Sherwood plot

The separation cost is often related directly to the degree of dilution for the component of interest in the initial mixture. This cost includes the fact that most separations use 50 times the minimum energy requirement based on the ideal thermodynamic requirements. To put the energy consumption in perspective, the chemical and petroleum refining industries in the US consume approximately 2.9 million barrels per day of crude oil in feedstock conversion [1], One method to visualize this cost factor is with the Sherwood plot shown in Figure 1.2. 

Figure 1.2 Sherwood plot [ 1 ]. Reproduced with permission of National Academy Press.

Using the Sherwood plot, what is the price differential for a product contained in a 1% and a 0.001% feed stream ... 

Metal Minimum concentration recoverable, from Sherwood Plot (mass fraction) Percent of metal, theoretically recoverable (%) Percent recycled in 1987 (%)... 

Fig. 7. The Sherwood plot for waste streams the minimum dilution (1/mass fraction) of metal wastes undergoing recycling is plotted against metal price. The Sherwood plot for virgin materials is provided for comparison. Points lying above the Sherwood plot indicate that the metals in the waste streams are only recycled at very high concentration, i.e., waste streams undergoing disposal are richer than typical virgin materials. Points lying below the Sherwood plot indicate that the waste streams are vigorously recycled.

Figure 2.1 Sherwood plot of material selling price as a function of the concentration of the material in the initial matrix. Reproduced from Grubler A. Technology and global change. Cambridge (UK) Cambridge University Press 1998.

The first criterion is not surprising since the separation process must be capable of accomplishing the desired separation and achieve a quality product. Sometimes a combination of two or more separation processes is necessary to attain these requirements. However, economical feasibility depends strongly on the value of the products isolated. This is often related to the concentration of the raw material. A decreasing concentration generally leads to an enhanced price for the pure product, as expressed by a so-called Sherwood-plot [4,5]. 

Figure 4.2. The Sherwood plot. [Adapted from a similar figure (Nystrom 1984) and discussed in an article by Lightfoot (1988). Additional data taken from texts by King (1971) Figure 1.16 Sherwood, Pigford, and Wilke (1975) Figure 1.2 and Blanch and Clark (1995) Figure 6.2.]...

The J function is plotted in Fig. 16-28 and tables are available (e.g., Sherwood et al., Ma.ss Transfer, McGraw-Hill, New York, 1975). Ver-meulen et al. (gen. refs.) discuss several approximations of the J function. For large arguments it approaches... 

A graphical stepwise procedure offered by Sherwood [62] also summarized by Reference 18. Y and X are plotted and handled stepwise as in distillation. The equilibrium line equation is for any single component ... 

Sherwood and Pigford(7) have shown that if the data of Gilliland and SHERWOOD<36) and others 35 38,395 are plotted with the Schmidt group raised to this power of 0.67. as shown in Figure 10.14, a reasonably good correlation is obtained. Although the points are rather more scattered than with heat transfer, it is reasonable to assume that both jd and 7/, are approximately equal to 0. Equations 10.224 and 10.226 apply in the absence of ripples which can be responsible for a very much increased rate of mass transfer. The constant of 0.023 in the equations will then have a higher value. 

SHERWOOD and Pigford(7) found that the effect of the Schmidt group was also influenced by the Reynolds group and that the available data were, fairly well correlated as shown in Figure 10.16, in which (hod )/D is plotted against Re Sc0-67. 

Taylor, Frank Sherwood. Alchemical papers of Dr. Robert Plot. Ambix 4, no. 1-2... 

Sherwood number under the thin concentration boundary layer assumption through Eq. (3-46). The results are plotted in terms of and in Fig- 9.7. For a rigid sphere in creeping flow, the relationship between these quantities and the velocity ratio K is... 

Plot and discuss the Sherwood number as a function of for different values of the homogeneous chemistry. Specifically, consider three cases where Da/, = 0, Dah = 1, and Da/, = 10. In all cases assume the limit of fast surface chemistry with... 

If we increase the values of the Sherwood number Sh to 5,000 and increase the Nusselt number likewise to 5,000, then we will generally not encounter any bifurcation. This is depicted below for (3 = 1 and 7 = 8, for example, by calling pellet4etacurve (0.01,10,1, 8,5000,5000,1,1,2) In this call, the very last parameter, called tt in pellet4etacurve is set to 2 in order to plot the nonbifurcating curve ( ) correctly. 

Rotating packed-bed devices handle high volumes of fluids in a small equipment volume, compared to packed towers, due to the acceleration of gravity. The Sherwood flooding correlation for packed towers (25) is expressed as a plot of... 

The capture efficiency or Sherwood number was shown to be a function of three dimensionless groups—the Peclet number, the aspect ratio (collector radius divided by par-dele radius), and the ratio of Hamaker s constant (indicating the intensity of London forces) to the thermal energy of the particles. Calculated values for the rate of deposition, expressed as Ihe Sherwood number, are plotted in Figure 6 as a function of the three dimensionless groups. 

A comparison of the various correlations for the Sherwood number in terms of a Sh/Sc1 3 versus Re plot is illustrated in Fig. 9-29. As indicated by Sano et al.121 the same correlations are applicable to agitated vessels and bubble-columns. 

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