Composition shortcut calculation

Example 1 Shortcut Calculation, Case A Consider a 100-kg/h feed stream containing 20 wt % acetic acid in water that is to be extracted with 200 kg/h of recycle MIBK that contains 0.1 wt % acetic acid and 0.01 wt % water. The aqueous raffinate is to be extracted down to 1% acetic acid. How many theoretical stages will be required and what will the extract composition be The equilibrium data for this system are listed in Table 15-8 (in units of weight percent). The corresponding Hand plot is shown in Fig. 15-20. The Hand correlation (in mass ratio units) can be expressed as Y = 0.930(X ) °, for X between 0.03 and 0.25. 

In many cases, shortcut calculations can fill in the gaps. An example used in Kenney s book (Kenny, 1984) gives good illustration for how to do it Consider the tower in Figure 13.2. As for many plants, cooling water rates are not measured and overhead product comes off on level control. However, since feed rate and composition and overhead product composition are known, much of the missing data can be derived by energy and mass balances. 

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. 

The Colburn method (39) This method calculates the minimum reflux ratio of the key components as if they formed a binary system, then corrects this value for light and heavy nonkeys. The Colburn method assumes constant molar overflow and constant relative volatility in each zone of constant composition in the column. This method is more elaborate, but has been recommended (28) as probably the most accurate shortcut method for minimum reflux. 

The shortcut model is developed in terms of reduced parameters that are not strongly dependent on stream compositions, temperature, and pressure. The shortcut model, represented by Equations 12.33 through 12.37b, is solved in conjunction with reduced equations for calculating enthalpies, vapor-liquid equilibrium coefficients, and effective stripping factors based on the rigorous base case. 

The enthalpies, which in the rigorous model are generally calculated by compositional methods appropriate to the mixture under consideration, are expressed in the shortcut model as a linear function of temperature only ... 

To begin the calculations the column variables must be first initialized to some estimated values. Simple methods can be used for this purpose, based on the column specifications and possibly supplemented by shortcut methods. The column temperature profile may be assumed linear, interpolated between estimated condenser and reboiler temperatures. The values for Lj and Vj may be based on estimated reflux ratio and product rates, assisted by the assumption of constant internal flows within each column section. The compositions Xj- and T, may be assumed uniform throughout the column, set equal to the compositions of the liquid and vapor obtained by flashing the combined feeds at average column temperature and pressure. The other variables to be initialized are Rf,Rj, and Sj, which are calculated from their defining equations. The values for Qj may either be fixed at given values (zero on most stages) or estimated. 

If the distillation were to be started at twice the minimum reflux ratio, determine the required number of stages. If the initial charge is 100 kmol and the distillate rate is 10 kmol/h, calculate the reflux rate, the amounts of distillate and residue, and the residue composition as a function of time. Irrespective of tray hydraulics and reboiler and condenser capacity constraints, when should the distillation be stopped Assume negligible tray holdups and use shortcut methods. 

Shortcut methods for handling multicomponent batch distillation have been developed for the two cases of constant reflux and constant distillate composition (Diwekar and Mandhaven, 1991 Sundaram and Evans, 1993). Both methods avoid tedious stage-by-stage calculations of vapor and liquid compositions by employing the Fenske-Underwood-Gilliland (FUG) shortcut procedure for continuous distillation, described in Section 6.8, at succesive time steps. In essence, they treat batch distillation as a sequence of continuous, steady-state rectifications. As in the FUG method, no estimations of compositions or temperatures are made for intermediate stages. 

Table 1 shows the differences between nf and n and 9, and for binary adsorption of CO2 (component 1) + CH4 (component 2) mixtures on BPL carbon at soil K [13]. They were estimated at three different total gas pressure levels and at different gas-phase compositions. The table also gives the fractional adsorbate loadings (6,) of the components [0 — nT(P, T, y,)/w]. m is the saturation capacity (surface excess) for both components. The pure and binary gas adsorption isotherms for this system can be described by the Langmuir model [17]. The model parameters are given in Table 1. A value of 0.80cm /g was used as for these calculations. It can be seem from Table 1 that the differences between nf and are relatively small because CO2 (component 1) is more selectively adsorbed than CH4 on the carbon. The differences between n and 2 are, however, much larger. Furthermore, the differences between qi and q, are much larger than the corresponding differences between and. The differences between qi and qi get even bigger as the system pressure P) and the mole fraction of component 1 (y) in the gas phase are increased. These examples demonstrate the weakness of the shortcut method.

Using shortcut method in PRO/II, Peng-Robinson EOS is used as a suitable property package. Process flowsheet and the product streams molar flow rates and compositions are shown in Figure 6.50. The summary of the Underwood calculations is shown in Figure 6.51. The minimum reflux ratio is 1.567, the minimum number of trays is 11 and the actual number of stages is 16 trays. Values are close to hand calculation results. 

Sebastian , E. Method speeds up calculation of phase composition. Chem. Engng. Calculation and Shortcut Deskbook. ... 

---