New Approaches for Prediction of Gas Holdups and Validation of the Mixing Length Concept in Gas-Liquid and Slurry Bubble Columns
text-align:center;line-height:14.0pt">
font-family:"Times New Roman","serif"'>NEW APPROACHES FOR PREDICTION OF GAS
HOLDUPS text-align:center;line-height:14.0pt"> font-family:"Times New Roman","serif"'>AND VALIDATION OF THE MIXING LENGTH
CONCEPT
of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf,Â
in (slurry) bubble columns is very important for both the design and scale-up
of these reactors. In the literature hitherto there are only few reliable empirical
gas holdup correlations (mainly for gas-liquid bubble columns). In this work, a
new approach has been developed for predicting the gas holdups at ambient
conditions in gas-liquid bubble columns (0.095 and 0.102 m in ID) operated with
21 pure organic liquids, 17 liquid mixtures and tap water. The same approach
was also applied for prediction of gas holdups in a slurry bubble column (0.095
m in ID) operated with 7 three-phase systems under ambient conditions. justify;text-indent:8.65pt;line-height:normal"> font-family:"Times New Roman","serif"'>The new model for gas holdup prediction in
(slurry) bubble columns is based on the theoretical calculation of the
gas-liquid interfacial area: a=6ɛG/ds.
This correlation is explicitly valid for rigid spherical bubbles. In the case
of slurry bubble columns, an empirical correlation (a=651UG0.87μeff-0.24)
developed by Schumpe et al. (1987) for the interfacial area prediction
is frequently used. When both correlations are set equal, then the theoretical
gas holdup can be calculated provided that one knows how to estimate the
Sauter-mean bubble diameter ds and the effective viscosity μeff.
The same approach was also applied to gas-liquid bubble columns. However, the
interfacial areas were estimated by the empirical correlation of Akita and
Yoshida (1974). justify;text-indent:8.65pt;line-height:normal"> font-family:"Times New Roman","serif"'>In the above-mentioned approaches the
estimation of the Sauter-mean bubble diameters ds was based
on empirical correlations (Wilkinson et al. (1994) for bubble columns
and Lemoine et al. (2008) for slurry bubble columns). justify;text-indent:8.65pt;line-height:normal"> font-family:"Times New Roman","serif"'>For given gas-liquid-solid system, gas
distributor layout and column diameter, the ds value is a
function of both the superficial gas velocity UG0.14
and gas holdup (1-ɛG)1.56 (Lemoine et al.,
2008). Following the above-described approach, the ɛG
value was calculated (based on a trial and error method) from the ratio ɛG/(1-ɛG)1.56.
The obtained ɛG value in this way was multiplied by a
correction factor (a function of Eӧtvӧs number Eo) since the
formed bubbles under the tested experimental conditions were oblate ellipsoidal
(i.e. non-spherical). In the case of slurry bubble columns, the Eo
number was based on the slurry density ρSL. A typical
gas holdup parity plot in a slurry bubble column is shown in Fig. 1. .0001pt;text-align:center;text-indent:14.45pt;line-height:normal">
14.2pt;line-height:normal">Â Fig.
1. Parity
plot of gas holdups in              Fig. 2. Entropy profile in
air-water bubble 14.2pt;line-height:normal">Â Â Â Â Â Â Â Â Â Â Â
air-ligroin-PVC system.                                  column.                    Â
justify;text-indent:8.65pt;line-height:normal"> font-family:"Times New Roman","serif"'>Following the above-described approach
in two-phase bubble columns, it was found that for given gas-liquid system,
column diameter and UG value the theoretical gas holdup could
be estimated from the simplified correlation: ɛG0.13=const.
