Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session A29: Porous Media Flows I |
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Chair: Ruben Juanes, Massachusetts Institute of Technology Room: 32B |
Sunday, November 18, 2012 8:00AM - 8:13AM |
A29.00001: Nonlinear Taylor dispersion in gravity currents in porous media Michael Szulczewski, Ruben Juanes Taylor dispersion describes how a non-uniform flow can accelerate diffusive mixing between fluids by elongating the fluid-fluid interface over which diffusion acts. While Taylor dispersion has been extensively studied in simple systems such as Poiseuille and Couette flows, it is poorly understood in more complex systems such as porous-media flows. Here, we study Taylor dispersion in porous media during a gravity-driven flow using theory and simulations. We consider a simple geometry for physical insight: a horizontal, confined layer of permeable rock in which two fluids of different densities are initially separated by a vertical interface. We show that the flow exhibits a non-uniform velocity field that leads to Taylor dispersion at the aquifer scale. Unlike the classical model of Taylor dispersion, however, the diffusive mixing is coupled to the flow velocity because it reduces the lateral density gradient that drives the flow. This coupling causes the flow to continually decelerate and eventually stop completely. To model the flow, we develop a non-linear diffusion equation for the concentration of the more dense fluid, which admits an analytical similarity solution. We discuss applications of the model to CO$_2$ sequestration. [Preview Abstract] |
Sunday, November 18, 2012 8:13AM - 8:26AM |
A29.00002: Flow through a free-moving porous cylinder within a rotating cylindrical vessel Mohit P. Dalwadi, Sarah L. Waters Tissue engineering aims to repair or replace damaged body tissue via the engineering of artificial tissues. One method is to seed cells onto a porous biomaterial construct which is then cultured within a rotating bioreactor. We investigate a rotating high-aspect ratio vessel bioreactor that contains a free-moving porous tissue construct. We extend the work of Cummings and Waters [2007], who considered a solid tissue construct, by coupling a single-phase flow external to the tissue construct (modeled by the Navier-Stokes equations) to two-phase flow through the porous tissue construct (modeled using Darcy's equations) via appropriate boundary conditions. We study two flow regimes, corresponding to \emph{near-to} and \emph{far-from} rigid body rotation. We determine the fluid flow through the system for a given construct trajectory. By considering a force balance to deduce the construct trajectory, we obtain a full description of the flow behaviour and the fluid particle paths. We ascertain the residence time of fluid within the construct and, in the future, this work will enable us to calculate the role of advection in the spatiotemporal nutrient distribution, an important consideration for the tissue growth problem. [Preview Abstract] |
Sunday, November 18, 2012 8:26AM - 8:39AM |
A29.00003: Convective Shutdown in a Porous Medium John Lister, Duncan Hewitt, Jerome Neufeld Convective flow in a porous medium, driven by a buoyancy source along one boundary, is found in many geophysical and industrial processes, and has recently been investigated in the context of CO$_2$ sequestration. If the domain is closed then the convective flux soon starts to decrease due to the slow evolution of the average interior density. We reveal a close link between such a ``one-sided'' shutdown system and the ``two-sided'' statistically steady Rayleigh--B\'enard cell. We present high-resolution numerical simulations of convective shutdown at high Rayleigh number $Ra$ in a two-dimensional porous medium. A simple analytic box model of the shutdown system is constructed, with time-dependent Rayleigh and Nusselt numbers, which is based on measurements of the convective flux from a Rayleigh--B\'enard cell (Hewitt {\it et al.} Phys. Rev. Lett. 2012) and gives excellent quantitative agreement with numerical results. These ideas are generalised to model fluids with a power-law equation of state. The dynamical structure of high-$Ra$ shutdown flow is dominated by vertical columnar flow in the interior, and the evolving horizontal wavenumber $k[Ra(t)]$ of the columns gives extremely good agreement with similar measurements of $k(Ra)$ from the columnar flow in a Rayleigh--B\'enard cell. [Preview Abstract] |
Sunday, November 18, 2012 8:39AM - 8:52AM |
A29.00004: Interfacial Motion and Convective Shutdown Duncan Hewitt, Jerome Neufeld, John Lister We present theoretical, numerical and experimental models of the shutdown of convection in a sealed porous domain that is initially stably stratified in two fluid layers. The equation of state is such that the solution which forms at the interface is more dense than either layer. The resultant convective flux across the moving interface slowly shuts down due to the increase in the average lower-layer density. We examine a variety of physical systems, comprised of either immiscible or miscible fluids. In the latter case, diffusion above the interface has a surprising and significant effect at late times. In each case, we develop theoretical box models, based on a rigid-lid assumption for the moving interface, which compare very well with numerical simulations. We explore the validity of the rigid-lid approximation using numerical simulations and experimental results from a Hele-Shaw cell. These both show that interfacial deformation can significantly increase the convective flux, particularly for miscible fluids. Our results have application to a range of geophysical systems, and are particularly relevant to the long-term stability of geologically sequestered CO$_2$ in a saline aquifer. [Preview Abstract] |
