BAHAN KULIAH TRK -1 Oleh Prof. Dr. Ir. Slamet, MT Departemen Teknik Kimia UI September 2012
Efek Difusi Eksternal
Tahapan Reaksi Katalitik 1. Transfer massa (difusi) reaktan, bulk permukaan eksternal pelet katalis
→
2. Difusi reaktan: mulut pori → permukaan internal katalis melalui pori. 3. Adsorpsi reaktan → permukaan katalis. 4. Reaksi pada permukaan katalis 5. Desorpsi produk (contoh: spesies B) dari permukaan katalis. 6. Difusi produk dari permukaan internal pelet menuju mulut pori pada permukaan eksternal katalis. 7. Transfer massa produk dari permukaan eksternal ke fasa bulk.
A
B A
B
1
External Diffusion
7
B A 2
6
3
Internal Diffusion
5 4
AB
Catalytic Surface
Difusi Eksternal
Dasar-dasar transfer massa • Neraca mol spesi A : 1. Sistem koordinat rectangular:
∂W Ax ∂W Ay ∂W Az ∂C A − − − + r A = ∂ x ∂ y ∂ z ∂t
(A)
2. Sistem koordinat silinder:
∂ ∂W Az ∂C A (rW Ar ) − − + r A = r ∂r ∂ z ∂t 1
(B)
Dasar-dasar transfer massa •
Fluks molar A, W A (mol/m2.s) merupakan jumlah dari fluks difusi molekuler (J A ) dan fluks dari gerakan bulk atau konveksi (B A )
= J A + BA BA = y A ΣWi = C A V WA
(1) (2)
•
Untuk sistem biner A dan B, fluks molar W A (mol/m2.s) adalah: WA = J A + yA (WA + WB ) (3)
•
Hukum Fick:
JA = -cDAB∇ yA
WA = -cDAB∇ yA + yA(WA + WB)
(4) (5)
Binary Diffusion 1. Equimolar Counter-diffusion (W A = -WB):
WA = -cDAB∇ yA
(6)
Utk konsentrasi total konstan:
WA = JA = - DAB∇C A
(7)
2. Dilute Concentrations ( yA ~ 0):
WA = - DAB∇C A
(8)
Contoh utk 1 M larutan tertentu: C W
= 55 .6
y A
=
mol / L
C A C W
+ C A
=
1 55 .6 + 1
= 0 .018
Binary Diffusion •
•
•
Pers (5) juga dpt disederhanakan menjadi pers (7) utk sistem katalis porous dg jari-jari pori sangat kecil. Difusi pd sistem tsb dikenal dg Difusi Knudsen, terjadi ketika ‘mean free path’ dari molekul lebih besar dari diameter pori katalis tumbukan molekul lebih sering terjadi dg dinding pori dibanding dg antar molekul. Pers fluks molar A utk difusi Knudsen adalah (D K : difusivitas Knudsen):
WA = - DK ∇C A
(9)
Binary Diffusion 3. Diffusion through a Stagnant Gas (WB = 0): •
•
Difusi solute A melalui stagnant gas B, biasanya terjadi pd sistem 2 fasa. Contoh: evaporasi, absorpsi gas. Pers (5) menjadi:
WA = -cDAB∇ yA + yAWA WΑ WΑ
−1 (10) cD y = AB ∇ A 1 − y A = cD AB ∇ ln(1 − y A ) = cD AB ∇ ln( y B )
Binary Diffusion 4. Forced Convection (J Az ≅ 0): • •
Asumsi: Difusi ke arah z (aksial) sangat kecil dibandingkan dg kontribusi aliran bulk. Pers (1) & (2) menjadi:
WA z = B A z = C A V z = C A
v
Ac
=
F A Ac
•
Ac: cross-sectional area, v: volumetric flow
•
rate. Ketika efek difusi dpt diabaikan (plug flow):
FA
= vC A
(11)
(12)
Binary Diffusion 5. Diffusion & Convective Transport: WA z = − D AB FAz •
dC A dz
+ C AU z
= W z A c = ⎡⎢ − DAB ⎣ Α
dC A dz
(13)
+ C AU z ⎤⎥ A c ⎦
Dg memasukkan WAx, WAy, dan WAz ke pers (A) diperoleh:
⎡ ∂ 2 C A ∂ 2 C A ∂ 2 C A ⎤ ∂C A ∂C A ∂C A ∂C A D AB ⎢ U U U r + + − − − + = x y z A 2 2 2 ⎥ x y z x y z ∂ ∂ ∂ ∂ ∂ ∂ ∂t ⎣ ⎦ •
•
Utk satu dimensi & SS: D AB
d 2 C A 2
dz
− U z
Neraca mol utk tubular flow reactor:
dC A dz
+ r A = 0
(14)
dF Az
(15)
dV
= r A
Example 11-1 Difusi melalui stagnant film pada pelet katalis
Pelajari buku Fogler ed. 4, hal. 766 .................
