D/b plots

The d/b plot provides a useful estimate of the distribution of nonkeys and intermediate keys in tbe products. Hengstebeck (14) and Geddes... 

Stupin and Lockhart (27) also noted that as reflux is lowered from total to minimum, the separation of nonkeys first worsens (curve 2, Fig, 2,21), then improves (curve 3, Fig. 2,21), The intermediate keys follow the converse pattern, At a reflux ratio of about 1,2 to 1,5 times the minimum, component distribution resembles that of the total reflux component distribution. Detailed discussion is elsewhere (7,27). Figure 2,16 demonstrates that light nonkey6 are fractionated out in the stripping section and heavy nonkeys in the rectifying section. The d/b plot depicts this behavior (Sec. 2,4,2). 

The d/b ratio plot is frequently non-linear, but should be smooth iSec, 2,3.8), The prime cause of bumps is a poor estimate of relative volatility. If a refined estimate (sse Sec, 3.2,1 for estimating guidelines) does not improve things, the bump may reflect anomalies or a need to relocate a feed, The d/b plot gives a measure of how relocating the feed point affects the nonkey component split,... 

Identify mislocated feed. For binary distillation the feed point should be where the q-line intersects the equilibrium curve. For multicomponent distillation this may or may not be the case. So for multicomponent distillation feed location, key ratio plots and d/b plots are preferred and discussed next. 

Kister says that d/b plots are primarily used when there is a tight spec, on a nonkey component or a concern about the distribution of an intermediate key component. His book shows d/b curves for various feed stage locations on a plot of the mole ratio of a reference component in the distillate to the bottom product, versus the relative volatility of each component to this reference component. This plot is made on log-log paper. The optimum feed produced a curve closest to linear. The d/b plot is suggested as a troubleshooting tool in the subsection of the Troubleshooting section, Fractionation Operating Problems. ... 

Figure 6-3. Representations of the hydrogen b and 2p orbitals (a) Plot of the angular wave function, A(0, d>) (b) plot of the squared angular wave function, A (0,

Fig. 3.26 Comparison plots for compacts of silica and magnesia. In each case the adsorption of nitrogen at 78 K on the compact is plotted against that on the uncompacted powder, (a) and (b), comparison plot and adsorption isotherm for silica powder compacted at 130 ton in (c) and (d), comparison plot and adsorption isotherm for precipitated magnesia compacted at 10 ton in. Note that the upward sweep of the comparison plot commences at a relative pressure below the inception of the loop.

Rearrange Equation (5.20) into the form y = mx + c so that m involves D only. Plot y against x using the data in Table 5.1 to obtain B and D, in hertz, for carbon monoxide (use a computer or calculator that will work to nine-figure accuracy). 

Ideally, the chance of a spherical particle having diameter t passing through an opening would be zero for all particles of relative size djb > 1 and one for all particles of relative size djb < 1. A plot of the probabiUty-of-passing vs size (Fig. 1, curve D) is a step function, and the separation size, so-called cut size, is d/b = 1. A perfect separation is one where all particles of size less than the cut size pass and all particles of size greater than the cut size are retained. 

To determine the reasonableness of the top and bottom compositions of a fractionation column, a Hengstebeck plot is fast and easy (Reference 4). First, select a heavy key component and determine the relative volatility (a) of all column components to the heavy key. The a can be otfeed or perhaps more accurately cc = (a,op oCboitom) - Plot In D/B versus In a and the component points should fall close to a straight line. If a fairly straight line does not result, the compositions are suspect. A nomenclature table is provided at the end of this chapter. 

Plot In (D/B) vs. In oc and the points should fall on a straight line (D = overhead molar rate, B = bottoms molar rate). If a fairly straight line does )wt result, the compositions are suspect. 

The g r) that results from the modified Verlet (MV) closure is very close to the simulation results in Figs. 2 and 3. The MV results for g d), or equivalently, y d), are plotted in Fig. 4(a). The resulting equation of state is similar to the CS expression. An even more demanding test is an examination of the MV results for y r) for r < d. As is seen in Fig. 4(b), the MV results for y(0) are quite good [25], and are better than the PY and HNC results. Some results have also indicated that the MV closure gives quite accurate results for a mixture of hard spheres [26]. 

Figure 4-339. D-exponent graph (a) grid (b) plot of the results.

The results of tests on the polymers A, B, C, D are plotted versus the absolute temperature in Fig. 3.1 in order to facilitate comparison with Eq. 3.1. Tests on polymer E were spoilt by plastic deformation. Straight lines were drawn through the points in Fig. 3.1 and through the origin (T = OK). Such lines correspond with the Eq. (3.1). At temperatures below the glass transition where the polymers... 

