Computational Simulation of Coupled Poromechanical Processes in Deformable Porous Media.
Abstract not provided.
Warren, Maria Elizabeth↗
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Results for “Poromechanics”
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Poromechanical Simulations and Fault Stability Assessments for CO2 Storage
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Geosciences↗
On the peridynamic effective force state and multiphase constitutive correspondence principle
This article concerns modeling unsaturated deformable porous media as an equivalent single-phase and single-force state peridynamic material through the effective force state. The balance equations of linear momentum and mass of unsaturated porous media are presented by defining relevant peridynamic states. The energy balance of unsaturated porous media is utilized to derive the effective force state for the solid skeleton that is an energy conjugate to the nonlocal deformation state of the solid, and the suction force state. Through an energy equivalence, a multiphase constitutive correspondence principle is built between classical unsaturated poromechanics and peridynamic unsaturated poromechanics. The multiphase correspondence principle provides a means to incorporate advanced constitutive models in classical unsaturated porous theory directly into unsaturated peridynamic poromechanics. Finally, numerical simulations of localized failure in unsaturated porous media under different matric suctions are presented to demonstrate the feasibility of modeling the mechanical behavior of such three-phase materials as an equivalent single-phase peridynamic material through the effective force state concept.
42 ENGINEERING↗
Fracture-matrix fluid exchange in oil-bearing unconventional mudstones
The poromechanical properties of unconventional reservoir materials are in large part dictated by their mineralogy. Since these properties govern the response to stress experienced during hydraulic fracturing, fluid production, and fluid injection, they play a central role in the formation of microcracks or bedding delaminations which ultimately dominate mass transport. In this work we study access to the porosity of end member unconventional reservoir materials, where the end members are predominantly dictated by carbonate content. Access to the porosity is quantified using state of the art 3D x-ray computed tomography coupled with physics informed data analytics. Xenon gas, which attenuates x-rays, provides a spatiotemporal map of access to the porosity. The accessible porosity is quantified over a range of net confining stress relevant to the manmade disturbances listed above. These experiments demonstrate that heavily carbonated mudstones are nearly impermeable at the core (~ cm) scale, while carbonate free analogues afford better access to the microstructure. Consistent with previous qualitative 2D radiographs, access to the interior of the clastic mudstones is first observed along planar microcracks, followed by slow penetration into the surrounding matrix. Physics informed data analytics of the 3D tomography measurements presented here show that these microcracks do not permit uniform access to the adjacent rock matrix. In addition, variation of the effective pressure elucidates the mechanisms that govern fracture/matrix fluid exchange. Under conditions consistent with hydrocarbon production fluid accumulates in the immediate vicinity of the nearest microcrack. While there is clear evidence that, as intended, part of this accumulation is from the more distant matrix, fluid is also squeezed out of the microcrack. The fluid build-up at the microcrack indicates that migration out of the rock is hindered by the coupled poroelastic response of the microcrack and adjacent rock matrix. We show that these mechanisms ultimately account for the meager oil recovery factors realized in practice. These insights have implications for making reservoir scale predictions based on core scale observations, and provide a basis for devising new asset development techniques to access more porosity, and enhance fluid extraction. Finally, these findings shed light on key features and mechanisms that govern shale storage capacity, with relevance to other important industrial processes, such as geologic CO 2 storage.
