7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Numerical and Experimental Investigation of Flow and Interfacial Mass Transfer in
Multiphase Microreactors
Furkan Ozkan* Achim Wenka* Peter Pfeifer* Sonja Geiss
Klemens Flick t Bettina KraushaarCzarnetzkit
Institute for Micro Process Engineering, Karlsruhe Institute for Technology, Karlsruhe, D 76344, Germany
t Institute for Chemical Process Engineering, Karlsruhe Institute for Technology, Karlsruhe, D 76131, Germany
SInstitute for Applied Research, Heilbronn University, Heilbronn, D 74081, Germany
furkan.oezkan@kit.edu
Keywords: Microreactor, Interfacial Mass Transfer, Multiphase Flow
Abstract
Effects on the flow regime in microchannels have been investigated and a model for mass transfer from gas to
liquid has been developed. For fluid flow two cases have been studied. In the first case important parameters on the
flow regime in microchannels have been determined by help of FLUENT simulations, while in the second case a
comparative study with experimental observations has been done. In order to model mass transfer from gas to liquid,
a virtual case in a minichannel was considered for demonstration and compared with analytical results.
Introduction
Microreactors have potential for process inllniiii.il kii n
due to their ability for better mass and heat transfer
Kraut (2006). The interfacial area between phases can
be enhanced Haverkamp (2001) in microstructured sys
tems. Examples for efficient mass transfer between the
phases are demonstrated for microfalling film reactors
Jahnisch (2000), microfluidic channel networks Gun
ther (2004) and monolith reactors Kreutzer (2005). In
order to enhance reaction yield, however, there is the
need to identify influences of the hydrodynamics on the
system. So far, experimental studies often give only in
tegral data on overall mass transfer or conversion.
Fluid regimes in multiphase systems, particularly in
micro/mini scales, are sensitive even to small changes.
Physical properties such as surface tension, viscosities,
densities, static contact angles are determined by the flu
ids and materials, but there is also a need to consider ge
ometric aspects and volumetric gasliquid ratios. More
over, different flow phenomena can occur for reactions
in two phase channel flow (see Figure 1 Xua (1999)).
In the present study we describe flow in a microchan
nel for the multiphase system hydrogen and nitroben
zene. The application is the heterogeneously catalysed
multiphase hydrogenation to aniline which suffers from
heat removal and low interfacial mass transfer in con
ventional reactors types.
Important parameters such as surface tension, buoy
ancy, inertia of liquid flow (countercurrent regime) have
been studied numerically. Multiphase flow has been ob
served in a microreactor setup. For mass transfer from
gas to liquid a virtual case has been considered to com
pare numerical results with analytical results. Therefore,
the model for the mass transfer has been integrated into
FLUENT by a user defined function.
Experimental Investigations of Multiphase
Fluid Flow
Surface properties may strongly influence the contact
angle which is a boundary condition for the simulation.
In a previous study we showed by simulation that the
flow field in microchannels is strongly influenced by
variation of the contact angle for a range from 5 to 165
Ozkan (2008), Ozkan (2010). Thus it is necessary to
experimentally determine the contact angle of the fluid
system on the microreactor material. In our study, we
applied the system hydrogen/nitrobenzene and polished
carbon or stainless steel material.
The setup for the static sessile drop measurement is
shown in Figure 2. The relative measurement error is
3.5 %. The mean contact angle was 5.66 and 12.51
with a standard deviation of 0.5 and 1.71 for carbon
Figure 1: Typical Flow Regimes in Minichannels: a)
bubbly flow b) cap bubbly flow c) slug flow
d) slugchur flow e) churn turbulent flow
f) annular flow
Figure 2: Static sessile drop analysis setup
and stainless steel surface, respectively.
In our contact angle measurements we focused also
on the influence of pressure (details see Hecht 1,21 11,.
However, there is not yet an indication for a strong in
fluence of pressure since we operated the microreactor
at a temperature pressure combination under which the
liquid is still far from the boiling point. Under these
conditions we can refer to the observations of Bercic et
al. Bercic (1997) for measurement of the static contact
angle of the system waterairaluminium at various tem
peratures and pressures. They observed that the influ
ence of temperature is minor until the surface tempera
ture reaches the boiling temperature. Near boiling the
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
contact angle suddenly decreases with increasing tem
perature Bercic (1997).
