The mass transfer coefficient for the bed was determined using the following correlation (Seader and Henley, 1998) for flow through a bed of spheres and utilising the equivalent spherical diameter to account for the needle shaped particles:
13
6 . 0
1 Re
. 1
2 Sc
A e g
Sh N N
D D N k
where:
G
NRe De (Reynolds Number)
A
Sc D
N
(Schmidt Number)
kg is the gas phase mass transfer coefficient [m/s]
De is the equivalent spherical diameter [m]
DA is the Diffusivity of component A (water) [m2/s]
G is the superficial gas mass velocity [kg/(m2s)]
µ is the viscosity of the gas phase [Pa.s]
ρ is the density of the gas phase [kg/m3]
The equivalent spherical diameter is determined as:
p
e D
D
In this equation φ is the sphericity of the particle which is defined as the ratio of the surface area of a sphere of the same volume as the particle to the surface area of the particle. Dp is the diameter of the particle.
In order to solve this equation for the mass transfer coefficient, the diffusivity, DAB, in the gas phase can be determined from the empirical equation developed by Fuller et al (1966):
13 13 212
75 .
00143 1
. 0
AB
v A
v BBA AB
PM D T
D
where: DAB is in cm2/s P is in atm T is in K
B A
AB
M M
M 1 1
2
Mi is the molar mass of component i
And
v is the summation of atomic and structural diffusion volumes from tablesIf one inputs the values for the HCl water system at 1 atm and a temperature of 160ºC, the equation for DAB becomes:
s m D
D
B A
BA
AB 6.97 10 /
48 . 21 44
. 9 461 . 136 02 . 118 ) 2 1 (
) 15 . 273 160 ( 00143 .
0 5 2
2 13 13
12
75 .
1
The sphericity of the particles was determined to be 0.35 for the particles:
0.35
614106
2.15104e D
The Reynolds and Schmidt numbers could be evaluated:
1.4610 100.011
0.1682 . 1
5 4
Re
N
0.511.
46
6.971010 5
0.415
NSc
Using all these values to input into the Sherwood number correlation resulted in a Sherwood number of 2.27.
Solving the Sherwood number equation for kgW resulted in:
m sD D k N
e A
gW Sh 0.74 /
10 82 . 1
10 97 . 6 25 . 2
4
5
APPENDIX J: MODEL RESULTS – PROFILES FOR EACH RUN
0 5
0 1 2 3
time, hours
Pentosan (B), kmol/m3
Run # 2
0 5
0 0.5 1 1.5
time, hours
B-HCl complex, kmol/m3
0 5
0 0.01 0.02 0.03
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 2 4 6 8x 10-5
time, hours
Furfural, kmol/m3
0 5
0 2 4 6x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.028 0.0285 0.029 0.0295
time, hours
Water, kmol/m3
0 5
0 2 4 6 8x 10-4
time, hours
HCl, kmol/m3
0 5
0.5 1 1.5 2 2.5 3
time, hours
Pentosan (B), kmol/m3
Run # 3
0 5
0 0.2 0.4 0.6 0.8
time, hours
B-HCl complex, kmol/m3
0 5
0 0.005 0.01 0.015
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 1 2 3 4x 10-5
time, hours
Furfural, kmol/m3
0 5
0 1 2 3x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0276 0.0277 0.0278 0.0279
time, hours
Water, kmol/m3
0 5
0 1
x 10-4
time, hours
HCl, kmol/m3
0 5 1
1.5 2 2.5 3
time, hours
Pentosan (B), kmol/m3
Run # 4
0 5
0 0.1 0.2 0.3 0.4
time, hours
B-HCl complex, kmol/m3
0 5
0 2 4 6 8x 10-3
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 0.5 1 1.5 2 2.5x 10-5
time, hours
Furfural, kmol/m3
0 5
0 0.5 1 1.5x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.028 0.028 0.028 0.028 0.028 0.0281
time, hours
Water, kmol/m3
0 5
0 2 4 6 8x 10-5
time, hours
HCl, kmol/m3
0 5
0 1 2 3
time, hours
Pentosan (B), kmol/m3
Run # 5
0 5
0 0.5 1 1.5
time, hours
B-HCl complex, kmol/m3
0 5
0 0.01 0.02 0.03
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 2 4 6 8x 10-5
time, hours
Furfural, kmol/m3
0 5
0 2 4 6x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0268 0.027 0.0272 0.0274 0.0276
time, hours
Water, kmol/m3
0 5
0 2 4 6 8x 10-4
time, hours
HCl, kmol/m3
0 5 0.5
1 1.5 2 2.5 3
time, hours
Pentosan (B), kmol/m3
Run # 6
0 5
0 0.2 0.4 0.6 0.8
time, hours
B-HCl complex, kmol/m3
0 5
0 0.005 0.01 0.015
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 1 2 3 4x 10-5
time, hours
Furfural, kmol/m3
0 5
0 1 2 3x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0281 0.0282 0.0283 0.0284
time, hours
Water, kmol/m3
0 5
0 1
x 10-4
time, hours
HCl, kmol/m3
0 5
0.5 1 1.5 2 2.5 3
time, hours
Pentosan (B), kmol/m3
Run # 7
0 5
0 0.2 0.4 0.6 0.8
time, hours
B-HCl complex, kmol/m3
0 5
0 0.005 0.01 0.015
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 1 2 3 4x 10-5
time, hours
Furfural, kmol/m3
0 5
