Uploaded by Azduwin Khasri

Mole balance

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PTT255/3 Reaction Engineering
By Dr Azduwin Khasri
[email protected]
• Chemical kinetics and reactor design are at the heart of producing almost
all industrial chemicals.
• The selection of a reaction system that operates in the safest and most
efficient manner can be the key to the economic success or failure of a
chemical plant.
Separators
Products
Reactor
Separator
Raw
materials
Separation
& purification
By products
2
• A chemical species is said to have reacted when it has lost
its chemical identity.
• The identity of a chemical species is determined by the
kind, number, and configuration of that species’ atoms.
• There are three ways for a species to loose its identity:
1. Decomposition
2. Combination
3. Isomerization
CH3CH3  H2 + H2C=CH2
N2 + O2  2 NO
C2H5CH=CH2  CH2=C(CH3)2
3
Can they be considered as different SPECIES?
Kind: Same (Butene)
Number of atoms: Same (C4H8)
Configuration: Different arrangement
ANSWER: Yes. We consider them as two different
species because they have different configurations.
4
• The reaction rate is the rate at which a species looses its
chemical identity per unit volume.
• The rate of a reaction can be expressed as either:
-rA, the rate of reaction: is the number of moles of A reacting
(disappearing) per unit time per unit volume (mol /dm3.s ).
rA, is the rate of formation (generation) of species A.
r'A , is a heterogeneous reaction rate: the no of moles of A
reacting per unit time per unit mass of catalyst (mol/s.g
catalyst)
5
 To perform a mole balance on any system, the system boundaries must first be specified.
 The volume 'enclosed by these boundaries will be referred to as the system volume.
Consider a system volume :
Fj0
System
volume
Gj
Fj
General mole balance:
Fj0
In
-
Fj
Out
+
+
Gj
=
Generation =
dNj/dt
Accumulation
6
• A mole balance of species j at any instant time:
Rate of flow
of j into the
system
(moles/time)
In
Fj0
-
-
Out
Fj
Rate of
accumulation
of j within
the system
(moles/time)
Rate of generation
of j by chemical
reaction within
the system
(moles/time)
Rate of flow
of j out of
the system
(moles/time)
+
+
Generation
Gj
=
=
Accumulation
dN j
dt
General Mole Balances
If spatially uniform (eg: T, C) throughout the
system volume :
G j  r jV
moles
moles

 volume
time time  volume
If NOT spatially uniform:

V1
r j1
G j1  rj1V1
V2
rj 2
The rate of generation ∆Gj1:
∆Gj1=rj1∆V1
G j 2  rj 2 V2

8
The total rate of generation within the system volume is the sum of all rates of
generation in each of the subvolumes.
M
M
i 1
i 1
G j   G ji  r ji Vi
 Taking the limit M∞, and ∆V0 and integrating,
V
G j   rj dV
0
In  Out  Generation  Accumulation
dN j
Fj 0  Fj
  rj dV

dt
From this general mole
balance equation we can
develop the design
equations for the various
types of industrial reactors:
batch, semibatch, and
continuous-flow.
9
TYPE OF REACTORS
Type of reactor
Batch
Continuos flow
Continuous
stirred tank
reactor (CSTR)
Plug flow reactor
(PFR)
Packed bed
reactor
Batch reactor has neither inflow nor outflow of reactants or
products while the reaction is carried out (Closed system).
FA0 = FA = 0
Operate under unsteady state condition.
The conditions inside the
reactor (eg: concentration,
temperature) changes over
time.
 General Mole Balance on System Volume,V;
FA0 -
FA
+
GA
=
dN A
dt
dN A
 GA
dt
11
• Assumption: Well mixed so that no variation in the rate
of reaction throughout the reactor volume:
dN A
 rAV
dt
• Rearranging;
dN A
dt 
rAV
• Integrating with limit at t=0, NA=NA0 & at t=t1, NA=NA1,
dN A N A0 dN A
t1  
 
N A0 rAV
N A1  rAV
N A1
12
1. Continuous-Stirred Tank Reactor
(CSTR/Backmix reactor)
 The CSTR is normally run at steady state
and is usually operated so as to be quite
well mixed.
 no spatial variations in concentration,
temperature, or reaction rate
throughout the vessel.
Reactants
Products
13
DERIVATION
General Mole Balance:
FA0 -
FA
Assumption:
1.steady state:
2. well mixed:
+
GA
=
dN A
dt
dN A
0
dt
GA  rAV
Mole balance: FA0 - FA + rAV = 0
FA  FA0 FA0  FA
V

rA
 rA
design equation
for CSTR
14
2. Tubular Reactor
 It consists of a cylindrical pipe and is
normally operated at steady state.
 The flow is highly turbulent and the flow
field may be modeled by that of plug
flow.
 That is, there is no radial variation in
concentration and the reactor is referred
to as a plug-flow reactor (PFR).
15
Plug Flow Reactor
DERIVATION
General Mole Balance:
V
FA0 -
FA
+
 rA dV
=
0
Assumption:
1.steady state:
dN A
dt
dN A
0
dt
V
FA0 - FA
+
 rA dV
= 0
0
Differentiate with respect to V:
0
dFA
 rA ,
dV
dFA
 rA
dV
16
DERIVATION
dFA
 rA
dV
Rearranging and integrating between
V = 0, FA = FA0
V = V1, FA = FA1
dFA
dV 
rA
V1
FA1
0
FA0
V  
dFA FA0 dFA
V1  
 
FA0 rA
FA1  rA
dFA
rA
FA1
17
3. Packed-Bed Reactor (fixed bed reactor)
 Often used for catalytic process
 Heterogeneous reaction system (fluid-solid)
 Reaction takes place on the surface of the
catalyst.
 No radial variation in velocity, conc, temp,
reaction rate
18
Packed Bed Reactor
DERIVATION
General Mole Balance:
FA0 -
FA
+
'
r
 AdW
Assumption:
1.steady state:
=
dN A
dt
the reaction rate is
based on mass of solid
catalyst, W, rather than
reactor volume
dN A
0
dt
FA0 - FA
+
'
r
 AdW
= 0
Differentiate with respect to W:
dFA
 rA'
dW
19
Packed Bed Reactor
DERIVATION
dFA
 rA'
dW
Rearranging and integrating between
W = 0, FA = FA0
W = W1, FA = FA1
dFA
dW  '
rA
V1
FA1
dFA
W   '
0
FA 0 rA
dFA FA0 dFA
W1   '  
'
r

r
FA0 A
FA1
A
FA1
20
Reactor
Differential Form Algebraic Form
Integral Form
Comment
No spatial
dN A
t1  
variations,
N A1  rAV unsteady state
N A0
Batch
CSTR
dN A
 rAV
dt
-
PFR
dFA
 rA
dV
PBR
dFA
 rA'
dW
FA0  FA
V
 rA
No spatial
variations,
steady state
-
V1 
FA 0
dFA
 r
A
FA1
FA 0
W1  
FA1
dFA
 rA'
Steady state
Steady state
21
Industrial Reactors
22
The end
Thank you
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