Supplemental Material: Axial Mixing and Mass
Transfer Performance of an Annular Pulsed Disc and
Doughnut Column
Jian-quan Liu, Shao-wei Li, Shan Jing
Contents
A. Supplemental Material on the Theory Models ............................................................. 2
A.1 Axial Dispersion Model ...................................................................................... 2
A.2 Plug Flow Model ................................................................................................ 3
B. Supplemental Material on the Chemicals ..................................................................... 4
B.1 Physical Properties .............................................................................................. 4
B.2 Equilibrium relationship of the system ............................................................... 5
C. Supplemental Material on the Conditions..................................................................... 6
D. Supplemental Material on the Operational Procedure .................................................. 7
D.1 Operational Procedure ........................................................................................ 7
D.2 Data Processing .................................................................................................. 8
A. Supplemental Material on the Theory Models
A.1 Axial Dispersion Model
The ADM was used to calculate thevalue of Ec and Noc in the present work. As shown in
Fig. A.1, only axial mixing of the continuous phase was considered in the ADM. The inlet of
the dispersed phase was set as location 0.
VdyF
VcxR
 Ec
h=0
dx
dh
Vcx
Vdy
h1
koc a  x  x 
dh
h1 + dh
Vd(y + dy)
Vc(x + dx)
Ec
d  x  dx 
dh
h=H
VdyR
VcxF
Figure A.1 Graphical presentation of the axial dispersion model (ADM)
Simultaneous AMD equations for the two phases at equilibrium are,[17]
 dx
1 d 2x


 dZ Pe dZ 2  N oc   x  x   0

c

 dy  N   x  x  Vc  0
oc
 dZ
Vd
(a.1)
with boundary conditions,
 dx
or x z 0  xR

z 0  0
Z = 0：  dZ
 y0  yF  0 or y0  yF
(a.2)
 dx
 Pec  xF  xZ 1 

 dZ z 1
Z = 1： 
 dy
or y z 1  yR
z 1  0

 dZ
(a.3)
After transforming the model (Eq. a.1) into an intermediate difference scheme, and the
boundary conditions (Eqs a.2 and a.3) into the forward or backward difference scheme, the
model could be described in the form of 2n + 2 equations with 2n + 2 unknown concentration
values. The concentration profiles could be obtained once the model parameters (Pec and Noc)
were provided. Conversely, once the concentration profiles were measured under stable
operation, these two parameters (Pec and Noc) could be determined based on a dual-parameter
optimization method.
A.2 Plug Flow Model
The PFM was applied to calculate the height of an “exterior apparent” mass transfer unit.
The axial mixing of phases was ignored in the PFM. The inlet of the dispersed phase was also
set as location 0. The equation and boundary conditions of the PFM are as follows,[17]
dx
 N oc , p   x  x   0
dZ
(a.4)
Z = 0, x  xR
(a.5)
Z = 1, x  xF
(a.6)
After integration, the number of “exterior apparent” mass transfer units (Noc,p) could be
calculated from Eq. a.7, if the inlet and outlet concentration, and the equilibrium relationship
were measured.
N oc , p  
xF
xR
dx
x  x*
(a.7)
B. Supplemental Material on the Chemicals
B.1 Physical Properties
Before and after the experiments, the nitric acid concentration of the two phases was
titrated with a pre-configured standard solution of NaOH, using the Metrohm 905 Titrando
automatic titrator (Swiss). Density of solutions was measured by a LEMIS Dendi densitometer
(USA). Viscosity was measured using a Brookfield LVDV-II+PRO viscometer (USA). The
interfacial tension between the two phases was determined with a Krüss K100 tensiometer
(Germany) using a standard Pt ring with circumference of 5.992 cm.
The physical properties before and after extraction are given in Table B.1. The organic
phase density increased from 819 kg/m3 to 835 kg/m3, and that of the aqueous phase decreased
from 1095 kg/m3 to 1063 kg/m3. The impact of nitrate concentration on the density of the two
phases is limited to within ± 3%. The viscosity of the organic phase increased from 0.00177
Pa·s to 0.00197 Pa·s, whereas that of the aqueous phase decreased from 0.00112 Pa·s to
0.00106 Pa·s.
Table B.1 Physical property changes before and after extraction
C (mol/L)
ρ (kg/m3)
μ (Pa·s)
Before
organic phase
0
819
0.00177
extraction
aqueous phase
3.0
1095
0.00112
After
organic phase
0.6
835
0.00197
extraction
aqueous phase
2.0
1063
0.00106
The physical properties before and after stripping are shown in Table B.2. Changes of the
two-phase density and viscosity after stripping are very small.
Table B.2 Physical property changes before and after stripping
C (mol/L)
ρ (kg/m3)
μ (Pa·s)
Before
organic phase
0.6
835
0.00197
stripping
aqueous phase
0.01
999
0.00101
After
organic phase
0
819
0.00177
stripping
aqueous phase
0.4
1012
0.00101
After measuring a series of samples, the interfacial tension of the system (9.6 mN/m),
which was measured at equilibrium, could be considered to be the same for the range of nitric
acid concentrations used.
Concentration of HNO3 in oil phase (mol/L)
B.2 Equilibrium relationship of the system
1.0
0.8
0.6
0.4
0.2
0.0
0
1
2
3
4
5
Concentration of HNO3 in aquous phase (mol/L)
Figure B.1 Equilibrium distribution curve of nitric acid in the system
The nitric acid equilibrium distribution between the two phases is shown in Fig. B.1, which
could be described as four sections of a linear relationship:
CO
 *
CO
 
