Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session PE: Porous Media II |
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Chair: Bojan Markicevic, Kettering University Room: 003A |
Tuesday, November 25, 2008 11:35AM - 11:48AM |
PE.00001: Numerical Analysis of Turbulent Flow in Porous Media Fatemeh Hassanipour, James K. Catoe, Jose Lage Modeling techniques and simulation of laminar flow through porous media have been applied for a number of years for designing particulate filters, catalytic reactors, thermal and sound insulators, combustors, and more recently fuel cells. Essential for further analysis, and in support of new synthesis, is the modeling necessary for simulating turbulent flows in porous media. This has been studied in the present work, in principle, through modeling that is an alternative to Direct Numerical Simulation. A natural approach to build a turbulence model for flow in porous media is to simply apply the time averaging (for handling turbulence) and the space averaging (for handling the morphology) to the microscopic equations valid at the pore level. When pursuing a combined time and space averaging approach, the averaging order (i.e. space-time or time-space) matters. The difference in pursuing a time-space or a space-time averaging order is now known to essentially impact the way in which the resulting model treats the interaction of a large flow structure. In the current study, these two different approaches have been investigated in parallel to the experiments for their validity range. The comparisons are based on flow structure visualization and on values of turbulence characteristics obtained from direct measurements of fluid velocity via digital particle image velocimetry. [Preview Abstract] |
Tuesday, November 25, 2008 11:48AM - 12:01PM |
PE.00002: Plume dynamics in heterogeneous porous media Jerome A. Neufeld, Herbert E. Huppert Buoyancy driven flows in layered porous media are present in many geological settings and play an important role in the mixing of fluids, from the dispersal of pollutants in underground aquifers to enhanced oil recovery techniques and, of more recent importance, the sequestration of carbon dioxide (CO$_2$). Seismic images of the rise of a buoyant CO$_2$ plume at Sleipner in the North Sea indicate that these plumes are greatly influenced by a vertical array of thin lenses of relatively low permeability material. We model propagation of CO$_2$ at each layer as a gravity current in a porous medium which propagates along, and drains through, a thin, low permeability seal. Drainage, driven both by hydrostatic pressure and the body force on the draining fluid, leads to an initial rapid advance followed by a gradual retreat of the current to a steady-state. By incorporating a vertical array of these single layer models we are able to capture the rise of the buoyant plume in layered reservoirs. We find that the plume is characterized by a broad head with a tail given by the steady state extent. [Preview Abstract] |
Tuesday, November 25, 2008 12:01PM - 12:14PM |
PE.00003: The competition between buoyancy and flow focussing in a two layer porous media flow Herbert Huppert, Jerome Neufeld Flow of relatively dense gravity currents in saturated porous media with two distinct layers has been pursued theoretically and experimentally and will be demonstrated by a table-top experiment. In such systems, where fluid flow is driven by buoyancy, there exists a competition between gravity acting on the heavy fluid and flow focusing driven by ease of flow within the high permeability layer. When these two effects act together -- the lower layer is more permeable -- the current extends more rapidly than in a uniform medium of equivalent permeability. When gravity and the permeability structure act in opposition there is a critical flux $Q_C=(g'k_LH/\nu)f(k_U/k_L)$, where $f(x)=0.9(x-1)^{-1/3}$, beyond which the upper layer attracts the current sufficiently to overrun the lighter interstitial fluid in the lower layer ($k_U$ and $k_L$ are the permeabilities of the upper and lower layers and $H$ is the lower layer depth). When the system is at an angle to the horizontal, flow is driven by the component of gravity down the incline, rather than by the slope of the upper surface of the current, with the critical flux dependent on the angle. The studies have applications to sequestering supercritical carbon dioxide in saline aquifers 1 to 2 km beneath the surface of the Earth. [Preview Abstract] |
Tuesday, November 25, 2008 12:14PM - 12:27PM |
PE.00004: Ensemble Phase Averaged Equations for Multiphase Flows in Porous Media Duan Zhang Many multiphase flows in porous media are modeled by application of Darcy's law to each phase separately. Sometimes, often in a fluid imbibition process, the flow is modeled as a diffusion process. Both models have been found applicable in some cases, but insufficient for others. In the present work, using the ensemble phase averaging technique for continuous multiphase flows, averaged momentum equations for multiphase flows in porous solids are studied. Under the assumption that the typical dimension of fluid interfaces is small compared to the macroscopic length scale, the averaged momentum equations for fluids are found to be in a form similar to Darcy's law, but with additional terms representing the effect of phase interactions on fluid interfaces. In a simple example of two fluids in a porous solid, we find that the difference in the average pressures of the two fluids is not necessary related to the surface tension effect. If the pressure difference, or the capillary pressure, is decomposed into a static part, representing the surface tension effect, and a dynamic part, then the dynamic part of the capillary pressure appears as terms in the averaged momentum equations. We also study conditions under which a fluid imbibition process can be modeled as a diffusion process. [Preview Abstract] |
