Research Journal of Chemistry and Environment______________________________________Vol.15 (2) June (2011) Res.J.Chem.Environ
Mathematical Model using Statistical Design of Experiments for the Determination of Minimum Fluidization Velocity in Inverse Fluidized Bed Bioreactor with Non-Newtonian Fluids Ashir A., Sivasubramanian V.,* Haribabu K. and Selvaraju N.
National Institute of Technology Calicut, Department of Chemical Engineering, Kozhikode, Kerala 673601, INDIA *
[email protected]
Abstract Fluidization is an operation, which involves the flow of solids in contact with gas, liquid or gas and liquid. Fluidized bed reactors are characterized by small pressure drop; high heat and mass transfer rates. Fluidized bed systems have proved their versatility in carrying out aerobic fermentation processes, bio-treatment of wastewater, refineries and hydro metallic operations, biochemical engineering and polymeric industries. In recent years considerable effort has been made in exploring and understanding the hydrodynamics of fluid flow and heat and mass transfer in two- and threephase fluidized beds. Inverse fluidization is a relatively new technique in which solid particles having density lower than the liquid phase are kept in suspension by a downward flow of continuous liquid phase. In three-phase systems with inverse fluidization, the gas phase is introduced counter currently to the liquid phase at the bottom of the reactor. The three-phase inverse fluidized bed technique seems very promising in the realization of biotechnological processes and application of novel organic catalysts.
Although similar advantages can be achieved in regular fluidized beds, with co-current upward gas and liquid flow, a slight decrease in particle density caused by gas evolution would result in considerable particle entrainment. Inverse threephase fluidized beds are not affected by this problem and have been successfully applied to wastewater treatment. The wide occurrence of non-Newtonian fluids has recently motivated the investigation of the flow behavior of these fluids in multi-particle systems. In the present study, various hydrodynamic characteristics on two-phase and three-phase inverse fluidized bed bio-reactors (IFBR) with non-Newtonian (0.02%, 0.04%, 0.06% and 0.08% aqueous solutions of Xanthan gum) liquid were investigated. Two types of particles having different characteristics 3 polypropylene (ρs=830 kg/m ) and low-density polyethylene (ρs=940 kg/m3) of 8 mm were used. Influence of various parameters such as concentration of the fluid, bed height, superficial liquid velocity and superficial gas velocity on minimum liquid and gas fluidization velocities was analyzed. Combined effect of parameters was studied by using Response Surface Methodology(RSM).
The important parameter involved in the design of fluidized bed technology is bed expansion and minimum fluidization velocity. The knowledge of this parameter not only facilitates the sizing of the equipment for an envisaged application but also exerts a significant influence on the performance of the fluidized bed as a heat or mass transfer exchanger and or as a chemical reactor. The main advantage of three-phase inverse fluidization is that the solids can be fluidized at low liquid velocity; minimize energy consumption and with low solids attrition.
The influence of operational parameters and effect of viscosity on minimum fluidization velocity Umf in a two-phase and Ulmf (minimum fluidization liquid velocity) and Ugmf (minimum fluidization gas velocity) in a three-phase inverse fluidized bed reactor was investigated using lowdensity polyethylene (LDPE) and polypropylene (PP) particles. It is found that minimum fluidization velocity, Umf decreased with an increase in concentration.
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Research Journal of Chemistry and Environment______________________________________Vol.15 (2) June (2011) Res.J.Chem.Environ Key words: Inverse fluidized bed bioreactor, minimum fluidization velocity, hydrodynamics, response surface method, low density particles, non-Newtonian liquid.
investigation, the bed expansion characteristics of threephase inverse fluidized bed reactor is studied with different diameters of LDPE and PP particles in nonNewtonian fluid (aqueous solutions of Xanthan gum) to determine the minimum gas fluidization velocity. Combined effects of parameters were studied by using Response Surface Methodology (RSM).
Introduction Inverse fluidization is a relatively new technique in which solid particles having density lower than the liquid phase are kept in suspension by a downward flow of continuous liquid phase. In the three-phase systems with inverse fluidization, gas phase is introduced counter currently to the liquid phase at the bottom of the reactor. The three-phase inverse fluidized bed technique seems very promising connected with the realization of biotechnological processes and application of the novel organic catalysts because it is characterized by a high gas hold-up1. Kawase and Ulbrecht2 developed an expression for the minimum fluidization velocity by using the results of power law fluid motion over assemblages of solid spheres. Kumar and Upadhyay3 measured mass transfer and pressure drop during flow of Newtonian and non-Newtonian fluids through fixed and fluidized beds of uniformly sized cylindrical pellets and spheres. They used demineralized water and 1.0% aqueous carboxy methyl cellulose (CMC) solution as the fluids.
