Darcy fluid flow through porous media

Flow of fluid through porous medium" (Darcy s Law, see Eq. 25-5) n i 8 = q (m s 1) h (m) Kq (m s 1) Discharge per area Hydraulic head (pressure change along flowpath x) Hydraulic conductivity of medium... 

Pervasive fluid flow through a porous, permeable medium is described by Darcy s law, written here for three dimensions (cf. Bear, 1972) ... 

Darcy s law (Darcy, 1856) is a phenomenological law that is valid for the viscous flow of a single-phase fluid (e.g. groundwater flow) through porous media in any direction. This basic law of fluid flow is a macroscopic law providing averaged descriptions of the actual microscopic flow behaviour of the fluids over some representative elementary volume of the porous medium. For isothermal and isochemical subsurface conditions, the law can be written as (Hubbert, 1953)... 

Permeability describes how easy a fluid flows through a porous medium. Physically it is defined by Darcy s law... 

Permeability is the rate of flow of fluid through the rock. It is expressed by Darcy s Law. This states that the rate of flow of a homogeneous fluid in a porous medium is proportional to the pressure gradient and inversely proportional to the fluid viscosity. This is generally expressed mathematically thus ... 

Any discussion of flow through porous media inevitably touches upon Darcy s law which is a relationship between the volumetric flowrate of a fluid flowing linearly through a porous medium and the energy loss of the fluid in motion. 

This section presents the governing equations for fluid flow in porous media with precipitation reactions, dissolution of minerals, and laminar premixed combustion, as well as similarity parameters. The model is based on Navier-Stokes equations. For modeling precipitation and dissolution, we used the Boussinesq approximation and Darcy s law, which wiU not be considered in the case of combustion in porous media. Darcy s law, in general, defines the permeability or the ability of a fluid to flow through a porous medium [29]. Another difference from the model of combustion lies in the equations for species, which are based on concentrations. 

Permeability is a measure of the ease of flow of fluid through a porous medium. A review on permeability properties, experimental evaluation and modeling permeability of textile preforms has been excellently detailed by Wong, 2006. Flow in porous media was first studied experimentally by Henri-Philibert Darcy in 1856 [3]. Later, through adoption of Darcy s law, researchers have introduced this permeability as a parameter for porous media where all the detailed microscopic interactions between the fluid and the porous medium were lumped into the permeability value. 

Consider the flow of an incompressible fluid through a two-dimensional porous medium, as illustrated in Fig. 13-2. Assuming that the kinetic energy change is negligible and that the flow is laminar as characterized by Darcy s law, the Bernoulli equation becomes... 

DARCY (D). A unit of permeability of a porous medium. One darcy equals 1 cF (cm/s)(cm/atm) equals 0.986923 square micrometers. (A permeability of 1 daicy will allow the flow of 1 cubic centimeter per second of fluid of 1 centipoise viscosity through an area of 1 square centimeter under a pressure gradient of 1 atmosphere per centimeter.)... 

The ease with which a fluid can flow through a porous medium, permeability, can be determined through the measurement of pressure drop (Ap) across the porous medium under steady flow. The intrinsic permeability (k) is defined by Darcy s law and is given by k=(Q/A)( /L/Ap) where Q is the discharge flow rate, A is the... 

Darcy s law the laminar flow of fluid through a porous medium. 

In the Darcy model of flow through a porous medium, it is assumed that the flow velocities are low and that momentum changes and viscous forces in the fluid are consequently negligible compared to the drag force on the particles, i.e., if flow through a control volume of the type shown in Fig. 10.5 is considered, then ... 

The basic law governing viscous flow of pure fluid through a porous medium with pores much larger than the mean free path is that of Darcy [13]. This law states that the rate of flow is directly proportional to the pressure gradient causing the flow. In terms of mole flow rate Darcy s law can be written as... 

