Breakpoint concentration

As C increases, f (C) increases such that, in a given time, z for lower concentrations is greater than for higher concentrations. Following the progress of the breakpoint concentration, C = 0.003 kmol/m3, then ... 

Pursell L., T. Dineen, J. Kerry, S. Vaughan, and P. Smith (1996). The biological significance of breakpoint concentrations of oxytetracycline in media for the examination of marine sediment microflora. Aquaculture 145 21-30. 

Using the Miura-Hashimoto model, calculate the time needed to reach a breakpoint concentration of 9.92 mg/L (10%). According to the experimental results given by Hashimoto et al., the time needed for the specified breakpoint concentration is 226 hr. What is the result if the solid diffusion control approximation is used ... 

According to the experimental data, the first appearance of toluene in the exit stream is at about 50 min, while after 100 min the exit concentration is 10% of the inlet one. Calculate the time needed for the same breakpoint concentration using the Wheeler-Jonas equation and Wood and Stampfer equation for die evaluation of kv. 

In the absence of more experimental data and for the purposes of the present example, we assume that the first appearance of toluene just after 50 min corresponds to an exit concentration of 0.01%, which is practically close to zero. This value will be used as the breakpoint concentration in the following calculations. 

In Figure 4.28, the model predictions are plotted for different breakpoint concentrations. Note that while the model works quite well for low Cbr, 0.01% in our case, it fails to represent the data for higher values. For example, for Cbl. = 1.7 mg/L (10%), it predicts a breakpoint time of only 47.2 min instead of 100 min, which is the approximate experimental value. This is an expected result as normally, this kind of breakpoint models are designed to work at relatively low breakpoint concentrations. On the other hand, by setting the first appearance at lower values of exit concentration, the model gradually predicts a much lower first appearance time than the experimental one. Thus, it seems that a breakpoint or first appearance concentration in the vicinity of 0.01-1% is adequate in order to have representative results (filled squares). 

In Figure 4.29, the breakpoint concentration for Cbl, = 1% is presented for different values of the interstitial velocity. 

Figure 4.29 Breakpoint concentration for Cbr =1% for different values of interstitial velocity.

The mean exit concentration Cavrbl, is always much lower than the breakpoint exit concentration in our example, it is almost 0.3% of the breakpoint concentration. 

Consider the idealized breakthrou curve of Fig. 11.43. This results from the flow of a solvent gas throu an adsorbent bed at the rate of Gs mass/(areaXtime), entering with an initial solute concentration Yq mass solu-te/mass solvent gas. The total solute-free effluent after any time is w mass/area of bed cross section. The breakthrough curve is steep, and the solute concentration in the effluent rises rapidly from essentially zero to that in the incoming gas. Some low value is arbitrarily chosen as the breakpoint concentration, and the adsorbent is considered as essentially exhausted when the effluent concentration has risen to some arbitrarily chosen value close to Jq. We are concerned principally with the quantity of effluent Wg at the breakpoint and the shape of the curve between Wg and Wg. The total effluent accumulated during the appearance of the breakthrough curve is = Wg Wg. The adsorption zone, of... 

It is desired to estimate the depth of bed required for the same molecular sieves operated at the same gas mass velocity, the same Fg and and the same breakpoint concentration, 1 X 10 mole fraction water, as in the laboratory test, but the breakpoint time 9 is to be IS h. 

A laboratory fixed-bed adsorption column filled with a synthetic sulfonic acid cation-exchange resin in the acid form is to be used to remove Na" ions from an aqueous solution of sodium chloride. The bed depth is 33.5 cm, and the solution to be percolated through the bed contains 0.120 meq Na /cm At saturation, the resin contains 2.02 meq Na /cm resin. The solution will be passed through the bed at a superficial Lnear velocity of 0.31 cm/s. For this resin, Michaels [70] reports that the overall liquid mass-transfer rate 0.86t>2 , where is the superficial liquid velocity, cm/s, and is expressed as meq Na /cm s (meq/cm ). The relative adsorptivity of Na" " with respect to for this resin is a 1,20, and this is constant for the prevailing concentration level. Define the breakpoint concentration as 5% of the initial solution concentration, and assume that practical bed exhaustion occurs when the effluent concentration is 95% of the iniital. Estimate the volume of effluent at the breakpoint, per unit bed cross section. 

The remaining matter requiring attention is the placement of the breakpoints. Similar considerations will apply here as outlined in Section 4.2(a) in connection with the finite-difference grid point distribution. That is, it is important to concentrate the breakpoints at the position where most reaction occurs, with progressively lower interior breakpoint concentrations towards the flame boundaries. For (presumably) an Eulerian calculation of an ozone... 

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