Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session CF: Porous Media II |
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Chair: Bojan Markicevic, Kettering University Room: Long Beach Convention Center 103A |
Sunday, November 21, 2010 1:00PM - 1:13PM |
CF.00001: Comparison of two-phase Darcy's law with a thermodynamically consistent approach Steffen Berg, Jennifer Niessner, S. Majid Hassanizadeh The extended Darcy's law is a commonly used description of immiscible two-phase flow in porous media. Fractional flow theory and reservoir engineering in the oil {\&} gas industry is to a large extent based on this approach. In this description, the hydraulic conductivities of the porous medium for the two phases are parameterized with relative permeability-saturation functions which were introduced as empirical relationships. Within the last two decades, more advanced and physically based descriptions for multiphase flow in porous media have been developed. In this work, the extended Darcy's law is compared to a thermodynamically consistent approach by Hassanizadeh and Gray (1990) which explicitly takes the important role of phase-interfaces into account, both as entities and as parameters. It turns out that the extended Darcy's law and the thermodynamically based approach are compatible if either (i) relative permeabilites are a function of saturation only, but capillary pressure is a function of saturation and specific interfacial area or (ii) relative permeabilities are a function of saturation and saturation gradients. The latter would imply a more complex material behavior than commonly assumed in particular for the general case of irreversible displacement. [Preview Abstract] |
Sunday, November 21, 2010 1:13PM - 1:26PM |
CF.00002: Two Phase Flow in Porous Media with Dynamic Capillary Pressure Kimberly Spayd, Michael Shearer The one dimensional Buckley-Leverett equation for two phase flow in porous media is modified by including a dependence of capillary pressure on the rate of change of saturation. This model, due to Gray and Hassanizadeh, results in a nonlinear partial differential equation that supports traveling waves corresponding to undercompressive shocks. These waves, which also appear in driven thin liquid films, have the property that small disturbances pass through them from front to back. We present analytic results that are confirmed by numerical simulations of initial value problems. [Preview Abstract] |
Sunday, November 21, 2010 1:26PM - 1:39PM |
CF.00003: Stokes' second problem for an Oldroyd-B fluid in a porous half space Balram Suman, Nazish Hoda A modified form of Darcy's law is used to study the flow of Oldroyd-B fluids in a semi-infinite porous domain bounded by an oscillating plate. A close form analytical expression is obtained using Laplace transform, which suggests that depending upon the choice of natural and forced frequencies markedly distinct velocity fields can be observed. The fluid oscillates in time with a frequency which is same as the plate frequency. However, there exists a phase lag that increases with increasing distance from the plate. At a fixed distance from the plate, the phase-lag increases with increasing Reynolds number, Re = $U\sqrt {K \mathord{\left/ {\vphantom {K \phi }} \right. \kern-\nulldelimiterspace} \phi } /\nu $, and Wiessenberg number, Wi = $\lambda $U$^{2}$/$\nu $, and decreasing viscosity ratio, $\beta $ = $\lambda _{t}$/$\lambda $, where U is the amplitude of plate oscillation, K and $\phi $ are permeability and porosity of the porous media, $\upsilon $ is the kinematic viscosity, and $\lambda _{t}$ and $\lambda $ are retardation and relaxation times, respectively. This is consistent with our analytical prediction that the phase-lag is pronounced when Wi Re$^{2}$ $>> \quad \beta ^{2}$. The phase lag also decreases with decreasing Strouhal number, St = $\nu \quad \omega $/U$^{2}$ where $\omega $ is the plate oscillation frequency, and it vanishes in the limit of St = 0. Furthermore, the fluid velocity increases with increasing $\beta $ and Re, and decreasing distance from the plate. Away from the plate the fluid velocity shows a strong transient effect where the amplitude of oscillation either increases or decreases with time depending upon Re, St, and $\beta $. [Preview Abstract] |
Sunday, November 21, 2010 1:39PM - 1:52PM |
