Porous media flows permeability

Durham et al., 2001] suggest an increased sensitivity of their transport properties to thermal, hydraulic, mechanical, and chemical processes, over porous medium flows. This is apparent even at temperatures as low as 100°C, where the mobile dissolved species is silica, the test duration is of the order of a month [Elias and Hajash, 1992 Lin et al., 1997], and where permeability may be reduced by a factor of 104 [Lin et al., 1997]. 

Rigid random arrays have generally been simulated by cell models that have not been limited to dilute suspensions. An early example of a cell model is that of Brinkman (1947), who eonsidered flow past a single sphere in a porous medium of permeability k. The flow is deseribed by an equation that collapses to Darcy s (1856) law (in its post-Darcy form, which includes viscosity) for low values of and to the creeping flow version of the Navier Stokes equation for high values of K. His solution is... 

The UK and American literature on porous medium flows often calls permeability the quantity we know as hydraulic conductivity. The quantity k/p (units m s/kg) is also found introduced with the name of permeability. We advise the reader being careful with these different definitions. It is quite easy passing from one definition to another, as the definition of permeability is readily identified by examining the units. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

Static leak-off experiments with borate-crosslinked and zirconate-cross-Unked hydroxypropylguar fluids showed practically the same leak-off coefficients [1883]. An investigation of the stress-sensitive properties showed that zirconate filter-cakes have viscoelastic properties, but borate filter-cakes are merely elastic. Noncrosslinked fluids show no filter-cake-type behavior for a large range of core permeabilities, but rather a viscous flow dependent on porous medium characteristics. 

Permeability (k) is the transport coefficient for the flow of fluids through a porous medium and has the units of length squared. NMR measures the porosity and the... 

The airflow equations presented above are based on the assumption that the soil is a spatially homogeneous porous medium with constant intrinsic permeability. However, in most sites, the vadose zone is heterogeneous. For this reason, design calculations are rarely based on previous hydraulic conductivity measurements. One of the objectives of preliminary field testing is to collect data for the reliable estimation of permeability in the contaminated zone. The field tests include measurements of air flow rates at the extraction well, which are combined with the vacuum monitoring data at several distances to obtain a more accurate estimation of air permeability at the particular site. 

These tests show that CC -foam is not equally effective in all porous media, and that the relative reduction of mobility caused by foam is much greater in the higher permeability rock. It seems that in more permeable sections of a heterogeneous rock, C02-foam acts like a more viscous liquid than it does in the less permeable sections. Also, we presume that the reduction of relative mobility is caused by an increased population of lamellae in the porous medium. The exact mechanism of the foam flow cannot be discussed further at this point due to the limitation of the current experimental set-up. Although the quantitative exploration of this effect cannot be considered complete on the basis of these tests alone, they are sufficient to raise two important, practical points. One is the hope that by this mechanism, displacement in heterogeneous rocks can be rendered even more uniform than could be expected by the decrease in mobility ratio alone. The second point is that because the effect is very non-linear, the magnitude of the ratio of relative mobility in different rocks cannot be expected to remain the same at all conditions. Further experiments of this type are therefore especially important in order to define the numerical bounds of the effect. 

The permeability of a porous medium (K) is defined as the proportionality constant that relates the flow rate through the medium to the pressure drop, the cross-sectional area, the fluid viscosity, and net flow length through the medium ... 

This equation defines the permeability (K) and is known as Darcy s law. The most common unit for the permeability is the darcy, which is defined as the flow rate in cm3/s that results when a pressure drop of 1 atm is applied to a porous medium that is 1 cm2 in cross-sectional area and 1 cm long, for a fluid with viscosity of 1 cP. It should be evident that the dimensions of the darcy are L2, and the conversion factors are (approximately) 10 x cm2/darcy C5 10-11 ft2/darcy. The flow properties of tight, crude oil bearing, rock formations are often described in permeability units of millidarcies. 

By making use of these analogies, electrical analog models can be constructed that can be used to determine the pressure and flow distribution in a porous medium from measurements of voltage and current distribution in a conducting medium, for example. The process becomes more complex, however, when the local permeability varies with position within the medium, which is often the case. 

