Becoming

When only the total system composition, pressure, and temperature (or enthalpy) are specified, the problem becomes a flash calculation. This type of problem requires simultaneous solution of the material balance as well as the phase-equilibrium relations. 

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. ... 

According to Equation (14), the fugacity of component i becomes equal to the mole fraction multiplied by the standard-... 

Figure 1 shows second virial coefficients for four pure fluids as a function of temperature. Second virial coefficients for typical fluids are negative and increasingly so as the temperature falls only at the Boyle point, when the temperature is about 2.5 times the critical, does the second virial coefficient become positive. At a given temperature below the Boyle point, the magnitude of the second virial coefficient increases with... 

The off-diagonal elements of the variance-covariance matrix represent the covariances between different parameters. From the covariances and variances, correlation coefficients between parameters can be calculated. When the parameters are completely independent, the correlation coefficient is zero. As the parameters become more correlated, the correlation coefficient approaches a value of +1 or -1. 

Large confidence regions are obtained for the parameters because of the random error in the data. For a "correct" model, the regions become vanishingly small as the random error becomes very small or as the number of experimental measurements becomes very large. 

If the parameters were to become increasingly correlated, the confidence ellipses would approach a 45 line and it would become impossible to determine a unique set of parameters. As discussed by Fabrics and Renon (1975), strong correlation is common for nearly ideal solutions whenever the two adjustable parameters represent energy differences. 

In the terms developed in Chapter 2, this latter requirement becomes... 

For the special case of a bubble-point calculation (incipient vaporization), a is 0 (also Q = 0) and Equation (7-13) becomes... 

In both of these cases. Equation (7-14) becomes trivial as h or... 

If the data are correlated assuming an ideal vapor, the reference fugacity is just the vapor pressure, P , the Poynting correction is neglected, and fugacity coefficient is assumed to be unity. Equation (2) then becomes... 

The addition of components to this set of 92, the change of a few parameter values for existing components, or the inclusion of additional UNIQUAC binary interaction parameters, as they may become available, is best accomplished by adding or changing cards in the input deck containing the parameters. The formats of these cards are discussed in the subroutine PARIN description. Where many parameters, especially the binary association and solvation parameters are to be changed for an existing... 

If the reaction involves more than one feed, the picture becomes more complex. Consider the reaction system from Eq. (2.6) with the corresponding rate equations ... 

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. 

The use of an excess of ammonia is home out in practice. A mole ratio of ammonia to ethylene oxide of 10 1 3delds 75 percent monoethanolamine, 21 percent diethanolamine, and 4 percent triethanolamine. Using equimolar proportions under the same reaction conditions, the respective proportions become 12, 23, and 65 percent. 

Generally speaking, temperature control in fixed beds is difficult because heat loads vary through the bed. Also, in exothermic reactors, the temperature in the catalyst can become locally excessive. Such hot spots can cause the onset of undesired reactions or catalyst degradation. In tubular devices such as shown in Fig. 2.6a and b, the smaller the diameter of tube, the better is the temperature control. Temperature-control problems also can be overcome by using a mixture of catalyst and inert solid to effectively dilute the catalyst. Varying this mixture allows the rate of reaction in different parts of the bed to be controlled more easily. 

Raw materials efficiency. In choosing the reactor, the overriding consideration is usually raw materials efficiency (bearing in mind materials of construction, safety, etc.). Raw material costs are usually the most important costs in the whole process. Also, any inefficiency in raw materials use is likely to create waste streams that become an environmental problem. The reactor creates inefficiency in the use of raw materials in the following ways ... 

Flotation. Flotation is a gravity separation process which exploits differences in the surface properties of particles. Gas bubbles are generated in a liquid and become attached to solid particles or immiscible liquid droplets, causing the particles or droplets to rise to the surface. This is used to separate mixtures of solid-solid particles and liquid-liquid mixtures of finely divided immiscible droplets. It is an important technique in mineral processing, where it is used to separate different types of ore. 