Then the obtained ɛG value was also multiplied by a
correction factor (a function of Eo). So, the objective of this part of
the research work was to find the best expressions for the correction factors
in two-phase and three-phase bubble columns, which fit successfully the
experimental gas holdups ɛG. justify;text-indent:.2in;line-height:normal"> font-family:"Times New Roman","serif"'>The determination of the scale of liquid
mixing in the main hydrodynamic regimes of bubble column operation is also of
essential importance for their design and scale-up. In this context, a new
method (and correlation) has been proposed by Kawase and Tokunaga (1991) for
the determination of the mixing length (L). The parameter L
characterizes the degree and scale of mixing. It can be also associated with
the distance over which a turbulent eddy retains its identity. justify;text-indent:.2in;line-height:normal"> font-family:"Times New Roman","serif"'>In this work, a new definition of
entropy (E) has been developed on the basis of gas holdup time series
data measured by a conductivity wire-mesh sensor in an air-water bubble column
(0.15 m in ID). The new entropy has been estimated by means of multiple
reconstructions of the signal. It was found that in the UG range
from 0.034 to 0.101 m/s (see Fig. 2), the entropy (E) decreased
monotonously and it was correlated to the mixing length L (a function of
both column diameter Dc and UG−0.38).
Secondly, a newly defined information entropy (IE) has been also
extracted from the gas holdup fluctuations and correlated to the mixing length
in almost the same UG range (0.022−0.101 m/s). justify;text-indent:.2in;line-height:normal"> font-family:"Times New Roman","serif"'>In a previous publication (Nedeltchev et
al., 2014), it was shown that the Kolmogorov entropy (KE) and a new
statistical parameter (called ?maximum number of signal?s visits in a region? Nvmax)
were capable of identifying the range of applicability (0.034≤ UG≤0.112 m/s) of
the mixing length concept. Another statistical parameter F 12.0pt;font-family:"Times New Roman","serif"'> (average/(3×average absolute
deviation)) was also introduced by Nedeltchev and Schubert (2015) for
validating the range of applicability of the mixing length concept. It was also
found that the F Â index is a
function of the mixing length L in the UG range from
0.034 to 0.112 m/s. justify;text-indent:.2in;line-height:normal"> font-family:"Times New Roman","serif"'>In this work, a comparison of the
results obtained by the five different parameters (E, IE, KE,
Nvmax and font-family:Symbol">F)
is performed. Most of them (except for KE) are new and such a comparison
has not been reported in the literature hitherto. It revealed that the determination
of the boundaries of the transition flow regime and the range of applicability
of the mixing length concept depends to some extent on the parameter used.
Based on the above-mentioned parameters it was found that the mixing length
concept was applicable only in the transition flow regime. Such a result has
not been reported in the previous papers (for instance, in Kawase and Tokunaga,
1991). justify;line-height:normal"> justify;line-height:normal">References justify;line-height:normal"> justify;line-height:normal">Akita,
K. and F. Yoshida, Ind. Eng. Chem., Process Des. Dev. 13, 84−91
(1974) justify;line-height:normal">Kawase,
Y. and M. Tokunaga, Can. J. Chem. Eng. 69, 1228−1231 (1991) margin-left:.2in;margin-bottom:.0001pt;text-align:justify;text-indent:-.2in;
line-height:normal">Lemoine,
R., A. Behkish, L. Sehabiague, Y. J. Heintz, R. Oukaci and B. I. Morsi, margin-left:.2in;margin-bottom:.0001pt;text-align:justify;text-indent:-.2in;
line-height:normal">Â Â Â Â
Fuel Processing Technology "Times New Roman","serif"'> 89, 322−343 (2008) margin-left:.2in;margin-bottom:.0001pt;text-align:justify;text-indent:-.2in;
line-height:normal">Nedeltchev,
S., Th. Donath, S. Rabha, U. Hampel and M. Schubert, J. Chem. Eng. Japan