58 GEOSCIENCES↗
Characteristics of Fluid‐Solid Interaction Constitutive Models Within Poroelastodynamics at Higher Strain‐Rates and Large Deformations Implemented in 1D
The large deformation, mixed formulation, finite element (FE) modeling approach presented in Irwin et al. 2024 is extended herein to include improved constitutive models for representing dynamic solid-fluid interactions at higher strain rates (𝒪(10 2 −10 3 )s −1 ) and larger overpressure magnitudes (𝒪(10 2 )kPa) within a biphasic soft porous material using Theory of Porous Media (TPM) at finite strain. Specifically, these constitutive modeling improvements are the following: (i) a more physically robust constitutive model for pore fluid seepage velocity via inclusion of pore fluid viscous stress, and (ii) a modified deformation-dependent-permeability model and updated hyperelastic constitutive model better suited for handling larger volumetric compressions and extensions. The novelty of the present work is mainly the contribution (i): inclusion of pore fluid viscous stress at higher strain-rate and large deformations, which requires 𝐶 1 continuity in the weak formulation, accomplished by employing Hermite cubic interpolation functions within a mixed nonlinear poromechanical finite element formulation. In (ii), the model is updated to weakly enforce solid phase incompressibility, such that this assumption is not violated numerically, which provides improved numerical stability for achieving larger overpressure magnitudes on 𝒪(10 2 ) kPa, which were not achievable with the previous Kozeny–Carman model in Irwin et al. 2024. Also in (ii), the volumetric part of the solid skeleton free energy function is modified to ensure proper bounds on the solid skeleton Jacobian of deformation 𝐽 s related to incompressibility of the solid phase. Uniaxial strain, unidirectional flow examples at higher strain rates (𝒪(10 2 −10 3 )s −1 ) and larger deformations (up to 0.2 (or 20%) nominal axial strain) demonstrate the improved physical representation—and numerical stability—of these constitutive model improvements.
42 ENGINEERING↗
Experimental Investigation of Elastodynamic Nonlinear Response of Dry Intact, Fractured and Saturated Rock
Nonlinear elastodynamic response of fractured rocks carries crucial information on fracture features that can be exploited to forecast flow properties, friction constitutive behavior and poromechanical response. Well-controlled laboratory experiments are designed to measure the nonlinear elastodynamic response of Westerly granite in three states: dry intact, dry fractured and saturated fractured. We study the effect of fracturing and saturation in modifying the elastodynamic response of the rock. Each sample is tested at a normal stress level of 15 MPa. We measure the elastodynamic response of an intact L-shaped sample of Westerly Granite subjected to normal stress oscillations of prescribed amplitudes (0.2–1 MPa) and frequencies (0.1, 1, 10 Hz). Ultrasonic waves transmitted across the sample are used to monitor the evolution of wave velocity before, during and after dynamic stressing. Furthermore, the nonlinearity of the elastodynamic response is measured in terms of: (1) the offset in normalized wave velocity; (2) the amplitude of wave velocity fluctuation during the oscillations; and (3) recovery rate of the wave velocity post-oscillation. We observe that the three nonlinearity parameters show a similar trend. Irrespective of the parameter, the nonlinearity measures higher for sample in dry-intact condition than that for dry-fractured and the saturated-fractured sample exhibits smaller nonlinearity than the dry-fractured sample. As expected, the saturated sample exhibits less nonlinearity than the dry intact and fractured samples due to the presence of interstitial fluid and the resulting increased interface stiffness. Conversely, the dry intact rock shows a higher nonlinearity than the dry fractured. We use numerical simulations to show that the presence of fracture significantly alters the strain distribution across the bulk of the sample and only the contacting asperities are highly strained, thus resulting in a decrease in the measured elastodynamic nonlinearity.
58 GEOSCIENCES↗
Modelling the development of capillary pressure in freshly 3D-printed concrete elements
3D concrete printing is a promising technology recently developed to automate construction. Since no formwork is used in this technology to support and protect fresh concrete, there are two aspects which considerably accelerate the development of capillary pressure in 3D-printed concrete in comparison to conventionally placed concrete: i) high stiffness of 3D-printed needed to provide sufficient buildability, and ii) very early and fast evaporation of pore water. Accelerated development of capillary pressure may lead to severe plastic shrinkage cracking in 3D-printed elements and, hence, need to be mitigated. This investigation aims at providing a poromechanical model for capillary pressure development in 3D-printed elements. To simulate the development of capillary pressure and plastic shrinkage, environmental factors, material properties, and element geometry need to be considered as a whole. The model inputs – coefficient of permeability, static bulk modulus, air entry pressure and chemical shrinkage rate – were determined experimentally. The model was validated for two fine-grained concretes. Both 3D-printed materials yielded faster capillary pressure increase in comparison to cast concrete, while partial substitution of cement with silica fume further accelerated the capillary pressure development. Furthermore, due to the lower permeability of the mixture containing silica fume, the gradient of capillary pressure between 3D-printed layers increased, as did the gradient of plastic shrinkage.
