chemical reaction engineering 제 1 장 mole balance 반응공학 i
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Chemical Reaction EngineeringChemical Reaction Engineering
제제 11 장장Mole BalanceMole Balance
반응공학 반응공학 II
Chapter 1. Mole Balance
1.1 Definition of the Rate of Reaction, -rA
1.2 The General Mole Balance Equation
1.3 Batch Reactors
1.4 Continuous-Flow Reactors
1.4.1 Continuous-Stirred Tank Reactor
1.4.2 Tubular Reactor
1.4.3 Packed-Bed Reactor
1.5 Industrial Reactors
Chapter 1. Mole Balance
ObjectivesAfter completing Chapter 1, the reader will be able to:
Define the rate of chemical reaction.
Apply the mole balance equations to
a batch reactor, CSTR, PFR, and PBR.
Describe two industrial reaction engineering systems.
Describe photos of real reactors.
The identity of a chemical species
The species nicotine is made up of a
fixed number of a specific atoms in the
specific atoms in a definite molecular
arrangement or configuration. The
structure shown illustrates the kind,
number, and configuration of atoms in
the species nicotine on a molecular
level.
The identity of a chemical species
C=CH H
CH3 CH3
C=CH CH3
CH3 H
2-butene has four carbon atoms and eight hydrogen atoms;
however the atoms in this compound can form two different
arrangements.cis-2-butene trans-2-butene
As a consequence of the different configurations, these two
isomers display different chemical and physical properties.
Therefore, we consider them as two different species.
We say that chemical reaction has taken place when
a detectable number of molecules of one or more
species have lost their identity and assumed a new
form by a change in the kind or number of atoms in
the compound and/or by a change in structure or
configuration of these atoms.
The identity of a chemical species is determined by
the kind, number, and configuration of that species’
atoms.
When has a chemical reaction taken place?
Three basic chemical reactions:
1. Decomposition ( 분해반응 )2. Combination ( 결합반응 )3. Isomerization ( 이성질화반응 )
A species can lose its identity by 3 reactions
Three basic chemical reactions:
When has a chemical reaction taken place?
CH(CH3)2
+ C3H6
DecompositionDecomposition
CombinationCombination
CH2=C-CH2CH3
CH3
CH3C=CHCH3
CH3
IsomerizationIsomerization
IsomerizationIsomerization
분 자 가 그 들 의 화 학 적 동 일 성 을 잃 을 때 어 떤 특 정 화학성분의 분자의 일정 개수가 반응 또는 소실되었다고 말한다 .
Reaction rate
The rate of a reaction can be expressed as the rate of disappearance of a reactant or as the rate of appearance of a product.
Consider species A:
A A → B→ B rrAA: the rate of formation of species A per unit volume -r-rAA: the rate of disappearance of species A per unit
volume rrBB: the rate of formation of species B per unit volume
2C6H5Cl + CCl3CHO (C6H4Cl)2CHCCl3 + H2OChlorobenzene Chloral DDT (Dichloro Diphenyl-Trichloroethane)
What is –r A (–r´A )?
Solely a function of properties of reacting materials.
(Concentration, temperature, pressure, catalyst or solvent) An intensive quantity. An algebraic function of concentration. such as. for homogeneous system:
for heterogeneous system:
The numerical value of the rate of reaction, -rA, is defined as
the number of moles of chloral reacting (disappearing) per unit time per unit volume [mol/dm3·s].
A
AA
AA
AA
Ck
Ckr
kCr
kCr
2
1
2
1
Fuming H2SO4
l
gmol
sec
catg
gmol
sec
Sodium Hydroxide Concentration in Batch Reactor
NaOH CH3COOC2H5
NaOH + CH3COOC2H5 CH3COONa + C2H5OH
dt
dCr A
A Time
CA
Constant-volume batch reactor
Ethyl Acetate Sodium Acetate
Ideal Reactor Type
Batch ReactorBatch Reactor-uniform composition everywhere in the reactor-the composition changes with time
Continuous-Stirred Tank Reactor (CSTR)Continuous-Stirred Tank Reactor (CSTR)
-uniform composition everywhere in the reactor (well mixed)
-same composition at the reactor exit
Tubular Reactor (PFR)Tubular Reactor (PFR)
-fluid passes through the reactor with no mixing of earlier
and later entering fluid, and with no overtaking.
-It is as if the fluid moved in single file through the reactor
-There is no radial variation in concentration (plug-flow reactor)
Is Sodium Hydroxide Reacting?
