Displacement coefficient

Table 1. Atomic coordinates (xlO ) and equivalent isotropic displacement coefficients (pm ) ...

Table H. Atomic Coordinates (XiQ ) and Equivalent Isotropic Displacement Coefficients (A X 10 ) for (RuFs)4...

Supplementary Material Available Tables SI and SlI, listing crystal data and details ofdaia collection and anisotropic displacement coefficients for RuFj (3 pages). Ordering information is given on any current masthead page. 

Table 2 gives the atomic coordinates and equivalent isotropic displacement coefficients (B ) of carbon atoms with their estimated standard deviations for the all-/ra 5-/3-carotene single crystal at 293 K (see Fig. 1 for numbering of carbon atoms). In Table 2, coordinates for only half of the carbon atoms are listed since the all-tra/J5 -/3-carotene molecule has C, symmetry in the crystal. B s ofC(2) and C(3) atoms are larger values than those of other carbon atoms, which indicates the fluctuation of these atoms in the crystal. This observation is consistent with that of Senge et al. (1992). 

The volumetric rate of displacement equal to 0.0111 cm /sec was assumed in accordance with the theory of approximate modeling. Each experiment was concluded after injection of four pore-volumes of water through the porous medium. During the entire time in which water was being displaced from the bed, the expelled liquid was being collected on exit from the bed. This procedure made it possible to determine the following three displacement coefficients in succession the water-less, the current, and the terminal. The results are given in Table 8. 

Fig. 9. Dependence of current displacement coefficient (T ) on volume of water (Qw) forced through the bed at different temperatures.

Table 8 and Fig. 9 show that with the increase in formation temperature, the indicators of displacement process improve. For example, the terminal displacement coefficient of 43.2%, at temperature of 30°C increases to 83.6%, at temperature of 200 C. Maximum increase in the terminal displacement coefficient obviously takes place at temperature increases from 30 to 120°C. In this case, it is directly dependent on temperature and reaches a value of 78% at 120°C. Subsequently, in the temperature interval of 120-1SO°C, this displacement coefficient increases only to about 80%, and in the 1S0-200°C interval, only to 83% (see Fig. 10). We can also look at it in a different way. As Fig. 10 indicates, at normal conditions, with a temperature of 30°C, the displacement coefficient attains the value of 43%. In order to raise it to 78%, that is, 35 percentage points above the initial level of 43%, a temperature jump of 100°C is required. To raise this displacement coefficient from that level (78%) to a new level of 83%, that is, only by an additional 5 percentage points, another temperature jump of 100 C (from 130 to 230°C) would be required. These calculations mean that energy input in the second zone along the curve drawn on Fig. 10 is 6-7 times higher than in the first lliis conclusion is of great importance as regards the application of any thermal treatment to the petroliferous formation. 

Fig. 10. Change in oil displacement coefficient (q) with reservoir temperature.

The experiments of the second kind, that is, without simulation of the initial water saturation, were carried out at temperature of 200°C. Results recorded in Table 8 for experiment No. 7 show that, in this case, the displacement coefficient amounted to 78.3%. This value was 5.3 percentage points lower than results obtained in experiment No. 6, that is, with the simulation of water saturation. The displacement of liquids from the bed is more complete in instances when initial water saturation is simulated. This phenomenon is explained by the character of distribution of oil and water in the bed and by the surface properties of die porous medium. 

Other factors affecting the mechanism of oil extraction from the formation were also studied. Thermal expansion of oil also exerts an influence on the process of oil displacement from a porous medium. The volume of displaced oil essentially depends on the oil s properties and on the thermodynamic conditions of the formation. The changes in the displacement coefficients attributed to thermal expansion of oil were given in Table 8. At temperatures of 125, 150, and 2(X)°C, the percentage share of oil yield due to its volumetric expansion within the reservoir rocks is 5.4. 

Fig. 13. Dependence of the displacement coefficient (t]) on the volume of displacing agent run through the bed model.

An example of coupling in the same direction ( i "T 2) would be a small amount of undissolved PbCl2 in a beaker with water that dissolves when KNO3 is added ( salting-in effect ). The first substance s rise in potential can be used to measure the strength of reciprocal action caused by the second substance. This is the so-called displacement coefficient (9/opposite effect, the displacement of the second substance by the first, which we describe by dpi/dn2)j p is just as great, as we can see by applying the flip rule ... 

For the mathematically inteiested In order to derive Eq. (12.2), we will refer back to the cross relation discussed in Sect. 9.3 known as n n coupling. When one substance tries to displace (or favor) another one, this happens reciprocally and with equal strength. The corresponding displacement coefficients are equal as can easily be shown by applying the flip rule (main equation dW = —pdV + TdS + ji drif + p dn ) ... 

The current seismic design criteria of Cahfornia Transportation Department (Caltrans 2010) suggests an effective initial abutment stiffness of Kj = 50 ft/in/ft to be used in seismic analysis. This fCj could generate a larger backfill soil capacity with 0.2 ft abutment movement. However, an abutment displacement coefficient is assigned to justify the contribution of the abutment stiffness in the analysis. 

For seismic analysis in bridge transverse direction, since the backfill soil is usually slopping away from abutment wingwall and there is a relatively weak connection between the abutment wingwaU and the stem, the displacement coefficient shall not be applied directly in the analysis. Reduced Rf or fully released abutment cases shall be studied. In order to increase the transverse stiffness of the abutment, interior supplemental shear walls may be attached to the abutment or the wingwall thickness may be increased, as shown in Figure 6.4. 

This expression has been adopted with refinements (soil effect, softening or hardening oscDlator characteristics) as the displacement coefficient method (DCM) for PBD (NEHRP 1985 EEMA-356 2000), where q is equal to the coefficient Cy in the target roof estimation equation. 

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