scholarly journals On the Transition From Creeping to Inertial Flow in Arrays of Cylinders

2010 ◽  
Author(s):  
K. Yazdchi ◽  
S. Srivastava ◽  
S. Luding
Keyword(s):  
Porous Media ◽  
Darcy’S Law ◽  
Computational Study ◽  
Darcy's Law ◽  
Natural Processes ◽  
Inertial Flow ◽  
Flow Through ◽  
High Reynolds ◽  
An Array Of Cylinders ◽  
Element Method

Many important natural processes involving flow through porous media are characterized by large filtration velocity. Therefore, it is important to know when the transition from viscous to the inertial flow regime actually occurs in order to obtain accurate models for these processes. In this paper, a detailed computational study of laminar and inertial, incompressible, Newtonian fluid flow across an array of cylinders is presented. Due to the non-linear contribution of inertia to the transport of momentum at the pore scale, we observe a typical departure from Darcy’s law at sufficiently high Reynolds number (Re). Our numerical results show that the weak inertia correction to Darcy’s law is not a square or a cubic term in velocity, as it is in the Forchheimer equation. Best fitted functions for the macroscopic properties of porous media in terms of microstructure and porosity are derived and comparisons are made to the Ergun and Forchheimer relations to examine their relevance in the given porosity and Re range. The results from this study can be used for verification and validation of more advanced models for particle fluid interaction and for the coupling of the discrete element method (DEM) with finite element method (FEM).

Incorporation of Interfacial Areas in Models of Two-Phase Flow

1999 ◽  
Author(s):  
William G. Gray ◽  
Michael A. Celia
Keyword(s):  
Porous Media ◽  
Hydraulic Conductivity ◽  
Single Phase ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Hydraulic Gradient ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Α Phase ◽  
Flow Through

The mathematical study of flow in porous media is typically based on the 1856 empirical result of Henri Darcy. This result, known as Darcy’s law, states that the velocity of a single-phase flow through a porous medium is proportional to the hydraulic gradient. The publication of Darcy’s work has been referred to as “the birth of groundwater hydrology as a quantitative science” (Freeze and Cherry, 1979). Although Darcy’s original equation was found to be valid for slow, steady, one-dimensional, single-phase flow through a homogeneous and isotropic sand, it has been applied in the succeeding 140 years to complex transient flows that involve multiple phases in heterogeneous media. To attain this generality, a modification has been made to the original formula, such that the constant of proportionality between flow and hydraulic gradient is allowed to be a spatially varying function of the system properties. The extended version of Darcy’s law is expressed in the following form: qα=-Kα . Jα (2.1) where qα is the volumetric flow rate per unit area vector of the α-phase fluid, Kα is the hydraulic conductivity tensor of the α-phase and is a function of the viscosity and saturation of the α-phase and of the solid matrix, and Jα is the vector hydraulic gradient that drives the flow. The quantities Jα and Kα account for pressure and gravitational effects as well as the interactions that occur between adjacent phases. Although this generalization is occasionally criticized for its shortcomings, equation (2.1) is considered today to be a fundamental principle in analysis of porous media flows (e.g., McWhorter and Sunada, 1977). If, indeed, Darcy’s experimental result is the birth of quantitative hydrology, a need still remains to build quantitative analysis of porous media flow on a strong theoretical foundation. The problem of unsaturated flow of water has been attacked using experimental and theoretical tools since the early part of this century. Sposito (1986) attributes the beginnings of the study of soil water flow as a subdiscipline of physics to the fundamental work of Buckingham (1907), which uses a saturation-dependent hydraulic conductivity and a capillary potential for the hydraulic gradient.

scholarly journals Inertial Effects on Dynamics of Immiscible Viscous Fingering in Homogenous Porous Media

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 79 ◽  
Author(s):  
Rabbani ◽  
Abderrahmane ◽  
Sassi
Keyword(s):  
Porous Media ◽  
Darcy’S Law ◽  
Inertial Force ◽  
Reynolds Numbers ◽  
Darcy's Law ◽  
Interfacial Instability ◽  
Porous Media Flow ◽  
Inertial Forces ◽  
High Reynolds Numbers ◽  
High Reynolds

