Solids in plug flow

The scale and complexity of an adsorption unit varies from a laboratory chromatographic column a few millimeters in diameter, as used for analysis, to a fluidised bed several metres in diameter, used for the recovery of solvent vapours, from a simple container in which an adsorbent and a liquid to be clarified are mixed, to a highly-automated moving-bed of solids in plug-flow. 

Unlike in distillation and absorption, very little is known about HETP values in adsorption. As a consequence, it may be preferable to use the transfer unit concept for continuous flow adsorbers like the solids in plug flow unit. A differential mass balance on the sorbate across an incremental length of bed, dz, as shown in Figure 6.6, yields ... 

The effectiveness of a fluidized bed as a ehemical reactor depends to a large extent on the amount of convective and diffusive transfer between bubble gas and emulsion phase, since reaction usually occurs only when gas and solids are in contact. Often gas in the bubble cloud complex passes through the reactor in plug flow with little back mixing, while the solids are assumed to be well mixed. Actual reactor models depend greatly on kinetics and fluidization characteristics and become too complex to treat here. 

In the TMB model, the adsorbent is assumed to move in plug flow in the opposite direction of the fluid, while the inlet and outlet lines remain fixed. As a consequence, each column plays the same function, depending on its location. An equivalence between the TMB and the SMB models can be made by keeping constant the liquid velocity relative to the solid velocity, i.e., the liquid velocity in the TMB is ... 

We will apply the steady state momentum balance to a fluid in plug flow in a tube, as illustrated in Fig. 5-6. (The stream tube may be bounded by either solid or imaginary boundaries the only condition is that no fluid crosses the boundaries other that through the inlet and outlet planes.) The shape of the cross section does not have to be circular it can be any shape. The fluid element in the slice of thickness dx is our system, and the momentum balance equation on this system is... 

One major difference between pneumatic transport and hydraulic transport is that the gas-solid interaction for pneumatic transport is generally much smaller than the particle-particle and particle-wall interaction. There are two primary modes of pneumatic transport dense phase and dilute phase. In the former, the transport occurs below the saltation velocity (which is roughly equivalent to the minimum deposit velocity) in plug flow, dune flow, or sliding bed flow. Dilute phase transport occurs above the saltation velocity in suspended flow. The saltation velocity is not the same as the entrainment or pickup velocity, however, which is approximately 50% greater than the saltation velocity. The pressure gradient-velocity relationship is similar to the one for hydraulic transport, as shown in... 

Solids and Gas Both in Plug Flow, When solids and gas pass through the reactor in plug flow, their compositions change during passage. In addition, such operations are usually nonisothermal. 

When in plug flow all solids stay in the reactor for the same length of time. From this and the kinetics for whatever resistance controls, the conversion X R) for any size of particle R can be found. Then the mean conversion of the solids leaving the reactor can be obtained by properly summing to find the overall contribution to conversion of all sizes of particles. Thus,... 

From the statement of the problem we may consider the solids to be in plug flow with tp = S min and the gas to be uniform in composition. Hence for a mixed feed Eq. 2 is applicable, or... 

Figures 26.4 and 26.5 present these results for solids in mixed flow in convenient graphical form. Figure 26.5 shows clearly that at high conversion the mixed flow reactor requires a much larger holding time for solids than does a plug flow reactor.

Cocurrent and Crosscurrent Plug Flow of Gas and Solids. In cocurrent flow, shown in Fig. 26.9a, all reaction occurs at the feed end, and this represents a poor method of contacting with regard to efficiency of heat utilization and preheating of entering materials. 

The solids in the emulsion phase flow smoothly downward, essentially in plug flow. 

Emulsion phase gas in plug flow Solutions for bubble phase free of solids In the following, a simplified solution is presented under the following assumptions first-order reactions, gas flow only through the bubble phase (fh = 1), and absence of solids in the bubble phase (yb = 0). Under these conditions, the material balances (3.519) and (3.520) become the following. 

Analytical solutions for x and y as functions of the bed-length, z, and time, t, are available [45,52], The expressions are a useful extension of two-phase model applied to plug-flow. These two models are appropriate in describing the extraction of crushed or broken seeds to recover the seed oil, either in shallow beds or in plug flow. As shown by Sovova [52], applying the plug-flow model requires corrections for non-ideal residence-time distribution (non-plug flow) of the fluid in contact with the solid. 

Heat Transfer in Rotary Kilns. Heat transfer in rotary kilns occurs by conduction, convection, and radiation. In a highly simplified model, the treatment of radiation can be explained by applying a one-dimensional furnace approximation (19). The gas is assumed to be in plug flow the absorptivity, Energy balances are performed on both the gas and solid streams. Parallel or countercurrent kilns can be specified. 

The solids are also assumed to be in plug flow. As part of the plug flow approximation, the gas and solids are assumed isothermal in the radial direction at a given axial location. Detailed models for kiln heat transfer are available (20,21). 

Using these results Van de Velden et al. (2008) were able to recommend design rules for operation of such reactors in terms of the gas velocity/solids loading parameters. For example, to ensure a narrow residence time distribution (operating, in effect, in plug flow), the superficial gas velocity should exceed the transport velocity by approximately lm/s and the solids circulation rate should exceed 200kg/m2s. 

It should be mentioned that a solventless method of hydrolytic modification of starch has recently been developed. The method employs solid superacids, per-fluorinated resin-sulfonic acids, which successfully catalyze hydrolysis of starch (and other polysaccharides) and offer the possibility of continuous-process applications in plug-flow reactors.34... 

The rotary kiln is a continuous countercurrent heterogeneous reactor. Solids traveling down the kiln are in plug flow, as are the gases passing upward. 

In moving-bed transport, solid particles are in contiguous contact with one another and are pushed along by the transporting fluid more or less in plug flow, with a voidage equivalent to that of the loosest fixed bed. The velocity of solids movement can be varied from zero to any practical upper limit. 

Church, J. and Woolbridge, D., Continuous high solids acid hydrolysis of biomass in a 1.5 in plug flow reactor. Industrial Engineering and Chemistry Product Research and development 1981, 20, 371-378. 

Consider a physical system shown schematically in Figure 1. A fluid stream containing reactant A is moving upwards in plug flow with a constant velocity U. The reactant is adsorbed by a stream of solid catalytic particles falling downwards with a constant velocity V and occupying the void fraction of 1 - e. On the surface of catalyst an irreversible chemical reaction A - B is occurring and the product B is then rapidly desorbed back into the fluid phase. Instantaneous adsorption equilibrium for the species A is assumed. 

To this author s knowledge, no data on three-phase stirred columns are available. Preliminary observations indicate that the axial dispersion in the gas phase is considerably reduced by the presence of solid particles. Under certain conditions, even for a very low L/dc (where L is the length and dc the diameter of the stirred column) the gas phase may move essentially in plug flow. 

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