0 1 2 3x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0288 0.0289 0.029 0.0291 0.0292
time, hours
Water, kmol/m3
0 5
0 1
x 10-4
time, hours
HCl, kmol/m3
0 5 0
1 2 3
time, hours
Pentosan (B), kmol/m3
Run # 8
0 5
0 0.2 0.4 0.6 0.8 1
time, hours
B-HCl complex, kmol/m3
0 5
0 0.005 0.01 0.015 0.02
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 2 4 6 8x 10-5
time, hours
Furfural, kmol/m3
0 5
0 1 2 3 4 5x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0284 0.0286 0.0288 0.029
time, hours
Water, kmol/m3
0 5
0 1 2 3 4x 10-4
time, hours
HCl, kmol/m3
0 5
1 1.5 2 2.5 3
time, hours
Pentosan (B), kmol/m3
Run # 9
0 5
0 0.1 0.2 0.3 0.4
time, hours
B-HCl complex, kmol/m3
0 5
0 2 4 6 8x 10-3
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 0.5 1 1.5 2 2.5x 10-5
time, hours
Furfural, kmol/m3
0 5
0 0.5 1 1.5
2x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0293 0.0293 0.0294 0.0294 0.0295
time, hours
Water, kmol/m3
0 5
0 0.2 0.4 0.6 0.8
1x 10-4
time, hours
HCl, kmol/m3
0 5 0
1 2 3
time, hours
Pentosan (B), kmol/m3
Run # 10
0 5
0 0.5 1 1.5
time, hours
B-HCl complex, kmol/m3
0 5
0 0.01 0.02 0.03
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 2 4 6 8x 10-5
time, hours
Furfural, kmol/m3
0 5
0 2 4 6x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.028 0.0285 0.029 0.0295
time, hours
Water, kmol/m3
0 5
0 2 4 6 8x 10-4
time, hours
HCl, kmol/m3
0 5
0 1 2 3
time, hours
Pentosan (B), kmol/m3
Run # 11
0 5
0 0.2 0.4 0.6 0.8 1
time, hours
B-HCl complex, kmol/m3
0 5
0 0.005 0.01 0.015 0.02
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 2 4 6 8x 10-5
time, hours
Furfural, kmol/m3
0 5
0 1 2 3 4 5x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0275 0.0276 0.0277 0.0278 0.0279 0.028
time, hours
Water, kmol/m3
0 5
0 1 2 3 4x 10-4
time, hours
HCl, kmol/m3
0 5 0
1 2 3
time, hours
Pentosan (B), kmol/m3
Run # 12
0 5
0 0.5 1 1.5
time, hours
B-HCl complex, kmol/m3
0 5
0 0.01 0.02 0.03
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 0.2 0.4 0.6 0.8
1x 10-4
time, hours
Furfural, kmol/m3
0 5
0 2 4 6 8x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0278 0.028 0.0282 0.0284 0.0286
time, hours
Water, kmol/m3
0 5
0 2 4 6 8x 10-4
time, hours
HCl, kmol/m3
0 5
0.5 1 1.5 2 2.5 3
time, hours
Pentosan (B), kmol/m3
Run # 13
0 5
0 0.2 0.4 0.6 0.8
time, hours
B-HCl complex, kmol/m3
0 5
0 0.005 0.01 0.015
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 1 2 3 4 5x 10-5
time, hours
Furfural, kmol/m3
0 5
0 1 2 3 4x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0283 0.0284 0.0285 0.0286
time, hours
Water, kmol/m3
0 5
0 1
x 10-4
time, hours
HCl, kmol/m3
0 5 0
1 2 3
time, hours
Pentosan (B), kmol/m3
Run # 14
0 5
0 0.2 0.4 0.6 0.8 1
time, hours
B-HCl complex, kmol/m3
0 5
0 0.005 0.01 0.015 0.02
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 2 4 6 8x 10-5
time, hours
Furfural, kmol/m3
0 5
0 1 2 3 4 5x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0282 0.0284 0.0286 0.0288
time, hours
Water, kmol/m3
0 5
0 1 2 3 4x 10-4
time, hours
HCl, kmol/m3
0 5
1 1.5 2 2.5 3
time, hours
Pentosan (B), kmol/m3
Run # 15
0 5
0 0.1 0.2 0.3 0.4
time, hours
B-HCl complex, kmol/m3
0 5
0 2 4 6 8x 10-3
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 0.5 1 1.5 2 2.5x 10-5
time, hours
Furfural, kmol/m3
0 5
0 0.5 1 1.5
2x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0285 0.0285 0.0286 0.0286 0.0287
time, hours
Water, kmol/m3
0 5
0 2 4 6 8x 10-5
time, hours
HCl, kmol/m3
0 5 1
1.5 2 2.5 3
time, hours
Pentosan (B), kmol/m3
Run # 16
0 5
0 0.1 0.2 0.3 0.4
time, hours
B-HCl complex, kmol/m3
0 5
0 2 4 6 8x 10-3
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 1 2 3x 10-5
time, hours
Furfural, kmol/m3
0 5
0 0.5 1 1.5 2 2.5x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0285 0.0285 0.0286 0.0286 0.0287
time, hours
Water, kmol/m3
0 5
0 0.2 0.4 0.6 0.8
1x 10-4
time, hours
HCl, kmol/m3
0 5
0 1 2 3
time, hours
Pentosan (B), kmol/m3
Run # 17
0 5
0 0.2 0.4 0.6 0.8 1
time, hours
B-HCl complex, kmol/m3
0 5
0 0.005 0.01 0.015 0.02
time, hours
P-HCl complex, kmol/m3
0 5
0 20 40 60 80 100
time, hours
Pentosan (B) conversion, %
0 5
0 2 4 6 8x 10-5
time, hours
Furfural, kmol/m3
0 5
0 2 4 6x 10-5
time, hours
Acetic acid, kmol/m3
0 5
0.0282 0.0284 0.0286 0.0288
time, hours
Water, kmol/m3
0 5
0 1 2 3 4x 10-4
time, hours
HCl, kmol/m3