Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L1: Porous Media Flows: General |
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Chair: Stefan Llewellyn Smith, UCSD Room: Auditorium |
Monday, November 23, 2015 4:05PM - 4:18PM |
L1.00001: Excess pore water pressure due to ground surface erosion Stefan Llewellyn Smith, Steven Gagniere Erosional unloading is the process whereby surface rocks and soil are removed by external processes, resulting in changes to water pressure within the underlying aquifer. We consider a mathematical model of changes in excess pore water pressure as a result of erosional unloading. Neuzil and Pollock (1983) studied this process in the case where the water table initially coincides with the surface. In contrast, we analyze an ideal aquifer which is initially separated from the ground surface by an unsaturated zone. The model is solved using Laplace Transform methods in conjunction with a boost operator derived by King (1985). The boost operator is used to boost the solution (in the Laplace domain) to a frame of reference moving at constant velocity with respect to the original frame. We use our solution to analyze the evolution of the pressure during erosion of the aquifer itself for small and large erosion rates. We also examine the flux at the upper boundary as a function of time and present a quasi-steady approximation valid for very small erosion rates in the appendix. [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L1.00002: A strategy for optimising well placement by combining historical well data with a geological model of a porous rock A.J. Evans, C.P. Caulfield, Andrew W. Woods Flow in porous media is subject to large uncertainties due to sparsity of available data and heterogeneity of reservoir properties over a range of length scales. We investigate the reduction in uncertainty which can be achieved through inversion of flux data between a point source and a point sink. A Monte Carlo simulation with stochastically generated permeabilities conditioned by flux data is used to estimate flux statistics for relocated wells. We demonstrate how the correlation length scale of the permeability influences the reduction in uncertainty for new well positions. Uncertainty is seen to be reduced for well positions within a region around the original well sites. This region scales with the permeability correlation length. Finally we show that a linearised method for flux estimation shows good agreement to fully non-linear simulations with a considerable reduction in computation time. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L1.00003: Abstract Withdrawn
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Monday, November 23, 2015 4:44PM - 4:57PM |
L1.00004: The permeability of poly-disperse porous media and effective particle size B.I. Markicevic, C. Preston, S. Osterroth, O. Iliev, M. Hurwitz The interactions between the fluid and solid phases in porous media account for the openness and length of the flow path that the fluid needs to travel within. The same reasoning applies for both mono- and poly-disperse media, and is reflected in the adoption of the same permeability models. The only difference is that an effective particle size diameter has to be used for the poly-disperse samples. A filtration experiment is used to form a particle layer, filter cake, consisting of particles of different sizes. Both inflow and outflow particle size distribution are measured by particle counting method, and from their difference, the particle size distribution in the cake is determined. In a set of experiments, the filtration history is altered by changing (i) filtration medium; (ii) suspension flow rate; and (iii) particle concentration, where in all cases investigated the cake permeability remains constant. In order to predict the permeability of poly-disperse cake from the analytical models, the particle size distribution moments are calculated, and the permeability is found for each moment. Comparing the experimental to the analytical permeability values the effective particle size is found, where the permeability calculated by using the harmonic mean of the particle size distribution reproduces the permeability experimental value best. Finally, in the parametric study, reducing the cake porosity and/or lowering the particle retention shifts effective particle size used in the permeability model toward higher moments of the particle size distribution function. [Preview Abstract] |
Monday, November 23, 2015 4:57PM - 5:10PM |
L1.00005: Momentum transfer at the interface between a porous medium and a pure fluid Howard Hu, Songpeng Zhang We examine the flow parallel to the interface between a porous medium and a liquid, focusing on the boundary conditions at the interface. When Darcy’s law is used to describe the momentum transport in the porous layer, the classic Beavers-Joseph condition relates the shear rate and the slip velocity at the interface with a slip parameter that depends on the structure of the porous surface. When the Brinkman equation is used, the averaged velocity is continuous at the interface, however the fluid shear stress across the interface commonly experiences a jump. This shear stress jump can be expressed in terms of the slip velocity at the interface divided by a length characterized by the square root of the permeability, and a dimensionless stress jump coefficient. In this work, we study the momentum transfer from the clear fluid onto the solid structure at the interface, and proposed a stress partition parameter that characterizes the stress transfer from the clear fluid to the fluid (and solid) phase of the porous medium. Simple models are developed to formulate this stress partition parameter for porous media that are brush-like, long fibers, and random, respectively. Our model predictions are compared with numerical and experimental results in the literature. [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L1.00006: Topological phase transition