Optimum loading factor

Due to the rapid decrease in specific efficiency with increasing load, the optimum load factor is equal to a... 

Solving this equation for gives the optimum loading factor for touching band... 

Inserting the optimum value of dp/L given by Eq. 18.45 into Eq. 18.36 gives the optimum colmnn efficiency (at negligible sample size). Combination of these equations with Eq. 18.43 gives the optimum loading factor... 

Golshan-Shirazi and Guiochon [21,23] have derived from the solution of the ideal model [22] the equations giving the optimum loading factor, Lj 2, for maximum production rate of the second component and the corresponding sample size, in the case of overlapping bands (see ref. 1, Eqs. 19 and 20)... 

Golshan-Shirazi and Guiochon have also derived the optimum experimental conditions for production rate with a yield constraint in the case of overlapping bands [23], They have shown that the optimum loading factor is given by... 

Top part, optimization for maximiun production rate of the first component. Bottom part, optimization for maximum production rate of the second component. k = 4. N, optimum plate number Ly, optimum loading factor m, optimum reduced or apparent sample size (Eq. 10.15c) Pr, maximum production rate. 

The chromatograms on the right-hand side of Figures 18.17a and b were obtained for the optimum separation when Pr xY is maximized instead of Pr. The optimum loading factor is smaller for both components in the case in which PrxY is maximized and the recovery yield is significantly higher, whereas the production rate is only slightly smaller than in the case in which Pr is maximized. 

The optimum loading factor is higher in gradient elution than in isocratic elution, because the band compression diminishes the tag-along effect of the more retained component. Accordingly, the average concentration of the collected... 

Usually both gradient elution and displacement chromatography offer higher optimum loading factors than isocratic elution, due to the band compression effect of the former two modes. Gradient elution chromatography requires less column efficiency than isocratic elution, ie. shorter columns packed with larger particles can be used which will result in shorter cycle times to the increased flow rate. 

Additional corrections are of course necessary. These include load factors, and cost corrections such as entrance and exit head losses and the manufacturing cost of the headers or water boxes. These last corrections must be included in order to find the optimum diameter of the tubing (via minimizing f Q t%opt xr... 

From calculation of the loading factor and using an estimated value for the column saturation capacity from the screening studies, the optimum amount loaded. for species / can be calculated, Eq. (7.13). 

Figure 18.5 shows the results calculated with the ideal model for the combined objective function of production rate and recovery yield. When the separation of the less retained component is optimized, the ideal model fails to identify an optimum value of the loading factor for maximum production rate. The production rate increases monotonously with increasing loading factor while the recovery... 

Assiuning that the band profiles are right triangles, a reasonable assumption when the relative retention is close to 1 and the loading factor has to be small, we can use Eqs. 18.30 and 18.31 instead of Eqs. 18.29 and 18.4b. Then, the equation giving the optimum value of the ratio dp/L can be solved to give... 

Combination of Eqs. 18.30,18.36, and 18.37 gives the optimum value of the loading factor for touching bands ... 

Calculations show that the specific production increases indefinitely with increasing colunm efficiency, but that this increase becomes very slow past a certain efficiency (Figme 18.20). Obviously, for each efficiency, there is an optimiun loading factor for maximiun specific production, and the recovery yield increases approximately as the specific production. Again, as in the maximization of the production rate, there is an optimum value of the retention factor. This value is also extremely low, below 0.5. This is in part due to the fact that, in this case, the columns are operated at higher efficiencies than in the simple maximization of the production rate. For practical reasons discussed already, however, it is probably not advisable to operate under conditions where k is lower than 1. 

The resolution equation is composed of three parts the efficiency parameter, N, the chemistry or selectivity parameter, alpha, and the capacity or loadability parameter, k In the resolution equation for the preparative environment, this equation is already fixed by the chemistry parameters. For example, the capacity factor is set for the optimum load from the analytical data the chemistry or selectivity parameter is set by the analytical work-up where one has tested all the possible combinations of chemistry required to get the separation and the efficiency parameter is fixed by the amount of load that is going to be put on that bed structure. 

As a first estimate the optimum flow velocity can be calculated by means of the F factor (= loading factor = measure of the kinetic energy Equation 2.4-15) ... 

At each of the 15 selected PEF sites, an average cost, delivery rate and moisture content of Energy Plantation fuel for the optimum-sized plantation were determined from the results of the Energy Plantation model calculations and put into the power plant model, with which the performance of the power plant and the cost of generated electricity were calculated. The power plant load factor at each site was determined by examining published data for the utility serving that site. 

The carbon black critical loading factor and the optimum loading level tvill be a function of the specific carbon black grade and specific grade of polymers in the rubber compound blend, and are therefore unique for each polymer and filler system. 

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