Plug Flow Column Reactor

A column reactor is assumed to operate under steady-state conditions. A positive flow is chosen as the liquid-phase flow direction. For a volume element A Vl in the liquid phase, the mass balance can be written as 

By considering the relation hu,o x — nujn = hu and by defining the volume fraction 

After division by the reactor volume element, AVr, and allowing AVr 0, we obtain 

260 Chemical Reaction Engineering and Reactor Technology For a gas-phase volume element, A Vg analogous to Equation 7.1, we obtain 

If the gas and the liquid flow in the same direction. Aha = G ,out - hG/jn, and the flow directions are opposite, Anci = nG/.in — WG/.out) we can rewrite Equation 7.6 for both concurrent (-) and countercurrent (-I-) flows, taking into account the definition of Uy, Equation 7.3  

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The expressions that we obtained for the molar flux of very slow, slow, normal, fast, and infinitely fast reactions are inserted into the mass balances of the ideal reactor models. The molar flux at the gas-liquid interface was derived for ideal reactor models for plug flow column reactors (Equations 7.15 and 7.16), for stirred tank reactors (Equations 7.22,7.25, and 7.26), and for BRs (Equations 7.33 and 7.34) ... 

Runaway criteria developed for plug-flow tubular reactors, which are mathematically isomorphic with batch reactors with a constant coolant temperature, are also included in the tables. They can be considered conservative criteria for batch reactors, which can be operated safer due to manipulation of the coolant temperature. Balakotaiah et al. (1995) showed that in practice safe and runaway regions overlap for the three types of reactors for homogeneous reactions (1) batch reactor (BR), and, equivalently, plug-flow reactor (PFR), (2) CSTR, and (3) continuously operated bubble column reactor (BCR). 

An adsorption isotherm is useful for scaling up small-scale batch processes usually carried out in a laboratory. Once the laboratory data are fitted to an isotherm, one can predict the amount of adsorbent required to reach a specific effluent solute concentration (in terms of a batch reactor) or the breakthrough time (for a plug-flow column). 

The simplest flow-sheet for the reaction Aj o Aj is the RD column sequence with an external recycling loop shown in Fig. 5.1. The system as a whole is fed with pure Aj. According to the assumed relative volatility of the two components a > 1, the reaction product A2 is enriched in the column distillate product whereas the bottom product contains non-converted reactant Aj, which is recycled back to the reactor (continuous stirred tank reactor, CSTR, or plug flow tube reactor, PFTR). The process has two important operational variables the recycling ratio cp = B/F, that is the ratio of recycling flow B to feed flow rate F, and the reflux ratio of the distillation column R = L/D. At steady-state conditions, D = F since the total number of moles is assumed to be constant for the reaction Aj A2. As principal design variables, the Damkohler number. 

Bubble columns in series have been used to establish the same effective mix of plug-flow and back-mixing behavior required for Hquid-phase oxidation of cyclohexane, as obtained with staged reactors in series. WeU-mixed behavior has been established with both Hquid and air recycle. The choice of one bubble column reactor was motivated by the need to minimize sticky by-products that accumulated on the walls (93). Here, high air rate also increased conversion by eliminating reaction water from the reactor, thus illustrating that the choice of a reactor system need not always be based on compromise, and solutions to production and maintenance problems are complementary. Unlike the Hquid in most bubble columns, Hquid in this reactor was intentionally weU mixed. 

Wiped film stills in place of continuous still pots —Centrifugal extractors in place of extraction columns —Flash dryers in place of tray dryers —Continuous reactors in place of batch —Plug flow reactors in place of CFSTRs —Continuous in-line mixers in place of mixing vessels... 

Continuous reactor liquid mixed ideally, plug flow of gas (bubble gas column, tall reactors with multistirrer system)... 

In a properly operated bubble-column reactor, the liquid phase can be considered to be perfectly mixed, i.e. concentrations in the liquid are the same everywhere and correspond to those in the effluent. The gas is supposed to flow like a piston, i.e. the reactor is a plug-flow reactor with respect to the gas. These two assumptions are not entirely true, but within a certain flow regime they are not far from the reality. 

Compounds A and B are available in the off-gas stream from an absorption column at concentrations of 20 moles/m3 each. 14 m3/sec of this fluid is to be processed in a long isothermal tubular reactor. If the reactor may be assumed to approximate a plug flow reactor, what volume of pipe is required to obtain 80% conversion of species A ... 

In a typical pulse experiment, a pulse of known size, shape and composition is introduced to a reactor, preferably one with a simple flow pattern, either plug flow or well mixed. The response to the perturbation is then measured behind the reactor. A thermal conductivity detector can be used to compare the shape of the peaks before and after the reactor. This is usually done in the case of non-reacting systems, and moment analysis of the response curve can give information on diffusivities, mass transfer coefficients and adsorption constants. The typical pulse experiment in a reacting system traditionally uses GC analysis by leading the effluent from the reactor directly into a gas chromatographic column. This method yields conversions and selectivities for the total pulse, the time coordinate is lost. 

The system mostly applied in practice for supply of ozone is the bubble column and the stirred tank reactor. With these reactor systems it is always possible to set up the complete reactor modification as a plug flow reactor, a continuous flow single stirred tank reactor or a cascade of stirred tank reactors. 

