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Jet ejector efficiency has been defined by researchers in different ways, like target efficiency, collection efficiency, overall efficiency and fractional efficiency (Mohebbi et al., 2003; Pulley 1997; Yung et al., 1977; Leith et al., 1985; Boll 1973; Calvert 1970). The overall collection efficiency is defined as
For particulate matter
For gaseous pollutant: Taheri et al. (2008) defined collection efficiency (the extentof absorption) as
where are the initial, final, and equilibrium partial pressure of gaseous pollutant in mm of , respectively
Collection efficiency have been reported with respect to gas/liquid ratio, gas and liquid flow rates , geometry of venturi scrubber like projection ratio length of throat, angle and length of convergent diffuser section and property of particulate/gas pollutants. Researchers have reported different empirical correlations to predict efficiency on the basis of different assumptions they have considered. The vast literature has been published on the subject. Table 2.6 is the summery of some of the earlier research. Typical graphical presentations are shown in Figure 2.15, 2.16, 2.17 and 2.18. E:\images\4.5.jpg
Figure 2.15 : Dependence of the overall collection efficiency of liquid gas ratio
(Vishwanath et al., 1997).
Figure 2.16 : The effect of throat gas velocity on the collection efficiency in venturi scrubber (GA-ANN no. 1). (Taheri et al., 2008)
E:\images\4.7.jpgFigure 2.17 : Effect of variation in venturi number and aspect ratio on collection efficiency for a constant venturi number.
(Ananthanarayanan and Vishwanathan, 1998)
E:\images\after 4.2 jet ejector.jpgE:\images\after 4.2 jet ejector 1.jpg
Figure 2.18 : Efficiency as a function of (A) particle diameter (B) liquid to gas ratio with liquid surface tension as a variable. (Ott el al., 1987)
Ott et al. (1987) developed a model studying the effect of surface tension on performance of venturi scrubber. They examined the effect of liquid surface tension on droplet size and on particle penetration into the droplet. (Figure 2.18A and B)
Economopoulou and Harrison (2007) developed graphical tools for estimating the overall collection efficiency of venturi scrubbers under the specified design and operating conditions based on the well-established theoretical formulations of Calvert (1970) and Yung et al. (1978).
Taheri et al. (2010) simulated gas absorption in a venturi scrubber and developed a
three-dimensional mathematical model, based on a non uniform droplet concentration distribution. They validated their model with the experimental data reported by Johnstone et al. (1954) and Wen and Fan, (1975) for removal by using alkaline solution and . They used Lagrangian approach for water droplet movement. Yung et al. (1978) and Crowder et al. (1981) have developed mathematical models to study different parameters of high energy venturi scrubbers.
2.3.2 Jet ejectors
The application of jet ejector as vacuum producing device and as jet pump is well known
(Gamisans et al., 2004; Govatos, 1981; Cunningham, 1974; Cunningham and Dopkin, 1974; Bonnington, 1956, 1960, 1964; Bonnington and King, 1972; Blenke et al., 1963; Kroll, 1947). With the fast growth of chemical process industry, their use as entraining and pumping device to handle corrosive fluids, slurries, fumes and dust laden gasses has increased. Their use as mass transfer equipment for liquid-liquid extraction, gas absorption, gas stripping, slurry reaction like hydrogenation, oxidation, chlorination, fermentation, etc. has increased. Due to increasing interest in the usage of jet ejectors, number of investigators have attempted to optimize their performance. (Das and Biswas, 2006; Gamisans et al., 2004; Gamisans et al., 2002; Dasappa et al., 1993; Mukharjee et al., 1988,1981; Radhakrishnan and Mitra, 1984; Pal et al., 1980, 1975; Biswas et al., 1977, 1975; Acharjee et al., 1975;Â Singh et al., 1974; Bhat et al., 1972; Davis et al., 1967; Mitra and Roy,1964; Mitra et al., 1963).
Working of jet ejector
A jet ejector is a device in which suction, mixing and dispersion of secondary fluid is done by utilizing the kinetic energy of a motive (primary) fluid. Das and Biswas (2006) stated that when jet ejectors are used as a device for contacting gas-liquid , the secondary fluid may be dispersed by the shearing action of the high velocity motive fluid or the motive fluid itself may get dispersed when it is arrested by a secondary fluid. Figure 1.1 shows the typical ejector system in which the jet of primary fluid issuing out of a nozzle creates a low pressure region around it. The pressure differential between the entry point of the secondary fluid and the nozzle tip provides the driving force for entrainment of the secondary fluid. Two principal flow regimes in ejectors are coaxial-flow and froth-flow. The coaxial-flow constitutes a central core of primary fluid with secondary fluid flowing in the annular region formed between the jet of primary liquid and ejector. Froth-flow regime is a co-current flow of fluids with one phase completely dispersed in the other. Witte (1969) termed the phenomenon of change from coaxial-flow to froth-flow as mixing shock. Here a part of the kinetic energy of the flow is dissipated in the shock creating the gas-liquid dispersion. The mixing shock results into generation of small bubbles and consequently creation of high interfacial area
(~ 2000m2/m3). Ejectors thus, give superior gas-liquid mass transfer rates and higher rates of reaction as compared to conventional gas-liquid contacting equipments like stirred tanks, bubble columns, packed columns, etc., Yadav and Patwardhan (2008) stated that there could be diverse objectives for ejector design depending on application as follows:
(a) To get large entrainment of the secondary fluid.
