Pressure coefficients, imperfection

Table I. Constants for Calculating Imperfection-Pressure Coefficients"...

In either case the relative distributions between the separable liquid and vapor phases are predicted from the pure component vapor pressures Pi°, liquid phase activity coefficients, y/s, and imperfection-pressure coefficients Oi s. Using these three quantities, the relative distribution is expressed as... 

The important quantities needed to represent the nonideal phase equilibria for extractive distillation are vapor pressures P<°, liquid-phase activity coefficients y and imperfection-pressure coefficients 6i. The... 

From Equations 1 and 2, the phase equilibria depend upon knowing the pure component vapor pressures P 0, liquid phase activity coefficients ji and imperfection-pressure coefficients ft. The computer program which has been developed uses any of four different vapor pressure equations for providing Pi°. It uses the modified van Laar Equations (5) to give liquid phase activity coefficients and a Modified van der Waals Equation of State (4,6) to give imperfection-pressure coefficients ft. 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

Internal recycle reactors are designed so that the relative velocity between the catalyst and the fluid phase is increased without increasing the overall feed and outlet flow rates. This facilitates the interphase heat and mass transfer rates. A typical internal flow recycle stirred reactor design proposed by Berty (1974, 1979) is shown in Fig. 18. This type of reactor is ideally suited for laboratory kinetic studies. The reactor, however, works better at higher pressure than at lower pressure. The other types of internal recycle reactors that can be effectively used for gas-liquid-solid reactions are those with a fixed bed of catalyst in a basket placed at the wall or at the center. Brown (1969) showed that imperfect mixing and heat and mass transfer effects are absent above a stirrer speed of about 2,000 rpm. Some important features of internal recycle reactors are listed in Table XII. The information on gas-liquid and liquid-solid mass transfer coefficients in these reactors is rather limited, and more work in this area is necessary. 

Everett (26) developed the thermodynamic analysis for a binary solution of components 1 (probe) and 2 (stationary phase) in the presence of a gas (3), which is insoluble in the solution. Assigning that the molar volume of the probe, V, does not vary greatly with pressure, the gas phases are only slightly imperfect, the system is in equilibrium, and the solute is infinitely dilute in both gas and solid phases, then the infinite dilution mole fraction activity coefficient of component 1 at temperature T and total pressure P can be written as... 

The durability of SPC structures in aggressive environments depends on the diffusion rate of chemically active reagents into a material. Fluid penetration is realized through imperfections in molecular packing of the binder and it is accelerated at an increase of temperature and pressure. In this connection, definition of a diffusion coefficient (as a key parameter of a liquid carryover) becomes the important problem. 

The velocity at the center of the flue, which is that measured by the instrument, is calculated by Eq, (8.52), using the coefficient 0.98 to correct for imperfections in the flow pattern caused by the presence of the tube. The necessary quantities are as follows. The absolute pressure at the instrument is... 

Due to imperfection of the Debye-Huckel theory and uncertainty of r j, activities coefficients calculated by this method for solutions of elevated temperature and pressure, even at moderate ionic strength (0.1 to 0.2), have precision only within the value order of magnitude. Because of this, the Debye-Huckel second approximation equation is used only for fresh and brackish waters with no greater than 0.2-0.5 (salinity less than 0.1 mole-kg" ) under conditions of low temperature and pressure. 

The most reliable and comprehensive g.l.c. activity coefficient measurements for n-alkane systems have been done by the Bristol group > " using medium-high-pressure g.l.c. and taking all carrier-gas and solute imperfections into account. They have looked at the Q to Cg n-alkane solutes in Cig to Cga n-alkane solvents. Generally, the results indicate that the smaller the disparity in carbon number between solute and solvent, the closer is the activity coefficient to unity. The measured activity coefficients range from 0.930 for heptane + hexadecane at 303 K to 0.695 for heptane + dotriacontane at 348 K. Activity coefficients for many alk-l-ene + alkane systems have also been measured by this group. ... 

The ELBT program on the CD-ROM permits the correlation of isothermal VLE data of homogeneous binary systems with equations derived from the Redlich-Kister expansion. Vapor-phase imperfection and the variation of the Gibbs energy of the pure liquid components are accounted for through the second molar virial coefficients By and the molar volumes V° under saturation pressures (Chap. 3.5.5). The correlated total vapor pressure P and... 

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