Gas holdup and liquid circulation rate in concentric-tube airlift bioreactors

Chmlcal

Engineering Science, Vol. 49, No. 3, pp. 303-312,

Printat in Omt

WXS-2509/a) E6.00 + 0.W 0 1993 Pcwamon h Ltd

1994.

Britain.

GAS

Advanced

HOLDUP AND LIQUID CIRCULATION RATE CONCENTRIC-TUBE AIRLIFT BIOREACTORS

IN

P. AYAZI SHAMLOU, D. J. POLLARD, A. P. ISON and M. D. LILLY Centre for Biochemical Engineering, Department of Chemical and Biochemical Enginering, University College London, Torrington Place, London WClE 7JE, U.K. (First received

8 May

1993; accepted

in revised form 26 July 1993)

model gas holdup and liquid circulation rate is presented for airlift bioreactors based on a drift -flux model and an energy balance that takes into account the physical interactions betweenthe liquid, the gas bubbles and the liquid-wake associated with the bubbles. A 250 I pilot-scale concentric cylinder airlift bioreactor is used to obtain gas holdup and liquid circulation data for the fermentation of a Newtonian (Saccharomyces cereuisiae) and a non-Newtonian (Saccharopolyspora erythraea) culture. The data are interpreted in terms of the model equations and the agreement between the two is considered to be good. Abstract-A

INTRODUCTION

Prediction of the performance of bubble columns and airlift bioreactors requires information on phase holdups and fluid circulation rates in the column. Despite the several theoretical and the many experimental studies of airlift devices (Freedman and Davidson, 1969; Joshi and Sharma, 1979; Fields and Slater, 1983; Belle et aI., 1985; Jones, 1985; Kawase and MooYoung, 1986; Clark and Jones, 1987; Garcia, 1989; Devanathan et aI., 1990; Philip et al., 1990 and Wachi et al., 1991), most of which have been reviewed extensively elsewhere (Shah et al., 1982; Verlaan et al., 1986 and Chisti and Moo-Young, 1987), well-established theoretical equations are not as yet available for the estimation of the hydrodynamics of these reactors. The hydrodynamic characteristics of bubble columns and airlift devices depend critically on the flow regime occurring in the column. At a relatively low superficial gas velocity and with a uniform distribution of small bubbles in the column, the Bow regime is referred to as “homogeneous bubbly*‘. Bubbles travel up the column with little interaction between them in this regime. This type of flow is desirable, particularly in situations where gas-liquid mass transfer is important, because of the relatively large interfacial area provided by the bubbles. However, most industrial airlifts operate under conditions in which gas flow rate is too high to maintain bubbly flow. As gas flow rate increases, “churn turbulent” flow develops. Here, bubble coalescence results in a distribution of small and large bubbles along the column. Industrial airlifts and bubble columns are normally designed to operate in this regime. At significantly high gas flow rates, a transition occurs from churn turbulent flow to “slug” flow where bubbles grow large enough to occupy almost the diameter of the column. The transition between the diRerent flow regimes is gradual and occurs over a range of gas flow rate. For example, Chisti and Moo-Young (1987) suggest that a transition flow regime, known as “coalesced bubble

flow”, occurs between homogenous bubbly flow and churn turbulent Bow. Gas holdup, E#, and liquid circulation, Urr, are two of the most important parameters characterising the hydrodynamics of pneumatically stirred column reactors and critically influence transport processes, e.g. heat and mass, occurring in the column. Analysis of the hydrodynamics of airlift contactors is made difficult by the fact that phase holdups and fluid circulation rates are interdependent and cannot be predicted separately from first principles. An alternative approach is to develop engineering correlations for eg and US, based on experimental observations (Chisti, 1989). For example, a typical class of correlations suggests that c8 = u(U,,)~ and US,= c(V_J*, where U, is the superficial gas velocity at the inlet to the column. Many variations to these simple equations are available, e.g. U, may be expressed in terms of the gas power input per unit volume of column content (P,/V) or as a dimensionless Froude number based on tank diameter (U$rg). The major drawback of this approach is that the effects of too many important parameters are lumped into the coefficients and exponents of the equations, and this often seriously limits their application. In the present investigation a new model is presented for the prediction of gas holdup and liquid circulation in airlift devices. The model is based on simple physical interactions between the liquid, the gas bubbles and the liquid-wake associated with the bubbles. These interactions are used as part of an energy balance which is carried out over the circulation path of the column, and the governing equation is solved in conjunction with an independent relationship between gas holdup and primary bulk liquid velocity based on the drift-flux model of Zuber and Findlay (1965). Experimental data are provided for gas holdup and liquid circulation for a concentric tube airlift fermenter operating in a simple mode, namely with continuous gas phase flowing upward through the liquid in the riser section of the airlift.

