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Joseph Howard
Joseph Howard

Dynamics Of Fluids In Porous Media Download Pdf



In many applications, free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight inconsistencies in the formulation of the governing equations can be found in the literature. The main goal of this paper is to identify these differences and provide a quantitative assessment of different approaches. Following a review of the different formulations, simulation results obtained from three alternative formulations are compared with experimental and numerical data. Results obtained by 2D and 3D test cases indicate that the predictive differences returned by the different formulations remain small for most applications, in particular for small porous Reynolds number ReP




Dynamics Of Fluids In Porous Media Download Pdf


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This article utilizes the usual formalism of the theory of mixtures to formulate compressible porous media models. The formulation allows for the effects of immiscibility and variable volume fractions. In addition, it allows for the effects of pore relaxation by treating the volume fractions as internal state variables. An attempt is made to relate the general results to classical porous media models. In particular, circumstances are presented which allow one to properly define a pore pressure for each fluid constituent. This article also contains the linear poroelasticity model which results from a formal linearization of the field and constitutive equations. One brief section is devoted to the specialization of this linear model to the one first proposed by Biot.


Multiphase flow in porous media is important in a number of environmental and industrial applications such as soil remediation, CO2 sequestration, and enhanced oil recovery. Wetting properties control flow of immiscible fluids in porous media and fluids distribution in the pore space. In contrast to the strong and weak wet conditions, pore-scale physics of immiscible displacement under intermediate-wet conditions is less understood. This study reports the results of a series of two-dimensional high-resolution direct numerical simulations with the aim of understanding the pore-scale dynamics of two-phase immiscible fluid flow under intermediate-wet conditions. Our results show that for intermediate-wet porous media, pore geometry has a strong influence on interface dynamics, leading to co-existence of concave and convex interfaces. Intermediate wettability leads to various interfacial movements which are not identified under imbibition or drainage conditions. These pore-scale events significantly influence macro-scale flow behaviour causing the counter-intuitive decline in recovery of the defending fluid from weak imbibition to intermediate-wet conditions.


Here, we use Computational Fluid Dynamics (CFD) modelling to perform direct numerical simulation of two-phase immiscible fluids displacement in a porous medium, which is designed based on the pore-scale X-ray tomography image of a real sand pack. Performing direct numerical simulations on 2D16, 17 and 3D18, 19 images of real porous media is an advanced tool that allows capturing more detailed fluid dynamics information compared to pore-network modelling approach20,21,22,23, specifically for complex pore morphologies. We present results of direct 2D numerical simulations performed on a wide range of wettability conditions with a particular focus on intermediate-wet condition. Our results demonstrate the co-existence of concave and convex interfaces under intermediate-wet conditions emanated from the interplay between the wetting characteristics and pore geometry. Such a phenomenon promotes (i) pinning of convex interface, (ii) pore-level reverse displacement and (iii) interface instability. These complex yet intriguing pore-scale displacement events provide novel explanations to the classical non-monotonic behaviour of recovery of defending fluid as a function of porous media wettability.


The obtained high resolution numerical results allow us to investigate another complex interfacial process occurring in intermediate-wet porous media that is related to the instability of interface in a single pore (Fig. 1(d)). As explained before, in the presence of intermediate-wet condition, the curvature of an interface can change from convex to concave or vice versa. Figure 1(d) illustrates that such morphological transformation of interface is not spontaneous, but occurs through an intermediate stage where the interface is instable. The morphology of the instable interface is significantly different from its stable counter parts that are concave and convex. Figure 1(d) shows that across one single interface, the sign of capillary pressure (defined by the difference between the pressures across the interface) changes. At macroscopic-scale, this will lead to non-uniform distribution of the capillary pressure.


Under intermediate-wet conditions, interaction of interface with pore surface leads to the co-existence of concave and convex interface (Fig. 1(a)) which has been observed in different pores (Fig. 1(c)) and even within a single irregular pore (Fig. 1(d)). To investigate the influence of these displacement events on the macroscopic flow behaviour, we quantified the recovery efficiency of the defending fluid as a function of the wettability of porous media with the results being presented in Fig. 2.


