Minimum HETP

One last contribution to HETP in this chapter is to establish tray efficiency by simply running one of the tray programs and inputting T for the tray method selection. The program will give you the well-proven tray efficiency two-film method [1]. Then refer to Table 3.10 and estimate your HETP minimum required. I always recommend adding at least 6 in to the HETP for a reasonable, safe design. 

Chromatographic efficiency Efficiency of peak A and B, respectively Height equivalent to a theoretical plate (HETP) Minimum HETP Effective HETP... 

The design objectives of the analyst and the production line engineer are generally quite different. For analysis the primary concern is typically resolution. Hence operating conditions near the minimum value of the HETP or the HTU are desirable (see Fig. 16-13). 

The HETP equation is not simply a mathematical concept of little practical use, but a tool by which the function of the column can be understood, the best operating conditions deduced and, if required, the optimum column to give the minimum analysis time calculated. Assuming that appropriate values of (u) and (Dm) and (Ds)... 

It is seen that by a simple curve fitting process, the individual contributions to the total variance per unit length can be easily extracted. It is also seen that there is minimum value for the HETP at a particular velocity. Thus, the maximum number of theoretical plates obtainable from a given column (the maximum efficiency) can only be obtained by operating at the optimum mobile phase velocity. 

Equations (4) and (5) predict that the optimum linear velocity should be linearly related to the diffusivity of the solute in the mobile phase, whereas the minimum value of the HETP should be constant and independent of the solute diffusivity. This, of course, will only be true for solutes eluted at the same (k ). It is seen, from Table 1, that (by appropriate adjustment of the concentration of ethyl acetate) the values of both (k ) and (k e) have been kept approximately constant for all the mobile phase... 

It is seen that there will be a unique value for (dp), the optimum particle diameter, (dp(opt)), that will meet the equality defined in equation (14) and allow the minimum HETP to be realized when operating at a maximum column inlet pressure... 

Tests by FRI and Nutter [132] emphasize that distribution of liquid must be uniform and at minimum values to achieve good HETP values over a range of system pressures for hydrocarbons distillation. 

A minimum HETP or HTU represents a maximum separation efficiency with a representing the relative volatility, i.e., vapor and liquid phase compositions of the more volatile component in a binary system ... 

The curve exhibits a minimum, which means that there is an optimum mobile phase velocity at which the column will give the minimum HETP and consequently a maximum efficiency. In practice this usually means that reducing the flow rate of a column will increase the efficiency and thus the resolution. In doing so, however, the analysis time will also be increased. As seen in figure 5, however, there is a limit to this procedure, as reducing the column flow rate so that the mobile phase velocity falls below the optimum will result in an increase in the HETP and thus a decrease in column efficiency. 

In liquid chromatography, the diffusion rates are slower than that in gas chromatography, and the values of DM and D are very small therefore, the minimum H value is obtained at a low flow rate, as shown by curve E in Figure 5.6. The value of H increases slowly at higher flow rates in liquid chromatography. An experimental result is shown in Figure 5.7. The HETP was minimal at a certain flow rate, and the measured optimum value was less than 10 pm for this column. The optimum flow rate was about 0.9 ml min - corresponding to a linear flow velocity of about 55 mm min -. ... 

Equation (5) is a hyperbolic function which indicates that there will be a minimum value of (H) for a particular value of (u). That is a maximum efficiency will obtained at a particular linear mobile phase velocity. An example of an HETP curve obtained in practice is shown in figure 1. 

The upper curve, which is the result of a curve fitting procedure to the points shown, is the HETP curve. The column was 25 cm long, 9 mm in diameter and packed with 8.5 micron (nominal 10 micron) Partisil silica gel. The mobile phase was a solution of 4.8 Sw/v ethyl acetate in n-decane. The minimum of the curve is clearly indicated and it is seen that the fit of the points to the curve is fairly good. As a result of the curve fitting procedure the values of the Van Deemter constants could be determined and the separate contributions to the curve from the multipath dispersion, longitudinal dispersion and the resistance to mass transfer calculated. 

The HETP curve clearly shows, that for a packed column, the particle size has a profound effect on the minimum value of the HETP of a column and thus the maximum efficiency attainable. It would also appear that the highest efficiency column would be obtained from columns packed with the smallest particles. This will in due course be shown to be a fallacy, but what is true, is that the smaller the particle diameter the smaller will be the minimum HETP and thus, the larger the number of plates per unit length obtainable from the column. At this time it will suffice to point out that the total number of theoretical plates that can be obtained will depend on the length of the column which, in turn, must take into account the available inlet pressure... 

The form of the HETP curve for a capillary column is the same as that for a packed column and exhibits a minimum value for (H) at an optimum velocity. 

Thus, substituting for (1) in equation (9) from equation (2) and using the optimum velocity and the minimum HETP,... 

What would be the minimum theoretical value of HETP for the propane at 40 °C ... 

If the liquid holdup is too low, fractionation efficiency will be bad. We say that the height equivalent to a theoretical plate (HETP) will be high. If the liquid holdup is too high, fractionation efficiency will also be poor. We again say that the HETP will be high. This idea is expressed in Fig. 7.6. When the holdup rises above the point that corresponds to the minimum HETP, we can say that the packing is beginning to flood. The minimum HETP point on Fig. 7.6 corresponds to the point of incipient flood, discussed in Chap. 1. 

Plate theory disregards the kinetics of mass transfer. Thus, it reveals little about the factors influencing HETP values. Plate theory tells us that HETP becomes smaller with decreasing flow-rate however, experimental evidence shows that a plot of HETP versus flowrate always goes through a minimum. 

Figure 14-67b compares continuous tilts with ratios of highest to lowest flow of 1.25 and 1.5 to a situation where one-half of the distributor passes 25 percent more liquid than the other half. The latter ("zonal ) situation causes a much greater rise in HETP than a uniform maldistribution with twice as much variation from maximum to minimum. 

Wu and Chen (167) recommend pilot testing over the entire range between the expected minimum and maximum operating rates, and taking the highest measured HETP as the basis for scaleup. The author concurs. With structured packings, the loed effect may be due to liqnid rather than vapor loads, and the pilot tests should cover the range of liquid loads (i.e., gpm per square foot of column cross section) that is expected in the prototype. 

Perform pilot tests over the entire range of vapor and liquid loads between the expected minimum and maximum operating rates. UBe the highest measured HETP as the basis for scaleup. 

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