Sunday, November 18, 2012 8:52AM - 9:05AM |
A29.00005: Scaling of convective dissolution in porous media Juan J. Hidalgo, Luis Cueto-Felgueroso, Jaime Fe, Ruben Juanes Convective mixing in porous media results from the density increase in an ambient fluid as a substance (a solute or another fluid) dissolves into it., which leads to a Rayleigh-B\`{e}nard-type instability. The canonical model of convective mixing in porous media, which exhibits a dissolution flux that is constant during the time period before the convective fingers reach the bottom of the aquifer, is not described by the Rayleigh number Ra [Hidalgo {\&} Carrera (2009), J. Fluid Mech.; Slim {\&} Ramakrishnan (2010), Phys. Fluids]. That suggests that dissolution fluxes should not depend on Ra. However, this appears to be in contradiction with recent experimental results using an analogue-fluid system characterized by a non-monotonic density-concentration curve, which naturally undergoes convection [Neufeld et al. (2010), Geophys. Res. Lett.; Backhaus, Turitsyn {\&} Ecke (2011), Phys. Rev. Lett.]. Here we study the scaling of dissolution fluxes by means of the variance of concentration and the scalar dissipation rate. The fundamental relations among these three quantities allow us to study the canonical and analogue-fluid systems with high-resolution numerical simulations, and to demonstrate that both the canonical and analogue-fluid systems exhibit a dissolution flux that is constant and independent of Ra. Our findings point to the need for alternative explanations of recent nonlinear scalings of the Nusselt number observed experimentally. [Preview Abstract] |
Sunday, November 18, 2012 9:05AM - 9:18AM |
A29.00006: Coarsening dynamics of 3D convective dissolution in porous media Xiaojing Fu, Luis Cueto-Felgueroso, Ruben Juanes Dissolution by convective mixing is an essential trapping mechanism during CO$_2$ sequestration in deep saline aquifers. Dissolution of the buoyant supercritical CO$_2$ into the underlying brine leads to a local density increase initially. The resulting CO$_2$-brine mixture is denser than the two initial fluids, leading to a Rayleigh-B\'{e}nard type instability, which greatly accelerates the dissolution process. Both bench-scale experiments and high-resolution computer simulations have shown the initiation and nonlinear interaction of gravity fingers during this density-driven convection process. While 2D analyses of this phenomenon have elucidated important aspects of the dominant flow mechanisms, fundamental issues regarding the coarsening of gravity fingers remain unclear from these studies. In this work, we present high-resolution, 3D simulations of convective dissolution. We observe a previously unreported phenomenon of self-organization of fingers that form coherent network structures in the top boundary layer. Based on this network pattern, we study the coarsening dynamics of convective dissolution in 3D. [Preview Abstract] |
Sunday, November 18, 2012 9:18AM - 9:31AM |
A29.00007: Chaotic Advection in a Bounded 3-Dimensional Potential Flow Guy Metcalfe, Lachlan Smith, Daniel Lester 3-dimensional potential, or Darcy flows, are central to understanding and designing laminar transport in porous media; however, chaotic advection in 3-dimensional, volume-preserving flows is still not well understood.\footnote{Wiggins, J. Fluid Mech. {\bf 654} (2010). } We show results of advecting passive scalars in a transient 3-dimensional potential flow that consists of a steady dipole flow and periodic reorientation. Even for the most symmetric reorientation protocol, neither of the two invarients of the motion are conserved; however, one invarient is closely shadowed by a surface of revolution constructed from particle paths of the steady flow, creating in practice an adiabatic surface. A consequence is that chaotic regions cover 3-dimensional space, though tubular regular regions are still transport barriers. This appears to be a new mechanism generating 3-dimensional chaotic orbits. These results contast with the experimental and theoretical results for chaotic scalar transport in 2-dimensional Darcy flows.\footnote{Metcalfe et al, Phil. Trans. R. Soc. {\bf A368} (2010a,b).}$^,$\footnote{Lester et al, Phys. Rev. {\bf E80} (2009), {\bf E81} (2010).} [Preview Abstract] |
Sunday, November 18, 2012 9:31AM - 9:44AM |
A29.00008: Galerkin Dynamical Modeling of Porous Medium Convection using an Eigenbasis from Upper Bound Theory Baole Wen, Navid Dianati, Greg Chini, Charles Doering Galerkin projection is a common strategy for generating ODE models of PDE systems, either as a means of performing highly resolved direct numerical simulation (DNS) or as a method for generating reduced-order dynamical models. Popular bases for the associated spectral expansions include Fourier and Chebyshev modes, eigenfunctions of linear stability operators about ``laminar'' base solutions or empirical mean flows, or modes arising from Proper Orthogonal Decomposition (POD) of numerical or experimental system realizations. Here we employ an alternative, fully a-priori spectral basis composed of eigenfunctions from upper bound theory, for both fully resolved and reduced dynamical modeling of porous medium convection -- a system that is receiving increased attention owing to applications in CO2 sequestration in terrestrial aquifers. Because this new basis is naturally adapted to the dynamics at a given Ra, our DNS requires a fraction of the total number of modes used in traditional (e.g. Fourier) spectral Galerkin simulations. Moreover, for ``moderate'' Rayleigh numbers ($Ra \la 10^3$) we demonstrate that mode slaving can be used to further reduce the dimension of the truncated dynamical systems. [Preview Abstract] |
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