Vapor-Liquid Equilibria Continued

Combined Chemical and Vapor-Liquid Equilibrium (Continued)... 

In the case of vapor-liquid equilibrium, the vapor and liquid fugacities are equal for all components at the same temperature and pressure, but how can this solution be found In any phase equilibrium calculation, some of the conditions will be fixed. For example, the temperature, pressure and overall composition might be fixed. The task is to find values for the unknown conditions that satisfy the equilibrium relationships. However, this cannot be achieved directly. First, values of the unknown variables must be guessed and checked to see if the equilibrium relationships are satisfied. If not, then the estimates must be modified in the light of the discrepancy in the equilibrium, and iteration continued until the estimates of the unknown variables satisfy the requirements of equilibrium. 

Component continuity Vapor-liquid equilibrium Densities of vapor and liquid... 

An equilibrium-flash calculation (using the same equations as in case A above) is made at each point in time to find the vapor and liquid flow rates and properties immediately after the pressure letdown valve (the variables with the primes F , F l, y], x j,.. . shown in Fig. 3.8). These two streams are then fed into the vapor and liquid phases. The equations describing the two phases will be similar to Eqs. (3.40) to (3.42) and (3.44) to (3.46) with the addition of (1) a multi-component vapor-liquid equilibrium equation to calculate Pi and (2) NC — 1 component continuity equations for each phase. Controller equations relating 1 to Fi and P to F complete the model. 

For continuous systems, molar flow rates Q can be used instead of n. The thermodynamic activity (ax) can be calculated according to Equation 2, but requires knowledge of the saturation pressure of the pure compound (Ppsatx). This data can be obtained from the saturation curves (vapor-liquid equilibrium curves) and is taken at the working temperature of the gas stream. The thermodynamic activity is then calculated using the following equation ... 

Vickery and Taylor [21] suggest using t as the exponent for the parts of expressions that are giving convergence difficulties. Used in this fashion, t can be termed a natural continuation parameter. For example, consider writing the following vapor-liquid equilibrium relationship with the parameter t included as shown. 

In order to correlate the results obtained, a modified SRK equation of state with Huron-Vidal mixing rules was used. Details about the model are reported in the paper by Soave et al. [16]. This approach is particularly adequated when experimental values of the critical temperature and pressure are not available as it was the case for limonene and linalool. Note that the flexibility of the thermodynamic model to reproduce high-pressure vapor-liquid equilibrium data is ensured by the use of the Huron-Vidal mixing rules and a NRTL activity coefficient model at infinite pressures. Calculation results are reported as continuous curves in figure 2 for the C02-linalool system and in figure 3 for C02-limonene. Note that the same parameters values were used to correlated the data of C02-limonene at 45, 50 e 60 °C. 

Ratzsch, M. T. and H. Kehlen Application of continuous thermoldynamics to the vapor-liquid equilibrium. Z. Chem.( Leipzig) 23, 389-394(1983)... 

Two early studies of the phase equilibrium in the system hydrogen sulfide + carbon dioxide were Bierlein and Kay (1953) and Sobocinski and Kurata (1959). Bierlein and Kay (1953) measured vapor-liquid equilibrium (VLE) in the range of temperature from 0° to 100°C and pressures to 9 MPa, and they established the critical locus for the binary mixture. For this binary system, the critical locus is continuous between the two pure component critical points. Sobocinski and Kurata (1959) confirmed much of the work of Bierlein and Kay (1953) and extended it to temperatures as low as -95°C, the temperature at which solids are formed. Furthermore, liquid phase immiscibility was not observed in this system. Liquid H2S and C02 are completely miscible. 

The continued research programs on extractive distillation by salt effect and on salt effect in vapor-liquid equilibrium at the Royal Military College of Canada are supported by the Defence Research Board of Canada, Grant No. 9530-40. 

A vapor-recirculating equilibrium still similar to that described by Hipkin and Myers (1) was used to determine vapor-liquid equilibrium data for the system, water-MEK-THF. In this still shown schematically in Figure 1, a recirculating vapor is continuously contacted with a static liquid sample. The vapor-liquid system is enclosed by a jacket where... 

