Continuous Stirred Tank Reactor Design - ChE...
Transcript of Continuous Stirred Tank Reactor Design - ChE...
Continuous –Stirred Tank Reactor Design
CHEMICAL REACTION RATE
The rate of a chemical reaction is the rate of formation or transformation of a
participant in a chemical reaction. It is expressed as the number of mass or mole of material
converted per unit volume of reactor per unit time. Thus, the rate of appearance or
disappearance of a chemical species i in a homogeneous reaction is (Levenspiel, 2003):
( / )
= ii
d n Vr
dt eq 5-1
If i is a reactant, the negative sign is used to signify depletion with time. Whereas, the
positive sign is used if it’s a product. Where in is the number of moles of component i, V
is the reactor volume and t is the reaction time.
For a constant volume reaction,
1= i i
i
dn dCr
V dt dt eq 5-2
As expressed in the Law of Mass Action, the rate of a chemical reaction is proportional
to the active masses of participating reactants. Therefore, the rate is dependent on the
concentration of the participating reactants. In elementary reaction, the stoichiometric
coefficient of the reactants is equal to the order of the reactions. This order becomes the
power to which the reactant is raised.
If the given chemical reaction is
aA bB cC dD eE eq 5-3
then, the rate of reaction for the disappearance of reactant A is
A
A A B C
dCr kC C C
dt eq 5-4
Again, except in elementary reactions, the order of the reaction is not equal to the
stoichiometric coefficients as in a , b , and c . k is the rate constant of the
reaction.
CSTR DESIGN 2
Elementary and Non-Elementary Reactions
Elementary Reaction
Elementary reaction occurs only in a single step.
Example: 1. A Product eq 5-5
2. A+B Product eq 5-6
Non-elementary Reaction
Non-elementary reaction occurs in two or more steps of reactions and there is no
direct correspondence between the stoichiometric coefficient and the rate expression of the
reaction.
Mechanism of Non-Elementary Reaction (Levenspiel, 2003)
Non-chain reaction mechanism
Reactants (intermediates)* eq 5-7
(intermediates)* Products eq 5-8
Chain Reaction Mechanism
Reactants (intermediates)* eq 5-9
(intermediates)* + Reactant (intermediates)*
+ Product eq 5-10
( intermediates)* Product eq 5-11
REACTION RATES OF DIFFERENT MECHNISMS
Reversible Reactions
First Order Reversible Reactions
1
2
k
kA R eq 5-12
The rate expression for substance A and R are written as
AA 1 A 2 Rnet
net
-dCr =k C -k C
dt eq 5-13
CSTR DESIGN 3
R1 A 2 Rnet
net
dC=k C -k C
dtRr eq 5-14
At equilibrium rnet = 0. Therefore,
1 Ae 2 Rek C =k C eq 5-15
Re1C
2 Ae
Ckk = =
k C eq 5-15
After establishing the material balance and upon integration, the final working
equation in terms of fractional conversion is:
A
2 C
Ae
Xln 1- =- k k +1 t
X eq 5-16
Irreversible Reactions in Parallel
1kA R assumed desired product eq 5-17
2kA T unwanted product eq 5-18
3kA S unwanted product eq 5-19
The rate equation is for reactant A
AA 1 2 3 A
-dCr = = (k k k )C
dt eq 5-20
Integration gives
1 2 3-(k +k +k )t
A AoC = C e eq 5-21
Irreversible Reactions in Series (Consecutive Reactions)
Consider the unimolecular first order reaction
1 2k kA B R eq 5-22
The rate equation for component A
A1 A
-dC=k C
dt eq 5-23
CSTR DESIGN 4
Rearranging and integrating :
1-k t
A AoC = C e eq 5-24
B
1 A 2 B
dC=k C -k C
dt eq 5-25
Homogeneous Catalyzed Reactions
In the homogeneous catalyzed type of reactions, the overall rate is the sum of rates of
both the uncatalyzed and catalyzed reactions.
The uncatalyzed reaction is
1kA R eq 5-26
and the catalyzed reaction is 2k
A + C R C eq 5-27
The rate expression of component A is
A
1 A 2 A C
-dC= k C + k C C
dt eq 5-28
The concentration of the catalyst (CC) is assumed to be constant.
A
1 2 C A
-dC= (k +k C )C
dt eq 5-29
Integration gives
A
1 2 C
Ao
Cln = (k +k C ) t
C eq 5-30
Autocatalytic Reactions
An autocatalytic reaction is a reaction in which one of the products of reaction acts as
a catalyst.
