Bubble and Dew point calculation n2 We have

Bubble and Dew point calculation (n>2) We have four dew and bubble point calculation with Raoult’s law: 1) Bubble T: Given Pt and xi’S Calculate TBm and yi’S 2) Dew T: Given Pt and yi’S Calculate TDm and xi’S 1) Bubble P: Given T and xi’S Calculate PBt and yi’S 1) Dew P: Given T and yi’S Calculate PDt and xi’S

Bubble T Calculation (BTC): Given Pt and xi’S Calculate TBm and yi’S i=1, 2, 3, …, n y 1 Pt=x 1 P 1 s Solution method: y 2 Pt=x 2 P 2 s ⁞ ⁞ yi. Pt=xi. Pis 2 - Calculate Pis’S (from Antoine Eq. ’s) 3 -Calculate xi. Pis ⁞ ⁞ yn. Pt=xn. Pns 4 - Calculate Pt(y 1+y 2+…. +yn)=(x 1 p 1 s+x 2 P 2 s+…. +xn. Pns) ∑yi=1. 0 Pt=∑(xi. Pis) T=∑ xi. TBi 1 - Assume T ∑(xi. Pis) yi=(xi Pis)/Pt s)=P → go step 5 s If ∑(x P i i t ∑xi. Pi If ∑(xi. Pis) ≠ Pt → go step 1 5 - Calculate yi’S yi=(xi. Pis)/ ∑(xi. Pis) If ∑(xi. Pis) < Pt → T ↑ yi=(xi. Pis)/∑(xi. Pis)

Dew T Calculation (DTC): Given Pt and yi’S y 1 Pt=x 1 P 1 s Calculate TDm and xi’S i=1, 2, 3, …, n →x 1=y 1 Pt /P 1 s x 2=y 2 Pt /P 2 s ⁞ ⁞ xi=yi. Pt /Pis ⁞ ⁞ T=∑ yi. TBi 3 -Calculate (yi /Pis) (x 1+x 2+…. +xn)=Pt(y 1/p 1 s+y 2/P 2 s+…. +yn/Pns) Pt=1/∑(yi /Pis) 1 - Assume T 2 - Calculate Pis’S (from Antoine Eq. ’s) xn=yn. Pt /Pns ∑xi=1. 0 Solution method: Pt∑(yi /Pis) 4 - Calculate 1/∑(yi /Pis) If 1/∑(yi/Pis)=Pt→ go step 5 If 1/∑(yi/Pis) ≠ Pt → go step 1 xi=(yi /Pis) Pt 5 - Calculate xi’S xi=(yi /Pis)/∑(yi /Pis) If 1/∑(yi/Pis) < Pt → T ↑ xi=(yi/Pis)/∑(yi/Pis)

Example (3): Find the bubble temperature and vapor composition for a liquid mixture of 50% pentane (1), 30% hexane (2) and 20% cyclohexane (3) (all in mole%) at 5 bar. The system conforms closely to Raoult’s law. Calculations are performed up to ≤ 1% accuracy. Vapor pressure for the pure species are given by the following Antoine equations: TBm (K) P 1 s P 2 s P 3 s ∑xi. Pis %D 387. 589 8. 036 3. 506 2. 522 5. 574 11. 488 380 6. 857 2. 921 2. 088 4. 722 -5. 553 383 7. 307 3. 143 2. 252 5. 047 0. 935 382. 5 7. 230 3. 105 2. 224 4. 992 -0. 169 382. 581 7. 243 3. 111 2. 228 5. 0005 0. 009

Homework (4):