ch12 - Exercise 12.1 Subject: Revision of rate-based...

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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 φ j = ratio of entrained liquid (in the exiting vapor) that leaves Stage j to the liquid leaving Stage j , y y i n i n , , and I . Then, the entrained component liquid flow rate leaving Stage j = φ j x i, (1 ) L j j r L + . Correspondingly, the entrained component liquid flow rate entering Stage j = φ j+1 x i,j +1 ( ) 1 1 1 + + + r L j L j . Occlusion: Let θ j = ratio of occluded vapor (in the exiting liquid) that leaves Stage j to the vapor leaving Stage j , ( ) 1 + r V j V j . Then the occluded component vapor flow rate leaving Stage j = θ j y i,j ( ) 1 + r V j V j . Correspondingly, the occluded component vapor flow rate entering Stage j = θ j -1 y i,j - 1 ( ) 1 1 1 + - - r V j V j . The liquid-phase component material balance, Eq. (12-4), and vapor-phase component material balance, Eq. (12-5), become, respectively, M r L x L x r L x f N i C i j L j L j j i j j i j j j L j i j i j L i j L , , , , , , ( ) ( ) , + + - - + - - = - - + + + + 1 1 0 1 1 1 1 1 1 φ φ = 1, 2, . .., M r V y V y r V y f N i j V j V j j i j j i j j j V j i j i j V i j V , , , , , , ( ) ( ) , + + - - + - + = + + - - - - 1 1 0 1 1 1 1 1 1 θ θ i C = 1 2 , , .... , The liquid-phase energy balance, Eq. (12-6), and vapor-phase energy balance, Eq. (12-7), become , respectively, E r L H L H r L H j L j L j j j L j j L j j L j j L + + - - + - - + + + + ( ) ( ) 1 1 1 1 1 1 1 1 φ φ , 1 0 C LF L L L j i j j j i H f Q e = - + - = 1 1 1 1 1 1 , 1 (1 ) (1 ) 0 C V V V V V V VF V V V j j j j j j j j j j j j i j j j i E r V H V H r V H H f Q e + + - - - - = + + θ - + - + + = The total phase material balances, Eqs. (12-16) and (12-17), become, respectively, M r L L r L f N T j L j L j j j j j L j i j L i C T j , , , ( ) ( ) + + - - + - - = - + + + = 1 1 0 1 1 1 1 1 φ φ M r V V r V f N T j V j V j j j j j V j i j V i C T j , , , ( ) ( ) + + - - + - + = + - - - = 1 1 0 1 1 1 1 1 θ θ
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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 ν ν ν A B R S A B R S + + where: ν ι = 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 due to reaction be: Δ n M r i j j i k k j , , = - ± ² ³ ´ µ ν ν (1) where: M j = volumetric holdup of liquid on stage j.
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ch12 - Exercise 12.1 Subject: Revision of rate-based...

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