Non-invasive determination of gas phase dispersion coefficients in bubble columns using periodic gas flow modulation
Graphical abstract
Introduction
Bubble columns are widely applied in the chemical, petrochemical, biochemical and environmental industries, for example for hydrocarbon syntheses, hydrogenation of saturated oils and waste water treatment. These gas-liquid contactors are characterized by a simple construction and low maintenance costs. Mainly, they are preferred for bulk processes with slow reactions and liquid-side mass transfer limitation as well as for processes with strong exothermic behavior (Cheremisinoff, 1986, Hertwig, 2007, deHaan, 2015).
The bubble column’s volumetric productivity as well as its mass and heat transfer rates are affected by the prevailing hydrodynamics covering gas holdup, bubble size, dispersion of gas and liquid phase as well as flow regime. Different theoretical approaches exist to link column performance to dispersion and mixing in bubble columns. Overviews about available mixing models are given e.g. by Schlüter et al., 1992, Levenspiel, 1998 and Shah et al. (2004). Most important mixing models are e.g. the mixed-cell model (Turner and Mills, 1990), the tanks-in-series model (Fogler, 2005) and the recirculation with cross-flow dispersion (RCFD) model (Degaleesan et al., 1967). The axial dispersion model (ADM) (Nauman, 2002, Davis and Robert, 2003) is the most widely applied one to consider the mixing behavior of the involved phases and was applied for process modelling in absorption columns (Deckwer, 1977) and chemical reactors (Stern et al., 1985, Turner and Mills, 1990, Behin and Shojaeimehr, 2013).
Similar to the classical diffusion theory for miscible fluids, dispersion of immiscible fluids, such as the gas in bubble columns, is described as a finite superimposing flow in main flow direction (Mangartz, 1977). The liquid phase dispersion in bubble columns is caused by rising gas bubbles, which partially carry the liquid upwards – preferentially in the column center – creating a circulating flow pattern with liquid downflow near the column wall (Groen et al., 1996). Gas dispersion in bubble columns, in turn, arises from the variety of bubble rise velocities depending on the evolving bubble size distribution, which is driven by coalescence and breakup events (Rubio et al., 2004). The gas phase dispersion is strongly increased at heterogeneous flow conditions with fast rising large bubbles and swarms of smaller bubbles at comparably low rise velocity (Zahradnik and Fialova, 1996). Dispersion processes are approximated by means of dispersion coefficients for the particular phase based on residence time measurement data. Since the residence time of the respective phase can hardly be measured directly, appropriate tracer substances (in terms of neutral buoyancy, insolubility, non-reactivity, detectability, Shah et al., 2004) are added and tracked. The residence time of a tracer is considered to be distributed depending on the dispersions magnitude (Mangartz, 1977). For example, small dispersion results in a narrow residence time distribution (RTD) of a tracer added as Dirac pulse, while increasing dispersion widens the RTD (Levenspiel, 1998). Here, the dispersion coefficient establishes the functional link between the theoretical mixing model and the measured RTD.
While liquid dispersion in bubble columns has widely been studied (Shah and Stiegel, 1978), only few gas phase dispersion data are currently available, which traces back to the fact that their experimental determination is challenging. Usually such experimental investigations are carried out by injecting and capturing a tracer gas of different properties (temperature, elemental composition, radioactivity) from the bulk gas. Depending on the way the (gas) tracer is added, RTD measurements are basically categorized into steady state and non-steady state methods (Mangartz, 1977, Hertwig, 2007). Although the dispersion of a (gas) tracer is inherently dynamic, the predominant convection in bubble columns allows the assumption of a stationary tracer concentration profile upon steady state tracer injection (Mangartz, 1977). However, such steady state methods require a uniform distribution of the gaseous tracer in the entire column cross-section at the injection height, which is practically not feasible. In contrast, non-steady state methods rely on measuring the tracer concentration downstream the injection point considering its relation to the initial value (Deckwer et al., 1974). Therefore, non-steady state methods preferably apply well-defined tracer injection signals such as jumps, ramps, pulses or periodic functions. While traveling from the injection point towards the downstream measurement positions, the initial tracer signal gets damped in amplitude and shifted in phase by dispersion, which is reflected in the tracer residence time. In the past, several techniques were developed and may be distinguished by the type of tracer and its detection method as well as by the imposed tracer signal (Table 1). It should be noted that gas dispersion studies in bubble columns operated with pronounced liquid superficial velocity higher than (e.g. Kulkarni and Shah, 1984) are not considered here for brevity and consistency.
