1 TAME synthesis problem Tert-Amyl Methyl Ether (TAME) is an ...

B. Steady state energy balance
For the steady state energy balance in the volume element of length dz, considering no dispersion, we
can write:
heat produced by
Total Flux IN + = Total Flux OUT
z
z+
dz
Chemical Re action
M reactions
h
R
h
( ε A) ϕ z + ρ b ∑(
∆H
j rj
) Adz
= ( ε A)
ϕ z+
dz + Alat
U ( T −Tw
)
j=
1
where ϕ h is the heat flux,
R
j
heat losses through
+
reactor walls
(B.1)
(B.2)
∆ H is the heat of reaction j, rj is the rate of reaction j, Alat is the lateral area
of the volume element, U is the overall heat-transfer coefficient, T is the reactor temperature and Tw is
the reactor wall temperature.
Re-writing equation (B.2):
M reactions
b ∑
j=
1
R Alat
( ∆H
r ) + U ( T −T
) = 0
h h
ϕ z+
dz −ϕ
x ε − ρ
j j
w
(B.3)
dz
A dz
The heat flux can be given by:
h
ϕ = ρ CpT
(B.4)
u i
where ρ is the solution density and Cp is the solution heat capacity.
If R0 is the reactor radius, the lateral area of the volume element of length dz is:
= 2π R dz
(B.5)
A lat 0
and its sectional area is:
A = π R
(B.6)
2
0
leading to:
Alat 2
= (B.7)
Adz
R
0
Substituting into equation (B.3):
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