We present a comparative study of the onset and propagation dynamics of the fingering phenomenon in uniform porous media with a radial configuration. With the help of the Finite Element Method (FEM)-based 2D simulations and image processing techniques, we investigate finger morphology, growth rate, interfacial length, finger length and the number of fingers which are affected due to inertial forces and convective acceleration in a two-phase porous media flow. We considered a modified Darcy’s law with inertial force coupled with convective acceleration and investigate their impact on interfacial instability with different velocity-viscosity combinations. Interestingly, the consequences of inertial corrections become significant with changes in viscosity at high Reynolds numbers. Due to the intrinsic bifurcation nature of inertial forces in the radial flow geometry, finger morphology is changed mostly at high viscosity ratios. We find that the effects of inertia and convective acceleration are markedly significant at relatively high Reynolds numbers while the interfacial length and the number of fingers—which are important parameters for Enhanced Oil Recovery (EOR)—are most affected by the neglecting of these forces. Moreover, at high Reynolds numbers, the rate of growth of fingering instabilities and the fractal number tend to deviate from that for Darcy’s law.

Darcy's Law for Saturated Porous Media

2015 ◽  
pp. 32-68
Author(s):  
Tian-Chyi Yeh ◽  
Raziuddin Khaleel ◽  
Kenneth C. Carroll
Keyword(s):  
Porous Media ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Saturated Porous Media

In-Plane Hydraulic Resistance Through Paper-Thin Porous Media

2018 ◽  
Author(s):  
Stefan Doser ◽  
Sang-Joon John Lee
Keyword(s):  
Porous Media ◽  
Filter Paper ◽  
Fluid Transport ◽  
Darcy’S Law ◽  
Average Pore Size ◽  
Pressure Profile ◽  
Darcy's Law ◽  
Porous Media Flow ◽  
Average Pore ◽  
Special Case

This work investigates the special case of in-plane fluid flow of a Newtonian incompressible fluid at low Reynolds numbers across a paper-thin porous medium in a confined conduit. Fluid transport in sheets with these characteristics are used in emerging devices such as microscale paper-based analytical devices (μPADs) and “e-paper” displays. Darcy’s law is applied and tested to determine if experimentally measured pressures at two flow rates of 5 μL/min and 10 μL/min agree with predicted values. A test device was designed using kinematic design principles to ensure a deterministic 318 μm gap that directs prescribed flow, unidirectionally across porous filter paper. The paper used was Grade 50 Whatman filter paper with an average pore size of 2.7 μm. Pressure was measured along the direction of flow over a 125 mm distance by six pressure ports placed at uniform increments of 25 mm to determine a profile of pressure along the flow path. Measurements were recorded at discrete time intervals over a period up to 48 hours with at least four replicates. Experimental measurements of the pressure profile show a linear relationship as predicted by Darcy’s law, allowing material permeability to be calculated. Among replicates measured under the same set of controllable conditions, experimental data also show a nonlinear relationship. The nonlinearity suggests evidence of transition into an inertia region, providing insight into the factors and behavior of the Darcy-Forchheimer transition for this special case of porous media flow.

Modelling of fluid flow in porous media and filtering water process: Langevin dynamics and Darcy’s law based approach

2020 ◽  
Vol 30 ◽  
pp. 870-875
Author(s):  
Yassine Hariti ◽  
Younes Hajji ◽  
Ahmed Hader ◽  
Hamza Faraji ◽  
Yahia Boughaleb ◽  
...  
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Darcy’S Law ◽  
Langevin Dynamics ◽  
Darcy's Law ◽  
Flow In Porous Media

Limitations of Darcy's Law in Glass Bead Porous Media

1973 ◽  
Vol 37 (2) ◽  
pp. NP-NP
Author(s):  
L. Boersma ◽  
F. T. Lindstrom ◽  
S. K. Saxena
Keyword(s):  
Porous Media ◽  
Glass Bead ◽  
Darcy’S Law ◽  
Darcy's Law
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