Materials and Methods Measurement of physical properties of particles: The diameters of various particles were found out using a micrometer. The densities were measured by weighing a known number of particles and the values are given in Table. I. Measurement of properties of liquids: The viscosity of different concentrations of aqueous Xanthan gum solution was determined using Brookfield viscometer. Values are given in Table II. Measurement of bed expansion and pressure drop in a three-phase inverse fluidized bed reactor: In three
phase-systems (gas-liquid-solid) with inverse fluidization, gas phase is introduced countercurrently to the liquid phase at the bottom of the reactor. Hydrodynamic characteristics viz. bed expansion and pressure drop of three phase inverse fluidized bed were determined. Two types of particles viz. LDPE, PP of diameter 8 mm were used.
Kawase and Moo-Young4 developed a hydrodynamic model for the liquid phase in bubble column. Machac et al5 investigated experimentally fluidization of spherical-particle beds with viscoelastic shear thinning polymer solutions in creeping- and transient-flow regions. Kawase and Hashimoto6 performed experiments in two model external-loop airlift bioreactors with aqueous solutions of carboxy methyl cellulose (CMC) and xanthan gum representing nonNewtonian flows. Miura and Kawase7 determined the minimum fluidization velocities using measurements of flow rate and pressure drop for non-Newtonian fluids in two- and three-phase fluidized beds. Aqueous solutions of carboxy methyl cellulose and xanthan gum have been used as the non-Newtonian liquids. Miura et al8 examined the bed expansion characteristics in Newtonian and non-Newtonian fluid-solid two-phase fluidized bed.
Experimental procedures: The experimental set-up of the three-phase inverse fluidized bed reactor is shown in Fig 1. The column (100 mm) was made up of Perspex with a maximum height of 1800 mm and a wall thickness of 3 mm. The column consisted of three sections, namely liquid distribution section, test section and the liquid discharge section. The liquid distribution section comprises an inverted conical shape liquid distributor and an overflow arrangement to maintain a constant liquid level inside the column. An air vent is also provided at the top of the column. The test section consists of a wire mesh provided both at the top and the bottom to prevent the elutriation of the particles. Above the liquid discharge section, the gas sparger is provided for airflow. The airline is connected to a compressor through a calibrated flow meter. The liquid discharge section connects a pipe to transfer the liquid to the tank so that it is recirculated. A control valve is also provided in the discharge line to adjust the flow-rate. All runs were made at room temperature.
The wide occurrence of non-Newtonian fluids has recently motivated the investigation of the flow behavior of these fluids in multi-particle systems. Examples of such flows include the flow of oil through porous rock, the movement of aqueous polymer solutions through sand and sand-stone in tertiary oil recovery, the filtration of polymer solutions and slurries, the flow of non-Newtonian liquids through the ionexchange beds, catalytic polymerization in hydroxydation processes, etc. In the present
A known quantity of solid particles was loaded through the provision in the test section. The pump was (2)
Research Journal of Chemistry and Environment______________________________________Vol.15 (2) June (2011) Res.J.Chem.Environ started and the column was filled with the liquid. An inverted U-tube manometer was used for the measurement of the pressure drop across the column. Prior to each experimental run the solid particles were fully fluidized subsequently the flow rate of liquid was gradually reduced until the solids rise up slowly to form a packed bed (Initial bed height). Then the airflow was introduced at the bottom. At a particular airflow rate, the liquid flow-rate was varied to observe the variation of bed height. The flow rate corresponding to the point where the bed heights just start changing was determined. The same procedure was repeated for a particular liquid flow-rate and varying gas flow-rate. The ranges of variables used for hydrodynamic studies in three-phase inverse fluidized bed reactor were given in Table III.
Where ‘Y’ is the response, ‘ƒ’ is the unknown function of response, X1, X2,……….Xn denote the independent variables, also called natural variables, ‘n’ is the number of independent variables and finally ‘e’ is the statistical error. These sources include the effects such as the measurement error. It is generally assumed that ‘e’ has a normal distribution with mean zero and variance. The design procedure of RSM is as follows: 1. Designing of series of experiments of adequate and reliable measurement of the response of interest. 2. Developing a mathematical model of the second order response surface with the best fittings. 3. Finding the optimal set of experimental parameters that produce a maximum or minimum value of response. 4. Representing the direct and interactive effects of process parameters through two and three dimensional plots.
Development of mathematical model and statistical design of experiment by Response Surface Methodology (RSM): Conventional and classical methods of studying a process by maintaining other factors involved at an unspecified constant level does not depict the combined effect of all the factors involved. This method is time consuming and requires large number of experiments to determine optimum levels, which are unreliable. These limitations of a classical method can be eliminated by optimizing all the affecting parameters collectively by statistical experimental design. Response surface methodology, first described by Box. G. E. P and Wilson. K. N is an experimental approach to identify the optimum conditions for a multivariable system.