(a) Fluid phase and pressure distribution under different wetting conditions at the end of simulation. White colour represents pathway of invading phase. Pressure is normalized with respect to the outlet pressure and it indicates the pressure in the defending phase. (b) Distribution of blobs size of defending fluid under different wettability scenarios. The inset illustrates the maximum blob size as a function of the contact angle. (c) The non-monotonic dependency of the defending phase recovery on the wettability of porous media.


Figure 2(a) shows the distribution of phases under different wetting conditions. Visual inspection of this figure along with Fig. 2(b) shows that under intermediate-wet conditions the blobs of defending fluid are more widespread compared to other wetting conditions which might be attributed to the interface coalescence. Furthermore, the recovery efficiency of the defending fluid (the area represented by white in Fig. 2(a)) as a function of the wettability of porous media is quantified and shown in Fig. 2(c).


Wetting characteristics of porous media significantly influence multiphase flow and transport processes. In the present study, we conducted a comprehensive series of investigation by means of direct numerical simulation to delineate the pore-scale mechanisms controlling immiscible two-phase flow in porous media under different wettability scenarios with a particular focus on intermediate-wet conditions which has been rarely discussed in literature. The present pore-scale analysis helps to rationalize the physics governing some of the unexplained previous observations8, 28. With the current experimental tools available, it is not feasible to experimentally observe some of the effects induced by the wettability condition which ultimately determine the dynamics of displacement in porous media (such as the pressure field developed at pore-scale influencing the interface dynamics as illustrated in Fig. 1(c,d)). Inspection and visualization of our numerical results enabled us to gain insights on the complex pore level dynamics controlling the displacement mechanisms as a function of wetting properties of porous media and the resulting macroscopic displacement patterns that emerge.


Our numerical results revealed a non-monotonic dependence of defending fluid recovery on the wetting characteristics of porous media with the recovery efficiency being the highest under the weak imbibition condition. At pore-scale, our results confirms the presence of both concave and convex interfaces under intermediate-wet conditions. We show that for a uniform contact angle, both concave and convex interface exists in heterogeneous porous media. This co-existence of concave and convex interface leads to several interfacial processes influencing the dynamics of multiphase flow. The illustrated processes including pinning of convex interface and reverse displacement causes decline in the recovery efficiency of defending fluid.


