Periodic flow

The explanation for the approach to a log-normal distribution is as follows. Consider, for simplicity, flows as those considered by Muzzio, Swanson, and Ottino (1991a) two-dimensional time periodic flows. Let An,k denote the length stretch experienced by a fluid element between periods n and k. The total stretching after m periods of the flow, A0,m, can be written as the product of the stretchings from each individual period ... 

D time periodic flows and spatially periodic duct flows can produce chaos. A necessary condition for chaos is crossing of streamlines. 

In general, time periodic (or spatially periodic) flows generate islands (or tubes). Stretching in islands and tubes is linear. Stretching in chaotic regions is exponential. 

Niederkom, T. C, and Ottino, J. M., Mixing of viscoelastic fluids in time-periodic flows. J. Fluid Mech. 256, 243-268 (1993). 

Several pilot plants have been built to test periodic flow direction reversal. Pilot-scale reactors with bed diameters from 1.6 to 2.8 m were operated with flow reversal for several years. The units, described by Bunimovich et al. (1984,1990) and Matros and Bunimovich (1996), handled 600 to 3000 m3/h and operated with cycle periods of 15 to 20 min. Table VIII shows the performance of these plants for different feeds and potassium oxide promoted vanadia catalysts. The SVD catalyst was granular the IK-1-4 was in the form of 5 (i.d.) x 10-mm cylinders, while the SYS catalyst was... 

The rate model contains four adjustable parameters, as the rate constant k and a term in the denominator, Xad, are written using the Arrhenius expression and so require a preexponential term and an activation energy. The equilibrium constant can be calculated from thermodynamic data. The constants depend on the catalyst employed, but some, such as the activation energy, are about the same for many commercial catalysts. Equation (57) is a steady-state model the low velocity of temperature fronts moving through catalyst beds often justifies its use for periodic flow reversal. 

There are many other S02 simulation using the models described in Tables IX and X or their further simplifications (Boreskov and Matros, 1984 Matros, 1989 Bunimovich etal., 1990 Sapundzhiev etal., 1990 Snyder and Subramanian, 1993 Xiao and Yuan, 1994, 1996 Zhang et al. 1995 Wu et al., 1996). These simulations are capable of reproducing operating data as demonstrated in Table VIII and in the preceding discussion. They have been useful in understanding the application of periodic flow reversal to S02 oxidation, as we shall see. 

Fig. 14. Influence of inlet SO2 concentration on behavior and performance in adiabatic, packed-bed SOj converters operating under periodic flow reversal. Simulation results for t = 30 min, SV = 514 h 1, Ta = 25°C (a) effect of inlet SO2 vol% on the temperature profile in the catalyst bed, (b) influence of inlet S02 on converter performance and the velocity of the temperature front. (Figure adapted from Xiao and Yuan, 1996, with permission of the authors.)...

A concern in the application of periodic flow reversal to converting S02 in smelter emissions is the variability of these emissions. Both S02 concentration and gas volume may vary, often irregularly. Like startup, this is a matter that could profit from simulation studies using models discussed in this section. 

Periodic Flow Reversal Model Employing the Balzhinimaev Unsteady State Kinetic Model for S02 Oxidation Over Vanadia Catalysts... 

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...

IV. Conversion of S02 in Trickle-Bed Catalytic Scrubbers Using Periodic Flow Interruption... 

Fig. 20. Schematic diagram showing the estimation of the time-average rate of S02 oxidation under periodic flow interruption or reduction employing steady-state oxidation rate vs liquid loading data (Figure from Haure etal., 1989, with permission, 1989, American Institute of Chemical Engineers.)...

Fig. 22. Thermocouple temperature readings in an experimental trickle bed operating under periodic flow interruption with t = 60 min and a time-average u = 1.65 mm/s (a) r = 0.5, (b) s = 0.25, (b) s = 0.1. (Figure from Haure et al., 1990, with permission, 1990 Elsevier Science Publishers.)...

Figure 23 shows a simulation of Haure s periodic flow interruption data at time-average u = 0.86 mm/s (Curves 1 and 1 ) and u = 1.65 mm/s (Curves 2 and 2 ). Data points and the fit (dashed line) are from Fig. 19. The simulation predictions are 28 to 35% too high, which is not bad considering the 25% variation in the experimental data shown in Fig. 19. The trends, however, are not properly represented. Figure 23 predicts enhancement factors declining with r, whereas data indicate an increase at low r and...

The attraction of periodic flow interruption for scrubbing is that the pressure drop is low relative to continuous, packed-bed scrubbers and a commercially useful acid can be produced. The catalyst is cheap, but that... 

The success of periodic flow interruption is due to the liquid static holdup within the porous catalyst pellets and the interstices of the catalyst bed. 

Several uncertainties in this periodic process have not been resolved. Pressure drop is too high at SV = 10,000 h 1 when packed beds of carbon are used. Study of carbon-coated structured packing or of monoliths with activated carbon washcoats is needed to see if lower pressure drops at 95% SO2 removal can be achieved. Stack gas from coal or heavy oil combustion contains parts-per-million or -per-billion quantities of toxic elements and compounds. Their removal in the periodically operated trickle bed must be examined, as well as the effect of these elements on acid quality. So far, laboratory experiments have been done to just 80°C use of acid for flushing the carbon bed should permit operation at temperatures up to 150°C. Performance of periodic flow interruption at such temperatures needs to be determined. The heat exchange requirements for the RTI-Waterloo process shown in Fig. 26 depend on the temperature of S02 scrubbing. If operation at 150°C is possible, gas leaving the trickle bed can be passed directly to the deNO, step without reheating. 

Xi, X2 conversion in the upflow(l) and downflow (2) directions in periodic flow reversal... 

Budman, H., Kryzonak, M., and Siiveston, P. L., Control of a nonadiabatic packed bed reactor under periodic flow reversal. Can. J. Chem. Eng. 74, 751-759 (1996). 

Eigenberger, G., and Nieken, U., Catalytic combustion with periodic flow reversal. Chem. Eng. Sci. 43, 2109-2115 (1988). 

Snyder, J. D., and Subramaniam, B., Numerical simulation of a periodic flow reversal reactor for sulfur dioxide production. Chem. Eng. Sci. 48, 4051-4064 (1993). 

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