Steady-State Countercurrent Operation

Based on the principle of countercurrent flow presented in Chapter 1.1, steady-state countercurrent flow operations are generally discussed in the following section. 

The separation of a mixture in a single stage does not normally separate the mixture into fractions of the required purity. To increase the separation effect, single stages may be connected to form a cascade (Fig. 1-50). A cascade is a separation device consisting of several similar stages, or several separation units connected in series. 

For the design of countercurrent flow columns, essentially two theories are used, 

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To develop the performance equation, we combine the rate equation with the material balance. Thus for steady-state countercurrent operations we have for a differential element of volume... 

The program BIOFILT solves the steady-state countercurrent biofiltration operation for MEK removal. The integration is started at the top of the column by assuming a desired concentration in the outlet air. The required column length is determined when the inlet gas concentration exceeds the actual inlet value. 

A steady-state, countercurrent, staged distillation column is to be used to separate ethanol from water. The feed is a 30 wt % ethanol, 70 wt % water mixture at 40°C. Flow rate of feed is 10,000 kg/h. The column operates at a pressure of 1 kg/cm. The reflux is returned as a saturated liquid. A reflux ratio of L7D = 3.0 is being used. We desire a bottoms composition of Xq = 0.05 (weight fraction ethanol) and a distillate composition of x = 0.80 (weight fraction ethanol). The system has a total condenser and a partial reboiler. Find D, B, Q, and Qr. 

Two basic approaches can be adopted for using fixed beds to simulate the operation of moving beds. In the first, multiple fixed beds are used in cascade, as shown in Figure 5.12 (and described later in Section 7.7.1) to gain most of the benefit of a continuous steady state countercurrent process. The concept is similar to that used in the pulsed bed. At each switch in the cascade a fully regenerated bed is added to the outlet end of a sequence of beds in series when breakthrough is about to occur. At the same time the... 

Use of Operating Curve Frequently, it is not possible to assume that = 0 as in Example 2, owing to diffusional resistance in the liquid phase or to the accumulation of solute in the hquid stream. When the back pressure cannot be neglected, it is necessary to supplement the equations with a material balance representing the operating line or curve. In view of the countercurrent flows into and from the differential section of packing shown in Fig. 14-3, a steady-state material balance leads to the fohowing equivalent relations ... 

Although the continuous-countercurrent type of operation has found limited application in the removal of gaseous pollutants from process streams (Tor example, the removal of carbon dioxide and sulfur compounds such as hydrogen sulfide and carbonyl sulfide), by far the most common type of operation presently in use is the fixed-bed adsorber. The relatively high cost of continuously transporting solid particles as required in steady-state operations makes fixed-bed adsorption an attractive, economical alternative. If intermittent or batch operation is practical, a simple one-bed system, cycling alternately between the adsorption and regeneration phases, 1 suffice. 

The conditions existing in a column during the steady state operation of a countercurrent process are shown in Figure 10.9. The molar rates of flow of the two streams are G and (j3, which will be taken as constant over the whole column. Suffixes 1 and 2 denote the two phases, and suffixes t and b relate to the top and bottom of the column. 

Example 6.4 Wetted wall column with a ternary liquid mixture We have the experimental data on distillation of ethanol (1), feri-butanol (2), and water (3) in a wetted wall column reported by Krishna and Standard (1976). As Figure 6.2 shows, the column operates at total reflux with countercurrent flow. Therefore, at steady state, the compositions of the liquid and vapor phases at ary point in the column are equal to each other. The measured compositions of the phases at the bottom are... 

The second issue for cooled tubular reactors is how to introduce the coolant. One option is to provide a large flowrate of nearly constant temperature, as in a recirculation loop for a jacketed CSTR. Another option is to use a moderate coolant flowrate in countercurrent operation as in a regular heat exchanger. A third choice is to introduce the coolant cocurrently with the reacting fluids (Borio et al., 1989). This option has some definite benefits for control as shown by Bucala et al. (1992). One of the reasons cocurrent flow is advantageous is that it does not introduce thermal feedback through the coolant. It is always good to avoid positive feedback since it creates nonmonotonic exit temperature responses and the possibility for open-loop unstable steady states. 

One further note, the University of Delaware gasifier model used in the pseudo steady state approximation assumes that the gas and solids temperatures are the same within the reactor. That assumption removes an important dynamic feedback effect between the countercurrent flowing gas and solids streams. This is particularly important when the burning zone moves up and down within the reactor in an oscillatory manner in response to a step change in operating conditions. 

The principle of operation can be best described with reference to the equivalent true countercurrently moving bed (TCC) configuration. Since the two configurations are equivalent, i.e they achieve the same separation performance provided the geometric and kinematic conversion rules are fulfilted, the simpler model of the equivalent TCC unit can be used to predict the steady state separation performances of SMB units, in particular, for design purposes. 

The transient behavior of a continuous countercurrent multicomponent system was considered in detail by Rhee, Aris and Amimdson [22,23] from the perspective of the equilibrium theory, i.e., assuming that axial dispersion and the mass transfer resistances are negligible and that equilibrium is established everywhere, at every time along the colinnn. The final steady-state predicted by the equilibrium theory is simply a uniform concentration throughout the colimm, with a transition at one end or the other. Therefore, the equilibriinn theory analysis is of lesser practical value for a coimtercurrent system, which normally operates rmder steady-state conditions, than for a fixed-bed (i.e., an SMB) system, which normally operates under transient conditions. The equilibrium theory analysis, however, reveals that, under different experimental conditions, several different steady-states are possible in a coimtercurrent system. It shows how the evolution of the concentration profiles may be predicted in order to determine which state is obtained in a particular case. 

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