(b) To produce intense mixing between the two fluids.
(c) To pump fluids from a region of low pressure to a region of high pressure.
Geometry of ejector
The significant parts of an ejector are (Refer Figure 2.19) primary fluid inlet, suction chamber, secondary fluid inlet, converging section, throat or mixing zone, diverging section or diffuser. The ejector may be specified by denoting nozzle diameter , throat diameter , diameter of suction chamber , length of throat , length of diffuser , distance between nozzle to commencement of throat , angle of converging sections and angle of diverging sections . Performance of the ejectors has been studied in terms of (a) area ratio , i.e., area of throat/area of nozzle, (b) throat aspect ratio i.e., length of throat/diameter of throat, (c) projection ratio i.e., distance between nozzle tip to the commencement of throat / diameter of throat and (e) suction chamber area ratio .
Figure 2.19 : Schematic diagram showing geometry of an ejector
Dutta and Raghavan (1987) studied and compared the performance of jet ejectors with and without venturi and throat. Similarly Gamisans et al. (2002) studied jet ejector without diffuser. Both of them concluded that the jet ejectors without diffuser or throat are less effective compared to ejector with them.
Many researchers have studied the mass transfer characteristics and performance of the jet ejectors followed by contactors, draft tube, packed column or bubble column
(Li and Li, 2011; Rahman et al., 2010; Balamurugan et al., 2008, 2007; Utomo et al., 2008; Mandal, 2010; Mandal et al., 2005; 2004, 2003a, 2003b; Havelka et al., 2000, 1997; Dutta and Raghavan, 1987; Ogawa et al., 1983; Mitchell, 1981; Biswas et al., 1977). All have similar conclusion that there is less mass transfer coefficient in the extended portion compared to that in the ejector itself.
Effect of ejector geometry
Das and Biswas (2006) reported that the efficient functioning of an ejector depends on the design of the suction chamber, the mixing throat, the divergent diffuser and the forcing nozzle. Besides, the relative dimensions of the various parts of the ejector, the factors such as shape of the entrance to the parallel throat, angle of divergence and the projection ratio are also important factors to be considered.
Different investigators have studied the effect of geometry of jet ejector like area ratio, angle of convergence and divergence, projection ratio, shape of entry of convergent section, length of throat etc., Yadav and Patwardhan (2008) compiled dimensions of different components of ejectors studied by different investigators (See Table 2.7).
Area ratio (AR)
The area ratio is defined as the ratio of area of throat to area of the nozzle
Bonigton (1964) studied the effect of changing the diameter ratio i.e. ratio of nozzle diameter to throat diameter ( / ) instead of area ratio of the jet ejector performance. Acharjee et al. (1975), Singh et al. (1974), Bhat et al. (1972) and Mitra et al. (1963) studied the effect
of area ratio on Mass ratio (ratio of mass of driving fluid to the entrained fluid). It can be concluded from these studies that as the area ratio is increased the entrainment ratio also increases. But at the higher area ratio the increase in entrainment ratio becomes less. A typical correlation is shown in Figure 2.20.
*Indicate the optimum value suggested by the investigator
Table 2.7 : Geometrical parameters of ejectors used by deferent investigators
(Yadav and Patwardhan, 2008)
Figure 2.20 : Effect of area ratio on mass ratio for water-water system
(Singh et al., 1974)
The projection ratio () is defined as the ratio of the distance between the injecting nozzle to the commencement of throat () to diameter of throat ()
A typical plot of vs. is presented in Figure 2.21. It is observed that as rises the entrainment ratio is not much effected but at definite value of, the MR, rises suddenly and E:\images\4.10.jpg
Figure 2.21 : Variation of entrainment of air with projection ratio of water-air system
(Acharjee et al. 1975)
again falls to previous value. Thus the at which it draws maximum entrained fluid is considered to be optimum. Biswas et al. (1975), Acharjee et al. (1975) and Devis et al. (1967) had similarly observed that at around 2.10 is optimum. Singh et al. (1974) in their research study observed optimum as around 0.5. It has been suggested that the optimum is influenced by geometry of entrance to the mixing tube. Table 2.7 shows that the optimum value of suggested by the different investigators is different. Yadav et al., (2008) utilized computational fluid dynamics (CFD) modeling to study the role of , angle of converging section and diameter of suction chamber. They studied the effect of PR (0, 2.5, 5, 10 and 14.5) on entrainment, pressure profile along the axis of ejector and power efficiency. They concluded that the rate of entrainment and power efficiency increases as the projection ratio increases that is because of the fact when one increases the it leads to the reduction in the generation of radial flow. However beyond > 5 negligible amount of radial flow is generated and hence the rate of entrainment and energy efficiency remain constant. Hence it may be considered that the optimum projection ratio is 5 Figure 2.22).
