Gas and liquid-phase coefficients

Kg and Kl are known as the overall gas and liquid phase coefficients, respectively. 

Instead of concentrating on the diffiisioii limit of reaction rates in liquid solution, it can be histnictive to consider die dependence of bimolecular rate coefficients of elementary chemical reactions on pressure over a wide solvent density range covering gas and liquid phase alike. Particularly amenable to such studies are atom recombination reactions whose rate coefficients can be easily hivestigated over a wide range of physical conditions from the dilute-gas phase to compressed liquid solution [3, 4]. 

Pave = average total pressure in tower, atmospheres Hl = height of liquid film transfer unit, ft Hg = height of gas film transfer unit, ft a = effective interfacial area for contacting gas and liquid phases, ft /ft. Because this is very difficult to evaluate, it is usually retained as a part of the coefficient such as Kca, Ki a, kca, and k.La. 

The mass transfer coefficients, Kg and Ky, are overall coefficients analogous to an overall heat transfer coefficient, but the analogy between heat and mass transfer breaks down for mass transfer across a phase boundary. Temperature has a common measure, so that thermal equilibrium is reached when the two phases have the same temperature. Compositional equilibrium is achieved at different values for the phase compositions. The equilibrium concentrations are related, not by equality, as for temperature, but by proportionality through an equilibrium relationship. This proportionality constant can be the Henry s law constant Kh, but there is no guarantee that Henry s law will apply over the necessary concentration range. More generally, Kyy is a function of composition and temperature that serves as a (local) proportionality constant between the gas- and liquid-phase concentrations. 

Onda, K., TAKEUCHI, H. and Okumoto, Y. (1968) J. Chem. Eng. Japan 1, 56. Mass transfer coefficients between gas and liquid phases in packed columns. 

The overall heat-transfer coefficient between the gas and liquid phases can be taken to be 5.0 Btu/h ft2 degF (28 W/m2 °C). 

Vejrosta, J., Novak, J., Jonsson, J. (1982) A method for measuring infinite-dilution partition coefficients of volatile compounds between the gas and liquid phases of aqueous systems. Fluid Phase Equil. 8, 25-35. 

Reaction between an absorbed solute and a reagent lowers the equilibrium partial pressure of the solute and thus increases the rate of mass transfer. The mass transfer coefficient likewise may be enhanced which contributes further to increased absorption rate. Three modes of contacting gas and liquid phases are possible The gas is dispersed as bubbles in the liquid, the liquid is dispersed as droplets, the two phases are contacted on a thin liquid film deposited over a packing or wall. The choice between these modes is an important practical problem. 

The diffusion coefficient allows for both gas and liquid phase diffusion. It is given by (Stephen et al, 1998a,b) ... 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

We therefore first briefly discuss the analysis of systems that involve diffusion in the gas and liquid phases, uptake, and reaction in the bulk liquid or at the interface. Following that, we give a brief description of some of the most common methods used to measure mass accommodation coefficients and reaction kinetics for heterogeneous atmospheric reactions. Included are some new approaches that appear to be especially promising. For a review of this area, see Kolb et al. (1995, 1997). 

The concept of equilibrium distribution is another area where names can cause much confusion. The equilibrium distribution of a compound between the gas and liquid phase has been expressed in various forms, i. e. Bunsen coefficientfi, solubility ratio s, Henry s Law constant expressed dimensionless Hc, or with dimensions H. These are summarized in along with equations showing the relationships between them. Another more general term to describe the equilibrium concentrations between two phases is the partition coefficient, denoted by K. It is often used to describe the partitioning of a compound between two liquid phases. 

These parameters, such as the coefficient of diffusion, D, mass-transfer coefficient in the gas and liquid phase or film, kg and k], Thiele modulus, Hatta number, Ha, and enhancement factor, E, are all dependent on the pressure. 

Bacterial inactivation is achieved by CO2 absorption in the liquid phase, even though the reason why it happens is still not clear. In this respect, batch- and semi-continuous operating modes are substantially different. In the batch system the residence time, i.e., the time of contact between gas- and liquid phase, must be sufficient to allow the diffusion of CO2 in the liquid, and is therefore a fundamental parameter to assure a desired efficiency. In the semi-continuous system the contact between the phases is localized in the surface of the moving micro-bubbles. In this second case, the efficiency of the process is influenced by temperature, pressure, gas flux, bubble diameter, and other parameters that modify the value of the mass-transfer coefficient. Therefore, it is not correct to use the residence time as a key parameter in the semi-continuous process. In fact, a remarkable microbial inactivation is reached even with an exposure time of 0 min (i.e., pressurizing and immediately depressurizing the system) these two steps are sufficient to allow CO2 to diffuse through the liquid phase. 

