Dew point temperature, calculation

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. 

The temperature of the rectifying section pinch point is obtained from either a bubble-point temperature calculation on x,-, or a dew-point temperature calculation on y,>. The result is 126°F. Similarly, the liquid-distillate temperature (bubble point) and the temperature of the vapor leaving the top stage (dew point) are both computed to be approximately 123°F. Because rectifying section pinch-point temperature and distillate temperatures are very close, it would be expected that (/ ) i and would be... 

At the tower inlet pressure, calculate the PO dew point temperature. Calculate the water dew point temperature assuming no previous condensation of PO. 

Solution. We may utilize Eq. (6.22) to obtain the bubble-point temperature by assuming a temperature, obtain the corresponding equilibrium constants from Table 6.2, and then repeat the operation until the equality is satisfied. For the dew-point temperature calculation the procedure is similar, but Eq. (6.21) must be satisfied. From Eq. (6.22) we have... 

Using a reasonable pressure drop between the condenser and the top of the column, we estimated the pressure there. A dew point temperature calculation then on the vapor leaving the top of the column determined ... 

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). 

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. 

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 the dew-point temperature y still equals Zj, and the relationshm X Xi = X i/K-i = 1.0 must be satisfied. As in the case of the bubble point, a trial-and-error search for the dew-point temperature at a specified pressure is involved. Or, if the temperature is specified, the dew-point pressure can be calculated. 

Calculate the bubble-point temperature and the dew-point temperature of the mixture in Exercise 12-6 at 5 psia. 

Six pound moles of ethane, three lb moles of propane and one lb mole of n-butane are mixed in a closed container and the temperature is adjusted to 75°F. What is the bubble-point pressure What is the dew-point pressure Calculate the composi-... 

Next, using RefFlsh, determine the dew point temperature of the debutanizer flashed feed problem at the 85-psig pressure. The answer found is a 396°F dew point. A rapid reading with a quick mental interpolation of Table 2.1 shows we have a mixture enthalpy of 431 Btu/lb at this dew point temperature. The following calculations derive the cooler/condenser duty. 

Calculate dew point temperature assuming the water layer forms first ... 

Calculate dew-point equilibrium for the feed. A vapor is at its dew-point temperature when the first drop of liquid forms upon cooling the vapor at constant pressure and the composition of the vapor remaining is the same as that of the initial vapor mixture. At dew-point conditions, K, = A = Ki Xt, or Xj = Nj /Kj, and Nj /Kj = 1.0, where Yj is the mole fraction of component i in the vapor phase, Xi is the mole fraction of component i in the liquid phase, A is the mole fraction of component i in the original mixture, and Kj is the vapor-liquid equilibrium K value. 

Calculate the dew-point temperature of the mixture at a pressure of 310 psia and an assumed convergence pressure of 800 psia. At various assumed temperatures and at a pressure of 310 psia, the K values for methane, nitrogen, and ethane, as obtained from Figs. 1.15,1.18, and 1.21, are fisted in Table 1.12, as are the corresponding values of A, /Ki. At the dew-point temperature, the latter will add up to 1.0. It can be seen from the table that the dew point lies between —60 and —50°F (222 and 227 K). Therefore, the condensation will take place in the last heat exchanger in the train, because that one lowers the stream temperature from —20°F (244 K) to —100°F (200 K). 

The boiling points of benzene and toluene at 1000 mmHg are first calculated (for instance, by using the Antoine equation, as discussed in Example 3.1). They are 89°C and 141°C, respectively. As a first guess at the dew-point temperature, try a linear interpolation of these boiling points T = (0.8)(89) + (0.2)(141), which approximately equals 100. Let subscript 1 refer to benzene subscript 2 to toluene. 

Table 3.3.3 Summary of Equations for Calculating the Dew-Point Temperature ... 

Similarly, calculate the dew-point temperature. Assume a temperature and then calculate values for the equilibrium relations fiom Equations 3.3.27 and 3.3.28 in Table 3.3.3. Next, calculate the liquid-phase mole fractions fiom 3.3.25 and 3.3.26. Check the results using Equation 3.3.24. Assume a new temperature and repeat the calculation until temperature converges to a desired degree of accuracy. 

