Coupled multiphase flow and geomechanical modeling of injection-induced seismicity
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Imaging techniques for the analysis of porous structures have revolutionized our ability to quantitatively characterize geomaterials. Digital representations of rock from CT images and physics modeling based on these pore structures provide the opportunity to further advance our quantitative understanding of fluid flow, geomechanics, and geochemistry, and the emergence of coupled behaviors. Additive manufacturing, commonly known as 3D printing, has revolutionized production of custom parts with complex internal geometries. For the geosciences, recent advances in 3D printing technology may be co-opted to print reproducible porous structures derived from CT-imaging of actual rocks for experimental testing. The use of 3D printed microstructure allows us to surmount typical problems associated with sample-to-sample heterogeneity that plague rock physics testing and to test material response independent from pore-structure variability. Together, imaging, digital rocks and 3D printing potentially enables a new workflow for understanding coupled geophysical processes in a real, but well-defined setting circumventing typical issues associated with reproducibility, enabling full characterization and thus connection of physical phenomena to structure. Here we report on our research exploring the possibilities that these technologies can bring to geosciences for coupled multiscale experimental and numerical analysis using 3D printed fractured rock specimens.
Water Resources Research
The migration and trapping of supercritical CO2 (scCO2) in geologic carbon storage is strongly dependent on the geometry and wettability of the pore network in the reservoir rock. During displacement, resident fluids may become trapped in the pits of a rough pore surface forming an immiscible two-phase fluid interface with the invading fluid, allowing apparent slip flow at this interface. We present a two-phase fluid dynamics model, including interfacial tension, to characterize the impact of mineral surface roughness on this slip flow. We show that the slip flow can be cast in more familiar terms as a contact-angle (wettability)-dependent effective permeability to the invading fluid, a nondimensional measurement which relates the interfacial slip to the pore geometry. The analysis shows the surface roughness-induced slip flow can effectively increase or decrease this effective permeability, depending on the wettability and roughness of the mineral surfaces. Configurations of the pore geometry where interfacial slip has a tangible influence on permeability have been identified. The results suggest that for large roughness features, permeability to CO2 may be enhanced by approximately 30% during drainage, while the permeability to brine during reimbibition may be enhanced or diminished by 60%, depending on the contact angle with the mineral surfaces and degrees of roughness. For smaller roughness features, the changes in permeability through interfacial slip are small. A much larger range of effective permeabilities are suggested for general fluid pairs and contact angles, including occlusion of the pore by the trapped phase.
Water Resources Research
The migration and trapping of supercritical CO
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Journal of Petroleum Science and Engineering
Economic feasibility of geologic carbon storage demands sustaining large storage rates without damaging caprock seals. Reactivation of pre-existing or newly formed fractures may provide a leakage pathway across caprock layers. In this study, we apply an equivalent continuum approach within a finite element framework to model the fluid-pressure-induced reactivation of pre-existing fractures within the caprock, during high-rate injection of super-critical CO2 into a brine-saturated reservoir in a hypothetical system, using realistic geomechanical and fluid properties. We investigate the impact of reservoir to caprock layer thickness, wellbore orientation, and injection rate on overall performance of the system with respect to caprock failure and leakage. We find that vertical wells result in locally higher reservoir pressures relative to horizontal injection wells for the same injection rate, with high pressure inducing caprock leakage along reactivated opening-mode fractures in the caprock. After prolonged injection, leakage along reactivated fractures in the caprock is always higher for vertical than horizontal injection wells. Furthermore, we find that low ratios of reservoir to caprock thickness favor high excess pressure and thus fracture reactivation in the caprock. Injection into thick reservoir units thus lowers the risk associated with CO2 leakage.
American Society of Mechanical Engineers Fluids Engineering Division Publication Fedsm
An enriched finite element method is described for capillary hydrodynamics including dynamic wetting. The method is enriched via the Conformal Decomposition Finite Element Method (CDFEM). Two formulations are described, one with first-order accuracy and one with second-order accuracy in time. Both formulations utilize a semi-implicit form for the surface tension that is shown to effectively circumvent the explicit capillary time step limit. Sharp interface boundary conditions are developed for capturing the dynamic contact angle as the fluid interface moves along the wall. By virtue of the CDFEM, the contact line is free to move without risk of mesh tangling, but is sharply captured. Multiple problems are used to demonstrate the effectiveness of the methods.