Figure 2.22 : Effect of projection ratio (LTN/DT ) on energy efficiency
(Yadav and Patwardhan, 2008)
Diameter of suction chamber
Though cross sectional area of the suction chamber is important parameter which effects the performance of venturi, it has not been given the necessary attention. Yadav and Patwardhan (2008) studied the effect of diameter of suction chamber. To study the effect of suction chamber diameter they defined suction chamber area as
They concluded that maximum power efficiency (20 to 25%) is obtained for =6.6 and for > 13.6 it remain constant. (Refer Figure 2.23)C:\Documents and Settings\ARCHITECTURE\Desktop\2.23.jpg
Figure 2.23 : Effect of area ratio on efficiency of ejectors for different values of projection ratio (Yadav and Patwardhan, 2008)
Effect of angle of convergent section and divergent section
It can be seen from Table 2.7 that number of investigators have worked to find optimum angle of convergence and divergence. Yadav and Patwardhan (2008) studied the effect of angle of convergence on entrainment and efficiency. In Figure 2.24 entrainment for different angles: 2.5Ëš, 10Ëš, 30Ëš and 90Ëš has been shown. It can be seen that the rate of entrainment is low for Î¸ = 2.5Ëš. It increases with increase in Î¸ and attains a maximum value for Î¸ =10Ëš. Further increase in Î¸ results in decrease in the rate of entrainment of the secondary fluid. Similarly their study shows that the largest pressure driving force is generated for Î¸ = 10Ëš and it results in the highest entrainment for this case. With increase in Î¸ beyond 10Ëš the pressure driving force was observed to reduce and it results in decrease in the rate of entrainment. They also showed that highest efficiency is obtained at Î¸ =10Ëšand larger values of Î¸ results in poor energy efficiency. Thus, they suggested for obtaining maximum entrainment the angle of convergent may be kept between 5Ëš-15Ëš. The angle of divergent section has been kept between 7Ëš to maximum 10Ëš by many of the investigators.
Figure 2.24 : Effect of angle of converging section ï€¨ï±ï€© on rate of entrainment
(Yadav and Patwardhan, 2008)
Utomo et al. (2008) developed three dimensional CFD model to investigate mass transfer characteristics. They varied the gas-liquid flow ratio in the range of 0.2 to 1.2 and the length to diameter ratio of mixing tube (/) from 4 to 10. Their CFD studies show that at
, the volumetric mass transfer coefficient increases with respect to gas flow rate. They observed that at , the graph of volumetric mass transfer coefficient vs gas-liquid flow rate ratio reaches the maximum at gas-liquid flow rate ratio of 0.6. A remarkable observation in their study was that volumetric mass transfer coefficient decreases with the increase of mixing tube length. They validated results obtained from CFD with the experimental result (configuration of ejector has a mixing tube diameter of 22 mm and diffuser outlet diameter of 40 mm, diffuser angle of 3.5 and a draft tube length of 100 mm.). The mixing tube lengths are varied between 88 and 220 mm with the nozzle diameter of 8.5 mm.
Kandakure et al. (2005) developed a CFD model to understand the hydrodynamic characteristics of ejectors. They varied the value of the slip velocity between the phases for validation keeping nozzle velocity constant (at different height to diameter ratio of throat) to validate the model. They found that when the slip velocity is made 13% of the axial water velocity, it matches the experimental data very well. They found that the predicted air entrainment is the maximum for the ejector with height to diameter ratio of throat equal to zero and the area ratio of 4. They justified that the CFD simulations eliminate all such empiricism.
Kim et al. (2007) studied the effect of the ejector geometry (nozzle diameter and mixing chamber diameter) and the operating conditions (liquid circulating rate, liquid level in column) on the hydraulic characteristics in a rectangular bubble column with a horizontal flow ejector. They found that the gas phase holdup increases with increasing liquid circulating rate and decreases with increasing liquid level in the column. They applied the multiphase CFD simulation with the mixture model and concluded that the gas suction rate increases with increasing liquid circulation rate contrarily the gas suction rate decreases with increasing the liquid level in the column and nozzle diameter. The predicted values obtained from CFD simulation were compared with the experimental data, which were well matching.
Li and Li (2011) investigated the entrainment behavior and performance of gas-liquid ejectors using different software and computational technique like Computational Fluid Dynamics (CFD) and validated with experimental data over a wide range of operating conditions for ejector with different configurations.
2.3.3 Parameters other than geometry of the ejector
Many investigators (Gamisans et al., 2004, Gamisans et al., 2002, Brahim et al.1984; Bhutada, and Pangarkar, 1987; Acharjee et al., 1975, Singh et al., 1974; Bhat et al., 1972; Davis et al., 1967; Mitra and Roy 1964; and Mitra et al., 1963 ) studied effect of mass ratio (MR) as a function of motive pressure, suction pressure, separator pressure, pressure drop, AR, PR , Reynold's number, Euler's number etc. Some of investigators (Mitra et al., 1963; Bonington 1964) studied the effect of head ratio on ejector performance, head ratio is defined as:
where = pressure head at discharge of ejector, m; = pressure head at suction of ejector, m; and = operating pressure, m. The empirical equations to predict mass ratio (MR) from dimensionless analysis given by various authors are summarized in Table 2.7a. Similarly table 2.7b summarizes mass ratio (MR) correlations from theoretical analysis given by various authors.
