Total relative mobility

In the preceding equation, the subscript j represents the phase j j = w, o, t for water phase, oil phase, and total relative mobility, respectively. The unit of relative mobihty is the inverse of the viscosity unit, for example, (mPa s) or (cP). An example of water and oil relative permeability curves is shown in Figure 4.1. The corresponding water, oil, and total relative mobihties are shown in Figure 4.2, with the water and oil viscosities being 1 and 10 mPa s, respectively. Figure 4.2 also shows the minimum total relative mobility, the water mobility, oil mobility, and total mobility at a given saturation. The total mobility is the sum of water and oil mobihties. 

Two methods are used to determine the design mobility. In the first method, the design mobility is estimated from relative permeability data for the reservoir rock. To find this minimum, total relative mobilities are calculated for all saturations and plotted vs. 

The total relative mobility is equal to the total mobility of the oil/water bank divided by the base permeability, which is usually the absolute liquid permeability or the permeability to oil at connate water saturation. Total relative mobility varies with saturation because relative permeabilities vary with saturations, as depicted in Fig. 5.84. 

Because oil- and water-bank saturations are not known a priori, there is uncertainty as to what saturation should be used to evaluate the total relative mobility. Gogarty et al. proposed that the... 

Estimation of from relative permeability data must consider the history or path followed in building the oil/water bank. For example, consider the creation of an oil bank in a strongly water-wet porous rock. When the chemical slug is injected, the oil saturation increases and fluid flow at the front of the oil bank is on the drainage path. Total relative mobilities should be computed from drainage relative permeability data. At the rear of the oil bank, the water... 

The second method used to determine the design mobility is to measure the mobility of the oU/water bank produced by the chemical flood in native-state cores. 131.132 xhe displacement process must produce a stable oil/water bank in a region where the interfacial tension (IFT) is not altered. Fig. 5.90132 presents the results of an oil displacement test in a 4-ft core in which an aqueous surfactant system was injected. A stabilized oil bank formed in the interval where the IFT was not affected by the surfactant. This region is shaded in Fig. 5.90. Total relative mobility was calculated from pressure data for the stabilized oil/water bank with... 

Fig. 5.89—Total relative mobilities for samples of the same reservoir.

TABLE 5.49- -COMPUTATION OF TOTAL RELATIVE MOBILITY, EXAMPLE 5.17 ... 

The minimum total relative mobility is 0.0423 cp, which is equivalent to an apparent viscosity of 23.6 ep. Thus, the chemical slug must exhibit an apparent viscosity of 23.6 cp to obtain mobility control between the slug and the oU/water bank. 

If the displacing fluid were pure solvent, then the total relative mobility of the displacing fluid would be... 

The oil-bank total relative mobility would be the same. Thus,... 

This rule of thumb does not apply to all polymers. For certain polymers, such as poly (propylene), the relationship is complicated because the value of Tg itself is raised when some of the crystalline phase is present. This is because the morphology of poly(propylene) is such that the amorphous regions are relatively small and frequently interrupted by crystallites. In such a structure there are significant constraints on the freedom of rotation in an individual molecule which becomes effectively tied down in places by the crystalhtes. The reduction in total chain mobility as crystallisation develops has the effect of raising the of the amorphous regions. By contrast, in polymers that do not show this shift in T, the degree of freedom in the amorphous sections remains unaffected by the presence of crystallites, because they are more widely spaced. In these polymers the crystallites behave more like inert fillers in an otherwise unaffected matrix. 

Accordingly, the total petroleum hydrocarbons at a gasoline spill site will be comprised of mostly Cs to Cu compounds, while total petroleum hydrocarbons at an older site where the fuel has weathered will likely measure mostly Cg to Cn compounds. Because of this inherent variability in the method and the analyte, it is currently not possible to directly relate potential enviromnental or health risks with concentrations of total petroleum hydrocarbons. The relative mobility or toxicity of contaminants represented by total petroleum hydrocarbons analyses at one site may be completely different from that of another site (e.g., Ce to Cn compared to Cio to C25). There is no easy way to determine if total petroleum hydrocarbons from the former site will represent the same level of risk as an equal measure of the total petroleum hydrocarbons from the latter. For these reasons it is clear that the total petroleum hydrocarbons value offers limited benefits as an indicator measure for cleanup criteria. Its current widespread use as a soil cleanup criterion is a function of a lack of understanding of its proper application and... 

