INTRODUCTION
Gasliquidsolid three phase sparged reactor have been widely used in petrochemical,
metallurgical, environmental and cool liquefaction process. They are the preferred
reactor type of synthesis gas conversion. They are flexible and may be tailored
to produce high quality transportation fuel and a verity of products. Thus it
is essential to improve its performance through the understanding of its hydrodynamic
properties. Several empirical correlations have been proposed for the estimation
of these hydrodynamic parameters but they are restricted in their application
to the geometry of which they were determined (Chen et
al., 1995; Wang et al., 2003; Majumder
et al., 2006).
Recently, many publications have established the potential of Computation Fluid
Dynamic (CFD) to describe the hydrodynamic characteristics of two phase system
like (Pfleger et al., 1999; Sokolichin
and Eigenberger, 1999) and some searchers reported modeling of pilot plant
size bubble column (Krishna et al., 2000; Krishna
and Van Beter, 2002; Van Beter et al., 2003;
MitraMajumdar et al., 1999; Padial
et al., 2000 ; Gamw et al., 1999).
But still most of these researches are limited to two and three phase system
for Newtonian liquid and little of them used to study CFD simulation with nonNewtonian
liquid.
The aim of this research is to study the gas flow structure inside a
pilot plant size slurry reactor with nonNewtonian liquid. The model system
used and especially the solid material have chosen to resemble the flow
situation inside a bubble column bioreactor.
THEORETICAL MODEL
The stress deformation behavior of nonNewtonian fluid can be represented by
the general HerschelBulkley model (Carreau et al., 1997).
For power, low model it was commonly used the OstwaldDewaele constitutive
equation which is the simplification of the HerschelBulkley relationship in
the absence of shear stress:
Note that the above equations restore the Newtonian low of viscosity
when the yield stress is zero or when the power low index is unity.
In this model it’s assumed that, for three phase slurry reactor, the
liquid phase is the continues phase while gas and solid are the dispersed
phases, according to their volume fraction. The continuity and momentum
conservation equations for gas and liquid phases in the Eulerian form
are applied.
The global assumptions involved are: isothermal steady state, axisymetric,
incompressible flow, the added mass and lift forces contributions were both
ignored and the drag force contribution between the continuous and the dispersed
phases had been included in keeping with studies of Sanyal
et al. (1999) and Sokolichin and Eigenberger (1999).
The conservation Eq:
The continuity Eq. for k phase:
Momentum Eq. for gas phase:
Momentum Eq. for liquid phase
The momentum balance equation for liquid phase is appropriate for Newtonian
liquid. It has been successfully determined that the momentum balance equations
for Newtonian liquid also apply to nonNewtonian liquids (Liu
and Masliyah, 1998) and the only difference is in the effective viscosity.
So, the effective viscosity for nonNewtonian liquid will be used instead of
the usual viscosity of Newtonian liquid.
The drag force exerted on the gas phase Fgl is a result of relative motion
between the flowing phases to oppose slip, neglecting the force between
the two dispersed phases gas and solid. The forces exerted on liquid phase
involve; the drag forces Fls experienced by the liquid due to shear, nearby,
the liquidsolid boundary and Fgl the gasliquid interfacial force.
Drag coefficient of gas phase was calculated depending on (Mpandelis
and Kelessidis, 2004) for nonNewtonian system as:
To avoid the complexities of turbulent in our model at higher superficial
velocity, only the laminar flow will be considered.
The slip velocity between liquid and gas velocity was also used in this
model.
For nonNewtonian liquid and for low gas hold up slip velocity can be calculated
depending on Clark and Flememer (1985).
NUMERICAL SOLUTION
Numerical solution of the form of equations listed before was made using
a finite volume technique with appropriate initial and boundary condition.
The mesh cells are fixed in two dimensional spaces. The scalar variables
are located at the cell and the vector variables at the cell boundary.
The momentum equation is solved using staggered mesh. The geometrical
method assumed an axial symmetry and the vessel was divided into 82x82
computation cells.
EXPERIMENTAL WORK
Experiments were carried out in a QVF vessel with 0.5 m inside diameter
and 1 m total height (Fig. 1) with static clear height
to vessel diameter of 1.1.
A stationary solid of alumina (Al_{2}O_{3}) with particle
size 500μm and solid loading 2 kg were used and a continues flow
gas of compressed air that passed through two calibrated flow meters and
distributed to the vessel through a single ring distributor made from
copper.
The liquid phase is a nonNewtonian solution of polyacrylamide (PAA) with different
concentrations (0.01, 0.03, 0.05 and 0.07 wt%). Different solutions were prepared
by dissolving highly purified and highly viscous polyacrylamide powder in water.

