CHEMICAL REACTION ENGINEERING (SKF3223) Chapter 2: …ocw.utm.my/file.php/187/CHAPTER_2.pdf ·...
Transcript of CHEMICAL REACTION ENGINEERING (SKF3223) Chapter 2: …ocw.utm.my/file.php/187/CHAPTER_2.pdf ·...
Chapter 2: Conversion and Reactor Sizing
CHEMICAL REACTION ENGINEERING (SKF3223)
WAN NORHARYATI WAN SALLEH
RAFIZIANA MD. KASMANI [email protected]
Conversion, X
To quantify how far a reaction has progressed
How many moles of C are formed for every mole A consumed
Consider :
The basis of calculation is always the limiting reactant
Irreversible reaction: Xmax = 1.0 (complete conversion)
Reversible reaction: Xmax = Xequilibrium (equilibrium conversion)
Da
d C
a
c B
a
b A
dD cC bB aA
CONVERSION
Batch system (X,t)
Flow system (X,V/W)
0
AA0 N-N
A
AN
X0
0
A
AAA
F
FFX
XNNmolN AAA 00)(
X = moles of A reacted / consumed
moles of A fed
XFFsmolF AAA 00)/(
FA0X= molar flow rate at which A is
consumed / reacted
NA0X= moles of A consumed
/ reacted
)1(0 XN A )1(0 XFA
BATCH REACTOR
For batch reactor , we are interested in determining how long to leave
the reactants in the reactor to achieve a certain conversion
From mole balance: From the conversion:
4
This is how the Design Equation derived from mole balance equation in
terms of conversion
dtVrA
AdNXNNN AAA 00
dt
dXN
dt
dNA
A00
Differentiating with respect of time:
NA0 = 0 : constant with respect of time
dt
dXNVr AA 0
X
A
AVr
dXNt
0
0dt
dXNVr AA 0
GAS FLOW SYSTEM
The entering molar flow rate, FA0 (mol/s)
0
00
0
00
0
3
3
000
system gasfor
.
RT
Py
RT
PC
C
s
dm
dm
mol
s
mol
CF
AAA
A
AA CA0= entering concentration,
mol/dm3
Ya0= entering mole fraction of A
P0= entering total pressure, kPa
T0=entering temperature, K
Pa0= entering partial pressure
R= ideal gas constant =
8.314k.Pa.dm3/mol.K
CSTR
A
AA
r
FFV 0
A
AAA
r
XFFFV
)( 000
From mole balance:
XFFF AAA 00
Design Equation:
From the conversion:
A
AAA
r
XFFFV 000
A
A
r
XFV 0
PFR
AA r
dV
dF
From mole balance:
Design Equation:
From the conversion:
XFFF AAA 00
dV
dXF
dV
dFA
A00
Differentiating with respect of volume:
FA0 = 0 : constant with respect of volume
dV
dXFr AA 0 dV
dXFr AA 0
X
A
Ar
dXFV
0
0
PBR
AA r
dW
dF'
From mole balance:
Design Equation:
From the conversion:
XFFF AAA 00
dW
dXF
dW
dFA
A00
Differentiating with respect of weight of catalyst:
dW
dXFr AA 0'
dW
dXFr AA 0'
X
A
Ar
dXFW
0
0'
DESIGN EQUATIONS
9
X
A
AOr
dXFW
0'
Design Equations for Isothermal Reactors
REACTOR DIFFERENETIAL ALGEBRAIC INTEGRAL
FORM FORM FORM
Vrdt
dXN AAO )(
X
A
AOVr
dXNt
0
)( AAO rdV
dXF
X
A
AOr
dXFV
0
CSTR ExitA
AO
r
XFV
)(
)(
BATCH
PFR
PBR )'( AAO rdW
dXF
REACTOR SIZING By sizing a chemical reactor we mean we're either determine the
reactor volume to achieve a given conversion or determine the conversion that
can be achieved in a given reactor type and size.
Normally, the process / experimental data will be given (X, -rA)
PFR
Simpson's One-Third Rule is one of the more common numerical
methods.
Other numerical methods (see Appendix A.4, pp 1013-1015):
(i) Trapezoidal Rule (2 data points)
(ii) Simpson's Three-Eighth's Rule (4 data points)
(iii) Five-Point Quadrature Formula (5 data points)
Reactor Sizing
PFR CSTR
Levenspiel Plot
REACTORS IN SERIES
Why?
Sometimes 2 CSTR reactor volumes in series is less than the
volume of 1 CSTR to achieve the same conversion.
Can model a PFR with a large number of CSTR in series.
In the case of PFR, whether you place 2 PFR in series or have 1
PFR, the total reactor volume required to achieve the same
conversion is identical.
REACTORS IN SERIES
X=0
FA0
X1 = conversion achieved in
the PFR
FA1
X2 = conversion achieved in
the PFR & CSTR
FA2
X3 = total
conversion
achieved by all
3 reactors
V1
V2
CSTR
V3
Valid only for NO side
streams:
PFR
PFR
FA3
3003
2002
1001
XFFF
XFFF
XFFF
AAA
AAA
AAA
(i) CSTR in series:
(ii) PFR in series:
V2
-rA2
X1
FA1
X2
FA2
X0
FA0
V1
-rA1
V1
V2
-rA2
-rA1
X1
FA1 X2
FA2
X0
FA0
1
101
A
A
r
XFV
1
0
01
X
A
Ar
dXFV
2
1
02
X
X A
Ar
dXFV
2
1202
)(
A
A
r
XXFV
V1
-rA1
V3
V2
-rA2
-rA3
X1
FA1 X2
FA2
X0
FA0
X3
FA3
(iii) CSTR + PFR in series:
1
101
A
A
r
XFV
2
12
02
X
X A
Ar
dXFV
3
2303
)(
A
A
r
XXFV
SPACE TIME,
The time necessary to process one reactor volume by
the volumetric rate entering the reactor
Also called the holding time or mean residence time
where 0 is entrance volumetric rate
timevolume
volumetime
V
/
0
16
SPACE VELOCITY (SV)
10
VSV
GHSV Gas Hourly Space Velocity, h-1
v0 at STP (standard temp. and pressure)
LHSV Liquid Hourly Space Velocity, h-1
v0 at some reference temperature
Reciprocal of the space time,
Two SV commonly used in industry:
Main Reference:
1. Fogler,H.S., “Elements of Chemical Reaction Engineering”, 4th
Edition,Prentice Hall, New Jersey, 2006.
Other References:
1. Davis, M.E and Davis, R.J, “Fundamentals of Chemical Reaction
Engineering”, Mc-Graw-Hill, New York, 2003
2. Schmidt, L.D, “The Engineering of Chemical Reactions”, Oxford,
New York, 1998
3. Levenspiel,O., “Chemical Reaction Engineering”, 3rd Edition,
Wiley,New York, 1998
4. Smith,J., “Chemical Engineering Kinetics”, 3rd Edition, McGraw-
Hill, New York, 1981
REFERENCES