In the experimental investigation of the flow phenom
ena in a vertically arranged microchannel the volumet
ric flow rates of hydrogen and nitrobenzene have been
varied. The temperature was 383 K and atmospheric
pressure was applied. The hydrogen flow rates were
2.5 ml/min and 5 ml/min at STP conditions. The mass
flow rates of nitrobenzene were 2.5 g/h, 5 g/h, 10 g/h,
20 g/h and 30 g/h. The applied microchannel is rectan
gular with dimensions of 1 mm x 0.4 mm. The channel
was mechanically fabricated and a carbon catalyst was
deposited on the channel walls. The details on catalyst
preparation will be published later. The channel is cov
ered by a glass sheet and the hydrogen is supplied from
the back of the channel via a 100 pm hole. Pressure
drop has been found to be negligible, i.e. is lower than
0.04 bar on both, the hydrogen and the nitrobenzene in
let. A system pressure variation will be conducted in the
future in order to allow higher hydrogen solubility and
thus higher conversions.
In Figure 3 and Figure 4 the flow field for the differ
ent hydrogen flow rates, i.e. 2.5 and 5 ml/min, is shown.
Each figure is a sequence of pictures of the single chan
nel for different nitrobenzene flow rates from 2.5 to 30
g/h. For all flow rates the gas bubble is located above
the gas inlet. Pulsation, i.e. slug formation, has been
observed at high liquid mass flows or/and high gas flow.
However, the flow mostly is of annular type. At the high
gas flow rate, i.e. 5 ml/min, there is a constriction of
the gas flow at the hydrogen inlet. We suppose that this
is an effect of liquid film formation at higher gas inlet
velocity. However, a contribution of the coating could
be possible. The coating started somewhat above the
hydrogen inlet hole. This space between inlet hole and
coating avoided the blocking of the hole during catalyst
preparation. Therefore a changing contact angle could
influence the flow field.
Numerical Investigation of Multiphase Fluid
Flow
Two Phase Flow
Simulation of the twophase system has been per
formed using ANSYS FLUENT@ based on Finite Vol
ume Method (FVM). According to the experiments
static contact angles of 5 and 12 were used as bound
ary condition in the simulation for carbon and stain
less steel surfaces, respectively. Buoyancy, surface ten
sion, hydrogen and nitrobenzene inlet direction have
also been varied numerically for a 1 mm x 0.4 mm rect
angular channel, i.e. in geometric accordance to the ex
periments. The inlet hole of hydrogen, however, was
different to the experiments. So far we used 40 pm hole
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
YX M_
Hydrqmh]
Figure 3: Pictures of the flow in a single microchannel;
hydrogen mass flow rate = 2.5 ml/min; ni
trobenzene mass flow rate 2.5 g/h, 5gr/h, 10
g/h, 20 g/h, 30 g/h from left to right side
X
ruft
Figure 4: Pictures of the flow in a single microchan
nel; hydrogen mass flow rate = 5 ml/min; ni
trobenzene mass flow rate 2.5 g/h, 5gr/h, 10
g/h, 20 g/h, 30 g/h from left to right side
diameter for the simulation, but the experiments have
been conducted with 100 pm inlet due to experimental
circumstances.
Figure 5: Computational Domain
Figure 5 shows the computational domain. It is repre
senting a part of the microreactor in the laboratory. The
hydrogen inlet is modelled as a cylinder. The length of
the hydrogen inlet cylinder is 0.1 mm. The dimension of
the computational domain is 2.92, 0.4, and 1 mm in the
z, y, and xdirection, respectively. So called YZ and
YX planes, two midplanes are shown in Figure 5.
Table 1 shows physical properties of nitrobenzene and
hydrogen at 393 K and 10 bar. These system parameters
have been chosen for simulation in order to investigate
pressure operation of the microreactor. System pressure
and temperature are treated as constant in the microre
actor. The maximum pressure drop in the computational
domain has been calculated to be very small with respect
to system pressure. Therefore, the gas has been consid
ered as incompressible in the calculation of FLUENT.
The basic concept of the VOF method is the defini
tion of a nondimensional scalar quantity f (or L), which
represents the fraction of the mesh cell volume occupied
by the continuous phase, which is in our case the liquid
phase. Thus, for f = 1 the mesh cell is entirely filled with
liquid, while for f = 0 it is entirely filled with gas. In a
mesh cell which has both phases the scalar is 0 < f < 1.
