Porosity terms

Note that in this definition, the porosity term is included. If the velocity is used, the preceding equation becomes Eq. 7.82. It is expected that for a group of rocks with different porosities, if the porosities are included, the calculated capillary numbers should be closer to their average. However, the data that is shown in Table 7.7 do not consistently support this expectation. The ratio of the average to the standard deviation decreases for the data from Chatzis and Morrow (1984) if the porosity is included, but it increases for data from Taber et al. (1973). From these two data sets, it seems as though the capillary numbers that do and do not include porosity are equally good. 

However, the porosity terms at the electrocatalyst s surface also has to be considered. According to Figure 17.7, the frontal surface area with open pores is Apores, and then the porosity, p (in analogy to the roughness factor), is defined as... 

Due to the porosity term, the linear rate for the electrolyte flow, v, that is related to

turbulent flow regime ... 

Canceling the porosity terms, dividing numerator and denominator of the right-hand side of Eq. (4) by Q and substituting... 

Equation (5.4-25) differs from the well-known Eigun equation (see Kister 1992) by the exponent 4.65 on the porosity e. The improved porosity term allows the prediction of the pressure loss of a bed of dispersed particles from knowledge of the friction factor of a single particle. Hence, (5.4-25) holds for the whole range of bed porosity. 

T. + 50 C, moduli of the starting leathers were approached. This shifting of moduli appears to result from the free space retained by each composition, as discussed in section A. This adds a porosity term (5e) to the moduli of each material. The fact that each phase was continuous, as seen in section C, and characterized by only weak interaction between phases further contributed to moduli residing between those of the starting materials. This permitted the mechanical response of the polymer-leather composites to shift from predominately plastic to predominately leather character as temperature rose. 

Kriegel et al modified Eq. (1) by inserting the porosity variable as a power function P". Rummler and Palmour demonstrated the validity of the porosity term as an independent variable and found two ranges of porosity dependence. Above 12-15% porosity m was about 4, but at lower porosities m was approximately 1.1. 

At many locales, other factors operate to influence and change the initial porosity in the top 1 m zone of the bed, which is of primary interest with regard to contaminant chemodynamics. These factors include bioturbation, particle resuspen-sion/deposition, and compaction. The initial porosities term used in the previous paragraph generally denotes the sediment layers in the top 1-20 cm of the bed. Bioturbation, when present, is primarily a particle and porewater mixing process caused by macrofauna species living on the bed, within it or both, which continually perturbs the physical and chemical structure of the bed. (See Chapter 13 for specific... 

In his tutorial An Introduction to Porosity , Hook (2003) gives a detailed explanation of porosity terms as they are used in different disciplines of geoscience and petroleum engineering (Table 2.1). 

The pores between the rock components, e.g. the sand grains in a sandstone reservoir, will initially be filled with the pore water. The migrating hydrocarbons will displace the water and thus gradually fill the reservoir. For a reservoir to be effective, the pores need to be in communication to allow migration, and also need to allow flow towards the borehole once a well is drilled into the structure. The pore space is referred to as porosity in oil field terms. Permeability measures the ability of a rock to allow fluid flow through its pore system. A reservoir rock which has some porosity but too low a permeability to allow fluid flow is termed tight . 

In nearly all oil or gas reservoirs there are layers which do not contain, or will not produce reservoir fluids. These layers may have no porosity or limited permeability and are generally defined as non reservoir intervals. The thickness of productive (net) reservoir rock within the total (gross) reservoir thickness is termed the net-to-gross or N/G ratio. 

When providing input for the STOMP calculation a range of values of porosity (and all of the other input parameters) should be provided, based on the measured data and estimates of how the parameters may vary away from the control points. The uncertainty associated with each parameter may be expressed in terms of a probability density function, and these may be combined to create a probability density function for STOMP. 

Tar Sands. Tar sands (qv) are considered to be sedimentary rocks having natural porosity where the pore volume is occupied by viscous, petroleum-like hydrocarbons. The terms oil sands, rock asphalts, asphaltic sandstones, and malthas or malthites have all been appHed to the same resource. The hydrocarbon component of tar sands is properly termed bitumen. 

Plate thickness is an important factor in electroplating, in terms of both performance and economics. Corrosion resistance, porosity, wear, appearance, and several other properties are proportional to plate thickness. Minimum plate thicknesses are, or should be, specified as should the location, or check-point, where the thickness is to be measured. In some appHcations, such as threaded fasteners, maximum thicknesses should be specified. Root diameters of finer machine threads can be adversely affected by as Htde as 10 p.m of plating. 

Values of Pp and dp are droplet density, g/cm, and droplet diameter, cm Ig is the gas viscosity, P. All other terms were defined previously. Table 14-19 gives values of J calculated from experimental data of Jackson and Calvert. Values of J for most manufactured packing appear to fall in the range from 0.16 to 0.19. The low value of 0.03 for coke may be due to the porosity of the coke itself. 

Polymer-based, synthetic ion-exchangers known as resins are available commercially in gel type or truly porous forms. Gel-type resins are not porous in the usual sense of the word, since their structure depends upon swelhng in the solvent in which they are immersed. Removal of the solvent usually results in a collapse of the three-dimensional structure, and no significant surface area or pore diameter can be defined by the ordinaiy techniques available for truly porous materials. In their swollen state, gel-type resins approximate a true molecular-scale solution. Thus, we can identify an internal porosity p only in terms of the equilibrium uptake of water or other liquid. When crosslinked polymers are used as the support matrix, the internal porosity so defined varies in inverse proportion to the degree of crosslinkiug, with swelhng and therefore porosity typically being more... 

Truly porous, synthetic ion exchangers are also available. These materials retain their porosity even after removal of the solvent and have measurable surface areas and pore size. The term macroreticular is commonly used for resins prepared from a phase separation technique, where the polymer matrix is prepared with the addition of a hq-uid that is a good solvent for the monomers, but in which the polymer is insoluble. Matrices prepared in this way usually have the appearance of a conglomerate of gel-type microspheres held together to... 

The skeletal density p, of a particle (or crystalline density for a pure chemical compound) is given in terms of internal porosity p by... 

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. 

Darcy s law is considered valid for creeping flow where the Reynolds number is less than one. The Reynolds number in open conduit flow is the ratio of inertial to viscous forces and is defined in terms of a characteristic length perpendicular to flow for the system. Using four times the hydraulic radius to replace the length perpendicular to flow and conecting the velocity with porosity yields a Reynolds number in the form ... 

Heterogeneity, nonuniformity and anisotropy are terms which are defined in the volume-average sense. They may be defined at the level of Darcy s law in terms of permeability. Permeability, however, is more sensitive to conductance, mixing and capillary pressure than to porosity. 

Superose gel material of Pharmacia Biotech is a highly epichloro-hydrine cross-linked agarose matrix that has a pH range of 3-12 (short term 1-14). Hydrophilic interactions may be noticeable for lipids, peptides, and small aromatic compounds, but such interactions might even improve resolution. Superose medium is available in two different porosities Superose 6 HR 10/ 30 (bead size 13 2 /um maximum pressure 1.5 MPa) and Superose 12 HR 10/30 (bead size 10 2 /um maximum pressure 3.0 MPa). 

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