Dew points

Suppose we raise the drum temperature to 160°F and repeat our bubble-point calculation  

Component Vapor Pressure at 160°F, Psia ConcentaaUitg Mol% In Liquid, % Partial Pressure, Psia 

Apparently, our guess of 160°F was wrong. If we had guessed the correct temperature, the calculated vessel pressure would have been 122 psia, not the 110 psia. Try to work this problem yourself by guessing a new flash drum temperature (answer 168°F). 

We will now derive the dew-point equation from the same basic statement of vapor-liquid equilibrium, starting with Eq. (14.3) in the previous section  

However, if we add up the concentration of the three components in the liquid phase on the right-hand side of Eq. (14.7), we would get 100 percent, which is unity or equal to one as before  

Component Vapor pressure at 160°F, psia Concentrating mol% In llquki, % Partial pressure, psia 

we divide both sides of the equation by P, the vessel pressure  

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Similarly, for a dew-point calculation (incipient condensation) a is 1 (again Q = 0) and Equation (7-13) leads to... 

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

For bubble-point and dew-point pressure calculations, the appropriate forms are, respectively ... 

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. 

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). 

ERF error flag, integer variable normally zero ERF= 1 indicates parameters are not available for one or more binary pairs in the mixture ERF = 2 indicates no solution was obtained ERF = 3 or 4 indicates the specified flash temperature is less than the bubble-point temperature or greater than the dew-point temperature respectively ERF = 5 indicates bad input arguments. 

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

Bubble-point temperature or dew-point temperatures are calculated iteratively by applying the Newton-Raphson iteration to the objective functions given by Equations (7-23) or (7-24) respectively. 

Bubble-point and dew-point pressures are calculated using a first-order iteration procedure described by the footnote to Equation (7-25). 

Example 6.4 The process in Fig. 6.2 is to have its hot utility supplied by a furnace. The theoretical flame temperature for combustion is 1800°C, and the acid dew point for the flue gas is 160°C. Ambient temperature is 10°C. Assume = 10°C for process-to-process heat transfer but = 30°C for flue-gas-to-process heat transfer. A high value for for flue-gas-to-process heat... 

Figure 6.30 shows the grand composite curve plotted from the problem table cascade in Fig. 6.186. The starting point for the flue gas is an actual temperature of 1800 C, which corresponds to a shifl ed temperature of (1800 — 25) = mS C on the grand composite curve. The flue gas profile is not restricted above the pinch and can be cooled to pinch temperature corresponding to a shifted temperature of 145 C before venting to the atmosphere. The actual stack temperature is thus 145 + 25= 170°C. This is just above the acid dew point of 160 C. Now calculate the fuel consumption ...

Both the reboiling and condensing processes normally take place over a range of temperature. Practical considerations, however, usually dictate that the heat to the reboiler must be supplied at a temperature above the dew point of the vapor leaving the reboiler and that the heat removed in the condenser must be removed at a temperature lower than the bubble point of the liquid. Hence, in preliminary design at least, both reboiling and condensing can be assumed to take place at constant temperatures. ... 

Once the bubble point is reached (at point B), the first bubble of ethane vapour is released. From point B to C liquid and gas co-exist in the cell, and the pressure is maintained constant as more of the liquid changes to the gaseous state. The system exhibits infinite compressibility until the last drop of liquid is left In the cell (point C), which is the dew point. Below the dew point pressure only gas remains in the cell, and as pressure is reduced below the dew point, the volume increase is determined by the compressibility of the gas. The gas compressibility is much greater than the liquid compressibility, and hence the change of volume for a given reduction in pressure (the... 

If the experiment was now reversed, starling from A and increasing the pressure, the first drop of ethane liquid would appear at point C, the dew point of the gas. Remember that throughoufthis process, isothermal conditions are maintained. 

The experiment could be repeated at a number of different temperatures and initial pressures to determine the shape of the two-phase envelope defined by the bubble point line and the dew point line. These two lines meet at the critical point, where it is no longer possible to distinguish between a compressed gas and a liquid. 

It is important to remember the significance of the bubble point line, the dew point line, and the two phase region, within which gas and liquid exist in equilibrium. 

When the two components are mixed together (say in a mixture of 10% ethane, 90% n-heptane) the bubble point curve and the dew point curve no longer coincide, and a two-phase envelope appears. Within this two-phase region, a mixture of liquid and gas exist, with both components being present in each phase in proportions dictated by the exact temperature and pressure, i.e. the composition of the liquid and gas phases within the two-phase envelope are not constant. The mixture has its own critical point C g. 

Using this mixture as an example, consider starting at pressure A and isothermally reducing the pressure to point D on the diagram. At point A the mixture exists entirely in the liquid phase. When the pressure drops to point B, the first bubble of gas is evolved, and this will be a bubble of the lighter component, ethane. As the pressure continues to drop, the gas phase will acquire more of the heavier component and hence the liquid volume decreases. At point C, the last drop of liquid remaining will be composed of the heavier component, which itself will vaporise as the dew point is crossed, so that below... 

The initial temperature of a gas condensate lies between the critical temperature and the cricondotherm. The fluid therefore exists at initial conditions in the reservoir as a gas, but on pressure depletion the dew point line is reached, at which point liquids condense in the reservoir. As can be seen from Figure 5.22, the volume percentage of liquids is low, typically insufficient for the saturation of the liquid in the pore space to reach the critical saturation beyond which the liquid phase becomes mobile. These... 

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