an average gas hold-up and liquid circulation velocity in airlift reactor with external loop

13
Chemical Engineering Science. Vol. 48, No. 23. pp. 40234035, 1993. 000-2509,93 S6.W + 0.M Printed in Gnnc Britain. 0 1993 Pergamon Press Ltd AN AVERAGE GAS HOLD-UP AND LIQUID CIRCULATION VELOCITY IN AIRLIFT REACTORS WITH EXTERNAL LOOP Z. KEMBLOWSKI. J. PRZYWARSKI and A. DIAB Department of Chemical Engineering, Faculty of Process and Environmental Engineering, Technical University of L6di Wblczahska 175.90-924 L&IS% Poland (First received 7 July 1992; accepted in revised form 12 February1993) Abstract-Experimental investigations were carried out in model airlift reactors with external loops. Two reactors of laboratory scale (height 1.95 m, internal diameter 0.1 m, volume 0.08 m3) and pilot-plant scale (height 7.1% m, internal diameter 0.2 m, volume 0.7 m3) were used. The influence of reactor geometry, gas sparger design, liquid properties (both Newtonian and non-Newtonian) and the amount of introduced air was investigated. The influence of gas sparger design on gas hold-up and liquid velocity was found to be negligible. A modified method for the prediction of liquid circulation velocity-based on the energy balance of the reactor-was proposed. An original dimensionless correlation for gas hold-up prediction involving superficial velocities of gas and liquid, cross-sectional areas, as well as Froude and Morton numbers, was obtained. 1. INTRODUCTION During the last two decades a large number of papers concerning airlift loop reactors have appeared. The principles of operation as well as the advantages and disadvantages of this type of reactors are discussed in the review papers (Chisti and Moo-Young, 1987; Blenke, 1979, 1983; Schiigerl et al., 1977). The basic hydrodynamic design parameters of an airlift loop reactor are the average gas hold-up and liquid circulation velocity. 1.1. Literuture survey Severai important papers dealing with the two in- terrelated parameters of average gas hold-up and liquid circulation velocity have been published (Bell0 et aI., 1984, 1985;Calve, 1989,Chisti et a& 1988;Chisti and Moo-Young, 1988; Hills, 1976; Hsu and DudukoviC, 1980; Jones, 1985; van der Lans, 1985; Merchuk and Stein, 1981; Nicol and Davidson, 1988a,b; Philip et al., 1990; Popovii: and Robinson, 1984, 1989; Roberts, 1979; Vatai and Tekib, 1986; Verlaan et al., 1986a). Most of them describe experi- mental investigations carried out for water-like media in various model reactors of different geometries and mostly laboratory scale [except the data presented by Hills (1976), van der Lans (1985) and Nicol and Davidson (1988a, b)]. Only a few papers concern highly viscous and non-Newtonian liquids (Chisti and Moo-Young, 1988; Popovil: and Robinson, 1984; 1989; Philip et al., 1990; Vatai and TekiC, 1986). Some correlations for gas hold-up prediction have been proposed in the literature (Bell0 et al., 1984, 1985; Hills, 1976; Hsu and Dudukovie, 1980; Merchuk, 1986; Nicol and Davidson, 1988a,b; Popovii: and Robinson, 1984, 1989; Roberts, 1979; Vatai and Teki& 1986;Weiland and Onken, 1981).The greatest disadvantage of most of the reported correla- tions is their dimensional form, which means that the constants of the equations depend on the geometry and properties of the system. Only the correlations proposed by Hsu and DudukoviC (1980) and Vatai and TekiC (1986) seem to be more general than the others because they contain dimensionless parameters such as Froude, Reynolds and Weber numbers, and superficial velocities ratio of gas and liquid. However, there is a lack of evidence showing that they have been applied for other geometries. According to some re- searchers there is an obvious need for studies of large- scale reactors (Blenke, 1979; Bello et al., 1984). Various equations for liquid velocity prediction have also been reported in the literature, generally for water or similar liquids. Most of them are simple correlations involving two or three parameters (Be110 et al., 1984; Nicol and Davidson, 1988a,b, Popovii: and Robinson, 1988; Roberts, 1979; Vatai and TekiC, 1986). Some of them are semitheoretical model equa- tions derived from energy or pressure balance equa- tions. They take into account most of the known factors that influence liquid circulation but not all of the terms involved are known or may be easily estim- ated for calculations (Chisti et al., 1988; Chisti and Moo-Young, 1988;Hsu and DudukoviE, 1980). There are also some very simple correlations available de- rived from drift flux model but they take into account neither the properties of gas and liquid nor the geometry of the reactor (Calvo, 1989; Nicol and Davidson, 1988a, b). Therefore, reported results are mostly limited to particular cases for which they were obtained. It follows from the above-mentioned literature data that there are two main approaches to the modelling of liquid circulation velocity in an airlift loop reactor. One of them begins with a pressure balance over the circulation loop (Blenke, 1979, Hsu and Dudukovik, 1980; Kubota et al., 1978; Merchuk and Stein, 1981; Verlaan et al., 1986b). The other one begins with a total energy balance of the reactor (Chisti et al., 1988; Chisti and Moo-Young, 1988; Calvo, 1989; Young et al., 1991). 4023