PTT 204\/3 APPLIED FLUID MECHANICS SEM 2 (2012\/2013)\n \n \n \n \n "," \n \n \n \n \n \n Soil water flow and Darcy\u2019s Law. Laminar flow in a tube Poiseuille\u2019s Law, 1840: where: Q = volume of flow per unit time (m 3 s -1 ) r = radius of the.\n \n \n \n \n "," \n \n \n \n \n \n Lecture Notes Applied Hydrogeology\n \n \n \n \n "," \n \n \n \n \n \n ME 254. Chapter I Integral Relations for a Control Volume An engineering science like fluid dynamics rests on foundations comprising both theory and experiment.\n \n \n \n \n "," \n \n \n \n \n \n KINEMATICS Kinematics describes fluid flow without analyzing the forces responsibly for flow generation. Thereby it doesn\u2019t matter what kind of liquid.\n \n \n \n \n "," \n \n \n \n \n \n Chapter 21: Molecules in motion Diffusion: the migration of matter down a concentration gradient. Thermal conduction: the migration of energy down a temperature.\n \n \n \n \n "," \n \n \n \n \n \n Basic Fluid Properties and Governing Equations\n \n \n \n \n "," \n \n \n \n \n \n Darcy\u2019s Law and Flow CIVE Darcy allows an estimate of: the velocity or flow rate moving within the aquifer the average time of travel from the head.\n \n \n \n \n "," \n \n \n \n \n \n \n \n \n \n \n "," \n \n \n \n \n \n Mass Transfer Coefficient\n \n \n \n \n "," \n \n \n \n \n \n Reynolds Transport Theorem We need to relate time derivative of a property of a system to rate of change of that property within a certain region (C.V.)\n \n \n \n \n "," \n \n \n \n \n \n Lecture 4: Isothermal Flow. Fundamental Equations Continuity equation Navier-Stokes equation Viscous stress tensor Incompressible flow Initial and boundary.\n \n \n \n \n "," \n \n \n \n \n \n ATM 301 Lecture #7 (sections ) Soil Water Movements \u2013 Darcy\u2019s Law and Richards Equation.\n \n \n \n \n "," \n \n \n \n \n \n Lecture Outline Chapter 9 College Physics, 7 th Edition Wilson \/ Buffa \/ Lou \u00a9 2010 Pearson Education, Inc.\n \n \n \n \n "," \n \n \n \n \n \n LECTURE 6 Soil Physical (Mechanical) Properties \u2013 Bulk density, porosity, strength, consistency.\n \n \n \n \n "," \n \n \n \n \n \n Darcy\u2019s Law Philip B. Bedient Civil and Environmental Engineering Rice University.\n \n \n \n \n "," \n \n \n \n \n \n CE 3354 Engineering Hydrology Lecture 21: Groundwater Hydrology Concepts \u2013 Part 1 1.\n \n \n \n \n "," \n \n \n \n \n \n 4. Properties of Materials Sediment (size) Physical States of Soil Concepts of Stress and Strain Normal and Shear Stress Additional Resistance Components.\n \n \n \n \n "," \n \n \n \n \n \n Soil Water Balance Reading: Applied Hydrology Sections 4.3 and 4.4\n \n \n \n \n "," \n \n \n \n \n \n Open Channel Hydraulic\n \n \n \n \n "," \n \n \n \n \n \n Properties of Aquifers\n \n \n \n \n "," \n \n \n \n \n \n Soil, Plant and Water Relationships\n \n \n \n \n "," \n \n \n \n \n \n Chapter1:Static pressure in soil due to water.\n \n \n \n \n "," \n \n \n \n \n \n Groundwater Review Aquifers and Groundwater Porosity\n \n \n \n \n "," \n \n \n \n \n \n College Physics, 7th Edition\n \n \n \n \n "," \n \n \n \n \n \n Chapter 4 Fluid Mechanics Frank White\n \n \n \n \n "," \n \n \n \n \n \n Continuum Mechanics (MTH487)\n \n \n \n \n "," \n \n \n \n \n \n Darcy\u2019s Law and Richards Equation\n \n \n \n \n "," \n \n \n \n \n \n Chapter 11 Fluids.\n \n \n \n \n "," \n \n \n \n \n \n Some Common Properties of Gases\n \n \n \n \n "," \n \n \n \n \n \n Soil water.\n \n \n \n \n "," \n \n \n \n \n \n Thin Walled Pressure Vessels\n \n \n \n \n "," \n \n \n \n \n \n 5. WEIGHT VOLUME RELATIONSHIPS\n \n \n \n \n "," \n \n \n \n \n \n Diffusion Mass Transfer\n \n \n \n \n "," \n \n \n \n \n \n Next adventure: The Flow of Water in the Vadose Zone\n \n \n \n \n "," \n \n \n \n \n \n Modeling and experimental study of coupled porous\/channel flow\n \n \n \n \n "," \n \n \n \n \n \n Subject Name: FLUID MECHANICS\n \n \n \n \n "," \n \n \n \n \n \n Philip B. Bedient Civil and Environmental Engineering Rice University\n \n \n \n \n "," \n \n \n \n \n \n Introduction to Effective Permeability and Relative Permeability\n \n \n \n \n "," \n \n \n \n \n \n Fluid statics Hydrostatics or Fluid Statics is the study of fluids at rest. It's practical applications are numerous. Some of which are Fluid Manometers,\n \n \n \n \n "," \n \n \n \n \n \n ENGINEERING MECHANICS\n \n \n \n \n "," \n \n \n \n \n \n FLUID MECHANICS REVIEW\n \n \n \n \n "," \n \n \n \n \n \n Relative permeability\n \n \n \n \n "," \n \n \n \n \n \n The Kinetic theory Pressure\n \n \n \n \n "," \n \n \n \n \n \n Asst. Prof. Dr. Hayder Mohammad Jaffal\n \n \n \n \n "," \n \n \n \n \n \n Asst. Prof. Dr. Hayder Mohammad Jaffal\n \n \n \n \n "," \n \n \n \n \n \n Philip B. Bedient Civil and Environmental Engineering Rice University\n \n \n \n \n "," \n \n \n \n \n \n WHAT IS FLUID? Fluid is a substance that is capable of flowing. It has no definite shape of its own. It assumes the shape of its container. Both liquids.\n \n \n \n \n "," \n \n \n \n \n \n Lecture Fluids.\n \n \n \n \n "]; Similar presentations


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