Poroelastic Effects Research Articles

Transient Deformation Excited by the 2021 M7.4 Maduo (China) Earthquake: Evidence of a Deep Shear Zone

AbstractWe use Sentinel‐1 and ALOS‐2 Interferometric Synthetic Aperture Radar (InSAR), and Global Navigation Satellite System (GNSS) data to investigate the mechanisms of coseismic and postseismic deformation due to the 2021 M7.4 Maduo (China) earthquake. We present a refined coseismic slip model constrained by the rupture trace and precisely located aftershocks. The InSAR time series corrected for the atmospheric and decorrelation noise reveal postseismic line of sight displacements up to ∼0.1 m. The displacements are discontinuous along the fault trace, indicating shallow afterslip and velocity‐strengthening friction in the top 2–3 km of the upper crust. The magnitude of shallow afterslip is however insufficient to compensate for the coseismic slip deficit, implying substantial off‐fault yielding. The observed surface deformation does not exhibit obvious features that could be attributed to poroelastic effects. We developed a fully coupled model that accounts for both stress‐driven creep on a deep localized shear zone and viscoelastic relaxation in the bulk of the lower crust. The mid‐ to near‐field data can be reasonably well explained by deep afterslip and/or non‐Maxwellian visco‐elasticity. Our results suggest a power‐law stress exponent of ∼4–4.5 assuming a power‐law rheology, and transient and steady‐state viscosities of 1018 and 1019 Pa s, respectively, assuming a bi‐viscous (Burgers) rheology. However, a good fit to the GNSS data cannot be achieved assuming the bulk viscoelastic relaxation alone, and requires a contribution of deep afterlip and/or a localized shear zone extending through much of the lower crust.

Poroelastic response of inclined wellbore geometry in anisotropic dual-medium/media

Shale gas formations are typically characterized by anisotropic and fracture properties. Existing shale wellbore stability models have only considered the anisotropy of shale rocks and have ignored the effect of fractures. However, the mechanism of wellbore instability under the combined effects of shale anisotropy and dual-media (DM) remains unknown. Therefore, based on anisotropic poroelasticity, the DM theory, and the assumption of generalized plane strain, this study established a pseudo-3D hydraulic-mechanical coupling finite element model considering the DM and anisotropy of shale in wellbores. The effects of elastic anisotropy, fracture volume fraction, fracture permeability, mass transfer coefficient, and fluid pressure on wellbore stress were analyzed parametrically. The results showed that an anisotropic single-medium predicts that the wellbore will fail when the formation is drilled, whereas an anisotropic DM predicts periodic wellbore instability. The poroelastic effect of the matrix pore pressure is much greater than that of the fracture pore pressure. The matrix elastic anisotropy parameters control the distribution of mechanical parameters throughout the DM, further affecting the poroelastic response of the entire DM. When the drilling direction was mostly parallel to the bedding plane, the anisotropy of the matrix and fracture system of the elastic parameters were larger, and the wellbore was more stable. A larger fracture permeability leads to a larger fracture volume fraction and mass transfer coefficient, the matrix pore pressure and fracture pore pressure increase, and the instability of the wellbore also increases.

Fully coupled two-phase hydro-mechanical model for wellbore stability analysis in tight gas formations considering the variation of rock mechanical parameters

Tight gas reservoirs are typically characterized by the unsaturated case that contains both water and gas fluids. However, previous wellbore stability analysis usually assumes that the porous rock is only saturated with a single fluid, thereby failing to describe the two-phase seepage behavior and the change in water content on the mechanical properties of the unsaturated rock, resulting in inaccurate mud weight predictions from wellbore stability analysis. Therefore, this paper aims to propose a fully coupled two-phase hydro-mechanical model that is available to obtain the change in water saturation and incorporates the variation of rock mechanical parameters with water saturation into the coupling relationship to assess the wellbore stability. By comparing five models representing the saturated and various unsaturated conditions, the influences of two-phase seepage and rock mechanical parameters on the evolution of pore pressure, stresses and wellbore stability are clarified. Finally, the influences of wellbore pressure, initial water saturation, porosity, and permeability on wellbore stability are discussed. The results show that the unsaturated pore pressure is influenced not only by the compressibility and viscosity of the fluid, but also by the saturation level and wellbore pressure. The difference in effective stresses is explained by the difference in poroelastic effect between saturated and unsaturated conditions. The decrease in elastic modulus and Poisson's ratio affects the effective tangential stress, while the increase in Biot's coefficient affects the effective radial stress. The prediction result of the present model that considers the combined effects of the two-phase hydro-mechanical coupling and the variation of all five mechanical parameters with water content is more consistent with the real borehole diameter curve. In the field case of the presented tight gas reservoir, the excessive overbalanced pressure is detrimental to wellbore stability, even worse than the underbalanced pressure. A near-balanced pressure may be the most beneficial for maintaining wellbore stability and protecting tight gas reservoirs. The higher risk of wellbore instability may correspond to formations with relatively high permeability, high porosity and high gas saturation.