Results and Discussion Effect of Ug, Static bed height and concentration of xanthan gum on Ulmf: The combined effect of Ug, static bed height and concentration of xanthan gum on Ulmf is studied by using Response Surface Methodology. Figure 2, 3 and 4 shows the variation of Ulmf with superficial gas velocity and bed height, by fixing the concentration values. From the contour plots it is found that, at constant gas velocity and concentration Ulmf increases with increase in bed height.
RSM has important application in the design, development and formulation of new products, as well as in the improvement of existing product design. It defines the effect of the independent variables, alone or in combination, on the process. In addition to analyzing the effects of the independent variables, this experimental methodology generates a mathematical model which describes the chemical or biochemical process. RSM consists of mathematical and statistical techniques that can be used to define the relations between the response and the independent variables. RSM defines the effect of the independent variables, alone or in combination, on the processes. In addition to analyzing the effects of the independent variables, this experimental methodology also generates a mathematical model. The graphical perspective of the mathematical model has led to the term response surface methodology.
The effect is more at higher gas velocity and lower concentration. As concentration increases the effect decreases. At constant bed height and concentration Ulmf decreases with increases in gas velocity. For lower solid loading the effect is predominant. As the bed height increases with constant value for concentration the variation in Ulmf with gas velocity decreases. But with increase in concentration Ulmf also increases. From the plots it is clear that at higher superficial gas velocities, with lower concentration of fluid, Ulmf decreases tremendously and one point even at zero liquid velocity fluidization begins that is at batch condition. It was experimentally observed that for batch liquid condition (zero liquid flow rates) layer by layer expansion occurred from the bottom of the bed. A close observation revealed that this expansion was due to the recirculation of the liquid near the wall, which was created by the gas. The bed expansion is smooth in the presence of gas phase either for batch liquid (Ul=0) or liquid flows through the column since the average
The relationship between the response and the input is given in equation below: Y = ƒ (X1, X2, X3,……………Xn) + e (3)
Research Journal of Chemistry and Environment______________________________________Vol.15 (2) June (2011) Res.J.Chem.Environ density of the fluid medium decreases making the particle less buoyant. The bed expansion is smooth for particles having density closer to that of liquid. It should be noted that recirculation velocities of liquid alone are insufficient to expand the bed if the density difference is very large beyond a particular particle size9.
Response Surface Methodology. The Ulmf decreased with an increase in Ug in air-xanthan gum solution with PP and LDPE particles. For non-Newtonian system (xanthan gum solution), with an increase in viscosity (concentration) both Ulmf and Ugmf decreased. The Ugmf decreased with an increase in Ul for the systems investigated. Combined effect of various parameters was studied using Response Surface Methodology. Effect of Ug, Static bed height and concentration of xanthan gum on Ulmf and effect of Ul, Static bed height and concentration of xanthan gum on Ugmf, were analyzed.
Effect of Ul, Static bed height and concentration of xanthan gum on Ugmf: The combined effect of Ul,
static bed height and concentration of xanthan gum on Ugmf is studied by using Response Surface Methodology. Figure 5,6 and 7 shows the variation of Ugmf with superficial gas velocity and bed height, by fixing the concentration values. From the contour plots it is observed that, at constant liquid velocity and concentration, Ugmf decreases with increase in bed height.
Table I Properties of solid particles
The effect is more at lower liquid velocity and lower concentration. As concentration increases the effect decreases and after certain value for concentration it is observed that Ugmf increases with increase in solid loading at constant superficial liquid velocity. Ugmf decreases with increase in superficial liquid velocity for constant value of bed height and concentration for higher values of concentration and bed height. It is observed that Ugmf increases with increase in superficial liquid velocity.
Particle
Diameter, dp (mm)
Initial Porosity, ε0
Density, ρs (kg/m3)
LDPE PP
8 8
0.431 0.433
940 830
Table II Physical properties of aqueous solutions of Xanthan gum Concentration of Density, Viscosity, 3 Xanthan gum ρl (kg/m ) μl (mPa.s) solution
Statistical model for non-Newtonian system: Mathematical model for Ugmf in terms of concentration, bed height and Superficial liquid velocity with R2 = 0.99.