In the following we will summarize available reports on previous experimental work in this field. So far, mainly, inert gases were used as tracers in bubble columns. For example, DeMaria and White, 1960, Diboun and Schügerl, 1967, Kago et al., 1989, Kawagoe and Otake, 1989, Shetty et al., 1992 and Kantak et al. (1995) used pure He or He mixed with N2, Ar or CO2. The helium concentration was mostly monitored by thermal conductivity analyzers (Diboun and Schügerl, 1967, Kago et al., 1989, Kawagoe and Otake, 1989), mass spectrometry (Shetty et al., 1992, Kantak et al., 1995) or ionization cells (DeMaria and White, 1960). Others used H2 tracers, which were detected by thermal conductivity analyzers (Carleton et al., 1967, Menśhchikov and Aerov, 1967) or dichloro-difluoromethane (CCl2F2) detected by gas chromatography (Wachi and Nojima, 1990) or ionization cells (Towell and Ackerman, 1972). Koelbel et al. (1962) replaced the initial gas phase (N2) by CO and monitored the change at the outlet using infrared gas sensors. A simple approach was used by Joseph et al. (1984). They switched gas supply from nitrogen to pure oxygen and analyzed the gas stream samples with an oxygen sensor. In most studies the gas was extracted by funnel-shape devices (Diboun and Schügerl, 1967, Carleton et al., 1967, Shetty et al., 1992, Kantak et al., 1995) or suction units (Kago et al., 1989, Kawagoe and Otake, 1989) connected to the respective sensors. Their additional impact on the tracer RTD had to be considered (Wachi and Nojima, 1990, Kawagoe and Otake, 1989). In few studies short-lived radioisotopes of argon (41Ar) and sodium (24Na) were used as tracers and detected via radiation detectors (Seher and Schumacher, 1978, Field and Davidson, 1980). It should also be mentioned that some of the applied techniques required additional sample treating such as gas drying (by heat or other separation principles), sample mixing (Joseph et al., 1984) or additional reference measurement runs (Shetty et al., 1992).
In the studies listed in Table 1, tracers were mostly injected according to step or impulse functions (e.g. additive to the normal gas supply or by replacing the original gas phase by the tracer gas). Kramers and Alberda (1953) and Böxkes and Hofmann (1972) discussed the experimental and mathematical challenges arising with the addition of discontinuous tracer signals to continuous flows and potential errors. Reference measurements from different operating conditions (Joseph et al., 1984, Kago et al., 1989) and mathematical corrections of considerable magnitude were inevitable to obtain feasible results. Furthermore, flow disturbances by sampling or sample guiding internals (Wachi and Nojima, 1990) were often accepted in favor of representativeness of experimental data. Hence, a universal applicability of those methods is limited by sampling procedure and guaranteeing of veridic signal transmission behavior.
An alternative approach is the frequency response analysis (FRA) for periodic tracer injections. Periodic tracer injection leads to downstream propagation of a tracer concentration wave. Here, the dispersion causes damping of the tracer concentration wave amplitude and phase shift at a downstream position. A detailed explanation of this method is given by Gray (1961). Mass transfer absorption experiments with square-wave CH4 and sinusoidal CO2 tracer inlet were performed by Coulon (1971) and Gray and Prados (1963), respectively. They discussed their results with respect to gas phase dispersion based on the amplitude damping and phase shift from inlet and outlet tracer signals. However, the effect of the transient mass transfer behavior was not considered ignoring the influence of the absorption on the shape of the tracer response (Kantak et al., 1995, Vermeer and Krishna, 1981) and possible overestimation of the gas dispersion coefficient (Field and Davidson, 1980, Shetty et al., 1992). Gray and Prados (1963) studied the effect of different sinusoidal frequencies and their applicability towards different mixing model approaches. The most comprehensive FRA-based gas dispersion study was performed by Mangartz and Pilhofer (1980), where the alteration of the tracer inlet signal was monitored via eight probes mounted at different axial positions. However, although the theoretical approach of FRA was considered very promising, only very few such studies were performed, which can be attributed to the complex measurement system including challenging periodic tracer injection, ensuring negligible interference with the steady state hydrodynamics and linear transmission behavior of the complete system (Gray, 1961) as well as difficulties in synchronized downstream detection.
Most of the gas dispersion studies addressed air/water systems only. Increasing the gas phase superficial velocity was found to intensify the gas dispersion, which is even more pronounced at heterogeneous flow conditions due to the formation of larger eddies in the liquid (Mangartz, 1977, Shetty et al., 1992). The influence of the liquid superficial velocity, however, was found to be negligible. While the effect of column height on the gas dispersion coefficient can be neglected (Mangartz, 1977, Koelbel et al., 1962), increasing column diameter was found to significantly boost axial gas dispersion (Mangartz, 1977, Kawagoe and Otake, 1989) and heterogeneity of the gas–liquid dispersion (Shetty et al., 1992). Consequently, the gas dispersion coefficient is mostly described by empirical correlations of the formwhereis the bubble swarm velocity, which depends on the mean gas holdup . Table 2 summarizes the constants and exponents of Eq. (1) from the literature. Few correlations also considered the contribution of different bubble size classes (Kawagoe and Otake, 1989), the effects of relative phase velocity (Shah and Stiegel, 1978), liquid circulation velocity and bubble slip velocity (Kraume and Zehner, 1989) as well as liquid phase properties (Zehner and Schuch, 1984).