The rate at which a porous medium will allow water to flow through it is referred to as permeability. Henry Darcy was the engineer who performed the first time-rate studies of water flowing through a sand filter. Darcy determined that, for a given material, the rate of flow is directly proportional to the driving forces (head) applied (hence, Darcy s law). 

Bolton EW, Lasaga AC, Rye DM (1996) A model for the kinetic control of quartz dissolution and precipitation in porous media flow with spatially variable permeability Eormulation and examples of thermal convection. J Geophys Res 101 22,157-22,187 Bolton EW, Lasaga AC, Rye DM (1997) Dissolution and precipitation via forced-flux injection in the porous medium with spatially variable permeability Kinetic control in two dimensions. J Geophys Res 102 12,159-12,172... 

In the past, various resin flow models have been proposed [2,15-19], Two main approaches to predicting resin flow behavior in laminates have been suggested in the literature thus far. In the first case, Kardos et al. [2], Loos and Springer [15], Williams et al. [16], and Gutowski [17] assume that a pressure gradient develops in the laminate both in the vertical and horizontal directions. These approaches describe the resin flow in the laminate in terms of Darcy s Law for flow in porous media, which requires knowledge of the fiber network permeability and resin viscosity. Fiber network permeability is a function of fiber diameter, the porosity or void ratio of the porous medium, and the shape factor of the fibers. Viscosity of the resin is essentially a function of the extent of reaction and temperature. The second major approach is that of Lindt et al. [18] who use lubrication theory approximations to calculate the components of squeezing flow created by compaction of the plies. The first approach predicts consolidation of the plies from the top (bleeder surface) down, but the second assumes a plane of symmetry at the horizontal midplane of the laminate. Experimental evidence thus far [19] seems to support the Darcy s Law approach. 

Kq depends not only on the structure of the porous medium (i.e., porosity, tortuosity, and grain size distribution), but also on the viscosity of the liquid that flows through the pores, and finally on the acceleration of gravity, g. In contrast, the permeability, ,... 

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.)... 

Apparent viscosity the viscosity of a fluid, or several fluids flowing simultaneously, measured in a porous medium (rock), and subject to both viscosity and permeability effects also called effective viscosity. 

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... 

Unidirectional flow through a porous medium can often be approximately modeled as flow through a series of parallel plane channels as show n in Fig. P10.1. Using this model derive an expression for the permeability. K, in terms of the channel size. W, and the porosity, . 

Very briefly, the Dave model considers a force balance on a porous medium (the fiber bed). The total force from the autoclave pressure acting on the medium is countered by both the force due to the spring-like behavior of the fiber network and the hydrostatic force due to the liquid resin pressure within the porous fiber bed. Borrowing from consolidation theories developed for the compaction of soils 22 23), the Dave model describes one-dimensional consolidation with three-dimensional Darcy s Law flow. Numerical solutions were in excellent agreement with closed-form solutions for one- and two-dimensional resin flow cases in which the fiber bed permeabilities and compressibility, as well as the autoclave pressure, are all held constant21). 

In dead-end filtration, a cake forms on the surface of the pad as the filtration proceeds. The cake permeability is the most important physical property of a porous medium and the hydraulic properties of the flow and the specific cake resistance are described by Darcy s Law ... 

In the petroleum industry, HC1 is routinely injected into carbonate formations in order to improve oil or gas production. It is known that the porous medium is not etched uniformly by the reactive fluid but that unstable dissolution patterns consisting of highly ramified, empty channels are formed. The channels are commonly called wormholes. As soon as a wormhole pattern develops, all the fluid will flow through it. Any local increase in the flow rate results in an increase in the local dissolution rate. A piece of porous medium in which a wormhole pattern has been created can be considered as composed of two parts the first part (wormholes) of very large permeability, and the second part keeping its original permeability. 

Fig. 10.17. Average capillary pressure as a function of gas fractional flow Us = 0.02 cm min 1 porous medium of 0.05 mm sand tube length L = 60 cm permeability 72 pm2 (darcy) porosity - 0.31 surfactant - 1% SiponateDS 10.

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