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  • Chemical Engineering Science. Vol. 48, No. 23. pp. 40234035, 1993. 000-2509,93 S6.W + 0.M Printed in Gnnc Britain. 0 1993 Pergamon Press Ltd

    AN AVERAGE GAS HOLD-UP AND LIQUID CIRCULATION VELOCITY IN AIRLIFT REACTORS WITH EXTERNAL LOOP

    Z. KEMBLOWSKI. J. PRZYWARSKI and A. DIAB Department of Chemical Engineering, Faculty of Process and Environmental Engineering, Technical

    University of L6di Wblczahska 175.90-924 L&IS% Poland

    (First received 7 July 1992; accepted in revised form 12 February 1993)

    Abstract-Experimental investigations were carried out in model airlift reactors with external loops. Two reactors of laboratory scale (height 1.95 m, internal diameter 0.1 m, volume 0.08 m3) and pilot-plant scale (height 7.1% m, internal diameter 0.2 m, volume 0.7 m3) were used. The influence of reactor geometry, gas sparger design, liquid properties (both Newtonian and non-Newtonian) and the amount of introduced air was investigated. The influence of gas sparger design on gas hold-up and liquid velocity was found to be negligible. A modified method for the prediction of liquid circulation velocity-based on the energy balance of the reactor-was proposed. An original dimensionless correlation for gas hold-up prediction involving superficial velocities of gas and liquid, cross-sectional areas, as well as Froude and Morton numbers, was obtained.

    1. INTRODUCTION

    During the last two decades a large number of papers concerning airlift loop reactors have appeared. The principles of operation as well as the advantages and disadvantages of this type of reactors are discussed in the review papers (Chisti and Moo-Young, 1987; Blenke, 1979, 1983; Schiigerl et al., 1977).

    The basic hydrodynamic design parameters of an airlift loop reactor are the average gas hold-up and liquid circulation velocity.

    1.1. Literuture survey Severai important papers dealing with the two in-

    terrelated parameters of average gas hold-up and liquid circulation velocity have been published (Bell0 et aI., 1984, 1985; Calve, 1989, Chisti et a& 1988; Chisti and Moo-Young, 1988; Hills, 1976; Hsu and DudukoviC, 1980; Jones, 1985; van der Lans, 1985; Merchuk and Stein, 1981; Nicol and Davidson, 1988a,b; Philip et al., 1990; Popovii: and Robinson, 1984, 1989; Roberts, 1979; Vatai and Tekib, 1986; Verlaan et al., 1986a). Most of them describe experi- mental investigations carried out for water-like media in various model reactors of different geometries and mostly laboratory scale [except the data presented by Hills (1976), van der Lans (1985) and Nicol and Davidson (1988a, b)]. Only a few papers concern highly viscous and non-Newtonian liquids (Chisti and Moo-Young, 1988; Popovil: and Robinson, 1984; 1989; Philip et al., 1990; Vatai and TekiC, 1986).

    Some correlations for gas hold-up prediction have been proposed in the literature (Bell0 et al., 1984, 1985; Hills, 1976; Hsu and Dudukovie, 1980; Merchuk, 1986; Nicol and Davidson, 1988a,b; Popovii: and Robinson, 1984, 1989; Roberts, 1979; Vatai and Teki& 1986; Weiland and Onken, 1981). The greatest disadvantage of most of the reported correla- tions is their dimensional form, which means that the constants of the equations depend on the geometry

    and properties of the system. Only the correlations proposed by Hsu and DudukoviC (1980) and Vatai and TekiC (1986) seem to be more general than the others because they contain dimensionless parameters such as Froude, Reynolds and Weber numbers, and superficial velocities ratio of gas and liquid. However, there is a lack of evidence showing that they have been applied for other geometries. According to some re- searchers there is an obvious need for studies of large- scale reactors (Blenke, 1979; Bello et al., 1984).

