Cocurrent and countercurrent

Fixed-bed reactors in the form of gas absorption equipment are used commonly for noncatalytic gas-liquid reactions. Here the packed bed serves only to give good contact between the gas and liquid. Both cocurrent and countercurrent operations are used. Countercurrent operation gives the highest reaction rates. Cocurrent operation is preferred if a short liquid residence time is required. 

Sinclair and Jackson 81 have presented a theoretical relation between pressure gradient and the flowrates of gas and solids over the whole range of possible conditions for both cocurrent and countercurrent flow. It predicts marked segregation of gas and particles in the radial direction. 

Solutions for the cocurrent and countercurrent cases are displayed in Figure 11.7. The countercurrent case requires calculations of the shooting type where values for = / (z = 0) are guessed until the initial condition that ( /), = 0 is satisfied. Normalized concentrations with = 1 can be used. 

Recently, hydrodynamic aspects of multiphase applications have been studied in detail for the cocurrent and countercurrent flow regimes. Useful correlations were determined and it was found that foams combine high rates and low pressure drop, proving their high potential in multiphase applications [9, 107, 108]. 

Fixed-bed reactors are used for testing commercial catalysts of larger particle sizes and to collect data for scale-up (validation of mathematical models, studying the influence of transport processes on overall reactor performance, etc.). Catalyst particles with a size ranging from 1 to 10 mm are tested using reactors of 20 to 100 mm ID. The reactor diameter can be decreased if the catalyst is diluted by fine inert particles the ratio of the reactor diameter to the size of catalyst particles then can be decreased to 3 1 (instead of the 10 to 20 recommended for fixed-bed catalytic reactors). This leads to a lower consumption of reactants. Very important for proper operation of fixed-bed reactors, both in cocurrent and countercurrent mode, is a uniform distribution of both phases over the entire cross-section of the reactor. If this is not the case, reactor performance will be significantly falsified by flow maldistribution. 

Illustrated in Figure 5-21 are possible temperatures of reactor and coolant versus position z for cocurrent and countercurrent operation. 

Compare T (z) and T Cz) trajectories of a wall-cooled PFTR with cocurrent and countercurrent flows. Which configuration is more likely to produce more problems with a hot spot in the reactor ... 

There are therefore two alternate types of equations in each phase, and for two phases there are three combinations mked-mked, mixed-unmixed, and unmixed-unmixed. If both phases are unmixed, cocurrent and countercurrent give distinctiy different behaviors. These combinations are shown in Figure 12-2. 

Since the O2 concentration remains constant, we do not need to solve a mass-balance equation in the gas phase, and cOCUrrent and countercurrent flows should give the same answer if velocities remain constant. The equation to be solved is therefore... 

The stability problem in the presence of a bounding gas stream (cocurrent and countercurrent) has been considered for a number of special cases (F3, G6, M10, Zl). The countercurrent solutions tend to confirm Benjamin s result that the flow is always inherently unstable on a vertical wall. 

Zhivaikin (Z3) has recently published the results of a detailed investigation of the effects of a gas stream on the film thickness for upward cocurrent, downward cocurrent, and countercurrent flow of the phases over a wide range of flow rates. Thus, downward cocurrent flow is little affected by gas velocities up to about 4 m./sec. For gas velocities between 4 m./sec. and the velocity at which spray formation commences (which has been determined experimentally as a function of the flow rates of gas and liquid and their physical properties), the film thickness is given by... 

The two mass-balance equations (6.28) and (6.29) remain the same for both cases. This is so because the difference between cocurrent and countercurrent flows does not appear in a single lumped stage. It appears in a sequence of stages, or takes the form of a distributed system as will be shown later. 

Adding the equations (6.28) and (6.29) again gives us equation (6.32). By replacing <7 according to relation (6.30) we obtain equation (6.33) as before. As evidenced, there is no difference in the equations for the cocurrent and countercurrent cases. There will be case differences, however, when we consider more than one stage of cocurrent and countercurrent operations or a distributed system. 

