Mechanical dispersion porous media

Films of wetting fluid that extend across pores and may cause dispersion formation are called lamellae. (See Figures 2 and 3.) Several mechanisms have been identified that collectively determine the number of lamallae and the distribution of droplet sizes of a dispersion in a porous medium. For noncondensible fluids they... 

Effects of Capillary Number, Capillary Pressure, and the Porous Medium. Since the mechanisms of leave-behind, snap-off, lamella division and coalescence have been observed in several types of porous media, it may be supposed that they all play roles in the various combinations of oil-bearing rocks and types of dispersion-based mobility control (35,37,39-41). However, the relative importance of these mechanisms depends on the porous medium and other physico-chemical conditions. Hence, it is important to understand quantitatively how the various mechanisms depend on capillary number, capillary pressure, interfacial properties, and other parameters. 

The three dispersion types described by Wellington et al. are important mechanistically, in view of the apparent importance of capillary snap-off. Extant descriptions of the snap-off mechanism explicitly treat the first type of dispersion, and they should be able to accommodate the second dispersion type by addition of a second fluid that does not wet the porous medium. However, if the aqueous phase of the first two dispersion types wets the porous... 

The processes of advection, diffusion, and mechanical dispersion transport chemical species in fluids. For a porous medium, the flux, F,-, of species i in the x, y, and z coordinate directions (mol m(rock) s ) can be written as... 

To develop an understanding of the emulsion flow in porous media, it is useful to consider differences and similarities between the flow of an OAV emulsion and simultaneous flow of oil and water in a porous medium. As discussed in the preceding section, in simultaneous flow of oil and water, both fluid phases are likely to occupy continuous, and to a large extent, separate networks of flow channels. Assuming the porous medium to be water-wet, the oil phase becomes discontinuous only at the residual saturation of oil, where the oil ceases to flow. Even at its residual saturation, the oil may remain continuous on a scale much larger than pores. In the flow of an OAV emulsion, the oil exists as tiny dispersed droplets that are comparable in size to pore sizes. Therefore, the oil and water are much more likely to occupy the same flow channels. Consequently, at the same water saturation the relative permeabilities to water and oil are likely to be quite different in emulsion flow. In normal flow of oil and water, oil droplets or ganglia become trapped in the porous medium by the process of snap-off of oil filament at pore throats (8). In the flow of an OAV emulsion, an oil droplet is likely to become trapped by the mechanism of straining capture at a pore throat smaller than the drop. 

FIGURE 1-7 Fickian transport by dispersion as water flows through a porous medium such as a soil. Seemingly random variations in the velocity of different parcels of water are caused by the tortuous and variable routes water must follow. This situation contrasts with that of Fig. 1-6, in which turbulence is responsible for the random variability of fluid paths. In this case as well as in the previous one, Fickian mass transport is driven by the concentration gradient and can be described by Fick s first law. The mass transport effect arising from dispersion can be further visualized in Fig. 3-17. There, a mass initially present in a narrow slice in a column of porous media is transported by mechanical dispersion in such a way as to form a wider but less concentrated slice. At the same time, the center of mass also is transported longitudinally in the direction of water flow. 

This section discusses diffusion coefficients in a bulk phase and a porous medium. It also briefly introduces a statistical representation of diffusion. Diffusion is less significant in reservoir flow than dispersion and their mechanisms are different, but the discussion of diffusion provides an analog to the formulation of dispersion. 

Diffusion, convection, and dispersion all contribute to the spread of a front. Let us see how much each mechanism contributes to the spread. First, let us see when the diffusion transport is important as compared to the convective transport. We use v2Dot to calculate the spreading distance from a point source 68% of the injected source is within this distance. Table 2.2 shows the results for different time periods compared with the traveled distances during the same time periods by a convective flow of 1 m/day. A typical flow rate in petroleum reservoirs is 1 m/day (interstitial velocity). A typical value of diffusion coefficient of 4 X 10 mVs in a porous medium is used. In the first 5 seconds, the diffusive transport is more important than the convective transport. Soon after, the convective flow becomes the dominant mechanism. 

Redncr et al. (1987) evaluated pure mechanical dispersion (no diffusion) in a self-similar hierarchical model of a porous medium. They expected their model... 

Soil structure, antecedent soil moisture and input flow rate control rapid flow along preferential pathways in well-structured soils. The amount of preferential flow may be significant for high input rates, mainly in the intermediate to high ranges of moisture. We use a three-dimensional lattice-gas model to simulate infiltration in a cracked porous medium as a function of rainfall intensity. We compute flow velocities and water contents during infiltration. The dispersion mechanisms of the rapid front in the crack are analyzed as a function of rainfall intensity. The numerical lattice-gas solutions for flow are compared with the analytical solution of the kinematic wave approach. The process is better described by the kinematic wave approach for high input flow intensities, but fails to adequately predict the front attenuation showed by the lattice-gas solution. 

Besides electrokinetic transport, chemical reactions also occur at the electrode surfaces (i.e., water electrolysis reactions with production of at the anode and OH at the cathode). Common mass-transport mechanisms like diffusion or convection and physical and chemical interactions of the species with the medium also occur. In a low-permeable porous medium under an electrical field, the major transport mechanism through the soil matrix during treatment for nonionic chemical species consists mainly of electro-osmosis, electrophoresis, molecular diffusion, hydrodynamic dispersion (molecular diffusion and dispersion varying with the heterogeneity of soils and fluid velocity [8]), sorption/ desorption, and chemical or biochemical reactions. Since related experiments are conducted in a relatively short period of time, the chemical and biochemical reactions that occur in the soil water are neglected [9]. 

As water flows over the soil surface, solute mass is transferred via mechanical dispersion from pore spaces into overland flow (64, 69). Shear stresses generated by overland flow accelerate removal of solutes from porous media into surface runoff (64, 72). The dispersion coefficient, D, resulting from overland shear flow increases in proportion to soil permeability, k, and the square of shear velocity, w D oc ku (64, 72). Flow regime is an important determinant of the mechanism responsible for interfacial frictional resistance between the porous medium and overland flow. 

Consider two fluids of equal viscosity and equal density. One of the fluids is displacing the other one from a porous medium. Initially, also assume that the flow is onedimensional. The mean position of the front of the second fluid will evolve according to the mean advective velocity. However, as the displacement progresses, both fluids will mix due to diffusion and mechanical dispersion. 

Harleman, D.R.R and R.R. Rumer. 1963. Longitudinal and lateral dispersion in an isotropic porous medium. Journal of Fluid Mechanics 16 385-394. 

Saffman, P.G. 1959. A theory of dispersion in a porous medium. Journal of Fluid Mechanics 6 312-349. 

In this example, a simple mechanism for breaking a colloid was chosen. The eggshells are made of porous calcium carbonate, their surface covered with innumerable tiny pores. The particles of fat in the broth accumulate in these small pores. Removing the eggshells from the broth (each with oil particles adsorbed on their surfaces) removes the dispersed medium from the broth. One of the two components of the colloid is removed, preventing the colloid from persisting. 

Dispersions of gas in solids are also called foams but the foam cells (bubbles) formed are isolated from one another. An example of such foams are the natural porous materials, cellular concrete, cellular glass and polymer foams. However, if in such disperse systems both phases are continuous (such as in many foamed polymers), they are called sponges. Many porous materials are partially sponge and partially solid foam. The properties of solid foams differ drastically from those of foams with liquid dispersion medium. At the same time the strength and other physical and mechanical characteristics of solid foams depend significantly... 

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