Based on f, it is possible to define a mixture density, p, ,
mixture viscosity, p,, and centreofmass velocity, v,,
from the individual gas and liquid properties with index
G (hydrogen) and L nitrobenzenee) respectively.
%ra"W
*IV
ErmH.
Table 1: System conditions and physical properties of
the fluids applied in the simulations
Variable Value Units
PL 1101.4 kg/m3
PG 0.618 kg/m3
tL 6.13. 104 kg/(ms)
PG 1.65 105 kg/(ms)
T 393.15 K
P 10.0 bar
ML 4.58 107 kg/s
AkG 3.22 109 kg/s
Pm =fPL + (1 f)PG
Pm = flL + (1 f)pG
fpLVL + (1 f)PGVG
Pm
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
This is the standard model in all commercial computa
tional fluid dynamic codes to consider surface tension
forces in combination with VOF methods. The surface
tension force in this code is written as
Pm KVf
f =aP (7)
1/2(pL + pc)
In this equation, a is the surface tension coefficient of
the nitrobenzene; p, is the mixture density, PL and pG
represent nitrobenzene and hydrogen phase densities, re
spectively. K is the surface curvature, which is important
for our computations since the contact angle has an in
fluence on the surface curvature. In the CSF model, a
surface curvature due to surface tension force is com
puted from local gradients in the surface normal at the
interface:
KV.
where n is the surface normal in this equation. It can
be normalized by help of the vector length
n
, (9)
Using the above definitions, the equations governing
the motion of the nitrobenzene and the hydrogen phase
as well as the dynamic boundary condition at the inter
face can be combined into one single set of continuity
and momentum equations that are valid in the entire two
fluid domain. In our case the fluids are treated as Newto
nian fluids with constant physical properties so that the
following equations are valid:
+ fVmy 0 (4)
at
V vm 0 (5)
S(pmvm) + V pmVmm = (6)
Vp + V Pm (VVm + (VVm)T) + pmg + f,
Here, g (0,0, g)T is the gravity vector,
g 9.81m/s2 is the gravitational acceleration and
f, standing for attractive forces between nitrobenzene
molecules, represents the surface tension force per unit
volume. For the determination of the surface tension
force, we applied the continuum surface force (CSF)
model developed by Brackbill et al. Brackbill (1992).
With this normalization, the wall adhesion angle or
so called apparent contact angle, O0, between fluid and
wall can be introduced with the following formula:
ii = nw cos 0, + tw sin 0,
where in and tw are the unit vectors normal and tan
gential to the wall, respectively. In the absence of other
forces (such as no flow), 0, will be identical to the static
contact angle.
Influence of surface tension, buoyancy, inlet angle and
flow direction have been calculated for 10 milliseconds
after start of hydrogen supply (see Figure 6) with a static
contact angle (SCA) of 15. Values of the average ve
locity at the inlets are 5 m/s and 0.001 m/s for hy
drogen and nitrobenzene, respectively. Influence of sur
face tension is very important, as shown in Figure 6A.
The interface lines are different for the "normal" case,
i.e. with surface tension, in comparison to calculated
interface lines with zero surface tension. This is coher
ent with the relevant dimensionless numbers. Relevant
numbers are: Capillary number
Ca PLUB 4.104
Weber number
pLLUB
We =
a
0.012
i I
Depth of the channel (mm) Depthofthechannel(mm)
Since both numbers are smaller than 1, surface tension
can not be neglected. The buoyancy effect is shown
in Figure 6B. The black line shows the "normal" case
(gravity against flow direction, i.e. downward) while the
red line shows the case in which buoyancy is not consid
ered in the computational domain. As can be seen from
the Figure the influence of the buoyancy is considerably
high. A pushing effect to the bubble by the liquid flow is
recognizable due to a slightly higher vertical position of
the bubble. To understand whether there is an influence
of the inlet direction of hydrogen into the microreactorh
I I ""i"
calculated with the diameter of the hydrogen inlet and
the hydraulic diameter of the channel are 10.6 (ReH)
and 1.02 (ReNB) at the inlets of hydrogen and nitroben
zene, respectively.
Higher SCA results in smaller film thickness as it is
shown in Figure 7 from the YZ midplane. An analysis
of the gas velocities in vertical direction shows negligi
ble influences of the SCA in the range < 15 (results not
shown).
