Should

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. 

At moderate densities. Equation (3-lOb) provides a very good approximation. This approximation should be used only for densities less than (about) one half the critical density. As a rough rule, the virial equation truncated after the second term is valid for the present range... 

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. 

The critical temperature of methane is 191°K. At 25°C, therefore, the reduced temperature is 1.56. If the dividing line is taken at T/T = 1.8, methane should be considered condensable at temperatures below (about) 70°C and noncondensable at higher temperatures. However, in process design calculations, it is often inconvenient to switch from one method of normalization to the other. In this monograph, since we consider only equilibria at low or moderate pressures in the region 200-600°K, we elect to consider methane as a noncondensable component. 

Liquid-liquid equilibria are much more sensitive than vapor-liquid equilibria to small changes in the effect of composition on activity coefficients. Therefore, calculations for liquid-liquid equilibria should be based, whenever possible, at least in part, on experimental liquid-liquid data. 

The primary purpose for expressing experimental data through model equations is to obtain a representation that can be used confidently for systematic interpolations and extrapolations, especially to multicomponent systems. The confidence placed in the calculations depends on the confidence placed in the data and in the model. Therefore, the method of parameter estimation should also provide measures of reliability for the calculated results. This reliability depends on the uncertainties in the parameters, which, with the statistical method of data reduction used here, are estimated from the parameter variance-covariance matrix. This matrix is obtained as a last step in the iterative calculation of the parameters. 

An apparent systematic error may be due to an erroneous value of one or both of the pure-component vapor pressures as discussed by several authors (Van Ness et al., 1973 Fabries and Renon, 1975 Abbott and Van Ness, 1977). In some cases, highly inaccurate estimates of binary parameters may occur. Fabries and Renon recommend that when no pure-component vapor-pressure data are given, or if the given values appear to be of doubtful validity, then the unknown vapor pressure should be included as one of the adjustable parameters. If, after making these corrections, the residuals again display a nonrandom pattern, then it is likely that there is systematic error present in the measurements. ... 

It is important to stress that unnecessary thermodynamic function evaluations must be avoided in equilibrium separation calculations. Thus, for example, in an adiabatic vapor-liquid flash, no attempt should be made iteratively to correct compositions (and K s) at current estimates of T and a before proceeding with the Newton-Raphson iteration. Similarly, in liquid-liquid separations, iterations on phase compositions at the current estimate of phase ratio (a)r or at some estimate of the conjugate phase composition, are almost always counterproductive. Each thermodynamic function evaluation (set of K ) should be used to improve estimates of all variables in the system. 

Large errors in the low-pressure points often have little effect on phase-equilibrium calculations e.g., when the pressure is a few millitorr, it usually does not matter if we are off by 100 or even 1000%. By contrast, the high-pressure end should be reliable large errors should be avoided when the data are extrapolated beyond the critical temperature. 

Appendix C presents the best set of constants for Equation (2). Also shown are the temperature limits of the real experimental data. Users must exercise caution when using the correlation outside the range of real data such use should, in general, be avoided. 

The computer subroutines for calculation of vapor-phase and liquid-phase fugacity (activity) coefficients, reference fugac-ities, and molar enthalpies, as well as vapor-liquid and liquid-liquid equilibrium ratios, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements and CDC 6400 execution times for these subroutines are given in Appendix J. 

GIVEN TEMPERATURE T K) AND ESTIMATES OF PHASE COMPOSITIONS XR AND XE (USED WITHOUT CORRECTION TO EVALUATE ACTIVITY COEFFICIENTS GAR AND GAE), LILIK NORMALLY RETURNS ERR=0, BUT IF COMPONENT COMBINATIONS LACKING DATA ARE INVOLVED IT RETURNS ERR=l, AND IF A K IS OUT OF RANGE THEN ERR=2 key SHOULD BE 1 ON INITIAL CALL FOR A SYSTEM, 2 (OR 6)... 

SHOULD BE AS IN VALIK. IF VALIK HAS NOT BEEN CALLED, KEY MUST BE 9. 

IF ESTIMATES ARE AVAILABLE FOR A,X,Y,(ANO T) THEY CAN BE ENTERED IN THESE VARIABLES - OTHERWISE THESE VARIABLES SHOULD BE SET TO ZERO. KEY SHOULD BE 1 ON INITIAL CALL FOR A NEW SYSTEM AND 2 OTHERWISE. 

The subroutines PARIN and PARCH are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and should be compatible with most computer systems where input can be taken from logical unit 3. 

Given that the objective is to manufacture a certain product, there are often a number of alternative reaction paths to that product. Reaction paths which use the cheapest raw materials and produce the smallest quantities of byproducts are to be preferred. Reaction paths which produce significant quantities of unwanted byproducts should especially be avoided, since they create significant environmental problems. 

Multiple reactions also can occur with impurities that enter with the feed and undergo reaction. Again, such reactions should be minimized, but the most efiective means of dealing with byproduct reactions caused by feed impurities is not to alter reactor conditions but to introduce feed purification. 

If the secondary reaction is reversible and inerts are present, then we should... 

If the byproduct reaction is reversible and inerts are present, then changing the concentration of inerts if there is a change in the number of moles should be considered, as discussed above. Whether or not there is a change in the number of moles, recycling byproducts can suppress their formation if the bj iroduct-forming reaction is reversible. An example is in the production of ethylbenzene from benzene and ethylene ... 

Temperature control. Let us now consider temperature control of the reactor. In the first instance, adiabatic operation of the reactor should be considered, since this leads to the simplest and cheapest reactor design. If adiabatic operation produces an unacceptable rise in temperature for exothermic reactions or an unacceptable fall in temperature for endothermic reactions, this can be dealt with in a number of ways ... 

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. 

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