Porous media fluid distribution

Consider a porous medium with magnetic susceptibility difference Ax between the confining solid and the permeating fluid (Figure 3.7.1). Magnetic field gradients will develop in the pore space. The spatial distribution of this internal magnetic... 

Magnetic resonance imaging (MRI) has been applied to the study of the distribution of fluid components (i.e., water or a polymer used as consolidant) in a porous material such as stone or waterlogged wood by a direct visualization of the water or fluid confined in the opaque porous medium [13]. 

Here the relative permeability, kri, is the fraction by which the fluid conductivity of the porous medium has to be modified to account for the presence of the other fluid. For a given fluid, kri increases with concentration, but is always less than or equal to one. Since the porous medium will usually have a wetting preference for one fluid over others, there will be a distribution of fluids among the different sizes of pores. Some of the factors that can influence the relative permeability of a particular fluid include [108,417-419] ... 

Figure 10.1 shows slug flow of a fluid through a rectangular porous medium. Compute the temperature distribution with the... 

In Chapter 3 it was show n that similarity-type solutions could be found for fluid flow over isothermal surfaces whose shape is such that the the velocity distribution outside the boundary is described by u = Axm. Investigate whether this is also true when such bodies are placed in a flow through a porous medium. 

Using the procedure outlined in this chapter for using the boundars laser equations to find the-forced convective heat transfer rate from a circular cylinder buried in a saturated porous medium, investigate the heat transfer rate from cylinders with an elliptical cross-section with their major axes aligned with the forced flow. The surface velocity distribution should be obtained from a suitable book on fluid mechanics. 

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... 

In actual use for mobility control studies, the network might first be filled with oil and surfactant solution to give a porous medium with well-defined distributions of the fluids in the medium. This step can be performed according to well-developed procedures from network and percolation theory for nondispersion flow. The novel feature in the model, however, would be the presence of equations from single-capillary theory to describe the formation of lamellae at nodes where tubes of different radii meet and their subsequent flow, splitting at other pore throats, and destruction by film drainage. The result should be equations that meaningfully describe the droplet size population and flow rates as a function of pressure (both absolute and differential across the medium). 

A porous medium in general will have flow channels of many different sizes consequently, the relative permeability of a given fluid will depend not only on what fraction of the available pore space it occupies but also on what types of flow channels it occupies. If the fluid occupies smaller channels, its relative permeability will be smaller. Therefore, the distribution of the fluids is an important factor in determining relative permeability. 

At a given fluid saturation in a given porous medium, the wetting preference of the solid for one of the two fluids present determines the fluid distribution within the porous medium, and consequently, it also determines... 

Wettability. Wettability of the porous medium controls the flow, location, and distribution of fluids inside a reservoir (7, 28). It directly affects capillary pressure, relative permeability, secondary and tertiary recovery performances, irreducible water saturations, residual oil saturations, and other properties. 

Pore-radius distributions and ab-/ desorption isotherms are important structural characteristics of generic porous media [80, 88]. The absorption isotherm provides a relation for the liquid uptake of a porous medium under controlled external conditions, viz., the pressure of an external fluid. Within a bounded system, such as a cylindrical tube, a discontinuity of the pressure field across the interface between two fluid phases exists. The corresponding pressure difference is called capillary pressure, Pc. In the case of contact between gas phase, Pg, and liquid water phase, P1, the capillary pressure is given by... 

Chemical reactions that attain equilibrium within the confines of the experimental setup do not affect the degree of mixing as long as they do not change the physical properties of the medium or the fluid rather they change only the velocity at which the tracer moves through the porous medium. However, reactions that are kineticaUy controUed, and do not reach equilibrium in the temporal or spatial confines of the experiment, do affect the concentration distribution and cannot be readily separated from mechanical mixing. 

FIGURE 10.17 Pressure and fluid distribution in a sand column during an alkaline waterflood, (a) oil being displaced from a sand-packed colunm by alkaline water, (b) pressure distribution within the sand-packed column during the alkaline waterflood, (c) distribution of oil within the sand-packed column during the alkaline waterflood, and (d) schematic representation of the disposition of oil and water in the porous medium during the alkaline waterflood. Source Cooke et al., (1974). 

Other than the particle dimension d, the porous medium has a system dimension L, which is generally much larger than d. There are cases where L is of the order d such as thin porous layers coated on the heat transfer surfaces. These systems with Lid = 0(1) are treated by the examination of the fluid flow and heat transfer through a small number of particles, a treatment we call direct simulation of the transport. In these treatments, no assumption is made about the existence of the local thermal equilibrium between the finite volumes of the phases. On the other hand, when Lid 1 and when the variation of temperature (or concentration) across d is negligible compared to that across L for both the solid and fluid phases, then we can assume that within a distance d both phases are in thermal equilibrium (local thermal equilibrium). When the solid matrix structure cannot be fully described by the prescription of solid-phase distribution over a distance d, then a representative elementary volume with a linear dimension larger than d is needed. We also have to extend the requirement of a negligible temperature (or concentration) variation to that over the linear dimension of the representa-... 

The pore size distribution is usually measured based on straight capillaries having a uniform cross-section. Under this condition, the pore neck diameter can be assigned to serve as the diameter of the capillary. If a given pressure pc is applied to a fluid-filled porous medium, the saturation of the medium will be a function of the applied pressure. The relation between the saturation S and the capillary pressure pc can be found for a nonwetting fluid as... 

This equation suggests that the capillary pressure in a porous medium is a function of the chemical composition of the rock and fluids, the pore size distribution, and the saturation of the fluids in the pores. Capillary pressures have also been found to be a function of the saturation history, although this dependence is not reflected in Eq. (1). Because of this, different values will be obtained dining the drainage process (i.e., displacing the wetting phase... 

The single layer glass bead model is a closer representation of a porous medium. This was used by Sharma to study toe foam drive process and Egbogah and Dawe to study toe size distribution of oil droplets. Mattax and Kyte used a network of etched capillaries to study fluid distributions under various wettability conditions. Davis and Jones studied the flow of foam in porous media using etched glass micromodels. A study of toe multiphase flow of oil and water di ersed in toe porous medium was carried out by Bonnet using an etched plastic micromodel. 

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. 

A porous medium with a distribution of pore sizes contains equal volumes of a wetting and a nonwetting fluid. With which fluid will most, if not all, of the small pores be filled Why ... 

In some circumstances a fluid can be totally wetting to a porous medium. In such cases a thin film of wetting fluid covers the solid. If bulk amounts of wetting fluid are present they connect to thin film through transition regions in which the film thickens the wetting fluid is then distributed not only in continuous and disconnected pendular states of bulk material, but also in thin film states. When the surface area of the solid is great, as it can be, for example because of clay minerals in sandstone oil reservoirs, the thin films can contain appreciable inventories of... 

---