Transient Global Modelling of Oxygen Mass Transfer in an Internal Gas-Liquid Airlift Reactor
Experimental study on the apparent drag law in dense bubble swarm
Transient global modelling of oxygen mass
transfer in an internal gas-liquid airlift loop.
Cockx A.a** , Liné A. a
de Rangueil, F-31077 Toulouse, France INRA, UMRA792 Ingénierie
des Systèmes Biologiques et des Procédés, F-31400 Toulouse, France CNRS, UMR5504,
F-31400 Toulouse, France *Present adress : Ansys Belgium, 4 avenue Pasteur, B-1300
Wavre, Belgium **Corresponding Author?s E-mail: arnaud.cockx@insa-toulouse.fr
such as fermentation and wastewater biological treatment, due to their efficient
mixing and high rate mass transfer. Airlift reactor is a particular multiphase
reactor, divided into two sections, a downcomer and a riser part which is
aerated, involving a liquid circulation inside the system. A lot of works has
been devoted to the hydrodynamics of the airlift, in particular works based on
CFD (Cockx et al., 1997 and Mudde & van den Akker, 2001,
van Baten et al., 2003; Talvy
et al., 2007a) but fewer are devoted to oxygen mass transfer (Darmana et al, 2005, Talvy et al.,
2007b). Â To describe global hydrodynamics in a
Gas-Liquid internal airlift loop reactors, many authors have also worked on the
development of 0D model (Heijnen et al. 1997, Freitas
et al. 1999, Couvert et al. 2004). The objective of this article is thus to present a global transient
modelling (0D) of oxygen mass transfer in an internal airlift loop reactor. The
global modelling of this system involves the resolution of global mass and
momentum equations for a gas-liquid flow. The internal airlift loop reactor is divided in four
sections where the cited equations are solved in the riser and in the
downcomer, the other sections are characterised by a pressure drop coefficient.
This modelling is based on the drift-flux model proposed by Zuber and Findlay
which predicts of gas volume fraction as well as each phase velocities. This
model was developed for a three-phase flow in Talvy
et al. (2005) and simplified for a two phase flow system. Gas superficial velocity is imposed
in the riser but the liquid superficial velocity remains unknown so that an
extra equation is required to solve this variable. The total pressure drop is
equal to difference of column weight between the riser and the downcomer. The model is completed with the calculation of
transient oxygen mass transfer to determine the oxygen mass transfer
coefficient in such a reactor. A 0D global model is preferred compared to a
full computational fluid dynamics (CFD) model for this transient analysis.
Since the experimental practice is to use sodium sulphite to determine the mass
transfer coefficient by deoxygenating the water, the same protocol is
implemented in the model. Literature often detailed models for external airlift
loop reactor, but few models investigate internal airlift loop reactor where
the bubbles do not recirculate and in which impoverishment of oxygen in bubbles
in the downcomer can occur. Previous paper form Talvy
et al. (2007, b) supposed that at the start of the oxygen recovery in the
liquid that the oxygen concentration in the gas in the whole reactor was at
full capacity. In order to avoid this questionable assumption, three transport
equations are considered to account for oxygen concentration in liquid and in
gas phase as well as sodium sulphite concentration in the liquid phase as
considered experimentally in the standard method for oxygen transfer
measurements. From the local expression of transport equation, the spatial average
in the riser and in the downcomer is developed in the case of a steady state
and fully developed two-phase flow. The resulting sets of equations are then
sequentially treated with Matlab and the Ordinary
Differential Equation toolbox (ODE) with the following chemical steps: ·
the sulphite is consuming
oxygen in the liquid while the gas-liquid transfer is occurring ·
the oxygen concentration in
liquid is equal to zero and remains null as long as the oxygen transferred from
the air bubble to the water is consumed by residual sodium sulphite, the
reaction rate will be limited by the transfer rate ·
as soon as all the sodium sulphite is consumed, its concentration is
zero and the oxygen recovery in the liquid, resulting from mass transfer
coefficient kLa, can be measured. The investigation is then led regarding the measured
oxygen recovery and the simulated one at several superficial gas velocities
between 0.017 and 0.045 m/s. Several methods of mass transfer measurement are
then compared by changing initial conditions in the modelling: ·
The sulphite method is the standard
method where excess mass of sodium sulphite is introduced in the reactor in
order to consumed the dissolved oxygen in the water and then to follow the
oxygen recovery. ·
The N2 method
consists in injecting nitrogen instead of air in order to drain all the oxygen
out from the liquid. Then nitrogen is replaced by air and the oxygen recovery
is followed. ·
The fully loaded bubbles method
is a virtual case the bubbles are fully loaded with oxygen as the liquid oxygen
recover. This case stands in between the two previous quoted methods in terms
of initial condition. The model was validated according to the concentration
of injected sodium sulphite and good agreement between modelled and
experimental data was obtained (figure 1).
