Transcript Chemical Kinetics and Reaction Engineering (Topochemical Model)

Chemical Kinetics and Reaction Dynamics
Chemical Kinetics and
Reaction Engineering
(Topochemical Model)
민 동
준
Chemical Kinetics and Reaction Dynamics
Kinetic Model for Indirect Reduction
Topochemical Model for gas/solid Reaction
(1) 가스 물질이동 : CO(b) -> CO(g.b)
(2) 가스확산이동 : CO(g.b) -> CO(g/s)
(3) 반응층내 기공확산 : CO(g/s)-> CO(inter)
(4) FeOx + CO(interface)= FeOx-1 + CO2
3
CO 가스농도가 순차적으로 감소
반응 진행에 따라 반응계면이 순차적이동
FeO 환원단계가 가장느린 단계
: 율속단계
2
1
CO
CO2
Chemical Kinetics and Reaction Dynamics
Simple Topochemical Model
rs
(CA)s
r
(CA)
(CA)s
(CA)b
rc
(CA)
(CA)s
(CA)s
가스조성
r
rs
(CA)b
반경
rc
Chemical Kinetics and Reaction Dynamics
Mathematical Treatment for Topochemical Rxt.
가스 물질이동 : CO(b) -> CO(g/s)
 dN A
 4rs 2 [(C A ) b  (C A )s ]
dt
Diffusion thorugh Product
 dN A
 dC A
 4rc D e [
]
dt
dr
Chemical Reaction at rc
 dN A
 4rc k c (C A ) ( rc )
dt
Chemical Kinetics and Reaction Dynamics
Mathematical Treatment for Topochemical Rxt.
In steady states, from Mass Conservation rule
J diffusion
 J r  r  0
r
Lim r  0
0
( 4)
하면
dC A
dC A
) r  ( r 2 D e )(
) r  r
dr
dr
d 2
dC A

(r D 2
)0
dr
dr
 ( r 2 D e )(
(5)
( 6)
Boundary condition for differential Eq.
C A  C AS
at
r  rs
C A  C AC
at
r  rc
(6)식에 대입하여 풀면
C A  C AC
rc
r
 [C AS  C AC ] 
r
1 c
rs
1
(7 )
Chemical Kinetics and Reaction Dynamics
Mathematical Treatment for Topochemical Rxt.
(7)식을 r에 대하여 미분 : 농도분포와 r-rc에서의 CA 농도를 도출
(
C  C AC
dC A
) r  rc  AS
r
dr
rC  (1  c )
rs
(8)
(8)식을 (2) 식에 대입
(
C  C AC
dN A
)  4    rc  D e  AS
r
dt
rc  (1  c )
rs
(9)
(1)(3)(4)식에서 CAS와 dNA/dt 를 소거하여 정리하면
C AC 
C AB
rc2 k C
k  r 1  rC
1 2  ( )  C C  (
)
rs k m
De
rS
(10)
Chemical Kinetics and Reaction Dynamics
Mathematical Treatment for Topochemical Rxt.
(3)식으로부터 단일입자당 반응속도, -dNA/dt는 : (10)식을 (3)식에 대입
4rc2 (C Ab )
dN A


r
1 rC2 1
1
dt
 2

 c
k C rS km De 1  rc
rS
(11)
 K 0  S  Driving force
여기서 S : 반응면적=
4rc2
3
Driving force : (공급환원가스농도 – 계면에서의 평형농도  C Ab (mol / cm )
K0 : 겉보기 총괄 반응 속도 상수
k0 
1
2
C
2
S
r
1 r
1
1
 

 c
k C r km De 1  rc
rS
(12)
전체 반응속도는 반응면적에 비례 : 대입자로서 Porous할수록 유리
환원가스의 조성에 대하여 1차적 함수 관계로 비례
Chemical Kinetics and Reaction Dynamics
Application for Processing Viewpoint
단계별 반응속도는 광석입자의 직경에 대한 부피로서 다음과 같이 표현
nb

Vg 
(CAb  CAs)
k
(여기서 C As : 가스 경막외측의 가스농도)
ng  4rs k m  (CAb  CA 0 )
(15)
(16)
( CA 0 : 고체입자 표면에서의 가스농도)
(C A 0  C Ac )
n d  4rs D e 
1
1
(  )
rc
rs
n c  4rc2 k c  (1 
1
)  (C Ac  C Bc )
k
(17)
(18)
(여기서 C Bc : 철광석중의 FeO 활동도에 의한 산소농도로서 평형상수 K dp
의해 가스 농도로 환산)
Chemical Kinetics and Reaction Dynamics
반응계면에서 환원가스 A에 의해 고체입자 중 산소가 감소하므로 입자중 초기
산소농도 d 0 (mol  O / m3 ) 를 정의하고, 정상상태를 고려 : (19)식.
4
d(  rc3 )
n b   n g   n d  d o  
dt
(19)
(15) ~ (18) 식과 (19)식을 결합하면
d( 4  rc3 )
4rc2 (CAb  Ceq
C )
 d0 

rs2
rs ( rs  rc )
rs2
1
1
dt
4k t Vg  De  rc  k c (1 1 )  r 2
k
단,
1 4x  rs2
(k f 