    Various equations for liquid velocity prediction have also been reported in the literature, generally for water or similar liquids. Most of them are simple correlations involving two or three parameters (Be110 et al., 1984; Nicol and Davidson, 1988a,b, Popovii: and Robinson, 1988; Roberts, 1979; Vatai and TekiC, 1986). Some of them are semitheoretical model equa- tions derived from energy or pressure balance equa- tions. They take into account most of the known factors that influence liquid circulation but not all of the terms involved are known or may be easily estim- ated for calculations (Chisti et al., 1988; Chisti and Moo-Young, 1988; Hsu and DudukoviE, 1980). There are also some very simple correlations available de- rived from drift flux model but they take into account neither the properties of gas and liquid nor the geometry of the reactor (Calvo, 1989; Nicol and Davidson, 1988a, b). Therefore, reported results are mostly limited to particular cases for which they were obtained.

    It follows from the above-mentioned literature data that there are two main approaches to the modelling of liquid circulation velocity in an airlift loop reactor. One of them begins with a pressure balance over the circulation loop (Blenke, 1979, Hsu and Dudukovik, 1980; Kubota et al., 1978; Merchuk and Stein, 1981; Verlaan et al., 1986b). The other one begins with a total energy balance of the reactor (Chisti et al., 1988; Chisti and Moo-Young, 1988; Calvo, 1989; Young et al., 1991).

    4023

  • 4024 2. K~MBLOWSKI et al.

    Only the model proposed by Chisti and Moo- Young (1988), concerning both Newtonian and non- Newtonian liquids, will be discussed further because this approach seems to be more convincing. The authors wrote the energy balance of the reactor in the following form:

    Ei=E,+ED+E,+ET+EF (1)

    where Ei is the energy input due to isothermal gas expansion

    E, is the energy dissipation due to wakes behind bubbles in the riser,

    E. = Ei -_p&,VLx&e~ (3)

    I?,, is the energy dissipation due to stagnant gas in the downwmer,

    .% = PLgh, VU&&, (4)

    & is the energy dissipation due to fluid turn around at the bottom of the reactor,

    z P&(1 -ed VLD 2

    -AD (5) (1 -eD)

    E, is the energy dissipation due to fluid turn around at the top of reactor,

    z PU --El!) VLR 2 (1 -.5x) AR (@

    and finally EP is the energy loss due to friction in the riser and the downcomer.

    EF = APFa VLx AR + APp, VLD AD. (7)

    Applying complicated experimental correlations for wall shear stress in tube flow of gas-liquid mixture, given by Sokolov and Metkin (1981) and Metkin and Sokolov (1982), Chisti and Moo-Young (1988) de- veloped an equation for the prediction of liquid circu- lation velocity (see Table 1). For the prediction of gas hold-up-which is necessary for the calcula- tions-they recommended the correlation proposed by Popovii: and Robinson (1984). This correlation was obtained for power-law liquids in a laboratory- scale model reactor.

    Summing up, it follows from the literature review that

    -the reported investigations were concerned mainly with Newtonian liquids of low viscosity,

    -the majority of the published data were obtained in laboratory-scale model reactors, and

    -the results of measurements were usually pres- ented in the form of dimensional dependencies.

    1.2. Scope of the work Taking into account the above statements our in-

    vestigations were concerned with highly viscous Newtonian and non-Newtonian fluids. The experi-

    ments were carried out in two external-loop model airlift reactors of distinctly different geometries. The purpose of the work was to develop

    -a dimensionless correlation for the prediction of average gas hold-up, and

    -a simple method for the prediction of liquid circulation velocity.

