Distillation mass balance problem

Figure 1 Distillation process mass balance problem...

First, pseudocomponents determined by the quadrature method may well be unrealistic ones for instance, if the label x is (proportional to) the number of carbon atoms, pseudocomponents may well correspond to noninteger jcjc values. This may be aesthetically unpleasant, but it does not represent a real problem. More seriously, the appropriate pseudocomponents obviously depend on the composition and, hence, in a repeated calculation such as is required in a distillation tower, pseudocomponents will need to be different at each step. This puts out of tilt the mass balance equations that are coupled to the equilibrium ones, and, even if this problem could be circumvented (as, at least in principle, it can), the procedure would certainly not be applicable to existing software for distillation column calculations. 

If one or more unit operations have been given infeasible specifications, then the flowsheet will never converge. This problem also occurs with multicomponent distillation columns, particularly when purity specifications or flow rate specifications are used, or when nonadjacent key components are chosen. A quick manual mass balance around the column can usually determine whether the specifications are feasible. Remember that all the components in the feed must exit the column somewhere. The use of recovery specifications is usually more robust, but care is still needed to make sure that the reflux ratio and number of trays are greater than the minimum required. A similar problem is encountered in recycle loops if a component accumulates because of the separation specifications that have been set. Adding a purge stream usually solves this problem. 

Equation (12.52) for batch distillation is the same as the mass balance equation for continuous distillation except for the term on the left side of the eqnation, which is normally zero for continuous distillation. Thus, it is theoretically possible to employ the same approach for batch distillation as previously presented for continnons distillation, provided an accnmnlation term is introdnced. However, although apparently simple, it is actually very difficult in practice becanse of problems in solving the many simnltaneons differential eqnations involved. In any event, it is erroneons to neglect tray and column holdnp in stage compntations for batch distillation. 

For binary flash distillation, the simultaneous procedure can be conveniently carried out on an enthalpy-composition diagram First calculate the feed enthalpy, hp, from Eq. t2-81 or Eq. (2=9b) then plot the feed point as shown on Figure 2-9 (see Problem 2-All. In the flash drum the feed separates into liquid and vapor in equilibrium Thus the isotherm through the feed point, which must be the T nun isotherm, gives the correct values for x and y. The flow rates, L and V, can be determined from the mass balances, Eqs. f2-51 and 2-61. or from a graphical mass balance. 

Now, how do we conpletely solve the external mass balances The unknowns are B, D, X2 X3 %,bot> %,bof There are six unknowns and five independent equations. Can we find an additional equation Unfortunately, the additional equations (energy balances and equilibrium expressions) always add additional variables (see Problem 5-Al), so we cannot start out by solving the external mass and energy balances. This is the first major difference between binary and multiconponent distillation. 

In Section 2.7 we looked at solution methods for multiconponent flash distillation. The questions asked in that section are again pertinent for multiconponent distillation. First, what trial variables should we use As noted, because N and Np are required to set up the matrices, in design problems we choose these and solve a number of simulation problems to find the best design. We select the tenperature on every stage Tj because tenperature is needed to calculate K values and enthalpies. We also estimate the overall liquid Lj and vapor Vj flow rates on every stage because these flow rates are needed to solve the conponent mass balances. 

Process Technology 2—Systems—study of common process systems found in the chemical process industry, including related scientific principles. Includes study of pump and compressor systems, heat exchangers and cooling tower systems, boilers and furnace systems, distillation systems, reaction systems, utility system, separation systems, plastics systems, instrument systems, water treatment, and extraction systems. Computer console operation is often included in systems training. Emphasizes scale-up from laboratory (glassware) bench to pilot unit. Describe unit operation concepts solve elementary chemical mass/energy balance problems interpret analytical data and apply distillation, reaction, and fluid flow principles. 

Number of products Number of products can change from 2 to 5. This classification is considered because the single column configurations and models do not consist of mass balances for the connection of distillation columns, thus these models cannot be used for three or more products problems. 

This example is different in nature from those represented by the grid in Figure 8.1 and illustrated in Examples 8.1 and 8.2. It couples a species mass balance to the VLE phase equilibrium problem. Such calculations are representative of the type encountered in design and analysis of separations processes such as distillation. 

Computer solutions entail setting up component equiUbrium and component mass and enthalpy balances around each theoretical stage and specifying the required design variables as well as solving the large number of simultaneous equations required. The expHcit solution to these equations remains too complex for present methods. Studies to solve the mathematical problem by algorithm or iterational methods have been successflil and, with a few exceptions, the most complex distillation problems can be solved. 

While we laud the virtue of dynamic modeling, we will not duphcate the introduction of basic conservation equations. It is important to recognize that all of the processes that we want to control, e.g. bioieactor, distillation column, flow rate in a pipe, a drag delivery system, etc., are what we have learned in other engineering classes. The so-called model equations are conservation equations in heat, mass, and momentum. We need force balance in mechanical devices, and in electrical engineering, we consider circuits analysis. The difference between what we now use in control and what we are more accustomed to is that control problems are transient in nature. Accordingly, we include the time derivative (also called accumulation) term in our balance (model) equations. 

Take a mixture of two or more chemicals in a temperature regime where both have a significant vapor pressure. The composition of the mixture in the vapor is different from that in the liquid. By harnessing this difference, you can separate two chemicals, which is the basis of distillation. To calculate this phenomenon, though, you need to predict thermodynamic quantities such as fugacity, and then perform mass and energy balances over the system. This chapter explains how to predict the thermodynamic properties and then how to solve equations for a phase separation. While phase separation is only one part of the distillation process, it is the basis for the entire process. In this chapter you will learn to solve vapor-liquid equilibrium problems, and these principles are employed in calculations for distillation towers in Chapters 6 and 7. Vapor-liquid equilibria problems are expressed as algebraic equations, and the methods used are the same ones as introduced in Chapter 2. 

Operating Line and "Equilibrium" Curve. Both terms are of importance for the graphical solution of a separation problem, i.e., for the graphical determination of the number of stages of a cascade. This method has been developed for the design of distillation columns by MacCabe and Thiele and should be well known. For all cases, the operating line represents the mass and material balances. In distillation, the equilibrium curve represents the thermodynamical va-por/liquid equilibrium. For an ideal binary system, the equilibrium curve can be calculated from Raoult s law and the saturation-pressure curves of the pure components of the mixture. In all other cases, however, for example, for all membrane processes, the equilibrium curve does not represent a thermodynamical equilibrium at all but will represent the separation characteristics of the module or that of the stage. 

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