Figure
1: oxygen recovery with the sulfite method: experimental and numerical results
at superficial gas velocities ──: 0.017 m/s,
── : 0.045 m/s The sulphite concentration variation is not followed
experimentally but it is worthwhile to notice that the time when the sulphite
is completely depleted corresponds logically to the oxygen recovery in the
liquid phase. From transient
modelling, it is also of great interest to follow oxygen concentration in the
gas phase, both in the riser and the downcomer (figure 2). Bubble oxygen
concentration in the riser is weakly affected during the sulfite consumption
but this is not the case in the downcomer where the concentration drops to
around 130 mg/l and 150 mg/l (plateau value). This significant decrease is due
to a poor renewal of the bubbles in the downcomer, which is typical in an
airlift reactor (Talvy et al 2007).
Figure
2: oxygen concentration in the gas (mg/l) at
superficial gas velocities  ── : 0.017
m/s, ── : 0.045 m/s The value of the
plateau of oxygen concentration in the gas in the downcomer and the riser is
also analytically developed thanks to stationary state in the oxygen
concentration during sulfite consumption. A simplified model is then proposed
to estimate accurately the mass transfer coefficient with the sulfite method
instead of solve the full ordinary differential equations (ODE). The sensitivity of the
oxygen transfer towards the initial sulfite concentration is then analyzed, as such
as the different methods of mass transfer coefficient estimation (nitrogen,
fully loaded bubbles, and sulfite consumption). According to the method used to
measure the mass transfer coefficient, it is shown with the full ODE model that
its value can significantly vary in the case of an airlift reactor due to poor
bubble renewal mainly in the downcomer. The nitrogen method gives the lower estimated
value of mass transfer, the fully loaded bubbles method usually used in CFD
gives the highest asymptotic value and the sulfite method gives intermediates
results depending on the renewal off the bubbles. A transient global modelling
is thus of great interest to better understand gas-liquid transfer in loop
reactors such airlift and to propose an accurate estimation of mass transfer
coefficient when poor bubble renewal involve oxygen impoverishment. References
Hydrodynamic model for three-phase internal and external loop airlift reactor. CES 54, 5253?5258
(1999)
RF, van den Akker HEA, 2D and 3D simulations of an internal airlift loop
reactor on the basis of a two-fluid model. CES. 2001; 56: 6351-6358. Talvy S., A. Cockx, A.Liné, 2007a, Modeling of
hydrodynamics of gas-liquid airlift reactor, AIChE Journal, 53, 2, 335-353. Talvy S., A. Cockx, A. Liné, 2007b, Modeling of oxygen
mass transfer in gas-liquid airlift reactor, AIChE Journal, 53, 2, 316-326.
transfer in an internal gas-liquid airlift loop.