303

P. AY~ZISHAMLOU

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These data are for fermentations of Saccharomyces cerevisiae and Saccharopolyspora erythraea. The results are used to test the applicability of the proposed model. THEORY

Consider a gas introduced in the form of discrete bubbles into the base of a stagnant column of liquid. The rising bubbles cause the liquid to circulate around the column by two separate mechanisms. In the first mechanism, liquid motion is caused by liquid entrainment and transport in the wake of the ascending bubbles. In the second mechanism, bulk liquid flow occurs by “natural circulation”, as a consequence of differences in the density of the mixture at the centre and that near the vertical walls of the vessel. In a bubble column, these density differences are always present because the rising bubbles tend to concentrate more towards the axis of the column, In a concentric tube, airlift device differences in gas holdup between the core and the wall region are increased significantly by the presence of the draft tube, which enhances the overall circulation of the liquid. Under steady-state operation in the column, the fractional phase holdups are related by Eg+EI+EW=l_

(1)

Experimental measurements of the liquid-wake volume are reported in the literature for multiphase flows (Ostergaard, 1965; Philip et al., 1990) and a simple equation that nevertheless gives an adequate fit with experimental data is provided by Darton and Harrison (1975) for the estimation of the ratio of the liquid-wake volume to bubble volume: +)4.4(~)“~33-l.

(2)

The gas voidage, cg, in eqs (1) and (2) is related to the superficial fluid velocities through the slip velocity, u,, which is the relative velocity between the gas and the liquid phase. Equations which permit the gas holdup of a bubble swarm to be estimated from superficial fluid velocities, and the bubble rise velocity generally take the form (Wallis, 1969)

et al.

without a significant loss of accuracy. Gas holdup in airlift contactors is normally sufficiently low enough to permit the use of eq. (5). According to the drift-flux model of Zuber and Findlay (1965), bubble rise velocity is given by Ua = C,
+ U,,.

(6)

The flux density has the units of velocity and is the sum of the volumetric flux density of each phase. Thus,


(7)

Substitution of eq. (5) into eq. (3) using eqs (6) and (7) and solving for cg gives % = (C, + I)(&

% + v,,) + war

(8)

where Cc is termed the distribution parameter. For axially symmetrical flow through a circular pipe, such as the riser section of an airlift column, and if radial power-law profiles are assumed for velocity and gas holdup distribution (Hills, 1974; Kawase and Moo-Young, 1986), theoretical expressions are available for Co (Zuber and Findlay, 1965). reveal that Co = 1.05 for These equations sew&e = 0.5. For most two-phase flow situations including bubble columns and airlift devices, the gas holdup at the centre exceeds that at the wall, and the data of Clark and Flemmer (1935) suggest that for airlifts Co = 1.07. Theoretical calculations suggest a maximum value of 1.6 for Co (Zuber and Findlay, 1965) and Govier and Aziz (1972) recommend a value of 1.15 for continuous bubble swarms and bubble sizes ranging from very small bubbles up to an equivalent bubble diameter if 2 cm. Clark and Jones (1987) use a value of 1.2 for C, in their calculation, and suggest that higher values of Co between 2 and 5 may be needed to explain certain two-phase flow situations, e.g. circulation due to the maldistribution of air caused, for example, by a single-pipe sparger. Determination of gas hold up from eq. (8) requires knowledge of the total superficial liquid velocity & and the single bubble terminal rise velocity, U,,. These are considered separately below.