Example 12-2 An aqueous solution contains 10 ppm by weight of an organic contaminant af molecular weight 120, which must be removed by air oxidation in a lo-cm-diameter bubble column reactor at 25°C. The liquid flows downward in the tube at an average velocity af 1 cm/sec. The air at 1 atm is admitted at 0.1 liter/sec and is injected as bubbles 1 mm diameter, which rise at 2 cm/sec. Assume no coalescence or breakup and that both gas and liquid are in plug flow. The reaction in the Hquid phase has the stoichiometry A + 2O2 products with a rate C. ... 

In real tubular (or column) reactors there is, usually, a back-mixing effect which influences the performance of the ideal plug-flow reactor. This axial dispersion is higher for fluidized-bed reactors than for packed-bed reactors, although comparatively lower than for continuous-feed stirred-tank reactors, where the mixing is complete. 

The modeling of real immobilized-enzyme column reactors, mainly the fluidized-bed type, has been described (Emeiy and Cardoso, 1978 Allen, Charles and Coughlin, 1979 Kobayashi and Moo-Young, 1971) by mathematical models based on the dispersion concept (Levenspiel, 1972), by incorporation of an additional term to account for back-mixing in the ideal plug-flow reactor. This term describes the non-ideal effects in terms of a dispersion coefficient. 

In the common case, in slurry bubble column reactors, the catalyst phase remains in the reactor while the liquid phase could remain in the reactor with a continuous flow of gas (semibatch operation). Both gas and liquid could be in plug flow or could be well mixed. 

For transport terms in eqs 1 and 3, the upper and lower reaches of Twelve Mile Creek were treated as one-dimensional advective (plug flow) systems. The upper basin of Lake Hartwell was modeled as a series of completely mixed reactors, with inflows into the first reactor from Twelve Mile Creek and the Keowee River. Analytical solutions for steady-state distributions of solids and PCB congeners in the water column and the active sediment layer were determined by using approaches outlined by O Connor (20-22). Because Kd values for a specific congener class were taken to be equivalent for the water column and active sediment layer, the solutions are independent of k[ values. 

The design of packed column reactors is very similar to the design of packed columns without reaction (Volume 2, Chapter 12). Usually plug flow is assumed for both gas and liquid phases. Because packed columns are used for fast chemical reactions, often the gas-side mass transfer resistance is significant and needs to be taken into account. The calculation starts on the liquid side of the gas-liquid interface where the chemical reaction rate constant is compounded with the liquid side mass transfer coefficient to give a reaction-enhanced liquid-film mass transfer... 

Although the most realistic model for a bubble column reactor is that of dispersed plug-flow in both phases, this is also the most complicated model in view of the uncertainty of some of the quantities involved, such a degree of complication may not be warranted. Because the residence time of the liquid phase in the column... 

The reactor system may consist of a number of reactors which can be continuous stirred tank reactors, plug flow reactors, or any representation between the two above extremes, and they may operate isothermally, adiabatically or nonisothermally. The separation system depending on the reactor system effluent may involve only liquid separation, only vapor separation or both liquid and vapor separation schemes. The liquid separation scheme may include flash units, distillation columns or trains of distillation columns, extraction units, or crystallization units. If distillation is employed, then we may have simple sharp columns, nonsharp columns, or even single complex distillation columns and complex column sequences. Also, depending on the reactor effluent characteristics, extractive distillation, azeotropic distillation, or reactive distillation may be employed. The vapor separation scheme may involve absorption columns, adsorption units,... 

FIGURE 1 Selected reactor configurations (a) batch, (b) continuous stirred-tank reactor, (c) plug flow reactor, (d) fluidized bed, (e) packed bed, (f) spray column, and (g) bubble column. 

The bubble column is a typical gas-liquid heterogeneous reactor with the design also applicable to liquid-liquid systems. The bubbles rise through the liquid in plug flow. The liquid is well mixed by the bubbling gas and seldom follows plug flow assumptions. 

The spray tower is a heterogeneous gas-liquid reactor. The gas passing up the column obeys plug flow conditions, and the liquid sprayed into the column behaves either as plug flow or as batch for individual droplets falling down the tower. 

This model is referred to as the axial dispersed plug flow model or the longitudinal dispersed plug flow model. (De)r can be neglected relative to (IT,), when the ratio of column diameter to length is very small and the flow is in the turbulent regime. This model is widely used for chemical reactors and other contacting devices. 

The plug-flow model indicates that the fluid velocity profile is plug shaped, that is, is uniform at all radial positions, fact which normally involves turbulent flow conditions, such that the fluid constituents are well-mixed [99], Additionally, it is considered that the fixed-bed adsorption reactor is packed randomly with adsorbent particles that are fresh or have just been regenerated [103], Moreover, in this adsorption separation process, a rate process and a thermodynamic equilibrium take place, where individual parts of the system react so fast that for practical purposes local equilibrium can be assumed [99], Clearly, the adsorption process is supposed to be very fast relative to the convection and diffusion effects consequently, local equilibrium will exist close to the adsorbent beads [2,103], Further assumptions are that no chemical reactions takes place in the column and that only mass transfer by convection is important. 

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