When used to separate solid-solid mixtures, the material is ground to a particle size small enough to liberate particles of the chemical species to be recovered. The mixture of solid particles is then dispersed in the flotation medium, which is usually water. Gas bubbles become attached to the solid particles, thereby allowing them to float to the surface of the liquid. The solid partices are collected from the surface by an overflow weir or mechanical scraper. The separation of the solid particles depends on the different species having different surface properties such that one species is preferentially attached to the bubbles. A number of chemicals are added to the flotation medium to meet the various requirements of the flotation process ... 

Separation becomes more difficult (relative volatility decreases) i.e., more plates or reflux are required. 

Latent heat of vaporization decreases i.e., reboiler and condenser duties become lower. 

If the total heat consumed is from an external utility (e.g., mains steam), then a high efficiency is desirable, even perhaps at the expense of a high capital cost. However, if the heat consumed is by recovery from elsewhere in the process, as is discussed in Chap. 15, then comparison on the basis of dryer efficiency becomes less meaningful. 

The minimum selectivity which can now be tolerated becomes 61 percent. 

The reader might wish to check that if the temperature of the phase split is increased or its pressure decreased, the separation between hydrogen, methane, and the other components becomes worse. 

The normal boiling points of the materials are given in Table 4.6. Synthesize a continuous reaction, separation, and recycle system for the process, bearing in mind that the process will later become batch. 

The reactor now becomes batch, requiring the reaction to be completed before the separation can take place. Figure 4.14 shows the time-event chart for a repeated batch cycle. Note in Fig. 4.14 that there is a small overlap between the process steps. This is to allow for the fact that emptying of one step and filling of the following step occur at the same time. 

Raw materials costs dominate the operating costs of most processes (see App. A). Also, if raw materials are not used efficiently, this creates waste, which then becomes an environmental problem. It is therefore important to have a measure of the efficiency of raw materials use. The process yield is defined as... 

Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

As the amount of temperature cross increases, however, problems are encountered, as illustrated in Fig. 7i8c. Local reversal of heat flow may be encountered, which is wasteful in heat transfer area. The design may even become infeasible. 

Figure 7.8 Designs with a temperature approach or small temperature cross can be accommodated in a single 1-2 shell, whereas designs with a large temperature cross become infeasible. (From Ahmad, Linnhoff, and Smith, Trans. ASME, J. Heat Transfer, 110 304, 1988 reproduced by permission of the American Society of Mechanical Engineers.)...

The economic tradeoffs now become more complex, and a new cost must be added to the tradeoffs. This is a raw material efficiency cost due to byproduct formation. If the PRODUCT formation is kept constant despite varying levels of BYPRODUCT formation, then the cost can be defined to be ... 

Also, if there are two separators, the order of separation can change. The tradeoffs for these two alternative flowsheets will be different. The choice between different separation sequences can be made using the methods described in Chap. 5. However, we should be on guard to the fact that as the reactor conversion changes, the most appropriate sequence also can change. In other words, different separation system structures become appropriate for different reactor conversions. 

We should be on guard for the fact that as the reactor conversion changes, the most appropriate separation sequence also can change. In other words, different separation system structures become appropriate for different reactor conversions. 

Sometimes waste streams can be recycled directly, but between different processes. Waste streams from one process can become the feedstock for another. The scope for such waste exchanges is often not fully realized, since it often means waste being transferred between different companies. 

There are many other sources of waste associated with process operations which can only be taken care of in the later stages of design or after the plant has been built and has become operational. For example, poor operating practice can mean that the process operates under conditions for which it was not designed, leading to waste. Such problems might be solved by an increased level of automation or better management of the process. These considerations are outside the scope of this text. 

While incineration is the preferred method of disposal for wastes containing high concentrations of organics, it becomes expensive for aqueous wastes with low concentrations of organics because auxiliary fuel is required, making the treatment expensive. Weak aqueous solutions of organics are better treated by wet oxidation (see Sec. 11.5). 

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