Continuous flow equilibrium stage

The extraction is represented by a single perfectly mixed constant volume, continuous flow equilibrium stage. This may actually consist of separate mixer-settler units. 

The important question for the designer of a continuous countercurrent extraction process is how many equilibrium stages are needed, given the flow rates and inlet and outlet concentrations A simple graphical procedure is possible for a single-solute extraction when the two... 

Absorption takes place in either staged or plate towers or continuous or packed contactor. However, in both cases the flow is continuous. In the ideal equilibrium stage model, two phases are contacted, well mixed, come to equilibrium, and then are separated with no carryover. Real processes are evaluated by expressing efficiency as a percentage of the change that would occur in the ideal stages. Any liquid carryover is removed by mechanical means. 

Estimate the diameter and height of an RDC to extract acetone from a dilute toluene-acetone solution into water at 293 K. The flow rates for the dispersed organic and continuous aqueous phases are 12,250 and 11,340 kg/h, respectively. The density of the organic phase is 858 kg/m3 and that of the aqueous phase is 998 kg/m3. For the desired degree of separation, 12 equilibrium stages are required. 

Single-stage, batch or continuous separation steps in multiphase systems can only lead to near-complete separations when the partition (or distribution) coefficients of the components over the various phases are sufficiently different. Because of the common structural similarity of main products and contaminants, this is usually not the case. The key parameter is the so-called separation factor S (Fig. 3). Assuming thermodynamic equilibrium between outlet flows of a single equilibrium stage, the separation factor S relates performance to the ratio of auxiliary flow (V) and feed flow (L) and the distribution coefficient of the... 

Continuous-contact operations are diametrically different from staged operations in almost every aspect. The two phases are in continuous flow and in continuous contact with each other, rather than repeatedly separated and re-contacted in an array of stages. Second, the attainment of equilibrium is shunned. An active driving force is maintained at all times and its constituent concentrations vary continuously from the point of entry to the exit. The result is that the concentrations are now distributed in space and, assuming a normal steady-state operation, are invariant in time. Thus, while staged operations vary at most with time, but not at all with distance, the exact opposite holds in continuous-contact operations. 

Eckert further showed that the packed depth necessary to achieve an equilibrium stage of mass transfer decreased only slightly with an increase in the continuous-phase velocity when this rate was greater than 80 ft/h. However, he found a small increase in the depth required to achieve an equilibrium stage with an increase in the dispersed phase velocity. Sherwood has postulated that at low rates the interfacial area increases with the dispersed phase flow rate while at higher rates the interfacial area attains a nearly constant value [20]. 

Grbber [33] computed the approach to equilibrium temperature of spherical particles immersed in an agitated fluid of constant temperature. Since the concentration of the solution in a well-stirred vessel in continuous flow is essentially uniform throughout at the effluent value, Grober s result can be adapted to cocurrent adsorption through the heat- mass-transfer analogy, as in Fig. 11.27. Here the approach of the particles to equilibrium concentration with the effluent liquid is expressed as the Muiphree stage efficiency,... 

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