)
kg
Vg
c
(20)
Chemical Kinetics and Reaction Dynamics
여기서 환원율에 해당하는 반응 율, F를 도입하고
환원시간 t=0~t 에 대한 F=0~F 의 조건에서 적분
rc 3
F  1 ( )
rs
(21)
(1) 가스 경막이 물질이동의 율속인 경우 : (20)식은 (22)식으로 근사
d( 4  rc3 )
4rc2 (CAb  Ceq
C )
 d0 

rs2
rs ( rs  rc )
rs2
1
1
dt
4k t Vg  De  rc  k c (1 1 )  r 2
k
(C Ab  Ceq
F
A )
kf 
t
3
3  rs  d 0
(22)
c
(20)
Chemical Kinetics and Reaction Dynamics
(2) 생성층내의 반응가스의 확산이 율속인 경우 : (20)식은 (23)식으로 근사
d( 4  rc3 )
4rc2 (CAb  Ceq
C )
 d0 

rs2
rs ( rs  rc )
rs2
1
1
dt
4k t Vg  De  rc  k c (1 1 )  r 2
k
3  3(1  F) 3  2F (C Ab  Ceq
Ab )

t
6D e
3  rs  d 0
rs
c
2
(24)
(20)
Chemical Kinetics and Reaction Dynamics
(3) 계면에서의 화학 반응이 율속인 경우 : (20)식은 (24)식으로 근사
d( 4  rc3 )
4rc2 (CAb  Ceq
C )
 d0 

rs2
rs ( rs  rc )
rs2
1
1
dt
4k t Vg  De  rc  k c (1 1 )  r 2
k
1  (1  F) 3 (C Ab  Ceq
A )

t
1
3  rs  d 0
k c  (1  )
K
(20)
c
1
(C Ab  Ceq
A )
t
3  rs  d 0
(24)
와 F의 관계를 Plot하여
직선 관계를 갖는 반응 단계가 율속
Chemical Kinetics and Reaction Dynamics
Graphical Analysis for Rate limiting Step
가스물질이동
반응층내확산율속
화학반응 율속
2
3  3(1  F) 3  2F
F