Talvy S. a*,
Cockx A.a** , Liné A. a
a Université de Toulouse, INSA,UPS,INP,LISBP, 135 Avenue
de Rangueil, F-31077 Toulouse, France INRA, UMRA792 Ingénierie
des Systèmes Biologiques et des Procédés, F-31400 Toulouse, France CNRS, UMR5504,
F-31400 Toulouse, France *Present adress : Ansys Belgium, 4 avenue Pasteur, B-1300
Wavre, Belgium **Corresponding Author?s E-mail: arnaud.cockx@insa-toulouse.fr
Keywords: Airlift, gas-liquid
flow, mass transfer, oxygen, sulphite, bubble
such as fermentation and wastewater biological treatment, due to their efficient
mixing and high rate mass transfer. Airlift reactor is a particular multiphase
reactor, divided into two sections, a downcomer and a riser part which is
aerated, involving a liquid circulation inside the system. A lot of works has
been devoted to the hydrodynamics of the airlift, in particular works based on
CFD (Cockx et al., 1997 and Mudde & van den Akker, 2001,
van Baten et al., 2003; Talvy
et al., 2007a) but fewer are devoted to oxygen mass transfer (Darmana et al, 2005, Talvy et al.,
2007b). Â To describe global hydrodynamics in a
Gas-Liquid internal airlift loop reactors, many authors have also worked on the
development of 0D model (Heijnen et al. 1997, Freitas
et al. 1999, Couvert et al. 2004). The objective of this article is thus to present a global transient
modelling (0D) of oxygen mass transfer in an internal airlift loop reactor. The
global modelling of this system involves the resolution of global mass and
momentum equations for a gas-liquid flow. The internal airlift loop reactor is divided in four
sections where the cited equations are solved in the riser and in the
downcomer, the other sections are characterised by a pressure drop coefficient.
This modelling is based on the drift-flux model proposed by Zuber and Findlay
which predicts of gas volume fraction as well as each phase velocities. This
model was developed for a three-phase flow in Talvy
et al. (2005) and simplified for a two phase flow system. Gas superficial velocity is imposed
in the riser but the liquid superficial velocity remains unknown so that an
extra equation is required to solve this variable. The total pressure drop is
equal to difference of column weight between the riser and the downcomer. The model is completed with the calculation of
transient oxygen mass transfer to determine the oxygen mass transfer
coefficient in such a reactor. A 0D global model is preferred compared to a
full computational fluid dynamics (CFD) model for this transient analysis.
Since the experimental practice is to use sodium sulphite to determine the mass
transfer coefficient by deoxygenating the water, the same protocol is
implemented in the model. Literature often detailed models for external airlift
loop reactor, but few models investigate internal airlift loop reactor where
the bubbles do not recirculate and in which impoverishment of oxygen in bubbles
in the downcomer can occur. Previous paper form Talvy
et al. (2007, b) supposed that at the start of the oxygen recovery in the
liquid that the oxygen concentration in the gas in the whole reactor was at
full capacity. In order to avoid this questionable assumption, three transport
equations are considered to account for oxygen concentration in liquid and in
gas phase as well as sodium sulphite concentration in the liquid phase as
considered experimentally in the standard method for oxygen transfer
measurements. From the local expression of transport equation, the spatial average
in the riser and in the downcomer is developed in the case of a steady state
and fully developed two-phase flow. The resulting sets of equations are then
sequentially treated with Matlab and the Ordinary
Differential Equation toolbox (ODE) with the following chemical steps: ·
the sulphite is consuming
oxygen in the liquid while the gas-liquid transfer is occurring ·
the oxygen concentration in
liquid is equal to zero and remains null as long as the oxygen transferred from
the air bubble to the water is consumed by residual sodium sulphite, the
reaction rate will be limited by the transfer rate ·
as soon as all the sodium sulphite is consumed, its concentration is
zero and the oxygen recovery in the liquid, resulting from mass transfer
coefficient kLa, can be measured. The investigation is then led regarding the measured
oxygen recovery and the simulated one at several superficial gas velocities
between 0.017 and 0.045 m/s. Several methods of mass transfer measurement are
then compared by changing initial conditions in the modelling: ·
The sulphite method is the standard
method where excess mass of sodium sulphite is introduced in the reactor in
order to consumed the dissolved oxygen in the water and then to follow the
oxygen recovery. ·
The N2 method
consists in injecting nitrogen instead of air in order to drain all the oxygen
out from the liquid. Then nitrogen is replaced by air and the oxygen recovery
is followed. ·
The fully loaded bubbles method
is a virtual case the bubbles are fully loaded with oxygen as the liquid oxygen
recover. This case stands in between the two previous quoted methods in terms
of initial condition. The model was validated according to the concentration
of injected sodium sulphite and good agreement between modelled and
experimental data was obtained (figure 1).
