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Separation Process Principles- 2n - Seader &amp; Henley - Solutions Manual

# Eq 12 4 becomes m ilj 1 rjl l j xi j l j 1 xi

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Unformatted text preview: 21 Water 90.0 0.1 83.47 Total: 100.0 300.1 92.30 Extract 291.38 9.79 6.63 307.80 Compared to the C-S results, a higher temperature, lower pressure, smaller CO2 flow rate, and higher number of equilibrium stages are required. Unlike the C-S result, the above is not the optimal result, but is feasible depending on the reliability of the PR EOS with the WS mixing rules. Energy balances were made around each stage, resulting in stage temperatures varying from 355 to 365 K. Exercise 12.1 Subject: Revision of rate-based equations to account for entrainment and occlusion. Given:. Rate-based model Eqs. (12-4) to (12-18). Find: Modified equations Analysis: Entrainment: Let φj = ratio of entrained liquid (in the exiting vapor) that leaves Stage j to the liquid leaving Stage j, yi ,n and yiI,n . Then, the entrained component liquid flow rate leaving Stage j = φjxi, (1 + rjL ) L j . Correspondingly, the entrained component liquid flow rate entering Stage j = φj+1xi,j+1 (1 + rjL 1 ) L j +1 . + Occlusion: Let θj = ratio of occluded vapor (in the exiting liquid) that leaves Stage j to the vapor leaving Stage j, (1 + rjV )V j . Then the occluded component vapor flow rate leaving Stage j = θj yi,j (1 + rjV )V j . Correspondingly, the occluded component vapor flow rate entering Stage j = θj-1 yi,jV 1 (1 + r j −1 )V j −1 . The liquid-phase component material balance, Eq. (12-4), and vapor-phase component material balance, Eq. (12-5), become, respectively, M iLj ≡ (1 + rjL + φ j ) L j xi , j − L j −1 xi , j −1 − φ j +1 (1 + rjL 1 ) L j +1 xi , j +1 − f i ,Lj − N iLj = 0, i = 1, 2, ..., C , + , M iV, j ≡ (1 + rjV + θ j )V j yi , j − V j +1 yi , j +1 − θ j −1 (1 + rjV−1 )V j −1 yi , j −1 − f iVj + N iV, j = 0, , i =1, 2, ...., C The liquid-phase energy balance, Eq. (12-6), and vapor-phase energy balance, Eq. (12-7), become , respectively, E jL ≡ (1 + rjL + φ j ) L j H jL − L j −1 H jL−1 − φ j +1 (1 + rjL 1 ) L j +1 H jL+1 − H jLF + E V ≡ (1 + rjV + θ j )V j H V − V j +1 H V+1 − θ j −1 (1 + rjV−1 )V j −1H V−1 − H VF j j j j j C i =1 C i =1 fi ,Lj + Q L − e L = 0 j j f iVj + QV + eV = 0 , j j The total phase material balances, Eqs. (12-16) and (12-17), become, respectively, M TL, j ≡ (1 + rjL + φ j ) L j − L j −1 − φ j +1 (1 + rjL 1 ) L j +1 − + V M T , j ≡ (1 + rjV + θ j )V j − V j +1 − θ j −1 (1 + rjV−1 )V j −1 − C i =1 C i =1 f i ,Lj − N T , j = 0 f iVj + N T , j = 0 , Exercise 12.2 Subject: Revision of rate-based equations to account for a chemical reaction in the liquid phase. Given:. Rate-based model Eqs. (12-4) to (12-18). Assumption: Perfect mixing in the liquid on a stage. Find: Modified equations for: (a) chemical equilibrium (b) kinetic rate law Analysis: Let the chemical reaction be: ν A A + ν B B ⇔ ν R R + νSS where: νι = stoichiometric coefficient of component i where it is (+) for products R and S, and (-) for reactants A and B. Let the change in flow rate of component i in the liquid on stage j...
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