Single-Stage Calculations

According to the phase rule, a three-component, two-phase system has three degrees of freedom. Thus, by specifying the temperature, pressure, and concentration of one component in one phase, the state of the system is defined. The component concentration in one phase defines one point on the equilibrium curve, and this point marks one end of a tie line. The other end is determined thermodynamically either from experimental data or on the basis of liquid activity coefficient predictions methods. 

Since all points on a tie line have the same temperature, pressure, component concentration in one phase, and component concentration in the other phase, one more variable must be specified to define the relative amounts of the phases at equilibrium. The specihed variable could itself be either the fraction of one phase out of the total or the mixture composition. Note that only two component concentrations are independent in a ternary. In the single-phase region there are four degrees of freedom according to the phase rule. Therefore, if the fraction of one phase or whether one or two phases exist is unknown, four independent variables must be specihed to completely dehne the system. 

In order to use the equilateral triangular phase diagram to calculate a single-stage 

The tie line through M together with an overall material balance determines the 

A single-stage extractor is used to extract component E from a feed stream. The feed and solvent stream compositions and flow rates are as follows  

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The same analysis can be repeated for precision. From the analysis in Sect. 6.4.2, we have (for a single-stage calculation)... 

There are three independent variables in coexisting equilibrium vapor/liquid systems, namely temperature, pressure, and fraction liquid (or vapor). If two of these are specified in a problem, the third is determined by the phase behavior of the system. There are seven types of vapor/liquid equilibria calculations in our program, as in Figure 1 under "Single Stage Calculation."... 

The presentation of equilibrium-stage calculation techniques is preceded by Chapter 6, which covers an analysis of the variables and the equations that relate the variables so that a correct problem specification can be made. Single-stage calculation techniques are then developed in Chapter 7, with emphasis on so-called isothermal and adiabatic flashes and their natural extension to multistage cascades. 

We note that there is but a slight dependence between the values of (L/D)min and E/D. This allows us to confine ourselves to the single-stage calculation of (L/D)min and to use the same series of values of L/D at different values of... 

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. 

The simplest continuous-distillation process is the adiabatic single-stage equihbrium-flash process pictured in Fig. 13-25. Feed temperature and the pressure drop across the valve are adjusted to vaporize the feed to the desired extent, while the drum provides disengaging space to allow the vapor to separate from the liquid. The expansion across the valve is at constant enthalpy, and this facd can be used to calculate To (or T to give a desired To). 

Calculate the suction capacity, horsepower, discharge temperature, and piston speed for the following single-stage double acting compressor. 

An average value is about 0.55 for the coefficient, p. Peripheral velocities will usually vary between 600-900 ft/sec however, this varies with the gas being compressed and may run up to 1,100 ft/sec. The results of this head calculation will give values of 8,000-12,000 ft for a single stage. From this value, the total number of stages in the compressor can be approximated. 

The calculation procedure for single-stage noncondensing general-purpose turbine is as follows ... 

HA A single-stage double-acting compressor running at 3 Hz is used to compress air from 110 kN/irr and 382 K to 1150 kN/nr. If the internal diameter of the cylinder is 20 cm, the length of stroke 25 cm and the piston clearance 5%, calculate (a) the maximum capacity of the machine, referred to air at the initial temperature and pressure, ami power requirements under isentropic conditions. 

Assume that 1 kmol of gas occupies 22.4 m3 at standard temperature and pressure (STP). For stage-cut fractions from 0.1 to 0.9, calculate the purity of hydrogen in the permeate, the membrane area and the fractional hydrogen recovery for a single-stage membrane. 

When the VOC-laden gas stream contains a mixture of VOCs, then the calculations must be performed using the methods described for single-stage equilibrium calculations in Chapter 4. The temperature at the exit of the condenser must be assumed, together with a condenser pressure. The vapor fraction is then solved by trial and error using the methods described in Chapter 4, and the complete mass balance can be determined on the basis of the assumption of equilibrium. 

Consider a single-stage FEP calculation with system 0 as the reference. For the situation illustrated in Fig. 6.1a, where T lies inside the T0, configurations in / are... 

Calculate the theoretical work required to compress 1 kg of a diatomic ideal gas initially at a temperature of 200 K adiabatically from a pressure of 10000 Pa to a pressure of 100000 Pa in (i) a single stage, (ii) a compressor with two equal stages and (iii) a compressor with three equal... 

The purity of the final product in a single-stage (ultra-short) column is defined through the separation factor calculated as ... 

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