A hydromechanical FEM fracturing simulator under the leak-off phenomenon perspective

Carter’s model of fluid loss is used in the oil and gas industry performing the numerical approach of leak-off. Its deduction applies some simplifying assumptions, such as the difference between fluid pressure and constant pore pressure and filtration process approximation to a unidirectional flow, perpendicular to the fracture plane. For this paper, the so-called Chimas is an hydromechanical simulator of oil reservoirs, fully coupled and implicit, in a way that considers the poroelastic effects on the propagation of fractures. The leak-off process is explicitly treated in the fracture boundary conditions using Darcy’s law. The objective of this work is to validate the filtration phenomenon of Chimas hydromechanical simulator comparing the parameters of length, width and injection pressure with those obtained using an iterative method implemented in MatLab and which includes Carter’s analytical equation. Numerical accuracy was validated against asymptotic analytical solutions. The agreement between the iterative method and the analytical solutions was particularly good in relation the length fracture and injection pressure.

Two-dimensional models for waterflooding induced hydraulic fracture accounting for the poroelastic effects on a reservoir scale

This work focuses on the developing of a computationally efficient numerical model for a waterflooding induced planar hydraulic fracture in a poroelastic medium. In particular, under certain assumptions it is possible to decouple the fully coupled model into poroelastic reservoir and purely elastic fracture subproblems. Further, the general 3D problem formulation for a planar fracture is reduced to two dimensions for early time plane strain fracture and late time constant height fracture. Noticeably, the division of the problem into two subproblems allows us to use the displacement discontinuity approach for the fracture related part, and finite element method for the reservoir related part. The latter is especially important for the constant height fracture, which cannot be modeled using exclusively the finite element approach in two dimensions. The algorithm is benchmarked against the available analytical solutions, as well as compared to other numerical codes. The developed numerical method is used to study the influence of the heterogeneous pore pressure and the corresponding stress for different waterflooding fracturing situations. We consider the cases with both injection and production wells operating nearby. With the presence of such wells, the fracture growth becomes asymmetrical and both the well type and location are important. The qualitatively different fracture behavior is observed for various cases. Other numerical examples include the simulation of a step-rate test as well as investigation of the possibility of fracture control by altering the injection rate.

Critical Conditions for Wellbore Failure during CO2-ECBM Considering Sorption Stress

Significant stress changes caused by sorption-induced swelling raise the coal wellbore failure potential, which directly impacts the safety and sustainability of CO2 enhanced coalbed methane (CO2-ECBM). Additionally, a mixture gas (CO2/N2) injection is recommended due to the sharp decline of permeability with pure CO2 injection. In this study, incorporating the impacts of mixture gas adsorption and poroelastic effects, a semi-analytical model of coal wellbore stability during mixture gas injection is proposed. Model results indicate that the stress field is significantly influenced by the boundary condition and sorption effect. In addition, parametric studies are performed to determine the influence of adsorption parameters, mechanical properties, and gas composition on the stress distribution and then on the wellbore failure index. Furthermore, mixture gas injection with a large proportion of CO2 or N2 both cause wellbore instability. Significant compressive hoop stress and shear failure are caused by the mixture gas injection with a large proportion of CO2. In contrast, the displacement of CH4 with weakly adsorptive N2 will result in less compressive and even tensile hoop stress, so shear or tensile failure may occur. Thus, mixture gas (including pure CO2/N2) injection must be controlled by coal wellbore failure, providing an accurate estimation of in-situ coal seams’ CO2 storage capacity from the perspective of wellbore stability.

