Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session L23: Porous Media Flows: Theory |
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Chair: Mojdeh Rasoulzadeh, University of Alabama Room: 231 |
Monday, November 21, 2022 8:00AM - 8:13AM |
L23.00001: Two-phase flow: Travelling waves in a reacting porous medium Danielle V Bullamore, Sam Pegler, Sandra Piazolo There are many situations where a fluid flows through a porous medium and reacts with it to alter the porosity and permeability of the medium. Important examples include flows in the Earth's mantle and crust, and formation of karst topography. An everyday example is the flow of water poured through a bed of dissolving sugar. Instabilities in these systems can create remarkable fingering patterns, arising from the localisation of flow in high permeability pathways. |
Monday, November 21, 2022 8:13AM - 8:26AM |
L23.00002: Stochastic porous media, towards a digital meniscus Anas Obeidat, Andreas Zilian Flow and transport computations for explicit microstructures of stochastic porous media, here the knee meniscus, are prohibitively time consuming. First, as the porous microstructure is geometrically complex, each simulation is considerably time consuming. Second, the porous microstructure is intrinsically stochastic as it varies from location to location and from specimen to specimen, requiring numerous experiments and flow computations to be performed. First, we address the continuum biological hydrodynamics simulation in complex geometries, by presenting a novel integrated computational approach using the Discretisation-Corrected Particle Strength Exchange (DC PSE) operator [1] discretisation in a mesh-less solver, the solver is coupled with Brinkman penalisation [2] to add a layer of robustness when dealing with complex geometries. Steady and unsteady Navier-Stokes equations are solved using the solver. Secondly, we introduce a data driven framework in which the porous microstructures are homogenised to enable simulations in which the explicit microstructural representation is omitted, but the stochastic transport characteristics are preserved. Only a few meniscuses need to be characterised and a few sub- scale microstructural simulations on statistical volume elements are required to probabilistically identify the parameters of the random spatial fields of the permeability coefficient. The probabilistic identifica- tion setting assumes that each spatial input field is a realisation from a single, joint multi-dimensional probability density function. The probabilistic identification setting is based on Bayes' theorem, which only requires a limited number of measurements. Finally, we will use the identified probability density function to rapidly propagate the uncertainty with the fast homogenised model. |
Monday, November 21, 2022 8:26AM - 8:39AM |
L23.00003: A multiscale mathematical model for particle filtration Arkady Wey, Ian Griffiths, Jon Chapman, Chris Breward
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Monday, November 21, 2022 8:39AM - 8:52AM |
L23.00004: Anomalous transport in vesicular porous media Mojdeh Rasoulzadeh Transport of chemical species in complex structured vesicular porous media with mesoscale fluid-filled vugs and cavities exhibit anomalous features that cannot be captured by Fickian transport approaches. The anomalous behavior originates from the occurrence of non-Gaussian and multiscale velocity distributions caused by porous medium structural complexities. Local flow instabilities, vorticities, stagnant zones, and reverse flow result in a significantly different velocity distribution for the tracer compared to the fluid. We investigate the nonreactive transport of particles in a porous medium with an embedded cavity located at the center. The Darcy-Stokes flow is solved for the matrix and cavity system, then the transport is modeled via particle tracking method. The effect of the size and shape of the cavity and the flow field features on tracer transport is quantified. Breakthrough curves confirm anomalous transport at the cell problem. We derive the upscaled continuous time random walk (CTRW) framework for the vesicular medium with a high degree of disorder. The key controlling factors that substantially affect the spread of tracer across all scales of heterogeneity are addressed. |
Monday, November 21, 2022 8:52AM - 9:05AM |
L23.00005: Non-equilibrium theory for non-ergodic systems based on time-and-space averaging James McClure, Steffen Berg, Ryan T Armstrong In an ergodic system spatial, temporal and ensemble averages are equivalent. Many theoretical approaches explicitly require ergodicity, and few general strategies have been advanced to treat non-equilibrium thermodynamic behavior associated with non-ergodic systems. We develop a non-equilibrium theory using time-and-space averaging, assuming that ergodic conditions hold only at very small length scales. Since the timescale for mixing is fast at small length scales, many non-ergodic systems can be described based on this approach. We show that fluctuations in these systems are constrained by the internal energy dynamics, deriving quasi-ergodic requirements that must hold for any stationary process due to conservation of energy. Since these requirements are formulated in terms of observable quantities, they can be used to explicitly identify the timescale where valid transport coefficients can be obtained. This result