Time-average cycling rate

Above t = 60 minutes, changes in the time-average cycling rate at an amplitude of 0.24 were too small to be significant. At the other end of the frequency spectrum, a different timer would have been required to achieve periods less than 1 minute. Periods of less than 1 minute were not investigated furthermore because at shorter periods the square wave becomes increasingly distorted by mixing in the system. 

Figure 4. Steady-state and time-average cycling rate envelopes vs. feed composition. Conditions T = 400°C P = 2.38 MPa and particle diam = 0.3 mm. Key -0-, steady-state and cycling.

The measured pressure surge and the time-averaged measured rate of 53 kg/h suggest that the rate cycled between about 44 kg/h at the low pressure point and 62 kg/h at the high pressure point via Eqs. 12.1 and 12.2. Thus, the difference in... 

As the period increases, the time-average synthesis rate falls towards the space-mean, quasi steady state value as expected. At large periods, the steady state is approached in each portion of the cycle. The quasi-steady state line in... 

Figure 3 was calculated from steady-state measurements. Curvature of the rate vs composition relation causes the quasi steady-state rate to be well below the steady-state reactor performance. This emphasizes the very large effect of cycling frequency on the time average synthesis rate. 

Figure 3. Effect of cycle-period on time-average reaction rate. Key Time-average Ht, 0.75 and cycle split, 0.4.

As a result it is of interest to examine some of the general characteristics of this component of the total response. If the real part of the dynamic shear viscosity is calculated for this component, tit, it is found to be a strong function of the strain amplitude and frequency. Data were obtained for BK-60 at 6 different amplitudes and 9 different frequencies. In an effort to systematize this Information, the dependence of on the shear rate was examined by plotting log (n] ) against the time average shear rate during the oscillatory cycle (Figure 8)... 

Therefore, the longer the material reacts, the more product is made. However, the rate at which product is formed slows with time, and the average production rate drops. These trends are shown by the curves plotted in Figure 14.11. Both the instantaneous and time-averaged production rate of Product B are seen to decrease with time. Because this is a batch operation, the optimal time to run the reaction must be determined. Because there are costs associated with cleaning and recharging feed to the equipment, these should be taken into account when determining the optimal cycle time for the batch. 

Throughput is in simple terms the average saleable production output per a given time unit. Cycle time is the average time between the release and completion of a job, in other words, the rate at which products are manufactured. Key parameters that affect throughput in a chemical plant include the chemical conversion, yield, capacity and availability of existing equipment, process time, cycle time, number of chemical steps, number of unit operations, plant layout, warehouse processes, raw material availability, process bottlenecks and labour availability, amongst others. 

Fig. 19. Time-average rate of S02 oxidation under periodic liquid flow interruption as a function of cycle period, cycle split, and the time-average superficial liquid velocity at 26°C, 1 bar using a BPL activated carbon. (Figure from Haure et al., 1990, with permission, 1990 Elsevier Science Publishers.)...

The net (average) filter capacity is determined by the amount of slurry processed during the total cycle time, not just the filter time, and represents the average flow rate (Q) ... 

The effect of forced concentration cycling was investigated on the oxidation of CO over industrial V2O5 catalyst. The resulting rate, when time-averaged, exhibited frequency-dependent harmonic behavior, with multiple extrema. Some preliminary interpretation is provided by analogy to an electrical network containing resistance and inductance. 

From the bubble size and the average flow rate, a first approximation of frequency (thereby total cycle time), as well as the limits between which the chamber pressure oscillates, is determined. The weeping time is calculated from the wave-form equations of chamber pressure, which are ... 

Figure 7. Calculated ozone production and loss rates for two different conditions from the AER two-dimensional model. Production and loss rates above 20 km are diurnally averaged loss rates for the spring equinox at 30°N. Midday loss rates are approximately two times larger. Production and loss rates for midday below 20 km are calculated for the chemically perturbed region over Antarctica on September 16,1987. The catalytic cycles responsible for the loss are explained in the text. Although ozone loss occurs at higher altitudes over Antarctica, in situ observations extend only to 19 km.

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. 

Anderson were able to derive explicit values for sorption, desorption, and removal rate constants. They reported rate constants for the uptake of thorium from solution (fej) that increased with increasing particle concentration, rising approximately from 0.2 yr to 1.0 yr over a particle concentration of 5-25 pg L Their rate constants for desorption (fe-i) were independent of particle concentration, and ranged between 1.5 yr and 4 yr Reasonable hts to °Th prohles could only be obtained with rate constants for removal of particulate Th kf) that were less than 0.1 yr The fact that 2 is much smaller than fej and fe j implies that °Th atoms, on average, cycle between dissolved and particulate phases many times before eventually being buried in sediments. 

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