For an uncatalyzed reaction:
1k
A R eq 5-31
For which the equation rate is:
A
A A R
-dCr = =k C C
dt eq 5-32
CSTR DESIGN 5
The corresponding catalyzed reaction where product R acts as a catalyts is
1kA + R R + R eq 5-33
the rate equation is
A
A A R
-dCr = =k C C
dt eq 5-34
Establishing the material balance and upon integration, the final rate expression is
o A Ao
o
o Ao A
C -C Cln =C kt
C -C C eq 5-35
CLASSIFICATION OF REACTORS
Although the purpose of this chapter is to present the determination of CSTR
specifications, Batch and Plug flow reactors will be briefly described
Batch Reactor
Batch reactors are usually simple in design with minimum auxiliary and
instrumentation requirements. It is commonly employed for small scale production, testing of
new productions, manufactured of expensive and easily contaminated system. High
conversion could be easily obtained by increasing the reaction time, although production
output is reduced correspondingly. It is usually not applicable for large industrial scale
production where labor cost would be high and production output is low compared to
continuous flow reactors. In batch reactor there is neither inflow nor outflow of both
reactants and products while the reaction is in progress.
Plug Flow Reactors (PFR)
In Plug flow reactor, reactant continually flows through a cylindrical vessel or pipe.
The reactant diminished along the length, and there is no radial variation in concentration.
This type of continuous flow reactors are simple in design and practically has no power
requirement.
reactat product
Figure 5-1. Plug Flow Reactor.
CSTR DESIGN 6
reactan
productow
Continuous-Stirred Tank Reactor (CSTR)
CSTR is commonly used for industrial production. It is assumed of having no spatial
variation in concentration and temperature. As name implies the reactor is well mixed,
allowing the assumption of same concentration at any point within the reactor and the
product. It is also called Backmix Reactor (Fogler, 1999). Even a well designed and
operated CSTR will produce lower conversion per unit reactor volume against Plug Flow
type reactors. In this chapter, design of Continuous Stirred Tank Reactor will be discussed.
Most homogeneous liquid phase reactions employs CSTR.
Figure 5-2. Continuous Stirred Tank Reactor.
CSTR DESIGN EQUATIONS
Space Time and Space Velocity concept
The space time, τ , is the time required to process one reactor volume of feed and is
given by the following equation:
Ao
Ao o
C V V
F v eq 5-36
where
CAo is the initial concentration
V is the volume of the reactor,
FAo is the molal flowrate of component A and,
vo is the volumetric flow rate.
CSTR DESIGN 7
Whereas, space velocity (S) refers to the number of reactor volumes of reactant fed
into the reactor per unit time and is given by the following equation:
1 Ao o
Ao
F vS
C V V eq 5-37
Overall Material Balance
Volume element reactant leaves
Reactant disappears by reaction
Reactant accumulates
Reactant enters Volume element reactant leaves
Reactant disappears by reaction
Reactant accumulates
Reactant enters
Figure 5-3. Over-all Material Balance.
rate of reactant rate of reactant rate of disappearance due rate of accumulation of
flow into element = flow out of element + to chemical rxn within + reactant in element of volume
of volume of volume the element of volume
eq 5-38
Input = output + rate of disappearance + rate of accumulation of A
At steady- state process, rate of accumulation of reactant = 0
FAo = FA + (-rA) V eq 5-39
However,
FA = FAo – FAo XA eq 5-40
Then,
-
A
A Ao
X V
r F eq 5-41
CSTR DESIGN 8
Where XA is the fractional conversion of reactant A
In terms of space time
-
Ao A
A
C X
r eq 5-42
REACTION RATES AND SPACE TIME
Zero Order irreversible chemical reaction
A-----------Product eq 5-43
(-rA) = k eq 5-44
substituting ( –rA) into space time equation,
Ao AC X
k eq 5-45
First Order irreversible chemical reaction
A-----------Product eq 5-46
(- )A Ar k C eq 5-47
substituting ( –rA) into space time equation,
Ao A
A
C X
kC eq 5-48
Second order irreversible chemical reaction
2A------------Product eq 5-49
2(- )A Ar k C eq 5-50
substituting ( –rA) into space time equation,
22 2 1-
Ao A Ao A
A Ao A
C X C X
k C k C X eq 5-51
CSTR DESIGN 9
N’th order irreversible chemical reaction
nA------------Product eq 5-52
(- ) n
A Ar k C eq 5-53
substituting ( –rA) into space time equation,
1-
Ao A Ao A
nn nA Ao A
C X C X
k C k C X eq 5-54
CSTR SIZING
CSTR sizing is dictated by residence time requirement. The longer the residence time,
the bigger the reactor volume at constant volumetric flow rate. This is expressed below:
τ = V / vo eq 5-55
where:
τ = Space time or Residence time, sec [hr]
V = Volume of Reactor, m³ [ft3]
vo = Volumetric flowrate, m³/sec [ft3/s]
Overall chemical kinetics which includes, chemical specie, amount of specie, reaction
temperature, presence of catalyst, agitation etc determines the degree of residence time as
shown in Table 5-1.
