Calculation apparent conductivity curves

Results of calculation of apparent conductivity curves as a function of parameter Xi/ai = 10 /ai) l0pi/are presented in Figs. 8.1-8.5. These data permit us to evaluate maximal frequencies for which it is still possible to eliminate the influence of the borehole and the intermediate zone. For example, when there is a deep penetration of the filtrate into the formation az/ai 16) and az < (Jz the value of the apparent... 

As is seen from Figs. 5.23-5.31, all curves of the apparent conductivity at the left-hand part, i.e. within the range of small parameters, are parallel to the axis of abscissa that corresponds to Doll s domain but with an increase of CT2/cti the influence of the skin effect manifests earlier. This behavior is in complete agreement with our understanding of the distribution of quadrature component of induced currents in a conducting medium. In fact, with an increase of the distance from the dipole this component becomes smaller than that according to Doll s theory, and since with an increase of conductivity of the surrounding medium the role of this part of the medium also increases, deviation between results of calculation by exact and approximate solutions also increases. Practically this... 

All curves are symmetrical with respect to the bed middle (Figs. 5.39-5.46). With an increase of parameter ri2, for example due to an increase of the frequency, the width of an intermediate zone where apparent conductivity, Oa, differs from that corresponding to a uniform medium with conductivity 02 becomes narrower. At the same time differentiation of curves to some extent decreases, i.e. the ratio of Oa/oi at the bed middle to that within the surrounding medium becomes smaller. For instance if H/L = 4 and oi/o2 = 4, the ratio Oa/oi calculated by Doll s theory is equal to 3.6 while for parameter U2 = 0.32 it is equal to 2.8. In another case when H/L = 4 and oi/o2 = 16, values of this ratio are equal to 11.9 and 9.5, correspondingly. 

Fig. 25. Calculated curve of apparent conductivity prefactor crj versus conductivity activation energy E for extrapolation from the 300°K < T < 400°K range. Experimental data for comparison— , O PH, , ASH3 A, A Sb(CH3)j V, Bi(CH3)3. Qosed symbols, 1% doping open symbols, 0.1% doping. [Experimental data from Carlson and Wronski (1979) figure from Overhof and Beyer (1983).]...

Figure 8 shows the results of these calculations as a plot of test-tank apparent thermal conductivity against compressive load on the insulation. Test-tank jKapparent varied from a value of 90 x 10 Btu/hr-ft- F, at the ground-hold condition, down to about 8 x lO" Btu/hr-ft-°F, at the lowest pressure load on the insulation. Also shown in Fig. 8 is the previously published data for Linde SI-62, which fall below the present test results. Note that on the lower curve is plotted performance of a pure insulation material, while the upper... 

The isothermal conduction calorimetry offers a method to follow the rate of hydration of cement at different temperatures of curing. Calorimetric curves of cement hydrated at 25,30,40, 50,60, and 80°C have been analyzed.It was found that as the temperature increased the C3S hydration peak appeared at earlier times. The shape of the curves also underwent changes. The apparent activation energy of hydration could be calculated. 

Interpretation of Fig. 5.54 requires consideration of polymer flow characteristics. When steady-slate displacement tests are conducted with a polymer solution, as discussed in Sec. 5.4, the polymer mobility is extracted from the experimental data. Permeability to polymer can be calculated if the apparent viscosity of the polymer solution is known at the Darcy velocity of the polymer phase. For the core in Fig. 5.54, the apparent viscosity was determined with Eq. 5.18 to be 2.3 cp at S r from the polymer mobility with kp=kwp. Because the effective polymer viscosity at Spr did not vary significantly with flow rate, the apparent viscosity for relative permeability computations was assumed to be constant throughout the steady-state tests. The relative permeability curve for polymer solution is significantly less than the corresponding relative permeability curve for the displacement of water before contact of the core with polymer solution. 

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