Model two-film

On tbe basis of tbe two-film model for mass transfer, and relating all efficiencies to gas-pbase concentrations (for convenience only a similar development can be made on tbe basis of bquid concentrations), point efficiency can be expressed in terms of transfer units ... 

In the treatment to follow, we first review the two-film model for gas-liquid mass transfer, without reaction, in Section 9.2.2, before considering the implications for ki-netics-in Section 9.2.3. 

Consider the transport of gaseous species A from a bulk gas to a bulk liquid, in which it has a measurable solubility, because of a difference of chemical potential of A in the two phases (higher in the gas phase). The difference may be manifested by a difference in concentration of A in the two phases. At any point in the system in which gas and liquid phases are in contact, there is an interface between the phases. The two-film model (Whitman, 1923 Lewis and Whitman, 1924) postulates the existence of a stagnant gas film on one side of the interface and a stagnant liquid film on the other, as depicted in Figure 9.4. The concentration of A in the gas phase is represented by the partial pressure, pA, and that in the liquid phase by cA. Subscript i denotes conditions at the interface and 8g and are the thicknesses of the gas and liquid films, respectively. The interface is real, but the two films are imaginary, and are represented by the dashed lines in Figure 9.4 hence, Sg and 8( are unknown. 

The two-film model is a steady-state model that is, the concentration profiles indicated in Figure 9.4 are established instantaneously and remain unchanged. 

Figure 9.4 Two-film model (profiles) for mass transfer of A from gas phase to liquid phase (no reaction)...

The rate expressions developed in this section for gas-liquid systems, represented by reaction 9.2-1, are all based on the two-film model. Since liquid-phase reactant B is assumed to be nonvolatile, for reaction to occur, the gas-phase reactant A must enter the liquid phase by mass transfer (see Figure 9.4). Reaction between A and B then takes place at some location within the liquid phase. At a given point, as represented in Figure 9.4, there are two possible locations the liquid film and the bulk liquid. If the rate of mass transfer of A is relatively fast compared with the rate of reaction, then A reaches the bulk liquid before reacting with B. Conversely, for a relatively fast rate of reaction ( instantaneous in the extreme), A reacts with B in the liquid film before it reaches the bulk liquid. Since the intermediate situation is also possible, we may initially classify the kinetics into three regimes ... 

Figure 9.7 shows concentration profiles schematically for A and B according to the two-film model. Initially, we ignore the presence of the gas film and consider material balances for A and B across a thin strip of width dx in the liquid film at a distance x from the gas-liquid interface. (Since the gas-film mass transfer is in series with combined diffusion and reaction in the liquid film, its effect can be added as a resistance in series.)... 

Suppose pure CO, (A) at 1 bar is absorbed into an aqueous solution of NaOH (B) at 20 C. Based on the data given below and the two-film model, how should the rate of absorption be characterized (instantaneous, fast pseudo-first-order, fast second-order), if cB = (a) 0.1 and (b) 6 mol L 1 ... 

Figure 9.9 Summary of rate or flux expressions for gas-liquid reactions (two-film model)...

For a gas-liquid reaction, represented by 9.2-1, which occurs only in the bulk liquid, the rate law resulting from the two-film model, and given by equation 9.2-18, has three special cases. Write the special form of equation 9.2-18 for each of these three cases, (a), (b), and (c), and describe what situation each refers to. 

In this chapter, we consider process design aspects of reactors for multiphase reactions in which each phase is a fluid. These include gas-liquid and liquid-liquid reactions, although we focus primarily on the former. We draw on the results in Section 9.2, which treats the kinetics of gas-liquid reactions based on the two-film model. More detailed descriptions are given in the books by Danckwerts (1970), by Kastanek et al. (1993), and by Froment and Bischoff (1990, Chapter 14). 

The choice between a tower-type and a tank-type reactor for a fluid-fluid reaction is determined in part by the kinetics of the reaction. As described by the two-film model... 

First, we must consider a gas-liquid system separated by an interface. When the thermodynamic equilibrium concentration is not reached for a transferable solute A in the gas phase, a concentration gradient is established between the two phases, and this will create a mass transfer flow of A from the gas phase to the liquid phase. This is described by the two-film model proposed by W. G. Whitman, where interphase mass transfer is ensured by diffusion of the solute through two stagnant layers of thickness <5G and <5L on both sides of the interface (Fig. 45.1) [1—4]. 

The volatilization of low-molecular-weight by-products from molten PET can be described by using the classical two-film model or the penetration theory of interfacial transport [95],... 

Rafler el al. [105] applied the two-film model to the mass transfer of different alkane diols in poly(alkylene terephthalate) melts and demonstrated a pressure dependency of the mass-transfer coefficient in experiments at 280 °C in a small 3.6L stirred reactor. They concluded that the mass-transfer coefficient kij is proportional to the reciprocal of the molecular weight of the evaporating molecule. 

In this paper, the volatilization of five organophosphorus pesticides from model soil pits and evaporation ponds is measured and predicted. A simple environmental chamber is used to obtain volatilization measurements. The use of the two-film model for predicting volatilization rates of organics from water is illustrated, and agreement between experimental and predicted rate constants is evaluated. Comparative volatilization studies are described using model water, soil-water, and soil disposal systems, and the results are compared to predictions of EXAMS, a popular computer code for predicting the fate of organics in aquatic systems. Finally, the experimental effect of Triton X-100, an emulsifier, on pesticide volatilization from water is presented. 

Two-Film Model for Volatilization of Organics from Water... 

The model provides a good approach for the biotransformation system and highlights the main parameters involved. However, prediction of mass transfer effects on the outcome of the process, through evaluation of changes in the mass transfer coefficients, is rather difficult. A similar mass transfer reaction model, but based on the two-film model for mass transfer for a transformation occurring in the bulk aqueous phase as shown in Figure 8.3, could prove quite useful. Each of the films presents a resistance to mass transfer, but concentrations in the two fluids are in equilibrium at the interface, an assumption that holds provided surfactants do not accumulate at the interface and mass transfer rates are extremely high [36]. 

The above results will be useful for the two-film model of air-water exchange (Chapter 20). A very different bottleneck boundary, that is, the unsaturated zone of a soil, is discussed in Illustrative Example 19.2. 

Diffusive boundaries also exist between different phases. The best known example is the so-called surface renewal (or surface replacement) model of air-water exchange, an alternative to the stagnant two-film model. It will be discussed in Chapter 20.3. 

HETP vs. Fundamental Mass Transfer The two-film model gives the following transfer unit relationship ... 

Considering homogeneous RSPs, mass transfer at the gas/vapor/liquid-liquid interface can be described using different theoretical concepts (57,59). Most often the two-film model (87) or the penetration/surface renewal model (27,88) is used, in which the model parameters are estimated via experimental correlations. In this respect the two-film model is advantageous since there is a broad spectrum of correlations available in the literature, for all types of internals and systems. For the penetration/surface renewal model, such a choice is limited. 

In the two-film model (Figure 13), it is assumed that all of the resistance to mass transfer is concentrated in thin stagnant films adjacent to the phase interface and that transfer occurs within these films by steady-state molecular diffusion alone. Outside the films, in the bulk fluid phases, the level of mixing is so high that there is no composition gradient at all. This means that in the film region, only one-dimensional diffusion transport normal to the interface takes place. 

Thus the gas/vapor/liquid-liquid mass transfer is modeled as a combination of the two-film model and the Maxwell-Stefan diffusion description. In this stage model, the equilibrium state exists only at the interface. 

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