Vapor-liquid equilibrium bubble point

The computer subroutines for calculation of vapor-liquid equilibrium separations, including determination of bubble-point and dew-point temperatures and pressures, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements for these subroutines are given in Appendix J their execution times are strongly dependent on the separations being calculated but can be estimated (CDC 6400) from the times given for the thermodynamic subroutines they call (essentially all computation effort is in these thermodynamic subroutines). 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

If the K-value requires the composition of both phases to be known, then this introduces additional complications into the calculations. For example, suppose a bubble-point calculation is to be performed on a liquid of known composition using an equation of state for the vapor-liquid equilibrium. To start the calculation, a temperature is assumed. Then, calculation of K-values requires knowledge of the vapor composition to calculate the vapor-phase fugacity coefficient, and that of the liquid composition to calculate the liquid-phase fugacity coefficient. While the liquid composition is known, the vapor composition is unknown and an initial estimate is required for the calculation to proceed. Once the K-value has been estimated from an initial estimate of the vapor composition, the composition of the vapor can be reestimated, and so on. 

The vapor-liquid x-y diagram in Figures 4.6c and d can be calculated by setting a liquid composition and calculating the corresponding vapor composition in a bubble point calculation. Alternatively, vapor composition can be set and the liquid composition determined by a dew point calculation. If the mixture forms two-liquid phases, the vapor-liquid equilibrium calculation predicts a maximum in the x-y diagram, as shown in Figures 4.6c and d. Note that such a maximum cannot appear with the Wilson equation. 

A procedure is presented for correlating the effect of non-volatile salts on the vapor-liquid equilibrium properties of binary solvents. The procedure is based on estimating the influence of salt concentration on the infinite dilution activity coefficients of both components in a pseudo-binary solution. The procedure is tested on experimental data for five different salts in methanol-water solutions. With this technique and Wilson parameters determined from the infinite dilution activity coefficients, precise estimates of bubble point temperatures and vapor phase compositions may be obtained over a range of salt and solvent compositions. 

Vapor-liquid equilibrium—e.g., a boiling liquid is at its bubble point, and a condensing vapor is at its dew point. 

The purpose of this chapter is to explain what is meant by the terms bubble point and dew point, and how we can use these ideas to improve the operation of the distillation tower. To begin, we will derive the bubble-point equation, from the basic statement of vapor-liquid equilibrium ... 

In most industrial processes coexisting phases are vapor and liquid, although liquid/liquid, vapor/solid, and liquid/solid systems are also encountered. In this chapter we present a general qualitative discussion of vapor/liquid phase behavior (Sec. 12.3) and describe the calculation of temperatures, pressures, and phase compositions for systems in vapor/liquid equilibrium (VLE) at low to moderate pressures (Sec. 12.4).t Comprehensive expositions are given of dew-point, bubble-point, and P, T-flash calculations. 

Related Calculations. The convergence-pressure K -value charts provide a useful andrapid graphical approach for phase-equilibrium calculations. The Natural Gas Processors Suppliers Association has published a very extensive set of charts showing the vapor-liquid equilibrium K values of each of the components methane to n-decane as functions of pressure, temperature, and convergence pressure. These charts are widely used in the petroleum industry. The procedure shown in this illustration can be used to perform similar calculations. See Examples 3.10 and 3.11 for straightforward calculation of dew points and bubble points, respectively. 

Upon computing the bubble point of the overhead product, we find that the measured reflux temperature is well below the estimated boiling point. Thus, we choose the subcooled condenser model. The steady-state concept of the subcooled condenser often does not exist in practice. Instead, the condenser is in vapor-liquid equilibrium with the vapor augmented by a blanket of noncondensable gas (that has the effect of lowering the dew point of the overhead vapor). The subcooled condenser is a convenient work-around for steady-state models (as is needed here), but not for dynamic models. We assume a partial reboiler. 

Thermodynamic calculations are used to evaluate vapor-liquid equilibrium constants, enthalpy values, dew points, bubble points, and flashes. Established techniques simulate the heat exchangers and distillation columns, and handle convergence and optimization. 

This would correspond to the bubble-point calculation as performed for vapor-liquid equilibrium, the object being to determine the temperature at a given pressure, or vice versa, whereby the first drop of vapor ensues from the vaporization of the liquid phase. That is, it would correspond to a point or locus of points on the saturated liquid curve. 

Dew points and bubble points can be calculated from a knowledge of the vapor-liquid equilibrium for the system. In terms of equilibrium constants, the bubble point and dew point are defined by the following equations ... 