NaOH CH3COOC2H5
C2H5OH,CH3COONa, andunreactedNaOH andCH3COOC2H5
NaOH + CH3COOC2H5 CH3COONa + C2H5OH
0dt
dCr A
A
CSTR
Steady state:Steady state: the product is continuously withdrawn from the product is continuously withdrawn from the tank at a rate equal to the total feed rate.the tank at a rate equal to the total feed rate.
CA @ 1P.M. = CA @ 3P.M.
Balance on control volume
A mole balance on species j, at any time, t, yields
Nj
Gj = rj · VFj0 Fj
control volume
Rate of flow of j into the
system (mole/time)
Rate of generation of j by chem. rxn within the system
(mole/time)
Rate of accumulation of j within the system
(mole/time)
Rate of flow of j out of the system
(mole/time)
- + =
in - out + generation = accumulation
dt
dNGFF j
jjj 0
volumevolumetime
moles
time
molesG j
molesN j
Rate of formation of species j by chem. rxn
rj1
rj2
V1V2 V
Suppose that the rate of formation of species j for the reaction varies with the position in the control volume. The rate of generation, Gj1, in terms of rj1 and sub-volume V1 is
M
iiji
M
ijij VrGG
11
If the total control volume is divided into M sub-volume, the total rate of generation is
111 V jj rG
By taking the appropriate limits (i.e., let M → and V → 0) and making use of the definition of integral, we can rewrite the foregoing equation in the form
V
jj dVrG
From this equation, we can see that r j will be an indirect function of position, since the properties of the reacting materials (e.g., conc., temp.) can have different values at difference locations in the reactor.
1.2 The General Mole Balance Equation
(GMBE)
dt
dNdVrFF jV
jjj 0
With this GMBE, we can develop the design equations for the various types of industrial reactors: batch, semi-batch, and continuous-flow. Upon evaluation of these equations we can determine the time (batch) or reactor volume (continuous-flow) necessary to convert a specified amount of reactants to products.
1.3 Batch Reactors
If the reaction mixture is perfectly mixed so that there is no variation in the rate of reaction throughout the reactor volume, we can take rj out of the integral and write the GMBE in the form
dt
dNdVrFF jV
jjj 0
0 0
Vrdt
dNj
j
t
NAA → B
V
jj VrdVrNo spatial variations in the rate of reaction
(1-5)
NA0
What time is necessary to reduce the initial number of moles from NA0 to NA1?
Vrdt
dNA
A
Vr
dNdt
A
A
1
01
A
A
N
NA
A
Vr
dNt (1-6)
Integrating with limits that at t = 0, NA = NA0
at t = t1, NA = NA1
Constant Volume or Constant Pressure
CH3-O-CH3 → CH4 + H2 + CO
Constant volume(variable pressure)
Constant pressure(variable volume)
dt
dN
Vr A
A
1
dt
dN
Vr A
A
1
VCN AA
dt
dV
V
C
dt
dCdt
VCd
Vr
AA
AA
)(1
dt
dCr A
A dt
VdC
dt
dCr A
AA
)(ln
1.4.1 Continuous-Stirred Tank Reactor (CSTR)
The CSTR is normally run at steady state and is assumed to be perfect mixed. - No temporal, spatial variations in conc., temp., or rxn rate throughout the vessel - Conc. and temp at exit are the same as they are elsewhere in the tank- Non-ideal mixing, residence-time distribution model is needed
dt
dNdVrFF jV
jjj 0
0
V
jj VrdVr
j
jj
r
FFV
0
j
jj
r
FFV
0
No spatial variations in the rate of reaction
Design Equation for a CSTR
Fj0
Fj
1.4.1 Continuous-Stirred Tank Reactor (CSTR)
j
jj
r
FFV
0
j
jj
r
FFV
0
time
volume
volume
moles
time
moles
vCF jj
Design Equation for a CSTRFj0
Fj
A
AA
r
vCCvV
00
A
AA
r
vCCvV
00
1.4.2 Tubular Reactor
- The reaction rate will also vary axially.- To develop the PFR design equation, we shall divide (conceptually) the reactor into a number of sub-volumes so that within each sub-volume V, the reaction rate may be considered spatially uniform.