    2. A MODEL FOR PREDICTION OF AVERAGE GAS

    HOLD-UP AND LIQUID CIRCULATION VELOCITY

    2.1. Gas hold-up It was decided to develop a classical dimensionless

    correlation for gas hold-up prediction in order to avoid the modelling of gas-liquid interaction in a two- phase flow. Reported results concerning the influence of various physical factors on the hydrodynamics of an airlift reactor are often contradictory and strongly affected by system properties. Therefore, they have limited general importance [e.g. Nicol and Davidson (1988a,b) and contradictory conclusions on surface tension influence reported by Wachi et al. (1991)]. Let US consider a generalized Newtonian liquid (i.e. purely viscous fluid with shear-rate-dependent viscosity) whose rheological properties can be approximated by the power-law model of Ostwald-de Waele. We as- sume, on the basis of literature data and our own considerations, that the average gas hold-up in the riser, &R, is a function of superficiti velocities of gas, V,,, and liquid, VLR, densities of gas, Pc, and liquid, pL, liquid rheological parameters, n and k, surface tension, crL, height of the liquid head, H, cross-sec- tional areas of the riser, AR, and downcomer, Ar,, total cross-sectional area of holes or nozzles of the gas sparger, A,, and acceleration due to gravity, g:

    ER = I(v,R, VLR, PC, PL, n, k OL,, H, AD, AR, Ag).

    (8)

    A dimensional analysis leads to the following rela- tion between gas hold-up and dimensionless moduli:

    where the Froude number is defined as

    Fr = (VLR + vGR)2 gdn

    and the Morton number is defined as

    (10)

    4(n-1) / 3n + 1 14

    \ 4n I *

    A classical relation of Morton well-known numbers is as follows:

    Eo Wet MO=-

    R&R

    (11) number to other

    (12)

  • Tab

    le I.

    Sele

    cted lit

    era

    ture

    corr

    ela

    tions f

    or

    the p

    red

    icti

    on

    of

    gas h

    old

    -up

    an

    d li

    qu

    id c

    ircu

    lati

    on velo

    city

    in a

    irlif

    t re

    act

    ors

    Auth

    or

    Pro

    pose

    d co

    rrela

    tion

    Exueri

    menta

    l range

    Belle

    et a

    l., 1

    984

    Bell0

    et a

    l., 1

    985

    Ch

    isti

    et

    al., 1

    988

    ER

    =

    ,.I,(

    I +

    +s)

    ($>

    VLR

    =

    Ch

    isti

    an

    d M

    oo-Y

    ou

    ng

    , 1989

    I +

    ~P&

    &

    _+L

    !!

    s ir

    ( >I

    (I

    -es)

    * (1

    -~

    a)*

    A

    ,,

    -0

    L

    where

    Ap =

    4 D

    7,

    For

    lam

    inar

    flow

    :

    ah

    vt

    Re,. 2000)

    0.0792 f=- Ret

    (18)

    (19)

    where the Reynolds number of the liquid is defined in the case of the riser by eq. (15) and in the case of the downcomer by the following equation:

    ReL1, = VtDdh

    * (20)

    8m-,k

    The above ranges of laminar and turbulent flow were proposed by Hsu and DudukoviC (1980).

    Combining eqs (l)-(6) and (17) for riser and down- comer columns, a general equation for the prediction of the liquid superficial velocity in the riser is ob- tained:

    If the phases are almost completely separated at the top of the reactor, gas hold-up in the downcomer is often less than 1%. In this case eq. (21) can be re- written in the form

  • An average gas hold-up and liquid circulation velocity 4029

    Equation (22) incorporates the geometrical dimen- sions of the reactor, the Fanning friction factors in the riser and downcomer, frictional loss coefficients at the top and bottom of the reactor, and the gas hold-up in the riser. The geometry of the reactor is known, the Fanning friction factors may be assumed roughly and checked after calculations, and the frictional loss coef- ficients at the top and bottom of the reactor may be taken from the literature. The only unknown para- meter is the average gas hold-up, which should be predicted separately.

    3.1. Media 3. EXPERIMENTAL

    Both Newtonian (tap water without and with added surfactants, glycol, sugar syrup) and non- Newtonian media (power-law CMC solutions) were used for investigations concerning verification of energy balance approach. The following ranges of media properties were obtained:

    -liquid density pL = 998-1286 kg/m, - surface tension oL = 0.0420-0.08 16 N/m, -power-law parameter n = 0.758-1, -power-law parameter k = 0.001-0.261 Pa s.

    The properties of the experimental media for which the data points presented in Figs 4-12 were obtained are summarized in Table 2.

