(600bh) A Comparative Study On Bubble Velocity in Mini Channels

A comparative study on bubble velocity in mini channels

Ch. Meitzner*, E. Reichelt*, M.H. Al-Dahhan°, R. Lange*

* Technische Universität
Dresden, Germany

°
Missouri University of Science & Technology, Rolla, MO, USA

Keywords: gas-liquid-solid
reactions, monolith, hydrodynamics, bubble velocity, mini channels

Introduction

A current trend in chemical reaction
engineering are catalytic reactions in mini channels. This is based on the
successful implementation of monolithic catalysts in the automotive industry as
catalytic converters since the mid-1970's. The application of this structured
catalysts in gas-liquid-solid-reactions is discussed in literature [1]. But this
implies a deep understanding of the hydrodynamics in the channels for a better
prediction of mass transfer and reaction kinetics. Additionally, scale up for
large throughputs would be easier when the hydrodynamic processes are clearly
understood.

Taylor Flow, an alternating liquid and gas
slug flow, is the mostly preferred flow regime in mini channels. It provides a high
mass transfer and a quasi periodic process. For this reason many correlations
exist to predict the particular parameters of the flow like bubble length,
bubble velocity or film thickness. In the following study present correlations
were tested and evaluated by means of two experimental studies. Thereby, two
liquids with highly differing properties were used to test the validity of the
models over a wide range. Additionally, the influence of the channel material
(fluid - wall contact angle) was tested.

Experimental work

In this work a first study was based on a
single channel experiment. A high viscous medium, squalane (0.029 Pa∙s), was used as liquid phase and
nitrogen as gas phase. Liquid and gas superficial velocities were varied
between 0.02 - 0.3 m/s respectively 0.04 - 0.5 m/s at an absolute pressure of 1
bar and a temperature of 293 K. The experiments were conducted in downstream. Due
to the transparency of the used acrylic glass channel, a high speed camera HCC
1000 combined with a computational evaluation of the images was used to
determine bubble velocity. The channel had a square cross section with a
hydraulic diameter of 1 mm.

A second series of downflow experiments was
executed in a ceramic monolith. Here the channels had a square cross section
and a hydraulic diameter of about 1 mm, too. The liquid phase consisted of deionized
water and pressurized air was used as the gas phase. Since the monolith is made
of an opaque material, optical measurements were not applicable in this case.
Consequently, a novel technique with a single tip optical fiber probe was applied
here. Bubble velocity was measured at various gas and liquid flow rates (u_G:
0.009 m/s - 1.1 m/s; u_L: 0.05 m/s - 0.3 m/s), whereas a uniform
phase distribution all over the entrance cross section of the monolith was
assumed.

Theoretical model

In open literature various theoretical
models were presented to predict bubble velocity on the basis of geometric and
fluidic parameters. Four models were considered in this work and had been compared
with the experimental results.

The drift flux model provided by Zuber and
Findlay [2] was considered first (eq. 1). It is based on the two phase velocity
u_TP (composed of liquid and gas superficial velocity). The two
constants, distribution coefficient C₀ and drift velocity u_∞, were
determined at various experimental conditions. But usually, investigations were
based on fluids with properties close to water and not on highly viscous
mediums.

                                                                                                                                                                (1)

The second model was proposed by Thulasidas
et al. [3]. The model is based on bubble shape and u_TP (eq. 2). It
includes the liquid film between bubble and channel wall. Thulasidas et al. [3]
investigated different fluids and demonstrated the validity also for a wide
range of viscosities (0.001 - 0.971 Pa∙s).

                                                                                                                                                    (2)

Abiev [4] presented a model in 2008 which
is rarely confirmed by other experiments to this time. In this work a model is
demonstrated based on mathematical derivations (eq. 3). The model contains empirical
constants, which vary for different flow directions. This was the first time
flow direction was included in considerations.

                                                                     (3)

For the present current calculation b = -
0.065, c = 0.4776, g = - 0.192 were used with respect to the work of Abiev [4].

The last model which was included in the current
study was published by Liu [5]. It is based on u_TP and the Capillary
Number Ca (eq. 4).

                                        with                                                                                                   (4)

This model, derived from upflow
experiments, was proposed to be valid for low Ca between 0.0002 - 0.39.

