(215a) Semi-Empirical Drag Correlation for a Gas Solid Vortex Reactor Starting from the Radial Momentum Balances

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Semi-empirical drag correlation
for a Gas Solid Vortex Reactor starting from the radial momentum balances

Friedle,
M; Niyogi, K; Torregrosa Galindo, M.M.; Heynderickx^*, G.J., Marin,
G.B.

Laboratory for Chemical
Technology, Department of Chemical Engineering, Ghent University,
Technologiepark 914, B-9052 Gent, Belgium

^*Corresponding author:
Geraldine.Heynderickx@UGent.be

The Gas Solid Vortex Reactor
(GSVR) is a novel rotating fluidized bed reactor with a stationary geometry, in
which the gravitational force in conventional fluidized bed is replaced by a
centrifugal force resulting in process intensification¹.
In a GSVR a stable solids bed can be obtained for high gas flow rates thereby
increasing the slip velocity between the phases. Consequently, the overall heat
and mass transfer increases as to compared to a gravitational fluidized bed^{2, 3}. The GSVR is a disc-like chamber where the process gas is introduced
through a series of azimuthally inclined injection slots, uniformly distributed
along the circumferential chamber wall. Inside the chamber the gas swirls
towards the unidirectional central  gas exhaust. When particles are fed inside
this swirling flow field the gas transfers part of its momentum to the
particles. The particles start to rotate in the chamber and form a stable,
dense, rotating bed at the circumferential wall (Fig. 1). The rotational motion
generates a radially outward directed centrifugal force on the particles. The
injected gas flowing through the solid bed towards the unidirectional central  gas
exhaust generates a counteracting radially inward directed drag force on the
particles. The GSVR compiles a unique set of characteristics typical for reactor
technologies that combine high gas-solid slip velocities, good particle mixing
and continuous operation under dense bed conditions⁴.
As such, the GSVR  technology has already been considered for different
applications, like drying of biomass⁵,
biomass pyrolysis¹, SO₂-NO_x adsorption from
flue gases⁶ or nuclear rocket fuel propulsion⁷.

As no universal understanding of
the in-depth hydrodynamics of the GSVR technology is readily available, scaling
and design of industrially-sized GSVRs are difficult up-to-date.  An in-depth
understanding of a technology often comes from a first principles approach. A first
step in understanding of the multiphase hydrodynamics in the GSVR based on the
radial momentum balances is aimed at in the present study.

An extensive set of experimental
data has been collected by different researchers^{2,
3, 8, 9} over the past years in an experimental semi-batch GSVR setup at
the Laboratory for Chemical Technology. The investigated range of operations
spans a wide range of gas flow rates, particle sizes, particle densities and
bed masses. The experimental data is used to verify the assumptions made and to
determine the model parameters of the semi-empirical drag formulation.

Following some simplifying
assumptions, like neglecting the weight of the gas, the wall force and
particle-particle interaction, the radial solids and gas momentum balances are
combined to:

The resulting one-dimensional,
averaged equation shows that the pressure drop over the bed height balances the
centrifugal force of the bed. Here  describes the
radial height of the bed,  the overall
volume of the bed,  the mass of the
bed and   the outer
radius of the unit. The azimuthal solids velocity  is averaged
over the height of the bed.

Pressure drop over a conventional
fluidized bed is usually estimated using semi-empirical correlations for the
drag force^10,
11. In the present work a semi-empirical correlation for the radial drag
force on the GSVR bed is developed, starting from the well-known correlations
for single-particle drag¹².
The resulting correlation is:

Here  is the void
fraction,  the particle
diameter, is the gas
density and  the radial
superficial gas velocity in the unit. Equations 1 and 2 are combined and
written in dimensionless form :

The correlation parameters are
obtained through linear regression of the available experimental data sets. The
parity plot for equation 3 is shown in Figure 3. The radial Reynolds number and
the centrifugal Archimedes number are calculated from equations 4 and 5, where  is the gas
viscosity.

Using this modeling approach a more
fundamental understanding of the interaction between gas and particles in a
dense rotating bed is obtained. The absence of the void fraction as a classic
modeling parameter, states that the gas interacts with every particle in the
same way and that particle-particle interaction is minimal. In this respect the
GSVR differs from conventional fluidization technologies operating in the dense
bed regime, confirming the appropriateness of the GSVR for innovative industrial
applications.

Acknowledgments

This
work was supported by the European Research Council under the European
Union’s Seventh Framework Program (FP7/2007-2013) / ERC grant agreement n°
290793.

References

1.            Ashcraft RW, Heynderickx GJ, Marin GB, 2012. Modeling fast biomass
pyrolysis in a gas-solid vortex reactor. Chemical Engineering Journal 207,
195-208.

2.            Ekatpure
RP, Suryawanshi VU, Heynderickx GJ, de Broqueville A, Marin GB, 2011.
Experimental investigation of a gas–solid rotating bed reactor with static
geometry. Chemical Engineering and Processing: Process Intensification 50,
77-84.

3.            Kovacevic
JZ, Pantzali MN, Heynderickx GJ, Marin GB, 2014. Bed stability and maximum
solids capacity in a Gas-Solid Vortex Reactor: Experimental study. Chemical
Engineering Science 106, 293-303.

4.            De
Wilde J, 2014. Gas–solid fluidized beds in vortex chambers. Chemical
Engineering and Processing: Process Intensification 85, 256-90.

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P, De Wilde J, 2013. Drying of Biomass Particles: Experimental Study and
Comparison of the Performance of a Conventional Fluidized Bed and a Rotating
Fluidized Bed in a Static Geometry. Drying Technology 31, 236-45.

6.            Ashcraft
RW, Kovacevic J, Heynderickx GJ, Marin GB, 2013. Assessment of a Gas-Solid
Vortex Reactor for SO2/NOx Adsorption from Flue Gas. Ind Eng Chem Res 52,
861-75.

7.            Lewellen
W. A study of fluid dynamics of gaseous nuclear rocketsQuarterly Progress
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8.            Pantzali
MN, Kovacevic JZ, Heynderickx GJ, Marin GB, 2015. Radial Pressure
Profiles in a Cold-Flow Gas-Solid Vortex Reactor. AIChE Journal 61,
4114-25.

9.            Kovacevic
JZ, Pantzali MN, Niyogi K, Deen NG, Heynderickx GJ, Marin GB, 2015. Solids velocity
fields in a cold-flow Gas–Solid Vortex Reactor. Chemical Engineering Science
123, 220-30.

10.         Gibilaro
LG, Di Felice R, Waldram SP, Foscolo PU, 1985. Generalized friction factor and
drag coefficient correlations for fluid-particle interactions. Chemical
Engineering Science 40, 1817-23.

11.         Ergun
S, 1952. Fluid flow through packed columns. Chem Eng Prog 48, 89-94.

12.         Gidaspow D, 1994. Multiphase Flow and
Fluidization. Academic Press, Boston.

Fig.
1. A schematic representation of the Gas-Solid Vortex Reactor²

Fig.
2. Plot for the centrifugal force of the bed and the force exerted by the
pressure on the bed (Equation 1).

Fig.
3. Parity plot for the semi-empirical correlation for the particle-gas
interaction in the GSVR (Equation 3).