Conductivity apparent

In 1981 we reported (2, 3) the first examples of free radical polymerizations under phase transfer conditions. Utilizing potassium persulfate and a phase transfer catalyst (e.g. a crown ether or quaternary ammonium salt), we found the solution polymerization of acrylic monomers to be much more facile than when common organic-soluble initiators were used. Somewhat earlier, Voronkov and coworkers had reported (4) that the 1 2 potassium persulfate/18-crown-6 complex could be used to polymerize styrene and methyl methacrylate in methanol. These relatively inefficient polymerizations were apparently conducted under homogeneous conditions, although exact details were somewhat unclear. We subsequently described (5) the... 

Boerhaave apparently conducted a great deal of chemical experimentation with much patience and care. Yet he seems out of the main stream of the thinking of chemical practitioners. He tacitly admitted this in the Author s Preface, where he states that he little imagined that he should do anything in chemistry ... 

The quantity (ka/pfCPf) is termed the apparent thermal diffusivity and will here be given the symbol aa. It is not the thermal diffusivity of the fluid since it is the ratio of the apparent conductivity of the porous medium to the product of the density and specific heat at constant pressure of the fluid. 

The apparent conductivity that occurs in the energy equation is a result of conduction in the solid material and in the fluid. If a simple parallel path model is assumed, ka will be given by ... 

The basic requirement for the development of a more generally applicable solvent concept is the need to try to separate the various factors responsible for the solvating power of a solvent. It is important to find criteria for the solvents character that can be correlated not only to salt solubility and apparent conductivity but also to the impact of the solvents on the thermodynamics and kinetics of the electrochemical reactions. There are several approaches to defining a typical solvent property that can represent its polarity and be correlated to the thermodynamics and kinetics of reactions conducted in its solutions (i.e., a linear free-energy relationship). A comprehensive review of such approaches by Reichardt [12] divides them into three categories ... 

The breaching in of water from a second aquifer has to be detected so it can be included in the pumping test interpretation. Otherwise, the conclusions based on the test will be erroneous apparent conductivities that are too large may be deduced, and exaggerated operation pumping rates may be suggested. 

EM instruments may be calibrated to read the true subsurface conductivity within a uniform earth. However, subsurface conditions are rarely uniform. In a layered earth where each layer has a different conductivity, the reading will be dependent upon the thickness of the layers, depth of the layers from the surface, and specific conductivities of each layer. The resulting conductivity measurement is a complex function of all these conditions and is called the apparent conductivity. A strict solution for this function requires some knowledge of the layer thicknesses, depths and relative conductivities. However, not all studies need become this involved because first order evaluations may be made by noting the relative lateral changes along a traverse (profiling). 

Note that the coefficient a / in the previous formula can now be treated as just a scaling factor, which can be found by minimizing the misfit between the observed and predicted data. Thus, on the basis of expression (11.44), we can introduce the so-called migration apparent conductivity, Aama [x, z),... 

Formula (11.45) plays an important role in fast inverse imaging. We can see from (11.45) that the migration apparent conductivity Aarnaix, z) is proportional (with some constant coefficient ko and weights w ) to the frequency stacked values of the product of the background (incident) field Ey (the field that corresponds to the background distribution of conductivity (Tj x, z)) and the migrated residual field E om, o,u>) — Ey x, o,u)]. We will show in the next sections of this... 

FIGURE 9 Real and apparent conductivities of TMTSF-TCNQ. Solid line d.c. 

The dielectric properties of soil determine the amount of RF power that can be dissipated in the soil. These properties are the relative dielectric constant (e ) and the loss-tangent. The loss-tangent, tan 6, is defined as o/oieQe where a is the apparent conductivity, w is the frequency of the applied electric field, radians/sec, and is the permittivity of free space which equals 8.85 X 10 Farads/meter. All the dielectric properties are a function of soil temperature, the frequency of the applied field, and the composition of the soil. 

In accord with eq. 3.109 the apparent conductivity a of the internal area, related with an actual conductivity distribution as ... 

Making use of the relation between the apparent conductivity and the field, introduced by Doll, we have ... 

First of all we will introduce the concept of the apparent conductivity which, as well as apparent resistivity, is widely used in all electrical methods. 

Making use of eq. 4.59 we have the following expression for the apparent conductivity ... 

Thus, measurements with a system of induction probes of different lengths allow us in principle to define parameters of a geoelectric section in the radial direction, that is to perform the lateral soundings. Correspondingly, the curve of the apparent conductivity for probes with various lengths presents the result of such soundings. 

First of all let us consider a two-layered model (the invasion zone is absent). The family of two-layered curves of apparent conductivity is shown in Fig. 4.3. Along the x-and y-axes Oa/(Ti and L/ui are plotted, respectively. The curve index is the ratio a-ijax. 

Curves with index 02/01 > 1 relatively quickly approach to the asymptote on the right and practically for L/ai 5 the value of the apparent conductivity is almost equal to the conductivity of the formation, 02- With a decrease of the curve index, that is with an increase of the resistivity of the formation or conductivity of the borehole, the approach to the asymptote to the right takes place for greater values L/a. In accord with eqs. 4.60 and 4.69 we have the following presentation for apparent conductivity Oa which is valid for relatively large values of a = L/oi ... 

Now let us consider the second and third cases when there is an invasion zone between the borehole and the formation. Corresponding apparent conductivity curves are presented in Figs. 4.4-4.11. As is seen from the curves in the second case (pi < p2 < ps) three-layered curves are similar to two-layered ones, but differ from them by a slower rate of change with an increase of a = L/ai. If the penetration of the borehole solution into the formation is relatively large the right-hand branch of a three-layered curve tends to that of a two-layered one with index Ozla2, but the left-hand branch almost coincides with the two-layered curve with index 02 o. ... 

As it concerns the intermediate part of the curve, it is more lifted than a two-layered curve with the same index. Since ctj > CT2 > CTs, the presence of the invasion zone usually causes a significant increase of the apparent conductivity with respect to a two-layered model and therefore it requires the application of longer probes for the determination of the conductivity of a formation, 0%. 

In the third case (<7i > 02 < (73) for a relatively small probe length the apparent conductivity curves have a more gentle slope than that of two-layered curves, provided the conductivity of the bed is significantly greater than the conductivity of the invasion zone. 

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