Continuous equilibrium stage

Figure 1. Continuous equilibrium stage extraction. Solute balances for each phase give ...

Figure 3.35. Information flow diagram for the continuous equilibrium extraction stage.

While offering a more inherently realistic method of solution, however, the technique may cause some additional problems in the numerical solution, since high values of Kl can lead to increased stiffness in the differential equations. Thus in using this technique, a compromise between the approach to equilibrium and the speed of numerical solution may have to be adopted. Continuous single-stage extraction is treated in the simulation example EQEX. Reaction with integrated extraction is demonstrated in simulation example REXT. 

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

This equilibrium-stage concept based on a transfer unit has been proposed for such continuous-contacting devices as, for example, packed towers. 

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... 

Nonequilibrium methods attempt to get around the difficulty of predicting efficiencies by doing away with the equilibrium-stage concept. Instead, they apply a transport phenomena approach for predicting mass transfer rates. The mass transfer rates are calculated continuously along the column length and not in discrete equilibrium stages. This process is similar to the transfer unit concept (Sec. 10.3.1). 

The methods based on the equilibrium stage model have existed for over 30 years and refinements continue, but serious development of nonequilibrium models has begun only recently. These methods are an alternative means to the stage model for predicting column performance. They are expected to make inroads, especially for systems for which stage efficiency prediction is very difficult, such as reactive distillation, chemical absorption, and three-phase distillation. However, their progress into systems where efficiency prediction is well-established is likely to be slower. Their complexity due to the restriction to... 

Solving the NEQ Model Equations In general, a nonequilibrium model of a column has many more equations than does an equivalent equilibrium-stage model. Nevertheless, we use may essentially the same computational approaches to solve the nonequilibrium model equations simultaneous convergence (Krishnamurthy and Taylor, op. cit.) and continuation methods [Powers et al., Comput Chem. Engng., 12, 1229 (1988)]. Convergence of a nonequilibrium model is likely to be slower than that of the equilibrium model because of the greater... 

A liquid mixture of benzene and toluene is to be separated in a continuous single-stage equilibrium flash tank. 

Packed towers are best employed when 3-6 equilibrium stages suffice, there is an interfacial tension of 15 dynes/cm or less, and the desired dispersed-to-continuous phase ratio is between 0.3 and 3. Packed columns provide the advantages of excellent interface control, low dispersed phase hold-up, and potentially high capacity. 

Growth continues until disruptive and growth forces are balanced in the process, similar to a coating stage of growth. This last equilibrium stage of growth represents a balance between dissipation and... 

The plate models assume that the column is divided into a series of an arbitrary number of identical equilibrium stages, or theoretical plates, and that the mobile and the stationary phases in each of these successive plates are in equihbrimn. The plate models are in essence approximate, empirical models because they depict a continuous column of length I by a discrete number of well-mixed cells. Although any mixing mechanism is dearly absent from the actual physical system, plate models have been used successfully to characterize the column operation physically and mathematically. Therefore, by nature, plate models are empirical ones, which cannot be related to first principles. 

Rather than using a continuous model and representing the system in terms of the dispersion model, one may consider each bed as equivalent to a number of theoretical equilibrium stages. A McCabe-Thiele diagram then provides a convenient representation of the system and shows clearly the effects of the process variables [10,30]. 

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