Fig. 1: 
Experimental approach 
The resulting solutions exhibited a pseudoplastic rehological behavior which
was well represented by means of simple power low Ostwald DeWaels model. The
consistency index k and power low index n fitted for each process and shown
in Table 1.
In order to measure the bubble characteristic of bubble rise velocity, bubble
diameter, and gas hold up a bubble monitoring and analytical system was used
which consists of a modified electrocunductivity probe (tips). It was similar
to that of (Burgress and Calderbank, 1975) but it consists
of four tips instead of two.
RESULTS AND DISCUSSION
Figure 2 shows the steady state radial velocity profile
from 2D simulations of the gas and liquid phases are shown in. All these
steady state values were determined at a position 20 cm above the distributor
and reported below. The flow structures that developed in three phase
bubble column far away from sparger is expected to mainly consists of
a parabolic radial profile of axial liquid and gas velocity. This is due
to the fact that large bubbles are rising quickly in the center of the
column dragging liquid with them, continuity consideration them lead to down flow area
close to the reactor wall, as it shown in Fig. 2.

Fig. 2: 
Radial liquid velocity distribution 

Fig. 3: 
Radial distribution of gas velocity with 0.01% of PAA 
Figure 2 shows that the predicted liquid velocity distribution
decreased with increasing of PAA concentration (and thus liquid viscosity).
At the center of the column, for example, the liquid velocity is 0.32
m sec^{1} in 0.01% PAA concentration; this value decreased to
0.27 m sec^{1} in 0.07% PAA concentration. This can be attributed
to that increasing of PAA concentration means an increase in effective
viscosity, i.e., increasing in liquid viscous force, also it can be attributed
due to the increase in bubble diameter (size), these large bubbles don’t
generate sufficient liquid circulation.

Fig. 4: 
Radial distribution of gas velocity with 0.03% of PAA 

Fig. 5: 
Radial distribution of gas velocity with 0.05% of PAA 
Table 2: 
The experimental results of gas velocity at different axial
position and PAA concentration 


Fig. 6: 
Radial distribution of gas velocity with 0.07% of PAA 
The experimental results of gas velocity at different axial positions
and different gas concentration are shown in Table 2.
It could be noticed from this table that gas velocity increases with increasing
PAA concentration. This Increasing is coupled with decreasing in gas hold
up. The later decreasing can be explain on the basis of hindered gas bubble
motion in viscous fluid, in which at very height drag forces will be height
enough to cause bubble coalescence. This means increasing PAA concentration
causes an increase in its viscous force that will depress bubble breakup.
The ability to compare the model prediction results with the corresponding
experimental data obtained with gas nonNewtonian solid system could be shown
in Fig. 3 6. These figures show the radial
gas velocity, experimentally and theoretically. It can be seen that the curves
corresponding well to the measured local gas velocity and the largest difference
simulation and experimental are detected in the region close to the center of
the column. This large difference may be due to the symmetry assumption and
to the absence of the continuity balance of the solid phase as well as to the
absence of third dimension .
The simulated gas flow pattern can shown in Fig. 7,
representing the central up flow and down flow at the wall. Also, in agreement
with experimental observation the model predicts that for a given gas
velocity an increasing in PAA concentration caused a decrease in its value,
for example at the center of the column the gas velocity in 0.01% PAA
concentration is 0.54 m sec^{1} and the predicted one is 0.68
m sec^{1} these values decrease to 0.4 and 0.51 m sec^{1},
respectively in 0.07% PAA concentration and this is due to the height
viscous force of the liquid.
CONCLUSIONS
In this study, a two dimensional model of CFD technique has been used
to describe the gas and liquid velocity distribution in slurry bubble
column for three phase reactor containing a nonNewtonian liquid. This
model based on the continuum and momentum equations and it seems to predict
reasonable radial profiles of velocity for gas and liquid.
The simulated liquid velocity was found to have the parabolic shape.
It decreases with increasing PAA concentration due to the increase of
viscous force.
The distribution of gas velocity also has the parabolic shape with increasing
in its value with increasing of flow consistency.
NOMENCLATURE
CD 
: 
Drag coefficient 
db 
: 
Bubble diameter (m) 
dp 
: 
Particle diameter (m) 
Fgl 
: 
Gasliquid interfacial force (N m^{1}) 
Fsl 
: 
Solidliquid interfacial velocity (N m^{1}) 
g 
: 
Gravity acceleration (N m^{1}) 
k 
: 
Consistency index (kg /ms^{2}n ) 
n 
: 
Flow behavior index 
P 
: 
Pressure 
Re 
: 
Reynold number 
uS 
: 
Slip velocity (m sec^{1}) 
Vb 
: 
Bubble rise velocity (m sec^{1}) 
VG 
: 
Gas velocity (m sec^{1}) 
VL 
: 
Liquid velocity (m sec^{1}) 
GREEK SYMBOLS
γ 
: 
Shear rate (sec^{1}) 
ε_{g} 
: 
Gas hold up 
ε_{L} 
: 
Liquid hold up 
ε_{S} 
: 
Solid hold up 
μ_{eff} 
: 
Effective viscosity (kg/ms) 
ρ_{G} 
: 
Gas density (kg m^{3} ) 
ρ_{L} 
: 
Liquid density (kg m^{G3} ) 
ρ_{S} 
: 
Solid density (kg m^{3}) 
σ 
: 
Surface tension (N m^{1}) 
τ 
: 
Shear stress (Pa) 
τ_{0} 
: 
Yield stress (Pa) 