Partial vaporization, calculation

Be able to do bubble point, dew point, and partial vaporization calculations for both ideal and nonideal systems (Secs. 10.1, 10.2, and 10.3)... 

As the liquid is depressurized, it partially vaporizes as the vapor is depressurized, it partially condenses. The vapor ratio X can in both cases be calculated from ... 

Relative humidity is usually considered only in connection with atmospheric air, but since it is unconcerned with the nature of any other components or the total mixture pressure, the term is applicable to vapor content in any problem. The saturated water vapor pressure at a given temperature is always known from steam tables or charts. It is the existing partial vapor pressure which is desired and therefore calculable when the relative humidity is stated. 

With the help of these data Ktot and b/p can be calculated, if the water pressure at the sublimation front (pj and the partial vapor pressure in the chamber, measured by a hygrometer, is taken from the respective curves. 

The water activity of food samples can be estimated by direct measurement of the partial vapor pressure of water using a manometer. A simple schematic diagram is shown in Figure A2.4.1. A sample of unknown water activity is placed in the sample flask and sealed onto the apparatus. The air space in the apparatus is evacuated with the sample flask excluded from the system. The sample flask is connected with the evacuated air space and the space in the sample flask is evacuated. The stopcock across the manometer is closed and temperatures are read. The equilibrium manometer reading is recorded (/, ). The stopcock over the sample is closed and the air space is connected with the desiccant flask. The manometer reading in the legs is read to give h2. The water activity of the sample is then calculated (Labuza et al., 1976) as ... 

Equation (9.1) is the preferred method of describing membrane performance because it separates the two contributions to the membrane flux the membrane contribution, P /C and the driving force contribution, (pio — p,r). Normalizing membrane performance to a membrane permeability allows results obtained under different operating conditions to be compared with the effect of the operating condition removed. To calculate the membrane permeabilities using Equation (9.1), it is necessary to know the partial vapor pressure of the components on both sides of the membrane. The partial pressures on the permeate side of the membrane, p,e and pje, are easily obtained from the total permeate pressure and the permeate composition. However, the partial vapor pressures of components i and j in the feed liquid are less accessible. In the past, such data for common, simple mixtures would have to be found in published tables or calculated from an appropriate equation of state. Now, commercial computer process simulation programs calculate partial pressures automatically for even complex mixtures with reasonable reliability. This makes determination of the feed liquid partial pressures a trivial exercise. 

To be useful, this type of simulator must calculate the thermodynamic properties of multicomponent mixtures in both liquid and vapor phases while predicting bubble and dew points or partial vaporizations or condensations. Using this basic information, the simulator must then make calculations for other processes, such as gas cooling by expansion, gas compression, multiple flashes condensations, and separations by absorption... 

If the attraction between the A and B molecules is stronger than that between like molecules, the tendency of the A molecules to escape from the mixture will decrease since it is influenced by the presence of the B molecules. The partial vapor pressure of the A molecules is expected to be lower than that of Raoult s law. Such nonideal behavior is known as negative deviation from the ideal law. Regardless of the positive or negative deviation from Raoult s law, one component of the binary mixture is known to be very dilute, thus the partial pressure of the other liquid (solvent) can be calculated from Raoult s law. Raoult s law can be applied to the constituent present in excess (solvent) while Henry s law (see Section 3.3) is useful for the component present in less quantity (solute). 

AjH (LlBr, g, 298.15 K) -36.8 3 kcal mol" (-153.971 13 kJ mol"" ) Is calculated from the selected enthalpy of vaporization and the enthalpy of formation for lithium bromide (t). Lithium bromide vaporizes to a mixture of monomeric and dimeric gases. (Higher polymers have been neglected In the calculation.) The enthalpies of vaporization to monomer and to dimer were chosen to satisfy (1) the total vapor pressure data measured by von Wartenberg and Schulz (1 ) and by Ruff and Mugdan (2) the partial vapor pressures of monomer and dimer derived from Miller and Kusch (3 ) In an analysis of the velocity distribution of molecules In... 