The parameter m has a value between 0 and 3, indicating that the slip velocity decreases as void fraction increases. Typically for bubbles with Rb x 0.035 cm, the value of m is set equal to 3, while for bubbles in the range of 0.05 < Rb < 1.0 cm, m has a value equal to 1.5. However, as eg + 0, eq. (4) may be written as

Total superjcial liquid uelocity In the present analysis, the total superficial flow velocity of liquid along the vertical axis of the column, IL’,,,is assumed to be equal to the sum of the contributions of gas holdup differences between the riser and the downcomer, and the liquid-wake associated with the rising bubbles. Equation (2) gives the ratio of the wake volume to bubble volume (Darton and Harrison, 1975) and Ostergaard (1965) has given an empirical equation relating bubble velocity to the wake. In the present model, it is assumed that the wake moves with the same velocity as the bubble Thus, the overall superficial liquid circulation velocity may be obtained from the following mass balance for the liquid:

USE, = J#I

u,, = LIbrsi+ Uw(s, + sw)

t&(1

- Er) = L&(1 - Eg) - U*& = JB,

(3)

where Jr, is the drift flux for which equations are known (Freedman and Davidson, 1969 and Wallis, 1969), including the following expression due to Zuber and Findlay (1965): r&(1 - EJ”Eg = J#,.

(4)

(5)

(9)

Gas holdup and liquid circulation rate in concentric-tube airlift bioreactors where U’, represents the primary bulk liquid flow velocity due to holdup differentials in the column and VW is the velocity of the liquid-wake. If it is assumed that the liquid-wake has a linear velocity equal to the bubble velocity, the liquid-wake velocity can be expressed as

305

column as a function of the radial position, r. Kawase and Moo-Young (1986) and Hills (1974) provide experimental evidence to show that the radial liquid velocity distribution in a bubble column and the riser section of an airlift contactor has the following form: (15)

Substituting eq. (10) into eq. (9) and using eq. (2) to eliminate eW from the resulting expression gives KJ,,= v,,[l

- E#(l + k)] + u,,(l

+ k).

(11)

Numerous equations are available for the estimation of V,, (Joshi and Sharma, 1979; Joshi, 1980; Heijnen and van’t Riet, 1984; Chisti et al., 1988 and Philip et al., 1990). These equations are based on either a pressure balance or an energy balance carried out over the circulation path of the column. In the present investigation, the energy balance approach is preferred as it provides a simple expression for V,, which nevertheless appears to give a good fit of experimental data. Additionally, models based on energy balances are considered to be more widely applicable (Chisti, 1989). The starting point of the energy balance is the following equation for the rate of energy input into the liquid by the gas:

(12) where it is assumed that the kinetic energy of the gas entering the sparger is negligible as this is generally found to be no more than 6% of the total energy input (Lehrer, 1968; Joshi and Sharma, 1979). Energy dissipation in the column occurs in several ways. These include energy dissipation due to the liquid-wake behind the bubbles, energy dissipated in forming the bubbles, energy losses associated with bubble breakeup, energy dissipation due to bulk liquid flow through the riser and frictional losses as the liquid changes direction at the top and at the bottom of the riser. However, some of these losses are relatively small and can be ignored, at least to a first approximation (Joshi and Sharma, 1979 and Garcia et al., 1991). In the analysis that follows, the most significant modes of energy dissipation in the airlift are considered to be due to the liquid-wake behind the bubbles, Ew, the bulk liquid flow through the riser, Es, and losses due to flow reversal at the base of the riser, Er. Thus, the total energy dissipation rate in the column is approximately (Es + EW + EF), and therefore using eq. (12) Ei = Ew + EB + EF.

(13)

The rate of energy dissipation in the liquid motion is obtained from the following equation which was developed originally by Rietema and Ottengraf (1970):

where U,,(r) is the axial liquid velocity in the bubble

where VG is the liquid velocity along the centre line of the column. Equation (15) has been shown to be applicable to Newtonian and non-Newtonian liquids, Kawase and Moo-Young (1986) used eq. (15) to solve eq. (14) for turbulent two-phase flows in bubble columns and airlifts containing power-law liquids. Their solution is given by E, = 0.S12n2spLH

T[Ug13.

(16)

Freedman and Davidson (1969) evaluated the energy dissipation rate in the bubble wakes, Ew, by assuming that it consists of three terms which are (i) rate of loss of pressure energy of the liquid, Ap,HU,,g(1 - eg). (ii) rate of gain of potential energy of the liquid which is AHp,&g, (iii) the rate of pressure loss of the gas Ap, HU,g( 1 - E@).Thus, EW = (r+WZHp~sCLrB$

- ES) -

u.14.