Results

Initially, the two experimental series were
compared with the model of Thulasidas et al. [3]. In Figure 1 the match
between the experimental data of the current work and the data of Thulasidas et
al. is illustrated. A medium agreement but a similar trend was observed with
respect to the general trend of the bubble velocity against Ca and fluid
viscosity.

Figure 1: Comparison of the model of Thulasidas (water:
□, silicone oil: ○)
with bubble velocity in monolithic channels (♦) and single channel experiments with squalane (▲)

However, the measured relations in our data
show a higher scatter, which could be based on the respective measurement
techniques and on the different hydraulic diameter of 1 mm instead of 2 mm in
Thulasidas et al. Furthermore, the curve of Thulasidas et al. should be shifted
to a lower u_B/u_TP - relationship to fit better with the
experimental results of the current work.

The experimental series based on
air-water-system showed various conformances of the other described theoretical
models with the experimental data. In Figure 2 an overview is presented.

Figure 2: Experimental data in the monolith (water-air
system) compared with a) drift flux model [2] b) correlations of Abiev [4] and
Liu [5]

It was noticeable that the experimental
results had a relatively high agreement with a linear approximation structured like
the drift flux model. But compared to recent work (Figure 2 a) the distribution
coefficient C₀ was obtained to be much lower than in open literature,
where it was determined to values between 1.1 and 1.3. Whereas, the data of
Abiev [4] and Liu [5] fit for low bubble velocity, but deviation and scatter increase
at velocities higher than 0.4 m/s.

The experiments with squalane in a single
channel showed the following behaviors (Figure 3).

Figure 3: Experimental data in the single channel (squalane-nitrogen
system) compared with a) drift flux model [2] b) correlations of Abiev [4] and
Liu [5]

Also a linear behavior was observed for a
highly viscous fluid. A linear approximation found C₀ closer to
literature values than in the monolith, but in both cases the u_∞ was gained as a positive
value. Comparing the squalane-nitrogen experiments with the models of Abiev [4]
and Liu [5] (Figure 3 b) it is recognizable that there is a similar trend to
the water-air experiments (Figure 2 b). In both cases the models overpredict
the bubble velocity for higher u_TP.

Principally, the measurements in single
channels and in monolithic channels showed the same behavior with respect to
various bubble velocity correlations. Therefore, the errors due to
maldistribution or the application of various measurement techniques were
negligible. Overall, the drift flux model was concluded to be the best one. The
experiments showed a linear dependence of bubble velocity from u_TP
respectively Ca. This model was flexible enough to fit to each experimental
setup. Finally, the empirical parameters C₀ and u_∞ were suggested to depend on
geometric and fluidic parameters. This should be an important issue for future
experiments. By means of different fluids and experimental parameters C₀
= f(Ca) or u_∞ =
f(Ca, flow direction) the detailed dependencies have to be figured out to
predict bubble velocity without experimental work.

Acknowledgement

The authors highly acknowledge the
Ernest-Solvay-Foundation for funding the experiments with the entire monolith. Furthermore the authors acknowledge Corning Inc. for providing
the monolith.

References

[1] Bauer, T., Roy, S., Lange, R., Al-Dahhan, M.H., Liquid saturation
and gas-liquid distribution in multiphase monolithic reactors, Chem. Eng. Sci.,
60 (2005) 3101-3106

[2] Zuber, N.;
Findlay, J.A., Average volumetric concentration in two-phase flow systems, J.
Heat Transfer, 87 (1965) 453-468

[3] Thulasidas, T.C., Abraham, M.A., Cerro,
R.L., Bubble train flow in capillaries of circular and square cross section.
Chem.Eng.Sci., 50 (1994) 183-199

[4] Abiev, R.Sh., Simulation of the Slug
Flow of a Gas-Liquid System in Capillaries, Theor. Found. of Chem. Eng., 42
(2008) 105-117

[5] Liu, H., Vandu, C.O., Krishna, R.,
Hydrodynamics of Taylor Flow in Vertical Capillaries: Flow Regimes, Bubble Rise
Velocity, Liquid Slug Length, and Pressure Drop, Ind. Eng. Chem. Res., 44
(2005) 4884-4897