The concept of plate theory was originally proposed for the performance of distillation columns (12). However, Martin and Synge (13) first applied the plate theory to partition chromatography. The theory assumes that the column is divided into a number of zones called theoretical plates. One determines the zone thickness or height equivalent to a theoretical plate (HETP) by assuming that there is perfect equilibrium between the gas and liquid phases within each plate. The resulting behavior of the plate column is calculated on the assumption that the distribution coefficient remains unaffected by the presence of other... 

The problem to be solved in this paragraph is to determine the rate of spread of the chromatogram under the following conditions. The gas and liquid phases flow in the annular space between two coaxial cylinders of radii ro and r2, the interface being a cylinder with the same axis and radius rx (0 r0 < r < r2). Both phases may be in motion with linear velocity a function of radial distance from the axis, r, and the solute diffuses in both phases with a diffusion coefficient which may also be a function of r. At equilibrium the concentration of solute in the liquid, c2, is a constant multiple of that in the gas, ci(c2 = acj) and at any instant the rate of transfer across the interface is proportional to the distance from equilibrium there, i.e. the value of (c2 - aci). The dispersion of the solute is due to three processes (i) the combined effect of diffusion and convection in the gas phase, (ii) the finite rate of transfer at the interface, (iii) the combined effect of diffusion and convection in the liquid phase. In what follows the equations will often be in sets of five, labelled (a),..., (e) the differential equations expression the three processes (i), (ii) (iii) above are always (b), (c) and (d), respectively equations (a) and (e) represent the condition that there is no flow over the boundaries at r = r0 and r = r2. 

The design of packed column reactors is very similar to the design of packed columns without reaction (Volume 2, Chapter 12). Usually plug flow is assumed for both gas and liquid phases. Because packed columns are used for fast chemical reactions, often the gas-side mass transfer resistance is significant and needs to be taken into account. The calculation starts on the liquid side of the gas-liquid interface where the chemical reaction rate constant is compounded with the liquid side mass transfer coefficient to give a reaction-enhanced liquid-film mass transfer... 

Experimental measurements of dispersion coefficients 91 have shown that, unless the liquid velocity is unusually high, both gas and liquid phase dispersion coefficients... 

CA] = concentration of diffusing vapor that is in equilibrium with the partial pressure of the diffusing vapor in the gas body, lb-mole/ft3 x",y" = the mole fractions corresponding to [CA]" and p, respectively. Kg,KL = overall mass transfer coefficients for the gas and liquid phases, respectively... 

The fluid properties of interest are represented by the Schmidt numbers of the gas and liquid phases. For gases, the Schmidt numbers are normally close to unity and independent of temperature and pressure. Thus, gas-phase mass-transfer coefficients are relatively independent of the system. 

The power input, required for calculation of the mass transfer coefficient, is calculated from Eqs. (36) and (37). For a motionless mixer, the power comes from the gas and liquid phases for the ejector, power comes from the liquid only. 

The overall mass phase coefficient kgj also depends on the gas and liquid phase transfer coefficients ... 

Some of this theoretical thinking may be utilized in reactor analysis and design. Illustrations of gas-liquid reactors are shown in Fig. 19-26. Unfortunately, some of the parameter values required to undertake a rigorous analysis often are not available. As discussed in Sec. 7, the intrinsic rate constant kc for a liquid-phase reaction without the complications of diffusional resistances may be estimated from properly designed laboratory experiments. Gas- and liquid-phase holdups may be estimated from correlations or measured. The interfacial area per unit reactor volume a may be estimated from correlations or measurements that utilize techniques of transmission or reflection of light, though these are limited to small diameters. The combined volumetric mass-transfer coefficient kLa, can be also directly measured in reactive or nonreactive systems (see, e.g., Char-pentier, Advances in Chemical Engineering, vol. 11, Academic Press, 1981, pp. 2-135). Mass-transfer coefficients, interfacial areas, and liquid holdup typical for various gas-liquid reactors are provided in Tables 19-10 and 19-11. 

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