Envelope diagrams

Boundary surfaces and atomic orbital envelope diagrams... 

Figure 1.1 The envelope diagrams of the 1 s, 2p ad 3d atomic orbitals of the H atom...

Figure 3.5 Orbital envelope diagrams showing the formation of the bonding and anti-bonding molecular orbitals when two 1s atomic orbitals overlap...

Figure 2.1 Typical pressure-enthalpy phase envelope diagram.

The specified variables are the final temperature and pressure, T2 and P2- The dependent variables are the vapor fraction, t /, the liquid and vapor compositions, X, and the total enthalpy of the two phases, /Z2 + H, and the heat duty, Q. The term isothermal should not be interpreted to imply that the transition from initial conditions to final conditions is at constant temperature is, in general, different from T. It simply means that within the flash drum the temperature, as well as the pressure, is fixed. The heat duty required to bring about the final conditions is equal to the enthalpy change, Q = (Hj + 2) - i> where is the enthalpy at and P,. Isothermal flash conditions may be represented by a point ( 2, P2) on tbs phase envelope diagram. It is clearly possible that this point may fall either within the phase envelope or outside it, in which case the system would be all vapor or all liquid (or dense phase). A flash drum operating at such conditions would have a single product and no phase separation would take place. In a single-phase situation, the dependent variables are the properties of the vapor or liquid product. The liquid or vapor composition is, of course, identical to the feed or overall composition, Z,. Note that any set of temperature and pressure specifications is feasible. 

Figure 1. An envelope diagram illustrating the distribution of total concentration of organic acid anions with temperature from recently published data.

Two methods aie used to represent the positive and negative values of the wave functions in atomic orbital envelope diagrams. Both are shown in Figure 2.7 for the 2p orbital. 

Figure 5.21 helps to explain how the phase diagrams of the main types of reservoir fluid are used to predict fluid behaviour during production and how this influences field development planning. It should be noted that there are no values on the axes, since in fact the scales will vary for each fluid type. Figure 5.21 shows the relative positions of the phase envelopes for each fluid type. 

The four vertical lines on the diagram show the isothermal depletion loci for the main types of hydrocarbon gas (incorporating dry gas and wet gas), gas condensate, volatile oil and black oil. The starting point, or initial conditions of temperature and pressure, relative to the two-phase envelope are different for each fluid type. 

The electron-spm echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadnipole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or J is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in tenns of the four-level spin energy diagram for the S = I = model system... 

Phase Diagrams. For binary mixtures, it is weU known that when a Hquid—Hquid envelope merges with a minimum boiling vapor—Hquid-phase envelope the resulting azeotropic phase diagram has the form shown in Figure 13. When the Hquid composition, as in Figure 13a, then the vapor... 

A convenient way of representing the T—x y phase diagram (Eig. 14b) is by projection onto the composition triangle at the base of the figure. It is understood that the temperature varies from point to point on the projected vapor line and on the projected boiling envelope. The latter looks like an isothermal Hquid—Hquid binodal envelope, but is not. Each tie line across the boiling envelope is associated with a different boiling temperature (Eig. 15). 

Vapor—Liquid Systems. The vapor-liquid region of a pure substance is contained within the phase or saturation envelope on a P-V diagram (see Figure 2-80), A vapor, whether it exists alone or in a mixture of gases, is said to be saturated if its partial pressure (P.) equals its equilibrium vapor pressure (P, ) at the system temperature T. This temperature is called the saturation temperature or dew point T ... 

Figure 2-80. Typical P-V diagram for a pure substance showing isotherms and saturation (phases) envelope.

It is seen that however sophisticated the software might be, it would be virtually impossible to de-convolute the peak into the three components. The peaks shown in the diagram are discernible because the peaks themselves were assumed and the composite envelope calculated. The envelope, however, would provide no basic data there is no hint of an approximate position for any peak maximum and absolutely no indication of the peak width of any of the components. The use of the diode array detector, monitoring at different wavelengths, might help by identifying uniquely one or more of the... 

Fig. 1.4 Diagram showing detailed structure of the envelope of Gram-negative bacteria.

Figure 8.1 (a) Block diagram of the femtosecond near-infrared laser microscope system, (b) Spectrum ofthe light pulse from the Cr F laser, (c) Interferometric autocorrelation trace of SHG signal with envelope curve calculated assuming a chirp-free Gaussian pulse with 35 fs fwhm. 

The composition points, the tie-lines and the phase envelope showing the multiphase regions were then plotted on the ternary diagram. Micellar solutions were selected... 

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