36 MATERIALS SCIENCE↗
An integrated numerical model for coupled poro-hydro-mechanics and fracture propagation using embedded meshes
Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard mitigation across such applications. This work extends the coupled model multiphase flow and poromechanical model of Ren et al. (2018) to admit fracture propagation (FP). The coupled XFEM-EDFM scheme utilizes a separate fracture mesh that is embedded on a static background mesh. The onset and dynamics of fracture propagation are governed by the equivalent stress intensity factor (SIF) criterion. A domain-integral method (J integral) is applied to compute this information. Additionally, an adaptive time-marching scheme is proposed to rapidly restrict and grow temporal resolution to match the underlying time-scales. The proposed model is verified with analytical solutions, and shows the capability to accurately and adaptively co-simulate fluid transport and deformation as well as the propagation of multiple fractures.
42 ENGINEERING↗
A coupled thermo-hydro-mechanical model for simulating leakoff-dominated hydraulic fracturing with application to geologic carbon storage
A potential risk of injecting CO2 into storage reservoirs with marginal permeability (≲ 10 mD (1 mD = 10 –15 m 2 )) is that commercial injection rates could induce fracturing of the reservoir and/or the caprock. Such fracturing is essentially fluid-driven fracturing in the leakoff-dominated regime. Recent studies suggested that fracturing, if contained within the lower portion of the caprock complex, could substantially improve the injectivity without compromising the overall seal integrity. Modeling this phenomenon entails complex coupled interactions among the fluids, the fracture, the reservoir, and the caprock. Here, we develop a simple method to capture all these interplays in high fidelity by sequentially coupling a hydraulic fracturing module with a coupled thermal-hydrological-mechanical (THM) model for nonisothermal multiphase flow. The model was made numerically tractable by taking advantage of self-stabilizing features of leakoff-dominated fracturing. The model is validated against the PKN solution in the leakoff-dominated regime. Moreover, we employ the model to study thermo-poromechanical responses of a fluid-driven fracture in a field-scale carbon storage reservoir that is loosely based on the In Salah project's Krechba reservoir. The model reveals complex yet intriguing behaviors of the reservoir-caprock-fluid system with fracturing induced by cold CO 2 injection. We also study the effects of the in situ stress contrast between the reservoir and caprock and thermal contraction on the vertical containment of the fracture. The proposed model proves effective in simulating practical problems on length and time scales relevant to geological carbon storage.
58 GEOSCIENCES↗
Prediction and demonstration of periodic tensile cracking in rate-dependent porous cement
Periodic dilation bands are shown to occur when cylinder-shaped saturated cement specimens are subjected to rapid decompression, with the spacing between the bands scaling as a power law of the decompression time. This behavior is predicted by theory, which is specified to this scenario based on prior work that was more general and applied to compaction. Specifically, the formation of the bands is shown to coincide with periodicity that naturally arises in the effective stress when the material follows a Terzaghi-type consolidation law, although in reverse for dilation and with material deformation described by a rate-dependent viscoplastic law. When strain rate is proportional to effective stress to a power that is greater than one, periodic regions of tensile effective stress arise through the poromechanical fluid-solid coupling. The theoretically-predicted exponent of the resulting power-law relationship between dilation band spacing and unloading time successfully brackets the experimental results, for which it is observed that the exponent is slightly stronger than a square-root relationship (0.28 to 0.67) at testing temperatures of 20 °C and 90 °C. Further, these results demonstrate that rapid-depressurization leads to periodic fracturing that could, on the one hand, be detrimental to the isolation provided by cement used to seal wellbores in the petroleum industry. On the other hand, the dilation bands could also be favorable to production if generated in low-permeability reservoir rocks such as shales that are targeted for petroleum production or granites that are targeted for geothermal energy.
