Factor binary interaction

Pitzer s acentric factor binary interaction parameter... 

A distillation calculation is to be performed on a multicomponent mixture. The vapor-liquid equilibrium for this mixture is likely to exhibit significant departures from ideality, but a complete set of binary interaction parameters is not available. What factors would you consider in assessing whether the missing interaction parameters are likely to have an important effect on the calculations ... 

Moraldi gives an estimate of this integral for large times t, on the basis of a dimensional argument. The integral must diverge as t for t — oo it must also be proportional to the cross section for binary interactions which is of the order of a1, the square of the zero of the intermolecular potential functions, V (a) = 0. In other words, the factor of proportionality not specified as yet has units of speed, i.e., the root mean square speed, or... 

Considering the formal system (5.112), we observe that the triple interaction is indirectly considered here. It is doubtful that the actual results could confirm this class of interaction but if we can prove that they are present, then the plan from Table 5.21 can be suggested. Table 5.22 shows the FFE plan from the case when the first relation from the assembly (5.111) is the production relation. It is important to observe that all the binary interactions are indirectly considered in the formal system of the correlations of the obtainable and theoretical coefficients (5.113). Therefore, if the interest is to keep all the binary interactions of factors in the process model relationship, this FFE plan can be used successfully. 

Beyond applications reported in the literature, process simulation is ubiquitous throughout the chemical industry and academia. Every time users select the Soave, or SRK, thermodynamics model, they apply the Soave equation. One motivation for this selection is the long experience with the model and the compilation of correction factors, when the basic model is deficient. For example, binary interaction parameters (ky s) have been compiled for a large number of binary mixtures to improve VLE correlation. It is also possible to compensate for inaccuracies in density through volume translations. ... 

The program VDWMIX is used to calculate multicomponent VLE using the PRSV EOS and the van der Waals one-fluid mixing rules (either IPVDW or 2PVDW see Sections 3.3 to 3.5 and Appendix D.3). The program can be used to create a new input file for a multicomponent liquid mixture and then to calculate the isothermal bubble point pressure and the composition of the coexisting vapor phase for this mixture. In this mode the information needed is the number of components (up to a maximum of ten), the liquid mole fractions, the temperatures at which the calculations are to be done (for as many sets of calculations as the user wishes, up to a maximum of fifty), critical temperatures, pressures (bar), acentric factors, the /f constants of the PRSV equation for each compound in the mixture, and, if available, the experimental bubble point pressure and the vapor phase compositions (these last entries are optional and are used for a comparison between the experimental and calculated results). In addition, the user is requested to supply binary interaction parameteifs) for each pair of components in the multicomponent mixture. These interaction parameters can be... 

Si and Sj are properties of the individual components i and /, BiS is an interaction parameter characteristic of the binary system t/, and is equal to zero. For any multicomponent system, allowing the weighting factor Si of one component to be unity enables calculation of weighting factors and interaction parameters for all components and binary combinations in the mixture. 

In order to compare the results with those of the previous illustration, we can also compute the solubility of carbon dioxide in carbon disulfide. There is no binary interaction parameter reported for the CO2-CS2 mixture, or for any similar mixtures. If we assume the binary interaction parameter is zero, we find that the CO solubility in CS at 1.013 bar CO partial pressure is 0.0159 mole fraction, which is greater than the measured value by a factor of 5 (Problem I l.l-7i. However, if we set co->-cs-. = 0.2, we obtain a CO solubility of 3.4 x 10 , which is in excellent agreement with experiment. ... 

The domain size and shape, as well as the interfacial thickness, depend on the following factors (i) magnitude of the repulsive interactions between the A and B blocks, x b (ii) conformation entropy loss necessary to maintain constant segment density (iii) the localization entropy loss that causes the chemical links to be present at the interface and (iv) the composition. These mutually compensating factors (i vs. ii H-iii) depend on molecular weight of each block and the binary interaction parameter [Helfand, 1975 Helfand and Wasserman, 1976,1978,1980 Hashimoto et al, 1980 Inoue et al, 1969 JCrause, 1980 Meir, 1969, 1987 Hashimoto et al, 1993],... 

Solution. We use our program (Dimian and Groenendijk, 1994). Bubble point pressures, equilibrium X-factors and densities are presented in Table 6.2. Values calculated using interaction coefficients are marked by star. The differences between properties with and without binary interaction parameters are considerable. 

Table 1. Critical parameters, acentric factors and binary interaction parameters used in the calculations.

Most of the values given in Table 1 are unremarkable, but the critical temperature, acentric factor and binary interaction parameter are high for the product BHP. This may be explained by the fact that BHP is a larger long molecule with an -OH group. 

Sometimes a contrast can present a high value not because of a main effect but because of a binary interaction involving two factors, both having important main effects. Consider for example factors 1 and 2, which individually seem to be important. The 12 interaction is contained in the l contrast, whose value is almost 0. If the 12 interaction were important, we would expect a higher value for the Z4 contrast. Since this is not the case, we conclude provisionally that this interaction must not be... 

Table 4.14 shows the combinations for the other contrasts. Note that, besides isolating main effect 5, we also were able to isolate all binary interactions involving this factor. The absolute values of these interactions are all inferior to 2.25. If we assume that the true values of all of them are 0, we can use the seven values of Table 4.14 that correspond to two-factor interactions to estimate an error for the value of a contrast ... 

Estimates of main effect 5 and all binary interaction effects involving this factor... 

Contrasts of the 2jy fraction as a function of the main and binary interactions of the 2 complete factorial, neglecting interactions involving more than two factors... 

Values for critical temperature, pressure, and acentric factor for all five components participating in the system are given in Table 9.2. Values for the binary interaction parameters used in Equation 9.28c are given in Table 9.3. Note that the values found in Table 9.3 were obtained from different sources. Where the interaction parameters are unknown, the k, values are zero for the purposes of demonstration. More accurate predictions may be obtained by fitting the relevant vapor-liquid equilibrium data, if available. 

---