A comprehensive review of the important factors that affect the flow of emulsions in porous media is presented with particular emphasis on petroleum emulsions. The nature, characteristics, and properties of porous media are discussed. Darcy s law for the flow of a single fluid through a homogeneous porous medium is introduced and then extended for multiphase flow. The concepts of relative permeability and wettability and their influence on fluid flow are discussed. The flow of oil-in-water (OfW) and water-in-oil (W/O) emulsions in porous media and the mechanisms involved are presented. The effects of emulsion characteristics, porous medium characteristics, and the flow velocity are examined. Finally, the mathematical models of emulsion flow in porous media are also reviewed. 

A fluid s motion is a function of the properties of the fluid, the medium through which it is flowing, and the external forces imposed on it. For onedimensional steady laminar flow of a single fluid through a homogeneous porous medium, the relationship between the flow rate and the applied external forces is provided by Darcy s law ... 

Permeability A measure of the ease with which a fluid can flow (fluid conductivity) through a porous medium. Permeability is defined by Darcy s law. For linear, horizontal, isothermal flow, permeability is the constant of proportionality between flow rate times viscosity and the product of cross-sectional area of the medium and pressure gradient along the medium. 

Permeability is a parameter defined to measure the physical influence of a porous structure on fluid flow, and for a CVI process it is an important physical parameter for fibre preforms. Another important parameter for porous structure is the porosity, which is the most important geometrical property. According to Darcy s law, the volumetric flow rate Q of a fluid through a porous medium is proportional to the hydrostatic pressure difference (AP) across the structure (see Figure 2.16), the permeability and the cross-section area, and is also inversely proportional to the length of the structure and the viscosity of the fluid, as given by [26]... 

On the other hand, when a macroscopic pressure gradient VP is applied to the porous medium, the fluid percolates through it with a Darcy velocity U. Additionally, the electrolyte flowing in the interstices affects the equilibrium ion distribution within the Debye layer, so that these ions are also set into motion. This results in a macroscopic electric current density I flowing through the porous medium in the absence of any external electric field. 

The flow of resin through a fibrous reinforcement is usually considered to follow Darcy s law for flow through a porous medium. Assuming low Reynolds number flow, a Newtonian fluid, and that the impregnated section of the reinforcement is fully saturated, Darcy s law can be written... 

Flow through a porous medium is described by Darcy s law, which, in its basic form, is only valid for a single flnid flow and was extended to a second fluid by Wyckoff Botset (1936). This yields equation 10 for the flow velocity of the fluid and gas phase, respectively. 

Note 5.4 (On the permeability andflow in a porous medium). The seepage equation can be obtained by substituting Darcy s law into the mass conservation equations of fluid and solid phases, as described above. The effects of the micro-structure and microscale material property are put into the hydraulic conductivity k, which is fundamentally specified through experiments. It is not possible to specify the true velocity field by this theory, whereas by applying a homogenization technique, we can determine the velocity field that will be affected by the microscale characteristics. In Chap. 8 we will outline the homogenization theory, which is applied to the problem of water flow in a porous medium, where the microscale flow field is specified. 

The Navier-Stokes (NS) equations can be used to describe problems of fluid flow. Since these equations are scale-independent, flow in the microscale structure of a porous medium can also be described by a NS field. If the velocity on a solid surface is assumed to be null, the velocity field of a porous medium problem with a small pore size rapidly decreases (see Sect. 5.3.2). We describe this flow field by omitting the convective term v Vv, which gives rise to the classical Stokes equation We recall that Darcy s theory is usually applied to describe seepage in a porous medium, where the scale of the solid skeleton does not enter the formulation as an explicit parameter. The scale effect of a solid phase is implicitly included in the permeability coefficient, which is specified through experiments. It should be noted that Kozeny-Carman s formula (5.88) involves a parameter of the solid particle however, it is not applicable to a geometrical structure at the local pore scale. 

The general development of capillary bundle/non-Newtonian flow models usually takes the following pattern the Darcy velocity, u, for single-phase steady-state flow of fluid through a porous medium of length L is given by rearranging Equation 6.1 as follows ... 

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