Kremser equations for stage

The stages are determined by combining the McCabe-Thiele graphical construction, for a suitable region in the middle, with the Kremser equations for the low and/or high ends, where absorption and stripping factors are almost constant. 

For mixer-settlers and centrifogal contactors, it is useful to define an ovradl stage efficiency relative to the Kremser equations. For ethanol extraction from dilute aqueous mixtutes, Tawfik obtained the following empiricd, overall efficiency corrdation for miniature mixer-settlets ... 

Here we make use of the fact that for systems with linear equilibria, an analytical expression can be derived that relates the number of stages to the operating parameters. That expression is known as the Kremser-Souders-Brown equation (or Kremser equation for short), and is given by... 

For the first time through a liqmd-liquid extrac tion problem, the right-triangular graphical method may be preferred because it is completely rigorous for a ternary system and reasonably easy to understand. However, the shortcut methods with the Bancroft coordinates and the Kremser equations become valuable time-savers for repetitive calculations and for data reduction from experimental runs. The calculation of pseudo inlet compositions and the use of the McCabe-Thiele type of stage calculations lend themselves readily to programmable calculator or computer routines with a simple correlation of equilibrium data. 

In countercurrent operation of several stages in series, feed enters This is of the same form as the Kremser-Brown equation for gas the first stage and final extract leaves it, and fresh solvent enters the... 

The concept of a mass-transfer unit was developed many years ago to represent more rigorously what happens in a differential contactor rather than a stage wise contactor. For a straight operating line and a straight equilibrium line with an intercept of zero, the equation for calculating the number of mass-transfer units based on the overall raffinate phase Nor is identical to the Kremser equation except for the denominator when the extraction factor is not equal to 1.0 [Eq. (15-23)]. 

The calculation procedure in Table 6.22 could also be used for a multi-component mixture. After calculating the number of stages for separating the key component from the mixture, then the composition of all other components in the exit stream can be calculated using the Kremser equation, Equation 6.21.5A for absorbers or 6.21.5S for strippers. 

A multi-component countercurrent extractor model may be delined for the shortcut column section method in a manner very similar to the vapor-liquid model. The extractor model is developed for liquid-liquid equilibrium stages leading to component flow relationships comparable to the Kremser equation ... 

An alternative method for the design of an absorption or stripping column is based on the modular group method (Kremser equation, 12.33), primarily for dilute mixtures. The required number of stages for a specified separation is first determined. Once this is known, the packing height can be estimated from the relation... 

Derive the Kremser equation. Equation (3.49). Refer to Figure 3.27 for a diagram of the equilibrium-stage process. 

The number of stages required for a specified amount of absorption may be calculated from the Kremser-Brown equation with stages numbered down from the top of the column ... 

The Kremser equation and its various modified forms consider only the number of theoretical plates, sot the number of actual plates in absorbers and strippers. For cases where the Murphree stage efficiency is known and relatively constant over the length of the tower, a correlation proposed by Nguyen can be used to estimate the total required number of actual plates NT as follows ... 

When D is constant, equations for the number of stages can be outlined by applying the Kremser equation (4.45) derived in Sec. 6.2. For the extracting section the appropriate flow ratio is E (F + S), and the extraction factor / is... 

This is the general equation for the number of theoretical stages needed in exchange columns. It is a form of the Kremser [K5, S5] equation, derived originally for gas absorption. 

For comparison purposes, we tried to estimate the number of ideal stages using the Kremser equations. By least-squares analysis, a straight line through the origin was fitted to the equilibrium data in the range of A between 0 and 0.6, giving a slope... 

To estimate the number of theoretical stages required, NTS, the Kremser-Sou-ders-Brown equations may be used. (The Kremser equation assumes that the operating and equilibrium lines are straight, the systems are nonreacting and that the concentrations are dilute (that is < 10%). These are reasonable assumptions for many absorptions.) The key parameter is the ratio of the product of the molar equilibrium constant m (as in y = mx ) with the molar gas flowrate divided by the molar liquid flowrate, = molar stripping factor = fnpG)/Pi = S. 

Equation (12-12) is a special case of the Kremser equation. When this equation is applicable, absorption and stripping problems can be solved quite sinple and accurately without the need for a stage-by-stage calculation. 

Bl. The Kremser equation can be used for more than just determining the number of stages. List as many types of problems (where a different variable is solved for) as you can. What variables would be specified How would you solve the equation ... 

All extraction systems are partially miscible to some extent. When partial miscibility is very low, as for toluene and water, we can treat the system as if it were conpletely immiscible and use McCabe-Thiele analysis or the Kremser equation. When partial miscibility becomes appreciable, it can no longer be ignored, and a calculation procedure that allows for variable flow rates must be used. In this case a different type of stage-by-stage analysis, which is very convenient for ternary systems, can be used. For multiconponent systems, corrputer calculations are required. 

C5. Single-stage systems (N = 1) can be designed as countercurrent systems, Figure 13-4. or as cross-flow systems, Figure 13-9. Develop the methods for both these designs. Which is easier If the system is dilute, how can the Kremser equation be used ... 

It is of interest to compare the predictions of the dispersed plug flow model with those of the discrete equilibrium stage model for a countercurrent system. For a linear equilibrium the dimensionless effluent concentration ( = Cy / Cq) for a system of N countercurrent equilibrium stages is given by the familiar Kremser equation ... 

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