Classification of transient triggering mechanisms of aftershocks in the post-seismic phase of the 2017 Pohang earthquake, South Korea

SUMMARY The 2017 Mw 5.5 Pohang earthquake occurred near an enhanced geothermal system site and generated thousands of aftershocks, the largest of which, a Mw 4.6 earthquake, occurred 87 d after the mainshock. Redistribution of the groundwater pressure perturbed by the mainshock has been suggested as a cause of the post-seismic stress changes triggering several aftershocks, including the time-delayed event. However, to date, possible effects of variations in pore pressure on the aftershock occurrence have not been quantified in this region. Therefore, we conducted poroelastic modelling to evaluate this contribution to spatiotemporal distribution of the aftershocks, including the delayed event, using a fully coupled hydromechanical code. To construct a poroelastic model, a segmented fault geometry and a layered lithological structure were used. In addition, we utilized a kinematic slip model, a split-node algorithm and in-situ properties to simulate reliable coseismic and post-seismic behaviour. Our reference model successfully reproduced coseismic surface deformation in a line-of-sight direction, comparable to the corresponding observation from interferometric synthetic aperture radar, and was calibrated using groundwater measurement in a well. In addition to constructing the reference model, a series of numerical simulations were conducted to explore the effects and sensitivities of various hydraulic conductivities. Finally, the modelled Coulomb stress changes and spatiotemporal distribution of the aftershocks were analysed to elucidate the transient triggering mechanisms based on conditional statements to classify the mechanisms into several subsets. The classification showed that the poroelastic effect driven by depth/conductivity-dependent fluid diffusion is more critical to aftershock occurrence than the diffusion in the entire simulation time, and we propose that the delayed earthquake of Mw 4.6 could be correlated with poroelastic triggering rather than diffusion triggering. Furthermore, we inferred that this poroelastic effect could contribute to decay of aftershocks, particularly relatively small-magnitude aftershocks, as well as slow this decay in bedrocks. However, the proposed model does not explain all of the observed aftershocks, and other driving forces or triggering mechanisms need to be considered.

Numerical investigation of poroelastic effects during hydraulic fracturing using XFEM combined with cohesive zone model

Hydraulic fracturing is an effective technology used to stimulate hydrocarbon production from unconventional reservoirs. Numerical simulation of the hydraulic fracturing process plays a key role in the design of hydraulic fracturing. However, most of existing models are overly simplified by neglecting the poroelasticity of rock matrix, which may have a substantial effect on the growth of hydraulic fractures, especially in oil and/or water saturated formations. In this study, we developed a fully coupled finite element model for hydraulic fracture propagation in permeable formations by combining XFEM technique with cohesive zone model, and used it to investigate the effects of poroelasticity on the geometry evolution of single fracture which initiated from an injection point. Fluid flow within the fractures, Darcy flow within the rock matrix, hydraulic fractures propagation, and fluid leak-off into the formation are simultaneously taking into account in the model. Then, the model is validated by comparing the results with available analytical solutions. To understand and quantify the poroelastic effects on the propagation of hydraulic fracture, several cases with different matrix permeability, leak-off coefficients, and bulk modulus of pore fluid are performed. The simulation results show that the total volume of leakage is controlled by the combined action of matrix permeability and leak-off coefficient. The fracture aperture and length decrease with the increase of matrix permeability or leak-off coefficient, while as the bulk moduli of pore fluid increases, the fracture aperture and length tend to increase.

Induced Seismicity by Groundwater Extraction at the Dead Sea Fault, Jordan

AbstractThe earthquake sequence, with a maximum earthquake magnitude of MW 3.8, that occurred during January–February 2022 at the northern Dead Sea fault, is shown to be induced by extensive groundwater abstraction in Wadi Al‐Arab basin. Wadi Al‐Arab basin, which is bordered in the west by the Dead Sea fault, has been overexploited by extensive groundwater abstraction causing significant drawdowns. Relative earthquake relocation indicates an elongated S‐N sequence subparallel to the Dead Sea fault. We simulate the three‐dimensional hydraulic head changes in the past 40 years at Wadi al Arab basin. Results show that the drawdowns at the Dead Sea fault wells reached a value greater than 180 m. We use these results to further model the poroelastic effects of the drawdown on the stability of the Dead Sea fault using a typical fault architecture including fault core surrounded by damage zone. Upward groundwater drainage through the permeable damage zone leads to compaction and strengthening. Failure on the Dead Sea fault is expected to occur on the impermeable fault core or at the protholith where weakening is expected. Groundwater abstraction in Wadi Al‐Arab basin cause changes of a few MPa in the Coulmb Failure Stress (ΔCFS) and trigger seismicity in these sections. This is the second location along the Dead Sea fault where groundwater abstraction was shown to recently induce earthquakes. With growing demand for water and long lasting droughts in the Middle East, seismicity induced by groundwater abstraction might reoccur in the near future.