Korelasi koefisien transfer massa
Analogi dg transfer panas, korelasi koefisien transfer massa (k c) utk aliran sekitar pelet bola (konveksi paksa) adalah sbb: 1 1 2 (16) Sh 2 0.6 Re Sc 3
= +
k c d p
Sh =
D AB
Re =
Sc =
( Bil. Sherwood)
ρ Ud p μ μ
ρ D AB
=
=
Ud p ν ν
D AB
(Bil. Reynold)
( Bil. Schmidt )
k c
=
D AB δ
Example 11-2 (Rapid reaction on a catalyst surface) Diketahui: Diameter pelet katalis = 1 cm Reaktan A : konsentrasi encer C Ab = 1 M Reaksi spontan di permukaan katalis (C As = 0) Kecepatan, U = 0.1 m/s Viskositas kinematik, μ /ρ = 0.5x10-6 m2 /s Difusivitas A, D AB = 10-10 m2 /s •
• •
• •
•
Ditanya: Fluks molar A (W Ar) Laju reaksi permukaan (-r ’’ As) • •
Example 11-2 (Rapid reaction on a catalyst surface) Jawab: Menghitung koefisien transfer massa: •
Re = Sc =
k c •
Ud p ν ν D AB
=
= 2000 = 5000
D AB Sh d p
Sh = 2 + 0.6( 2000) (5000) 1
2
1
3
= 460.7
= 4 . 61 x10 − 6 m/s
Untuk konsentrasi encer: " W Ar = k c (C Ab − C As ) = 4.61x10 −3 mol/(m2 .s) = -r As
Transfer massa pada partikel tunggal •
•
Terdapat 2 kasus yg terkait dengan difusi & reaksi pada partikel katalis: 1. Reaksi sangat cepat “difusi” sbg penentu laju reaksi 2. Reaksi sangat lambat “reaksi” sbg penentu laju reaksi. Reaksi isomerisasi : A B terjadi di permukaan katalis padat berbentuk bola. Reaksi permukaan mengikuti mekanisme L-H ‘single site’, shg pers kinetiknya adalah sbb:
− r = " As
k r C As
(1 + K A C As + K B C Bs )
(17)
•
Jika suhu cukup tinggi adsorpsi sangat lemah <<< 1 pers (17) menjadi:
K A &
− r As" = k r C As •
(18)
Dengan kondisi batas 2b & 2c (Fogler, Tabel 11-1) diperoleh:
W A surface
•
K B
= − r As"
W A
= k c (C A − C As ) = k r C As
C As
=
k c C A k r
+ k c
Maka pers (18) menjadi:
− r = W A = " As
k r k c k r + k c
C A
= k eff C A
(19)
Reaksi cepat •
Jika reaksi sangat cepat
− r = " As
•
k r >> k c
k c 1 + k c / k r
pers (19) menjadi:
C A
≈
k c C A
Sc biasanya >> 2, sehingga utk Re > 25, maka menjadi:
k c
⎛ D AB = 0 . 6 ⎜⎜ ⎝ d p
1
⎞ ⎛ Ud p ⎞ ⎛ ν ⎟ ⎜⎜ ⎜⎜ ⎟ ⎟ ⎟ ⎠ ⎝ ν ⎠ ⎝ D AB
⎛ D AB ⎜⎜ ⎝ ν 2
3
⎞ ⎟⎟ ⎠
2
⎛ U ⎞ ⎜ ⎟ ⎜ d p ⎟ ⎝ ⎠
k c
=
0 .6 x
k c
=
0 . 6 x (Term 1 ) x (Term
1
6
x
1
2
2)
⎞ ⎟⎟ ⎠
1
(20)
pers (16)
3
(21)
Reaksi lambat •
Jika reaksi sangat lambat
− r = " As
-r A ”
Diffusion Limited
k r << k c
k r 1 + k r / k c
C A
pers (19) menjadi:
≈
Reaction Limited
(U/dp)1/2
k r C A
(22)
Mass Transfer-Limited Reactions in Packed Beds •
Dari penjabaran neraca mol di reaktor packed-bed (Fig. 11-7, Fogler) utk kecepatan superficial (U) konstan, diperoleh:
− U •
•
d (C A ) dz
+
r A" a c
=
0
Utk reaksi-reaksi pd kondisi steady state, maka: − r A" = W Ar = k c ( C A − C As ) Utk reaksi-reaksi yang dibatasi transfer massa, C As dpt diabaikan (C A >> C As) & tdk perlu mengetahui pers. Laju reaksi, maka:
− U
X
dC A dz
=
k c a c C A
= 1 − exp ⎛ ⎜− ⎝ (23)
⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ →
k c a c U
int egrasi pd z = 0 , C A =C Ao
⎞ ⎠
z ⎟
dan
− r A" =
exp
⎛ − ⎜ ⎝
k c a c
k c C Ao exp
⎛ − ⎜ ⎝
k c a c
C A C Ao
=
U
U
⎞ ⎠
z ⎟
⎞ ⎠
z ⎟
Mass Transfer-Limited Reactions in Packed Beds •