    3.2. Apparatus and procedure Two mode1 reactors were used for the experiments.

    One, of laboratory-scale, was 1.95 m high, of 0.1 m internal diameter of the riser and the downcomer, and 80 dm3 volume. The other one, of pilot-plant scale, was 7.18 m high and had a riser of 0.2 m internal diameter. It had two possible geometrical arrange- ments, with the downcomer internal diameter equal to 0.15 or 0.2 m. The total volume of the second reactor was 700 dm.

    Liquid circulation was directed through one of the two downcomers of the pilot-plant scale reactor by butterRy valves placed in the bottom connections of the reactor. There were only two possible positions of

    the valves applied in the experiments-one totally open and the other completely closed. The schematic views of the reactors and the photograph of the upper part of the pilot-plant scale apparatus are shown in Figs l-3.

    Compressed air was introduced only through the bottoms of the reactors by means of various gas spargers. There were gas spargers containing porous plates made of glass beads of three different size ranges: 100-160, la-250 and 250-500~. Each of them was applied with three diameters: 30, 50 and 70 mm. Single-nozzle gas spargers of six dia- meters-l, 1.4, 2, 2.8, 3 and 4 mm-were also used. For the pilot-plant scale reactor only the 3 mm gas sparger was applied.

    Air flow rate, average gas hold-up in the riser and downcomer, liquid velocity in the downcomer, pres- sure of compressed air, temperature of the system and atmospheric pressure were measured during the ex- periments. For each run properties of the liquid phase were carefully determined. Rheological properties were measured by means of the rotational rheometer Rheotest 2. Surface tension was determined by the classical stalagmometric method. Average gas hold- up was determined by means of the manometric tcch- nique described by Hills (1976). The following equa- tion was applied for the estimation of the average gas hold-up:

    Ah, s=-

    AZ

    where Ah,,, is the difference of manometer readings and AZ is the vertical distance between the connec- tions of manometers to the column.

    Liquid circulation velocity was measured in the downcomer according to the flow follower method, described previously by Jones (1985) and Philip et al. (1990), and modified by Diab (1991). Separation of phases was complete at the tops of the model reactors. Therefore, only a single-phase flow existed in the downcomers. In this way, it was possible to determine the liquid superficial velocity in the riser applying the continuity equation for liquid flow. The procedure for evaluation of the mean linear velocity of the liquid in the downwmer was as follows:

    Table 2. Properties of experimental media used for data presentation in Figs 4-12

    Figure

    4

    5, 8

    6, 9

    7, 10

    Medium

    Glycol solution

    Water Water with surfactant Glycol Glycol solution Sugar syrup CMC solution

    Water CMC solution

    Water

    Power-law parameters Density Surface tension k b/m) V/m) n (Pa s)

    1011 0.0699 1 0.0015

    1000 0.0735 1 0.001 997 0.0690 1 0.001

    1115 0.0420 1 0.0176 1011 0.0699

    : 0.0015

    1284 0.0814 0.141 1010 0.0769 0.758 0.261

    998 0.0726 1 0.001 1018 0.0802 0.855 0.212

    998 0,0726 1 0.001

  • 4030 Z. KEMBLOWSKI et a/.

    Fig. 1. Schematic diagram of the laboratory scale airlift model reactor with external loop.

    - The velocity of small thin aluminium flakes floating in the liquid was measured in the down- comer 10 to 15 times in order to obtain the maximum velocity in the axis of the column,

    - According to the velocity profile determined previously as a function of Reynolds number of the liquid in the downcomer, the mean linear velocity was calculated. All details were given by Diab (1991).

    4.1. 4. RESULTS AND DISCUSSION

    Gas spargers The influence of gas sparger geometry on the aver-

    age gas hold-up in our model reactors, despite the changes offlow regime from uniform bubbly to chum- turbulent flow, has proved to be negligible during the experiments. Figure 4 presents some experimental data obtained in the model reactor of laboratory scale for ethylene glycol solution and for various gas spargers. For other media the results are similar. Therefore, the correlation obtained for gas hold-up prediction, proposed below, can be regarded-as a first approximation-as being independent of gas sparger geometry.