Assume a total condenser. The composition of the vapor from the top tray is equal to the composition of the distillate. Calculate the dew-point temperature of the vapor, which is the temperature at the top tray. 

When a liquid is heated slowly at constant pressure, the temperature at which the first vapor bubble forms is the bubble-point temperature of the liquid at the given pressure. When a gas (vapor) is cooled slowly at constant pressure, the temperature at which the first liquid droplet forms is the dew-point temperature at the given pressure. Calculating bubble-point and dew-point temperatures can be a complex task for an arbitrary mixture of components. However, if the liquid behaves as an ideal solution (one for which Raoult s or Henry s law is obeyed for all components) and the gas phase can also be considered ideal, the calculations are relatively straightforward. 

The dew-point temperature of a gas (vapor) may be found using a method similar to that for bubble-point temperature estimation. Again, suppose a gas phase contains the condensable components A, B. C. .. and a noncondensable component G at a fixed pressure P. Let y/ be the mole fraction of component i in the gas. If the gas mixture is cooled slowly to its dew point, Tdp, it will be in equilibrium with the first liquid that forms. Assuming that Raoult s law applies, the liquid-phase mole fractions may be calculated as... 

Calculate the temperature and composition of a vapor in equilibrium with a liquid that is 40.0 mole% benzene-60.0 mole% toluene at 1 atm. Is the calculated temperature a bubble-point or dew-point temperature ... 

A fuel gas containing methane and ethane is burned with air in a furnace, producing a stack gas at 300°C and 105 kPa (absolute). The slack gas contains CO2 at a partial pressure of 80 mm Hg and no CO, O2, methane, or ethane. Calculate the mole fraction of methane in the fuel and the dew-point temperature of the stack gas. 

Prepare a Fortran program that uses either (a) the dry-bulb temperature plus the wet-bulb temperature, or (b) the dry-bulb temperature and the dew point, or (c) the dry-bulb temperature and the relative humidity of (1) the inlet air and (2) the outlet air, respectively, to calculate the amount of water condensed, the heat added or removed, and the dew point temperature of outlet air for a cooling unit given the input of wet air in mVmin. 

After calculating the temperature of the top and bottom products, obtain a new estimate of the column relative volatility for each component. Find the relative volatility of each component in the bottom and top product. Assuming that we have a total condenser, the composition of the vapor rising above the top tray is equal to the composition of the top product. The calculation for the dew-point temperature will give the composition of the liquid on the top tray as well as the temperature. The temperature and liquid composition at the bottom tray is obtained from a bubble point calculation. Next, calculate the relative volatility of each component at the top and bottom tray. Using these values of the relative volatility and the values for the feed, calculate the geometric average volatility, (oCj)avg, of each component from Equation 6.26.19. This calculation is summarized in Table 6.7.2... 

The summations in Equations 2.20 and 2.21 are carried over all components in the system. If the temperature is fixed, the bubble point and dew point pressures may be calculated directly from Equations 2.20 and 2.21. If, however, the pressure is fixed and the bubble point or dew point temperature is required. Equation 2.20 or 2.21 must be solved by an iterative technique such as the Newton-Raphson method because the equations are implicit in the temperature. 

When the distribution coefficients are composition-dependent, the above method must be modified to account for the effect of composition. A search for the unknown bubble point or dew point temperature or pressure is started on the basis of some composition-independent relationship between the X-values and the temperature and pressure, such as Equations 2.20 and 2.21. Component fugacities are then calculated for the vapor phase and the liquid phase, and the /f-values are updated using Equation 2.15. The calculations are repeated until Equation 2.16 or 2.17, as well as Equation 2.12, are satisfied. The iterative scheme for the bubble point pressure calculation may proceed along the following steps ... 

Using the simultaneous method, calculate the bubble point and dew point temperatures at 35 kPa of a mixture of 60% mole benzene (1) and 40% mole toluene (2). Assume Raoult s law applies, and use the vapor pressure data in Example 2.8. 

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