1
kf
t
광석주위에서의 가스 유속
- 광석간 거리 : 광석 입도/분포
- 가스 공급량 : Coke/공기공급량
- 온 도 : PV=nRT
1
1  (1  F) 3
 De
t
광석 고유 특성
-광석내 기공율
-불순물 영향
- 환원 Fe 성장특성
 kc
t
반응온도/촉매거동
-반응온도/전열거동
-불순원소의 종류
Chemical Kinetics and Reaction Dynamics
Mathematical Treatment for Topochemical Rxt.
KC의 온도 의존성 : Arrhenius Relationship
Q act
k c  k  exp( 
)
RT
0
c
로 표현
(13)
온도가 증가할 수록 계면에서는 화학 반응 속도가 증가
(3) Km : Gas phase mass transfer 는 Ranz-Mashall Equation 으로 표현
여기서
Sh 
km 
1
1
k m  rs
 2.0  0.664  Re 2  Sc 3
Dg
Dg
rs
 [2  (
Vg  rs
v
1
)2  (
K m  Vb 2
1
v 12
) ]
Dg
v : 가스 점성 계수
Dg : 가스 확산 계수 (cm2/sec)
rs : 입자 반경 (cm)
Vg : 가스 유속 (cm/sec)
Km : 가스 물질 이동 계수 (cm/sec)
가스 유속에 비례하여 증가
Chemical Kinetics and Reaction Dynamics
Mathematical Treatment for Topochemical Rxt.
(4) (12) 식 : De 는 rs의 1차항적 상관관계
- De ∝f (pore size, Mean free pass)
- 온도가 과도하게 높으면 용융에 의해 Pore size가 감소
- 입자가 적을수록 확산 거리가 감소하여 반응속도가 증가 : 유동층
(5) 총괄적 고찰
- 반응 온도가 증가하면 화학 반응 속도가 증가하여
Km이나 De에의한 율속 : 최적 반응 온도 유지
- 가스 속도가 낮으면 Km이나 De 에 의한 율속
: 고로의 형태와 가스 유량 유지
- 입자가 치밀하면 De에 의한 율속
: 원료 처리시 Pore를 적절하게 유지
Chemical Kinetics and Reaction Dynamics
율속 단계의 도출
율속단계(Rate Limiting/Controlling step)의 정의
화학반응(Kc), 가스물질이동(Km), 반응층 내의 물질이동(De)등으로 이루어진 전체 반응단계
에서 전체반응속도를 지배하는 가장 속도가 느린 단계
(11)식 : 각 소반응의 속도상수인 Km, Kc, De를 이론적으로 비교 : 율속단계 도출
nb : 가스상 중에서 반응생성가스 잔류에 의한 반응 구동력의 저하를 고려한 반응속도
(mol / sec)
ng : 가스 경막 내 물질 이동 속도 (mol / sec)
nd : 반응 생성층 내의 확산 속도 (mol / sec)
nc : 계면에서의 화학반응속도
(mol / sec)
Vg : 가스유속 (cm / sec)
x : 가스 유량에 따른 가스 경막 외측의 조성변화에 따른 수지저항(무차원 함수)
Chemical Kinetics and Reaction Dynamics
General Phenomena for Kinetics
De
Kc & De
KC
koverall
1
T
- 기본조건 : 가스 유량은 충분 : kg>> De, Kc (Airwnd N2농도 80%)
- 고온영역 : FeO/Fe Eutectic Meling : Pore Closing
- 저온영역 : 반응계면에서의 화학반응 율속
온도 : 850 ~ 1000oC and Ore Blending & Sintering for Pore control
Chemical Kinetics and Reaction Dynamics
A Kinetic Study on the Decarburization
of Stainless Steel Containing Cu
Chemical Kinetics and Reaction Dynamics
 Introduction
 Advantage of stainless steel containing Cu
• High corrosion resistance
• High fabricability
• Non-magnetism & Anti-biotic property
 Technical obstacle
• The rate of decarburization
• No previous studies on the effect of Cu
on the decarburization of stainless steel
 The aspect of thermodynamics
• The effect of alloying element
• [%Ceq]
 The aspect of kinetics
• Reaction mechanism
• Rate limiting step
Chemical Kinetics and Reaction Dynamics
[ wt %Cu ]
0
5
10
15
20
25
30
0.07
The addition of Cu to Fe-(18%)Cr
The addition of Cr to Fe
0.06
0.05
[ wt %C
eq
]
CO 2  Cin melts  2CO
0.04
log K  
0.03
Cu
log  C   0.357  6.9 X C  5.1X Cr  4.1X Cu
0.02
Cr
0.01
0.00
0
5
7558
 6.765
T
10
15
20
25
30
[ wt %Cr ]
Fig. Theoretical limit of decarburization of Fe-Cr and
Fe-Cr-Cu melts ( 1600℃, PCO 2  0.7atm, PCO  0.3 atm )
Chemical Kinetics and Reaction Dynamics
 Reaction Mechanism
CO2(g)
Mass transfer in gas
Interfacial reaction
CO2(g) = CO2(ad)
CO2(ad) = CO(ad) + O(ad)
[M] + xO(ad) = MxO
(M=Cr,Fe)
MxO + xC(ad) = [M] + xCO(ad)
CO(ad) = CO(g)
Mass transfer in liguid-phase
[C] = C(ad)
Fe-Cr-C
Chemical Kinetics and Reaction Dynamics
5
-1.5
-2.0
4
-2.5
3
[ wt %C ]
log K
Present study
after Sain & Belton
-3.0
-3.5
-4.0
6.0
Fe-(18%)Cr-(4%)Cu
Fe-(18%)Cr
Pure Iron
2
1
6.2
6.4
6.6
6.8
7.0
4
1/T ( ¡¿10 )
Fig. Decarburization rates of Fe-C melts by CO2
0
0
100
200
300
400
500
600
time (sec)
Fig. Decarburization rates of various melts
by CO2 at 1600℃
Chemical Kinetics and Reaction Dynamics
0.007
0.20
- ln (C/C0)
0.15
Rate Constant K1 ( Low Carbon Conc )
Cu = O wt%
Cu = 2 wt%
Cu = 4 wt%
Cu = 6 wt%
0.10
0.05
Present study (Fe-(18%)Cr-C-Cu)
after Fruehan (Fe-(11%)Cr-C)
0.006
0.005
0.004
0.003
0.002
0.001
0.000
0.00
0
10
20
30
40
time (sec)
Fig. First-order reaction with respect to carbon
at low concentrations of carbon
0
2
4
6
8
10
[ wt %Cu ]
Fig. The rate constant of decarburization of
Fe-18%Cr-Cu-C melts with carbon
concentrations at low concentrations of carbon
Chemical Kinetics and Reaction Dynamics
 Estimation of interfacial reaction rates
– The effect of M on the interfacial reaction rate

