ELECTRONIC SUPPLEMENTARY MATERIAL
Title: Determination of methanolysis rate constants for low and high fatty acid
oils using heterogeneous surface reaction kinetic models
Journal: Reaction Kinetics, Mechanisms and Catalysis
Author Names & Affiliations:
Yousuf Jamal
Institute of Environmental Sciences and Engineering, School of Civil
and Environmental Engineering, National University of Sciences and
Technology, H-12, Islamabad 44000, Pakistan
Ahmed Rabie
Department of Petroleum Engineering, Texas A&M University,
College Station, TX 77843, USA.
Bryan Boulanger
Department of Civil Engineering, Ohio Northern University, Ada, OH
45810, USA
Corresponding author email address: yousuf.jamal@iese.nust.edu.pk
1
ELEY RIDEAL REACTION MECHANISM
REACTION: A+B ßà C+D
One or more reactants are not surface adsorbed
B
B
B
D
A
A
A
1
Catalyst Surface
C
2
3
B moved from bulk
solution to A
A Adsorbed
D
C
Surface reaction
D
C
4
Reaction site on
the catalyst surface
Desorption
5
Desorption
Fig. S1 Graphical depiction of the reaction mechanism involved in the EleyRideal kinetic
model.
2
LANGMUIR HINSHELWOOD HOUGEN WATSON REACTION MECHANISM
REACTION: A+B ßà C+D
All the reactants are surface adsorbed before reaction.
B
B
A
A
A
B
2
1
Catalyst Surface
B Adsorbed
A Adsorbed
C
C
D
D
4
3
Surface reaction
D
C
Desorption
5
Desorption
Reaction site on
the catalyst surface
Fig. ESM 2 Graphical depiction of the reaction mechanism involved in the Langmuir
HinshelwoodHougenWatson kinetic model.
3
APPENDIX A
ER surface reaction model derivation
Based upon the assumptions provided, the following series of equations can be derived for ER
surface reaction model solution. The stepwise reactions in the ER model derivation include:
k1
Step 1:
MeOH +∗ →← MeOH ∗
Step 2:
T + MeOH ∗
Step 3:
D + MeOH ∗
Step 4:
M + MeOH ∗
Step 5:
D +∗ →← D∗
Step 6:
M +∗ →← M∗
Step 7:
G +∗ →← G∗
k_1
k2
→
←
k_2
k3
→
←
k_3
k4
→
←
k_4
(1)
E + D∗
(2)
E + M∗
(3)
E + G∗
(4)
k5
k_5
(5)
k6
k_6
(6)
k7
k_7
(7)
where: MeOH = methanol; T = triglyceride; E = methyl ester; G = glycerol; * = resin surface
site; and MeOH*, T*, E*, D*, M* and G* are bounded resin surface sites; kn=forward
reaction; k-n= backward reaction, n = reaction step
4
Note:
K
Adsorption =
kforward
kbackward
and
K
k
Desorption = backward
kforward
Therefore, the rate equations for the adsorption of methanol and the surface reaction of
adsorbed MeOH with T, D, M, and G can be written as follows:
Methanol adsorption as rate limiting step
r1 = k1 [MeOH][∗] − k −1 [MeOH ∗ ]
K1 =
(8)
k1
k −1
1
r1 = k1 ([MeOH][∗] − K [MeOH ∗ ])
1
(8a)
Because MeOH adsorption is the rate limiting step, k2 through k7 will be much larger than
r
r
r
r
r
r
k1. Therefore, k2 , k3 , k4 , k5 , k6 and k7 in the following series of equations are assumed to be
2
3
4
5
6
7
very small (almost zero).