is significant because it provides a straightforward way to homogenize the dynamics of systems that do not obey equipartition of energy, particularly systems with slow fluctuations. We apply our theory to derive transport coefficients for immiscible fluid flow through porous media, demonstrating that pressure fluctuations observed in experiments can be non-Gaussian due to cooperative effects that are caused by capillary events. We show that the macroscopic dynamics can still be homogenized as long as the timescale for averaging is chosen such that these fluctuations perform no net work on the system. We further demonstrate that changes to fluid topology are responsible for non-ergodic effects, and that time-and-space averages provide a natural mechanism to account for discrete changes based on the topological residence time associated with particular micro-states of the system. |
Monday, November 21, 2022 9:05AM - 9:18AM |
L23.00006: Small-amplitude heave oscillations of an annular disk Muhammad Usman, Hassan Masoud We study small-amplitude broadside oscillations of an annular disk in an unbounded domain of fluid. Specifically, we formulate a semi-analytical framework to examine the effects of the oscillation frequency and pore radius on the added mass and damping coefficients of the disk. We break down the original problem into two simpler ones. The sub-problems are then bridged together by the reciprocal theorem and simplified further via a perturbation expansion in terms of the pore radius to arrive at dual integral equations. These equations are eventually reduced to two systems of algebraic equations and solved numerically. Our analysis reveals that the annular (porous) disk behaves nearly as a solid (impermeable) one in the Stokes regime, with the change in the force coefficients scaling with the cube of the pore radius. Remarkably, as the inertial effects become more pronounced, the damping coefficient initially increases with increasing the pore radius, reaches a maximum, and then decays as the inner hole of the disk becomes larger. The rate of decay of both the damping and added-mass coefficients scale with the pore radius in the asymptotic limit of high oscillation frequency. The non-monotonic damping behavior of annular disks can be harnessed in engineering applications. |
Monday, November 21, 2022 9:18AM - 9:31AM |
L23.00007: The interaction of fluid layers from simultaneous injection of two gravity currents Kai-En Yang, Zhong Zheng We study the displacement and interaction process of multiple fluid layers from simultaneous injection of two gravity currents into a confined porous medium, partly inspired by the practice of enhanced oil recovery and geological CO2 sequestration. Two coupled nonlinear advective-diffusive equations are derived to describe the time evolution of the interface shape of both the upper (lighter) and lower (heavier) intrusive layers. At early times, the governing PDEs decouple and reduce to two nonlinear diffusion equations for the spreading of two gravity currents along either the top or bottom boundary of the porous medium. As time progresses, the upper and lower currents approach each other and start to interact; the flow becomes mainly advective in the bulk, with non-negligible diffusive (buoyancy) effects near the propagating front. We also find that there are many sub-regimes of gravity current interaction at late times, impacted by four dimensionless parameters, representing the flow rate partition, ratio of buoyancy over injection forces, and the viscosity contrasts between the injecting and displaced fluids. Finally, by defining appropriate similarity variables at early or late times, the governing PDEs reduce to ODEs, corresponding to a class of self-similar solutions in different asymptotic regimes. |
Monday, November 21, 2022 9:31AM - 9:44AM Author not Attending |
L23.00008: Upscaling unsaturated flows in vertically heterogeneous porous layers Zhong Zheng Characterising interfacial and unsaturated flows in heterogeneous porous layers is of both fundamental and practical interest. Under the assumption of vertical gravitational-capillary equilibrium, we present a theoretical model to describe one-dimensional flows in a porous layer with vertical variations in average pore size, porosity, intrinsic permeability, and capillary pressure jump between invading and displaced fluids. The model leads to asymptotic solutions for the saturation distribution and outer envelope of the invading fluid, and for the background pressure drop across the porous layer. Eight dimensionless parameters are recognised after appropriate non-dimensionalisation of the governing equations, the influence of which are demonstrated through a series of example calculations. In particular, four asymptotic regimes are identified, representing unconfined sharp-interface flows, confined sharp-interface flows, unconfined unsaturated flows, and confined unsaturated flows. Finally, in the context of flow upscaling, analytical solutions are derived for the effective relative permeability curves on the basis of exact solutions of the saturation field and interface shape, shedding light on the subtle influence of competition between injection/pumping and gravitational forces, wetting and capillary effects, viscosity contrast between the invading and displaced fluids, and vertical heterogeneity of the porous layer. |
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