Surface characterization of an ultra-soft contact lens material using an atomic force microscopy nanoindentation method

As new ultra-soft materials are being developed for medical devices and biomedical applications, the comprehensive characterization of their physical and mechanical properties is both critical and challenging. To characterize the very low surface modulus of the novel biomimetic lehfilcon A silicone hydrogel contact lens coated with a layer of a branched polymer brush structure, an improved atomic force microscopy (AFM) nanoindentation method has been applied. This technique allows for precise contact-point determination without the effects of viscous squeeze-out upon approaching the branched polymer. Additionally, it allows individual brush elements to be mechanically characterized in the absence of poroelastic effects. This was accomplished by selecting an AFM probe with a design (tip size, geometry, and spring constant) that was especially suited to measuring the properties of soft materials and biological samples. The enhanced sensitivity and accuracy of this method allows for the precise measurement of the very soft lehfilcon A material, which has an extremely low elastic modulus in the surface region (as low as 2 kPa) and extremely high elasticity (nearly 100%) in an aqueous environment. The surface-characterization results not only reveal the ultra-soft nature of the lehfilcon A lens surface but also demonstrate that the elastic modulus exhibits a 30 kPa/200 nm gradient with depth due to the disparity between the modulus of the branched polymer brushes and the SiHy substrate. This surface-characterization methodology may be applied to other ultra-soft materials and medical devices.

Distinguishing poroelasticity and viscoelasticity of brain tissue with time scale

Brain tissue is considered to be biphasic, with approximately 80% liquid and 20% solid matrix, thus exhibiting viscoelasticity due to rearrangement of the solid matrix and poroelasticity due to fluid migration within the solid matrix. However, how to distinguish poroelastic and viscoelastic effects in brain tissue remains challenging. In this study, we proposed a method of unconfined compression-isometric hold to measure the force versus time relaxation curves of porcine brain tissue samples with systematically varied sample lengths. Upon scaling the measured relaxation force and relaxation time with different length-dependent physical quantities, we successfully distinguished the poroelasticity and viscoelasticity of the brain tissue. We demonstrated that during isometric hold, viscoelastic relaxation dominated the mechanical behavior of brain tissue in the short-time regime, while poroelastic relaxation dominated in the long-time regime. Furthermore, compared with poroelastic relaxation, viscoelastic relaxation was found to play a more dominant role in the mechanical response of porcine brain tissue. We then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue. Because of the draining of pore fluid, the Young's moduli in poroelastic relaxation were lower than those in viscoelastic relaxation; brain tissue changed from incompressible during viscoelastic relaxation to compressible during poroelastic relaxation, resulting in reduced Poisson ratios. This study provides new insights into the physical mechanisms underlying the roles of viscoelasticity and poroelasticity in brain tissue. Statement of significanceAlthough the poroviscoelastic model had been proposed to characterize brain tissue mechanical behavior, it is difficult to distinguish the poroelastic and viscoelastic behaviors of brain tissue. The study distinguished viscoelasticity and poroelasticity of brain tissue with time scales and then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue, which helps to accurate selection of constitutive models suitable for application in certain situations (e.g., pore-dominant and viscoelastic-dominant deformation).