We begin the analysis of phase equilibria (for those cases where phase splitting does in fact occur) with the simplest possible case, that of vapor-liquid equilibrium where both the liquid and the vapor phase are ideal, so that Raoult s law applies (Astarita, 1989 Bowman, 1949 Edminster, 1955). In this case the only parameter that completely characterizes every individual component is its vapor pressure b at the temperature considered hence, one begins by using b itself as the (dimensional) component label. Let X (b) and X (fc) be the mole fraction distributions in the liquid and vapor phases, respectively, and let p be the total pressure. Obviously, the zeroth moments of both distributions are unity. The continuous form of Raoult s law is ... 

Moore, P. K., and Anthony, R. G., The continuous-lumping method for vapor-liquid equilibrium calculations. AIChEJ. 35, 1115 (1989). 

Wahnschafft. O. M. A Simple and Robust Continuation Method for Determining All Azeotropes Predicted by a Multicomponent Vapor-Liquid Equilibrium Model, in preparation (1994). 

A three-stage batch distillation column is charged with a 100 kmol mixture containing 60% mole component 1 and 40% mole component 2. The column pressure is maintained at 100 kPa, and the distillate rate is 20 kmol/h. It is desired to produce two distillation cuts. The first cut will be produced by continuously adjusting the reflux ratio to maintain the distillate composition at 90% mole component 1. Production of the second cut starts when the L/V ratio is 0.80. The L/V ratio will be fixed at this value until the second cut cumulative composition is 75% mole component 1. Determine the amount of each cut. Assume negligible tray holdups and use vapor-liquid equilibrium data from Problem 6.1. 

Gmehling, J., U. Onken, and W. Arlt, Vapor-Liquid Equilibrium Collection (continuing series, Frankfurt DECHEMA, 1979-). 

Consider one mole per hour of a stream consisting of n volatile liquids with known compositions, and Xf i to be continuously separated into vapor and liquid streams at a given temperature and pressure (Reklaitis, 1983). It is desired to determine the steady-state flow rates of the vapor stream and of the liquid stream and their compositions. Let /f be the vapor-liquid equilibrium constants, Ki = yJXi, where X and are the liquid and vapor fractions, respectively. Ki is calculated from Raoult s law, A" = Pi(T)IP, where is the vapor pressure obtained from the Antoine equation. The flow rate of vapor stream, V, is obtained by solving the following nonlinear equation resulting out of the material balance on each of the species ... 

Vapor-Liquid Equilibrium Collection, Chemistry Data Series (continuing series), DECHEMA, Frankfurt, Germany.]... 

One hundred kilogram/moles per hour of a saturated liquid mixture of 12mole% ethyl alcohol in water is distilled continuously by direct steam at I atm. Steam is introduced directly to the bottom plate. The distillate required is 85 mole% alcohol, representing 90% recovery of the alcohol in the feed. The reflux is saturated liquid with L/D = 3. Feed is on the optimum stage. Vapor-liquid equilibrium data are given in Problem 8.30. Calculate ... 

Othmer and his coworkers have studied esterification reactions to develop a theoretical basis for the design of continuous reactors. For a given system of acid and alc(fliol, the kinetics are studied and an equation is developed which relates the rate constant to the mole ratio of reactants, catalyst concentration, and reaction temperature. Vapor-liquid equilibrium data are obtained by operation of a small continuous reactor. 

Analogously to batch distillation and the RCM, the simplest means of reactive distillation occurs in a still where reaction and phase separation simultaneously take place in the same unit. Additionally, we can choose to add a mixing stream to this still, and the overall process thus consists of three different phenomena chemical reaction, vapor liquid equilibrium, and mixing. Such a system is referred to as a simple reactive distillation setup. This setup is shown in Figure 8.1 where a stream of flowrate F and composition Xp enters a continuously stirred tank reactor (CSTR) in which one or more chemical reaction(s) take place in the liquid phase with a certain reaction rate r =f(kf, x, v) where v represents the stoichiometric coefficients of the reaction. Reactants generally have negative stoichiometric coefficients, while products have positive coefficients. For example, the reaction 2A + B 3C can... 

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