Coefficient composite

A,B K-value or temperature dependence parameters a,b Activity coefficient composition dependence parameters C,D Vapor enthalpy temperature dependence parameters E,F Liquid enthalpy temperature dependence parameters F Total feed molar flow rate... 

Effect of composition. The main effect of composition on K-values and relative volatilities is a result of the effect of composition on the liquid activity coefficient. Composition also has an effect on the fugacify coefficient. The latter effect is generally small at low pressorea. 

In these equations, Asebum and Age are the actual areas of the sebum and stratum comeum routes. >sebum and D c are the effective diffusion coefficients (composite diffusion coefficients for heterogeneous phases) for the drag in question through sebum and the stratum comeum, while Tsebum and are the drag s partition coefficients in sebum/ water and stratum comeum/water, respectively. The terms, Asebum and refer to the functional thicknesses of the sebum and stratum comeum, respectively. 

Two miscible components having an appreciable difference in their boiling points form a mixture with widely separated dew points and bubble points. The mixture has a wide boiling range, and the distribution coefficients of the two components differ considerably. An example of this type of mixture is the ethane n-hexane system, with 50-50% mole composition. The equilibrium temperature, distribution coefficients, compositions, and recovery of ethane in the vapor are calculated at a fixed pressure of 690 kPa and over a vapor mole fraction ranging from 0 to 1. Selected results are given in Table 2.1. The temperature, mole fraction ethane in the vapor, and ethane recovery in the vapor are plotted versus mole fraction vapor in Figure 2.5. 

FIGURE 12.9 Representative activity coefficient-composition curves. Ethanol-water system, one atmosphere. Shown are the following (i) experimental data [Figure 12.8], (ii) van Laar curves with constants computed from the aceotrope condition, and (iii) curves based on the UNIFAC model. 

Parameters included in this group, e.g., temperature, viscosity, diffusion coefficient, composition of the sample and reagent solutions, occurrence of chemical reactions and the presence of solid particles, are usually less susceptible to variations, because in most applications they cannot be modified at will. 

Foam fractionation Fractional extraction Fractionation, seeDistillation Free-volume theory of diffusion Freezing-point determination Fugacity of nitrogen standard state Fugacity coefficient composition dependence of acetic acid vapor... 

The van Laar equation can fit activity coefficient-composition curves corresponding to both positive and negative deviations from Raoult s law, but cannot fit curves that exhibit minima or maxima such as those in Fig. 5.2c. 

Pourabas and Peyghambardoost [70] prepared positive temperature coefficient composites by using metal-modified and unmodified carbon black in a matrix of high-density polyethylene. Modification with metallic particles led to properties that were related to changing the surface properties of the carbon black. The intrinsic electrical conduction of carbon black also changed after modification. These changes in properties endowed some desirable characteristics to the positive temperature coefficients. 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

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. ... 

If we vary the composition of a liquid mixture over all possible composition values at constant temperature, the equilibrium pressure does not remain constant. Therefore, if integrated forms of the Gibbs-Duhem equation [Equation (16)] are used to correlate isothermal activity coefficient data, it is necessary that all activity coefficients be evaluated at the same pressure. Unfortunately, however, experimentally obtained isothermal activity coefficients are not all at the same pressure and therefore they must be corrected from the experimental total pressure P to the same (arbitrary) reference pressure designated P. This may be done by the rigorous thermodynamic relation at constant temperature and composition ... 

The fugacity coefficient is a function of temperature, total pressure, and composition of the vapor phase it can be calculated from volumetric data for the vapor mixture. For a mixture containing m components, such data are often expressed in the form of an equation of state explicit in the pressure... 

For a pure vapor the virial coefficients are functions only of temperature for a mixture they are also functions of composition. An important advantage of the virial equation is that there are theoretically valid relations between the virial coefficients of a mixture and its composition. These relations are ... 

A component in a vapor mixture exhibits nonideal behavior as a result of molecular interactions only when these interactions are very wea)c or very infrequent is ideal behavior approached. The fugacity coefficient (fi is a measure of nonideality and a departure of < ) from unity is a measure of the extent to which a molecule i interacts with its neighbors. The fugacity coefficient depends on pressure, temperature, and vapor composition this dependence, in the moderate pressure region covered by the truncated virial equation, is usually as follows ... 

When a condensable solute is present, the activity coefficient of a solvent is given by Equation (15) provided that all composition variables (x, 9, and ) are taicen on an (all) solute-free basis. Composition variables 9 and 4 are automatically on a solute-free basis by setting q = q = r = 0 for every solute. 

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... 

Since we make the simplifying assumption that the partial molar volumes are functions only of temperature, we assume that, for our purposes, pressure has no effect on liquid-liquid equilibria. Therefore, in Equation (23), pressure is not a variable. The activity coefficients depend only on temperature and composition. As for vapor-liquid equilibria, the activity coefficients used here are given by the UNIQUAC equation. Equation (15). ... 

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 ternary diagrams shown in Figure 22 and the selectivi-ties and distribution coefficients shown in Figure 23 indicate very good correlation of the ternary data with the UNIQUAC equation. More important, however, Table 5 shows calculated and experimental quarternary tie-line compositions for five of Henty s twenty measurements. The root-mean-squared deviations for all twenty measurements show excellent agreement between calculated and predicted quarternary equilibria. 

Subroutine MULLER. MULLER iteratively solves the equilibrium relations and computes the equilibrium vapor composition when organic acids are present. These compositions are used by subroutine PHIS2 to calculate fugacity coefficients by the chemical theory. 

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)... 

PHIS calculates vapor-phase fugacity coefficients, PHI, for each component in a mixture of N components (N 5. 20) at specified temperature, pressure, and vapor composition. 

CALCULATE VAPOR PHASE FUGACITY COEFFICIENTS FOR ACTUAL COMPOSITION OF... 

Equation (F.l) shows that each stream makes a contribution to total heat transfer area defined only by its duty, position in the composite curves, and its h value. This contribution to area means also a contribution to capital cost. If, for example, a corrosive stream requires special materials of construction, it will have a greater contribution to capital cost than a similar noncorrosive stream. If only one cost law is to be used for a network comprising mixed materials of construction, the area contribution of streams requiring special materials must somehow increase. One way this may be done is by weighting the heat transfer coefficients to reflect the cost of the material the stream requires. 

The value of coefficient depends on the composition. As the mole fraction of component A approaches 0, approaches ZJ g the diffusion coefficient of component A in the solvent B at infinite dilution. The coefficient Z g can be estimated by the Wilke and Chang (1955) method ... 

For a binary mixture of two components A and B in the gas phase, the mutual diffusion coefficient such as defined in 4.3.2.3, does not depend on composition. It can be calculated by the Fuller (1966) method ... 

Figure C2.3.8. Self-diffusion coefficients at 45°C for AOT ( ), water ( ) and decane ( ) in ternary AOT, brine (0.6% aqueous NaCl) and decane microemulsion system as a function of composition, a. This compositional parameter, a, is tire weight fraction of decane relative to decane and brine. Reproduced by pennission from figure 3 of [46].

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