Cross parameters

The PPM ammonia remaining in the bottoms product stream of the stripper tower are shown in Figure 4 as a function of the kilograms of steam injected into the tower. The number of theoretical stages used is shown as a cross-parameter. What is observed is that in a practical sense, the Wilson and Mason-Kao methods yield essentially the same ammonia purity in the stripped water product, whereas very substantial differences are obtained when the classical van Krevelen correlation is applied to design the wastewater stripper. 

The LJ parameters, elk and a, have been determined from the critical constants, Tc and pc, by adopting the recommendation of Nicolas et al. [11] kTJe = 1.35 andpco3/e = 0.142. However, different values for the potential depth of benzene, 22, have been determined so as to fit the vapor pressure at temperatures from 307.2 K to 553.2 K. The LJ parameters used in this work are summarized in Table 1, where the parameters for graphitic carbon atom are taken from those suggested by Steele [10]. We used the modified Lorentz -Berthelot rule for the cross parameters, that is, the arithmetic mean for o and the geometric mean for e by introducing the binary parameter ktj defined as Eq. (4). 

Simulations of ternary systems were performed using the pure component parameters in Table I and the cross parameters for the systems acetone/ CO2 and water/C02 determined previously (fi j - 1 and 0.81 respectively). Because of expected difficulties similar to the ones mentioned for the water/C02 system, no attempt was made to simulate the system acetone/water near room temperature. Thus, we set the acetone/water interaction parameters to the values from the Lorenz-Berthelot rules with fi j-l. Direct simulations of ternary phase equilibria have not been previously reported to the best of our knowledge. 

In the next step, the cross parameter an and the mixture parameters a and h for the liquid phase with the help of the mixing rules (Eqs. (4.98-4.100)) are calculated. 

For nearly athermal systems, the proportionality factors, S. and Sy, are taken as equal to 1. Thus, for the systems without strong interactions, the binary parameters are weU approximated by the geometric and algebraic averages. For example, for PS/PVME blends, the assumption 5 = 5v = 1 resulted in 0.1 % deviation for the experimental values of the cross-parameters (Xie et al. 1992 Xie and Simha, 1997, private communication ). In contrast, it is to be expected that for systems with strong intermolecular interactions such mixture rules may fail and experimental values for the cross-factors may have to be found. However, least squares lit of Eqs. 2.42 and 2.43 to experimental values of CO2 miscibilities in PS (in a wide range of P and T) yielded values for and Sy close to 1 (Xie et al. 1997). 

That we can assign values to the cross-parameters fij and hy with i not equal to j. 

Point at which the potential is minimum Cross-parameters for adsorbent-adsorbate interaction Thickness of the adsorbed phase Potential well depth... 

The cross-parameters for the pair ij are calculated by the Lorentz-Bertherot rale. The cut-off distance for the intermolecular interaction was set at 3.5... 

The second approach is indirect and involves diabatiza-tion of MO-CI (or CASSCF) calculations and/or projection of the wave functions unto VB situations which define the intersecting curves. The major inconvenience of the indirect approaches is that the values of the avoided crossing and curve crossing parameters depend on the way one defines the VB structures. The structures may sometimes lose their original chemical nature, and the avoided crossing interactions... 

The cross-parameters, o,j, and were calculated using the Lorentz-Berthelot... 

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