36 MATERIALS SCIENCE↗
Nonlinear elastodynamic behavior of intact and fractured rock under in-situ stress and saturation conditions
Not provided.
Materials Science↗
How Equivalent Are Equivalent Porous Media?
Abstract Geoenergy and geoengineering applications usually involve fluid injection into and production from fractured media. Accounting for fractures is important because of the strong poromechanical coupling that ties pore pressure changes and deformation. A possible approach to the problem uses equivalent porous media to reduce the computational cost and model complexity instead of explicitly including fractures in the models. We investigate the validity of this simplification by comparing these two approaches. Simulation results show that pore pressure distribution significantly differs between the two approaches even when both are calibrated to predict identical values at the injection and production wells. Additionally, changes in fracture stability are not well captured with the equivalent porous medium. We conclude that explicitly accounting for fractures in numerical models may be necessary under some circumstances to perform reliable coupled thermohydromechanical simulations, which could be used in conjunction with other tools for induced seismicity forecasting.
58 GEOSCIENCES↗
Automatic Time Step Control to Resolve Hydromechanically Driven Fault Reactivation, Spontaneous Nucleation, and Seismic Arrest
Abstract A physical understanding of the progression from flow‐driven (quasi‐static) poromechanical deformation to dynamic fault rupture is critical to the resilient operations of several engineering systems. These processes are bridged by a progression from fault reactivation to the spontaneous nucleation of unstable sliding. Toward addressing this challenge, novel automatic time step size control methods are developed to enable accurate and efficient simulation of these dynamics and transitions from the first principles. The controllers combine local models for discretization error and Coulomb failure conditions to automatically adjust the time step size across several orders of magnitude. The methods do not require additional empirical or theoretical input and can resolve the pre‐rupture, interseismic, and seismic periods to the allowed accuracy. The computational results reveal that the proposed methods automatically capture the onset of reactivation and nucleation for homogeneous and heterogeneous fields. Hydrodynamic and structural heterogeneity lead to disparate critical nucleation sizes compared to those predicted by theory. The results highlight its potential in predicting induced seismicity in realistic subsurface engineering systems and at practical scales.
Environmental Sciences & Ecology↗
The Effect of Hydrothermal Alteration and Microcracks on Hydraulic Properties and Poroelastic Deformation: A Case Study of the Blue Mountain Geothermal Field
Abstract Geothermal energy plays a vital role in decarbonizing electricity and heat supply. Effective utilization of geothermal resources hinges on identifying or generating permeable reservoir zones and understanding how effective pressure variations affect fluid circulation and reservoir properties by poroelastic deformation. Hydrothermal alteration can modify the petrophysical properties of geothermal reservoir rocks, which may increase or decrease its productivity. Understanding these alteration effects is essential to predict and optimize long‐term sustainable geothermal operations. Here, we investigate the impact of hydrothermal alteration on poroelastic and hydraulic properties of diverse lithologies in a series of deformation tests performed at several confining (0–80 MPa) and pore pressure (10–30 MPa) levels. Experimental results of hydrothermally altered dikes and phyllites obtained from the Blue Mountain geothermal field (Nevada, USA) are compared to thermally cracked La Peyratte granite (France) and correlated with petrophysical properties, mineral composition, and microstructures. Argillic alteration of dikes increases porosity and storage capacity but lowers thermal conductivity and increases pore compressibility. Conversely, silicate precipitation in phyllites increases stiffness and thermal conductivity but also reduces porosity and permeability. Experimentally determined effective pressure coefficients range from 0.1 to 0.9, differ for permeability and volumetric strain and decrease with increasing effective pressure. The presence of compliant microcracks and crack‐like pores significantly increases the stress sensitivity of La Peyratte granite and silicified phyllites. This study demonstrates how thermal and chemical alteration impacts poromechanical and petrophysical characteristics of geothermal targets, which ultimately govern reservoir stability and subsidence, induced seismicity as well as fluid and heat extraction efficiency during geothermal operations.