0.02%
1000.466
5.554
0.04%
1000.506
5.659
0.06%
1000.685
5.764
0.08%
1000.794
5.869
Table III Ranges of variables used for hydrodynamic studies in three-phase inverse fluidized bed reactor 100 mm Column diameter, Dc 1800 mm Column height, Hc Gas sparger dimensions 1 mm Diameter of hole 5 mm Pitch (triangular) Particle diameter, dp 8 mm Low-density Polyethylene 8 mm (LDPE) Polypropylene (PP) Superficial liquid velocity, Ul 0-0.02005 m/s Superficial gas velocity, Ug 0-0.00024 m/s Concentrations aqueous 0.02%, 0.04%, solution of Xanthan gum 0.06%, 0.08%. (weight % in water)
U gmf = 0.000604 − 0.00224 X 1 − 0.000025 X 2 − 0.016958 X 3 + 0.00012 X 1 X 2 + 0.000599 X 2 X 3 + 0.0399 X 1 X 2 X 3 Mathematical model for Ulmf in terms of concentration, bed height and Superficial gas velocity with R2 = 0.98.
U lmf = 0.0377435 − 0.086 X 1 − 0.0018 X 2
− 175.196 X 3 + 0.014 X 1 X 2 + 450.88 X 1 X 3 + 12.35 X 2 X 3 − 83.46 X 1 X 2 X 3
Conclusion The hydrodynamic characteristics of two-and three-phase inverse fluidized bed were experimentally investigated. Individual and combined effect of various hydrodynamic characteristics was analyzed. Combined effect of various parameters was studied by using
List of Symbols (4)
Research Journal of Chemistry and Environment______________________________________Vol.15 (2) June (2011) Res.J.Chem.Environ
εo
Column diameter, m Particle diameter, m Column height, m Superficial gas velocity, m/s Minimum gas fluidization velocity, m/s Superficial liquid velocity , m/s Minimum liquid fluidization velocity, m/s Density of liquid, kg/m3 Density of solid, kg/m3 Viscosity of solution, mPa. s Initial porosity
Parameters in high level 0.8
0.000 0.004 0.008 0.012
0.4 gas velocity
Dc dp Hc Ug Ugmf Ul Ulmf ρl ρs µl
U lmf < – – – – >
0.000 0.004 0.008 0.012 0.016 0.016
H o ld Valu es c o n c en tratio n 1
0.0
-0.4
-0.8 -1.0
-0.5
0.0 bed height
0.5
1.0
Fig.4 Contour plot for Ulmf Vs gas velocity and bed height by holding higher value for concentration Sparger Distribut or plate Solid
Rota meter
°
Control
Air
Bypas
Manometer
Fig 1 The schematic diagram of Inverse Fluidized Bed Reactor
Fig.5 Contour plot for Ugmf Vs liquid velocity and bed height by holding lower values for concentration
Parameters in low level Ulmf < – – – – – – >
0.8
0.002 0.004 0.006 0.008 0.010 0.012
gas velocity
0.4
0.0
0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.014
Hold Values concentration -1
-0.4
-0.8 -1.0
-0.5
0.0 bed height
0.5
1.0
Fig. 2 Contour plot for Ulmf Vs gas velocity and bed height at lower concentration Fig. 6 Contour plot for Ugmf Vs liquid velocity and bed height by holding middle values for concentration
Parameters in middle level Ulmf < – – – – >
0.8
0.003 0.006 0.009 0.012
gas velocity
0.4
0.003 0.006 0.009 0.012 0.015 0.015
Hold Values concentration 0
0.0
-0.4
-0.8 -1.0
-0.5
0.0 bed height
0.5
1.0
Fig. 3 Contour plot for Ulmf Vs gas velocity and bed height by holding middle value for concentration
Fig. 7 Contour plot for Ugmf Vs liquid velocity and bed height by holding higher values for concentration
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Research Journal of Chemistry and Environment______________________________________Vol.15 (2) June (2011) Res.J.Chem.Environ Sci., 43, 2109 (1993).
References 1.
Nikolov V.R. and Nikov I., Hungarian J. Ind. Chem., 22, 125 (1994).
6.
Kawase Y. and Hashimoto N., J. Chem. Tech. Biotechnol., 65, 325 (1996).
2.
Kawase Y. and Ulbrecht J.J., Chem. Eng. Sci., 36, 1193 (1981).
7.
Miura H. and Kawase Y., Powd. Technol., 97, 124 (1998).
3.
Kumar S. and Upadhyay S.N., Ind. Eng. Chem. Fund., 20, 186 (1981).
8.
Miura H., Takahashi T., Ichikawa J. and Kawase Y., Powd. Technol., 117, 239 (2001).
4.
Kawase Y. and Moo-Young M., Chem. Eng. Sci., 41, 1969 (1986).
9.
Renganathan T. and Krishnaiah K.., Can. J. Chem. Eng., 81, 853 (2003).
5.
Machac I., Mikulasek P. and Ulbrichova I., Chem. Eng.
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