Tuesday, November 25, 2008 12:27PM - 12:40PM |
PE.00005: On electronkinetically driven flows in swelling clays B.S. Tilley, B. Vernescu, J.D. Plummer Clays are formed in parallel layers of minerals, called lamellae, which have negative surface charge due to imperfections in the crystal lattice. The space between the lamellae, the galley, is filled with a liquid in which cations are drawn to the charged platelet surfaces, resulting in a double-layer. The aspect ratio of the galley thickness to its length is small. Spatial variations on the lamella shape depend on the mechanical stresses being applied to the clay, the local flow rate, and the local cation and anion concentrations. We have developed a model in the small tortuosity limit for the bulk flow in the clays which takes into account local charge distributions, local displacements, and applied electric fields. Lubrication theory is applied to an individual galley/lamella system to describe the charge concentration and flow and electric fields and local displacements in the lamella. These fields then provide jumps in shear and tangential stresses within the lamellae, whose net force balance is found through homogenization over the size of the sample. Numerical simulations of the model are presented and are compared to experiments. [Preview Abstract] |
Tuesday, November 25, 2008 12:40PM - 12:53PM |
PE.00006: Onset of density-driven convection in heterogeneous porous media: Non-modal stability analysis Saikiran Rapaka, Rajesh Pawar, Philip Stauffer, Dongxiao Zhang, Shiyi Chen When carbon dioxide (CO$_{2})$ is injected into saline aquifers, it slowly dissolves into the brine resulting in a gravitationally unstable state. Under suitable conditions, this instability manifests itself in the form of ``fingers'' of CO$_{2}$-rich brine penetrating into the system resulting in a significant enhancement of the rate of dissolution of CO$_{2}$ into the system. Recently, we applied the idea of non-modal growth of perturbations to compute the length and time scales characteristic of the onset of convection in a homogeneous porous medium. Non-modal stability theory is a theoretically rigorous extension of the traditional eigenvalue approach to non-normal and non-autonomous operators. In this work, we extend this approach to horizontally layered porous media generated with a Gaussian covariance model. We use a Monte-Carlo approach to analyze the effects of correlation length and the variance of the log-permeability field on the critical time for the onset of convection. We present the probability density function for the critical time and show that its variance increases with both the variance of the permeability field and its correlation length. [Preview Abstract] |
Tuesday, November 25, 2008 12:53PM - 1:06PM |
PE.00007: Analytical Model for Post-Injection Spreading and Migration of CO$_2$ in Saline Aquifers, including Capillary Trapping, Solubility, and Leakage Christopher MacMinn, Ruben Juanes In geological CO$_2$ storage, careful site selection and effective injection methods are the two primary means of maximizing reservoir ``fill'' and assessing and avoiding potential leakage paths. An accurate understanding of the subsurface spreading and migration of mobile CO$_2$ during and after injection is essential for these purposes. We present an analytical model for the post-injection spreading and migration of a plume of CO$_2$ in a saline aquifer, including the effects of gravity segregation, capillary trapping, natural groundwater flow, dissolution of CO$_2$ into groundwater, and leakage through the caprock. We account rigorously for the injection period, using the true end-of-injection plume shape as an initial condition. This comprehensive model allows us to estimate reservoir capacity for CO$_2$ storage at the basin scale, and to assess dynamically the relative importance of structural, capillary, and solution trapping mechanisms. [Preview Abstract] |
Tuesday, November 25, 2008 1:06PM - 1:19PM |
PE.00008: An airborne jet train that flies on a soft porous track Parisa Mirbod, Yiannis Andreopoulos, Sheldon Weinbaum This paper explores the quantitative feasibility of developing an airborne jet train that flies on a soft porous track within centimeters of the earth's surface at speeds approaching current commercial jet aircraft. The jet train employs a lift mechanism first proposed in Feng {\&} Weinbaum (2000) J. Fluid Mech. 422:282 and a nearly frictionless track suggested in Wu et al. (2004) Phys. Rev. Lett. 93(19):194501. Using an asymptotic analysis for large values of the permeability parameter H/$\surd K_{p}$, where H is the porous layer thickness and $K_{p}$ the Darcy permeability, we first show that it is possible to support a 70 metric ton jet train carrying 200 passengers on a confined porous material if its $K_{p}$ is approximately 5 x 10$^{-9}$ m$^{2}$. For this $K_{p }$one finds that the tilt of the planform is $<$ 0.1 degrees and the lift-off velocity is $<$ 5 m/s. Compression tests on a fiber-fill material with these properties show that the fibers contribute $<$ 0.2 percent of the total lift and hence the friction force of the fiber phase is negligible. Using jet engines of 10,000 lbf thrust, about 1/5 that of a 200 passenger jet aircraft, one is able to obtain a cruising velocity approaching 700 km/hr. This would allow for huge fuel savings, especially on short flights where much of the energy is used to climb to altitude and overcoming lift induced drag. [Preview Abstract] |
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