Schuster, Valerian [Helmholtz Centre Potsdam GFZ G↗
Multiphysics modelling in PyLith: poroelasticity
SUMMARY PyLith, a community, open-source code for modelling quasi-static and dynamic crustal deformation with an emphasis on earthquake faulting, has recently been updated with a flexible multiphysics implementation. We demonstrate the versatility of the multiphysics implementation by extending the code to model fully coupled continuum poromechanics. We verify the newly incorporated physics using standard benchmarks for a porous medium saturated with a slightly compressible fluid. The benchmarks include the 1-D consolidation problem as outlined by Terzaghi, Mandel’s problem for the 2-D case, and Cryer’s problem for the 3-D case. All three benchmarks have been added to the PyLith continuous integration test suite. We compare the closed form analytical solution for each benchmark against solutions generated by our updated code, and lastly, demonstrate that the poroelastic material formulation may be used alongside the existing fault implementation in PyLith.
Geochemistry & Geophysics↗
Fracturing in Wet Granular Media Illuminated by Photoporomechanics
Here, we study fluid-induced deformation and fracture of granular media and apply photoporomechanics to uncover the underpinning grain-scale mechanics. We fabricate spherical photoelastic particles of 2-mm diameter to form a monolayer granular pack in a circular Hele-Shaw cell that is initially filled with a viscous fluid. The key distinct feature of our system is that, with spherical particles, the granular pack has a connected pore space, thus allowing for pore-pressure diffusion and the study of effective stress in coupled poromechanical processes. We inject air into the fluid-filled photoelastic granular pack, varying the initial packing density and confining weight. With our recently developed experimental technique, photoporomechanics, we find two different modes of fluid invasion: fracturing in fluid-filled elastic media (with strong photoelastic response) and viscous fingering in frictional fluids (with weak or negligible photoelastic response). We directly visualize the evolving effective stress field and discover an effective stress shadow behind the propagating fracture tips, where the granular pack exhibits undrained behavior. We conceptualize the behavior of the system by means of a mechanistic model for a wedge of the granular pack bounded by two growing fractures. The model captures the pore-pressure build-up inside the stress shadow region and the grain compaction in the annular region outside. Our model reveals that a jamming transition determines the distinct rheological behavior of the wet granular pack, from a friction-dominated to an elasticity-dominated response.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Utah FORGE 5-2615: Laboratory Data for Insights on Hydraulic Fracture Closure and Stress Measurement
This dataset includes data from injection/fall-off experiments conducted in controlled laboratory settings. The aim is to investigate the physics governing fracture closure and the associated stress measurements during hydraulic fracturing. These time series data include flow rate, pressure, and volume measurements. These experiments were conducted as part of Utah FORGE Project 5-2615: Thermo-poromechanical Response of Fractured Rock.
15 GEOTHERMAL ENERGY↗
GEOS: A performance portable multi-physics simulation framework for subsurface applications
GEOS is a simulation framework focused on solving tightly coupled multi-physics problems with an initial emphasis on subsurface reservoir applications. Currently, GEOS supports capabilities for studying carbon sequestration, geothermal energy, hydrogen storage, and related subsurface applications. The unique aspect of GEOS that differentiates it from existing reservoir simulators is the ability to simulate tightly coupled compositional flow, poromechanics, fault slip, fracture propagation, and thermal effects, etc. Extensive documentation is available on the GEOS documentation pages (GEOS Documentation, 2024). Note that GEOS, as presented here, is a complete rewrite of the previous incarnation of the GEOS referred to in (Settgast et al., 2017).
58 GEOSCIENCES↗