Unformatted text preview: due to reaction be: νi
rk , j
(1)
νk
where: Mj = volumetric holdup of liquid on stage j.
rk,j = chemical reaction rate, dck,j /dt , for the limiting reactant, k, on stage j.
Let the rate law be a powerlaw expression, in terms of the reference limiting reactant, k,
∆ni , j = − M j C − where: k f , j = A f e − dck , j
dt = kf ,j C ∏c
i =1 ni
i, j − ∏c
i =1 mi
i, j KC , j Ef
RT j ci , j = xi , j cT , j
cT , j = total concentration of all components in the liquid on stage j
K C , j = chemical equilibrium constant in terms of concentrations on stage j
superscripts n, m = reaction orders for forward and backward reactions,
respectively, which are related to the stoichiometric coefficients by ν i = mi − ni Exercise 122 (continued)
Analysis (a): (continued)
(a) Chemical equilibrium
Eqs. (125), (127) to (1215), and (1217) to (1218) apply . In Eq. (124), liquid mole
fractions xi,j are in chemical equilibrium as governed by the chemical equilibrium constant and
the stoichiometry, such that: M iLj ≡ (1 + rjL ) L j xi , j − L j −1 xi , j −1 − ∆ni , j − f i ,Lj − N iLj = 0, i = 1, 2, ..., C
,
,
In energy balance, Eq. (126), liquid enthalpies include heats of formation. Eq. (1216)
becomes:
C
C
νi
M TL, j ≡ (1 + rjL ) L j − L j −1 − ∆nk , j
−
f i ,Lj − N T , j = 0
i =1 ν k
i =1
(b) Kinetic rate law
Eqs. (125), (127) to (1215), and (1217) to (1218) apply. Eq. (124) becomes: M iLj ≡ (1 + rjL ) L j xi , j − L j −1 xi , j −1 − ∆ni , j − f i ,Lj − N iLj = 0, i = 1, 2, ..., C
,
,
where ∆ni , j is computed from the reaction rate equation, Eq. (1), above.
In Eq. (126), enthalpies must include heat of formation.
Eq. (1216) becomes:
C
C
νi
M TL, j ≡ (1 + rjL ) L j − L j −1 − ∆nk , j
−
f i ,Lj − N T , j = 0
i =1 ν k
i =1 Exercise 12.3
Subject: Reduction of the number of equations in the ratebased model.
Given:. Ratebased model based on Eqs. (124) to (1218).
Find: Method to reduce the number of equations.
Analysis:
either: In Chapter 10, equilibriumstage models are written for each equilibrium stage in terms of Case 1: xi , j , yi , j , L j ,V j , and Tj (2C + 3) variables Case 2: li , j , υ i , j , and Tj (2C + 1) variables In Section 12.1, the ratebased model is written in terms of : xi , j , yi , j , xiI, j , yiI, j , N i , j , TjL , TjV , TjI , L j , and V j (5C + 5) variables The equations could be rewritten to replace: xi , j , yi , j , L j , and V j by li , j and υ i , j to give (5C + 3) variables.
For example, Eq. (124) would become: M iLj ≡ (1 + rjL )li , j − li , j −1 − f i ,Lj − N iLj = 0, i = 1, 2, ..., C
,
,
This would eliminate Eqs. (1211) and (1212).
In Ref. 16, Taylor and his colleagues use component flow rates. This has the advantage
that the component material balances are linear and fewer equations are needed because there are
two fewer variables per stage. In Ref. 17, Taylor and his colleagues use component mole
fractions and total flow rates. This choice is preferable when total flow rates are useful, such...
View
Full Document
 Spring '11
 Levicky
 The Land

Click to edit the document details