Geometry and range investigated
Mass ratio correlation
Davies et al. (1967)
Water, glycerin, kerosene
Bhat et al. (1975)
Water, glycerin, kerosene
Acharjee et al. (1975)
Water, mono ethylene glycol
Ben Brahim et al. (1984)
Dutta & Raghvan (1987)
Bhutada & Pangarkar (1987)
Singh et al. (1974)
Table 2.7a : Mass ratio correlations from dimensionless analysis given by various authors (Balamurugan et al. (2007)
Geometry and range investigated
Geometry and the locations where the energy and momentum balance were taken
Correlation and remarks on loss coefficient
Bhat et al. (1975)
Primary fluid-water, glycerine and kerosene
All the losses are clubbed as loss factor and values of were fitted using experimental results
Secondary fluid-air maximum
was empirically fitted to and
Each area ratio has different and the value ranges from 0.01 to 0.06
Acharjee et al. (1975)
Water, glycerin, kerosene
All the losses are clubbed as loss factor and was fitted to match
the experimental values
Each area ratio has different and value ranges from 0.01 to 0.28
Total suction was obtained for single phase from loss at each section
Biswas and Mitra (1981)
Primary fluid-water, nacl, acetone-water mixture (30%) and glycerol (30%)
Total suction created partially utilized for entrainment and dispersion
and are fitted from experimental data
Flow-horizontal: review of existing data, single phase
Total loss coefficient = 1 âˆ’ diffuser efficiency + oss coefficient of throat
and were obtained from experimental data of previous authors also single loss coefficient was proposed. Value of ranges from 0.21 to 0.34
Table 2.7b continued
Continued from previous page
Brahim et al. (1984)
Primary fluid-water, mono ethylene glycol
All the losses are clubbed as loss factor and was fitted with
experimental values. Values of ranges from 3-7
Maximum L/G = 15
Table 2.7b : Mass ratio correlations from theoretical analysis given by various authors
Bonington (1964) published a plot of power efficiency vs head ratio with diameter ratio as parameter. As per their co relation the maximum efficiency achieved is around 33% at head ratio 4 and diameter ratio (ratio of diameter of nozzle to throat diameter) 0.52. Similar studies have also been done by Yadav and Patwardhan (2008), Gamisans et al. (2004), Cunningham (1974) and Blenke et al. (1963).
Yadav and Patwardhan (2008) defined Energy efficiency of ejector as
where is absolute pressure at diffuser outlet, Pa; is absolute pressure at throat, Pa; flowrate of secondary fluid, is density of the primary fluid, ;
, diameter of nozzle, m; , velocity of primary fluid at outlet of nozzle.
2.4 Gas absorption in jet ejector
In any absorption process, whether followed by a chemical reaction or not the gas must first be dissolved in the liquid. Thus, gas liquid mass transfer is one of the most fundamental steps in determining the absorption rate or the overall reaction rate. (Charpentier, 1976)
There is scanty literature available on the study of mass transfer in jet ejector. The rate of mass transfer is expressed by studying interfacial area between two phases, liquid side mass transfer coefficient and gas side mass transfer coefficient (Shabani, 2010). There are different factors which influence the value of a, and .
Solubility of solute in liquid phase and its diffusivity, concentration of reacting reagent in the liquid, reaction rate constant, reaction equilibrium constant, viscosity and density of liquid, etc. are important physico-chemical factors. Danckwerts (1967) showed the effect of change in temperature at the surface (resulting due to the heat of absorption and the heat of reaction) on change in concentration of the product of the reaction at the surface and depletion of reactant dissolved in liquid at the surface (in case of pseudo-first order reaction).
Shabani et al. (2010) has been reported that mass transfer rate is a severe function of solution concentration and effective interfacial area.
Gas flow rate, liquid flow rate and gas to liquid flow ratio are main hydrodynamic factors which affect the rate of absorption. Laurent (1978) established the hydrodynamic characteristics in the jet ejector. They studied the influence of the gas and liquid flow rates and the diameter of the ejector on the rate of mass transfer.
2.4.1 Methods of determination of interfacial area
There are mainly three methods used to determine the interfacial area that are reported in the literature:
1. Measuring the drop size and drop size distribution
2. Photographic method
3. Chemical method
In the present study the chemical method for measuring interfacial area is used. In this method, gas-liquid chemical reaction is utilized to measure the interfacial area and volumetric mass transfer coefficient. One of reacting component (known as solute) like and from gas phase is absorbed in liquid phase which contains another reactant like ammonia, sodium carbonate, dithionite, cuprous chloride, caustic soda or sodium sulfite. Oyevaar and Westerterp (1989) concluded that the error in interfacial area measured by chemical method is less than 10% and 20% for mechanically agitated reactor and bubble column respectively, if the conversion is less than 99%. Raghuram (2009) used photographic method to determine interfacial area and bubble diameter.
Weisweiler and Rosch (1978) studied interfacial area and bubble size distribution in jet reactors using system. They used chemical method to investigate interfacial area.
2.4.2 Determination of interfacial area by chemical method
According to the study of Dehkordi and Savari (2011), the theory of gas absorption accompanied by a chemical reaction explained by Danckwerts (1970, 1968), has been widely used to evaluate the volumetric liquid-side mass-transfer coefficient and the specific interfacial area a in various gas-liquid contactors.
Consider a chemical reaction between gas component and a component in liquid phase. This reaction may be written as follow:
If the reaction is irreversible of the mth order in and order in , the local rate of reaction per unit volume may be expressed by
where and are the local concentrations of and respectively. Doraiswamy and Sharma (1984) stated that if reaction satisfies
where , , , and are the solubility of gas in the aqueous solution, initial concentration of reactant B, molecular diffusivity of in the aqueous solution, and the mass-transfer coefficient, respectively.