Lithium vapor contains an appreciable amount of dimer, whose enthalpy of dissociation has been selected by Evans (5), from spectroscopic and molecular beam measuresments to be 25.76 0.10 kcal mol at 0 K. This enthalpy of dissociation, together with the thermodynamic functions calculated in this work, has been used to find the partial pressures of Li(g) and Li2(g) from the measured total vapor pressures. Hartmann and Schneider (6), report values from 1204 to 1353 K while Mancherat (7) reports effusion measurements from 735 to 915 K. Mancherat s (7 ) pressures are calculated on the assumption of monatomic vapor and have been recalculated to fine the true total pressure. Effusion measurements by Lewis (8) and Bogros (9) have been disregarded. Mancherat (7) considers them to be inaccurate because of impurities In the lithium used, and Lewis (S used a doubtful calibration method. Enthalpy of sublimation to monatomic vapor calculated from the vapor pressures of Hartmann and Schneider (6) and of Mancherat (7) agree to within 2% and the average value has been adopted. The enthalpy of sublimation of the dimer was then calculated using this value. 

A stream of hydrofluoric acid (1) in water (2) at 120°C and 200 kPa contains 12% mole hydrofluoric acid (HF). It is proposed to concentrate the HF in solution by partial vaporization in a single stage, by means of temperature and pressure control. Calculate the resulting liquid composition and the fraction vaporized at 120°C and 135 kPa. Can this process be used to concentrate the liquid for any starting composition Use the van Laar equation for liquid activity coefficients and assume ideal gas behavior in the vapor phase. The vapor pressures of HF and water at 120°C are 1693 and 207 kPa, respectively, and the van Laar constants are Ajj = -6.0983, A2] = -6.9658 (see Problems 1.8 and 1.9). 

The stream defined below is heated to 100°C to be partially vaporized in a flash drum before entering a distillation column. The fraction vaporized is controlled by the flash drum pressure. Calculate the required pressure at 100°C to have 20% mole vaporization, assuming Raoult s law applies. What are the products flow rates and compositions The constants for the Antoine Equation 2.19 are given for each component, with the pressure in kPa and the temperature in K. 

A number of studies have explored ways in which partial vapor pressures may be obtained using TGA data, thereby allowing both prediction of vapor pressure under a range of circumstances and calculation of the constants associated with the approaches described previously. In particular, Price and Hawkins (12) have argued that the rate of mass loss for vaporization and sublimation within a TGA should be a zero-order process, and hence should be constant for any given temperature, subject to the important condition that the available surface area also remains constant. This means that the value of v from Equation 6.4 should be easily calculated from the TGA data. If one performs this experiment for materials with known vapor pressure and temperature relationships (the authors used discs of acetamide, benzoic acid, benzophenone, and phenanthrene), then the constant k for the given set of TGA experimental conditions may be found. Once this parameter is known, the vapor pressure may be assessed for an unknown material in the same manner. 

For the analysis of distillation and other vapor-liquid separation processes one must estimate the compositions of the vapor and liquid in equilibrium. This topic is considered in detail in this chapter with particular reference to the preparation of mixture vapor-liquid equilibrium (VLE) phase diagrams, partial vaporization and condensation. calculations, and the use of vapor-liquid equilibrium ippasurements to,obtain infonnac-. 

Equations 10.1-7 and 10.1-8, together with the equilibrium relations, can be used to solve problems involving partial vaporization and condensation processes at constant temperature. For partial vaporization and condensation processes that occur adiabatically, the final temperature of the vapor-liquid mixture is also unknown and must be found as part of the solution. This is done by including the energy balance among the equations to be solved. Since the isothermal partial vaporization or isothermal flash calculation is already tedious (see Illustration 10.1-4), the.adiabatic partial vaporization (or adiabatic flash) problem will not be considered here. ... 

Partial Equilibrium Vaporization Calculation and its Relation to Separation Processes... 