Rate of triglycerides surface reaction
r2 = k 2 [MeOH ∗ ][T] − k −2 [D∗ ][E]
K2 =
(9)
k2
k −2
5
r2
k2
1
≅ 0 = ([MeOH ∗ ][T] − K [D∗ ][E])
2
(9a)
Rate of diglycerides surface reaction
r3 = k 3 [MeOH ∗ ][D] − k −3 [M ∗ ][E]
K3 =
r3
k3
(10)
k3
k −3
1
≅ 0 = ([MeOH ∗ ][D] − K [M ∗ ][E])
3
(10a)
Rate of monoglycerides surface reaction
r4 = k 4 [MeOH ∗ ][M] − k −4 [G∗ ][E]
K4 =
r4
k4
(11)
k4
k −4
1
≅ 0 = ([MeOH ∗ ][M] − K [G∗ ][E])
4
(11a)
Rate of diglycerides desorption:
r5 = k 5 [D][∗] − k −5 [D∗ ]
K5 =
(12)
k5
k −5
6
r5
k5
1
≅ 0 = ([D][∗] − K [D∗ ])
5
[D ∗] = K 5 [D][∗]
(12a)
Rate of monoglycerides desorption:
r6 = k 6 [M][∗] − k −6 [M ∗ ]
K6 =
r6
k6
(13)
k6
k −6
1
≅ 0 = ([M][∗] − K [M ∗ ])
6
[M ∗] = K 6 [M][∗]
(13a)
Rate of glycerol desorption:
r7 = k 7 [G][∗] − k −7 [G∗ ]
K7 =
r7
k7
(14)
k7
k −7
1
≅ 0 = ([G][∗] − K [G∗ ])
[G ∗] = K 7 [G][∗]
7
(14a)
7
Solving for [MeOH*] in equations (9a-14a)
1 [G∗ ][E]
[MeOH ∗ ] = K
1 K7 [G][E] [∗]
[M]
4
=K
[M]
4
1 [M∗ ][E]
[MeOH ∗ ] = K
1 K6 [M][E] [∗]
=K
[D]
3
1 [D∗ ][E]
[MeOH ∗ ] = K
Therefore,
(16)
[D]
3
1 K5 [D][E] [∗]
[T]
2
=K
[T]
2
(15)
1 K7 [G]
[MeOH ∗ ] = (K
4 [M]
(17)
1 K6 [M]
=K
3
[D]
1 K5 [D]
=K
2
[T]
) [E] [∗]
(18)
The equation that represents the overall mass balance on the surface sites is:
ST = [∗] + [MeOH ∗ ] + [D∗ ] + [M ∗ ] + [G∗ ]
(19)
where ST is the total binding sites on the surface.
Considering
[MeOH ∗ ] =
1 K5 [D][E] [∗]
K2
[T]
(20)
and substituting [MeOH*] into the site balance equation
1 K5 [D][E] [∗]
ST = ([∗] + (K
[*] =
2
[T]
) + K 5 [D][∗] + K 6 [M][∗] + K 7 [G][∗])
ST
1 K5 [D][E]
([1]+ (
K2
[T]
)+ K5 [D] +K6 [M] +K7 [G])
(21)
(22)
8
Rate of methanol adsorption from equation 8a
1
r1 = k1 ([MeOH][∗] − K [MeOH ∗ ])
1
Substituting in the value of [MeOH*] from equation 20
r1 = k1 ([MeOH][∗] −
r1 = k1 ([MeOH] −
1 K5 [D][E] [∗]
K1 K2
[T]
1
(
))
1 1 K 5 [D][E]
(
)) [∗]
K1 K 2
[T]
Substituting in the value of [*] from equation 22
k1 ST ([MeOH]−
r1 =
([1]+ (
1 K5 [D][E]
K2
[T]
1 1 K5 [D][E]
(
K 1 K2
[T]
))
)+ K5 [D] +K6 [M] +K7 [G])
(23)
Because the model assumes that methanol adsorption is the rate limiting step, neglecting the
presence of intermediates formed during the reaction and combining k1ST into k reduces the
model to the following final form shown in equation 24.
Rate of methanol consumption
r1 =
d[MeOH]
dt
k([MeOH])
7 [G])
= − ([1]+K
(24)
For the case of high FA content in soybean oil, an additional term for FFA adsorbed at the
resin surface only is added to the model in the following form.
