Media Unconsolidated

The term porosity refers to the fraction of the medium that contains the voids. When a fluid is passed over the medium, the fraction of the medium (i.e., the pores) that contributes to the flow is referred to as the effective porosity of the media. In a general sense, porous media are classified as either unconsolidated and consolidated and/or as ordered and random. Examples of unconsolidated media are sand, glass beads, catalyst pellets, column packing materials, soil, gravel and packing such as charcoal. 

Equation 4-207 is used in carbonates (limestone and dolomite) and Equation 4-208 is used in unconsolidated to medium consolidated sandstones. A third Equation 4-209 can be used in highly consolidated sandstones. This is... 

Figure 13-1 Porous media, (a) Consolidated medium (b) unconsolidated medium.

The medium, with overall dimensions AL, is assumed to be made up of a collection of individual particles and may be either consolidated or unconsolidated. The number of particles in the medium can be expressed as... 

For an unconsolidated porous medium with uniform pore size distribution, the ratio of VJHa approaches its maximum value much more rapidly than that found in a medium where pore size distribution is nonuniform, leading to the significant variation of water saturation in the contaminated zone. 

Washing. As ice moves upward through the column, it behaves as an unconsolidated porous medium and carries brine with it, held by viscous and capillary forces. The flow is entirely laminar, because the Reynolds number based on particle diameter is always less than 0.05. The brine is carried thus at the surface and in the fillets between the particles. The downward flowing wash water moves between the particles and mixes with the brine mainly by molecular diffusion. Salt will diffuse from the brine to the wash water. 

The unconsolidated mineral or organic material on the immediate surface of the earth that serves as a natural medium for the growth of land plants. 

The liquid saturations in foam flow are typically close to irreducible liquid saturation. As a result, the liquid saturation in a foam filled medium is generally not a good measure of the quality of the in situ foam, but rather the fraction of pore segments completely filled with liquid. More permeable media, such as unconsolidated media, generally have smaller residual liquid saturations (32,33) and thus tend to have higher gas saturations when foam is flowing. 

Soil Unconsolidated, dynamic three-phase system comprised of solids, liquids, and gases found at the Earth s surface that serves as a medium for plant growth. 

In Figure 22.39, idealized deposition of cakes in a press is shown. Slurry enters the frame and deposits cakes on plates on either side as illustrated. The cakes, A and B, build out from the plates and meet at the center when the press is full. The cake surfaces meet at the dotted centerline, and a porosity vs. distance curve is developed as shown. Porosity varies from a maximum Sq at the unconsolidated cake surface to its minimum value Sj at the medium. In the washing mode for presses, liquid flows in one plate, passes through both cakes, and exits from the opposing plate. It traverses cake A in reverse flow with respect to the filtrate. The reversal in flow direction brings about a marked change in the frictional stresses and causes the cake to compact. 

Clinchfield Sand. The Lisbon Formation is unconformably overlain by about 27 ft of interfingering unconsolidated quartz sand and quartz sand containing calcareous cement. The medium-grained, well-sorted quartz sand is stratigraphically equivalent to the basal upper Eocene sand deposit that Herrick (19) described as the Clinchfield Sand. 

The typical Clarendon profile consists of a dark grayish-brown, sandy horizon underlain by a yellowish-brown, sandy clay loam horizon, which is underlain by a mottled yellowish-brown, red, and gray, sandy clay loam horizon that contains 5 to 30 percent plinthite. Clarendon soils originate from unconsolidated sediments of medium texture. They are typically found on uplands and have a slope gradient of less than 2 percent. The soils are moderately well drained and have slow runoff. The upper part of the soil profile is more permeable than the lower part. 

A. K. Verma, K. Pruess, C. F. Tsang, and P. A. Withespoon, A Study of Two-Phase Concurrent Flow of Steam and Water in an Unconsolidated Porous Medium, in Heat Transfer in Porous Media and Particulate Flows, ASME HTD, (46) 135-143,1984. 

Porous medium is a material consisting of a solid matrix with interconnected pores. The interconnected pores are responsible for allowing a fluid to traverse through the material. For the simplest situation, the medium is saturated with a single fluid ( single fluid flow ). In multiphase fluid flow, several fluids (liquids and/or gas) share the open pores. Porous media are classified as unconsolidated and consolidated. 