Table 5-1. Residence Time and/or Space Velocities in Industrial Chemical Reactors.
Product
(raw materials)
Reactor
Phase
(CSTR)
Catalyst T, °C P, atm
Residence
Time or
Space
Velocity
Alkylate (i-C4, butanes) L H2SO4 5-10 2-3 5-40 min
Alkylate (i-C4, butanes) L HF 25-38 8-11 5-25 min
Butadiene sulfone (butadiene, SO2) L t-Butyl catechol 34 12 0.2 LHSV
Caprolactam (cyclohexane oxime) L Polyphosphoric acid 80-110 1 0.25-2 h
Chloral (Cl2, acetaldehyde) LG None 20-90 1 140 h
Cumene hydroperoxide (cumene, air) L Metal porphyrins 95-120 2-15 1-3 h
Cyclohexanone (cyclohexanol) L N. A. 107 1 0.75 h
Dextrose (starch) L H2SO4 165 1 20 min
Dextrose (starch) L Enzyme 60 1 100 min
Dodecylbenzene (benzene, propylene tetramer)
L AlCl3 15-20 1 1-30 min
Ethyl acetate (ethanol, acetic acid) L H2SO4 100 1 0.5-0.8 LHSV
Ethylene, propylene chlorohydrins (Cl2, H2O) LG None 30-40 3-10 0.5-5 min
CSTR DESIGN 10
Table 5-1 continued...
Product
(raw materials)
Reactor
Phase
(CSTR)
Catalyst T, °C P, atm
Residence
Time or
Space
Velocity
Glycerol (allyl alcohol, H2O2) L H2WO4 40-60 1 3 h
o-Methyl benzoic acid (xylene, air) L None 160 14 0.32 h 3.1 LHSV
Nitrobenzene (benzene, HNO3) L H2SO4 45-95 1 3-40 min
Phenol (cumene hydroperoxide) L SO2 45-65 2-3 15 min
t-Butyl methacrylate (methacrylic acid, i-butene)
L H2SO4 25 3 0.3 LHSV
Aldehydes (diisobutene, CO) LG Co Carbonyl 150 200 1.7 h
LHSV – Space velocity (hourly) – liquid N. A. – Not Available Adapted from Table 23 - 1 Section 23 - 7 Perry’s Chemical Engineer’s Handbook 7th ed.
Standard Stirred Tank Configuration
Stirred tank configuration for a six flat blade turbine Trambouze et. al., (1988),
provide for the standard type agitation system. As shown below, the following are standard
configuration:
Figure 5-4. Dimensions for CSTR Design.
Dd
DI
m
I
b
ZI
ZL
W
H
T
D
T
CSTR DESIGN 11
1L
T
Z
D eq 5-56
1
3
I
T
D
D eq 5-57
1
10T
W
D eq 5-58 1I
I
Z
D eq 5-59
3
4
d
I
D
D eq 5-60
1
4I
I
D eq 5-61
1
5I
b
D eq 5-62
1
5T
m
D eq 5-63
where:
LZ = Static liquid depth
TD = Tank diameter
ID = Impeller diameter
IZ = Impeller distance from tank bottom
W = Baffle width
dD = Impeller disc diameter
I = Impeller blade length
b = Impeller blade width
TH = Tank height
m = Baffle tip distance from tank bottom
Mixing Time
To estimate the mixing time, Norwood and Metzner correlation provides for the
equation applicable for six flat blade turbine:
2 0.5
1
65I Lm Fr
T T
D ZN t N
D D eq 5-64
where:
mt = Mixing time
N = Impeller revolutions per unit time
ID = Impeller diameter
TD = Tank diameter
LZ = Static liquid depth
FrN = Froude Number
CSTR DESIGN 12
2
IFr
N DN
g eq 5-65
where g = acceleration due to gravity
Impeller Selection
Agitation is designed to increase fluid turbulence, and is often employed in the
following (Mc Cabe, 2001):
1. homogenization of a fluid phase
2. increased heat transfer between a solid surface and a fluid phase
3. creation of interfacial area between two immiscible fluid phases.
4. maintenance of a divided solid in suspension in a fluid phase
Agitation as used in the process industries is the production of irregular disturbances
or turbulent motion within a fluid by means of mechanical devices acting on that fluid
(Brown, 1950). Most of the fluids handled in the process industry are low viscosity
Newtonian fluids.
