Bubble and Dew Points

As we have seen in the previous Chapter in the first case, B.P., a liquid of specified composition Xj, X2,. .. is given, and we calculate  

The iteration is carried out until the sum, over all mixture components, of calculated y, s is equal to unity  

Bubble and dew point calculations are presented in the next two Examples with the simplest approach, the use of K values from Eqs 14.5.1 through 14.5.5. They can be also carried out with the computer subroutines, using the SRK EoS, given by Daubert (1985), that can be easily adapted to other EoS and for bubble point pressure calculations, using the EoS of Chapter 10, with the Program VLEEOS presented in Appendix E, which can be easily modified to perform B.P. temperature calculations. 

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For bubble and dew-point calculations we have, respectively, the objective functions... 

The bubble and dew-point temperature calculations have been implemented by the FORTRAN IV subroutine BUDET and the pressure calculations by subroutine BUDEP, which are described and listed in Appendix F. These subroutines calculate the unknown temperature or pressure, given feed composition and the fixed pressure or temperature. They provide for input of initial estimates of the temperature or pressure sought, but converge quickly from any estimates within the range of validity of the thermodynamic framework. Standard initial estimates are provided by the subroutines. 

At low or moderate pressures,a Newton-Raphson iteration is not required, and the bubble and dew-point pressure iteration can be, respectively. 

For a given drum pressure and feed composition, the bubble- and dew-point temperatures bracket the temperature range of the equilibrium flash. At the bubble-point temperature, the total vapor pressure exerted by the mixture becomes equal to the confining drum pressure, and it follows that X = 1.0 in the bubble formed. Since yj = KjXi and since the x/s stiU equal the feed concentrations (denoted bv Zi s), calculation of the bubble-point temperature involves a trial-and-error search for the temperature which, at the specified pressure, makes X KjZi = 1.0. If instead the temperature is specified, one can find the bubble-point pressure that satisfies this relationship. 

At a pressure of 10 bar, determine the bubble and dew point of a mixture of hydrocarbons, composition, mol per cent n-butane 21, n-pentane 48, n-hexane 31. The equilibrium K factors can be estimated using the De Priester charts in Chapter 8. 

The following experimental techniques were used to measure the pressures and temperatures for solid-liquid-gas equilibrium, phase compositions (bubble and dew points) for gas-liquid equilibrium, and solid solubilities in supercritical pentane. Experimental procedures and the apparatus are described in detail elsewhere (13). 

Table V. Measured Bubble and Dew Points for Binary Mixtures of...

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... 

Estimating the unknown but required starting values of conditions and compositions is an important and sensitive part of these calculations. The composition of the feed is always known, as is the composition of one of the two phases in bubble and dew point calculations. With the Chao-Seader, Grayson-Streed, and Lee-Erbar-Edmister methods, it is possible to assume that both phases have the composition of the feed for the first trial. This assumption leads to trouble with the Soave-Redlich-Kwong, the Peng-Robinson and the Lee-Kesler-Ploecker... 

A similar representation is based on distillation tines [1], which describe the composition on successive trays of a distillation column with an infinite number of stages at infinite reflux (°°/°° analysis). In contrast with relation (A.8) the distillation lines may be obtained much easier by algebraic computations involving a series of bubble and dew points, as follows ... 

The bubble- and dew-point equations. The equilibrium equation (Eq. 4.3) and the composition constraint [Eq. (4.1)] are combined to get the bubble-point equation,... 

This modified Raoult s law was used for data reduction in Sec. 11.6. Bubble- and dew-point calculations made with Eq. (11.74) are, of course, somewhat simpler than those shown by Figs. 12.12 through 12.15. Indeed, the BUBL P calculation yields final results in a single step, without iteration. The additional assumption of liquid-phase ideality (yk - 1), on the other hand, is justified only infrequently. We note that yk for ethanol in Table 12.1 is greater than 8. 

Curve ABC in each figure represents the states of saturated-liquid mixtures it is called the bubble-point curve because it is the locus of bubble points in the temperature-composition diagram. Curve ADC represents the states of saturated vapor it is called the dewpoint curve because it is the locus of the dew points. The bubble- and dew-point curves converge at the two ends, which represent the saturation points of the two pure components. Thus in Fig. 3.6, point A corresponds to the boiling point of toluene at 133.3 kPa, and point C corresponds to the boiling point of benzene. Similarly, in Fig. 3.7, point A corresponds to the vapor pressure of toluene at 100°C, and point C corresponds to the vapor pressure of benzene. 

The condition at which the liquid just begins to form is called the dew point. The condition at which the vapor just begins to form is called the bubble point. A curve can be plotted showing the temperature and pressure at which a mixture just begins to liquefy. Such a curve is called a dew-point curve or dew-point locus. A similar curve can be constructed for the bubble point. The phase envelope is the combined loci of the bubble and dew points, which intersect at a critical point. The phase envelope maps out the regions where the various phases exist. 

The phase of a given mixture is determined by a method similar to the rules for a pure component. At pressures greater than the bubble point pressure, the mixture exists as a liquid. At pressures less than the dew point, the mixture exists as a gas. At a pressure between the bubble and dew points, the mixture is two phase. 

There are three basic phase equilibrium calculations (1) a flash calculation - phase split at specified conditions, (2) bubble point calculation, and (3) dew point calculation. For bubble and dew points, there are two types of calculations. First, the temperature is specified and the pressure is calculated. The alternative occurs when the pressure is specified and the temperature is calculated. 

The solution of the equations listed in Table 3.3.1 requires an iterative procedure. Thus, it is good strategy to examine the variables to determine if there are limits on their values. For example, the mole fractions of the components will vary from zero to one. This fact greatly simplifies the solution procedure. Also, the final flash temperature will lie somewhere between the bubble and dew-point temperatures. The bubble-point temperature is that temperature at which the first... 

Assume a temperature, T2, between the bubble and dew point temperatures. 

To obtain the composition of the top and bottom products, first calculate the relative volatility of each component using the conditions of the feed as a first guess. The relative volatility depends on temperature and pressure. The bubble point of the feed at 400 psia (27.6 bar) and at the feed composition, calculated using ASPEN [57], is 86.5 °F (130 °C). The K-values of the feed are listed in Table 6.7.1. Bubble and dew points could also be calculated using K-values from the DePriester charts [31] and by using the calculation procedures given in Chapter 3. Next, calculate the relative volatility of the feed stream, defined by Equation 6.27.18, for each component relative to the heavy key component. 

Use a Txy or Pxy diagram to determine bubble- and dew-point temperatures and pressures, compositions and relative amounts of each phase in a two-phase mixture, and the effects of varying temperature and pressure on bubble points, dew points, and phase amounts and compositions. Outline how the diagrams are constructed for mixtures of components that obey Raoult s law. 

Once you have a Txy diagram like that of Figure 6.4-1, bubble- and dew-point calculations become trivial. To determine a bubble-point temperature for a given liquid composition, go to the liquid curve on the Txy diagram for the system pressure and read the desired temperature from the ordinate scale. (If you are not sure why this works, go back and consider again how the curve was generated.) You can then move horizontally to the vapor curve to determine the composition of the vapor in equilibrium with the given liquid at that temperature. 

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