Reator BATCH NÃO ISOTÉRMICO

1. Reactores Batch não isotérmicos
Equação geral de balanço de energia
Energy balance general equation
dt
dE
H
F
H
F
W
Q
i
i
i
i
i
i
mec =
-
+
- 
 0
0
&
&
Não existem correntes
de entrada nem de
saída!
Non-isothermal batch reactors
There are no entering or
exiting currents

2. Desprezando-se o trabalho mecânico:
dt
dE
Q =
&
Mas
 


 -
=
=
= i
i
i
i
i
i
i V
P
H
N
U
N
E
N
E
 

 -
=
=
 i
i
i
i
i V
P
H
N
dt
d
E
N
dt
d
Q
&
Soma para todos
os componentes
Geralmente a
principal
contribuição para
a energia é a
energia interna
U = H – P V
Usually the main contribution for total
energy is internal energu
Sum for all
components

3.    


 -
=
-
=
 i
i
i
i
i
i
i
i V
P
N
H
N
dt
d
V
P
N
H
N
dt
d
Q
&
 

 -
=
 i
i
i
i V
N
P
H
N
dt
d
Q
&

 -
=
 i
i
i
i V
N
P
dt
d
H
N
dt
d
Q
&
dt
dP
V
H
N
dt
d
Q i
i -
=
 
&
 
dt
dP
V
H
N
dt
d
Q i
i -
=
 
&
V
dt
dP
V
dt
dH
N
dt
dN
H
Q i
i
i
i -
÷





+
=
 
&
dt
dP
V
dt
dH
N
dt
dN
H
Q i
i
i
i -
+
=
 

&
dt
dP
V
dt
dT
Cp
V
C
dt
V
C
d
H
Q i
i
i
i -
+
=
 

&
Ci V
Cpi dT

4. Particular case of constant pressure and volume

5. From the mole balance to i component

6.     

+
-

=
-

dt
dT
Cp
V
C
V
r
T
H
T
T
A
U i
N
i
dt
dX
N
A
R
a
i
A





0
)
(
  
+

=
-

dt
dT
Cp
N
dt
dX
N
T
H
T
T
A
U i
i
A
R
a 0
)
(
Do balanço
molar ao
reagente A
 
X
N
N i
i
A
i 
+

= 0
   
 
-

+

=
-

dt
dT
Cp
X
N
dt
dX
N
T
H
T
T
A
U i
i
i
A
A
R
a 0
0
)
(
From the mole
balance to A

7. Operação adiabática:
  0
=
-
= T
T
A
U
Q a
&
  0
)
( 0
0 =
+
+
  dt
dT
Cp
X
N
dt
dX
N
T
H i
i
i
A
A
R 


  0
)
( 0
0 =
+
+
  dt
dT
X
Cp
Cp
N
dt
dX
N
T
H i
i
i
i
A
A
R 


  0
)
( 0
0 =
+
+
  dt
dT
X
Cp
Cp
N
dt
dX
N
T
H i
i
i
i
A
A
R 


Adiabatic operation

8.   0
)
( 0
0 =
+
+
 
 dt
dT
X
Cp
Cp
N
dt
dX
N
T
H i
i
i
i
A
A
R 


  0
)
( 0
0 =
+
+

dt
dT
X
C
C
N
dt
dX
N
T
H p
ps
A
A
R 

  0
)
( =
+
+

dt
dT
X
C
C
dt
dX
T
H p
ps
R 

 
  0
)
(
)
(
=
+
+

-
+
dt
dT
X
C
C
dt
dX
T
H p
ps
T
T
C
T
H
R
R
p
R
o
R









Cps Cp


9.     0
)
( =
+
+





 -
+

dt
dT
X
C
C
dt
dX
T
T
C
T
H p
ps
R
p
R
o
R 


   
dt
dX
T
T
C
T
H
dt
dT
X
C
C R
p
R
o
R
p
ps 




 -
+
-
=
+
 

 )
(
    dX
T
T
C
T
H
dT
X
C
C R
p
R
o
R
p
ps 




 -
+
-
=
+
 

 )
(
   
X
C
C
dX
T
T
C
T
H
dT
p
ps
R
p
R
o
R


 +
=





 -
+
-

)
(
x dt

10.    

 +
=





 -
+
-

X
p
ps
T
T R
p
R
o
R
X
C
C
dX
T
T
C
T
H
dT
0
0
)
( 


   X
p
ps
p
T
T
R
p
R
o
R
p
X
C
C
C
T
T
C
T
H
C 0
ln
1
)
(
ln
1
0





+
=





 -
+
-

    X
p
ps
p
T
T
R
p
R
o
R
p
X
C
C
C
T
T
C
T
H
C 0
ln
1
)
(
ln
1
0





+
=





 -
+
-

   X
p
ps
p
T
T
R
p
R
o
R
p
X
C
C
C
T
T
C
T
H
C 0
ln
1
)
(
ln
1 0





+
=





 -
+

 
 
 
ps
p
ps
p
R
p
R
o
R
R
p
R
o
R
p C
X
C
C
C
T
T
C
T
H
T
T
C
T
H
C







+
=





 -
+





 -
+
 ln
1
)
(
)
(
ln
1 0

11.  
 
 
ps
p
ps
R
p
R
o
R
R
p
R
o
R
C
X
C
C
T
T
C
T
H
T
T
C
T
H 



 +
=





 -
+





 -
+
 ln
)
(
)
(
ln
0
 
 
 
ps
p
ps
R
p
R
o
R
R
p
R
o
R
C
X
C
C
T
T
C
T
H
T
T
C
T
H 



 +
=





 -
+





 -
+

)
(
)
( 0
 
 
ps
R
p
R
o
R
R
p
R
o
R
ps
p C
T
T
C
T
H
T
T
C
T
H
C
X
C -





 -
+





 -
+
=






)
(
)
( 0
HR(T)

12.  
  ps
R
R
p
R
o
R
ps
p C
T
H
T
T
C
T
H
C
X
C -





 -
+
=





0
)
(
   
 
T
H
T
H
C
T
T
C
T
H
C
X
C
R
R
ps
R
p
R
o
R
ps
p





-





 -
+
=

0
)
(
   
 
T
H
C
T
H
C
T
T
C
T
H
C
X
R
p
R
ps
R
p
R
o
R
ps




 -





 -
+
=

0
)
(
   
 
T
H
T
H
T
T
C
T
H
C
C
X
R
R
R
p
R
o
R
p
ps





-





 -
+
=

0
)
(
 




 -
+ R
p
R
o
R T
T
C
T
H 
 )
(

13.    
 
T
H
T
T
C
T
H
T
T
C
T
H
C
C
X
R
R
p
R
o
R
R
p
R
o
R
p
ps











 -
+
-





 -
+
=

)
(
)
( 0
   
 
T
H
T
T
C
T
H
T
T
C
T
H
C
C
X
R
R
p
R
o
R
R
p
R
o
R
p
ps






-
-
-
-
+
=

)
(
)
( 0
 
T
H
T
C
T
C
T
C
T
C
C
C
X
R
R
p
p
R
p
p
p
ps






+
-
-
=
 0
 
 
 
T
H
T
T
C
C
C
T
H
T
C
T
C
C
C
X
R
p
p
ps
R
p
p
p
ps







-
=
-
=
 0
0
 
 
 
 
T
H
T
T
C
T
H
T
T
C
X
R
pi
i
R
ps

 -
-
=
-
-
=

 0
0 