47, 722−729 (2014) margin-left:.2in;margin-bottom:.0001pt;text-align:justify;text-indent:-.2in;
line-height:normal">Nedeltchev,
S. and M. Schubert, J. Chem. Eng. Japan 48 (2015), in press. justify;line-height:normal">Schumpe,
A., A. K. Saxena and L. K. Fang, Chem. Eng. Sci. 42, 1787−1796
(1987) line-height:normal">Wilkinson,
P. M., H. Haringa and L. L. Van Dierendonck, Chem. Eng. Sci. 49,
1417−1427 (1994)
HOLDUPS text-align:center;line-height:14.0pt"> font-family:"Times New Roman","serif"'>AND VALIDATION OF THE MIXING LENGTH
CONCEPT
IN
GAS-LIQUID AND SLURRY BUBBLE COLUMNS
Stoyan
Nedeltchev, Markus Schubert
of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf,Â
Bautzner
Landstraße 400, 01328 Dresden, Germany
in (slurry) bubble columns is very important for both the design and scale-up
of these reactors. In the literature hitherto there are only few reliable empirical
gas holdup correlations (mainly for gas-liquid bubble columns). In this work, a
new approach has been developed for predicting the gas holdups at ambient
conditions in gas-liquid bubble columns (0.095 and 0.102 m in ID) operated with
21 pure organic liquids, 17 liquid mixtures and tap water. The same approach
was also applied for prediction of gas holdups in a slurry bubble column (0.095
m in ID) operated with 7 three-phase systems under ambient conditions. justify;text-indent:8.65pt;line-height:normal"> font-family:"Times New Roman","serif"'>The new model for gas holdup prediction in
(slurry) bubble columns is based on the theoretical calculation of the
gas-liquid interfacial area: a=6ɛG/ds.
This correlation is explicitly valid for rigid spherical bubbles. In the case
of slurry bubble columns, an empirical correlation (a=651UG0.87μeff-0.24)
developed by Schumpe et al. (1987) for the interfacial area prediction
is frequently used. When both correlations are set equal, then the theoretical
gas holdup can be calculated provided that one knows how to estimate the
Sauter-mean bubble diameter ds and the effective viscosity μeff.
The same approach was also applied to gas-liquid bubble columns. However, the
interfacial areas were estimated by the empirical correlation of Akita and
Yoshida (1974). justify;text-indent:8.65pt;line-height:normal"> font-family:"Times New Roman","serif"'>In the above-mentioned approaches the
estimation of the Sauter-mean bubble diameters ds was based
on empirical correlations (Wilkinson et al. (1994) for bubble columns
and Lemoine et al. (2008) for slurry bubble columns). justify;text-indent:8.65pt;line-height:normal"> font-family:"Times New Roman","serif"'>For given gas-liquid-solid system, gas
distributor layout and column diameter, the ds value is a
function of both the superficial gas velocity UG0.14
and gas holdup (1-ɛG)1.56 (Lemoine et al.,
2008). Following the above-described approach, the ɛG
value was calculated (based on a trial and error method) from the ratio ɛG/(1-ɛG)1.56.
The obtained ɛG value in this way was multiplied by a
correction factor (a function of Eӧtvӧs number Eo) since the
formed bubbles under the tested experimental conditions were oblate ellipsoidal
(i.e. non-spherical). In the case of slurry bubble columns, the Eo
number was based on the slurry density ρSL. A typical
gas holdup parity plot in a slurry bubble column is shown in Fig. 1. .0001pt;text-align:center;text-indent:14.45pt;line-height:normal">
14.2pt;line-height:normal">Â Fig.1. Parity
plot of gas holdups in              Fig. 2. Entropy profile in
air-water bubble 14.2pt;line-height:normal">Â Â Â Â Â Â Â Â Â Â Â
air-ligroin-PVC system.                                  column.                    Â
justify;text-indent:8.65pt;line-height:normal"> font-family:"Times New Roman","serif"'>Following the above-described approach
in two-phase bubble columns, it was found that for given gas-liquid system,
column diameter and UG value the theoretical gas holdup could
be estimated from the simplified correlation: ɛG0.13=const.