Bubble formation in flow devices at constant physical
properties has been reported to be influenced by the ratio
between the volumetric gas flow rate (QG) and the vol
umetric liquid flow rate (QL) Yu (2007); Shao (2008);
Chen (2009). In our computations, the ratio (QG) :
(QL) = 176 represents stoichiometric conditions for the
desired hydrogenation reaction. Larger ratios than those
do not lead to bubbly flow. Chur or wavy flows are
usually reported Yu (2007). This is in accordance with
both, our experimental and numerical investigations. In
our cases of (QG) : (QL) > 1.76 the two wider channel
I
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
on the flow field, two different inlet angles (between hy
drogen and nitrobenzene flow direction) have been sim
ulated. A 45 angle and a 90 angle are compared in Fig
ure 6C. The Figure shows that the inlet angle does not
play a ignilik.ii role for our computations. This might
be different for other velocity ratios between hydrogen
and nitrobenzene. The Figure 6D shows the compari
son of co and countercurrent flow of hydrogen and ni
trobenzene. The red line represents the bubble shape in
countercurrent flow whereas the black line represents
cocurrent flow. The extent of influence of the flow di
rection is similar to the influence of buoyancy. In some
of the above simulations very small liquid drops in gas
phase have been observed. It is assumed that the reason
is numerical diffusion, i.e. a shortcoming of the applied
time step size in the gas entry region. The velocity is
rather high in that region.
Simulations with static contact angles less than 15 as
well as with different gasliquid volume ratios are dis
cussed in the following paragraphs. Three cases of con
tact angle computations were performed: 5, 12 and
15. Gas (hydrogen) and liquid nitrobenzenee) mass
flow rates were varied between (over)stoichiometric hy
drogen conditions (high gasliquid ratio > 176) for the
reaction as well as for increased shear rates (low gas
liquid ratio z 0.1), i.e. understoichiometric hydrogen
supply. For the latter it was assumed that the conditions
will lead to a higher interfacial area. Results are com
pared 100 ms after starting the hydrogen supply.
In simulations using stoichiometric conditions, the
Reynolds numbers
1,4
E
E
0)
_r_
0
0,00 0,01 0,02 0,03 0,04
Channel Width (mm)
Figure 7: Influence of Contact angle on liquid film at
YZ midplane
walls (1 mm width) are not "active" for surface reaction,
since they are not wetted (compare for example Figure 5
for gaswall contact on the YX midplane). Contact line
formation (between gas and wall) has been theoretically
investigated by Wong et al. Wong (1995). They wanted
to find out the pressurevelocity relation of bubble flow
in polygonal capillaries for low values of the Capillary
number (Ca0). It is reported there, that drag force
dominates and liquid flows through the comers of the
channel. Wong et al. call this behaviour a bubble
"leaky piston". Liquid flow can not push the bubble
and, instead, liquid flows surrounding the bubbles in the
corners. However, such behaviour would not be desired
for the chemical reaction, since a thin film between
gas phase and wall is necessary to provide higher mass
transfer and consequently a higher overall reaction rate
on the wetted catalyst surfaces. Optimum gasliquid
ratio has been found in our simulations for 0.176 <
QG QL < 1.76 where bubbly flow is established. This
would, however, yield understoichiometric hydrogen
conditions for the reaction inside the microreactor.
Liquid flow has to pass the reactor several times in order
to complete the reaction.
Developing An Interfacial Mass Transfer Model
Three interfacial mass transfer models are known:
film theory, penetration model (Higbie model), and sur
J
t
film theory, penetration model (Higbie model), and sur
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Table 2: Physical properties of gas and liquid in compu
tational domain for interfacial mass transfer
Variable Value Units
PL 998.2 kg/m3
PG 1.416 kg/m3
PL 1.0. 103 kg/(ms)
UPG 1.919105 kg/(ms)
T 273.15 K
P 1.0 bar
face renewal model. The first two models are convenient
for laminar flows and the latter is valid more especially
for turbulent flows.
For the first model the determination of the mass
transfer coefficient is the key issue. In order to determine
the mass transfer coefficient three different approaches
are eligible. A mass transfer coefficient could be cal
culated from the Sherwood number depending on lo
cal physical and geometrical parameters Kiick (2009).
