Phase equilibrium and mass transfer

Successful approaches to designing an extraction process begin with an appreciation of the fundamentals (basic phase equilibrium and mass-transfer principles) and generally rely on both experimental studies and mathematical models or simulations to define the commercial technology. Small-scale e3q)eriments using representative feed usually are needed to accurately quantify physical properties and phase equilibrium. Additionally, it is common practice in industry to perform... 

The melt process depends on the reaction rates, the thermodynamic phase equilibrium, and mass transfer between the phases. Detailed mechanistic studies of the Li-catalyzed melt process have been published by Choi et al. [152], and of the solubility of DPC and phenol in polycarbonate by Webb [153]. The liquid-gas equilibrium has to take into account at least two components phenol and DPC. 

Separation processes rely on various mechanisms, implemented via a unit operation, to perform the separation. The mechanism is chosen to exploit some property difference between the components. They fall into two basic categories the partitioning of the feed stream between phases and the relative motion of various chemical species within a single phase. These two categories are often referred to as equilibrium and mass transfer rate processes, respectively. Separation processes can often be analyzed with either equilibrium or mass transfer models. However, one of these two mechanisms will be the limiting, or controlling, factor in the separation and is, therefore, the design mechanism. 

Recent advances in solution chemistry, thermodynamics and computer technology make it possible to describe quantitatively equilibrium and mass transfer among minerals and aqueous electrolytes in geochemical processes involving large numbers of components, phases, and chemical species at both high and low temperatures and pressures. 

All these processes are, in common, liquid-gas mass-transfer operations and thus require similar treatment from the aspects of phase equilibrium and kinetics of mass transfer. The fluid-dynamic analysis ofthe eqmpment utihzed for the transfer also is similar for many types of liquid-gas process systems. 

We have considered thermodynamic equilibrium in homogeneous systems. When two or more phases exist, it is necessary that the requirements for reaction equilibria (i.e., Equations (7.46)) be satisfied simultaneously with the requirements for phase equilibria (i.e., that the component fugacities be equal in each phase). We leave the treatment of chemical equilibria in multiphase systems to the specialized literature, but note that the method of false transients normally works quite well for multiphase systems. The simulation includes reaction—typically confined to one phase—and mass transfer between the phases. The governing equations are given in Chapter 11. 

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. 

An alternative approach to the solution of the system dynamic equations, is by the natural cause and effect mass transfer process as formulated, within the individual phase balance equations. This follows the general approach, favoured by Franks (1967), since the extractor is now no longer constrained to operate at equilibrium conditions, but achieves this eventual state as a natural consequence of the relative effects of solute accumulation, solute flow in, solute flow out and mass transfer dynamics. 

Mass transfer in either the stationary or mobile phase is not instantaneous and, consequently, complete equilibrltui is not established tinder normal separation conditions. The result is that the solute concentration profile in the stationary phase is always displaced slightly behind the equilibrluM position and the mobile I se profile is similarly slightly in advance of the equilibrium position. The combined peak observed at the column outlet is broadened about its band center, which is located where it would have been for instantaneous equilibrium, provided the degree of nonequllibrluM is small. The stationary phase contribution to Mass transfer is given by equation (1.25)... 

The assumptions inherent in the derivation of the Hertz-Knudsen equation are (1) the vapor phase does not have a net motion (2) the bulk liquid temperature and corresponding vapor pressure determine the absolute rate of vaporization (3) the bulk vapor phase temperature and pressure determine the absolute rate of condensation (4) the gas-liquid interface is stationary and (5) the vapor phase acts as an ideal gas. The first assumption is rigorously valid only at equilibrium. For nonequilibrium conditions there will be a net motion of the vapor phase due to mass transfer across the vapor-liquid interface. The derivation of the expression for the absolute rate of condensation has been modified by Schrage (S2) to account for net motion in the vapor phase. The modified expression is... 

The types of equipment used, which range from stirred tanks and mixer-settlers to centrifugal contactors and various types of columns, affect both capital and operating costs [9]. In the decision to build a plant, the choice of the most suitable contactor for the specific situation is most important. In some systems, because of the chemistry and mass transfer rates involved, several alternative designs of contacting equipment are available. In the selection of a contactor, one must consider the capacity and stage requirements solvent type and residence time phase flow ratio physical properties direction of mass transfer phase dispersion and coalescence holdup kinetics equilibrium presence of solids overall performance and maintenance as a function of contactor complexity. This may appear very complicated, but with some experience, the choice is relatively simple. 

Solvent extraction processes usually run at ambient pressures and temperatures. If higher pressures are applied, it is mostly because a higher extraction temperature is required when equilibrium or mass transfer conditions are more favorable at an elevated temperature. Distillation, on the other hand, is usually carried out at higher temperatures and ambient pressures. To avoid thermal degradation, the pressure sometimes has to be lowered below ambient pressure. Distillation is based on the differences in vapor pressures of the components to be separated, whereas solvent extraction utilizes the differences in intermolecular interactions in the liquid phase. 

Prior to a discussion on the impact of processing air dew point and temperature on the drying rate behavior of a product, it is necessary to consider heat and mass transfer. Water will move from the granule to air in an attempt to reach an equilibrium, or saturated condition, determined by thermodynamics, which can be read from a phase diagram or psychrometric chart. The rate at which water will move from liquid in the granule to vapor in the air increases the further away the system is from equilibrium. When the water evaporates, it requires an amount of energy, the heat of vaporization, in order to change from liquid to vapor. Because of this, we must also consider transfer of heat as well as movement of material. These concepts can be described by equations shown in Table 5. 

A commonly used mass transfer reaction model is presented in Figure 8.1a, where the reaction occurs in the bulk aqueous phase [35, 47]. It is assumed that the substrate dissolved in the organic phase diffuses into the aqueous phase, reaching equilibrium. In the absence of reaction, once equilibrium is achieved, apparent mass transfer ceases. Given the presence of active enzyme, depletion of substrate in the aqueous phase occurs, and the system moves into a new equilibrium. Thus, the overall reaction rate depends both on reaction and mass transfer. 

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]. 

Sometimes it is possible to evaluate the range of validity of measurements and correlations of physical properties, phase equilibrium behavior, mass and heat transfer efficiencies and similar factors, as well as the fluctuations in temperature, pressure, flow, etc., associated with practical control systems. Then the effects of such data on the uncertainty of sizing equipment can be estimated. For example, the mass of a distillation column that is related directly to its cost depends on at least these factors ... 

Design techniques for gas-phase adsorption range from empirical to theoretical. Methods have been developed for equilibrium, for mass transfer, and for combined dynamic performance. Approaches are available for the regeneration methods of heating, purging, steaming, and pressure swing. Several broad reviews have been published on analytical equations... 

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