Journal of Petroleum Science and Engineering
Coupled reservoir and geomechanical simulations are significantly important to understand the long-term behavior of geologic carbon storage (GCS) systems. In this study, we performed coupled fluid flow and geomechanical modeling of CO2 storage using available field data to (1) validate our existing numerical model and (2) perform parameter estimation via inverse modeling to identify the impact of key geomechanical (Young's modulus and Biot's coefficient) and hydrogeological (permeability and anisotropy ratio) properties on surface uplift and the pore pressure buildup at In Salah in Algeria. Two sets of surface uplift data featuring low and high uplifts above two injection wells and the maximum change in the pore pressure due to CO2 injection were used to constrain the inverse model. Forward simulation results with representative parameter values from the literature match both low and high surface uplifts reasonably well and predicted the maximum change in the pore pressure. In particular, forward modeling results with estimated Biot's coefficients for reservoir and caprock layers, match the observed uplift well, highlighting the significance of Biot's coefficient in coupled reservoir and geomechanical models. Parameter estimation with 12 parameter sets for both low and high uplift data demonstrates that multiple sets of parameters can match the observed data equally well and the inclusion of the pore pressure data is critically important to constrain the parameter solution during inverse modeling. For a majority of cases, estimation results for both low and high uplift data show the vertical intrinsic permeability and Young's modulus of the reservoir remained close to 13 mD (1.3×10−14 m2) and 10 GPa, respectively, suggesting that these parameters may represent the actual effective properties. Additionally, higher correlations between reservoir permeability and caprock's Biot's coefficient with high surface uplift data were observed consistently under the pore pressure constraint, suggesting the inclusion of the pore pressure constraint is required to estimate the proper values of coupled flow and geomechanical properties associated with different surface uplift data. Overall, this study suggests that given limited data, including Biot's coefficient, in addition to permeability and Young's modulus can enhance parameter estimation of the geomechanical response during GCS.
American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM
An enriched finite element method is described for capillary hydrodynamics including dynamic wetting. The method is enriched via the Conformal Decomposition Finite Element Method (CDFEM). Two formulations are described, one with first-order accuracy and one with second-order accuracy in time. Both formulations utilize a semi-implicit form for the surface tension that is shown to effectively circumvent the explicit capillary time step limit. Sharp interface boundary conditions are developed for capturing the dynamic contact angle as the fluid interface moves along the wall. By virtue of the CDFEM, the contact line is free to move without risk of mesh tangling, but is sharply captured. Multiple problems are used to demonstrate the effectiveness of the methods.
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Water Resources Research
Geologic carbon storage in deep saline aquifers is a promising technology for reducing anthropogenic emissions into the atmosphere. Dissolution of injected CO2 into resident brines is one of the primary trapping mechanisms generally considered necessary to provide long-term storage security. Given that diffusion of CO2 in brine is woefully slow, convective dissolution, driven by a small increase in brine density with CO2 saturation, is considered to be the primary mechanism of dissolution trapping. Previous studies of convective dissolution have typically only considered the convective process in the single-phase region below the capillary transition zone and have either ignored the overlying two-phase region where dissolution actually takes place or replaced it with a virtual region with reduced or enhanced constant permeability. Our objective is to improve estimates of the long-term dissolution flux of CO2 into brine by including the capillary transition zone in two-phase model simulations. In the fully two-phase model, there is a capillary transition zone above the brine-saturated region over which the brine saturation decreases with increasing elevation. Our two-phase simulations show that the dissolution flux obtained by assuming a brine-saturated, single-phase porous region with a closed upper boundary is recovered in the limit of vanishing entry pressure and capillary transition zone. For typical finite entry pressures and capillary transition zone, however, convection currents penetrate into the two-phase region. As a result, this removes the mass transfer limitation of the diffusive boundary layer and enhances the convective dissolution flux of CO2 more than 3 times above the rate assuming single-phase conditions.
International Journal for Multiscale Computational Engineering
Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. Here, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipated during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.
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