Example 3 Detv and Bubble Point Calculations As indicated by Example 2a, a binary system in vapor/liquid equilibrium has 2 degrees of freedom. Thus of the four phase rule variables T, P, x, and t/i, two must be fixed to allow calculation of the other two, regardless of the formulation of the equilibrium equations. Modified Raoults law [Eq. (4-307)] may therefore be applied to the calculation of any pair of phase rule variables, given the other two. 

This chapter considers the vapor-liquid equilibrium of mixtures, conditions for bubble and dew points of gaseous mixtures, isothermal equilibrium flash calculations, the design of distillation towers with valve trays, packed tower design. Smoker s equation for estimating the number of plates in a binary mixture, and finally, the computation of multi-component recovery and minimum trays in distillation columns. 

The method described here is based on the vapor-liquid equilibrium relationships given in handbooks available from the Gas Processors Suppliers Association. This technique will handle flash calculations with feed streams containing up to 15 components. As an added feature, the calculation will check the feed composition at flash conditions for dew point or bubble point condition (i.e., whether the feed is either all vapor or all liquid). These checks are done before the flash calculations are started. If the feed is above the dew point or below the bubble point, an appropriate message is displayed on the computer screen. A default value for R (L/V) = 1.0 is used to start the iterative process. 

A feed stream made up of 40% mole benzene and 60% mole toluene is to be separated into benzene-rich and toluene-rich products using a distillation column. The column has ten equilibrium stages including a partial condenser and a partial reboiler and is operated at 172 kPa. The feed stream, with a flow rate of 100 kmol/h, is at its bubble point at 172 kPa and is placed in the fourth stage from the top. It is required to determine the compositions of the two products at different reflux ratios. Vapor-liquid equilibrium data for the benzene-toluene system are provided in Table 5.1 at 172 kPa. 

Column l. N = 20 and /= 11. The column has a partial condenser, and is to be operated at a reflux ratio Lul/Di = 4.0 at a pressure of 250 lb/in2 abs. The pressure drop across each plate is negligible. The feed enters the column as a liquid at its bubble point (551.56°R) at the column pressure. The boilup ratio of column 1 is to be selected such that the reboiler duty QRl of column 1 is equal to the condenser duty Qc2 of column 2. Use the vapor-liquid equilibrium and enthalpy data given in Tables B-l and B-2. Since the K values in Table B-l are at the base pressure of 300 lb in2 abs, approximate the K values at 250 lb/in2 abs as follows... 

The column has a total condenser which is to be operated at 40 mmHg. The pressure drop per stage may be taken to be 4.69 mmHg. The flow rate of the feed is 220.55 lb mol/h, and before entering the column, it is a liquid at its bubble-point temperature of 572°R at a pressure of 270 mmHg. The vapor-liquid equilibrium data and the enthalpy data are given in Tables B-3 and B-4. 

The column has a partial condenser which is to be operated at 300 lb/in2 abs. The distillate is removed as dewpoint vapor. The bottoms and the sidestream products are removed as bubble-point liquids. Feeds enter as liquids at their bubble point at the column pressure. Vapor-liquid equilibrium data and enthalpy data are given in Tables B-l and B-2. 

At the lowest pressure in the figure, P = 0.133 bar, the vapor-liquid equilibrium curve intersects the liquid-liquid equilibrium curve. Consequently, at this pressure, depending on the temperature and composition, we may have only a liquid, two liquids, two liquids and a vapor, a vapor and a liquid, or only a vapor in equilibrium. The equilibrium state that does exist can be found by first determining whether the composition of the liquid is such that one or two liquid phases exist at the temperature chosen. Next, the bubble point temperature of the one or either of the two liquids present is determined (for example, from experimental data or from known vapor pressures and an activity coefficient model calculation). If the liquid-phase bubble point temperature is higher than the temperature of interest, then only a liquid or two liquids are present. If the bubble point temperature is lower, then depending on the composition, either a vapor, or. a vapor and a liquid are present. However, if the temperature of interest is equal to the bubble point temperature and the composition is in the range in which two liquids are present, then a vapor and two coexisting liquids will be in equilibrium. 

Equilibrium methods, as proposed originally by Silver [200] and extended by Bell and Ghaly [201] and others, all assume that there is local equilibrium between the vapor and the condensate throughout the condenser. Even though condensation is a nonequilibrium process, the gas temperature Tg is assumed to follow a vapor-liquid equilibrium curve at T, as the vapor mixture is cooled from the mixture dew point 7"dew to the mixture bubble temperature Tbub. These methods therefore require the generation of a cooling or condensation curve (not to be confused with the condensation curve described in Fig. 14.1), as shown in Fig. 14.25,... 

Bubble- and dew-point calculations are useful to determine saturation conditions for liquid and vapor streams, respectively. It is important to note that when vapor-liquid equilibrium is established, the vapor is at its dew point and the liquid is at its bubble point. 

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