Effect of Poroelasticity on the Integrity of Cement Sheath in Heavy Oil Wells

Effect of Poroelasticity on the Integrity of Cement Sheath in Heavy Oil Wells

Analysis of fracture interference – Coupling of flow and geomechanical computations with discrete fracture modeling using MRST

A new discrete fracture model (DFM) is implemented in the MATLAB Reservoir Simulation Toolbox (MRST) – an open-source reservoir simulation software – to couple flow and geomechanical computations. Unstructured meshing is used to discretize the gridding domain. The matrix-to-matrix, fracture-to-fracture, and fracture-to-matrix fluxes are computed explicitly in the computational domain following the control volume formulation. The flow calculations and the geomechanical computations are solved sequentially: the governing equations for poroelasticity are incorporated, and the fixed stress splitting coupling methodology is employed. The results are compared with an uncoupled model, where the geomechanical effects are ignored.Several case studies demonstrate the utility of the proposed coupling strategy for analyzing production performance and stress evolution in hydraulically fracturing formations. This model considers the effects of poroelasticity and stress or strain variation in the fractured domains, and factors influencing the behaviour of fracture interference are examined. Finally, an analysis of the computational costs is also presented.This simulation approach can more accurately capture the dynamic behaviour of stress evolution and fracture interference in hydraulically fractured wells. This flexible framework can incorporate more functional modules, including fracture propagation, in future works. The results illustrate the significance of incorporating geomechanical effects in the flow simulation process. Insights pertinent to the operational strategies are also highlighted based on the simulation results.

Numerical simulation of rock erosion performance of a high-speed water jet using an immersed-body method

Water jet drilling (WJD) is an effective technique for drilling micro-holes in the subsurface for reservoir stimulation . This study aims to investigate numerically the failure mechanism of rock during WJD and to assess the WJD performance before drilling. A 3D fluid-solid coupling model is developed for simulating WJD by coupling a mechanical solver based on the combined finite-discrete element method (FDEM) with a fluid solver using an immersed-body method. The new numerical model is capable of simulating crack initiation and propagation and fragment removal under the impact load of a high-speed water jet. The poroelastic effect is implemented via Biot's theory of poroelasticity . The numerical results show that: (1) rock failure is only observed in the Gildehaus sandstone with the lowest strengths among the three types of rock tested, (2) most of the cracks are tensile failures and pure shear cracks are rare, mixed mode cracks account for 15%∼40% of the total crack number depending on the mechanical boundary conditions , (3) increased water back pressure significantly suppresses jet erosion. The poroelastic effect on the rock failure is insignificant in the mesoscale simulations and will be further investigated using a microscale model in future.

Viscoporoelasticity of coagulation blood clots

A blood clot is an essential biological tissue in physiological hemostasis and pathological thrombus in human bodies. In both physiological and pathological activities, the blood clots are often under external force from the blood flow. Quantifying the mechanical properties of the blood clot is important for the diagnosis and treatment of bleeding disorders and thrombotic diseases. In this work, the blood clot is shown to be viscoporoelastic and its properties are quantitatively characterized through combined rheology and indentation measurements. First, the viscoelasticity of the blood clot is determined by the shear rheology measurement because shear deformation does not induce volume change, and thus does not invoke the poroelastic behavior (i.e., coupled solvent migration and deformation) of the blood clot. Subsequently, an indentation test is carried out. Using a micromechanical testing machine, a spherical bead is pressed onto the blood clot to a certain depth and held for a period, meanwhile, the force is measured as a function of time. The force relaxation is contributed by both viscoelastic and poroelastic effects. Since the viscoelasticity of the blood clots has been fully characterized in shear rheology, the indentation data is used to determine the poroelastic properties of the blood clots. A general viscoporoelastic model is formulated and based on this model the relaxation indentation problem is simulated. By fitting the experimental force relaxation curves with the simulation results, the poroelastic parameters including permeability and drained Poisson’s ratio are obtained. Interestingly, the value of the drained Poisson’s ratio of the blood clot is very close to zero. To verify this behavior, we also carry out unconfined compression measurements to directly observe the volume evolution of the blood clot. The small value of drained Poisson’s ratio is validated by the unconfined compression result. Using the viscoporoelastic parameters determined in this work, we discuss the contribution of solvent migration and viscoelastic effect on the apparent modulus of the blood clot in physiologically relevant conditions. The high poroelasticity indicates the blood clot can withstand high instantaneous loads in the normal direction by resistance to solvent migration. Both poroelastic and viscoelastic processes dissipate energy, and thus could delay the fracture process of the material. This study systematically measures the viscoporoelastic properties of the blood clot and provides an understanding of the contributions of the two mechanisms to the time-dependent responses of coagulation blood clots.