0jF exitFj ,
)(yFj )( yyFj V
y
y yy
Let Fj(y) represent the molar flow rate of species j into volume V at y
Fj(y+y) represent the molar flow rate of species j out of volume V at (y+y)
In a spatially uniform sub-volume V,
VrdVrV
jj
1.4.2 Tubular Reactor
dt
dNdVrFF jV
jjj 0
0
rj is a function of reactant concentration, which is function of the position y down the reactor.
Steady state
0)()( VryyFyF jjj
yAV
(1-8)
Substitute V into Eq. 1-8 and divide by y to yield
jjj Ar
y
yFyyF
)()(
Taking the limit as y approaches zero, we obtain
jj Ar
dy
dF
Tubular Reactor
It is usually most convenient to have the reactor volume V rather than the reactor length y as the independent variable. Using dV=Ady,
jj r
dV
dF
The tubular reactor design equation can be applied to the PFR with variable and constant cross-sectional area.
Tubular Reactor
It is usually most convenient to have the reactor volume V rather than the reactor length y as the independent variable. Using dV=Ady,
jj r
dV
dF
The tubular reactor design equation can be applied to the PFR with variable and constant cross-sectional area.
Packed-Bed Reactor (PBR)For a fluid-solid heterogeneous system, the rate of reaction of a substance A is defined as
catalystg
reactedAgmolrA
sec
'
The mass of solid is used because the amount of the catalyst is what is important to the –r’A
0AF AF
)(WFA )( WWF A
WrA'
W
W WW
0)()( ' WrWWFWF AAA
In - out + generation = accumulation
A
A
F
FA
A
r
dFW
0' No pressure drop
No catalyst decay
The first-order reaction (liquid phase rxn)
A Bis carried out in a tubular reactor in which the volumetric flow rate, v0, is
constant.
(1) Derive an equation relating the reactor volume (V) to the entering concentration of A (CA0), the rate constant k, and the volumetric flow
rate v0.
(2) Determine the reactor volume necessary to reduce the exiting concentration (CA) to 10% of the entering concentration (CA0) when the
volumetric flow rate (v0) is 10 ℓ/min and the specific reaction rate, k, is
0.23 min-1.
Example 1-1 How large is it? (PFR)
CA0 v0 CAV
rA=-kCA
Example 1-1 How large is it? (PFR)
dVC
dC
k
v
kCrdV
dCv
rdV
dCv
dV
vCd
dV
dF
kCr
rdV
dF
A
A
AAA
AAAA
AA
AA
0
0
00 )(
ll
C
ClV
C
C
k
vV
dVC
dC
k
v
A
A
A
A
VC
CA
AA
A
10010ln23.0
10
1.0ln
min23.0
min/10
ln
0
01
00
0
0
0
(GMBE for tubular reactor)
(first-order reaction)
Tubular, 1st order rxn
The first-order reaction (liquid phase rxn)
A Bis carried out in a CSTR in which the volumetric flow rate, v0, is
constant.
(1) Derive an equation relating the reactor volume (V) to the entering concentration of A (CA0), the rate constant k, and the volumetric flow
rate v0.
(2) Determine the reactor volume necessary to reduce the exiting concentration (CA) to 10% of the entering concentration (CA0) when the
volumetric flow rate (v0) is 10 ℓ/min and the specific reaction rate, k, is
0.23 min-1.
P1-6B How large is it? (CSTR)
V
rA=-kCA
Fj0
Fj
For CSTR, the mole balance on species A was shown to be
P1-6B How large is it? (CSTR)
V
rA=-kCA
Fj0
Fj
3.391
)min23.0/(min)/10)(9(
1.0
9.0
1.0
min23.0min,/10,1.0
1
0
0
000
100
0000
k
v
kC
vCvCV
kandvCC
kC
vCvC
r
FFV
A
AA
AA
A
AA
A
AA
3.391
)min23.0/(min)/10)(9(
1.0
9.0
1.0
min23.0min,/10,1.0
1
0
0
000
100
0000
k
v
kC
vCvCV
kandvCC
kC
vCvC
r
FFV
A
AA
AA
A
AA
A
AA
The CSTR is almost 4 times larger than the PFR for getting 90% conversion
Reactor Differential Algebraic Integral
Mole Balance on Different Reactor
Vrdt
dNA
A
A
A
F
FA
A
r
dFV
0
AA r
dV
dF
AA r
dW
dF A
A
F
FA
A
r
dFW
0
A
A
N
NA
A
Vr
dNt
0
A
AA
r
FFV
0
Batch
CSTR
PFR
PBR