Numerical Simulation of Ferrofluid Flow for Subsurface Environmental Engineering Applications

Ferrofluids are suspensions of magnetic particles of diameter approximately 10nm stabilized by surfactants in carrier liquids. The large magnetic susceptibility of ferrofluids allows the mobilization of ferrofluid through permeable rock and soil by the application of strong external magnetic fields. We have developed simulation capabilities for both miscible and immiscible conceptualizations of ferrofluid flow through porous media in response to magnetic forces arising from the magnetic field of a rectangular permanent magnet. The flow of ferrofluid is caused by the magnetization of the particles and their attraction toward a magnet, regardless of the orientation of the magnet. The steps involved in calculating the flow of ferrofluid are (1) calculation of the external magnetic field, (2) calculation of the gradient of the external magnetic field, (3) calculation of the magnetization of the ferrofluid, and (4) assembly of the magnetic body force term and addition of this term to the standard pressure gradient and gravity force terms. We compare numerical simulations to laboratory measurements of the magnetic field, fluid pressures, and the twodimensional flow of ferrofluid to demonstrate the applicability of the methods coded in the numerical simulators. We present an example of the use of the simulator for a fieldscale application of ferrofluids for barrier verification.     

Mixing of Stably Stratified Gases in Subsurface Reservoirs: A Comparison of Diffusion Models

Numerical simulations of the mixing of carbon dioxide (CO₂) and methane (CH₄) in a gravitationally stable configuration have been carried out using the multicomponent flow and transport simulator TOUGH2/EOS7C. The purpose of the simulations is to compare and test the appropriateness of the advective–diffusive model (ADM) relative to the more accurate dusty-gas model (DGM). The configuration is relevant to carbon sequestration in depleted natural gas reservoirs, where injected CO₂ will migrate to low levels of the reservoir by buoyancy flow. Once a gravitationally stable configuration is attained, mixing will continue on a longer time scale by molecular diffusion. However, diffusive mixing of real gas components CO₂ and CH₄ can give rise to pressure gradients that can induce pressurization and flow that may affect the mixing process. Understanding this coupled response of diffusion and flow to concentration gradients is important for predicting mixing times in stratified gas reservoirs used for carbon sequestration. Motivated by prior studies that have shown that the ADM and DGM deviate from one another in low permeability systems, we have compared the ADM and DGM for the case of permeability equal to 10^–15 m² and 10^–18 m². At representative reservoir conditions of 40 bar and 40°C, gas transport by advection and diffusion using the ADM is slightly overpredicted for permeability equal to 10^–15 m², and substantially overpredicted for permeability equal to 10^–18 m² compared to DGM predictions. This result suggests that gas reservoirs with permeabilities larger than approximately 10^–15 m² can be adequately simulated using the ADM. For simulations of gas transport in the cap rock, or other very low permeability layers, the DGM is recommended.     

Untersuchung von Milch

Ohne Zusammenfassung     

Buoyancy Effects on Upward Brine Displacement Caused by CO2 Injection

Upward displacement of brine from deep reservoirs driven by pressure increases resulting from CO₂ injection for geologic carbon sequestration may occur through improperly sealed abandoned wells, through permeable faults, or through permeable channels between pinch-outs of shale formations. The concern about upward brine flow is that, upon intrusion into aquifers containing groundwater resources, the brine may degrade groundwater. Because both salinity and temperature increase with depth in sedimentary basins, upward displacement of brine involves lifting fluid that is saline but also warm into shallower regions that contain fresher, cooler water. We have carried out dynamic simulations using TOUGH2/EOS7 of upward displacement of warm, salty water into cooler, fresher aquifers in a highly idealized two-dimensional model consisting of a vertical conduit (representing a well or permeable fault) connecting a deep and a shallow reservoir. Our simulations show that for small pressure increases and/or high-salinity-gradient cases, brine is pushed up the conduit to a new static steady-state equilibrium. On the other hand, if the pressure rise is large enough that brine is pushed up the conduit and into the overlying upper aquifer, flow may be sustained if the dense brine is allowed to spread laterally. In this scenario, dense brine only contacts the lower-most region of the upper aquifer. In a hypothetical case in which strong cooling of the dense brine occurs in the upper reservoir, the brine becomes sufficiently dense that it flows back down into the deeper reservoir from where it came. The brine then heats again in the lower aquifer and moves back up the conduit to repeat the cycle. Parameter studies delineate steady-state (static) and oscillatory solutions and reveal the character and period of oscillatory solutions. Such oscillatory solutions are mostly a curiosity rather than an expected natural phenomenon because in nature the geothermal gradient prevents the cooling in the upper aquifer that occurs in the model. The expected effect of upward brine displacement is either establishment of a new hydrostatic equilibrium or sustained upward flux into the bottom-most region of the upper aquifer.     