CF.00004: Double diffusive miscible viscous fingering M. Mishra, P.M.J. Trevelyan, C. Almarcha, A. De Wit Miscible viscous fingering (VF) classically occurs when a less viscous fluid displaces a miscible more viscous one in a porous medium. We analyze the influence on such VF of differential diffusion between two species each of them influencing the viscosity of the fluids at hand. We show that such double diffusive effects can destabilize the classically stable situation of a more viscous fluid displacing a less viscous one. On the basis of a time-dependent linear stability analysis, all possible instability scenarios are classified in a parameter space spanned by the log-mobility ratios of each species and by the ratio of diffusion coefficients. Numerical simulations of the full nonlinear problem confirm the existence of the predicted instability scenarios and highlight the influence of differential diffusion effects on the nonlinear fingering dynamics. [Preview Abstract] |
Sunday, November 21, 2010 1:52PM - 2:05PM |
CF.00005: Geometry-driven charge accumulation in electrokinetic flows through laminates B.S. Tilley, B. Vernescu, J.D. Plummer In the remediation of charged species from contaminated saturated soils, electric fields are applied to move the charge from the bulk toward the electrodes. Debye-layers occur at the soil/fluid interface which allows for advective transport of charge through electroosmosis, along with transport due to electrodiffusion (electrophoresis). However, depending on the valence of the species, these effects may act in concert to remove charge or may compete. We model the soil as an array of purely dielectric laminates with nonuniform thickness whose spatial variation in the streamwise direction occurs on a much longer length scale than the spacing between laminates (i.e. pore spacing). We derive an asymptotic model that incorporates lubrication pressures, dispersive effects in the electric field correction, and species equations for ion concentrations in the liquid. Electroneutrality is not assumed in the fluid region. In the case of monovalent species, we find that spatial variations in the pore structure can lead to accumulation of charge where both the fringe electric field converges and the advective transport of charge is weak. Comparisons with results found in experiments are discussed. [Preview Abstract] |
Sunday, November 21, 2010 2:05PM - 2:18PM |
CF.00006: Capillary climb dynamics in the limits of prevailing capillary and gravity force H.K. Navaz, B. Markicevic, B. Bijeljic The dynamics of the capillary climb of a wetting liquid into a porous medium that is opposed by gravity force is studied numerically. The capillary network model, in which an actual porous medium is represented as a network of pores and throats, is used. The numerical results for the capillary climb reveal that there are at least two distinct flow regimes. The first regime is characterized by the capillary force being much larger than the gravity force. In this regime the Washburn solution can be used to predict the changes of climbing height over time. In the second regime the capillary and gravity forces become comparable, and one observes a slower increase in the climbing height as a function of time. The numerical results from this study, expressed as the climbing height as a power law function of time, indicate that the two powers, which correspond to the two distinct regimes, differ significantly. The comparison of the powers with experimental data indicates a good agreement. Furthermore, the power value from the Washburn solution is analyzed, where it should be equal to one half for purely capillary force driven flow. This is in contrast to the value of around 0.43 that is found experimentally. We show from the numerical solution that this discrepancy is due to the momentum dissipation on the liquid interface. [Preview Abstract] |
Sunday, November 21, 2010 2:18PM - 2:31PM |
CF.00007: The types of boundary conditions in the secondary capillary flow and liquid distribution B. Markicevic, H.K. Navaz After depositing a wetting liquid onto a porous medium surface, and under the influence of the capillary pressure, the liquid is imbibed into porous medium creating a wetted imprint. The flow within the porous medium does not cease once all liquid is imbibed, but it continues as a secondary capillary flow, where the liquid flows from large pores into small pores along the liquid interface. The flow is solved using the capillary network model, and influence of the boundary condition on the liquid distribution within porous medium is investigated. The porous medium boundaries can be defined as open or closed boundaries, where an open boundary is treated as a part of the liquid interface. In contrast, the closed boundary is defined as a static entity, in which the potential condition for flow to take place is never satisfied. By defining the porous medium boundaries as open or closed, one is able to obtain a very different liquid distribution within the porous medium. The liquid saturation profiles along the principal flow direction ranging from constant, to steadily decreasing, to the profile with a local maximum, are found numerically. Finally, it is shown that these saturation profiles are also related to the geometrical dimension that is perpendicular to the pertinent boundary, and changing the boundary type from open to closed allows the liquid distribution within porous medium to be controlled. [Preview Abstract] |
