HOFTIJZER

Pag), where y o mole fraction of A in bulk gas phase can be determined iteratively, yAi = mole fiaction of A in gas inlet. Equations (1) to (6) were solved using fourth order Runge-Kutta method [1, 8]. The value of enhancement factor, E, was predicted using equation of Van Krevelen and Hoftijzer [2]. 

In this case, an exact analytical solution of the continuity equations for A and B does not exist. An approximate solution has been developed by Van Krevelen and Hoftijzer (1948) in terms of E. Results of a numerical solution could be fitted approximately by the implicit relation... 

An approximate implicit solution (van Krevelen and Hoftijzer, 1948) for the enhancement... 

An approximate analytical solution to this system has been proposed by van Krevelen and Hoftijzer (Eq. (27) and Fig. 45.3)) ... 

The numerical solution of these equations is shown on the plot which is due to van Krevelen Hoftijzer (Trans Instn Chem Engrs 32 S360, 1954). The plot is of the enhancement factor E against the Hatta number (3 which is defined in P8.02.01. The parameters along the curves are of a ratio, a = CbLDb/CaLD0. The uppermost curve is for a first order reaction. 

Beutier and Renon(6) have used a similar model but adjusted their ionic activity coefficient parameters to fit selected ternary data. Our own approach, initiated before we became aware of the Prausnitz work, was to analyze the ternary data by modification of the method of van Krevelen, Hoftijzer, and Huntjens(7 and to extend its range by use of ionization constants, Henry s law correlations, and correlations of activity coefficients as needed. Thus, in many areas we needed the same basic data as in the Prausnitz or Renon approach. 

Van Krevelen and Hoftijzer developed an empirical correlation in which the coefficient, on an ionic strength basis, is considered to be the sum of contributions from the cation, the anion, and the gas(24) ... 

This contribution describes and compares three procedures for representing vapor-liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. Starting from the basic thermodynamic relations, the approximations and simplifications applied by van Krevelen, Hoftijzer and Huntjens ( ), Beutier and Renon (2) and Edwards, Maurer, Newman and Prausnitz (3) are discussed the necessary information for using these correlations is compiled. Results calculated with these procedures are discussed and compared with literature data. 

This equation closely resembles the empirical expression of Van Krevelen and Hoftijzer (VI) for the bubble formation in inviscid liquids, provided that the gas density is negligible compared to the liquid density. Their relationship... 

This simplified equation is of the same form as the equations of Van Krevelen and Hoftijzer (VI) for air-water system and the theoretical equation of Davidson and Schuler (D9) for inviscid liquids. It is interesting to observe that the various equations differ only in the value of the constant although they are based on different mechanisms. 

The simplest method of representing data for gas-film coefficients is to relate the Sherwood number [(hod/Dv)(PBm/Z3)] to the Reynolds number (Re) and the Schmidt number (p,/pDv). The indices used vary between investigators though van Krevelen and Hoftijzer(28) have given the following expression, which is claimed to be valid over a wide range of Reynolds numbers ... 

The difference between a physical absorption, and one in which a chemical reaction occurs, can also be shown by Figures 12.11a and 12.11 b, taken from a paper by van Krevelen and Hoftijzer(28 Figure 12.11a shows the normal concentration profile for... 

Figure 23.4 The enhancement factor for fluid-fluid reactions as a function of Mf and modified from the numerical solution of van Krevelens and Hoftijzer (1954).

Comment. In this example we see that two distinct zones are present. Situations may be encountered where even another zone may be present. For example, if the entering liquid contains insufficient reactant, a point is reached in the tower where all this reactant is consumed. Below this point physical absorption alone takes place in reactant-free liquid. The methods of these examples, when used together, deal in a straightforward manner with this three-zone situation and van Krevelens and Hoftijzer (1948) discuss actual situations where these three distinct zones are present. 

Van Krevelen, D. W., P. J. Hoftijzer, and F. J. Huntjens, Composition and Vapor Pressures of Aqueous Solutions of Ammonia, Carbon Dioxide, and Hydrogen Sulfide, Reel. Trav. Chim. Pays-Bas, 68 191-216 (1949). 

The enhancement factor can be evaluated from equations originally developed by Van Krevelen and Hoftijzer (1948). A convenient chart based on the equations is shown in Fig. 6. The parameter for the curves is — 1, where 0V is the enhancement factor as Ha approaches... 

FIGURE 6 Effect of chemical reaction on liquid-phase mass transfer coefficient (assumes bimolecular irreversible reaction). [Data based on Van Krevelen, D. W., and Hoftijzer, P. J. (1948). Rec. Trav. Chim. 67, 563.]... 

D. W. van Krevelen, P. J. Hoftijzer, Kinetics of gas-liquid reactions -Part I General theory, Reel. Trav. 

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