Experimental correlations are needed therefore Bercic
(1997). A mass transfer coefficient based on the penetra
tion model can also be adapted with knowledge of phys
ical and geometrical parameters Kreutzer (2005). The
better way, however, is based on a rigorous numerical
approach with a mass transfer coefficient depending on
the numerical concentration gradients Onea (2009).
In the following paragraphs, we have considered the
film theory approach with mass transfer coefficients
from numerical concentration gradients to perform in
terfacial mass transfer simulations and to compare them
with a virtual problem for which, in certain cases, an an
alytical solution exists. We have also integrated a user
defined function into FLUENT in order to provide a so
lution for the gas bubble shrinkage in the VOF method
due to mass transfer.
For comparison with the analytical solution a mass
transfer problem from the book of Diffusion from Cus
sler Cussler (1997) has been chosen. Physical properties
of oxygen and water as well as system conditions have
been applied according to Table 2. The mass transfer for
the analytical solution and the transfer in the interface
cell have been written as:
d(m )
d(m) kAAC kA(Csat Cliq) (11)
d(t)
The analytical solution is possible, when Ci, = 0 is
assumed. Then the mass transfer coefficient gets
k 1.6 x 10 5m/s
Figure 8 shows the computational domain for the nu
merical case. The maximum saturation concentration
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
of 4.8 102 kg/m3 in the liquid phase has been imple
mented into FLUENT. The interfacial area has been cal
culated in the user defined function using Equation 12.
The mass transfer source term (Equation 11) has been
added into the calculation of the void fraction by help of
a user defined function. The mass term is negative for
the gas phase and positive for the liquid phase. Distribu
tion of the species in the liquid phase has been provided
by the standard species transport equation (Equation 13).
A = Vf.dV
(PmY) + V *pmVmYi
(12) Figure 9: Concentration distribution
water phase
of oxygen in the
Comparision of Bubble Volume
Time(second)
O
Figure 10: Comparison of Bubble Volumes
N,
Figure 8: Computational Domain of Interfacial Mass
Transfer
The results from the simulation are shown in Figure
9 and 10. The colour in Figure 9 represents the concen
tration of gas in the liquid phase. Cells filled with pure
gas have the same colour than the liquid phase with zero
gas concentration since a volumetric mass transport was
only applied for f 7 0. The cells along the left and right
side of the bubble exhibit higher mass transfer. This is
an effect of lower fvalues. However, this issue should
be investigated more detail, especially by help of a finer
grid.
In Figure 10, i.e. a plot of the bubble volume against
time, we have numerically solved three different cases
by assuming different concentrations in the liquid phase
along with the analytical approach. The cases are
Case 1: C0q=0
Case 2: Cltq=Cave (average gas concentration in
the liquid phase), and
Case 3: Cqi=Ci,nt (gas concentration in the inter
face cell)
The blue line in Figure 10 represents the analytical
solution while the pink line corresponds to the numeri
cal result of Case 1. These two lines are almost parallel
but the mesh size may influence the preciseness of the
numerical results compared to the analytical solution.
The yellow line shows that mass transfer is slower for
case 2 compared to case 1. This has been expected as the
driving concentration gradient is smaller. One problem
with case 2 (and case 3) exists: The applied k value is
from the analytical solution. The real k value, however,
should be smaller than the applied k value.
Case 3 shows the consequence when the concentra
tion of gas in the interface cell is considered. The mass
transfer drops dramatically. We expect that this case is
nearest to the real mass transfer. However, this assump
tion has to be proven by experimental validation.
Conclusions
Parameters on flow regime in micro/mini channels are
microreactor design, surface tension, specific gas to liq
uid flow ratio and static contact angle. Since experi
mental results give limited data, computational fluid dy
namic methods can be used to predict the flow regime
and the interfacial mass transfer in mini/micro reactors.
Nowadays standard CFD codes are able to dynamically
describe the interface in immiscible flows in minichan
nels by consideration of surface tension force and wall
adhesion Ozkan (2007); Oztaskin (2009). In order to
correctly model a physical motion of the contact line be
tween three phases (here gasliquidsolid) depending on
the wall boundary conditions, additional user effort may
be needed to implement the required boundary condi
tion into codes; e.g. for slip length and dynamic contact
angle there is not yet an universal model available Re
nardy (2001); Rosengarten et.al (2006). For the imple
mentation we assume that user defined functions can be
a useful tool. For example, the user defined functions for
interfacial mass transfer, which have been applied in our
study, show good potential for a detailed description of
multiphase reactions.
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