Separation factor overall

The overall scale-up faclor used to convert a rate calculated from bench-scale data to a design rate for a commercial installation must incorporate separate factors for each of the following ... 

A more quantitative and lengthy method, but still very useful for checking of the type required here is the Smith-Brinkley method (Reference 5). It uses two sets of separation factors for the top and bottom parts of the column for a fractionator or reboiled absorber and one overall separation factor for a simple absorber. The method is tailor-made for analysis of a column design or a field installed column. The Smith-Brinkley method starts with the column parameters and calculates the resulting product compositions unlike other methods that require knowing the compositions to determine the required reflux. 

The rapid increase in the separation factors observed for the individual series of columns reflected not only the improvement in the intrinsic selectivities of the individual selectors but also the effect of increased loading with the most potent selector. Although the overall loading determined from nitrogen content remained virtually constant at about 0.7 mmol g for all CSPs, the fractional loading of each selector increased as the number of selectors in the mixture decreased. Thus, the whole method of building block selection and sublibrary synthesis can be also viewed as an amplification process. 

The separation factor, r, in an isotope separation process is the ratio of the relative concentration of desired isotope in the product, p, to its relative concentration in the feed, f. Denoting the feed to the i th stage, the i th section of an overall plant, or the ith overall plant, as mol/s of isotope with an isotope fraction Zj, yielding product at a rate of Yj mol/s of analysis yi, and waste at a rate of Xj mol/s and isotope analysis Xj, we have for a two isotope feed... 

Principally, the overall assessment factor is established by multiplication of the separate factors. The authors note that in practice it is not possible to distinguish all above-mentioned factors, and some factors are not independent of each other. Therefore, straightforward multiplication may lead... 

The values of permeability coefficients for He, O2, N2, CO2, and CH4 in a variety of dense (isotropic) polymer membranes and the overall selectivities (ideal separation factors) of these membranes to the gas pairs He/N2,02/N2, and CO2/CH4 at 35°C have been tabulated in numerous reviews (Koros and Heliums, 1989 Koros, Fleming, and Jordan et al., 1988 Koros, Coleman, and Walker, 1992). Moreover, several useful predictive methods exist to allow estimation of gas permeation through polymers, based on their structural repeat units. The values of the permeability coefficients for a given gas in different polymers can vary by several orders of magnitude, depending on the nature of the gas. Thevalues oftheoverall selectivities vary by much less. Particularly noteworthy is the fact that the selectivity decreases with increasing permeability. This is the well-known inverse selectivity/permeability relationship of polymer membranes, which complicates the development of effective membranes for gas separations. 

The overall separation depends on the single stage separation factor, the number of separating elements, and design and operating characteristics of the cascade. Equations 5-8 are insufficient to determine all the variables. It is instructive to consider three types of cascades the minimum stage cascade, the minimum reflux cascade, and the ideal cascade. The material balance equations from the i + 1 th stage to the product of the cascade lead to... 

Generally, alcohols showed higher separation factors when present in model multicomponent solutions than in binary systems with water. On the other hand, aldehydes showed an opposite trend. The acmal tea aroma mixmre showed a rather different behavior from the model aroma mixmre, probably because of the presence of very large numbers of unknown compounds. Overall, the PDMS membrane with vinyl end groups used by Kanani et al. [20] showed higher separation factors and fluxes for most of the aroma compounds. Pervaporation was found to be an attractive technology. However, as mentioned above the varying selectivities for the different aroma compounds alter the sensory prohle and therefore application of PV for recovery of such mixmres needs careful consideration on a case-by-case basis. 

A mathematical model to be solved numerically has been developed and used to predict the separation effects caused by nonstationary conditions for a liquid membrane transport. Numerical calculations were made to compute pertraction characteristics such as input and output membrane selectivity (ratio of respective fluxes), concentration profiles for cations bound by a carrier in a liquid membrane phase, and the overall separation factors. These quantities are discussed as dependent... 

There is growing interest by investors to invest in firms and funds that reflect the investors own social values. These funds are tending to focus on the more immediate sustainability factors such as carbon footprint, energy efficiency, and environmental performance. As analysts become more familiar with process safety metrics— and those metrics are demonstrated to be useful predictors of a company s future safety performance—it is reasonable that a similar value could be placed on firms that are demonstrating their commitment to process safety as a separate factor or process safety as an element of other social values. Such demonstrated commitment to safety performance should also provide additional information, above and beyond financial information, on which the analyst can assess the overall risk of a firm or facility. 

Introducing a separation factor. A, defined as a ratio of the total overall mass-transfer coefficients of the solutes (metal species) ... 

Individual mass-transfer coefEcients are determined experimentally for every metal species in the processing time intervals between sampling (ti—t ), (tj—tj), (tf—tj), and so on. Then, for every metal transported, the overall mass-transfer coefficients on the feed side, Kp/p(t), and strip side, 1 e/r(V, the total overall mass-transfer coefEcients of the BAHLM system, were calculated, using Eqs (8), (9), and (47), respectively, for every samphng time interval. Separation factors of two metal species,... 

By combining Eqs. (21.1-14) and (21.1-1B), fractionel extraction can be obtained as a function of ovVQf for different ratios of feed io dialysate flow rate. These relationships are shown in Fig. 21.1-6. The separation factor in a dialytic process can be considered to be the ratio of the fractional masses of two solutes removed from their commou Teed stream, under a given asi of operating conditions. By applying Eq. (21.1-16) to each solute, we can see diet a is equal to the ratio of the fractional extractions of the two solutes. Thus. Fig, 21.1-6 can be used to estimate the relative separation of two solutes from a keowlcdge of their overall mess transfer coefficients, membrane area, and feed and dialysate Aow rates. 

Because there is no separation of boron isotopes in the equilibrium vsqmrization of the complex, the overall separation factor in the combined process of evaporation and dissociation is... 

The minimum number of stages increases as the overall separation increases and as the separation factor approaches unity. Because both these conditions hold in a typical isotope separation plant, the minimum number of stages is often very large. For example, in a gaseous diffusion plant (a = 1.00429) making product containing 90 percent and tails 0.3 percent. 

In the ideal cascade discussed up to this point, each stage receives as feed two streams of the same composition, a tails stream from the stage next higher in the cascade and a heads stream from the stage next lower in the cascade. In such a cascade the heads separation factor /, tails separation factor 7, and overall separation factor a are related by... 

If the heads separation factor p is constant throughout such a simple cascade, the fraction of deuterium that may be recovered depends on the number of stages n and the overall enrichment oj in accordance with... 

A high, but attainable, overall separation factor of a = 7 will be used. A heads separation factor such as the one that would be used in an ideal recycle cascade of 3 = y/a = y/f = 2.646 will be assumed. Then the number of stages n is given by... 

---