9
Rate of FFA adsorption:
r8 = k 8 [FFA][∗] − k −8 [FFA∗ ]
K8 =
r8
k8
(25)
k8
k −8
1
≅ 0 = ([FFA][∗] − K [FFA∗ ])
8
[FFA ∗] = K 8 [FFA][∗]
(25a)
The site balance from equation (21) with this additional term becomes
1 K5 [D][E] [∗]
[T]
2
ST = ([∗] + (K
) + K 5 [D][∗] + K 6 [M][∗] + K 7 [G][∗] + K 8 [FFA][∗]) (26)
which represents the addition of one extra term to the derivation of the methanol adsorption:
r1 = −
kMeOH ST ([MeOH]−
([1]+ (
1 K5 [D][E]
K2
[T]
1
1 K5 [D][E]
(
Keq K2
[T]
))
)+ K5 [D] +K6 [M] +K7 [G]+K8 [FFA])
(27)
Therefore, equation 28 represents the final derived form of the ER model with FFA present
when k1ST is combined into k and all assumptions are considered:
r1 =
d[MeOH]
dt
=−
k([MeOH])
([1]+K7 [G]+K8 [FFA])
(28)
10
APPENDIX B
LHHW surface reaction model derivation
Based upon the assumptions provided, the following series of equations can be derived for the
LHHW surface reaction model solution. The stepwise reactions in LHHW model derivation
include:
k1
Step 1:
MeOH +∗ →← MeOH ∗
(1)
k–1
k2
Step 2:
T +∗
→
←
T∗
(2)
k–2
Step 3:
T ∗ + MeOH ∗
k3
→
←
E ∗ + D∗
(3)
E∗ + M∗
(4)
E ∗ + G∗
(5)
k–3
Step 4:
D∗ + MeOH ∗
k4
→
←
k–4
Step 5:
M ∗ + MeOH ∗
k5
→
←
k–5
k6
Step 6:
E +∗ →← E ∗
(6)
k–6
k7
Step 7:
D +∗ →← D∗
(7)
k–7
k8
Step 8:
M +∗ →← M ∗
(8)
k–8
11
k9
G +∗ →← G∗
Step 9:
(9)
k–9
where: MeOH = methanol; T = triglyceride; E = methyl ester; G = glycerol; * = resin surface
site; and MeOH*, T*, E*, D*, M*, and G* are bounded resin surface sites; kn=forward
reaction; k-n= backward reaction, n = reaction step
Note:
K
Adsorption =
and
kforward
kbackward
K
k
Desorption = backward
kforward
Therefore, the rate equations for the adsorption of methanol and the surface reaction of
adsorbed MeOH with T, D, M, and G can be written as follows:
Methanol adsorption as rate limiting step
r1 = k1 [MeOH][∗] − k −1 [MeOH ∗ ]
K1 =
(10)
k1
k −1
1
r1 = k1 ([MeOH][∗] − K [MeOH ∗ ])
(10a)
1
Because MeOH adsorption is the rate limiting step, k2 through k9 will be much larger than
r
r
r
r
r
r
r
r
k1. Therefore, k2 , k3 , k4 , k5 , k6 , k7 , k8 , and k9 in the following series of equations are assumed
2
3
4
5
6
7
8
9
to be very small (almost zero).
Rate of triglycerides adsorption:
12
r2 = k 2 [T][∗] − k −2 [T ∗ ]
K2 =
r2
k2
(11)
k2
k −2
1
≅ 0 = ([T][∗] − K [T ∗ ])
(11a)
2
Rate of surface reaction of bound triglyceride with bound methanol
r3 = k 3 [MeOH ∗ ][T ∗ ] − k −3 [D∗ ][E ∗ ]
K3 =
r3
k3
(12)
k3
k −3
1
≅ 0 = ([MeOH ∗ ][T ∗ ] − K [D∗ ][E ∗ ])
3
(12a)
Rate of diglycerides surface reaction
r4 = k 4 [MeOH ∗ ][D∗ ] − k −4 [M ∗ ][E ∗ ]
K4 =
r4
k4
(13)
k4
k −4
1
≅ 0 = ([MeOH ∗ ][D∗ ] − K [M ∗ ][E ∗ ])
4
(13a)
Rate of monoglyceride surface reaction
13
r5 = k 5 [MeOH ∗ ][M ∗ ] − k −5 [G∗ ][E ∗ ]
K5 =
r5
k5
(14)
k5
k −5
1
≅ 0 = ([MeOH ∗ ][M ∗ ] − K [G∗ ][E ∗ ])
5
(14a)
Rate of methyl ester desorption
r6 = k 6 [E][∗] − k −6 [E ∗ ]
K6 =
r6
k6
(15)
k6
k −6
1
≅ 0 = ([E][∗] − K [E ∗ ])
6
[E ∗] = K 6 [E][∗]
(15a)
Rate of diglycerides desorption
r7 = k 7 [D][∗] − k −7 [D∗ ]
K7 =
r7
k7
(16)
k7
k −7
1
≅ 0 = ([D][∗] − K [D∗ ])
7
14
[D ∗] = K 7 [D][∗]
(16a)
Rate of monoglycerides desorption
r8 = k 8 [M][∗] − k −8 [M ∗ ]
K8 =
r8
k8
(17)
k8
k −8
1
≅ 0 = ([M][∗] − K [M ∗ ])
8
[M ∗] = K 8 [M][∗]
(17a)
Rate of glycerol desorption
r9 = k 9 [G][∗] − k −9 [G∗ ]
K9 =
r9
k9
(18)
k9
k −9
1
≅ 0 = ([G][∗] − K [G∗ ])
9
[G ∗] = K 7 [G][∗]
(18a)
Solving for [MeOH*] in equations (11a-18a)
15
[MeOH ∗ ] =
K9 K6 [G][E][∗]
[MeOH ∗ ] =
K6 K8 [M][E][∗]
[MeOH ∗ ] =
K6 K7 [D][E][∗]
K5 K8 [M]
=
=
K4 K7 [D]
K3 K2 [T]
=
K9 K6 [G][E][∗]
(19)
K5 K8 [M]
K6 K8 [M][E][∗]
(20)
K4 K7 [D]
K6 K7 [D][E][∗]
(21)
K3 K2 [T]
K K [G]
Therefore [MeOH ∗ ] = (K 9K 6[M] =
5 8
K6 K8 [M]
K4 K7 [D]
=
K6 K7 [D]
) [E][∗]
K3 K2 [T]
The equation that represents the overall mass balance on the surface sites is:
ST = [∗] + [MeOH ∗ ] + [T ∗ ] + [E ∗ ] + [D∗ ] + [M ∗ ] + [G∗ ]
(22)
where ST is the total binding sites on the surface.