in 2D porous media flows Nicolas Waisbord, Norbert Stoop, Vasily Kantsler, Jeffrey S. Guasto, Jorn Dunkel Since the establishment of Darcy's law, analysis of porous-media flows has focused primarily on linking macroscopic transport properties, such as mean flow rate and dispersion, to the pore statistics of the material matrix. Despite intense efforts to understand the fluid velocity statistics from the porous-media structure, a qualitative and quantitative connection remains elusive. Here, we combine precisely controlled experiments with theory to quantify how geometric disorder in the matrix affects the flow statistics and transport in a quasi-2D microfluidic channel. Experimentally measured velocity fields for a range of different microstructure configurations are found to be in excellent agreement with large-scale numerical simulations. By successively increasing the matrix disorder, we study the transition from periodic flow structures to transport networks consisting of extended high-velocity channels. Morse-Smale complex analysis of the flow patterns reveals a topological phase transition that is linked to a qualitative change in the physical transport properties. This work demonstrates that topological flow analysis provides a mathematically well-defined, broadly applicable framework for understanding and quantifying fluid transport in complex geometries. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L1.00007: ABSTRACT WITHDRAWN |
Monday, November 23, 2015 5:36PM - 5:49PM |
L1.00008: Viscous fingering with partial miscible fluids Xiaojing Fu, Luis Cueto-Felgueroso, Ruben Juanes When a less viscous fluid displaces a more viscous fluid, the contrast in viscosity destabilizes the interface between the two fluids, leading to the formation of fingers. Studies of viscous fingering have focused on fluids that are either fully miscible or perfectly immiscible. In practice, however, the miscibility of two fluids can change appreciably with temperature and pressure, and often falls into the case of partial miscibility, where two fluids have limited solubility in each other. Following our recent work for miscible (Jha et al., PRL 2011, 2013) and immiscible systems (Cueto-Felgueroso and Juanes, PRL 2012, JFM 2014), here we propose a phase-field model for fluid-fluid displacements in a Hele-Shaw cell, when the two fluids have limited (but nonzero) solubility in one another. Partial miscibility is characterized through the design of thermodynamic free energy of the two-fluid system. We elucidate the key dimensionless groups that control the behavior of the system. We present high-resolution numerical simulations of the model applied to the viscous fingering problem. On one hand, we demonstrate the effect of partial miscibility on the hydrodynamic instability. On the other, we elucidate the role of the degree of fingering on the rate of mutual fluid dissolution. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L1.00009: Modeling and simulation of multiphase multicomponent multiphysics porous media flows in the context of chemical enhanced oil recovery Sourav Dutta, Prabir Daripa One of the most important methods of chemical enhanced oil recovery (EOR) involves the use of complex flooding schemes comprising of various layers of fluids mixed with suitable amounts of polymer or surfactant or both. The fluid flow is characterized by the spontaneous formation of complex viscous fingering patterns which is considered detrimental to oil recovery. Here we numerically study the physics of such EOR processes using a modern, hybrid method based on a combination of a discontinuous, multiscale finite element formulation and the method of characteristics. We investigate the effect of different types of heterogeneity on the fingering mechanism of these complex multiphase flows and determine the impact on oil recovery. We also study the effect of surfactants on the dynamics of the flow via reduction of capillary forces and increase in relative permeabilities. [Preview Abstract] |
Monday, November 23, 2015 6:02PM - 6:15PM |
L1.00010: On the stabilizing role of species diffusion in chemical enhanced oil recovery Prabir Daripa, Craig Gin In this talk, the speaker will discuss a problem on the stability analysis related to the effect of species diffusion on stabilization of fingering in a Hele-Shaw model of chemical enhanced oil recovery. The formulation of the problem is motivated by a specific design principle of the immiscible interfaces in the hope that this will lead to significant stabilization of interfacial instabilities, there by improving oil recovery in the context of porous media flow. Testing the merits of this hypothesis poses some challenges which will be discussed along with some numerical results based on current formulation of this problem. Several open problems in this context will be discussed. This work is currently under progress. [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L1.00011: Evaporation and Settling in an Idealized Porous Medium Daniel Anderson, Matthew Gerhart We investigate a mathematical model of a periodic array of solid blocks supported by squeeze films and separated by vertical fluid-filled channels. Evaporation occurs at the open fluid surface at the top of the vertical channels between the blocks and is coupled to the motion of the blocks through mass conservation and pressure, viscous, surface tension and external forces on the blocks. We derive a simplified mathematical model in the form of coupled ordinary differential equations for the thickness of the squeeze film layer, the height of the fluid in the vertical channels and the contact angle at the free surface. We present numerical solutions of this model that address the coupling between block motion and height of the fluid in the channel in an effort to understand the question of channel dry-out versus wetting and fluid resupply via the underlying squeeze film. [Preview Abstract] |
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