The three-stage rotating disk reactor is illustrated in Fig. 30. Each stage consists of one cylindrical and two conical elements and is connected to the next stage by another cylindrical element with a relatively small diameter. Fluid motion and gas dispersion are achieved by a rotating flat plate that contains holes at its outer edge to generate gas bubbles. The reactor can be used for cocurrent and countercurrent flow of gas and liquid or slurry. 

Figure 3.3 Tubular reactor showing cocurrent and countercurrent modes of operation. (The inner rectangle with diagonals represents a bed of catalyst.)...

Cova (3 ) measured the solid concentration profiles of a Raney nickel catalyst with an average diameter of 15.7 ym in a h.6 cm id reactor, using water and acetone as the liquids. He developed a sedimentation diffusion model, assuming solid and liquid dispersion coefficients were equal, and slurry settling velocities were independent of solid concentration. The model was then applied to data for Raney nickel in 6.35 and kk.J cm id bubble columns, in both cocurrent and countercurrent flow. 

Cross-flow monoliths have been explored by Degnan and Wei (11-12) as cocurrent and countercurrent reactor-heat exchangers. Four cross-flow monoliths in series were employed the individual blocks were analyzed by a one-dimensional approximation. They found good agreement between theory and experiment. 

Figure 4.17. Temperature profiles for heat exchangers operated in cocurrent and countercurrent modes.

Applying Eqs. (4.187) and (4.189) for cocurrent and countercurrent operations, we find Cocurrent heat exchanger I ... 

Consider a simple mixer for extraction. In minimal entropy production, size I. time t. and duty J are specified and the average driving force is also fixed. We can also define the flow rate Q and the input concentration of the solute, and at steady state, output concentration is determined. The only unknown variables are the solvent flow rate and composition, and one of them is a decision variable specifying the flow rate will determine the solvent composition. Cocurrent and countercurrent flow configurations of the extractor can now be compared with the... 

One of the most appealing methods for process intensification is the combination of more fimctions in a single unit. Reactive distillation— combining reaction and separation— is a prime example. However, reactive distillation can be applied only for processes in which the temperature window for reaction and separation coincides. In this respect, reactive stripping is more flexible. Another difference between the two is that reactive distillation is limited to countercurrent operation, whereas for reactive stripping both cocurrent and countercurrent operation are possible, because of the low degree of interaction between the two phases in this regime of separation (23). 

Govindarao10 also postulated generalized nonisothermal (constant reactor wall temperature) models for batch as well as cocurrent- and countercurrent-flow three-phase gas-liquid-solid systems carrying out a first-order reaction. 

The cooling fluid is fed at point A or at point B for cocurrent and countercurrent operation, respectively. Next, the reactor temperature profiles from the two modes of operation... 

Same as above, with the exclusion of the surface flow contribution, owing to the high operating temperatures (about 500°C). An analytically solved model is also proposed under the hypothesis of very fast kinetics, which shrink the reaction zone to a surface. Cocurrent and countercurrent operation are considered... 

When the reference plane moves with mean net liquid velocity of -UJii - Cb) (+ indicates cocurrent and - countercurrent), Eq. (4-3) remains valid u, the liquid velocity relative to the moving reference plane, is given from Eqs. (3-15) and (3-17) by setting [/l = 0- This is justified because the net flow term, which defines the moving reference plane, cancels with the net flow term included in the linear velocity term u, [see Eqs. (3-15) and (3-17)]. In what follows in this section we takeu as velocity relative to the moving plane. 

Incremental models track the local conditions of the gas and particles through the dryer, mainly in one dimension. They are especially suit le for cocurrent and countercurrent dryers, e.g., flash (pneumatic conveying) and rotary dryers. The air conditions are usually treated as uniform across the cross-section and dependent only on axial position. This method can also be used to determine local conditions (e.g., temperature) where a simpler model has been used to find the overall drying rate. A two- or three-dimensional grid can also be used, e.g., modeling vertical and horizontal variations in a band dryer or plug-flow fluidized bed. 

---