Porosity. The fraction of total (bulk) volume occupied by the voids is defined as the porosity of the porous medium. A porous medium can be classified according to the type of porosity involved. In sandstone and unconsolidated sand, the voids are between sand grains, and this type of porosity is known as intergranular. Carbonate rocks are more complex and may contain more than one type of porosity. The small voids between the crystals of calcite or dolomite constitute intercrystalline porosity (47). Often carbonate rocks are naturally fractured. The void volume formed by fractures constitutes the fracture porosity. Carbonate rocks sometimes contain vugs, and these carbonate rocks constitute the vugular porosity. Still some carbonate formations may contain very large channels and cavities, which constitute the cavernous porosity. 

Porous Medium A solid containing voids or pore spaces. Normally such pores are quite small compared with the size of the solid and well-distributed throughout the solid. In geologic formations, porosity may be associated with unconsolidated (uncemented) materials, such as sand, or a consolidated material, such as sandstone. 

Where K, is the modulus of the solid grain, is porosity, and c is a consolidation parameter that represents the sediments and fluid inside the vugs (unconsolidated material). We use c = 200. The effective compressional modulus (harmonic average of the Ki and /fj drained moduli) and the shear bulk modulus, G, of the double porosity medium can be obtained, respectively, from... 

The last model assumes that porous media can be idealised as parallel capillaries along the direction of flow. Porous media such as adsorbents and catalysts are usually formed by compressing small grains into pellet, and for such particles the model for unconsolidated media will be particularly useful. There are a number of equations available in the literature to describe the Knudsen flow through a unconsolidated medium. They are identical in form and differ only in the numerical proportionality coefficient. 

To describe the transition flux when the Knudsen and viscous flow mechanisms are operating inside a unconsolidated medium, we assume that the flux is additive (Kraus et al., 1953), that is the transition flux is the sum of the viscous flux (eq. 7.5-28a) and the Knudsen flux (eq. 7.4-36) ... 

The reservoir rock consists primarily of unconsolidated fine to medium grained, litharenites with quartz, rock fragments, feldspars and clay minerals. Sands are moderately to well sorted with good intergranular porosity. These immature sands are slightly compacted to uncompacted, and cores tend to explode after retrieval due to the trapped gas. The clay minerals which constitute 5% - 7% of the rock are kaolinite, chlorite and illite. Clays also occur as aggregates. 

The distribution of the oil, gas and water in the porous medium was better understood when Botset and Wyckoff (9) carried out the first experiments on relative permeability. They showed that either oil or gas would flow only if a specific minimum saturation of the phase in question existed in the flow region of the porous material. Some of the early workers also recognized that either the oil or gas droplets could be discontinuous, and in this condition, would be hard to displace by flowing water because of the Jamin effect. In 1927, Uren and Fahmy (10) investigated a number of "factors which affect the recovery of petroleum from unconsolidated sands by waterflooding. Table 1 lists these factors and the general results observed by Uren and Fahmy. With one exception (rate), the results observed by Uren and Fahmy are similar to generalizations which most experts in this field claim today after work of more than 50 years. 

The porous medium consists of unconsolidated Ottawa sand contained in a cylindrical lucite or lexan polycarbonate core holder. 

Isotropic A medium, such as unconsolidated sediments or a rock formation, whose properties are the same in all directions. 

The correlations represented by Eqs. 5.26a through 5.26e can be extended to interpolate for polymer concentrations between 1,000 and 2,000 ppm by use of a correlation based on the modified Blake-Kozeny model for the flow of non-Newtonian fluids. 62 Eq. 5.27 is an expression for A bk derived from the Blake-Kozeny model. Note that all parameters are either properties of the porous medium or rheological measurements. Eq. 5.27 underestimates A/ by about 50%. However, Hejri et al. 6 were able to correlate pBK and A for the unconsolidated sandpack data with Eq. 5.28. Eqs. 5.27 and 5.28, along with Eq. 5.24, predict polymer mobility for polymer concentrations ranging from l.,000 to 2,000 ppm within about 7%. 

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