Then the reaction between and occur entirely in the film, and the concentration of B at the interface is practically the same as that in the bulk of the liquid phase. Here represents the ratio of the amount of reacting in the film to that of amount A reacting in the bulk. If the reaction is pseudo-mth order in and the rate of absorption of component per unit volume of the reactor can be expressed by
Here, it may be interpreted that under these condition the rate of absorption is independent of or the hydrodynamic conditions. So it means that if reaction is fast pseudo-mth order, then by having the knowledge of solubility of the gas (), the molecular diffusivity of the gas component dissolved in the liquid phase ( and the kinetic parameters of the reaction
(i.e., , and), specific interfacial area can be evaluated by determining experimentally rate of absorption of per unit volume of the reactor ().
Jhaveri and Sharma (1968) compared the work of different researchers who studied absorption accompanied by pseudo order reaction to evaluate the effective interfacial area, , as a function of the liquid flow rate in a laboratory packed column. Oxygen was absorbed in aqueous solutions of cuprous chloride and sodium dithionite. Isobutylene was absorbed in an aqueous solution of sulfuric acid. There is a good agreement among the values of obtained by using different systems. The value of appears to be a unique function of the liquid flow rate in the range of liquid properties covered in their investigation (ionic strength 1 to 34.5 g ion/1, viscosity 1 to 9 cP).They further concluded that the effective interfacial area remains practically the same irrespective of the reacting species and the kinetics of the reaction. Similarly Gemisans et al. (2002) studied different arrangement of jet ejector like single stage, two stage with and without secondary jet and without throat using absorption of and from the gas into and solutions respectively. They studied the effect of variation in solute concentration, air flow rate and absorbing solution flow rate. They observed that the liquid flow rate have strong influence on where as the solute concentration and gas flow rate have slight influence. These results are in consonance with the observations of Jhaveri and Sharma (1968). They have also concluded that there was considerable improvement in absorption efficiency in case of two stage jet ejector having only one jet, but there was increased energy consumption. Shabani et al. (2010) and Laurent et al. (1978) studied the parameters affecting the interfacial area in a jet ejector using system. Both of them have reported similar results that interfacial area increases with increasing liquid velocity up to certain level. There are several investigators who worked on the chemical method for the determination of interfacial area in gas liquid contactors (Raghuram et al., 1992; Oyevaar and Westerterp, 1989; Ogawa et al., 1983; Virkar and Sharma, 1975; Sahay and Sharma, 1973; Volgin et al., 1968).
2.4.3 Determination of overall volumetric mass-transfer coefficient by chemical method
Doraiswamy and Sharma (1984) derived a correlation which may be used to determine the overall volumetric mass-transfer coefficient by chemical method. If the reaction is an irreversible mth order with respect to and order with respect to , and satisfy the condition
then the reaction between the gas and the liquid can take place entirely in the bulk of the liquid phase and there is negligible reaction occurring in the film. Moreover, if the reaction between the gas component and the liquid is sufficiently fast, such that the concentration of un-reacted component in the bulk of liquid phase is negligible then the absorption rate of gas per unit volume of the gas-liquid reactor () can be expressed as
To ensure such condition the reaction should satisfy
Thus if and the solubility of the gas component in the liquid phase are
known, then the volumetric mass transfer coefficient can be experimentally evaluated using the above equation.
2.4.4 Limitations of the chemical method for the determination of mass transfer coefficient
The specific surface area for mass transfer in the gas-liquid contactor is the cumulative area of all the bubbles or drops or film divided by the volume of sample.
However the physical methods of determining interfacial area measure the local Sauter mean diameter and hence local interfacial area. But for practical purposes one need to determine an overall interfacial area for the entire contactor. The chemical method of determining interfacial area makes it possible to determine directly the overall interfacial area over the entire contactor. Charpentier (1982) observed that the difference between the interfacial area measured by the chemical method and photographic method may be due to a small number of large bubbles dominating the interfacial area by the inadvertent exclusion of small bubbles by the photographic method.
Joosten and Danckwerts (1973) introduced correction factor Î³ which they defined as ratio of increase of liquid absorption capacity to increase of mass transfer due to chemical reaction.
Parameter to determine
Minimum value of
Maximum value of
Physical absorption or slow chemical reaction
Intermediary pseudo th order chemical reaction
Rapid pseudo th order chemical reaction
Instantaneous chemical reaction
Instantaneous chemical reaction at the interface
= inlet solute gas concentration. = rate of absorption, = gas residence time, = reduced diffusion time,
= absorption efficiency.
Table 2.8 : Limiting values of and for the various chemical regimes used to measure the mass transfer parameters (Midoux et al., 1980)
Due to presence of chemical compound the coalescence rate reduces considerably and hence chemical method may lead to error for the fast coalescing systems. Midoux et al (1980) proposed a flow model for shrinking & non shrinking bubbles. Table 2.8 presents the limiting conditions which can be used to minimize the error in estimating mass transfer parameters by chemical method.
Charpenter (1982) suggested that complimentary conditions proposed by researchers be verified before using their data for scale up.
