Initial permeability

An important property of soft magnetic materials is the initial permeability. Its dependence on microstructure can be understood in terms of the Globus model. A calculation of the (relative) initial permeability (Globus, Duplex Guyot, 1971) leads to the following expression  

The thermal behaviour of the initial permeability is important for many applications. In a representative spinel solid solution series, Ni-Zn ferrites, the relative permeability can be varied from 20 for NiFe204, to 8000 for Zno.7Nio.3Fe204, Fig. 4.47. As stated by Eq. (4.59), the initial permeability varies as Since anisotropy decreases faster than 

Measurement of the initial permeability as a function of temperature can therefore be used as a material characterisation method. The value of Tq depends only on the composition the verticality of the permeability drop at the Curie point indicates the degree of homogeneity in the sample composition (Cedillo et at., 1980 Valenzuela, 1980). 

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The formation brine used to establish the core s initial permeability contained 2.7% total dissolved solids, TDS, with a monovalent-divalent (calcium) ratio of 30. Once a core is equilibrated with this brine, any increase in the ratio or drastic decrease in TDS has the potential for decreasing permeability. Obviously fresh water represents a significant decrease in TDS and, hence, the 54% permeability damage. Adding KC1 helps overcome the decreased salinity but, in so doing, increases the ionic ratio resulting in still measureable but usually reduced permeability damage. 

The thus obtained high-density Mn-Zn ferrite was investigated in detail from the view of physical and mechanical properties, that is, the relationships between the composition of metals (a,) ) and <5 the magnetic properties such as temperature and frequency dependence of initial permeability, magnetic hysteresis loss and disaccommodation and the mechanical properties such as modulus of elasticity, hardness, strength, and workability. Figures 3.13(a) and (b) show the optical micrographs of the samples prepared by the processes depicted in Fig. 3.12(a) and (b), respectively. The density of the sample shown in Fig. 3.13(a) reached up to 99.8 per cent of the theoretical value, whereas the sample shown in Fig. 3.13(b) which was prepared without a densification process, has many voids. 

A quantitative study of the process indicates that, as the field intensity H increases, the magnetic induction B also increases in a manner characteristic of the substance, This is conveniently represented by a graph, which is called the magnetization curve. See Fig. 1. Its initial slope is the initial permeability (/Xo). If H is carried to some maximum value H , and then reduced (to - //,), R follows the dotted hysteresis curve. B does not fall off as it was built up (solid line) the residual induction B, is... 

Recovery of only 20 % was observed in the separation of influenca virus components on a RP column (250x4.6 mm dG = 30 nm) with a water/acetonitrile gradient. The virus consists of three protein components with molar mass alues ranging from 28 to 55 kg/mol. After several runs, the column back pressure increased from 60 to 90 bars. Overnight treatment with 0.1 % sodium dodecylsulfate and 0.05 % TFA helped to regain approximately the initial permeability 67 ... 

The experiments were carried out in the set-up shown in Fig. 1. The cores that were used for the experiments were cylindrically shaped Berea sandstone samples. The length of the cores was 20 cm and the diameter 7.62 cm. The porosity was about 0.25. The initial permeability was 100-300 mD for all samples. During an experiment a core was placed in a rubber sleeve to keep it fixed during the experiment. It was then placed in a steel vessel in which downhole reservoir conditions of up to 150 bars and 100°C were simulated. An acoustic horn was placed at one end of the core (see Fig. 1). The high pressure in the vessel made it possible to avoid cavitation. For pressures lower than 100 bars the influence of cavitation becomes noticeable. The space between the vessel and sleeve, which was filled with water, was pressurized to 180 bars to make the rubber sleeve completely seal off. 

Figure 1. Saturation magnetization and initial permeability of various soft magnetic materials. The open squares and circles denote FINEMET [1, 6] and NANOPERM [8, 25], respectively.