Prepare a table of relative mobilities of all bands in the gel. Compare the profile for isolated a-lactalbumin to that of standard a-lactalbumin. Is a-lactalbumin the predominant protein in your preparation from milk In whey Try to estimate the percentage of the isolated sample that is a-lactalbumin. Assume that all proteins on the gel stain to the same extent with the dye, even though this is probably not true. Approximately what percent of total whey proteins is a-lactalbumin Use the molecular weight standards to estimate the molecular weight of a-lactalbumin and other proteins. 

Iodide in vitamin tablets can be found by amperometric detection [88]. Nonaqueous eluents of methanol-containing ammonium perchlorate, which are relatively oxidant resistant, have been used in conjunction with a silica column to detect a wide range of drugs [89]. The use of higher potentials not possible in totally aqueous mobile phases allows for the detection of secondary and tertiary aliphatic amines 462 drugs have been detected in this manner. For compounds that are not electroactive, a procedure using a postcolumn photolysis can generate electroactive species [90] for penicillins [91], proteins [92], and barbiturates [93]. 

The functional forms and relative importance of mechanisms which change the density of bubbles in flowing and stationary foam still are not well known. In particular, the functional form of d, h, i=f,t, and that of y and 6 in Equations (5) and (6) needs to be investigated more thoroughly. Also, a model linking the flowing fraction of foam, X, to the gas flux and predicting the conditions of total bubble mobilization should be developed. 

Fig. 10.5. Electrophoretic mobility-chain length calibration (4% acylamide gel) for double-stranded DNA, derived from fragments shown in Fig. 10.4. The relative mobility refers to one of the fragments (if in-G) as the standard. Note that here the chain lengths are not expressed in absolute terms, but rather as a percentage of the total viral genome (Dat na et aL 1973).

Unlike Voorhoeves model, in our concept XRD undetectable Cu-Si surface species with a very low total copper content steadily react with methyl chloride and can be steadily restored by copper dififtision from a copper source like q-CusSi onto the silicon surface. The plausibility of this idea was demonstrated in Fig. 1. Both Voorhoeve s and our model predict a break-down of the reaction, as soon as the silicon grain surface is essentially covered by high amounts of copper-rich species. As a matter of fact, the models only differ in the assumption about the relative mobility of the atoms involved. The high mobility of copper atoms in the Cu/Si system [19, 20], which has been shown only after Voorhoeves work, seems to favor our proposal. 

World sulfur reserves. The earth s crust contains about 0.6% S, where it occurs as elemental S (brimstone) in deposits associated with gypsum and calcite combined S in metal sulfide ores and mineral sulfates as a contaminant in natural gas and crude oils as pyritic and organic compounds in coal and as organic compounds in tar sands (Tisdale and Nelson, 1966). The elemental form commonly occurs near active or extinct volcanoes, or in association with hot mineral spings. Estimates by Holser and Kaplan (1966) of the terrestrial reservoirs of S suggest that about 50% of crustal S is present in relatively mobile reservoirs such as sea water, evaporites, and sediments. The chief deposits of S in the form of brimstone and pyrites are in Western European countries, particularly in France, Spain, Poland, Japan, Russia, U.S.A., Canada, and Mexico. World production of S in the form of brimstone and pyrites was approximately 41 Tg in 1973 other sources accounted for about 8 Tg, making a total of 49 Tg (Anon, 1973). Byproduct S from sour-gas, fossil fuel combustion, and other sources now accounts for over 50% of S used by western countries, as shown in Fig. 9.1. This percentage may increase as pollution abatement measures increase the removal of SO2 from fossil fuel, particularly in the U.S.A. Atmospheric S, returned to the earth in rainwater, is also a very important source of S for plants. 

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