Breakthrough curves for the example

The values of breakthrough curve (C vs t) for first two values of Z are shown in Table 8.1. 

These equations can also be converted into dimensionless numbers [6] given below. 

These dimensionless numbers result in simpler partial differential equations given below. The breakthrough curves in terms of dimensionless numbers are shown in Table 8.2. 

Breakthrough curves for the example in terms of dimensionless munbers 

Here we are only showing one integration step because Euler is the simplest numerical integration technique and may not be suitable for these equations for longer horizon. 

---

Figure 3.3.51 shows the breakthrough curves for the example of H2S adsorption on a molecular sieve, where we have such a constant pattern behavior of the profiles... 

Figure 3.3.51 Breakthrough curves for the example of H2S adsorbed on a molecular sieve dp = 2.2 mm, p = 60 bar, Ph2s, in = 43 mbar, Us = 15 cm s ). Data from Croninger, Hedden, and Rao (1987).

The reactor in Fig. 5 operates as follows. A feed solution containing a given concentration of pollutant is pumped to the adsorbent module at a fixed volumetric flow rate. The module is kept isothermal by a temperature control unit, such as a surrounding water bath. Finally, the concentration of the outlet solution is measured as a function of time from when the feed was introduced to the adsorbent module. These measurements are often plotted as breakthrough curves. Example breakthrough curves for an aqueous acetone solution flowing... 

Example 10 Transition Types For the constant separation-factor isotherm given by Eq. (16-31), determine breakthrough curves for r = 2 andr = 0.5 for transitions from cf=0 to cf = 1. 

Initially, all the hydrocarbon is adsorbed on the core and none is observed at the outlet. Once the core is saturated, hydrocarbon breakthrough is observed. Example breakthrough curves for two temperatures are shown in Fig. 27. The amount of hydrocarbon adsorbed is given by the area above the breakthrough curve (after correction for the residence time of the reactor). By conducting experiments with different hydrocarbon concentrations and at different temperatures, the temperature and concentration dependency of the amount stored can be determined and hence isotherms generated. 

Breakthrough curves from column experiments have been used to provide evidence for diffusion of As to adsorption sites as a rate-controlling mechanism. Darland and Inskeep (1997b) found that adsorption rate constants for As(V) determined under batch conditions were smaller than those necessary to model breakthrough curves for As(V) from columns packed with iron oxide coated sand the rate constants needed to model the breakthrough curves increased with pore water velocity. For example, at the slowest velocity of 1 cm/h, the batch condition rate constant was 4 times smaller than the rate constant needed to model As adsorption in the column experiment. For a velocity of 90 cm/h, the batch rate constant was 35 times smaller. These results are consistent with adsorption limited by diffusion of As(V) from the flowing phase to sites within mineral aggregates. Puls and Powell (1992) also measured more retardation and smaller rate constants for As(V) at slower flow velocities where there was sufficient time for diffusion to adsorption sites. 

As an example, Fig. 6.20 gives the experimental breakthrough curve for a racemic mixture of EMD53986 using Chiralpack AD (dp = 20 gm, Daicel) as adsorbent and ethanol as eluent. Here a two-detector set-up of polarimeter and UV-detector was used, permitting the solute-specific detection of both components (Mannschreck, 1992, Jupke, 2004 and Epping, 2005). 

Fig. 8 gives a brief description of the reaction mechanism initiated by the use of rotary hearth furnace coke for desulfurization and, in addition, shows some SO2 breakthrough curves as an example. 

The breakthrough curves measured for the monolithic columns with different proteins are very sharp and confirm again the fast mass transport kinetics of the monoliths [133, 134]. The frontal analysis used for the determination of the breakthrough profile can also be used for calculation of the dynamic capacity of the column. For example, the capacity for the 60x16mm i.d. monolith at 1% breakthrough is 324 mg of ovalbumin and represents the specific capacity of 40.0 mg/g of separation medium or 21.6 mg/ml of column volume. 

Fig. 6.11 Using rollups to efficiently prescreen mixtures for the presence of "hits". In this example, six mixtures of approximately 90 compounds each (A-E) were screened in a dual protein FAC assay (/S-galactosidase, GS1B4). The dashed red and blue curves in each chromatogram represent the breakthroughs of the /S-galactosidase and GSl B4 indicators, respectively, in the absence of the...

Figure 4.27 Examples of theoretical breakthrough curves calculated from the analytical solutions for the Freundlich isotherm (Fr = 0.5).

In Figure 4.27, some examples of theoretical breakthrough curves calculated from the analytical solutions for the Freundlich isotherm (Fr = 0.5) are presented. As is clear, the curve corresponds to the case of equal and combined solid and liquid-film diffusion resistances ([ = 1) which is between the two extremes, i.e. solid diffusion control (l = 10,000) and liquid-film diffusion control ( = 0.0001). 

As one example, Fig. 6.31 shows the results for Troger s base using isotherm data determined from breakthrough curves (Eq. 6.187). 

As an example of the experimental validity of the solution derived by Lapidus and Amundson, Figme 6.3 shows the breakthrough curve measured by Rixey and King [26] (symbols) for succinic acid on pre-wet Porapak Q (Waters-Millipore). The experimental results are in excellent agreement with the analytical solution (solid line) derived by Lapidus and Amtmdson [3]. The Peclet number and the external mass transfer coefficient were estimated using conventional relationships taken from the literature [26]. 

---