Distillation mass transfer rates

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. For the simpler geometries, determining the interfacial area is straightforward. For packed beds of particles a, the interfacial area per volume can be estimated as shown in Table 5-27-A. For packed beds in distillation, absorption, and so on in Table 5-28, the interfacial area per volume is included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated... 

Bakowsld [B/ Chem. Eng., 8, 384, 472 (1963) 14, 945 (1969)]. It is based on tbe assumption that tbe mass-transfer rate for a component moving to tbe vapor phase is proportional to tbe concentration of tbe component in tbe liquid and to its vapor pressure. Also, tbe interfacial area is assumed proportional to liquid depth, and surface renewal rate is assumed proportional to gas velocity. The resulting general equation for binaiy distillation is... 

When the mass transfer rates of the two components are equal and opposite the process is said to be one of equimolecular counterdiffusion. Such a process occurs in the case of the box with a movable partition, referred to in Section 10.1. It occurs also in a distillation column when the molar latent heats of the two components are the same. At any point in the column a falling stream of liquid is brought into contact with a rising stream of vapour with which it is not in equilibrium. The less volatile component is transferred from... 

In distillation, equimolecular counterdiffusion takes place if the molar latent heats of the components are equal and the molar rate of flow of the two phases then remains approximately constant throughout the whole height of the column. In gas absorption, however, the mass transfer rate is increased as a result of bulk flow and, at high concentrations of soluble gas, the molar rate of flow at the top of the column will be less than that at the bottom, At low concentrations, however, bulk flow will contribute very little to mass transfer and, in addition, flowrates will be approximately constant over the whole column. 

Using a steady-state film model, obtain an expression for the mass transfer rate across a laminar film of thickness /. in the vapour phase for the more volatile component in a binary distillation process ... 

The reason for the disparity in performance of such devices in the two services has been clearly outlined by Hachmuth (HI). Bubble-tray towers for distillation, for example, use as the source of energy for dispersion of the gas and for developing the desirable turbulent flow conditions both the expansion of the vapor as it experiences a pressure drop in flowing through the tray, and the liquid head available between trays. In liquid extraction only the liquid head is available. When it is considered that the difference in densities of the contacted phases in distillation may be of the order of 50 to 60 lb./cu. ft., whereas in extraction it is more likely to be of the order of 5 or less, it is easy to understand that in the latter case there is simply insufficient energy available from this source to provide for adequate dispersion and interphase movement. Interfacial area between phases remains small, turbulences developed are of a low order, and mass transfer rates are disappointingly small. 

At a particular location in a distillation column, where the temperature is 350 K and the pressure 500 m Hg, the mol fraction of the more volatile component in the vapour is 0.7 at the interface with the liquid and 0.5 in the bulk of the vapour. The molar latent heat of the more volatile component is 1.5 times that of the less volatile. Calculate the mass transfer rates (kmol m 2s 1) of the two components. The resistance to mass transfer in the vapour may be considered to lie in a stagnant film of thickness 0.5 mm at the interface. The diffusivity in the vapour mixture is 2 x 10 5 m2s Calculate the mol fractions and concentration gradients of the two components at the mid-point of the film. Assume that the ideal gas law is applicable and that the Universal Gas Constant R = 8314 J/kmol K. 

A number of industrially important processes, such as distillation, absorption, and extraction, bring two phases into contact. When the phases are not in equilibrium, mass transfer occurs between the phases. The rate of transfer of each species depends on the departure of the system from equilibrium. Quantitative treatment of mass-transfer rates requires knowledge of the equilibrium states (T, P, and compositions) of the system. 

Real distillation processes, however, nearly always operate away from equilibrium. In recent years it has become possible to simulate distillation and absorption as the mass-transfer rate-based operations that they really are, using what have become known as nonequilibrium (NEQ) or rate-based models [Taylor et ah, CEP (July 28, 2003)]. 

In recent years a new approach to the modeling of distillation and absorption processes has become available the nonequilibrium or rate-based models. These models treat these classical separation processes as the mass-transfer rate governed processes that they really are, and avoid entirely the (a priori) use of concepts such as efficiency and HETP [Krishnamurthy and Taylor, AZChE/., 31, 449-465 (1985) Taylor, Kooijman, and Hung, Comput. Chem. Engng., 18, 205-217 (1994)]. 

For gentle evaporation of volatiles, the rotary evaporator is used in the laboratory (Fig. 2.45). The rotating distillation flask creates high turbulence and a new thin film in the upper part of the flask with every rotation. This allows a high heat and mass transfer rate and overheating of the liquid is prevented. 

The total mass transferred is the product of the average flux and the total interfacial area (ahfA j). These expressions for the mass transfer rates in distillation are useful in the prediction of the performance of distillation columns (Chapter 14). 

The mass transfer rates can be evaluated from a model of mass and energy transfer in distillation such as those developed in Chapters 11 and 12. We review the necessary material here for convenience. The molar fluxes in each phase are given by... 

Discuss how the fundamental models of mass transfer in Sections 12.1.7 (binary systems) and 12.2.4 (multicomponent systems) may be used to estimate mass transfer rates for use in a nonequilibrium simulation of an existing distillation column. Your essay should address the important question of how the model parameters are to be estimated. 

The assumption that stages in a distillation column are in equilibrium allows calculations of concentrations and temperatures without detailed knowledge of flow patterns and heat and mass transfer rates. This assumption is a major simplification. 

The efficiency of a stage or plate in a distillation, absorption, or extraction operation is a function of the mass-transfer rates and transfer coefficients. When material is removed from a permeable solid, as in leaching or drying operations, the transfer rates and sometimes the stage efficiencies can be estimated from diffusion theory. 

SFE and PLE are continuous extraction techniques that have enhanced mass transfer rates due to an increase of the concentration gradient between the phases, whereas Soxhlet is a batch technique, though it can be considered a continuous technique because freshly distilled solvent is contacted with the solid matrix with each cycle. 

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