Sunday, November 21, 2010 2:31PM - 2:44PM |
CF.00008: Modeling of Wormhole Growth in Porous Media Using the Material Point Method (MPM) Balaji Jayaraman, Duan Zhang, Brian VanderHeyden Modeling of wormhole growth in porous media such as a sand bed has been a subject of significant interest to the petroleum geological modeling and allied research communities. The challenge of simulating such problems, in spite of advances in computing resources and numerical methods, arise from the limitations in the algorithmic framework that can handle a whole range of problems such as moving boundary, large deformation and large separation in timescales. Here, we use the MPM, which combines mesh and particle capabilities for modeling solids and is extended to model generic multi-material interaction using continuous multiphase flow theory without the need for separate interface tracking and contact algorithms. This multiphase flow approach using an ensemble phase averaging method is often more convenient in dealing with problems of fluid-structure interaction where the material interaction is represented by coupling model terms in the mixed cells. The fluid and the sand bed are considered as two different phases (materials) having their own constitutive relations. Further, we use the material points to represent the solid sand particles to accurately capture its transport by the fluid medium. To handle the widely separated time scales in the problem we use sub-cycling to resolve the various physical processes. [Preview Abstract] |
Sunday, November 21, 2010 2:44PM - 2:57PM |
CF.00009: High-performance Integrated numerical methods for Two-phase Flow in Heterogeneous Porous Media Chih-Che Chueh, Ned Djilali, Wolfgang Bangerth Modelling of two-phase flow in heterogeneous porous media has been playing a decisive role in a variety of areas. However, how to efficiently and accurately solve the governing equation in the flow in porous media remains a challenge. In order to ensure the accurate representative flow field and simultaneously increase the computational efficiency, we incorporate a number of state-of-the-art techniques into a numerical framework on which more complicated models in the field of multi-phase flow in porous media will be based. Such a numerical framework consists of a h-adaptive refinement method, an entropy-based artificial diffusive term, a new adaptive operator splitting method and efficient preconditioners. In particular, it is emphasized that we propose a new efficient adaptive operator splitting to avoid solving a time-consuming pressure-velocity part every saturation time step and, most importantly, we also provide a theoretically numerical analysis as well as proof. A few benchmarks will be demonstrated in the presentation. [Preview Abstract] |
Sunday, November 21, 2010 2:57PM - 3:10PM |
CF.00010: Pore-scale Modeling of Transport Phenomena in a Vanadium Redox Battery using X-ray Tomography and the Lattice Boltzmann Method Abhijit Joshi, E. Caglan Kumbur, Ying Sun The Vanadium Redox Battery (VRB) promises to be an attractive option for storing electrical energy from renewable energy sources and delivering the stored energy to the grid whenever it is required. In this work, a novel methodology is proposed for modeling the transport mechanisms in the VRB including the flow of electrolyte, chemical species transport through the electrolyte and electrochemical reactions at active sites. The detailed geometry of the electrode is obtained using X-ray computed tomography (XCT) and this geometry is characterized to calculate porosity, pore-size distribution, connectivity and the active surface area. The processed XCT data is then used as geometry input for modeling transport processes in the VRB. The flow of electrolyte through the pore-space within the electrodes and the transport of ionic species in these pores is modelled using the lattice Boltzmann method (LBM). An electrochemical model using the Butler-Volmer equations is used to provide species flux boundary conditions at the surface of the carbon fibers and to provide the necessary coupling to the local concentration of these species present in the pore space. Finally, model predictions for the steady-state discharge of the VRB are then compared with results reported in the literature. [Preview Abstract] |
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