scholarly journals Determination of the Upper Limit Up To Which the Linear Flow Law (Darcy's Law) Can Be Applied

2021 ◽  
Author(s):  
Sudad H Al-Obaidi ◽  
Chang WJ ◽  
Falah H Khalaf
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Darcy’S Law ◽  
Direct Determination ◽  
Darcy's Law ◽  
Linear Flow ◽  
Linear Character ◽  
Upper Limit ◽  
Flow Law

In the practice of hydrodynamic calculations the linear flow law, commonly called Darcy's law, is now widely used. It is well known that it is violated at large pressure gradients. This means that there is a certain limit value of the pressure gradient Δp* above which a deviation from the linear character of the flow law begins. This value of the pressure gradient is the upper limit of applicability.A method is presented for the direct determination of the upper limit of the validity of the linear flow law (Darcy's law) for any porous media. The method is based on the principles of percolation modelling of fluid flows in porous media. The influence of the structure of the pore space on the value of the boundary gradient is analysed. A qualitative comparison with the experimental data is performed.

scholarly journals Experimental and numerical determination of Darcy's law for yield stress fluids in porous media

2019 ◽  
Vol 4 (6) ◽  
Author(s):  
D. Bauer ◽  
L. Talon ◽  
Y. Peysson ◽  
H. B. Ly ◽  
G. Batôt ◽  
...  
Keyword(s):  
Porous Media ◽  
Yield Stress ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Numerical Determination ◽  
Yield Stress Fluids

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 Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 364 ◽  
Author(s):  
Huimin Wang ◽  
Jianguo Wang ◽  
Xiaolin Wang ◽  
Andrew Chan
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Water Saturation ◽  
Flow Behavior ◽  
Low Permeability ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Linear Flow ◽  
Multi Scale ◽  
Non Linear

Low-permeability porous medium usually has asymmetric distributions of pore sizes and pore-throat tortuosity, thus has a non-linear flow behavior with an initial pressure gradient observed in experiments. A threshold pressure gradient (TPG) has been proposed as a crucial parameter to describe this non-linear flow behavior. However, the determination of this TPG is still unclear. This study provides multi-scale insights on the TPG in low-permeability porous media. First, a semi-empirical formula of TPG was proposed based on a macroscopic relationship with permeability, water saturation, and pore pressure, and verified by three sets of experimental data. Second, a fractal model of capillary tubes was developed to link this TPG formula with structural parameters of porous media (pore-size distribution fractal dimension and tortuosity fractal dimension), residual water saturation, and capillary pressure. The effect of pore structure complexity on the TPG is explicitly derived. It is found that the effects of water saturation and pore pressure on the TPG follow an exponential function and the TPG is a linear function of yield stress. These effects are also spatially asymmetric. Complex pore structures significantly affect the TPG only in the range of low porosity, but water saturation and yield stress have effects on a wider range of porosity. These results are meaningful to the understanding of non-linear flow mechanism in low-permeability reservoirs.

An Approximate Method for Non -Darcy Radial Gas Flow

1964 ◽  
Vol 4 (02) ◽  
pp. 96-114 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Linear Equation ◽  
Flow Rate ◽  
Analytical Solutions ◽  
Gas Flow ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Non Linear Equation ◽  
Approximate Analytical Solutions ◽  
Non Linear ◽  
Flow Law

Abstract Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is shown to be very good. Some observations on the interpretation of gas well tests are made. Introduction The flow of gases in porous media is a problem that has been the subject of much study in recent years, and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law (1) leads to a non-linear equation of the form (2) in a homogeneous medium, assuming an equation of state(3) It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form (4) This form of equation was first suggested by Forchheimer and, later, Katz and Cornell, and Irmay, developed a similar equation. Houpeurt derived this form of equation using the concept of an idealized pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type, for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al., and Aronofsky and Jenkins, but the latter solutions, apart from the simple linearization of equation [2] to yield a diffusion equation in p2, are not so well-known. SPEJ P. 96ˆ

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).

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
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