Supplementary information
High performance catalytic distillation using CNTs-based
holistic catalyst for production of high quality biodiesel
Dongdong Zhang†1, Dali Wei†1, Qi Li, Xin Ge1, Xuefeng Guo1, Zaiku Xie2 and Weiping Ding*1
1
Key Lab of Mesoscopic Chemistry, the School of Chemistry and Chemical Engineering, Nanjing
University, Nanjing 210093, China
2
Shanghai Research Institute of Petrochemical Technology, Shanghai 201208, China
† The
authors are equal contributors to this investigation. * Correspondence author, Email:
Dingwp@nju.edu.cn
Mathematical model and calculation
A mathematical model is developed to describe the current catalytic distillation column for the
biodiesel production. This model is valid under the following assumptions:
a) Due to very small diameter of the catalytic distillation column, only the concentration gradient
along axial direction is considered.
b) The in situ conversion of glycerol to other chemicals is included for calculation with only
forward reactions and the reverse reactions are neglected.
c) Because the boiling point of FAME is much higher than reaction temperature, the FAME
flows to the column bottom mainly. According to Fig. 4a, it implies that the FAME
concentration in the gas phase is independent with the position of the column. Thus, in
calculation, the concentration of FAME in the gas phase is considered as a constant.
d) The temperature of the column is considered homogeneous and keeps at constant.
e) Unequal mole flow of liquid phase and equal mole flow of gas phase are adopted.
The reaction and production increasing is given by
dFD  dRD
(6-1)
Where dFD and dRD are the production and reaction increment in the unit, and
1
dRD   rD*  Sdl '
(6-2)
Where γ is enhancement factor of mass transfer by convection, γD* is the intrinsic reaction rate
(kmol·s-1·kg-1), ρ is bulk density of the catalysts (kg·m-3), S is sectional area of the catalytic
distillation column (m2), column bottom is defined as 0 mm and column top is 200mm. Because
the concentration of FAME decreases with the column height increasing, l´is the difference of 200
and l.
Combine 6-1 and 6-2:
dFD   rD*  Sdl
(6-3)
FD is expressed by mole fraction:
dFD  FD 0 (1   R)dxD
(6-4)
Because the rate of FAME producing by transesterification reaction is three times than that of
triglyceride, it is considered that FD0 = βFB0，where β is adopted 1~3 and R is reflux ratio, ε is a
parameter relating to reflux ratio.
 FB 0 (1   R)
S
dxD   rD dl
(6-5)
According to assumption b, γD can be expressed as:
rD  kC 3A CB
(6-6)
Because methanol and bio oil have a given feed rate, then, CB=αCA, C A  C A0  CD , CD=CD0xD,
CD 0   CB 0 ， C 3A CB   (CA0   CB 0 xD )4 ，where relates to residence time of gas and liquid
phase in the catalytic distillation column.

FB B
FA A
Combine 6-5 and 6-6:
 FB 0 (1   R)
S
dxD
  k dl
(C A0   CB 0 xD ) 4
(6-7)
Integrate 6-7 by boundary condition，xD=0，L=0.2；xD= xD，L=l:
 FB 0 (1   R)
  k l  2.82 104
3 SC A4 0 (1   xD )3
Replace the parameter of temperature into 6-8
2
(6-8)
1.29(1   R)
 7.52 l  2.82
(1   xD )3
(6-9)
Transform form：
xD  4.2  4.57  (2.82  7.66l )

1
3
( 0  l  0.2 )
(6-10)
Calculate by mass fraction，
mD 
xD * M D
xD M D  xB' M B'
(6-11)
Fig. S1. Reaction-transfer unit in the catalytic distillation column used for calculation. (A:
Composition of liquid phase (wt.%)
methanol; B: Triglyceride; C: Glycerol; D: FAME.)
100
Theoretical
Experimental
80
60
40
20
0
0
50
100
150
200
Height of the catalytic column (mm)
Fig. S2. Theoretical and experimental compositions of liquid phase at different heights of the
catalytic column.
3