Relative importance of poroelastic effects and viscoelastic relaxation for postseismic velocity fields after normal and thrust earthquakes: Insights from 2D finite-element modelling

Earthquakes on faults in the brittle upper crust evoke sudden changes in pore fluid pressure as well as postseismic viscoelastic flow in the lower crust and lithospheric mantle but the relative importance of these processes during the postseismic phase has not been systematically studied. Here, we use two-dimensional finite-element models to investigate how pore fluid pressure changes and postseismic viscoelastic relaxation interact during the earthquake cycle of an intracontinental dip-slip fault. To isolate the effects from pore fluid flow and viscoelastic relaxation from each other, we performed experiments with and without pore fluid flow and viscoelastic relaxation, respectively. In different experiments, we further varied the permeability of the crust and the viscosity of lower crust or lithospheric mantle. Our model results show poroelastic effects dominate the velocity field in the first months after the earthquake. In models considering poroelastic effects, the surfaces of both hanging wall and footwall of the normal fault subside at different velocities, while they move upwards in the thrust fault model. Depending on the permeability and viscosity values, viscoelastic relaxation dominates the velocity field from about the second postseismic year onward although poroelastic effects may still occur if the permeability of the upper crust is sufficiently low. With respect to the spatial scales of poroelastic effects and viscoelastic relaxation, our results show that pore fluid pressure changes affect the velocity field mostly within 10–20 km around the fault, whereas the signal from viscoelastic relaxation is recognizable up to several tens of kilometres away from the fault. Our findings reveal that both poroelastic effects and viscoelastic relaxation may overlap earlier and over longer time periods than previously thought, which should be considered when interpreting aftershock distributions, postseismic Coulomb stress changes and surface displacements.

Stress-Strain-Sorption Behaviour of Smectites Upon Exposure to Dry and Wet CO2

The swelling-shrinkage behavior of smectites induced by interlayer uptake or sorption of CO2 and H2O has been investigated with increasing interest recent years, primarily because of its potential impact on the sealing efficiency of clay-bearing caprocks overlying CO2 storage reservoirs. To get a better understanding of the stress-strain-sorption coupling in smectite exposed to supercritical CO2, we performed multiple stepwise axial loading and unloading, oedometer-type experiments on ∼1 mm thick discs of pre-pressed Na-SWy-1 and of Ca-SAz-1 montmorillonite. Initially air-dry (AD) samples were first tested in the presence of wet CO2 (20% RH) at 10 MPa pressure, and in the vacuum-dry (VD) state in the presence of pure (dry) CO2 at 10 MPa. The samples were incrementally loaded and unloaded at 40°C, employing effective axial stresses ranging from 0.5 to 44 MPa. Control tests using wet and dry He or Ar instead of CO2, were performed to distinguish strains due to loading-related CO2 sorption/desorption from purely poroelastic effects. All samples saturated with CO2 exhibited 30–65% lower apparent stiffness moduli than when saturated with He or Ar, showing that CO2 adsorption/desorption altered the mechanical response of pre-pressed smectites. Relative to the He and Ar tests, swelling strains of a few % (corrected for poroelastic effects) were measured for AD Na-SWy-1 smectite exposed to wet CO2, decreasing from 4.9 to 3.8% with increasing effective axial stresses in the range 1.6–36.2 MPa. AD SAz-1 material exhibited similar tends. VD samples tested with dry CO2 showed much smaller relative swelling strains (0.5–1.5%), which also decreased with increasing applied effective stresses. The experimental data on relative swelling strain versus effective stress are well fitted by a recent thermodynamic model for stress-strain-sorption behavior in coal. Results derived from model fits indicate that smectite-rich rocks have significant storage capacity for CO2 at shallow depths (up to 1.5–2 km) through CO2 sorption by the clay minerals. However, this component of storage capacity is reduced by more than 80% with increasing burial depth beyond 3 km. The model provides a first step towards modelling stress-strain-sorption effects in smectite rich caprocks penetrated by CO2, though further refinements are needed for broader application to the smectite-CO2-H2O system.

