Design variables in distillation

It was shown in Chapter 1 that to carry out a design calculation the designer must specify values for a certain number of independent variables to define the problem completely, and that the ease of calculation will often depend on the judicious choice of these design variables. 

In manual calculations the designer can use intuition in selecting the design variables and, as he proceeds with the calculation, can define other variables if it becomes clear that 

To design the column this number of variables must be specified completely to define the problem, but the same variables need not be selected. 

Typically, in a design situation, the problem will be to determine the number of stages required at a specified reflux ratio and column pressure, for a given feed, and with the product compositions specified in terms of two key components and one product flow-rate. Counting up the number of variables specified it will be seen that the problem is completely defined  

Note specifying (n — 1) component compositions completely defines the feed composition as the fractions add up to 1. 

Feed flow, composition, enthalpy Reflux (sets qc) 

---

Design variables. The principal design variables in a water distillation plant are... 

The economic optimal process flowsheet was obtained by minimization of the total annual cost (TAG) with five design variables IPA distillate composition (XD2) in the recovery column, total number of stages for the heterogeneous azeotropic column and the recovery column (Ni and N2), and the two feed stages (Api and Apa). The product specification of IPA is set to be ultrapure (99.9999 mol%) to be used in the semi-conductor industry. The product specification of water is set to be 99.9 mol%. In each simulation run, the IPA product specification is achieved by varying the reboiler duty of the heterogeneous azeotropic column, and the water product specification is achieved by varying the reboiler duty of the recovery column. The entrainer makeup flowrate will be very small to balance the entrainer loss from the two bottom streams. 

Optimization. Optimi2ation of the design variables is an important yet often neglected step in the design of extractive distillation sequences. The cost of the solvent recovery (qv) step affects the optimi2ation and thus must also be included. Optimi2ation not only yields the most efficient extractive distillation design, it is also a prerequisite for vaUd comparisons with other separation sequences and methods. 

Extensive design and optimization studies have been carried out for this sequence (108). The principal optimization variables, ie, the design variables that have the largest impact on the economics of the process, are the redux ratio in the azeo-column the position of the tie-line for the mixture in the decanter, determined by the temperature and overall composition of the mixture in the decanter the position of the decanter composition on the decanter tie-line (see Reference 104 for a discussion of the importance of these variables) and the distillate composition from the entrainer recovery column. 

In Table 13-6, the number of design variables is summarized for several distillation-type separation operations, most of which are shown in Fig. 13-7. For columns not shown in Figs. 13-1 or 13-7 that... 

Example 3 Calculation of TG Method The TG method will he demonstrated hy using the same example problem that was used above for the approximate methods. The example column was analyzed previously and found to have C -I- 2N + 9 design variables. The specifications to be used in this example were also hstedat that time and included the total number of stages (N = 10), the feed-plate location (M = 5), the reflux temperature (corresponding to saturated liquid), the distillate rate (D = 48.9), and the top vapor rate (V = 175). As before, the pressure is uniform at 827 kPa (120 psia), but a pressure gradient could be easily handled if desired. 

Though the total degrees of freedom is seen to be (C + 4) some of the variables will normally be fixed by general process considerations, and will not be free for the designer to select as design variables . The flash distillation unit will normally be one unit in a process system and the feed composition and feed conditions will be fixed by the upstream processes the feed will arise as an outlet stream from some other unit. Defining the feed fixes (C + 2) variables, so the designer is left with ... 

If the composition (or flow-rate) of one stream is fixed by internal or external constraints, this may fix the composition and flows of other process streams. In Chapter 1, the relationship between the process variables, the design variables and design equations was discussed. If sufficient design variables are fixed by external constraints, or by the designer, then the other stream flows round a unit will be uniquely determined. For example, if the composition of one product stream from a distillation column is fixed by a product specification, or if an azeotrope is formed, then the other stream composition can be calculated directly from the feed compositions see Section 2.10. The feed composition would be fixed by the outlet composition of the preceding unit. 

Transformed concentration variables were first introduced by Doherty and co-workers [2, 41] for the steady-state design of reactive distillation processes. In the... 

In this problem, there are 3 outer loop decision variables, N and the recovery of component 1 from each mixture (Re1 D1B0, Re D2,BO)- Two time intervals for reflux ratio were used for each distillation task giving 4 optimisation variables in each inner loop optimisation making a total of 8 inner loop optimisation variables. A series of problems was solved using different allocation time to each mixture, to show that the optimal design and operation are indeed affected by such allocation. A simple dynamic model (Type III) was used based on constant relative volatilities but incorporating detailed plate-to-plate calculations (Mujtaba and Macchietto, 1993 Mujtaba, 1997). The input data are given in Table 7.3. 

The first three are intensive variables. The fourth is an extensive variable that is not considered in the usual phase rule analysis. The fifth is neither an intensive nor an extensive variable but is a siugle degree of freedom that the designer uses in specifying how often a particular element is repeated in a unit. For example, a distillation column section is composed of a series of equilibrium stages, and when the designer specifies the number of stages that the section contains. 

Tphis work explores the important variables which must be considered - to design an extractive distillation process. The discussion identifies the economic effects of these variables and their possible interactions. Some of the design variables may have synergistic effects in terms of separation cost while others may not. As a result, the optimum design for an economic extractive distillation process must be a compromise set of values for the different process variables. These compromises are discussed and are illustrated for a particular case—i.e., separation of propane-propylene mixtures. For this commercially important separation fractional distillation is most often used, regardless of the low relative volatility (about 1.13-1.19 at 200 psia). 

---