Vapor-liquid equilibrium bubble point pressures

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). 

BUDEP calculates the bubble-point pressure or the dew-point pressure for a mixture of N components (N j< 20) at specified temperature and liquid or vapor composition. The subroutine also furnishes the composition of the incipient vapor or liquid and the vaporization equilibrium ratios. 

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 pressure at the suction of the pump falls to its bubble or boiling point, the liquid will start to vaporize. This is called cavitation. A cavitating pump will have an erratically low discharge pressure and an erratically low flow. As shown in Fig. 23.5, the bubble-point pressure of the liquid, is the pressure in the vessel. We usually assume that the liquid in a drum is in equilibrium with the vapor. The vapor is then said to be at its dew point, while the liquid is said to be at its bubble point. 

Let us see what cavitation means in reference to the pump shown in Fig. 25.1. The liquid shown in the vessel is presumed to be in equilibrium with the vapor leaving the drum. This means that the liquid is at its bubble-point pressure and the vapor is at its dew-point temperature. 

Answer—no Unfortunately, it is not only the pressure of the liquid at the pump that changes. The composition of the liquid will also be altered. As the pressure in the drum increases, additional lighter components dissolve in the liquid. The composition of the liquid then becomes lighter. The vapor pressure of the liquid will also increase by 5 psi. This must happen because the liquid in the drum, which is in equilibrium with the vapor, is at its bubble-point pressure. 

Compositions and Quantities of the Equilibrium Gas and Liquid Phases of a Real Solution — Calculation of the Bubble-Point Pressure of a Real Liquid—Calculation of the Dew-Point Pressure of a Real Gas Flash Vaporization 362... 

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. 

Calculation of Bubble-Point Pressure and Dew-Point Pressure Using Equilibrium Constants. Since the total pressure P

bubble-point and dew-point pressure as was done in the case of ideal solutions. A method will now be presented for calculating the bubble-point pressure and the dew-point pressure, which is applicable to both binary and multicomponent systems which are non-ideal. At the bubble point the system is entirely in the liquid state except for an infinitesimal amount of vapor. Consequently, since ti, = 0 and n — n% equation 19 becomes... 

The pressure at which the first vapor forms when a liquid is decompressed at a constant temperature is the bubble-point pressure of the liquid at the given temperature. Equation 6.4-4 can be used to determine such a pressure for an ideal liquid solution at a specific temperature, and the mole fractions in the vapor in equilibrium with the liquid can then be determined as... 

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. 

Different approaches to modeling the ternary S-L-V equilibrium reported so far essentially differ in the calculation procedure adopted for the S-L equilibrium. For example, the liquid phase composition in the ternary S-L equilibrium for different pressures at any temperature may be calculated by means of (a) the expanded liquid EOS and activity coefficient model, (b) the EOS model, or (c) the PMVF of solvent. Subsequently, the isofugacity criterion for the L-V equilibrium is considered to predict the bubble point pressure and the vapor phase composition to ensure that all three (S-L-V) phases will coexist. Clearly, the ternary liquid and vapor phase mole fractions can be... 

At the specified temperature, estimate the bubble point pressure and the equilibrium vapor composition using the K-values based on Raoult s law (Equations 2.18 through 2.20). The liquid composition is the same as the feed composition. 

Calculate the bubble point pressure at 63°C of the liquid solution given in Example 1.6A. What is the equilibrium vapor composition Assume ideal gas behavior in the vapor phase. The component properties are given below ... 

One more variable that may require special consideration in extractor calculations is the column pressure. In the rigorous multistage methods the stage pressures are considered fixed. In extractor calculations the pressure profile is also considered fixed, and although its effect on liquid-liquid equilibrium may be neglected, it should be checked to ascertain that it is above the bubble point pressure, and that no vapor phase exists. 

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. 

Phase equilibrium calculations with equations of state are iterative and sufficiently complicated to be best done on a digital computer. Consider, for example, the calculation of the bubble point pressure and vapor composition for a liquid of known composition at temperature T. One would need to make an initial guess for the bubble point pressure, P s,.and the vapor mole fractions (or, perhaps more easily, for the values of K = y /x ), and then check to ensure that at the equality of species... 

Since liquids are not very compressible, at low and moderate pressures liquid-liquid equilibrium compositions are almost independent of pressure. Therefore, assuming that the liquid-liquid equilibrium of the isobutane (l)-furfural (.2) mixture at 37.8°C calculated in Illustration 11.2-2 is unaffected by pressure, compute the pr essure at which the first bubble of vapor will form (i.e., compute the bubble point pressure of this system) and the composition of the vapor that forms. Data ... 

Use the Peng-Robinson equation of state and the van der Waals one-fluid mixing rules, with 12 = 0.114, to compute the bubble point pressure and vapor composition in equilibrium with the two coexisting liquid phases in the C02-)i-decane system of Illustration 11.2-5. 

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. 

The formulation of the problem in the previous illustration permits solutions for various pressures, and the same MATHCAD program was used to obtain solutions for most of the pressure range. The results of such calculations are shown in the accompanying figure in terms of the molar extent of reaction X and the molar fraction of the total mixture that is liquid, denoted by /. There are several things to notice in the solution to this problem. First, for pressures above about 33 kPa there is no equilibrium vapor phase (i.e., / = 1). That is, the bubble point pressure of this equilibrium reacting mixture at 25°C is 33 kPa, so for higher pressures only a liquid phase is present. Also, and only coincidentally, the reaction is essentially at completion (X = 2) at this pressure. At other temperatures and certainly for other reactions, the disappearance of the vapor phase and the point of essentially complete reaction would not coincide. 

Consider a liquid stream composed of two components A and B at a ligh pressure pj and temperature 7. If the pressure p/ is larger than the nubble-point pressure of the liquid at temperature Tf, no vapor phase will ne present. The liquid stream passes through a restriction (valve) and is. flashed in a drum that is, its pressure is reduced from Pf to p (Figure 1.6). This abrupt expansion takes place under constant enthalpy. If the pressure p in the drum is smaller than the bubble-point pressure of the [iquid stream at the temperature Tf, the liquid will partially vaporize and wo phases at equilibrium with each other will be present in the flash drum. 

These tables summarize the thermophysical properties of air in the liquid and gaseous states as calculated from the pseudo-pure fluid equation of state of Lemmon et al. (2000). The first table refers to liquid and gaseous air at equilibrium as a function of temperature. The tabulated properties are the bubble-point pressure (i.e., pressure at which boiling begins as the pressure of the liquid is lowered) the dew-point pressure (i.e., pressure at which condensation begins as the pressure of the gas is raised) density (/ ) enthalpy (H) entropy (S) isochoric heat capacity (CJ isobaric heat capacity (C ) speed of sound (u) viscosity (rj) and thermal conductivity (A). The first line of identical temperatures is the bubble-point (liquid) and the second line is the dewpoint (vapor). The normal boiling point of air, i.e., the temperature at which the bubble-point pressure reaches 1 standard atmosphere (1.01325 bar), is 78.90 K (-194.25 °C). 

Figure 2.3-2 (a) Vapor-liquid equilibrium of the system C02-toluene at 311 K. Experimental bubble points (O) and dew points ( ) are shown as a function of the pertinent composition. The bubble and dew curves are calculated with the Peng-Robinson equation of state, (b) Percent volumetric expansion of the liquid phase in the system C02-toluene at 298 K as a function of pressure. The curve was calculated with the Peng-Robinson equation of state. 

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