Phases composition

The catalytically active phase is often formed from the fresh catalyst under reaction conditions. This can be recognized by a change in crystal structure from the new to the used catalyst. However, only in situ methods (e.g., XRD, EXAFS, XANES, DRIFTS [KrauR 1999, Dochner 1999a] see also Appendix 8.18) can identify the catalytically active phase, but only when it exceeds a ceratin size ( 3 nm). 

Ethylene oxide catalyst, silver-based calcium increases selectivity 

Ammonia catalyst, iron-based KjO lowers binding energy between Fe and N2 

Acrylic acid catalyst, based on Mo/V mixed oxide copper lowers reaction temperature 

Electrochemical methods can be applied to the determination of the composition of solid phases as well as mixtures of solids [224-228], The first situation is illustrated in Fig. 4.1, where cathodic voltammograms of CuS, CuSe, and a solid phase of composition CuSeoASo.e reported by Meyer et al. [227] are shown. This last can be described as a solid solution formally regarded as a copper sulfide, in which 40% of sulfide ions have been replaced by selenide ions. The new phase produces a voltammetric peak at a potential intermediate between those for CuS and CuSe. 

The mixed phase is reduced at a potential that depends on the molar ratio of the two salts formally forming the mixed crystal, as can be seen in Fig. 4.2, where peak potentials of different mixed crystals of CuSei xSx are plotted against the molar ratio xs/(xse + xs) [224], Since the peak potentials vary slightly with the total amount of charge (Q) consumed in the electrochemical reaction, standardized peak potentials extrapolated to values for Q = 0 were taken. 

In the presence of iron oxide there is a tendency for the replacement of alumina by iron oxide. Consequently, at Al203/Fe203 0.64, C3A will be replaced by C4AF 

In conclusion, the sequence of reactions occurring during formation of the cUnker minerals can be summarized as shown in Table 5.3 (Roy, 1983). It should 

For details and up-to-date information the reader is referred to the excellent summary by Pollmann (2002). 

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In vapor-liquid equilibria, if one phase composition is given, there are basically four types of problems, characterized by those variables which are specified and those which are to be calculated. Let T stand for temperature, P for total pressure, for the mole fraction of component i in the liquid phase, and y for the mole fraction of component i in the vapor phase. For a mixture containing m components, the four types can be organized in this way ... 

Using UNIQUAC, Table 2 summarizes vapor-liquid equilibrium predictions for several representative ternary mixtures and one quaternary mixture. Agreement is good between calculated and experimental pressures (or temperatures) and vapor-phase compositions. ... 

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 Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

The equilibrium ratios are not fixed in a separation calculation and, even for an isothermal system, they are functions of the phase compositions. Further, the enthalpy balance. Equation (7-3), must be simultaneously satisfied and, unless specified, the flash temperature simultaneously determined. 

Equation (7-8). However, for liquid-liquid equilibria, the equilibrium ratios are strong functions of both phase compositions. The system is thus far more difficult to solve than the superficially similar system of equations for the isothermal vapor-liquid flash. In fact, some of the arguments leading to the selection of the Rachford-Rice form for Equation (7-17) do not apply strictly in the case of two liquid phases. Nevertheless, this form does avoid spurious roots at a = 0 or 1 and has been shown, by extensive experience, to be marltedly superior to alternatives. 

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. 

Figure 7-1. Incipient equilibrium vapor-phase compositions calculated with subroutine BUDET.

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. 

Liquid-liquid equilibrium separation calculations are superficially similar to isothermal vapor-liquid flash calculations. They also use the objective function. Equation (7-13), in a step-limited Newton-Raphson iteration for a, which is here E/F. However, because of the very strong dependence of equilibrium ratios on phase compositions, a computation as described for isothermal flash processes can converge very slowly, especially near the plait point. (Sometimes 50 or more iterations are required. )... 

Figure 7-2. Conjugate liquid phase compositions for water-acrylonitrile-acetonitrile system calculated with subroutine ELIPS for feeds shown by . ...

The calculational procedure employed in BLIPS, when used with the particular initial phase-composition estimated included in the subroutine, has converged satisfactorily for all systems we have encountered (except very near plait points as noted). 

The subroutine is well suited to the typical problems of liquid-liquid separation calculations wehre good estimates of equilibrium phase compositions are not available. However, if very good initial estimates of conjugate-phase compositions are available h. priori, more effective procedures, with second-order convergence, can probably be developed for special applications such as tracing the entire boundary of a two-phase region. 

In the highly nonlinear equilibrium situations characteristic of liquid separations, the use of priori initial estimates of phase compositions that are not very close to the true compositions of these phases can lead to divergence of iterative computations or to spurious convergence upon feed composition. 

XM(I,2) cols 21-30 measured liquid-phase composition of component one (mole or weight fraction)... 

ZM(I) cols 31-40 measured vapor-phase composition of component... 

EVX(I,2) - ERROR VARRIANCE OF THF LIQUID-PHASE COMPOSITION MEASUREMENT. 

USE MULLER.S METK)0 TO SOLVE NONLINEAR EQUATIONS FOP THE TRUE VAPOR-PHASE COMPOSITION. 

TEMPERATURE T(K), PRESSURE PCBARI, ANO ESTIMATES O PHASE COMPOSITION... 

LILIK calculates liquid-liquid equilibrium ratios, K(I), for each component in a mixture of N components (N < 20) at specified temperature and liquid-phase compositions. 

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)... 

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. 

BLIPS calculates equilibrium phase compositions for a partially miscible liquid system of N components (N 20). 

Liquid phase compositions and phase ratios are calculated by Newton-Raphson iteration for given K values obtained from LILIK. K values are corrected by a linearly accelerated iteration over the phase compositions until a solution is obtained or until it is determined that calculations are too near the plait point for resolution. 

KAC Integer control variable for acceleration of phase compositions at alternate iterations. 

ELIPS CALCULATES C0NJU ATE PHASE COMPOSITIONS XR AND XE FOP PARTIALLY... 

CONOUCT ITERATION OVER PHASE COMPOSITION 1 OUTER LOOP I 200 IT IT 1... 

AT ALTERNATE ITERATIONS AFTER 3 ACCELERATE PHASE COMPOSITIONS BY... 

Equations (4.5) to (4.7) can now be solved to give expressions for the vapor- and liquid-phase compositions leaving the separator ... 

Organic Solvent/H20 Mobile-Phase Compositions Having Approximately Equal Solvent Strength... 

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