Fig. 1 summarizes available experimental data and derived empirical correlations for the gas phase dispersion coefficient in bubble columns, accounting for the effects of (left) superficial gas velocity and (right) bubble swarm velocity, respectively. It should be noted that only experimental data for air/water systems, which is the vast majority of the available data, are shown for a clear and concise overview as well as for easier comparability. Experimental data and corresponding correlations are accordingly color-coded. Black lines indicate correlations (Joshi, 1982, Heijnen and Riet, 1984) fitted against data from several studies (Table 2). There is a fair agreement in the general effect of the superficial gas velocity shown by the similar slopes of lines and experimental data of respective studies. Although, the dispersion coefficients were found to increase with increasing column diameter (compare Wachi and Nojima, 1990; Carleton et al., 1967 and Kago et al., 1989), the dispersion coefficients obtained from different authors for the same column diameter differ significantly (compare Diboun and Schügerl, 1967, Carleton et al., 1967, Shetty et al., 1992 and Kantak et al., 1995 for ). Similar scattering was also found for other column diameters such as and . Plotting the dispersion coefficients against the bubble swarm velocity was proposed to reduce the data scattering as shown in the right plot of Fig. 1. Although not shown here, Mangartz and Pilhofer (1980) confirmed that the gas holdup accounts fairly for the effects of liquid properties and sparging devices on the dispersion. However, the available database is still rather small.
It can be concluded that the prediction of the gas phase mixing behavior in bubble columns is still subject to pronounced uncertainties, in particular at low bubble swarm velocities. Although not fully recorded, it is hypothesized that results of previous studies were remarkably influenced by the applied measurement approach indicated by the systematic deviations (offsets) as discussed above.
Thus, a new approach, recently patented by Hampel (2015), will be introduced in this paper. Contrary to the above mentioned methods using tracer substance addition, this approach is fully non-invasive. Here the gas inlet flow is slightly modulated in its flow rate and thus produces a gas holdup disturbance wave moving upward with the gas phase. The modulated gas holdup is recorded via gamma-ray densitometry in a synchronized manner and with a special count-wise data collecting mode to ensure lock-in detection with a highest signal-to-noise ratio. In the following we will introduce the method in detail, discuss experimental findings and present results of a confidence level and sensitivity analysis.
Section snippets
Theoretical model
The new approach bases on the axial dispersion model (ADM) (Hertwig, 2007, Deckwer, 1985, Gray, 1961, Shah and Stiegel, 1978, Degaleesan et al., 1967). Being applied to the dispersed gas phase, this model (Eq. 3) assumes, that the gas in the column rises with a mean rise velocity and is being dispersed in axial direction , which is quantified by the axial dispersion coefficient . Hence, gas phase holdup follows the linear partial differential equation
Now we assume a
Data processing
The gas holdup values allocated to one modulation period were fitted with the MatLab® Curve-Fitting-Toolbox by the elementary regression modelwhere is the index of the current sample in the range of . The coefficient of determination for the regression model was used for evaluating the holdup curves of different runs. Variation of as it was discussed in Section 2.3, also showed influence on . In consequence, only measurements with
Conclusion
In this paper, a new method for the determination of gas phase dispersion coefficients in bubble columns was presented. Thereby, the superficial gas velocity was periodically modulated by a sinusoidal voltage input at the gas phase mass flow controller and the resulting damping and phase shift in gas holdup signals were analyzed. Manipulation on gas dispersion was found to be negligible for a low magnitude of gas flow modulation. The new approach is advantageous in terms of non-invasiveness
References (60)
- et al.
Design of a high-resolution gamma-ray detector module for tomography applications
Nucl. Instrum. Methods Phys. Res., Sect. A
(2007) - et al.
Hydrodynamics Analysis in Micro-Channels of a viscous coupling using gamma-ray computed tomography
Flow Meas. Instrum.
(2015) - et al.
Some properties of a packed bubble column
Chem. Eng. Sci.
(1967) Absorption and reaction of isobutene in sulfuric acid
Chem. Eng. Sci.
(1977)- et al.
Mixing and mass transfer in tall bubble columns
Chem. Eng. Sci.
(1974) - et al.
Eine Blasensäule mit Gleichstrom von Wasser und Luft - Mischungsvorgänge in der Gasphase
Chem. Eng. Sci.
(1967) - et al.
Coherent structure and axial dispersion in bubble column reactors
Chem. Eng. Sci.
(1996) - et al.
Hydrodynamics of co-current two-phase flow in an inclined rotating tubular fixed bed reactor - wetting intermittency via periodic catalyst immersion
Chem. Eng. Sci.
(2015) - et al.
Mass transfer, mixing and heat transfer phenomena in low viscosity bubble column reactors
Chem. Eng. J.
(1984) Gas phase dispersion in bubble columns
Chem. Eng. J.
(1982)