Mathematical Modeling and Simulation for Production of MTBE

Chapter Two Literature Survey
dm
dt
j
= L
j−
1
+ V
j+
1
+ F
j
− S
v
j
−V
j
− L
j
− S
l
j
+
r c
∑∑ υ i,
j R i,
mε
j
(2.4)
m=
1 i=
1
dm j xi,
j
v l r c
= L
j−1
x
i,
j−1
+ V
j+
1
y
i,
j+
1
+ Fj
zi,
j − ( S j + V j ) yi,
j − ( L j + S j ) xi,
j + ∑ ∑ i,
j
dt
m=
1i= 1
22
υ R (2.5)
i,
mε
j
y
i,
j k x
i,
j i,
j
= (2.6)
1
1 , = ∑ c
X (2.7)
i=
i j
c
∑
i=
1
y 1
(2.8)
i,
j =
dH j xi,
j
v v l l
= L
j−1
h
i,
j−1
+ V
j+
1
H
i,
j+
1
+ F j H − ( S j + V j ) H i j − ( L j + S j ) h + Q
dt
j
,
j j
The (mj) is the hold-up on the stage j. With very few exceptions, mj
(2.9)
considered to be the hold-up only of the liquid, it is, however, important to
include the hold up of vapor phase at higher pressure. The last term in equations
r c
(2.4 to 2.5) ( ∑ ∑ νi
Ri m j
m=
1i= 1
, j , ε ) is the rate of the disappearance of the total
moles due to any m reaction of the stage j. Equation (2.5) is the component
material balance (neglecting the vapor hold-up), vi, m represents the
stocheometric coefficient of component i in reaction m and εj
reaction volume.
The E equations are phase equilibrium relations, the compositions of the
stream leaving stage are in thermodynamic equilibrium. Therefore, the mole
is
represents the