The
dispersion of gases in liquids in stirred tanks is a common operation in
chemical, petrochemical, food and environmental processes. In these processes,
the contact of the gas with a liquid must be performed in an efficient manner
to achieve adequate mass transfer rates between the phases, especially when
chemical reaction is involved. The gas-liquid mass transfer rate is directly
related to the amount of the interfacial area generated between the phases and
local values of turbulence intensity in the flow. Different technologies to
promote the dispersion of the gas into the liquid, such as spargers, gas
ejectors and self-inducing impellers, are used from the laboratorial to the industrial
scale. Self Inducing impellers have hollow shafts that drowns gas down into the
liquid, captured from above the free-surface, without extra devices. The flow turbine
of the self inducing impeller promotes simultaneously the dispersion and mixing
of the gas in the liquid. Its operation principle is based on the pressure gradient
generated, due to rotation, between the inlet orifices at the top of the shaft,
above the liquid surface, and orifices placed near the impeller blades,
immersed in the agitated liquid. The pressure gradient generated between the
two orifices, for sufficiently high impeller speeds, promotes a continuous
suction of top gas that flows through the hollow shaft and is dispersed into
the liquid. If the reactor is operated in batch, the gas that is not absorbed
into the liquid is released from the free surface to be re-circulated again.
This makes self-inducing impellers an attractive solution when the recycling
gas is costly, not abundant, or hazardous. In these devices, the induced gas flow
rate depends on the impeller geometry and dimension, its rotational speed, and
the physical properties of the two fluids.

The objective
of this work was developing a Computational Fluid Dynamics (CFD) model of the
multiphase flow in a lab-scale stirred tank reactor equipped with a self
inducing impeller. The simulations are used for the prediction of the spatial
distribution of the gas-liquid mass transfer rate, k_La,
in the flow. This allows verifying if a homogeneous spatial distribution of k_La
is achieved in the reactor and identifying zones with poor mass transfer rates.
The studied device is a transparent replica of a cylindrical, flat-bottomed reactor
with a diameter of 58 mm and a total volume of 300 cm³. Mixing
is promoted by a stainless steel radial flow self-inducing impeller with a
diameter of 19 mm, resembling a double disk Rushton type turbine. Four
baffles with a width of 10 mm and a thickness of 1 mm are placed inside
the reactor to avoid formation of a free-surface vortex. The multiphase system
considered in the simulations was the mixture methylcyclohaxane/hydrogen at
10 bar and 20 Â°C.

A 3D CFD model of the flow in the stirred
reactor was created, with the computational domain consisting of the volume of
the reactor filled with the liquid phase until a height of 50 mm from the
bottom. All the elements of the reactor were generated with the same geometric
dimensions as the ones of the existing setup, with the exception of the
thickness of the impeller and baffles, which were neglected. The
Eulerian-Eulerian multiphase flow model was used for the simulation of the
gas-liquid mixture flow. Gravity was set in the model to act on the system
vertically, i.e., along the impeller axis, and down. The considered momentum
exchange terms between the two phases were the drag force felt by the bubbles,
and turbulent dispersion. Other contributions to the exchange of momentum
between phases, like lift and virtual mass forces, are not dominant in
multiphase stirred vessels (Scargiali et al., 2007). The drag
coefficient was calculated from the Schiller-Naumann correlation assuming a
spatially invariant bubble diameter in the reactor. The Brucato drag
coefficient correction correlation was also used to include in the calculations
the increase of drag due to the liquid phase turbulence. This correction takes
into account the liquid's turbulent energy dissipation rate in the estimation
of a corrective term for the drag coefficient (Brucato et al, 1998).
Turbulence-induced gas dispersion was modeled as a turbulent diffusion term in
the governing equations of phase volume fractions, instead of being treated as
an interfacial momentum force in the phase momentum equations. This was defined
with the Diffusion in VOF model available in Fluent. The motion of the
self-inducing turbine was modeled by using the Multiple Reference Frame (MFR)
methodology. Turbulence in the flow was simulated with the Multiphase
Realizable k - ε Model for each phase, which solves a set of
turbulent kinetic energy and turbulent energy dissipation rate transport
equations for each of the two fluids. This turbulence model allows a more
detailed simulation of turbulence interaction between phases.