1: oxygen recovery with the sulfite method: experimental and numerical results
at superficial gas velocities ──: 0.017 m/s,
── : 0.045 m/s The sulphite concentration variation is not followed
experimentally but it is worthwhile to notice that the time when the sulphite
is completely depleted corresponds logically to the oxygen recovery in the
liquid phase. From transient
modelling, it is also of great interest to follow oxygen concentration in the
gas phase, both in the riser and the downcomer (figure 2). Bubble oxygen
concentration in the riser is weakly affected during the sulfite consumption
but this is not the case in the downcomer where the concentration drops to
around 130 mg/l and 150 mg/l (plateau value). This significant decrease is due
to a poor renewal of the bubbles in the downcomer, which is typical in an
airlift reactor (Talvy et al 2007).
 In the riser |
In the downcomer |
2: oxygen concentration in the gas (mg/l) at
superficial gas velocities  ── : 0.017
m/s, ── : 0.045 m/s The value of the
plateau of oxygen concentration in the gas in the downcomer and the riser is
also analytically developed thanks to stationary state in the oxygen
concentration during sulfite consumption. A simplified model is then proposed
to estimate accurately the mass transfer coefficient with the sulfite method
instead of solve the full ordinary differential equations (ODE). The sensitivity of the
oxygen transfer towards the initial sulfite concentration is then analyzed, as such
as the different methods of mass transfer coefficient estimation (nitrogen,
fully loaded bubbles, and sulfite consumption). According to the method used to
measure the mass transfer coefficient, it is shown with the full ODE model that
its value can significantly vary in the case of an airlift reactor due to poor
bubble renewal mainly in the downcomer. The nitrogen method gives the lower estimated
value of mass transfer, the fully loaded bubbles method usually used in CFD
gives the highest asymptotic value and the sulfite method gives intermediates
results depending on the renewal off the bubbles. A transient global modelling
is thus of great interest to better understand gas-liquid transfer in loop
reactors such airlift and to propose an accurate estimation of mass transfer
coefficient when poor bubble renewal involve oxygen impoverishment. References
Van Baten JM, Ellenger
J, Krishna R. Using CFD to describe the hydrodynamics of internal airlift
reactors. Canadian Journal of Chemical Engineering. 2003; 81: 660-668.
Cockx A, Liné A, Roustan M, Doquang Z and Lazarova
V, Numerical simulation and physical
modelling of the hydrodynamics in an air-lift internal loop reactor. CES, 1997; 52(21-22): 3787-3793.
Couvert
A., D. Bastoul, M. Roustan, P.Chatellier, 2004a, Hydrodynamic and mass transfer
study in a rectangular three-phase air-lift loop reactor, Chemical Engineering
and Processing, 43, 1381-1387.
Darmana
D., Deen N.G., Kuipers J.A.M., 2005, Detailed modeling of hydrodynamics, mass
transfer and chemical reactions in a bubble column using a discrete bubble
model, CES, 60(12), 3383-3404.
Hydrodynamic model for three-phase internal and external loop airlift reactor. CES 54, 5253?5258
(1999)
Heijnen, J.J.,
Hols,J., van der Lans, R.G.M.M,., van Leeuwen H.L.J.M, Mulder A., Welteverde
R., ?A simple hydrodynamic model for liquid circulation velocity in a full
scale two- and three-phase internal airlift reactor operating in the gas
recirculation regime?, CES Vol 52, 2527-2540 (1997)
RF, van den Akker HEA, 2D and 3D simulations of an internal airlift loop
reactor on the basis of a two-fluid model. CES. 2001; 56: 6351-6358. Talvy S., A. Cockx, A.Liné, 2007a, Modeling of
hydrodynamics of gas-liquid airlift reactor, AIChE Journal, 53, 2, 335-353. Talvy S., A. Cockx, A. Liné, 2007b, Modeling of oxygen
mass transfer in gas-liquid airlift reactor, AIChE Journal, 53, 2, 316-326.