Another possibility is to use a two-stage process in which we vaporize some of the liquid to get a vapor enriched in n-pentane, condense this liquid, and then partially vaporize it to produce a vapor that has even a higher concentration of n-pentane. For example, if we vaporized just 10 mol % of the original liquid (L = 0.9), we would obtain a vapor containing 86.9 mol % n-pentaiie. Now condensing this stream to a liquid and using it as the feed to a second partial vaporization process, repeating the calculation above with this new-feed, we obtain... 

Consider now the partial reboiler shown schematically in Figure 6.17. Saturated liquid leaving the last equilibrium stage in the tower enters the reboiler at a rate of 271.4 kmol/h (75.4 mol/s). Saturated vapor leaves the reboiler and returns to the column at the rate of 193.6 kmol/h (53.8 mol/s), while the liquid residue is withdrawn as the bottoms product at the rate of 77.8 kmol/h (21.6 mol/s). The bottoms product is a saturated liquid with a composition of 5 mol% benzene. A flash-vaporization calculation is done in which the fraction vaporized is known (53.8/75.4 = 0.714) and the concentration of the liquid residue is fixed at xw = 0.05. The calculations yield the following results TR = 381.6 K, xl2 = 0.093, and y]3 = 0.111. The liquid entering the reboiler is at its bubble point, which is Tn = 319.7 K. An energy balance around the reboiler is... 

The following stream is at 200 psia and 200°F. Determine whether it is a subcooled liquid or a superheated vapor, or whether it is partially vaporized, without making a flash calculation. 

A certain ratio of partial vapor pressures of the more-permeable component at the permeate and at the feed side is usually fixed and maintained in the laboratory experiment. When calculating the performance of a real plant in the above-described manner this ratio has to be kept even for the last increment of the membrane area, otherwise a transfer of the laboratory data to the full-scale plant will lead to large errors. By an additional efficiency factor corrections for any differences between the more ideal conditions in the laboratory experiment and the more realistic conditions in an industrial plant may be introduced. 

Here it and are the permeabilities of the better permeable and the retained component and Ap and Ap differences in the respective partial vapor pressures. Both R values have to be determined experimentally and are assumed to be constants for a given feed mixture and membrane and a narrow concentration range. Otherwise the same equations (12) to (15) as for pervaporation can be used and the respective constants have to be determined by regression analysis. Calculation of any practical installation is performed analogous to the method as described above for pervaporation plants. 

In the above calculations and considerations diffusion through the nonporous layer of the membrane was assumed to be the rate-determining process and thus the only transport resistance. In every membrane process, however, additional transport steps at the feed occur, usually summarized as polarization . By the preferential transport of one component out of a mixture through the membrane the fluid layer directly adjacent to the membrane surface will be depleted of that component, and its concentration will be lower than that in the bulk of the feed mixture. This (unknown) lower concentration determines the sorption and thus the effective activity and partial vapor pressure of the component directly at the feed side of the membrane. The flux reduction caused by the additional resistance for the transport of matter by diffusion through the liquid layer adjacent to the feed side of the membrane is known as concentration polarizatioif, and effective in all membrane processes. Due to the phase change... 

With pervaporation membranes the water can be removed during the condensation reaction. In this case, a tubular microporous ceramic membrane supplied by ECN [124] was used. The separating layer of this membrane consists of a less than 0.5 mm film of microporous amorphous silica on the outside of a multilayer alumina support. The average pore size of this layer is 0.3-0.4 nm. After addition of the reactants, the reactor is heated to the desired temperature, the recyde of the mixture over the outside of the membrane tubes is started and a vacuum is apphed at the permeate side. In some cases a sweep gas can also be used. The pressure inside the reactor is a function of the partial vapor pressures and the reaction mixture is non-boiling. Although it can be anticipated that concentration polarization will play an important role in these systems, computational fluid dynamics calculations have shown that the membrane surface is effectively refreshed as a result of buoyancy effects [125]. 

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