Batch flux curve

Figure 14-7 Typical batch flux curve with operating lines (...) underloaded ...

All the data to produce a batch flux curve, i.e. G-C, which is inqjortant design information for continuous thickener design procedures, can be obtained in the following... 

From the single-batch settling test data given in the previous exan le construct a batch flux curve. Determine the required area for continuous thickening from 3 to 15% by (a) the Yoshioka Construction and (b) by the Coe-Clevenger procedure. 

If a tangent is drawn from the point on the abscissa corresponding to the required underflow concentration C , it will meet the if curve at a concentration value CL at which fT has the minimum value (A/v. and will intersect the ordinate axis at a value equal to irTL. The construction is dependent on the fact that the slopes of the tangent and of the iru line are equal and opposite ( uu). Thus, in order to determine both Cl and (An, it is not necessary to plot the total-flux curve (ibatch sedimentation (if ) curve. The value of (A/ /, determined in this way is then inserted in equation 5.46 to obtain the required area A. 

The air factor curves of the conversion system look very much like the inverted mass flux curves, see Figure 21. As a matter of fact, they are negatively coupled, that is, if one goes up the other one goes down. This particular selection of graphs is representative for the whole test. Consequently, the air factors for the wood chips and the wood pellets were close to or below one, whereas the fuel wood in most of the cases were above one during the whole batch run. 

Figure 5.4.5 Flux curve for batch sedimentation with hindered settling.

Figure 5.4.6 Simple concave downward flux curve with a maximum and no inflection point for batch sedimentation with hindered settling.

An interesting situation arises if it is desired to avoid the upward propagation of kinematic waves by moving the sediment downward at a rate such that the upward-propagating concentration differences are stationary relative to the container walls. The downward motion of the sediment is obtained by its continuous withdrawal uniformly over the settler cross section. The process is termed continuous thickening. The continuous sedimentation process is thus composed of the batch gravitational flux and solid convective flux pu. This is illustrated in Fig. 5.4.7, where the total solids flux curve is the sum of the batch flux and the convective flux the shape of the curve of Fig. 5.4.5 illustrates the batch flux (Petty 1975). 

We recorded the water content of individual vials in the order of their moving out from the freeze-dryer and constructed the water content distribution over the vials in the freeze-drayer. Based on those data we obtained information about the operation state, i.e., the bias of heat flux in the shelf or the residence of water vapor in the chamber. The information was very helpful in the maintenance of the machine to achieve uniform conditions in the chamber. Furthermore, we determined the uniformity of the vials in each batch or the consistency among batches based on the information of the water content distribution by statistical analysis. An example of allocation of trays in a freeze-dryer and three-dimensional distribution of moisture levels in individual vials is shown in Figure 24. Frequency distributions of vial moisture and their normal distribution curves in different batches made with different freeze-dryers are shown in Figure 25. 

Figure 2.32 Batch UF membrane flux vs. concentration curve for a surfactant feed water. Cross-flow cell at 2.76 bar g 1100 ml/min 20°C Amicon regenerated cellulose YM-10 membrane with MWCO of 10,000 Da. Source [49],...

The curve shown in Figure 2.32 is a standard flux vs. concentration plot and holds true for almost all UF/MF cases. A slight variation of the plot for batch UF of a protein solution is shown in Figure 2.33 [50]. In this plot, gel polarisation seems to be a two-step process involving build-up and closing at low concentrations followed by compaction of the sublayer. The test run used three membranes DP06, an isotropic microfilter with a pore size of 6000 A PM-10, a polysulphone UF membrane with a MWCO = 10,000 Da and PM-30, a polysulphone UF membrane with a MWCO = 30,000 Da. The pure water... 

Figure 2.33 Batch cross-flow membrane filtration flux vs. concentration curve for a protein feed solution for various UF and MF membranes. Amicon polysulphone PM-10 and PM-30 membranes with MWCO of 10,000 and 30,000 Da. The "gel layer" concentration is between 30 and 40%.

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