    4.2. Gas hold-up The gas hold-up data obtained in our two model

    reactors-as well as other complete data available in the literature (Bell0 et al., 1985; Merchuk and Stein, 1981; Roberts, 1980) concerning airlift external-loop reactors with complete phase separation at the top-were applied in order to obtain a dimensionless correlation for gas hold-up prediction. The final form

    Fig. 2. Schematic diagram of the pilot-plant scale airlift model reactor with external loop.

    of the equation is

    (24)

    The range of experimental data used to develop eq. (24) was as follows:

    Ea = 0.002-0.21

    V,, = 0.001-0.50 m/s

    V,, = 0.07-1.3 m/s

    V -YE = l-153 V CR

    Fr = 0.00-14.1

    MO = 2.47 x lo- -0.390

    AD - = 0.11-l. AR

    Additionally, geometrical parameters not included in the correlation were of the following ranges:

    H - = 10.2-22s DR

    A AR = (5.60-360) x lo- 5

    ReLR = 40-130,000.

  • An average gtts hold-up and liquid circulation velocity

    Fig. 3. View of the upper part of the pilot-plant scale airlift reactor with external loop.

    The exponent of the Morton number in eq. (24) is actually very small. One may, therefore, expect that the Morton number is negligible. However, the range of numerical values of this number for the experi- mental data is so wide that even taking the power to be 0.012 it changes from 0.746 to 0.989.

    Plots presenting the dependencies of the experi- mental values of the average gas hold-up as a function of gas superficial velocity, obtained in our model reactors, are shown in Fig. 5. They illustrate a strong influence of liquid properties and reactor geometry on

    the results obtained. The values of the experimental average gas hold-up in the riser are plotted against those calculated using eq. (24) in Figs 6-8. Their com- parison shows a satisfactory validity of eq. (24) with up to f20% deviation.

    4.3. Liquid circulation velocity Hots presenting the dependencies of the experi-

    mental values of the liquid superficial velocity in the riser as a function of gas superficial velocity, obtained in our model reactors, are shown in Fig. 9. They

  • 2. KEMIILOWSKI et al. 4032

    0.07

    O.Ci5

    0.05

    0.04

    I -=0.03

    0.02

    O.oi

    n

    A 4A 0

    0

    0.00 L 0.00 0.06 0.10 O.i5

    OR Imlsl

    Fig. 4. Experimental values of the average gas hold-up in the riser column of the laboratory model airlift reactor obtained for various gas spargers (experimental medium-glycol solu- tion); single-nozzle spargers: (0) 4 mm; (A) 2.8 mm; (I) 2 mm; (A) 1.4 mm; (Cl) 1 mm; porous-plate spargers: (0)

    3Omm;(+)50mm;(V)70mm.

    J

    V, Lm/sl

    Fig. 5. Experimental values of the average gas hold-up in the riser column of model reactors; laboratory scale model reac- tor (single-hole gas sparger 2.8 mm), experimental media: (0) water; (0) water with added surfactant; (A) glycol; (A) glyml solution; ( W) sugar syrup; (Cl) CMC solution; pilot- plant scale model reactor (single-hole gas sparger 3 mm), water: (0) AD/AR = 1; (V) AD/AR = 0.56; CMC solution:

    (+) AD/AR = l;(V) AD/AR =0.56.

    illustrate a strong influence of liquid properties and

    reactor geometry on the results obtained. Fig- ures lo-12 present a comparison of the proposed model with our experimental data and the data given by Roberts (1979). One may see that over a large range of reactor size and liquid properties, the pro- posed model predicts liquid superficial velocity in the riser with up to + 20% error. The higher deviation of the calculated values observed in the range of small velocities (i.e. in the laminar region) may be caused by the assumption that friction loss coefficients at the top and the bottom of the reactor do not depend on the superfkial Reynolds number of the liquid. Therefore,

    0.06

    1 0.04

    1 Ox)3 . 0.02 S

    0.0 1

    0.00 0.00 0.0 1 0.02 0.03 0.04 0.06 0.06

    en. predicted 1-l Fig. 6. Comparison of the experimental values of the aver- age gas hold-up in the riser column of the laboratory model airlift reactor with those. predicted by eq. (20); single-hole gas

    sparger 2.8 mm (symbol; asin Fig. 5).

    J 0.00 0.0 1 0.02 0.03 0.04

    6, Cxedlcted I-l

    Fig. 7. Comparison of the experimental values of the aver- age gas hold-up in the riser column of the pilot-plant model airlift reactor with those predicted by eq. (20); single-hole gas

    sparger 3 mm (symbols as in Fig. 5).

    slightly too conservative values of these coefficients are used in the calculations in the laminar region (the values of the coefficients actually used are sum- marized in Table 3).