k app
dC A
 k app PCO 2
dt
k0

 kr
1  K M [ wt%M]
k0 = the reaction rate constant of M-free melts
kr = the residual rate constant at high M level
Chemical Kinetics and Reaction Dynamics
 The effect of Cr
0.00016
2100
0.0004
1900
0.0003
1800
0.0002
1700
0.0001
1600
0.0000
1500
0
10
20
30
Present study
Derived values
0.00014
0.00012
2
2000
after Song et al.
(1550¡É, Surface Tension of Fe-Cr alloys)
Surface Tension(mN/m)
0.0005
Rate Constant ( mole / cm atm sec )
Present study(1600¡É, P CO2/PCO=0.7/0.3)
Derived values
2
Rate Constant(mole/cm atm sec)
0.0006
0.00010
0.00008
0.00006
0.00004
0.00002
0.00000
0
2
[wt%Cr]
k
0
Cu  free
3.202 10 4

 7.08810 5
1  2.89[ wt%Cr ]
Fig. Effect of Cr in Fe-Cr-C melts on the rate
constants of the CO2 reaction at 1600℃
4
6
8
10
[ wt% Cu ]
k app
k 0Cu free

1  0.087 [ wt%Cu ]
Fig. Effect of Cu in Fe-Cr-Cu-C melts on the rate
constants of the CO2 reaction at 1600℃
Chemical Kinetics and Reaction Dynamics
 Reactions of shifting order
– At low C : First-order Reactions
  
dC A
 k CA
dt
 ln
k  k1
CA
 kt
CA0
CA0 = Initial conc. of A
– At high C : Zero-order Reactions
  
dC A
 k
dt
k
k1
k2
CA 0  CA  CA 0 X A  kt
– Reactions of shifting order
  
dC A
k1 CA

dt
1  k 2 CA
Chemical Kinetics and Reaction Dynamics
0.0012
Cu = 0 wt%
-rA = -dC/dt ( g/sec )
0.0010
Cu = 2 wt%
0.0008
0.0006
0.0004
Cu = 4 wt%
Cu = 6 wt%
0.0002
Low C Conc.
High C Conc.
0.0000
0
1
2
3
4
5
eq
[ wt %C ] - [ wt %C ]
Fig. Decarburization rate with carbon concentrations
( Reaction of shifting order from first to zero order )
Chemical Kinetics and Reaction Dynamics
-2.0
Fe-C
Fe-(18%)Cr-C
Fe-(18%)Cr-(4%)Cu-C
after Sain & Belton (Fe-C)
-2.5
 log k  
log k
-3.0
-3.5
4489.95
 0.72
T
 log k FeCr  
2777.20
 2.42
T
 log k FeCr Cu  
2641.85
 2.63
T
-4.0
-4.5
-5.0
6.0
6.2
6.4
6.6
6.8
4
1 / T ( ¡¿10 )
Fig. The dependence of rate constants on
the temperature in various melts
7.0
Chemical Kinetics and Reaction Dynamics
 The calculation of total reaction rate
– At low C
– At high C
k1  0.002 g / sec
k app 
k1
k2
( 3.91  2.05[%Cr] )  10 4

1  0.087 [%Cu]  2.89 [%Cr]  0.251[%Cu][%Cr]
– Total reaction rate
  
dC A
k1 C A

dt
1  k 2 CA
Chemical Kinetics and Reaction Dynamics
5
Fe-(18%)Cr-(4%)Cu-C (Derived value)
Fe-(18%)Cr-C (Derived value)
Fe-(18%)Cr-(4%)Cu-C (Present study)
Fe-(18%)Cr-C (Present study)
[ wt %C ]
4
3
2
1
0
0
50
100
150
200
250
300
350
400
time (sec)
Fig. Decarburization rate of Fe-Cr-Cu-C melts
by CO2 at 1600℃
Chemical Kinetics and Reaction Dynamics
 Conclusion
A kinetic study on the decarburization rate of Fe-Cr-Cu-C by CO2 has been carried out at
1600℃
The conclusions follow as below.
1)
In high concentration of carbon, the reaction rate was controlled by 0th order reaction
and in low concentration of carbon, by 1st order reaction
2)
In low concentration of carbon, the effect of Cu on the decarburization rate of Fe-CrCu-C melt was small
3)
It was considered the addition of Cu in Fe-Cr-C decreased the interfacial reaction rate
in initial stage of highly carbon concentrated region through the region of shifting
order
4)
The decrease of decarburization rate by Cu in Fe-Cr-Cu-C was quantitized by
introducing of adsorption coefficient as below
k app
( 3.91  2.05[%Cr ] )  10 4

1  0.087 [%Cu ]  2.89[%Cr ]  0.251[%Cu ][%Cr ]