ch12 - CHAPTER12 GasLiquidEquilibria...

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  CHAPTER 12  Gas-Liquid Equilibria Gas-Liquid Equilibria Simulation of Flash Vaporization for Nonideal  Liquids: Given: a. Total composition of mixture (z) b.Total moles of mixture (n) c. Pressure (P) d.Temperature (T) Calculate: 1. How many phases are present. 2. Amount of gas present if P and T are such  that the mixture exists in  the 2-phase  region (n g m g ). 3. Amount of liauid present if P and T are such  that the mixture exists in the 2-phase region  (n L m L ). 4. Liquid composition (x) 12 - 1
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5. Gas composition (y) 6. Bubble point pressure of mixture at T (P b ) 7. Dew point pressure of mixture at T (P d ) 12 - 2
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12 - 3
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Flash Calculation Equations If two phases are present, the liquid and gas  compostions must sum to one: = = = N i i i x 1 1 (1) = = = N i i i y 1 1 (2) where N is the total number of components in the  mixture.  A material balance on the total mixture gives n n n L g = + (3) A material balance on the ith component in the  mixture gives                                                        i i L i g nz x n y n = + (4)   12 - 4
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Flash Calculation Equations  Continued For gas-liquid equilibrium, i i i x y k = (5) where   k i   is   an   experimentally   determined  equilibrium ratio for component i in the mixture.   The   equilibrium   ratio,   which   is   a   function   of  pressure,   temperature   and   composition   of   the  mixture, may be obtained from correlations such  as those shown in Figures A-1 to A-14 of McCain. Substituting   for   y i   In   Eq.(4),   using   Eq.(5),   and  solving for x one obtains i g L i i k n n n n z x + = (6) 12 - 5
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Flash Calculation Equations  Continued Let n n n g g = (7) and n n n L L = (8) Substituting Eqs. (3), (7) and (8) into (6) gives                                           ) 1 ( 1 - + = i g i i k n z x (9) Substituting Eq. (9) into (1) gives the condition for  equilibrium as        1 ) 1 ( 1 1 1 = - + = = = = = N i i i g i N i i i k n z x (10) 12 - 6
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Flash Calculation Equations  Continued It can be shown that elimination of x i  from Eqs. (4)  and   (5)   would   have   resulted   in   the   following  equations for y i  and the condition for equilibrium:                                           - + = 1 1 1 i L i i k n z y (11)        1 1 1 1 1 1 = - + = = = = = N i i i L i N i i i k n z y (12) 12 - 7
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Flash Calculation Equations  Continued At the bubble point pressure,  n L  = 1, and Eq. (12)  becomes 1 1 = = = N i i i i k z (13) At the dew point pressure,   n g   = 1, and Eq. (10)  becomes 1 1 = = = N i i i i k z (14) 12 - 8
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ch12 - CHAPTER12 GasLiquidEquilibria...

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