2.4.5 Effect of the ejector geometry on the mass transfer characteristics
Cramers and Beenackers (2001) investigated the effect of geometrical design parameters like the presence of a swirl device in the upstream section of the nozzle, the mixing tube length and the ratio of nozzle to mixing tube diameter ratio. They observed that all these parameters have significant effect on the mass transfer characteristics. They also studied the influence of gas density on mass transfer characteristics and observed that the volumetric mass transfer coefficient () increases when higher density gases are used. There are some other researchers who carried out similar studies (Balamurugan et al., 2008, 2007; Gourich, 2007; Baier, 2001). Table (2.9) is comprehensive list and the co-relations given by different investigators (Balamurugan et al., 2007).
Their investigations may be summarized as follows:
Influence of the swirl device
For the same the ejector with swirl device causes higher gas phase pressure difference. The ejector without a swirl device creates higher values compared to the ejector with a swirl device in the nozzle. The value of increases with increase in . In case of presence of swirling device, there are two distinguished flow regimes seen viz. bubble flow and annular flow. The ejector without a swirl device creates higher values as compared to the ejector without swirling device because it utilizes the supplied energy more effectively. In similar study , Zheng et al. (2010) and Baier (2001) (Figure 2.25) concluded that the gas holdup and interfacial area are larger in case of jet ejector without swirl compared to jet ejector with swirl.
Method of measurement
Otake et al. (1981)
Zahradnik et al. (1982)
Zahradnik et al. (1982)
Ogawa et al. (1983)
Rylek and Zahradnik (1984)
Zahradnik et al. (1985)
Bhutada and Pangarkar (1987)
Table 2.9 continued
Continued from previous page
Downward, primary-solution of
secondary-air + mixture
Dutta and Raghavan (1987)
Upward, primary-sodium sulfite
Bando et al. (1990)
Cramers and Dierendonck (1992)
Cramers and Dierendonck (1992)
Zahradnik et al. (1997)
Havelka et al. (1997)
Cramers and Beenackers (2001)
Mandal et al. (2003)
Mandal et al. (2003)
Holdup measurement methods: 1. Bed expansion method; 2. difference of static pressure along the column; 3. spark photography for bubble size estimation; 4. photography for bubble size estimation. Mass transfer estimation measurement methods: 1. Dynamic method-monitoring of unsteady oxygen absorption into previously deoxygenized water in the bed, i.e. on the evaluation of system response to an input step change nitrogen-air; 2. absorption in sodium sulfite solution with Cobaltous sulfate as catalyst; 3. absorption of lean in the mixture of and . Interfacial area measurement methods: 1. absorption in sodium sulfite solution with Cobaltous sulfate as catalyst; 2. absorption of CO2 in aqueous solution of sodium hydroxide.
Table 2.9 : Hold-up, and measurement methods and correlations given by various authors
Figure 2.25 : Influence of the swirl device on the total gas holdup (Îµtot)
Influence of the nozzle to mixing tube diameter ratio or )
When using a swirl device decreases with increasing diameter ratio. When no swirling device is used then there exists an optimum diameter ratio approximately 0.38. They correlated as follow
Influence of the mixing tube length
For the standard ejector (/ = 2), the mixing zone is located in both the mixing tube and in a large volume of the diffuser. However, when the mixing tube length is increased, it is found that the mixing is nearly completed in the mixing tube. This indicates that the initial dispersion volume (mixing zone volume) is influenced by the ejector configuration. From this visual observation, it can be concluded that the mixing zone volume of an ejector with a / ratio of 10 is smaller compared to the mixing zone volume of an ejector with a shorter mixing tube. They also noted that this observation is in disagreement with the
experiment of Dirix and Wiele (1990), the mixing tube length has no influence on (kLa). (Figure 2.26)
Figure 2.26 : Influence of the mixing tube length on (Baier, 2001)
Utomo et al. (2008) have also studied the effect of mixing tube length on volumentric mass transfer coefficient. They concluded that an ejector with longer mixing tube creates lower volumetric mass transfer coefficient compared to shorter mixing tube. It is seen that by increasing /ratio, the volumetric mass transfer coefficient decreases for any gas liquid flow rate ratios. They also explained that when the mixing tube length is increased, the pressure drop is also increased.
Influence of the gas density on mass transfer characteristics
In the bubble flow regime, the volumetric mass transfer coefficient increases when higher density gases are used. The results could be explained by using Levich's theory, i.e. when the gas density increases, smaller bubbles get dispersed resulting in an increase of the kLa value.
Figure. 2.27: Influence of gas density on without swirl device (Baier, 2001)
Influence of liquid viscocity on mass transfer characteristics
kLa [s-1]Baier (2001) investigated the effect of viscocity on mass transfer coefficient.They explained that the volumetric mass transfer coefficient decreases with increase in liquid viscosity (Figure 2.28). They compared their results with Terasaka and Hideki (1991), Sedelies et al. (1987) and Stein and Schafer (1984) and found good agreement
Figure 2.28 : Influence of the liquid viscosity on (Baier, 2001)
2.4.6 Factors effecting mass transfer characteristics
Biswas et al. (1977) studied the effective interfacial area in a liquid jet induced horizontal gas-liquid contactor. They determined the effective interfacial area at various gas liquid throughputs by chemical method. Their results are summarized as follows:
At same motive liquid flow rate, interfacial area increases with increasing secondary liquid flow rate. Interfacial area is proportional to flow of secondary fluid (gas), .
Maximum interfacial area (approx. 2400mÂ²/mÂ³) is created by the nozzle having area ratio 9.3
At same suction gas flow rate, higher interfacial area is achieved by increasing motive fluid flow rate (liquid).