A systematic study by Herzer [44] on the effect of Si content on the field induced Ku in the nanocrystalline Fe-Si-B-Nb-Cu alloys indicated that Ku is mainly induced in the crystallites. By appropriate choice of alloy composition and annealing conditions, transverse field annealing of nanocrystalline Fe-Si-B-Nb-Cu alloys allows to induce anisotropies in the range of Au 5 - 100 J/m3. This corresponds to initial permeabilities of about fii 104 - 2 x 105. They perfectly cover the needs of applications like common mode chokes or earth leakage circuit breakers [45] which require high permeabilities. 

It is worth mentioning here that a compound-free bcc-Fe nanostructure with grain sizes smaller than L0 can be obtained even in a binary Fe Zrg alloy [3, 60] although the initial permeability of nanocrystalline Fe92Zr8 (2 x 103 at 1 kHz) is similar to that of magnetically soft Fe-Si steels. Weak... 

Figure 11. Compositional dependences of initial permeability (pc at 1 kHz) and saturation magnetization (Js) for nanocrystalline (a) Fe-Zr-B [3] and (b) Fe-Zr-B-Cu [34] alloys.

Note that there is a period after installation of new membranes, where the performance of the membranes is not stable. During this period, which can last up to 2 weeks of continuous operation, the permeability and salt passage of the membrane both decline.4 The decline in performance is due somewhat to compaction and is worse for seawater and wastewater applications. Other reasons for the decline are not clear but may include the degree of hydration of the membrane upon start up. Up to 10% of initial permeability and salt passage can decline during this time of destabilized performance.4 The decline in permeate flow is shown in Figure 14.2. 

In the third test, the core was not saturated with oil before waterflooding, and the oil saturation was only 34%, resulting in higher initial permeability. Under this condition, the reduction in effective permeability increased to 43%. In all three tests, oil-in-water emulsions were produced from the core which had droplet size distributions appropriate to cause blockage of pore throats. These three tests illustrate that it is difficult to simulate in a one-dimensional model the conditions which exist in an actual reservoir after a steamflood, but that it is possible to create "emulsion blocks" in situ under appropriate conditions. 

Soo and Radke (11) also studied the effect of average droplet size of emulsion on the flow behavior in porous media. The droplet size distribution of the emulsions that were prepared with surfactants and NaOH in a blender are shown in Figure 12. These droplet size distributions were found to be log-normal distributions. Others (9, 27) have also observed that the size of emulsion droplets was log-normally distributed. Soo and Radke (11) conducted experiments with emulsions having different average mean diameter in fine Ottawa water-wet sand packs. Their results of the reduced permeability, k/ko, and reduced effluent volume concentration as a function of the pore volume of oil (in the emulsion) injected are shown in Figure 13. All emulsions were of 0.5% quality, and the initial permeability, ko, was 1170 mD (millidarcies). The lines in the figure represent results of flow theory (12,13) based on deep-bed filtration principles. 

Permeability reductions were also observed by McAuliffe (9), and his results are shown in Figure 14. He used a Boise sandstone core with an initial permeability of 1600 mD and injected a 0.5% OAV emulsion having average oil-droplet sizes of 1 and 12 xm. The small-diameter emulsion reduced the permeability from 1600 to 900 mD after 10 pore volumes of the injected emulsion the 12-fxm emulsion was much more effective in reducing the core permeability. After 10 pore volumes had been injected, the permeability was reduced to 30 mD, almost a 50-fold reduction. 

Figure 19. Experimental permeability reduction (filled symbols) and breakthrough concentration histories (open symbols) for two initial permeabilities with a 3.3- xm droplet size emulsion. (Reproduced from reference 11. Copyright 1984 American Chemical Society.)...

The model correctly describes the permeability reduction as a function of pore volume injected and takes into account the effect of emulsion droplet saturation and droplet-size to pore-size ratios. The main drawbacks of this theory are that the permeability reduction is caused as long as the emulsion is flowing and that the initial permeability is restored once the emulsion injection is followed by water alone. In other words, the emulsion droplets all pass through the porous medium, and none of them is captured inside. However, experimental evidence 9,11) suggests that the permeability reduction cannot be restored after subsequent water injection (Figure 16). 

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