CO
C*
 O
 0.00099 mol/L  0.06285C A , (0 mol/L  C A  0.15 mol/L)
= - 0.01935 mol/L  0.18731C A , (0.15 mol/L  C A  0.4 mol/L)
 0.03654 mol/L  0.24777C A , (0.4 mol/L  C A  2.1 mol/L)
= 0.16865 mol/L  0.156C A , (b.1)
(2.1 mol/L  C A  5 mol/L)
The nitric acid concentration in the aqueous phase ranged from 2.0 mol/L to 3.0 mol/L for
the extraction process, and from 0.01 mol/L to 0.4 mol/L for the stripping process. Different
sections of the equilibrium distribution curve were chosen for the calculation of these two
processes.
C. Supplemental Material on the Conditions
0.014
0.012
Vc+Vd (m/s)
0.010
Flooding 1
Flooding 2
0.008
0.006
0.004
Mixer-settler
regime
Dispersed
regime
Emulsion
regime
0.002
0.000
0.000
0.002
0.004
0.006
0.008
0.010
0.012
Af (m/s)
Figure C.1 Diagram of the stripping experiment points within operating window[21]
Since the aqueous phase was chosen to be the continuous fluid in the stripping process,
which wetted stainless steel internals, a relatively good mass transfer efficiency could be
obtained in both the dispersed and emulsion regimes. Two operating points, with the same total
flux rate (F = 0.0069 m/s), were chosen in the two operation window regimes obtained from
the hydraulic experiments,[21] to study the impact of pulsation intensity on axial mixing and
mass transfer performance (see Fig.C.1).
For the extraction process, internals could be wetted easily by the dispersed phase, there
were numbers of droplets coalesce on the internal in the dispersed regime, which lead to a
significantly reduction in mass transfer efficiency in the column. Therefore, mass transfer
experiments were carried out only in the emulsion regime for the extraction process, as shown
in Fig.C.2.
0.016
0.014
0.012
Vc+Vd (m/s)
0.010
Flooding 2
Flooding 1
0.008
Dispersed
regime
0.006
0.004
Mixer-settler
regime
Emulsion
regime
0.002
0.000
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020
Af (m/s)
Figure C.2 Diagram of the extraction experiment points within operating window[21]
D. Supplemental Material on the Operational Procedure
D.1 Operational Procedure
The sampling method was applied to measure the concentration profiles. Nine sampling
points were established over the active section of the APDDC. After steady state operation was
established in the APDDC, using the method described previously,[21] the aqueous outlet was
sampled every 10 min to determine the nitric acid concentration, and its variation with time was
studied. The experimental results show that the nitric acid concentration in the aqueous outlet
remained unchanged after 80 min, which implies that a steady concentration profile was
obtained in the APDDC. Then, slow and stable sampling was carried out using syringes at the
nine selected sampling points, to avoid the influence of sampling on the flow status in the
APDDC. The two phases were separated rapidly after sampling. These volumes were measured
to calculate the holdup, and the concentration were determined by titration to achieve
concentration profiles that corresponds to the corresponding sampling point location. The
average deviation of the concentration values was within 10% between two different parallel
experiments, and within 5% for the holdup.
D.2 Data Processing
3.2
2.8
2.4
aqueous phase (dispersed)
organic phase (continuous)
C (mol/L)
2.0
1.6
1.2
0.8
0.4
0.0
0
2
4
6
8
10
12
N
Figure D.1 Concentration profiles of the extraction process at a steady state
(F = 0.0069 m/s, Af = 0.011 m/s)
An example of the concentration profiles of the extraction process is given in Fig. D.1 (N
= 0 for the organic inlet and aqueous outlet, and N = 10 at the last sampling point). Mass transfer
mainly occurred in the lower part of the active section from sampling points 0 to 5, and an
equilibrium state was obtained in the upper part from sampling points 6 to 10, where little
change in concentration existed. Similarly, as shown in Fig. D.2, mass transfer of the stripping
process occurred mainly happened samplings point 0 and 6.
0.5
aqueous phase (continuous)
organic phase (dispersed)
0.4
C (mol/L)
0.3
0.2
0.1
0.0
0
2
4
6
8
10
12
N
Figure D.2 Concentration profiles of the stripping process at a steady state
(F = 0.0069 m/s, Af = 0.005 m/s)
Therefore, in the data processing, only the mass transfer in the lower part of the active
section was considered, the height of which was defined as Hmt. The average of the
concentrations of the two phases measured in the upper section was equal to the aqueous inlet
and the organic outlet.
The ADM discussed above was applied to correlate with the concentration profile data. Ec
and Noc were regressed from this model using the Matlab software with a dual-parameter
optimization method. The PFM was correlated with the inlet and outlet concentration, and the
equilibrium relationship to calculate the number of “exterior apparent” mass transfer units.