Interfacial area can be predicted by empirical correlation
Where is the fraction of gas hold up based on total system volume (dimensionless)
is the fraction of gas holdup at no slip(dimensionless)
Specific interfacial area produced for same energy/volume to jet ejector is much higher compared to that produced in packed bed, jet contactor and bubble column.
2.4.7 Use of jet ejector in reactor
The use of jet ejector in the loop-reactor has been reported in the literature (Gourich et al., 2007; Tang et al., 2006; Ping-fang Han et al., 2005; Havelka et al., 2000; Dierendonck et al., 1998; Ogawa et al., 1983). These studies have reported about the hydrodynamics and the factors affecting the mass transfer characteristics of the jet ejector used in the different profiles of loop-reactors.
Weisweiler and Rosch (1978) observed that the interfacial area and percentage conversion increase with increasing jet velocity. When jet velocity is increased the conversion increases depending on the gas throughput and at high jet velocity a maximum conversion of nearly 100% is achieved. Liquid jet velocities of less than 10 m/s hardly affect the interfacial area for the dispersion of the gas stream into small bubbles. The liquid jet must be highly turbulent which is ensured when the jet velocity exceeds 10 m/s.
Gourich et al., (2007) and Dierendonck et al., (1998) compared the performance of jet ejector in loop reactor with conventional gas liquid contractors. Their findings were similar to Weisweiler and Rosch (1978) that loop ejector venturi contactors are versatile tools to carry out both fast and slow reactions.
Raghuram (2009) studied interfacial area in gas-liquid ejector for a sodium chloride-air system for a ejector having same nozzle and throat diameter (3mm). They observed that for given flow rate of air and liquid the interfacial area decreases slowly as dispersion is moves away from the nozzle. They also reported that interfacial area increases with increasing liquid to air ratio. They achieved interfacial area of the tune of
Dierendonck et al. (1998) concluded that the loop ejector venturi reactors are an efficient alternative to the stirred tank reactors, offering easier scale-up.
2.4.8 Mass transfer characteristics in multi nozzle jet ejector
Radhakrishnan and Mitra (1984) studied multi nozzle liquid gas ejectors, and observed that optimum ratio of length of throat to diameter of throat is between 6 to10. Similarly optimum area ratio is from 14.56 to 16.39 and gave the co-relation for gas hold up as
Where fractional liquid hold up i.e. ratio of liquid volume to the volume of system
- number of orifices in the nozzle plate and are Reynold's numbers based on superficial liquid and gas velocity on the tube diameter.
They reported co-relation for interfacial area of system, :
They also reported that the optimum performance is obtained with nozzle having = 14.6, This nozzle gave maximum specific interfacial area per unit energy input.
2.4.9 Mass transfer with chemical reaction
Danckwerts (1970) proposed in agitated film diffusion, convection and reaction proceed simultaneously. To make any useful prediction about the behavior of such systems, it is necessary to use highly-simplified model which simulate the situation sufficiently well for practical purposes without introducing a large number of parameters which are difficult to determine.
There are many hypothetical models to predict the effect of chemical reaction on absorption rate in the literature.
Whitman's 'Laminar film model' (1923): steady-state diffusion through a stagnant film
Higbie's 'Systematic surface renewal (penetration) model' (1935): transient absorption into surfaces which are systematically replaced by fresh liquid
Danckwerts's 'Random surface renewal model' (1951): transient absorption into surfaces which are randomly replaced.
Danckwerts and Kennedy (1954) compared these three models and showed that the three models lead to closely similar predictions about the effect of physico-chemical variables (solubility, diffusivity, reaction rate etc.) on the rate of absorption.
Wall and Beek (1967) compared chemisorption and physical absorption and concluded that chemsorption is more than physical absorption.
Vieth et al. (1963) derived an equation which describes the mass transfer to a fluid in fully developed turbulent flow in a pipe. They explained that their correlation for mass transfer is identical with the well-known Chilton-Colburn analogy (1934). They extended their analysis to the case of simultaneous mass transfer and irreversible first-order chemical reaction and found that the solutions of their correlation in agreement with fact is reported by Danckwerts and Kennedy (1954) for penetration and film models.
However the studies by Beltran et al. (1998), Danckwerts et al. (1963) and Richards et al. (1964) had compared different models for different systems and have reported the effect of various parameters.
2.4.10 Reaction systems used to characterize mass transfer with chemical reaction
Sadek et al. (1977) proposed a model for the simultaneous absorption of sulfur dioxide and chlorine into mixed acid.
Ravindram and Pyla (1986) also proposed a theoretical model (based on simultaneous diffusion and an irreversible chemical reaction) for predicting the amount of gaseous pollutant removed in a venturi scrubber. For validation of their model they used system of and absorption in dialute . They found excellent agreement between the results predicted by the model and those experimentally determined.
