Overall fractional

The following details establish reactor performance, considers the overall fractional yield, and predicts the concentration profiles with time of complex reactions in batch systems using the Runge-Kutta numerical method of analysis. 

In each subreactor, the dispersed-phase holdup fraction should be the same as the overall fraction thus... 

Equation (28) is valid only for monodisperse drugs. For polydisperse drugs, the overall fraction of dose absorbed may be estimated on the basis of the particle size distribution [44],... 

Obviously this approach is not easily extended to cascades containing more than three reactors and, in those cases, an alternative trial and error procedure is preferable. One chooses a reactor volume and then determines the overall fraction conversion that would be obtained in a cascade of N reactors. When one s choice of individual reactor size meets the specified overall degree of conversion, the choice may be regarded as the desired solution. This latter approach is readily amenable to iterative programming techniques using a digital computer. 

If the system is to operate isothermally at 50 °C where the reaction rate constant is equal to 0.9 m3/kmole ksec, determine the reactor volume necessary to achieve an overall fraction conversion of 0.80. Species A is to be fed at a rate of 0.3 mole/sec and an initial A concentration of 2 kmoles/m3. 

Consider the reaction studied in Illustration 10.1. Autothermal operation is to be achieved using a CSTR with an effective volume of1000 gal followed by a PFR of undetermined volume. Pure species A enters at a rate of 40.0 gal/hr and at a temperature of 20 °C. The overall fraction conversion is to be 0.97. This flow rate and conversion level will suffice to meet the annual production requirement of 2 million lb of B. Both the CSTR and the PFR are to be operated adiabatically. What PFR volume will be required, and what will be the temperature of the effluent stream ... 

For the proposed design the reactor volumes are both 0.8 m3, the input volumetric flow rate is 1.10m3/ksec, and the overall fraction conversion of the initial B is to be 0.80. Since the reaction is carried out in dilute liquid solution, the effective heat capacity of the liquid mixture is substantially unaffected by the reaction and may be regarded as a constant that is equal to 3.47 J/cm3 °K. If the initial concentration of species B is 5.6 kmole/m3 and the feed stream enters at 70 °C, determine the required heat transfer area for each reactor. 

The F(t) curve for a system consisting of a plug flow reactor followed by a continuous stirred tank reactor is identical to that of a system in which the CSTR precedes the PFR. Show that the overall fraction conversions obtained in these two combinations are identical for the case of an irreversible first-order reaction. Assume isothermal operation. 

Y r overall fractional yield of species R ep porosity of pellet or particle... 

The fractional yield of a product is a measure of how selective a particular reactant is in forming a particular product, and hence is sometimes referred to as selectivity.1 Two ways of representing selectivity are (1) the overall fractional yield (from inlet to a particular point such as the outlet) and (2) the instantaneous fractional yield (at a... 

For the stoichiometric scheme in Section 5.2.3, the overall fractional yield of D with respect to A, SD/A, is... 

Assuming that the feed contains only A and B, compare (i) the overall fractional yield, SD/A, at the outlet, and (ii) the rate of production of D from a PFR consisting of (a) a single 30-L vessel (Figure 18.4a), and (b) three 10-L vessels in series, with the feed of B split... 

Determine the overall fractional conversion of naphthalene, and the selectivity to phthalic anhydride. 

Find the following (a) the specific rate at 50 C (b) the concentration Cal leaving the CSTR (c) the concentration Ca2 entering the storage tank (d) the overall fractional conversion. 

The overall fractional-time-stepping process can be represented by... 

Frequently, one of the isotopes is present only in trace quantities (usually the heavier isotope) and the overall fraction of reaction, f, reduces to fi, to good approximation. If this is not the case Equations7.17 and 7.18 can be easily rewritten in terms of f or fq instead of fL. By the same token, with one isotopomer present in trace amounts (the commonly occurring case) the probability of reaction between two labeled molecules is very low, and formal second and higher order kinetics can be approximated using the first-order kinetic expressions developed above. 

Equations 7.17 and 7.18 have been developed assuming that the fraction of reaction for the light isotopomer (fL) is the one monitored. Frequently, however, the chemical (overall) fraction of reaction ... 

Figure 10. Summary of experimentally determined fractionation factors for Ca isotopes in the formation of foraminifera and coccolith shell carbonate, and for rapid inorganic precipitation of aragonite from an Mg-Ca-Cl solution. Data for the foraminifer G. ornatissima and the coccolith E. huxleyi are from De La Rocha and DePaolo (2000). Data on G. sacculifer are from Nagler et al. (2000). Data for O. universa and aragonite are from Gussone et al. (2003). Two of the forams and the coccolith E. huxleyi have similar fractionation behavior, with an overall fractionation factor of-1 to -1.5%o, and a small temperature dependence of about 0.02 per °C. The foram G. sacculifer appears to have a strongly temperature dependent fractionation factor.

If the cell is well supplied with nutrients, then the production of activated enzyme is great and this step is relatively fast. If the transport of sulfate into the cell cannot keep up with the reduction of sulfate, the concentration of sulfate within the cell becomes small, and very little of the isotopically fractionated sulfate inside the cell can leak back out of the cell. Thus, the effect of the internal isotopic fractionation on the outside world is minimal and the overall fractionation of the process is small. In a hypothetical extreme case, every sulfate anion entering the cell would be consumed by reduction. This would require a complete lack of isotopic fractionation, because when all S atoms entering are consumed, there can be no selection of light vs. heavy isotopes. The isotopic fractionation of the overall reduction reaction would be equal to that which occurs during the diffusion step only. 

Mo(OH)6 may still play a role in isotope frachonation if they adsorb because, at equilibrium, the overall fractionation factor for Mo04 Mo-surface necessarily equals the product of the... 

For any particular set of reactions and rate equations is a function of Ca, and since in general varies through the reactor, cp will also change with position in the reactor. So let us define O as the fraction of all the reacted A that has been converted into R, and let us call this the overall fractional yield o/R. The overall fractional yield is then the mean of the instantaneous fractional yields at all points within the reactor thus we may write... 

It is the overall fractional yield that really concerns us for it represents the product distribution at the reactor outlet. Now the proper averaging for cp depends... 

For a series of 1, 2,. .., N mixed flow reactors in which the concentration of A is Cai, Ca2, . , Cpj, the overall fractional yield is obtained by summing the fractional yields in each of the N vessels and weighting these values by the amount of reaction occurring in each vessel. Thus... 

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