Uses for

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6. 

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

This chapter presents a general method for estimating nonidealities in a vapor mixture containing any number of components this method is based on the virial equation of state for ordinary substances and on the chemical theory for strongly associating species such as carboxylic acids. The method is limited to moderate pressures, as commonly encountered in typical chemical engineering equipment, and should only be used for conditions remote from the critical of the mixture. 

Numerous empirical equations of state have been proposed but the theoretically based virial equation (Mason and Spurling, 1969) is most useful for our purposes. We use this equation for systems which do not contain carboxylic acids. 

In this monograph we use for g the UNIQUAC model of Abrams (1975) as slightly modified by Anderson (1978)... 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

In most cases only a single tie line is required. When several are available, the choice of which one to use is somewhat arbitrary. However, our experience has shown that tie lines which are near the middle of the two-phase region are most useful for estimating the parameters. Tie lines close to the plait point are less useful, since no common models for the excess Gibbs energy can adequately describe the flat region near the... 

For multicomponent VLE, the method used for obtaining binary parameters is of some, but not crucial, importance. Provided that the binary parameters give good representation of the binary data, good multicomponent results are usually obtained... 

However, some ternary data may be useful for fixing binary parameters. 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

The sum of the squared differences between calculated and measures pressures is minimized as a function of model parameters. This method, often called Barker s method (Barker, 1953), ignores information contained in vapor-phase mole fraction measurements such information is normally only used for consistency tests, as discussed by Van Ness et al. (1973). Nevertheless, when high-quality experimental data are available. Barker s method often gives excellent results (Abbott and Van Ness, 1975). 

The maximum-likelihood method, like any statistical tool, is useful for correlating and critically examining experimental information. However, it can never be a substitute for that information. While a statistical tool is useful for minimizing the required experimental effort, reliable calculated phase equilibria can only be obtained if at least some pertinent and reliable experimental data are at hand. 

The convergence rate depends somewhat on the problem and on the initial estimates used. For mixtures that are not extremely wide-boiling, convergence is usually accomplished in three or four iterations,t even in the presence of relatively strong liquid-phase nonidealities. For example, cases 1 through 4 in Table 1 are typical of relatively close-boiling mixtures the latter three exhibit significant liquid-phase nonidealities. 

The criterion used for "too near the plait point" is that ratio of K s for the two "solvent" components is less than seven with the feed composition in the two-phase region. 

The Lewis fugacity rule is used for calculating the fugacity coefficients of the true species, and (2) the second virial co-... 

VSTR is useful for estimating partial molar volumes at infinite dilution but is not used here because of Equation (4-17)... 

SL Scaler used for step-limiting, or damping, the Newton-Raphson iteration. 

Value of the objective function [(7-23) or (7-24)] at T + AT used for finite difference approximation of the derivative. 

Figure 2.1 The idealized models used for reactor design. (From Smith and Petela, Thz Chemical Engineer, Dec. 17, 1991 reproduced by permission of the Institution of Chemical Engineers.)...

In fact, cooling of the reactor effluent by direct heat transfer can be used for a variety of reasons ... 

The liquid used for the direct heat transfer should be chosen such that it can be separated easily from the reactor product and so recycled with the minimum expense. Use of extraneous materials, i.e., materials that do not already exist in the process, should be avoided because it is often difficult to separate and recycle them with high efficiency. Extraneous material not recycled becomes an effluent problem. As we shall discuss later, the best way to deal with effluent problems is not to create them in the first place. 

Multiple reactions producing byproducts. The arguments presented for the effect of pressure on single vapor-phase reactions can be used for the primary reaction when dealing with multiple reactions. Again, selectivity is likely to be more important than reactor volume for a given conversion. 

Figure 3.1 Settling processes used for the separation of heterogeneous mixtures.

Drying refers to the removal of water from a substance through a whole range of processes, including distillation, evaporation, and even physical separations such as with centrifuges. Here, consideration is restricted to the removal of moisture from solids and liquids into a gas stream (usually air) by heat, namely, thermal drying. Some of the types of equipment for removal of water also can be used for removal of organic liquids from solids. 

Example 4.4 Butadiene sulfone (or 3-sulfolene) is an intermediate used for the production of solvents. It can be produced from butadiene and sulfur dioxide according to the reaction ... 

Clearly, the time chart shown in Fig. 4.14 indicates that individual items of equipment have a poor utilization i.e., they are in use for only a small fraction of the batch cycle time. To improve the equipment utilization, overlap batches as shown in the time-event chart in Fig. 4.15. Here, more than one batch, at difierent processing stages, resides in the process at any given time. Clearly, it is not possible to recycle directly from the separators to the reactor, since the reactor is fed at a time different from that at which the separation is carried out. A storage tank is needed to hold the recycle material. This material is then used to provide part of the feed for the next batch. The final flowsheet for batch operation is shown in Fig. 4.16. Equipment utilization might be improved further by various methods which are considered in Chap. 8 when economic tradeoffs are discussed. 

Probably the most common method used for sequence selection for simple distillation columns is heuristic. Many heuristics have been proposed, but they can be summarized by the following four ... 

The output from the turbine might be superheated or partially condensed, as is the case in Fig. 6.32. If the exhaust steam is to be used for process heating, ideally it should be close to saturated conditions. If the exhaust steam is significantly superheated, it can be desuperheated by direct injection of boiler feedwater, which vaporizes and cools the steam. However, if saturated steam is fed to a steam main, with significant potential for heat losses from the main, then it is desirable to retain some superheat rather than desuperheat the steam to saturated conditions. If saturated steam is fed to the main, then heat losses will cause excessive condensation in the main, which is not desirable. On the other hand, if the exhaust steam from the turbine is partially condensed, the condensate is separated and the steam used for heating. 

The data from Table 7.4 are presented graphically in Fig. 7.11. The optimal is at 10°C, confirming the initial value used for this problem in Chap. 6. 

Eliminate extraneous materials for separation. The third option is to eliminate extraneous materials added to the process to carry out separation. The most obvious example would be addition of a solvent, either organic or aqueous. Also, acids or alkalis are sometimes used to precipitate other materials from solution. If these extraneous materials used for separation can be recycled with a high efficiency, there is not a major problem. Sometimes, however, they cannot. If this is the case, then waste is created by discharge of that material. To reduce this waste, alternative methods of separation are needed, such as use of evaporation instead of precipitation. 

In early designs, the reaction heat typically was removed by cooling water. Crude dichloroethane was withdrawn from the reactor as a liquid, acid-washed to remove ferric chloride, then neutralized with dilute caustic, and purified by distillation. The material used for separation of the ferric chloride can be recycled up to a point, but a purge must be done. This creates waste streams contaminated with chlorinated hydrocarbons which must be treated prior to disposal. 

In both batch and continuous processes, it may be necessary to clean equipment to prevent contamination of new product. Materials used for equipment cleaning often cannot be recycled, leading to waste. 

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