Chlorine is one of the most polluting gases in process industries. The absorption of chlorine in aqueous solution of sodium hydroxide is commonly commercially practiced method to deal with chlorine pollution. There have been a few studies on the absorption of in to aqueous sodium hydroxide solution in different gas-liquid contactors. (Roy and Rochelle, 2004; Ashour et al., 1996; Lahiri et al., 1983; Hikita et al., 1973)
Hikita et al. (1973) studied the rate of absorption of pure chlorine into various concentrations of aqueous sodium hydroxide solution at They used a liquid-jet column for their research study. They applied penetration theory for gas absorption accompanied by a two-step instantaneous chemical reaction. The experimental results were in good agreement with the theoretical predictions. They termed their model "two reaction-plane model" as shown below:
Aqueous solution containing and exists in the region between the gas liquid interface and the first reaction plane (region 1in Figure 2.29), C:\Phd 1-6-2012\edit thesis final\ksa fig 1 22-6-12.jpg
Figure 2.29 : Concentration profiles for absorption of into aqueous solution
(Hikita et al., 1973)
Aqueous solution containing , and exists in the region between the first reaction plane and the bulk of liquid (region 2 in Figure 2.29),
The theoretical predictions and the experimental observations by Spalding and Takahashi et al. are in good agreement.
Tamir et al. (1975) concluded that the neglecting of the effect of the gaseous environment as well as bulk flow contribution is not justified for absorption of gases with high solubilities and large heat effects. They presented a penetration model and validated the model by using the absorption of chlorine into toluene (investigated experimentally by others). They found a deviation of 25% between calculations based on simplified model and the more general model presented by them
Lahiri et al. (1983) deliberated on the absorption of chlorine in aqueous solution of sodium hydroxide with concurrent desorption of hypochlorous acid (followed by its dissociation to chlorine monoxide) at 55Â°C and 75Â°C in a stirred contactor with a flat gas-liquid interface. A reasonably good agreement has been found between the theoretical predictions and experimental observations.
Roy and Rochell (2004) measured the absorption rate of chlorine into aqueous solution of sulfite/bisulfite using a stirred-cell reactor and a wetted-wall column in the range pH 4.7 and 5.7. They developed a model using the theory of mass transfer with fast reaction. They also reported that there is enhancement of absorption by using the succinate buffer on the rate of chlorine hydrolysis. They also found that the di-succinate results in greater enhancement of absorption than the mono-succinate anion and the addition of sodium chloride () as well oxygen did not affect the rate of absorption in S(IV). They opined that these results are relevant in the simultaneous removal of chlorine, sulfur dioxide and elemental mercury from flue gas.
Uchida and Wen (1973) simulated absorption of in and alkaline solution using a mathematical model developed by them. They compared the calculated results based on their model with experimental data obtained in several types of venturi scrubbers that showed satisfactory agreement.
Charpentier (1976) published a review paper in which he presented. Different theoretical and empirical correlations to calculate and .
Laurent et al (1978) studied absorption with chemical reaction in venturi jet scrubber. They used slow irreversible reaction to measure and fast pseudo mth order reaction for .
Asai et al. (1986) analyzed the rate of mass transfer accompanied by chemical reaction of general order proceeding in two continuous phases on the basis of the two-film theory. They could find satisfactory accuracy.
Atay et al. (1987) developed empirical models to describe the fluid flow characteristics and gas absorption efficiency of ejector venturi scrubber. They determined the sulfur dioxide absorption efficiency experimentally on a commercial scrubber.
Bandyopadhyay and Biswas (2007, 2006, 2006a) , studied the removal of using water and dilute alkali as scrubbing media in a tapered bubble column scrubber. They observed the enhancement of removal of due to presence of particulate matter in the alkali scrubbing media.
Mandal et al. (2003b) investigated experimentally, and , in a down flow bubble column by chemical method viz., absorption of in aqueous sodium hydroxide and sodium carbonate/bicarbonate buffer solutions respectively. The equipment consists of jet ejector followed by bubble column. They developed correlations to predict and in terms of superficial gas velocity by applying Polynomial regression analysis of the experimental data,
They also compared the experimental data with the predicted values obtained from above equation and found that it fitted very well.
Silva and Danckwerts (1973) studied the effect of adding a small quantity of halogen (chlorine or bromine) to a stream of carbon dioxide on absorption rate of carbon dioxide. The addition of a small quantity of chlorine or bromine increases greatly the rate of absorption of the carbon dioxide into alkaline solutions. This is due to the formation of hypochlorite ion or hypobromite ion in the solutin which are catalysts for the reaction between and water.
Similar studies were done by using -alkali systems by different researchers (Cents, 2005; Gomez and Navaza, 2005; Meikap et al., 2004, 2001; Dimicocoli et al., 2000; Alvarez et al., 1980, 1981; Pohoreckie, 1968;Vidwans and Sharma, 1967; Danckwert and Kennedy, 1958).
Many researchers, (Bhatt et al., 2010, 2007; Gandhi et al., 2009; Ahari et al., 2008; Gulbeyi and Cevdet, 2006; Yusuf et al., 1999; Cooney, 1992, 1985; Yaici et al., 1988; Cooney and Olsen, 1987; Botton et al., 1987; Mahajani and Sharma, 1981, 1980, 1979; Midoux et al., 1984; Ogawa et al., 1983; Charpentier, 1982, 1976; Laurent and Charpentier, 1974; Shende and Sharma, 1974; Volgin et al., 1968; Jhaveri and Sharma, 1968, Danckwerts and Sharma, 1966) have proposed models to predict absorption with chemical reaction by studying different reaction systems.
Kordac and Linek (2008) studied the effect of addition of salt and super saturation, on the mass transfer coefficient of carbon dioxide-water system. Their experiments show that mass transfer coefficients are enhanced by the effect of liquid super saturation.