    Two basic equations [eqs (22) and (24)] enable the

    prediction of the liquid circulation and gas hold-up in airlift external loop reactors with almost complete phase separation at the top. These parameters can be predicted provided the geometry of the reactor, the liquid properties and the amount of gas to be intro- duced are known. The procedure for the prediction of the gas hold-up and liquid circulation velocity in the riser can be summarized as follows:

    (1) Assume liquid superficial velocity in the riser. (2) Estimate gas hold-up using eq. (24). (3) Predict liquid velocity using eq. (22) and other

    related equations.

  • An average gas hold-up and liquid circulation velocity 4033

    -I

    0.20 0.30 0.40

    en. aedcted f-1

    Fig. 8. Comparison of the experimental values of the aver- age gas hold-up in the riser column of airlift reactor, pub- lished in the literature, with those predicted by eq. (20) (experimental medium-water); Be110 et al. (1985): (A) AD/AR=0.25; (V) AD/AR = 0.11; Roberts (1979), AD/AR = 1: (0) ID 75 mm; (I) ID 25 mm; (0) Merchuk

    (1986), AD/AR = 1.

    I

    Fig. 9. Experimental values of the liquid superficial velocity in the riser column of model reactors (symbols as in Fig. 5).

    (4) If the assumed and calculated values of the liquid velocity do not agree satisfactorily, then return to point (2) with the last calculated value of the liquid velocity until sufficient agreement is obtained.

    5. CONCLUSIONS

    The results of the experimental investigations pres- ented lead to the following conclusions:

    -The influence of the gas sparger geometry on the average gas hold-up proved to be negligible, despite the observed changes of flow regime from uniform bubbly to churn-turbulent flow.

    -The liquid circulation velocity cannot be directly related to the gas superficial velocity because it depends also on reactor geometry and gas and liquid properties.

    Fig. 10. Comparison of the experimental values of the liquid superficial velocity in the riser column of the laboratory model airlift reactor with those predicted by the proposed

    model (symbols as in Fig. 5).

    f ,

    -1 0

    , v o 0 _-,f-p 0 ,e*

    , 4

    I #I

    , , I 1 ii/

    _- ,.*~~,o

    ,* , ,?-

  • 4.034 Z. KEMFJLOWSKI et al.

    Table 3. Values of the local friction factors applied in the calcu- lations, according to Maksimov and Orlov (1949)

    Experimental data obtained in/by

    Laboratory scale model reactor 1.8 1.3 Pilot-plant scale model reactor, 200/200 mm 2.95 1.3 Pilot-plant scale model reactor, 200/150 mm 3.01 1.43 Roberts, 1979 2.4 2.4

    -The same conclusion is valid for the average gas hold-up.

    -The simple model [see eqs (H-(22)] proposed for the prediction of the liquid circulation velo- city in an airlift reactor with external loop gives satisfactory results in a relatively wide range of physical and geometrical parameters for both Newtonian and nun-Newtonian liquids.

    -The proposed dimensionless correlation for the prediction of the average gas hold-up in the riser column of an airlift reactor with external loop [see eq. (24)] also gives satisfactory results for a relatively wide range of physical and geometri- cal parameters for both Newtonian and non- Newtonian liquids.

    Acknowledgement~The authors acknowledge the financial support provided by the Polish State Committee of Scientific Research (Grant no. 3 1266 9101).

    A d E Eo

    f Fr

    9 h, H k L MO

    ;

    Q Re

    V We Ah

    AP AZ

    NOTATION

    cross-sectional area, m* internal diameter, m energy dissipation or input rate, W Eijtvijs number, defined by eq. (13) Fanning friction factor Froude number, defined by eq. (10) acceleration due to gravity, m/s2 height, m power-law parameter, Pa s length of the tube, m generalized Morton number for power-law liquids, defined by eq. (11) power-law parameter pressure, Pa gas flow rate, m3/s Reynolds number, defined by eqs (15) and

    (20) superficial velocity, m/s Weber number, defined by eq. (14) height difference, m pressure drop, Pa vertical distance of manometer connec- tions, m

    Greek letters & gas hold-up,

    e friction loss coefficient

    p viscosity, Pas

    P density, kg/m3 d surface tension, N/m

    Subscripts B bottom of the reactor d gas-liquid dispersion D downcomer et7 effective F friction G gas phase h head space i input L liquid phase m manometer

    : nozzle or hole of the gas sparger riser

    T top of the reactor

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