The spatial distribution of k_La,
in the stirred reactor was obtained from the flow simulations by combining them
with Danckwert's surface renewal model (Danckwerts, 1951). Danckwerts proposed that
the mass transfer rate between phases could be related to an average surface
renewal rate, which is resulting from the contact of the bubble's interface
with the turbulent eddies in the liquid phase. Lamont and Scott (1970) developed
Danckwerts' assumption further with the statistical theory of turbulent
diffusion. The molecular diffusivity of hydrogen in methylcyclohexane was
estimated with the Wilke-Chang correlation for diffusion coefficients in dilute
solutions (Wilke and Chang, 1955) to be included in
Danckwert's surface renewal model. Figure 1 shows the contour maps of k_La
values in a vertical plane in the reactor, passing through the impeller axis, for
the different impeller rotational velocities, N, and assuming a
spatially invariant bubble diameter of 2 mm.

Figure 1. Contours of k_La
values in a vertical plane of the reactor passing through the axis for a
constant bubble diameter of 2 mm and different impeller rotational speeds.

The CFD results show that the mass transfer
rate between the two phases is not spatially uniform in the reactor, varying
several orders of magnitude. As expected, k_La values
are higher in the region closer to the impeller where both gas fraction and
turbulent energy dissipation rate are higher as well. The results also show
that in the range from 1000 to 2000 rpm, the values of k_La
can increase substantially inside de vessel, by at least one order of
magnitude, with the increase of N. This is due simultaneously to the
increase of the gas induction rate into the system and to the increase of
turbulent energy dissipation in the domain with the increase of the impeller
rotational velocity. The numerical predictions of k_La
have been compared with experimental measurements of average mass transport
rates from Braga (2013), using the same device, and for the
same flow conditions and fluids. While showing a similar trend and predicting
values in the same order of magnitude, the CFD simulations tend to overestimate
the values of k_La (Figure 2). This overestimation
is thought to be associated to the calculation of k_La
in the region surrounding the impeller blades where the gas volume fraction is
higher (>60%), or to the uncertainties associated to the diffusivity
coefficient estimation. This matter is being further invested and new results
will be presented at the conference.

Figure 2. Volume-average value of k_La
as a function of the impeller rotational speed determined experimentally by
Braga (2013) and from the CFD simulations for a bubble diameter
of 2 mm. The error bars indicate the uncertainty associated to the mass
diffusion coefficient.

References

Braga, M., 2013. Etude des phénomènes de transfert et de
l?hydrodynamique dans des réacteurs agités à panier catalytique. Université
Claude Bernard Lyon 1, Lyon, France.

Brucato, A., Grisafi, F., Montante, G., 1998. Particle drag coefficients in turbulent fluids. Chem. Eng. Sci. 53,
3295?3314. doi:10.1016/S0009-2509(98)00114-6

Danckwerts, P., 1951. Significance of
liquid-film coefficients in gas absorption. Ind. Eng. Chem. 43, 1460?1467.

Lamont, J.C., Scott, D.S., 1970. An eddy
cell model of mass transfer into the surface of a turbulent liquid. AIChE J.
16, 513?519. doi:10.1002/aic.690160403

Scargiali, F., D?Orazio, a., Grisafi, F.,
Brucato, a., 2007. Modelling and Simulation of Gas?Liquid Hydrodynamics in
Mechanically Stirred Tanks. Chem. Eng. Res. Des. 85, 637?646.
doi:10.1205/cherd06243

Wilke, C.R., Chang, P., 1955.
Correlation of diffusion coefficients in dilute solutions. AIChE J. 1, 264?270.
doi:10.1002/aic.690010222