Respectively

In Chapter 2 we discuss briefly the thermodynamic functions whereby the abstract fugacities are related to the measurable, real quantities temperature, pressure, and composition. This formulation is then given more completely in Chapters 3 and 4, which present detailed material on vapor-phase and liquid-phase fugacities, respectively. 

X, y) for the 1-2 binary and 2-3 binary, respectively. Data points M+1 through N are ternary liquid-liquid equilibrium measurements (T, x, x, x, . The 1-rich phase is indicated... 

The molar excess enthalpy h is related to the derivatives of the activity coefficients with respect to temperature according to... 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

In an equilibrium separation, a feed stream containing m components at given composition, pressure, and enthalpy (or temperature if in a single phase) is split into two streams in equilibrium, here taken to be a vapor and a liquid. The flow rates of the feed, vapor, and liquid streams are, respectively,... 

F, V, and L moles/unit time and their mole-fraction compositions are, respectively, w, y, and x. ... 

X and y are vectors containing the liquid mole fractions and vapor mole fractions respectively. 

With derivatives with respect to temperature and composition of necessity found by finite difference approximation. 

For bubble and dew-point calculations we have, respectively, the objective functions... 

For bubble-point and dew-point pressure calculations, the appropriate forms are, respectively ... 

At low or moderate pressures,a Newton-Raphson iteration is not required, and the bubble and dew-point pressure iteration can be, respectively. 

In the case of the adiabatic flash, application of a two-dimensional Newton-Raphson iteration to the objective functions represented by Equations (7-13) and (7-14), with Q/F = 0, is used to provide new estimates of a and T simultaneously. The derivatives with respect to a in the Jacobian matrix are found analytically while those with respect to T are found by finite-difference approximation... 

However, because the differences are not large, there are some cases where a four-parameter fit was used instead of a five-parameter fit, to avoid maxima or minima with respect to temperature. 

Third card FORMAT(8F10.2), size of increments to be used in central difference formula for calculating derivatives with respect to the independent variables. 

DX(1) cols 1-10 increment for derivative with respect to the temperature, default value is 0,5... 

FORMAT (43H1DERIVAT IVES WITH RESPECT TO THE PARAMETERS/)... 

ERF error flag, integer variable normally zero ERF= 1 indicates parameters are not available for one or more binary pairs in the mixture ERF = 2 indicates no solution was obtained ERF = 3 or 4 indicates the specified flash temperature is less than the bubble-point temperature or greater than the dew-point temperature respectively ERF = 5 indicates bad input arguments. 

DFA Partial derivative of the Rachford-Rice objective function (7-13) with respect to the vapor-feed ratio. 

DGT Partial derivative of the enthalpy balance equation (7-14) with respect to the temperature. 

THE SUBROUTINE ACCEPTS BOTH A LIQUID FEED OF COMPOSITION XF AT TEMPERATURE TL(K) AND A VAPOR FEED OF COMPOSITION YF AT TVVAPOR FRACTION OF THE FEED BEING VF (MOL BASIS). FDR AN ISOTHERMAL FLASH THE TEMPERATURE T(K) MUST ALSO BE SUPPLIED. THE SUBROUTINE DETERMINES THE V/F RATIO A, THE LIQUID AND VAPOR PHASE COMPOSITIONS X ANO Y, AND FOR AN ADIABATIC FLASHf THE TEMPERATURE T(K). THE EQUILIBRIUM RATIOS K ARE ALSO PROVIDED. IT NORMALLY RETURNS ERF=0 BUT IF COMPONENT COMBINATIONS LACKING DATA ARE INVOLVED IT RETURNS ERF=lf ANO IF NO SOLUTION IS FOUND IT RETURNS ERF -2. FOR FLASH T.LT.TB OR T.GT.TD FLASH RETURNS ERF=3 OR 4 RESPECTIVELY, AND FOR BAD INPUT DATA IT RETURNS ERF=5. 

Bubble-point temperature or dew-point temperatures are calculated iteratively by applying the Newton-Raphson iteration to the objective functions given by Equations (7-23) or (7-24) respectively. 

Change in extract-feed ratio from one iteration to the next. Partial derivative of Rachford-Rice objective function with respect to extract-feed ratio. 

Examples of main programs calling subroutines FLASH and ELIPS for vapor-liquid and liquid-liquid separation calculations, respectively, are described in this Appendix. These are intended only to illustrate the use of the subroutines and to provide a means of quickly evaluating their performance on systems of interest. It is expected that most users will write their own main prograns utilizing FLASH and ELIPS, and the other subroutines presented in this monograph,to suit the requirements of their separation calculations. 

Table 2.2 gives the compositions of the reactor feed and effluent streams. Calculate the conversion, selectivity, and reactor yield with respect to (a) the toluene feed and (b) the hydrogen feed. 

Because there are two feeds to this process, the reactor performance can be calculated with respect to both feeds. However, the principal concern is performance with respect to toluene, since it is much more expensive than hydrogen. 

If inert material is to be added, then ease of separation is an important consideration. For example, steam is added as an inert to hydrocarbon cracking reactions and is an attractive material in this respect because it is easily separated from the hydrocarbon components by condensation. If the reaction does not involve any change in the number of moles, inert material has no effect on equilibrium conversion. 

The secondary reactions are series with respect to the chloromethane but parallel with respect to chlorine. A very large excess of methane (mole ratio of methane to chlorine on the order of 10 1) is used to suppress selectivity losses. The excess of methane has two effects. First, because it is only involved in the primary reaction, it encourages the primary reaction. Second, by diluting the product, chloromethane, it discourages the secondary reactions, which prefer a high concentration of chloromethane. 

Polyethylbenzenes (diethylbenzene, triethylbenzene, etc.) are also formed as unwanted byproducts through reversible reactions in series with respect to ethylbenzene but parallel with respect to ethylene. For example,... 

The secondary reactions are parallel with respect to ethylene oxide but series with respect to monoethanolamine. Monoethanolamine is more valuable than both the di- and triethanolamine. As a first step in the flowsheet synthesis, make an initial choice of reactor which will maximize the production of monoethanolamine relative to di- and triethanolamine. 

Solution We wish to avoid as much as possible the production of di- and triethanolamine, which are formed by series reactions with respect to monoethanolamine. In a continuous well-mixed reactor, part of the monoethanolamine formed in the primary reaction could stay for extended periods, thus increasing its chances of being converted to di- and triethanolamine. The ideal batch or plug-flow arrangement is preferred, to carefully control the residence time in the reactor. 

Thus an excess of ammonia in the reactor has a marginal eflFect on the primary reaction but significantly decreases the rate of the secondary reactions. Using excess ammonia also can be thought of as operating the reactor with a low conversion with respect to ammonia. 

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. 

Can the loss of useful material in the purge be avoided or reduced by additional separation on the purge The roles of refrigerated condensation, membranes, etc. in this respect have already been discussed. 

Specifying the hot utility or cold utility or AT m fixes the relative position of the two curves. As with the simple problem in Fig. 6.2, the relative position of the two curves is a degree of freedom at our disposal. Again, the relative position of the two curves can be changed by moving them horizontally relative to each other. Clearly, to consider heat recovery from hot streams into cold, the hot composite must be in a position such that everywhere it is above the cold composite for feasible heat transfer. Thereafter, the relative position of the curves can be chosen. Figure 6.56 shows the curves set to ATn,in = 20°C. The hot and cold utility targets are now increased to 11.5 and 14 MW, respectively. 

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