1. Lecture 6: Bubble and Dew Point 1 Bubble Point and Dew Point Calculations In the last lecture we discussed: An isothermal flash separations The derivation and solution of the Rachford Rice equation Newton’s iterative procedure to solve for the roots of the RR equation A numerical example to demonstrate this approach. This lecture will cover: An example of using the Rachford Rice Procedure with a simple spreadsheet Bubble point and Dew Point temperature and pressure calculations An example of a dew point temperature calculation

2. Lecture 6: Bubble and Dew Point 2 Multicomponent Flash Calculations For this system there are 3C+10 variables: F, V, L, {T, P} 3, Q, {x i, y i,z i } C and C+5 degrees of freedom. We specify the C+3 variables F, z i, T F, P F and two additional variables Liquid Feed Vapor out Flash Drum F, z i, T F, P F L, x i, T L, P L Liquid out V, y i, T V, P V Q Common Specifications: T V,P V Isothermal Flash V/F=0, P L Bubble-Point Temperature V/F=1, P V Dew-Point Temperature V/F=0, T L Bubble-Point Pressure V/F=1, T V Dew-Point Pressure Q=0, P V Adiabatic Flash Q, P V Nonadiabatic flash V/F, P V Percent Vaporization Flash Last lecture

3. Lecture 6: Bubble and Dew Point 3 Isothermal Flash Calculations Liquid Feed If we specify F, z i, T F, P F and T V,P V then we apply the Rachford-Rice procedure: Vapor out Flash Drum F, z i, T F, P F L, x i, T L, P L Liquid out V, y i, T V, P V Q Steps 1&2: Step 3:Solve Rachford-Rice for V/F. Step 4: Steps 5 and 6: Step 7: Step 8: Determine V Determine L Determine Q

4. Lecture 6: Bubble and Dew Point 4 Bubble Point Pressure Calculations Liquid Feed For a bubble point pressure calculation we specify F, z i, T F, P F, T L and that we are at the bubble point. Vapor out Flash Drum F, z i, T F, P F L, x i, T L, P L Liquid out V=0, y i, T V, P V Q At the bubble point there is equilibrium between the vapor and liquid phases, but the system is completely liquid and thus the vapor fraction  is zero.

5. Lecture 6: Bubble and Dew Point 5 Bubble Point Temperature Calculations Liquid Feed For a bubble point temperature calculation we specify F, z i, T F, P F, P L and that we are at the bubble point. Vapor out Flash Drum F, z i, T F, P F L, x i, T L, P L Liquid out V=0, y i, T V, P V Q At the bubble point there is equilibrium between the vapor and liquid phases, but the system is completely liquid and thus the vapor fraction  is zero.

6. Lecture 6: Bubble and Dew Point 6 Dew Point Temperature Calculations Liquid Feed For a Dew Point Temperature calculation we specify F, z i, T F, P F, P V and that we are at the dew point. Vapor out Flash Drum F, z i, T F, P F L=0, x i, T L, P L Liquid out V, y i, T V, P V Q At the dew point there is equilibrium between the vapor and liquid phases, but the system is completely vapor and thus the vapor fraction  is one.

7. Lecture 6: Bubble and Dew Point 7 Dew Point Pressure Calculations Liquid Feed For a Dew Point Pressure calculation we specify F, z i, T F, P F, P V and that we are at the dew point. Vapor out Flash Drum F, z i, T F, P F L=0, x i, T L, P L Liquid out V, y i, T V, P V Q At the dew point there is equilibrium between the vapor and liquid phases, but the system is completely vapor and thus the vapor fraction  is one.

8. Lecture 6: Bubble and Dew Point 8 Bubble Point and Dew Point Calculations To solve the bubble point and dew point problems we must find the unspecified temperature or pressure which satisfies the Rachford Rice expressions. Dew Point Bubble Point Bubble Point or Dew Point Temperature Procedure: Step 1: Guess a temperature. Step 2: Use the given product pressure and guess temperature to determine the K-values from the DePriester chart. Step 3: Calculate the Rachford Rice expression appropriate to the equilibrium condition. Step 4: Guess a new higher temperature if K values must be higher. Otherwise, guess a lower temperature. Step 5: Repeat Steps 3 and 4 until the Rachford Rice equation is satisfied. Bubble Point or Dew Point Pressure Procedure: Step 1: Guess a pressure. Step 2: Use the given product temperature and guess pressure to determine the K-values from the DePriester chart. Step 3: Calculate the Rachford Rice expression appropriate to the equilibrium condition. Step 4: Guess a new lower pressure if K values must be higher. Otherwise, guess a higher pressure. Step 5: Repeat Steps 3 and 4 until the Rachford Rice equation is satisfied.

