Conversion time-averaged

Computer simulation generates information at the microscopic level, and the conversion of this information into macroscopic terms is the province of statistical thermodynamics. An experimentally observable property A is just the time average of A(F) taken over a long time interval,... 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

It was found [1] that the values of and a, obtained in minimizing the error of fitting experimental conversion-time data, satisfactorily described the temporal evolutions of the molecular weight averages. Also, the model performed better in the description of the experimental data when a value of 3 = 1/2 was used. 

CO concentration at the outlet of each zone was continuously measured using a CO analyzer (Shimadzu CGT-7000). To evaluate the performance of the reactors, the conversion of CO for the PBR (Xco) with 4g of catalyst and the time-average conversion of CO for the SCMBR (Tea) with 2g of catalyst in each zone were calculated and compared. It should be noted that the CO concentration wave used for Eq. (1) was obtained whrai the system is at cyclic steady state (after 30 min of operation). 

Performance of a simulated countercurrent moving bed reactor, SCMCR is experimentally investigated for oxidation of CO at low concentration in the absence of hydrogen over Pt/AljOs catelyst/adsorhent. The time-average conversion of CO obtained in the SCMBR was higher than the conversion of CO obtained from a conventional PBR for all over the tested range (period = 2-15 min). For the next step, the effects of operating variables on its performance are planed for both CO oxidation in the absence of H2 and Hz-rich gas system. 

The calculated conversions presented in Table VIII used Eq. (57). They are quite remarkable. They reproduce experimental trends of lower conversion and higher peak bed temperature as the S02 content in the feed increases. Bunimovich et al. (1995) compared simulated and experimental conversion and peak bed temperature data for full-scale commercial plants and large-scale pilot plants using the model given in Table IX and the steady-state kinetic model [Eq. (57)]. Although the time-average plant performance was predicted closely, limiting cycle period predicted by the... 

Fig. 17. Comparison of the variation of the time-average S02 conversion and the maximum bed temperature predicted for stationary cycling condition by an unsteady-state and a steady-state kinetic model for a packed-bed S02 converter operating with periodic flow reversal...

Although time-averaged conversion measurements provide valuable information, a detailed analysis of the dynamic behavior of three-way catalysts requires direct observation of catalyst responses to rapid changes in exhaust composition. 

Figure 5. Time-averaged CO and NO conversions measured using the laboratory reactor system shown in Figure 4. A fresh, pelleted Pt/Rh/AltOs catalyst was operated at a middle-bed temperature of 820 K and a space velocity of 52,000 h 1 (STP). The feedstreams simulated exhaust that would be obtained with various engine air-fuel ratios (A/F) but did not contain SOs. The feedstream compositions were cycled at 0.25 and 1 Hz at an amplitude of 0.25 A/F about the mean A/F. For the curves labeled Steady-State, conversions were measured with feedstreams at the mean A/F values (8).

Figure 5. Proportion of conversation time devoted to different topics. The data are average values from three separate studies (two conducted in university canteens, one in public places). Social topics include anything concerned with personal relationships, personal experiences and arrangemenst for future social activities. The category politics includes all topics relating to religion, ethics and morals as well as politics. Source Dunbat et al. submitted.

Time average values of air factor of the conversion system were calculated. However, the mathematical model of the method is unclear. No verification methods were given and no uncertainty analysis was discussed. The method used is difficult to reproduce. 

As already indicated Eq. (39) (Eq. (40)) gives the rate of ideal time and frequency resolved emission. If compared with experimental data gained by single photon counting, F(iv t) has to undergo a time averaging with the respective apparatus function which determines the possible time resolution of the measurement (for up conversion techniques see [44]). 

The other parameters are the same as for the FFB model. Similar to the FFB model, Equations 30-32 give the instantaneous conversion to obtain time averaged values, integration is required for X (Equation 23) and T ... 

Longer contact time resulting in lower time averaged conversion. 

Situation (I) corresponds to a fluid isotropic solution where a uniform time averaged environment should exist. Under such conditions single exponential decay would be expected for the guest excited states and the photoreactivity should be predictable on the basis of a single effective reaction cavity. In situation (II) there should be two kinetically distinct excited states in two noninterconverting sites resulting in nonexponential decay of the excited state of A. The quantum efficiency of product formation and the product distribution may depend upon the percent conversion. An example of mechanism (II) is provided in Sch. 22 [137]. The ratio of products A, B, and C has been shown to depend on the crystal size. With the size of the crystal the ratio of molecules present on the surface and in the interior changes which results in different extents of reactions from two the distinct sites namely, surface and interior. 

The effect of feed composition cycling on the time-average rate and temperature profile was explored in the region of integral conversion in a laboratory fixed bed ammonia synthesis reactor. Experiments were carried out at 400°C and 2.38 MPa over 40/50 US mesh catalyst particles. The effect of various cycling parameters, such as cycle-period, cycle-split, and the mean composition, on the improvement in time-average rate over the steady state were investigated. 

The results Illustrated by Figures 3 and 4 resemble those obtained in the Berty recycle reactor under similar conditions. The space-mean, time average rates for the fixed-bed reactor were only about 50% of those measured in the Berty reactor, because, of course the former reactor achieved conversions high enough for the back reaction to become important. The significance of these observations is that 1) CSTR and differential reactors, widely used for laboratory studies, seem to reflect performance improvements obtainable with fixed-bed, integral reactor which resemble commercial units, and 2) improvement from periodic operation are still observed even tfien reverse reactions become important. 

Lewis and Stevens mathematical treatment is fairly general, as it allows the conversion rate and deposition velocities to vary with time, as expected. For example, the rate of SO2 conversion is probably higher during daytime than at night. The value of their formulation is that the dispersion of both SO2 and SO4 and the deposition of SO4 are handled by normalization to the concentration of fine primary particles from the SO2 source. They made various assumptions about the time dependence of conversion and deposition rates and concluded that the errors are only about 10% or less if one assumes that the rates are equal to the time-averaged values. 

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