Considering [MeOH ∗ ] =
K6 K7 [D][E][∗]
(23)
K3 K2 [T]
and substituting [MeOH*] into the site balance equation
ST = (
[*] =
K6 K7 [D][E][∗]
K3 K2 [T]
[∗] + (
) + k 2 [T][∗] + k 6 [E][∗] + k 7 [D][∗]
+k 8 [M][∗] + k 9 [G][∗]
ST
K K [D][E]
([1]+ ( 6 7 [T]
K3 K2
)+ k2 [T]+ k6 [E]+k7 [D] +k8 [M] +k9 [G])
)
(24)
(25)
16
Rate of methanol adsorption from equation 10a is
1
r1 = k1 ([MeOH][∗] − K [MeOH ∗ ])
1
Substituting in the value of [MeOH ∗ ] from equation 23
r1 = k1 ([MeOH][∗] −
1
K1
1
(
r1 = k1 ([MeOH] − K (
1
K6 K7 [D][E][∗]
K3 K2 [T]
))
K6 K7 [D][E]
)) [∗]
K3 K2 [T]
Substituting in the value of [*] from equation 25
k1 ST ([MeOH]−
r1 =
1 K6 K7 [D][E]
(
))
K1 K3 K2 [T]
K K [D][E]
([1]+( 6 7 [T] )+ K2 [T]+ K6 [E]+K7 [D] +K8 [M] +K9 [G] )
(26)
K3 K2
Because the model assumes that methanol adsorption is the rate limiting step, neglecting the
presence of intermediates formed during the reaction and combining k1ST into k reduces the
model to the following final form shown in equation 27.
r1 =
d[MeOH]
dt
=−
k([MeOH])
([1]+K2 [T]+K6 [E]+K9 [G])
(27)
For the case of high FFA content in soybean oil, an additional term for FFA adsorbed at the
resin surface only is added to the model in the following form.
17
Rate of FFA adsorption:
r10 = k10 [FFA][∗] − k −10 [FFA∗ ]
k10
k −10
K10 =
r10
k10
(28)
1
≅ 0 = ([FFA][∗] − K [FFA∗ ])
10
[FFA ∗] = K10 [FFA][∗]
(28a)
The site balance from equation (24) with this additional term becomes
ST = (
K6 K7 [D][E][∗]
K3 K2 [T]
[∗] + (
) + K 2 [T][∗] + K 6 [E][∗] + K 7 [D][∗] + K 8 [M][∗]
+K 9 [G][∗] + K10 [FFA][∗]
)
(29)
Rearranging eq (29)
[*] =
ST
K K [D][E]
([1]+ ( 6 7 [T]
K3 K2
)+ K2 [T]+ K6 [E]+K7 [D] +K8 [M] +K9 [G]+K10 [FFA])
(30)
which represents the addition of one extra term to the derivation of the methanol adsorption:
18
r1 = −
k1 ST ([MeOH]−
1 K6 K7 [D][E]
(
))
Keq K3 K2 [T]
K K [D][E]
([1]+( 6 7 [T] )+ K2 [T]+ K6 [E]+k7 [D] +K8 [M] +K9 [G]+ K10 [FFA])
(31)
K3 K2
Therefore, equation 32 represents the final derived form of the LHHW model with FFA
present when k1ST is combined into k and all assumptions are considered:
r1 =
d[MeOH]
dt
=−
k([MeOH])
([1]+K2 [T]+K6 [E]+K9 [G]+K10 [FFA])
(32)
19