Calculated transfer rates

Diatomic harmonic oscillator levels (hv 110 cm-1) to v = 3 for the H cluster are found to contribute to the observed rates with up to 1500 cm-1 of vibrational energy in the n = 3 cluster. Table 5-7 presents the results of these calculations agreement between the calculated transfer rates (tj 1) based on the above model and the experimental results is excellent. 

Table II shows examples of the calculated transfer rates when no corrections are made, when the back-exchange of unlabeled lipid from the acceptor particles is corrected for, and when corrections are made for the back-exchange of both labeled and unlabeled lipid.

Percent Error in the Calculated Transfer Rate when Particle B Functions as the Acceptor... 

Calculated Transfer Rates for Aniline Collisions with Argon ... 

For comparison of the observed and calculated transfer rates, it is useftd to write kr in terms of a bimolecular (b) rate constant. For spherical donors and acceptors, the rate is given by ... 

Figure 15. Electronic energy levels, major excitation funneling pathways, and their calculated transfer rates in LH2 of Rs. molischianum. Internal conversion is represented by dashed arrows whereas interpigment energy flows are shown by solid arrows. Wavy arrows point to the light-harvesting states. Reprinted with permission from ref 94. Copyright 2000 American Chemical Society.

Here t. is the intrinsic lifetime of tire excitation residing on molecule (i.e. tire fluorescence lifetime one would observe for tire isolated molecule), is tire pairwise energy transfer rate and F. is tire rate of excitation of tire molecule by the external source (tire photon flux multiplied by tire absorjDtion cross section). The master equation system (C3.4.4) allows one to calculate tire complete dynamics of energy migration between all molecules in an ensemble, but tire computation can become quite complicated if tire number of molecules is large. Moreover, it is commonly tire case that tire ensemble contains molecules of two, tliree or more spectral types, and experimentally it is practically impossible to distinguish tire contributions of individual molecules from each spectral pool. 

Mavri, J., Berendsen, H.J.C. Calculation of the proton transfer rate using density matrix evolution and molecular dynamics simulations Inclusion of the proton excited states. J. Phys. Chem. 99 (1995) 12711-12717. 

Van der Spoel,D., Berendsen, H.J.C. Determination of proton transfer rate constants using ab initio, molecular dynamics and density matrix evolution calculations. Pacific Symposium on Biocomputing, World Scientific, Singapore (1996) 1-14. 

Design Procedure. The packed height of the tower required to reduce the concentration of the solute in the gas stream from to acceptable residual level ofjy 2 may be calculated by combining point values of the mass transfer rate and a differential material balance for the absorbed component. Referring to a sHce dh of the absorber (Fig. 5),... 

The Plane Wall. To calculate the heat-transfer rate through a plane wall, Fourier s law can be appHed directly. 

If it is desired to calculate the rate of transfer from the overall concentration difference based on bulk-hquid compositions (x° — x), the appropriate overall coefficient Kl is related to the individual coefficients by the equation... 

The predictions of correlations based on the film model often are nearly identical to predictions based on the penetration and surface-renewal models. Thus, in view of its relative simphcity, the film model normally is preferred for purposes of discussion or calculation. It should be noted that none of these theoretical models has proved adequate for maldug a priori predictions of mass-transfer rates in packed towers, and therefore empirical correlations such as those outlined later in Table 5-28. must be employed. 

The values of h, and AP, calculated by this procedure are for clean exchangers and are intended to be as accurate as possible, not conservative. A fouled exchanger will generally give lower heat-transfer rates, as reflected by the dirt resistances incorporated into Eq. (11-2), and higher pressure drops. Some estimate of fouling effects on pres-... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

As the oxygen transfer rate under steady-state conditions must equal oxygen uptake, K a may be calculated ... 

The exponent in this formula is readily obtained by calculating the difference of quasiclassical actions between the turning and crossing points for each term. The most remarkable difference between (2.65) and (2.66) is that the electron-transfer rate constant grows with increasing AE, while the RLT rate constant decreases. This exponential dependence k AE) [Siebrand 1967] known as the energy gap law, is exemplified in fig. 14 for ST conversion. 

Fig. 18. Rate constant calculated with the use of (2.80a) plotted against (m/mH). The hydrogen transfer rate is assumed to be 10 s the effective symmetric vibration mass 125mH. The ratio of force constants corresponding to the intra (Kq) and intermolecular (K,) vibrations is (Ki/Ko) = 2.5 x 10 , 5 x 10 and l.Ox 10 for curves 1-3, respectively.

Figure 1.5.1 Table of calculated heat transfer rates. ...

The ROTOBERTY internal recycle laboratory reactor was designed to produce experimental results that can be used for developing reaction kinetics and to test catalysts. These results are valid at the conditions of large-scale plant operations. Since internal flow rates contacting the catalyst are known, heat and mass transfer rates can be calculated between the catalyst and the recycling fluid. With these known, their influence on catalyst performance can be evaluated in the experiments as well as in production units. Operating conditions, some construction features, and performance characteristics are given next. 

In the Direct SCF method, we do. not store the two-electron integrals over the basis functions, we recalculate them on demand every cycle of the HF procedure At first sight, this may seem wasteful, but Conventional methods rely on disk input/output transfer rates whilst Direct methods rely on processor power. There is obviously a balance between processor speed and disk I/O. Just for the record my calculation on aspirin (73 basis functions) took 363 s using the Direct method and 567 s using the Conventional method. 

The oxygen transfer rate is calculated based on oxygen concentration gradient, by determination of the oxygen level in the liquid phase and the equilibrium value. 

With an assumption of oxygen concentration at the interface, equilibrium with liquid phase is 6 ppm, the oxygen transfer rate is calculated. 

Calculate mass transfer coefficient in a 60 m3 fermenter with a gas and liquid interfacial area of a = 0.3 m2-m 3, given pbroth = 1200kg m-3. The small reactor has working volume of 0.18m3, 1 vvm aeration rate. Oxygen transfer rate (OTR) is 0.25kmol in 3 h 3. There are two sets of impellers, and flat-blade turbine types of impeller were used, HL= 1.2/),. Find the exact specifications of a large fermenter. 

This objection is supported by recent results of Moffat ef al. (109, 110), who observed severe interphase mass transfer limitations for the same system, in spite of calculations which predicted the mass transfer rate to be several orders of magnitude greater than the observed rate. As... 

The absorption of reactants (or desorption of products) in trickle-bed operation is a process step identical to that occurring in a packed-bed absorption process unaccompanied by chemical reaction in the liquid phase. The information on mass-transfer rates in such systems that is available in standard texts (N2, S6) is applicable to calculations regarding trickle beds. This information will not be reviewed in this paper, but it should be noted that it has been obtained almost exclusively for the more efficient types of packing material usually employed in absorption columns, such as rings, saddles, and spirals, and that there is an apparent lack of similar information for the particles of the shapes normally used in gas-liquid-particle operations, such as spheres and cylinders. 

Gal-Or and Resnick (Gl) have developed a simplified theoretical model for the calculation of mass-transfer rates for a sparingly soluble gas in an agtitated gas-liquid contactor. The model is based on the average gas residencetime, and its use requires, among other things, knowledge of bubble diameter. In a related study (G2) a photographic technique for the determination of bubble flow patterns and of the relative velocity between bubbles and liquid is described. 

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