9. Lecture 6: Bubble and Dew Point 9 Example: Rachford-Rice A flash chamber operating 80 degrees C and 500kPa is separating 1000 kg moles/hr of a feed that is 10 mole %ethane, 5 mole %propane, 15 % n-butane, 10 % n-pentane, 12 mole % isopentane, 8 mole %n-hexane, 30 mole %heptane and 10% nonane. What are the product compositions and flow rates? y 1 (ethane) = 0.358 y 2 (propane) = 0.132 y 3 (n-butane) = 0.236 y 4 (n-pentane) = 0.11 y 5 (isopentane) = 0.079 y 6 (n-hexane) = 0.03 y 7 (heptane) = 0.051 y 8 (nonane) = 0.003 x 1 (ethane) = 0.033 x 2 (propane) = 0.029 x 3 (n-butane) = 0.128 x 4 (n-pentane) = 0.123 x 5 (isopentane) = 0.105 x 6 (n-hexane) = 0.093 x 7 (heptane) = 0.365 x 8 (nonane) = 0.125 V/F=0.207 V=207kg/hr L=793kg/hr K 1 (ethane) = 11.0 K 2 (propane) = 4.6 K 3 (n-butane) = 1.85 K 4 (n-pentane) = 0.75 K 5 (isopentane) = 0.9 K 6 (n-hexane) = 0.32 K 7 (heptane) = 0.14 K 8 (nonane) = 0.026 From the Depriester chart:

10. Lecture 6: Bubble and Dew Point 10 Depriester Determination of K-Values

11. Lecture 6: Bubble and Dew Point 11 Example: Dew Point Temperature A flash chamber operating 400 kPa pressure is producing a top product of 35 % n-butane, 30 % n-pentane, 15 mole %n-hexane, 20 mole %heptane. What is the temperature of the flash drum to operate at the dew point? x 1 (n-butane) = x 2 (n-pentane) = x 3 (n-hexane) = x 4 (heptane) = V/F= T= From the Depriester chart: y 1 (n-butane) = 0.35 y 2 (n-pentane) = 0.3 y 3 (n-hexane) = 0.15 y 4 (heptane) = 0.2 T= K 1 (n-butane) = K 2 (n-pentane) = K 3 (n-hexane) = K 4 (heptane) = T= K 1 (n-butane) = K 2 (n-pentane) = K 3 (n-hexane) = K 4 (heptane) = T= K 1 (n-butane) = K 2 (n-pentane) = K 3 (n-hexane) = K 4 (heptane) = T= K 1 (n-butane) = K 2 (n-pentane) = K 3 (n-hexane) = K 4 (heptane) =

12. Lecture 6: Bubble and Dew Point 12 K-Values Iterations for Dew Point Temperature

13. Lecture 6: Bubble and Dew Point 13 Example: Bubble Point Pressure A flash chamber operating 80 degrees C is producing a bottoms product of 15 % n-butane, 20 % n-pentane, 25 % n-hexane, 40 % heptane. What is the pressure of the flash drum to operate at the bubble point? x 1 (n-butane) = 0.15 x 2 (n-pentane) = 0.20 x 3 (n-hexane) = 0.25 x 4 (heptane) = 0.4 V/F= P= K 1 (n-butane) = K 2 (n-pentane) = K 3 (n-hexane) = K 4 (heptane) = From the Depriester chart: y 1 (n-butane) = y 2 (n-pentane) = y 3 (n-hexane) = y 4 (heptane) = P= K 1 (n-butane) = K 2 (n-pentane) = K 3 (n-hexane) = K 4 (heptane) = P= K 1 (n-butane) = K 2 (n-pentane) = K 3 (n-hexane) = K 4 (heptane) = P= K 1 (n-butane) = K 2 (n-pentane) = K 3 (n-hexane) = K 4 (heptane) =

14. Lecture 6: Bubble and Dew Point 14 Depriester Determination of K-Values

15. Lecture 6: Bubble and Dew Point 15 Summary Next Lecture will cover: Ternary Liquid-Liquid extractions. Ternary phase diagrams. A procedure to determine the product compositions and flow rates of a liquid-liquid extraction separation. This lecture covered: Using a simple spreadsheet to apply the Rachford Rice Procedure Bubble point and Dew Point temperature and pressure calculations An example of a dew point temperature calculation