Separation calculations multistage

Multistage separation calculations require heat balances involving transition between the phases. The enthalpy balance equations must, therefore, include heats of vaporization and condensation. Usually these heats are not calculated separately but are implied by using appropriate methods for calculating liquid enthalpies and vapor enthalpies. Consider, for instance, a system where a vapor stream and a liquid stream enter with enthalpies and / respectively, and leave as a mixed phase stream with vapor enthalpy H2 and liquid enthalpy h2- These are total stream enthalpy rates with units such as Btu/hr. If no heat is added to or removed from the system, a heat balance is written as... 

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. 

In rate-based multistage separation models, separate balance equations are written for each distinct phase, and mass and heat transfer resistances are considered according to the two-film theory with explicit calculation of interfacial fluxes and film discretization for non-homogeneous film layer. The film model equations are combined with relevant diffusion and reaction kinetics and account for the specific features of electrolyte solution chemistry, electrolyte thermodynamics, and electroneutrality in the liquid phase. 

To simulate multistage separation processes with reactions, the reaction equations must be included in the model equations. The component balances. Equation 13.2 or 13.49, will include an additional term that represents the rate of generation or disappearance of components by kinetic reactions. Another equation is included in the model to represent composition changes due to equilibrium reactions. The kinetic reaction rate is calculated by a power law expression. A holdup term is computed... 

The prediction of the performance of three-phase multistage separation processes is dependent on the ability to describe the thermodynamics of three-phase behavior. The mathematical solution of three-phase distillation columns is similar to two-phase vapor-liquid columns, the difference being in the model used to calculate the /(-values. If the A -valuc model predicts two liquid phases, two liquid profiles must be considered in the column instead of one. 

Extraction Calculations by Triangular Diagrams Approximate Methods for Multicomponent, Multistage Separations... 

The model equations (discussed in Sect. 2.1.3) are used as the basis for the design of a multistage separation system where the separation driving force is electromagnetic (Fig. 3). In staged magnetic separation, the final distribution of separands can be calculated from a simple relationship involving the number of transfers and the equivalent of a partition coefficient, K, defined as the ratio of upper and lower compartment concentrations. 

Flash vaporization and multistage distillation calculation methods have been shown to be adaptable to membrane separations, which indicates the degree of separation that can be achieved. Furthermore, the use of multistage or cascade operations enhances the sharpness of separation and can be used to separate components with low relative selectivity. 

Table A4.1 Excel Spreadsheet Designators and Formulas for Multistage Membrane Separations Calculations ...

Techniques used in steady-state flash vaporization calculations and multistage distillation calculations can be utilized to show that membrane separations are enhanced by the use of cascade or multistage operations. This is of importance particularly in the use of membrane materials showing low selectivity between the components to be separated. 

The calculation of multistage separation processes involves the solution of phase equilibrium relationships, mass balances, and energy balances. Energy balances require the computation of enthalpies of streams entering and leaving an equilibrium stage. The enthalpy is a function of state, defined in Section 1.1.2 as H = f/ + PV. It is a function of the stream composition, its temperature, and its pressure. 

The crude oil vapor pressure will be the same as the pressure of the final flash calculation. Assuming this is a stock-tank at 14.7 psia (101.4 kPa) and 100 °F (37.8 °C), then the vapor pressure is 14.7 psia (101.4 kPa). If a sales product vapor pressure less than 14.7 psia (101.4 kPa) is necessary and multistage separators are used, the crude may require heating above 100 °F (37.8 °C) prior to entering the low-pressure separator. 

Although the most useful extraction process is with countercurrent flow in a multistage battery, other modes have some application. Calculations may be performed analytically or graphically. On flowsketches like those of Example 14.1 and elsewhere, a single box represents an extraction stage that may be made up of an individual mixer and separator. The performance of differential contactors such as packed or spray towers is commonly described as the height equivalent to a theoretical stage (HETS) in ft or m. 

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