing a cationic tantalum oxide nanoparticle (Ta2O5-cNP) contrast agent and novel photon-counting µCECT utilizing a dual-contrast agent, comprising Ta2O5-cNP and neutral iodixanol. The results demonstrate the capacity to evaluate fibrillar and non-fibrillar functionality of cartilage, along with permeability-affected fluid flow in cartilage. This finding indicates the feasibility of incorporating these specific functional properties into biomechanical computational models, holding potential for personalized approaches to cartilage diagnostics and treatment.

A mechano-regulation model to design and optimize the surface microgeometry of titanium textured devices for biomedical applications

In a technological context where, thanks to the additive manufacturing techniques, even sophisticated geometries as well as surfaces with specific micrometric features can be realized, we propose a mechano-regulation algorithm to determine the optimal microgeometric parameters of the surface of textured titanium devices for biomedical applications. A poroelastic finite element model was developed including a portion of bone, a portion of a textured titanium device and a layer of granulation tissue separating the bone from the device and occupying the space between them. The algorithm, implemented in the Matlab environment, determines the optimal values of the root mean square and the correlation length that the device surface must possess to maximize bone formation in the gap between the bone and the device. For low levels of compression load acting on the bone, the algorithm predicts low values of root mean square and high values of correlation length. Conversely, high levels of load require high values of root mean square and low values of correlation length. The optimal microgeometrical parameters were determined for various thickness values of the granulation tissue layer. Interestingly, the predictions of the proposed computational model are consistent with the experimental results reported in the literature. The proposed algorithm shows promise as a valuable tool for addressing the demands of precision medicine. In this approach, the device or prosthesis is no longer designed solely based on statistical averages but is tailored to each patient's unique anthropometric characteristics, as well as considerations related to their metabolism, sex, age, and more.

Stability of highly inclined non-circular wellbores in isotropic formations

The shear and tensile stabilities of highly inclined non-circular wellbores are investigated in this study. Using the equivalent-ellipse hypothesis, the non-circular geometry was approximated as an ellipse, and the corresponding stress concentration equations are presented. With the new set of stress concentration equations, a comprehensive study of the tensile and shear stabilities of an elliptical borehole was conducted, including the impact of well inclination and azimuthal angles, horizontal stress difference, degree of ellipticity, and orientation of the maximum horizontal stress to the major axis of the ellipse. Using five commonly used shear failure criteria, we observed that both Mohr–Coulomb and Drucker Prager (inscribed) failure criteria predicted higher collapse pressures, relative to the others including Drucker Prager (inscribed), Mogi-Coulomb, and Modified Lade. While Drucker Prager's (circumscribed) failure criterion underestimates the collapse pressure. Both the linear elastic and poroelastic models were used in investigating the fracture initiation orientation and pressure of highly inclined elliptical boreholes. The prediction from the poroelastic model is always less than the linear elastic model. In some instances, they predict different fracture initiation orientations. From this study, we observed that generally, a near-circular wellbore is more stable than elliptical borehole in both shear and tension. Nevertheless, there are some well inclination and azimuthal angles than can make an elliptical borehole have more shear and tensile stabilities than a near-circular wellbore.