Vapor/liquid equilibrium definition

Vapor permeation and pervaporation are membrane separation processes that employ dense, non-porous membranes for the selective separation of dilute solutes from a vapor or liquid bulk, respectively, into a solute-enriched vapor phase. The separation concept of vapor permeation and pervaporation is based on the molecular interaction between the feed components and the dense membrane, unlike some pressure-driven membrane processes such as microfiltration, whose general separation mechanism is primarily based on size-exclusion. Hence, the membrane serves as a selective transport barrier during the permeation of solutes from the feed (upstream) phase to the downstream phase and, in this way, possesses an additional selectivity (permselectivity) compared to evaporative techniques, such as distillation (see Chapter 3.1). This is an advantage when, for example, a feed stream consists of an azeotrope that, by definition, caimot be further separated by distillation. Introducing a permselective membrane barrier through which separation is controlled by solute-membrane interactions rather than those dominating the vapor-liquid equilibrium, such an evaporative separation problem can be overcome without the need for external aids such as entrainers. The most common example for such an application is the dehydration of ethanol. 

To express the composition of the vapor in equilibrium with the liquid phase of a binary liquid mixture, we first note that the definition of partial pressure (PA = xAP for component A) and Dalton s law (P = PA + PB) allow us to express the composition of the vapor of a mixture of liquids A and B in terms of the partial pressures of the components ... 

A theoretical plate is defined as the degree of separation attained for an infinitesmal vaporization at equilibrium (i.e., the concentration of liquid in a theoretical plate is that of the first bit of vapor to be formed from the liquid in the previous one). Using this definition, approximately how many theoretical plates would be required to achieve a separation into a vapor with xB = 0.1 and a liquid with xB = 0.9 for the system described by the boiling-point diagram in Fig. 9. 

The nature of the phase rule can be induced from some simple examples. Consider the system represented in Figure 24-3. It is made of water-substance (water in its various forms), in a cylinder with movable piston (to permit the pressure to be changed), placed in a thermostat with changeable temperature. If only one phase is present both the pressure and the temperature can be arbitrarily varied over wide ranges the variance is 2. For example, liquid water can be held at any temperature from its freezing point to its boiling point under any applied pressure. But if two phases are present the pressure is automatically determined by the temperature, and hence the variance is reduced to 1. For example, pure water vapor in equilibrium with water at a given temperature has a definite pressure, the vapor pressure of water at that temperature. And if three phases are present in equilibrium, ice, water, and water vapor, both the temperature and the pressure are exactly fixed the variance is then 0. This condition is called the triple point of ice, water, and water vapor. It occurs at temperature +0.0099 C and pressure 4.58 mm of mercury. 

At a given temperature a liquid of definite composition is in equilibrium with its own vapor when the pressure supported by these fluids has a certain value this value does not depend upon the size or the form of the containing vessel, of the masses of the liquid and vapor it depends solely upon the nature of tiie liquid and upon the temperature it is called the tension of scUwraied vapor of the given fluid at the temperature considered. 

A system which encloses, simultaneously, an aqueous solution of a gas, a mixture of this gas with water vapor, and a definite solid compound formed by the union of the gas and water is in equilibrium, at each temperature, when the pressure has a definite value the liquid mixture and the gaseous mixture has, at the same time, a definite composition the total mass of gas and the total mass of water contained in the system do not influence either this tension nor this composition this law was first recognized by Isambert in studying the dissociation of chlorine hydrate the curves of transformation tension of a great number... 

Vapor pressure—The pressure exerted by the vapor at equilibrium condition where the rate of condensation is equal to the rate of vaporization (all liquids and solids exhibit definite vapor pressure at aU temperature). 

The Oldershaw mating provides values of the point efficiency. It is still necessary to correct this efficiency to the Mutphree and overall effidencfea, and approaches for this will be given later. For the moment It is important to consider the potential importance of die Oldershaw scaleup method a specific definition of the system may not be necessary the matter of vapor-liquid equilibria can be bypassed (in effect, the Oldershaw column serves as a multiple-stage equilibrium still) and efficiency modeling can be minimized or even eliminated. 

Although liquid temperatures are uniform throughout the Venturi in noncavitating flow, the effective tensions obtained at incipient cavitation (Fig. 7) indicate that the fluid is locally superheated and thus not in a state of thermodynamic equilibrium. When the fluid ruptures or cavitates, a phase change occurs because the voids rapidly fill with vapor. Vapor generation requires heat of vaporization, which must be drawn from the surrounding liquid. This should result in a cooling of the vapor-liquid interface and a reduction in temperature around and within the cavity. If conditions within the cavity are in thermodynamic equilibrium, then a definite pressure drop should accompany the drop in temperature. 

For the design of RD processes, besides information on the reaction, information on phase equUibria is of prime importance, especially on vapor-liquid equilibria and in some cases also on liquid-liquid equilibria (see above). The systematic investigation of phase equUibria for the design of RD processes will generally involve also studies of reactive systems (see examples above). Studies of phase equUibria in reactive systems generally pose no problem if the reaction is either very fast or very slow as compared with the time constant of the phase equilibrium experiment (high or low Damkohler number Da). In the first case, the solution will always be in chemical equUibrium, in the second case, no reaction will take place. The definition of the time constant of the phase equilibrium experiment win depend on the type of apparatus used. If the RD process is catalyzed and the catalyst does not substantially influence the phase equilibrium, the phase equilibrium experiments can often be performed without catalyst and again no or only little conversion will take place. 

As the vapor pressures p and pi strongly depend on temperature, evaluation of (5.1-3) requires a knowledge of temperature. A simpler formulation of gas-liquid equilibrium is possible by using relative volatilities a according to the following definition ... 

A problem with concentration (or partial pressure) as used in Pick s law is that the respective component concentrations (or partial pressures) are different within two phases at equilibrium, save in the case of homogeneous azeotropes. Therefore, this phase-equilbrium feature of absolute activity is not apparent. It can be accommodated, however, by assigning an equilibrium absolute activity to the one phase that, by definition, would be equal to that of the other. This accommodation is most apparent in its assignment to the behavior of vapor-liquid systems. 

The analogy is with equilibrium-stage vapor-liquid operations such as absorption, stripping, or distillation, where the liquid phase is, by definition, considered at its bubble point, that is, at saturation. In distillation, however,... 

The combinations of physical properties and parameters briefly represent different chemical processes. They describe chemical bonds, structure of the components, working conditions, further calculations desired, accuracy of the methods, simplicity and speed of calculations, data availability and exact definition of phase equilibrium methods applicability in vapor-liquid and liquid-liquid regions. The combinations of phase equilibrium methods represent one or more phase equilibrium methods that are appropriate for designing and simulating such chemical processes. Fifteen ones are chosen that are usually used in practice ... 

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