Then the obtained ɛG value was also multiplied by a
correction factor (a function of Eo). So, the objective of this part of
the research work was to find the best expressions for the correction factors
in two-phase and three-phase bubble columns, which fit successfully the
experimental gas holdups ɛG. justify;text-indent:.2in;line-height:normal"> font-family:"Times New Roman","serif"'>The determination of the scale of liquid
mixing in the main hydrodynamic regimes of bubble column operation is also of
essential importance for their design and scale-up. In this context, a new
method (and correlation) has been proposed by Kawase and Tokunaga (1991) for
the determination of the mixing length (L). The parameter L
characterizes the degree and scale of mixing. It can be also associated with
the distance over which a turbulent eddy retains its identity. justify;text-indent:.2in;line-height:normal"> font-family:"Times New Roman","serif"'>In this work, a new definition of
entropy (E) has been developed on the basis of gas holdup time series
data measured by a conductivity wire-mesh sensor in an air-water bubble column
(0.15 m in ID). The new entropy has been estimated by means of multiple
reconstructions of the signal. It was found that in the UG range
from 0.034 to 0.101 m/s (see Fig. 2), the entropy (E) decreased
monotonously and it was correlated to the mixing length L (a function of
both column diameter Dc and UG−0.38).
Secondly, a newly defined information entropy (IE) has been also
extracted from the gas holdup fluctuations and correlated to the mixing length
in almost the same UG range (0.022−0.101 m/s). justify;text-indent:.2in;line-height:normal"> font-family:"Times New Roman","serif"'>In a previous publication (Nedeltchev et
al., 2014), it was shown that the Kolmogorov entropy (KE) and a new
statistical parameter (called ?maximum number of signal?s visits in a region? Nvmax)
were capable of identifying the range of applicability (0.034≤ UG≤0.112 m/s) of
the mixing length concept. Another statistical parameter F 12.0pt;font-family:"Times New Roman","serif"'> (average/(3×average absolute
deviation)) was also introduced by Nedeltchev and Schubert (2015) for
validating the range of applicability of the mixing length concept. It was also
found that the F Â index is a
function of the mixing length L in the UG range from
0.034 to 0.112 m/s. justify;text-indent:.2in;line-height:normal"> font-family:"Times New Roman","serif"'>In this work, a comparison of the
results obtained by the five different parameters (E, IE, KE,
Nvmax and font-family:Symbol">F)
is performed. Most of them (except for KE) are new and such a comparison
has not been reported in the literature hitherto. It revealed that the determination
of the boundaries of the transition flow regime and the range of applicability
of the mixing length concept depends to some extent on the parameter used.
Based on the above-mentioned parameters it was found that the mixing length
concept was applicable only in the transition flow regime. Such a result has
not been reported in the previous papers (for instance, in Kawase and Tokunaga,
1991). justify;line-height:normal"> justify;line-height:normal">References justify;line-height:normal"> justify;line-height:normal">Akita,
K. and F. Yoshida, Ind. Eng. Chem., Process Des. Dev. 13, 84−91
(1974) justify;line-height:normal">Kawase,
Y. and M. Tokunaga, Can. J. Chem. Eng. 69, 1228−1231 (1991) margin-left:.2in;margin-bottom:.0001pt;text-align:justify;text-indent:-.2in;
line-height:normal">Lemoine,
R., A. Behkish, L. Sehabiague, Y. J. Heintz, R. Oukaci and B. I. Morsi, margin-left:.2in;margin-bottom:.0001pt;text-align:justify;text-indent:-.2in;
line-height:normal">Â Â Â Â
Fuel Processing Technology "Times New Roman","serif"'> 89, 322−343 (2008) margin-left:.2in;margin-bottom:.0001pt;text-align:justify;text-indent:-.2in;
line-height:normal">Nedeltchev,
S., Th. Donath, S. Rabha, U. Hampel and M. Schubert, J. Chem. Eng. Japan
47, 722−729 (2014) margin-left:.2in;margin-bottom:.0001pt;text-align:justify;text-indent:-.2in;
line-height:normal">Nedeltchev,
S. and M. Schubert, J. Chem. Eng. Japan 48 (2015), in press. justify;line-height:normal">Schumpe,
A., A. K. Saxena and L. K. Fang, Chem. Eng. Sci. 42, 1787−1796
(1987) line-height:normal">Wilkinson,
P. M., H. Haringa and L. L. Van Dierendonck, Chem. Eng. Sci. 49,
1417−1427 (1994)