Spatially resolved observations of strain fields at necking and fracture of anisotropic hardened steel sheet material

In this work plastic strain localization, also referred to as necking, of press-hardened ultra-high strength steel is observed using digital speckle correlation. The region of the neck is studied during tensile tests of specimens specially designed to facilitate strain localization at an inner point of the material, thus avoiding edge effects on localization and fracture. By using measurements with a length scale small enough to properly resolve the neck, its growth and shape can be studied. Furthermore, the anisotropy of the material is investigated by examining specimens cut out at different angles to the rolling direction. It is seen that the local fracture strain of specimens cut out along the rolling direction is approximately twice as high as it is for specimens cut out perpendicular to the rolling direction.     

Foreword

Transport in Porous Media -     

Mixing with first-order decay in variable-velocity porous media flow

The transport and mixing of solutes undergoing first-order decay is central to many problems in groundwater hydrology. Mixing in porous media flow occurs due to advective dilution, hydrodynamic dispersion, and molecular diffusion. Mixing is stronger in regions of higher velocity, and weaker in slower-moving regions. Two-dimensional numerical experiments show that concentration profiles normal to the flow direction are displaced toward regions of slower flow in a flow field with a velocity gradient. Variable-velocity flow fields occur in subsurface flow around permeability heterogeneities, between recirculation cells, and in flow driven by natural convection. We examine two-dimensional solute concentration fields rather than breakthrough curves since for many complicated flow patterns, the breakthrough curve cannot discern important details of the concentration field. For the case of a species undergoing first-order decay, the effect of parent accumulation in regions of low velocity is enhanced for the daughter species because (i) the rate of daughter production is proportional to the local concentration of parent, and (ii) mixing is proportional to the local velocity. The resulting displacement of concentration profiles toward low-velocity regions may have important consequences for subsurface radionuclide transport and also for flows in chemically reactive systems and strongly coupled systems.Nomenclature d daughter component - d, ^(k) molecular diffusivity m² s^-1 - D dispersion coefficient m² s^-1 - dispersion tensor m²s^-1 - g acceleration of gravity vector m s^-2 - F Darcy flux vector kg m² s^-1 - identity matrix - k permeability m² - Kd distribution coefficient m³ kg^-1 - M mass accumulation term kg m^-3 - MW molecular weight kg mol^-1 - n outward unit normal vector - NK number of mass components (species) - p parent component - P total pressure Pa - q source term kg m^-3 s^-1 - R retardation factor - t time s, years - t _1/2 half-life s, years - u Darcy velocity in Y-direction m s^-1 - u Darcy velocity vector m s^-1 - v pore velocity m s^-1 - V volume m³ - X mass fraction - Y Y-coordinate - Z Z-coordinate (positive upward) - intrinsic dispersivity m - x distance interval m - surface area m² - decay constant s^-1 - dynamic viscosity kg m^-1 s^-1 - Ø porosity - fluid density kg m^-3 - tortuosity factor - d dispersion - L longitudinal - 0 reference value - T transverse - k mass component index