Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session S16: Porous Media IV |
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Chair: Marcus Hilpert, Johns Hopkins University Room: 319 |
Tuesday, November 22, 2011 3:05PM - 3:18PM |
S16.00001: Mass Transport Measurement in 3D Porous Media for Carbon Sequestration Robert Ecke, Scott Backhaus, Konstantin Turitsyn To determine the storage potential for carbon sequestration strategies involving porous media, accurate determination of mass transport efficiency is required. We have made accurate measurements of mass transport in geometries similar to those relevant for sequestration, namely a gravitationally stable two layer system where the diffusion interface between the two phases is unstable. We use water and propylene glycol as the fluids in cells with cylindrical geometry. For a range of Rayleigh numbers between 150 and 5000, we find mass transport efficiency that is consistent with steady state thermal heat transport convection in porous media and with 2D mass transport in a Hele-Shaw geometry [1]. A transition from a high mass transport state to a lower mass transport state typically occurs between 4 and 6 convective times and is observed over the full Ra range. \vskip 10pt \noindent [1] S. Backhaus, K. Turitsyn, and R.E. Ecke, Physical Review Letters {\bf 106}, 104501 (2011). [Preview Abstract] |
Tuesday, November 22, 2011 3:18PM - 3:31PM |
S16.00002: Evaporation from a semi-infinite porous medium: The role of capillary flow H.K. Navaz, B. Markicevic, S.J. Paikoff The liquid evaporation from the semi-infinite porous medium is solved numerically using the dynamic capillary network model in which the interface shape and multiphase flow front thickness between dry and fully wet parts of porous medium are tracked in time. Both convective and diffusion mass transport limited regimes are identified and liquid pseudo-velocity due to the evaporation is calculated. The numerical analysis is extended for in-parallel capillary flow and evaporation liquid transport, and again, the changes of the interface shape and multiphase flow front thickness are investigated. It turns out that the convective evaporation is prolonged due to the capillary flow as evaporated liquid close to the evaporating boundary is replenished by capillary flow. However, the evaporation curve has an elongated ``tail'' for longer evaporation times as capillarity tends to transport the liquid deeper into the porous medium. The contributions of the capillary flow and the mass transport on the overall evaporation dynamics is best visible by comparing the liquid pseudo-velocity for pure evaporation and evaporation with capillary flow. Two pseudo-velocities are equal for time for which there is a transition from convection to diffusion controlled evaporation. In this point, the remaining liquid is always distributed in the multiphase pattern, where the thickness of the multiphase region depends on capillary flow and mass transport rates. [Preview Abstract] |
Tuesday, November 22, 2011 3:31PM - 3:44PM |
S16.00003: New upper bounds for convection in a fluid-saturated porous layer Baole Wen, Greg Chini, Charles Doering There has been renewed interest in buoyancy-driven convection in porous media owing in part to applications relating to carbon dioxide sequestration in terrestrial aquifers. As in other convection problems, a key quantity of interest is the normalized volume and time averaged heat flux through the layer, i.e. the Nusselt number (Nu). Here, we present an improved upper bound on Nu as a function of Rayleigh number (Ra) for a model of thermally driven porous medium convection. The bound is obtained by numerically solving the full ``background field" variational problem first posed by Doering and Constantin (1998) for this model. We describe an efficient numerical algorithm for solving the variational problem and present improved bounds indicating that Nu $\sim$ c Ra (for computed constant c). [Preview Abstract] |
Tuesday, November 22, 2011 3:44PM - 3:57PM |
S16.00004: Gravity Current in Horizontal Porous Media with A Permeability Gradient Zhong Zheng, Peichun Tsai, Talal Al-Housseiny, Howard Stone We study the influence of a power-law porosity and permeability gradient on the front propagation of a gravity current in an unconfined porous media. We neglect mass transfer and surface tension on the interface. A similarity solution is found for the propagating front, which is different from the homogeneous case. Experiments have been performed using liquid pushing air in a Hele-Shaw cell with a constant gradient in gap thickness in the vertical direction. We measure the speed of the front and the shape of the interface. We observe a third layer of trapped air in the region where the permeability is low, while it appears that the propagating front still satisfies the similarity solution with a modified coefficient. [Preview Abstract] |
Tuesday, November 22, 2011 3:57PM - 4:10PM |
S16.00005: PIV measurement of solute diffusion natural convection in a Hele-Shaw cell Dana Ehyaei, Matthew Baldus, Ken Kiger Dissolution trapping of CO$_2$ is regarded as a critical mechanism for sequestration of carbon in deep saline aquifers. Currently, however, there is significant variability in the literature concerning the critical time required for onset of the convective fingering instabilities that are responsible for accelerating the dissolution of CO$_2$ into the brine. In the current work, we focus on making a direct measure of the velocity field during the onset, growth and saturation of the convection in a Hele-Shaw cell analog of the porous media problem. The working fluids consisted of aqueous mixtures of methanol and ethylene glycol (MEG), which when dissolved into water, results in a negatively buoyant solution similar to CO$_2$ in brine. The velocity field was measured using PIV, and procedures were developed to circumvent traditional implementation difficulties within thin-gap flows through careful particle selection and manipulation prior to starting the experiment. The results of these measurements provide the unsteady evolution of the flow from onset to late-time mixing, as revealed by the velocity and vorticity field during the finger growth and saturation. Features of the flow and the rate of mixing will be discussed. [Preview Abstract] |
Tuesday, November 22, 2011 4:10PM - 4:23PM |