Korelasi Thoenes-Kramers utk aliran melalui packed-bed: Sh'
=
⎡ k c d p ⎢ D ⎣ AB •
1
(Re' ) 2 ( Sc )
1
3
⎛ φ ⎞ 1 ⎤ ⎡ ρ Ud p ⎤ ⎜⎜ ⎟⎟ ⎥ = ⎢ ⎥ 1 φ − ⎝ ⎠ γ ⎦ ⎣ μ (1 − φ ) γ ⎦
1
2
⎛ μ ⎞ ⎜⎜ ⎟⎟ ρ D ⎝ AB ⎠
Korelasi di atas berlaku untuk:
< φ < 0 . 50 40 < Re' < 4000 1 < Sc < 4000
0 . 25
Pelajari Example 11-3 & 11-4
1
3
(24)
Mass Transfer-Limited Reactions on Metallic Surfaces
A. Catalyst Monolith •
•
•
In packed-bed reactors, when a gaseous feed stream contains significant amounts of particulate matter, dust tends to clog the catalyst bed. To process feed streams of this type, parallel-plate reactors (monoliths) are commonly used. The reacting gas mixture flows between the parallel plates, and the reaction takes place on the surface of the plates.
A. Catalyst Monolith
1. Mol balance
(R11.1-1)
1. a m : the catalytic surface area per unit volume of reactor, 2. A c : the cross-sectional area normal to the direction of gas flow. 3. r A ” : the rate of surface reaction is equal to mass flux to the surface. 4. Taking the surface concentration equal to zero for mass transferlimited reactions
(R11.1-2)
A. Catalyst Monolith Substituting Equation (R11.1-2) into (R11.1-1) and taking the limit as 0 yields : (R11.1-3)
(R11.1-4)
The surface area per unit volume, a , for n plates is: (R11.1-5)
•
•
•
Typical spacing between the plates = 0.005 - 0.01 m, The length ranges between 0.05 - 0.5 m, and Gas velocities between 5 - 20 m/s.
A. Catalyst Monolith
•
The mass transfer coefficient (k c ) can be calculated from the correlation :
(R11.1-6)
•
For no volume change with reaction, Equation (R11.1-4) can be integrated to give:
(R11.1-7)
B. Wire Gauzes •
•
•
Figure R11.1-4 •
•
One can assume plug flow through the gauze, in which case the design equation is similar to that for monolith reactors:
Wire gauzes are commonly used in the oxidation of ammonia and hydrocarbons. A gauze is a series of wire screens, stacked one on top of another (Figure R11.1-4). The wire is typically made out of platinum or a platinum-rhodium alloy. The wire diameter ranges between 0.004 and 0.01 cm
(R11.1-8)
B. Wire Gauzes •
where a g = total screen surface area per total volume of one screen, m2 /m3 or in2 /in3
•
The porosity can be calculated from the equation: (R11.1-10)
•
The values of a g can be calculated from the equations: •
The mass transfer coefficient can be obtained from the correlation for one to three screens:
(R11.1-9)
where d = wire diameter, in. N = mesh size, number of wires per linear inch
(R11.1-11)
B. Wire Gauzes •
For one to five screens, the correlation is: (R11.1-14) (R11.1-12)
•
where is the minimum fractional opening of a single screen: (R11.1-13)
•
When more than one or two screens are necessary, some backmixing takes place. Shimizu et al. account for this backmixing by introducing dispersion in the axial direction:
•
•
Equation (R11.1-14) is then combined with Eqn. (R11.1-8) and solved. When dispersion is significant it was shown that, depending on the flow conditions, 33 to 300% more screens were required than predicted by the plug-flow model