Permeability of Bituminous Coal to CH4 and CO2 Under Fixed Volume and Fixed Stress Boundary Conditions: Effects of Sorption

Permeability evolution in coal reservoirs during CO2-enhanced coalbed methane (ECBM) production is strongly influenced by swelling/shrinkage effects related to sorption and desorption of CO2 and CH4, respectively. Recent research has demonstrated fully coupled stress–strain–sorption–diffusion behavior in small samples of cleat-free coal matrix material exposed to a sorbing gas. However, it is unclear how such effects influence permeability evolution at the scale of a cleated coal seam and whether a simple fracture permeability model, such as the Walsh elastic asperity loading model, is appropriate. In this study, we performed steady-state permeability measurements, to CH4 and CO2, on a cylindrical sample of highly volatile bituminous coal (25 mm in diameter) with a clearly visible cleat system, under (near) fixed volume versus fixed stress conditions. To isolate the effect of sorption on permeability evolution, helium (non-sorbing gas) was used as a control fluid. All flow-through tests reported here were conducted under conditions of single-phase flow at 40°C, at applied Terzaghi effective confining pressures of 14–41 MPa. Permeability evolution versus effective stress data were obtained under both fixed volume and fixed stress boundary conditions, showing an exponential correlation. Importantly, permeability (κ) obtained at similar Terzaghi effective confining pressures showed κhelium > κCH4 >> κCO2, while κ-values measured in the fixed volume condition were higher than those in the fixed stress case. The results show that permeability to CH4 and CO2, under in situ conditions where free swelling of rock is not possible, is strongly influenced by the coupled effects of 1) self-stress generated by constrained swelling, 2) the change in effective stress coefficient upon sorption, 3) sorption-induced closure of transport paths independently of poroelastic effect, and 4) heterogeneous gas penetration and equilibration, dependent on diffusion. Our results also show that the Walsh permeability model offers a promising basis for relating permeability evolution to in situ stress evolution, using appropriate parameter values corrected for the effects of stress–strain–sorption.

Poroelastic effects on gas transport mechanisms and influence on apparent permeability in shale

Poroelasticity and gas slippage on the walls of nanopores are two major mechanisms that regulate shale permeability concurrent with hydrocarbons depletion. Nonlinear Klinkenberg plots reported in experiments indicate that gas slippage has a complex relationship with the variation of effective stress; however, a theoretical framework that explains the underlying physics is still missing. In the present contribution, a series of experiments were designed and conducted on intact Utica shale samples to study the simultaneous effects of gas slippage and poroelasticity under constant confining and constant effective stress conditions. In addition, an apparent permeability model was developed considering the effects of rock poroelasticity and a non-constant velocity gradient for gas flow at the pore wall. The model was calibrated and tested against the presented experimental results for Utica shale as well as previously published data. Results show that the concavity in Klinkenberg plots is caused by two separate parameters, each dominant within different ranges of pore pressures: second-order gas slippage and effective stress coefficient. The model demonstrates that gas slippage is inherently coupled with effective stress at low pore pressures. However, the evolution of apparent permeability with gas pressure deviates from the classical Klinkenberg theory only when the pore diameter is sufficiently small. When the effective stress coefficient is smaller than unity, the permeability evolution deviates from the linear Klinkenberg trend only at high pore pressures. In addition to the pore size, gas slippage is found to be closely correlated with the variation of gas viscosity with pressure and temperature.

Coupled Hydromechanical Modeling of Induced Seismicity From CO2 Injection in the Illinois Basin

AbstractInjection of CO2 for geologic carbon sequestration into deep sedimentary formations involves fluid pressure increases that engage hydromechanical processes that can cause seismicity by activation of existing faults. In this work, we use a coupled multiphase fluid flow and geomechanical simulator to model spatiotemporal fluid pressure and stress changes in order to study the poroelastic effect of CO2 injection on faults in crystalline basement rock below the injection zone. The seismicity rate along features interpreted to be basement faults is modeled using Dieterich's rate‐and‐state earthquake nucleation model. The methodology is applied to microseismicity detected during CO2 injection into the Mount Simon formation during the Illinois Basin—Decatur Project. The modeling accurately captures an observed reduction in seismicity rate when the injection in the second well was into a slightly shallower zone above the base of the Mount Simon formation. Moreover, the modeling shows that it is important to consider poroelastic stress changes, in addition to fluid pressure changes for accurately modeling of the observed seismicity rate.