Maranzana G, Perry I, Maillet D (2004) Mini and Micro-channels Influence of axial conduction in the wads. Int J Heat Mass Transfer 47 3993 004 Platzer B, Plot A, Maurer G (1990) Thermophysical properties of refrigerants. Springer, Berlin Heidelberg New York... 

Variations of the maximum Karlovitz number and laminar burning velocities with the equivalence ratio, showing the accessible domain when the maximum/= 170Hz is operated, (a) CH4/air mixtures (b) CH4 diluted with 20-60% N2 (c) CH4 diluted with 20-60% CO2 and (d) combined plots of these maximum-Ka = 170 Hz) lines from (a-c) for comparison. (From Yang, S.I. and Shy, S.S., Proc. Combust. Inst, 29,1841, 2002. 

Figure 3.1 Four-step construction of the Bjerrum difference plot for a three-pi molecule, whose constants are obscured in the simple titration curve (see text) (a) titration curves (b) isohydric volume differences (c) rotated difference plot (d) Bjerrum plot. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]...

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

Figure 2.1 (a) A schematic representation of the apparatus employed in an electrocapillarity experiment, (b) A schematic representation of the mercury /electrolyte interface in an electro-capillarity experiment. The height of the mercury column, of mass m and density p. is h, the radius of the capillary is r, and the contact angle between the mercury and the capillary wall is 0. (c) A simplified schematic representation of the potential distribution across the metal/ electrolyte interface and across the platinum/electrolyte interface of an NHE reference electrode, (d) A plot of the surface tension of a mercury drop electrode in contact with I M HCI as a function of potential. The surface charge density, pM, on the mercury at any potential can be obtained as the slope of the curve at that potential. After Modern Electrochemistry, J O M. 

Figure 7. Comparison of (a, solid) electrochemical and (b, dashed) UHV measurements of the H, coverage/potentiaI differential versus potential on Pt(lll).1.) cathodic sweep (25 mV/s) voltammogram in 0.3 M HF from Ref. 20, constant double layer capacity subtracted, b.) dB/d(A ) versus A plot derived from A versus B plot of Ref. 26. Potential scales aligned at zero coverage. Areas under curves correspond to a.) 0.67 and b.) 0.73 M per surface Pt atom.

Fig. 7.11 Electrochemical performance of different carbons using a three-electrode cell in 1 mol L 1 H2S04 (a) cyclic voltammograms at a scan rate of 1 mV s 1, (b) galvanostatic charge/discharge curves at a current density of 0.2 Ag 1, (c) relationship of the specific capacitance with respect to the charge/discharge specific currents, and (d) Ragone plots.

Fig. 11.3 Energy diagram for the reaction given in equation 11.1. As usual in diagrams of this sort energy (ordinate) is plotted against progress along the reaction coordinate (See, for example, Northrop, D. B. in Cleland,...

Fig. 10.5. Molecular surface of the archaeal (A), the euka otic 20S (B) and the HsIV proteasome (C). The accessible surface is colored in blue, the clipped surface (along the cylinder axis) in white. To mark the position of the active sites, the complexes are shown with the bound inhibitor calpain (yellow). (A) The disorder of the first N-terminal residues in the archaeal a-subunits generates a channel in the structure of the CP, (B) whereas the asymmetric but well-defined arrangement of the a N-terminal tails seals the chamber in eukaryotic CPs. (C) The eubacterial "miniproteasome" has an open channel through which unfolded proteins and small peptides can access the proteolytic sites. (D) Ribbon plot of the free...

Scheme 4.7 Stoichiometry-induced partner displacement in a four-component mixture (a) equilibria considered, (b) constraints imposed, (c) mole fraction definitions, and (d) a plot of mole fraction versus guest concentration ([M ] = [N ]).

Figure 12 Plots of the energy surfaces appropriate to the D-B-A (left) and D -B-A (right) species as functions of the reaction coordinate along which the diabatic surfaces cross and the adiabatic surfaces undergo an avoided crossing (as shown) (appears as Figure 10.2 in ref. 12).

Figure 1.34. E a < Epi, = 0 (a) 3D band structure and (b) contour plot. E a < Epb < 0 (c) 3D band structure and (d) contour plot. E a = E t < 0 (e) 3D band structure and (f) contour plot. FSs of half-tilled systems are represented by black lines while FSs of lower and higher band fillings by short dashed and continuous grey lines, respectively.

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