Several references classify impellers according to their form, functions and uses in the
mixing operations (Brown, 1950; Foust et. al, 1980 and McCabe, 2001) as shown in Figure 5-
5. Figure 5–6 may be used I n the selection of appropriate impeller type.
Figure 5-5. Types of Impeller. Adapted from Doran, Pauline M. 1995
Bioprocess Engineering Principles.
Anchor Propeller 6 flat blade disc-turbine
Paddle Gate anchor Helical screw
CSTR DESIGN 13
Impeller Type
Vis
co
sit
y (
cen
tip
ois
e)
103
104
105
106
107
102
10
1
An
ch
ors
Prop
ell
ers
Fla
t-b
lad
e tu
rb
ines
Pad
dle
s
Gate
an
ch
ors
Hel
ical
Scre
ws
Hel
ical
Rib
bon
s
A graphical method of impeller selection is presented on Figure 5-6.
Figure 5-6. Viscosity Ranges for Different Impellers. Adapted from F.A Holland and
F.S. Chapman, 1966, Liquid Mixing and Processing in Stirred Tanks
as cited by Doran, Pauline M. (1995) Bioprocess Engineering
Principles.
Baffles
Baffles are flat vertical strips set radially along the tank inner wall. They are mounted
inside the tank to produce higher mixing and horizontal liquid surface (Perry and Green,
1997). In the absence of baffles in a stirred tank, vortex are formed because of the centrifugal
force acting on the liquid and could reach deep to the impeller which is undesirable (Mc Cabe,
2001). Due to the motion of the impeller in the fluid and the resultant movement of the liquid
past the baffles and wall, the skin friction and the drop form have to be considered in relation
to the speed of rotation and design of blade and tank.
Figure 5-7 provides for baffle inclination and attachment selection guide.
CSTR DESIGN 14
Figure 5-7. Baffle Arrangements (a) Baffles are attached to the wall for low-viscosity
liquids. (b) Baffles set away from the wall for moderate-viscosity
liquids. (c) Baffles set away from the wall and at an angle for high-
viscosity liquids. Adapted from F.A Holland and F.S. Chapman, 1966,
Liquid Mixing and Processing in Stirred Tanks as cited by Doran, Pauline
M. 1995. Bioprocess Engineering Principles)
Power Dissipation
Power dissipated by the agitator maybe computed by:
53
IPa DNNP eq 5-66
where
Pa = Power dissipated by an agitator
N = RPM of the impeller
ρ = Density of the mixture
DI = Impeller diameter
NP = Power number
CSTR DESIGN 15
An estimation of typical horsepower for agitators is given below (Parker, 1964; Schlegel,
1972): This maybe used to approximate power requirement due to mixing of CSTR.
Fluid Approximate Horsepower
Blending vegetable oil 1.0 hp per 100,000 lb
Blending gasoline 0.019 hp per m3
Clay dispersion 10 – 12 hp per 1,000 gal
Fermentation (pharmaceutical) 3 – 10 hp per 1,000 gal
Suspension polymerization 6 – 7 hp per 1,000 gal
Emulsion polymerization 3 – 10 hp per 1,000 gal
Solution polymerization 15 – 40 hp per 1,000 gal
Radius of Action of an Agitator
Radius of action of an agitator should be checked after reactor, blade and baffle sizes
have been calculated to ensure there is enough intensity of mixing inside the reactor, as this
will affect reaction conversion. Radius of Action AR may be calculated as:
2
1
2109P
RA eq 5-67
Horizontal radius of action HRa and vertical radius of action VRa are 50% and 20%
respectively of the computed radius of action.
where
P = Power, watts
= Viscosity, Pa . s
aR = Radius of action, m
HRa = Half major axis ellipsoidal
VRa = Half minor axis ellipsoidal
To ensure high degree of agitation a linear speed at blade tip should be greater than 4. Where
tip speed is given by:
Vp = πNDI (m/s) eq 5-68
Another indicator of high degree of agitation is Power dissipated per unit volume of fluid
which should have at least 1,500 3m
Wvalue.
Below is the summary of degree of agitation against tip blade speed and Power per unit
volume (Trambouze et. al, 1988):
CSTR DESIGN 16
Degree of Agitation Tip Speed s
m 3m
watt
VolumePower
Low 3.25 750
Medium 3.25 to 4 750 to 1500
High 4 up 1500 up
For an initial condition, a 50% on blade tip speed of 4 s
m and Power per unit volume of
1500 3m
watt could be a good choice. On the other hand, a good compromise should be
reached, so that just enough mixing is provided for certain required residence time for power
requirement to be justifiable. An acceptable criteria used is:
tm
τ eq 5-69
< 0.1