S16.00006: Transient double-diffusive convection in an axisymmetric wavy-walled enclosure Fausto Sanchez, Simon Martinez, Hugo Ramirez, Jesus Chavez, Abraham Medina Transient double-diffusive convection within a vertical wavy-wall cylinder was numerically studied. The enclosure is filled with a saturated porous medium, the fluid is Newtonian and the Boussinesq approach was applied. The cavity is heated from below while the lateral wavy wall is thermally insulated. The saturation concentration of a passive tracer is assumed to exist at the top. The initial condition considers the fluid is at rest with zero concentration. An analytical coordinate transformation was used to change the computational domain into a square. Heat and mass transfer were analyzed using non-dimensional parameters which include the cavity aspect ratio, dimensionless wavelength and amplitude of the wavy-wall, the Rayleigh-Darcy, effective Prandtl and Schmidt numbers. The average Nusselt and Sherwood numbers were evaluated while the transport phenomena evolve within the cavity. After a large dimensionless time the concentration gradients become weak and thermal stratification arises promoting low heat transfer, specially when the wave amplitude is large. [Preview Abstract] |
Tuesday, November 22, 2011 4:23PM - 4:36PM |
S16.00007: Gravity currents arrested by convective mixing Christopher MacMinn, Michael Szulczewski, Juan Hidalgo, Ruben Juanes The large-scale injection of carbon dioxide (CO2) into deep saline aquifers is a promising tool for reducing atmospheric CO2 emissions to mitigate climate change. Trapping of the buoyant CO2 after injection is essential in order to minimize the risk of leakage into shallower formations through a pre-existing well or fracture, or via the activation of a fault. However, traditional reservoir-simulation tools are currently unable to resolve the impact of small-scale trapping processes on fluid flow at the scale of a geologic basin. Here, we use analog experiments to study solubility trapping of the CO2 via convective mixing, where dense fingers of CO2-rich groundwater carry CO2 away from the buoyant plume as it dissolves. We study the impact of convective mixing on a buoyant gravity current migrating up-dip in a sloping aquifer (a Hele-Shaw cell packed with glass beads), and we show that a simple upscaled model reproduces the macroscopic features of this complex physical process both qualitatively and quantitatively. We then estimate the dimensionless rate of solubility trapping for several large saline aquifers in the United States in order to assess the importance of solubility trapping in practice. [Preview Abstract] |
Tuesday, November 22, 2011 4:36PM - 4:49PM |
S16.00008: Density-Driven Convection with an Inclined Boundary Peichun Tsai, Talal Al-Housseiny, Zhong Zheng, Howard Stone We experimentally investigate convective instability and transport in a Hele-Shaw geometry and in a porous medium with inclined boundaries. The initial fluid configuration is buoyantly stable: a lighter liquid is placed above a dense one. The convection is generated by the dissolution of the two liquids which results in a heavier fluid layer at the interface, advecting into the underlaid, lighter fluid. Phenomenologically, in a vertical cell, heavier, mushroom-like plumes mostly travel downward and then partially merge. In contrast, in an inclined cell, the dense fingerings initially transport vertically downward and subsequently tilt and move laterally due to the inclined boundaries. We examine the width, wavelength, and dynamics of the dense plumes. We find that the tilting angle of the inclined boundary profoundly affects the dynamics of the density-driven plumes. In addition, the permeability of the porous media strongly changes the convective rate. These findings show key implications for geological carbon dioxide (CO2) storage in a silane aquifer when the dissolved CO2 into brine produces a heavier mixture with an enhancement of the mass transfer by convection. [Preview Abstract] |
Tuesday, November 22, 2011 4:49PM - 5:02PM |
S16.00009: How convective mixing slows down Michael Szulczewski, Ruben Juanes Convective mixing is a key CO2-trapping mechanism during geologic sequestration. While this mechanism has been shown to increase the CO2 dissolution rate at short times after onset, it has not been studied at late times when the CO2-rich fingers interact with the bottom of the aquifer. Here, we study the late-time behavior in a simple system: a linear, homogeneous aquifer in which the CO2-brine interface spans a finite region along the top of the aquifer. We perform high-resolution simulations and experiments that involve dissolving CO2 in a Hele-Shaw cell filled with water and a pH indicator. We show that the late-time dissolution rate decreases after the fingers reach the bottom due to two mechanisms: (1) fill up, in which the CO2-rich fingers accumulate beneath the free-phase CO2, decreasing the density difference that drives convective mixing; and (2) shielding, in which the accumulation of CO2-rich fluid forms a wedge that blocks water without CO2 from reaching the entire CO2-brine interface. We further show that the dissolution rate decreases according to a power law in time. These results will be helpful for calculating the timescale over which a volume of injected CO2 will completely dissolve. [Preview Abstract] |
Tuesday, November 22, 2011 5:02PM - 5:15PM |
S16.00010: Purple fingers: convection in carbon sequestration Anja Slim, Mahesh Bandi, L. Mahadevan In geological carbon sequestration, CO$_2$ injected into a saline formation is less dense than the resident brine and floats above it. It is slightly soluble in brine and progressively dissolves. Brine with dissolved CO$_2$ is slightly denser than ``pure" brine giving the potential for convective overturning. We experimentally study the dissolution process from first contact between CO$_2$ and brine through onset of convection to almost complete saturation for Rayleigh numbers between 80 and 1200. We present an analogue experiment using potassium permanganate as our solute, which closely mimics relevant CO$_2$ properties. We describe the different dynamical regimes and connect these with trends in several global measures, including the dissolution flux. We find onset of convection using both amplitude and flux deviations from pure diffusion. [Preview Abstract] |
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