(17)

Noting that the slip velocity is given by [CJ&/E~- U,,/(l - ee)] and using Turner’s definition of the shp veloctty, I.e. U, = UB, (Turner, 1966) eq. (17) can be written as Ew = (x/4)T2H&P~gsg(1

- eg)

(18)

which is identical to the expression used by Joshi and Sharma (1979) in their multi-cell circulation model for bubble columns. The energy losses, EF, arising from changes in flow direction at the top and bottom of the riser of an airlift reactor can be calculated by employing the concept of frictional loss coefficients which is well established For pipe flow. Chisti et al. (1988) suggest that flow in the head space of an internal loop, concentric cylinder airlift reactor is similar to that of an open channel and, therefore, energy losses due to flow reversal at the top of the column are expected to be relatively small compared with the bottom section. The energy losses due to flow reversal at the entrance to the riser can be expressed as (19) where KF is the loss coefficient For the bottom section of the riser and has a value which appears to depend on the ratio of AD/AR. Available data suggest that for low-viscosity fluids, e.g. water, K, has a value in the range between about 5 and approximately 17 (Chisti et al., 1988), while higher values are expected for more viscous liquids (Garcia et al., 1991).

P. AKAZI SHAMLOU

306

Substituting eqs (12), (16),(18) and (19) into eq. (13) and solving for the liquid centre-line velocity, U&, gives U& = 0.8

TQCQQ- (1 - &#)E#UBT] l/3 4(0.512nz

’

+ K,/ZrtHT)

(20)

The mean primary liquid velocity in the column, U,, is approximately equal to 0.755 l_J&(Verlaan et al., 1986). Thus,

y, = 0.6

~CICV,,- (1 - Eg)EgUIJTl 1’3 4(0.512nZ + KJ2nHT)

3

+

(211

Bubble rise welocity The terminal rise velocity of single air bubbles in water has been extensively studied (Clift et al., 1987) and Table 1 provides several equations for its prediction. Data for airlift columns suggest that, for orifice and perforated disc spargers, bubble diameter in the column appears to fall in the range O.&O.6 cm. This is fortuitous because Table 1 indicates that, in this range, the terminal rise velocity of single bubbles is independent of bubble diameter. Using the properties of water and Table 1 gives UeT = 25 cm/s which agrees closely with the mean value used by most researchers in this field. Model verification Equations (2), (8), (11) and (21) effectively permit gas holdup and overall liquid superficial velocity to be estimated for bubble columns and airlifts operating in the coalesced bubble flow and lower churn turbulent flow regimes. Numerical solutions of these equations may be obtained using an iterative technique as outlined below for the case of the riser section of an airlift. (i) For a fixed airlift configuration, a liquid of known rheological behaviour and a given superficial gas velocity in the riser, a value of gas holdup, 5, is assumed and the contribution to the total liquid circulation due to holdup differentials in the riser, Q,,, is calculated from eq. (21). For low-viscosity liquids, e.g. fermentation of Saccharomyces cerevisiae and bubbles in the range 0.4-0.6 cm, reasnably good initial estimates may be obtained by using KF = 5 and ZJ,, = 0.25 m/s, otherwise V,, can be calculated using the appropriate equation from Table 1. For highviscosity fermentation broths, higher values of the loss coefficient, KF. may be necessary. Table 1. Terminal rise velocity of an isolated bubble as a function of bubble diameter Equivalent bubble radius Ra (cm) -C0.035 0.035 < Rb < 0.07 0.07 -Z Rb i 0.2 0.2 < Rd < 0.6 R, z 0.6

Single bubble terminal rise velocny, U,, (l/g) (@f/v) 0.33(g0.76Rb’.=8/v0.5=) 1.35 Co/(& AJQ]‘.~ 1.53(grr A~/P:)~.=~ l.O(gR,)-

et al.

(ii) Using the assumed value of E# and the calculated value of Ub,, the magnitude of the overall liquid circulation velocity U,, is determined from eq. (ll), noting that the value of the parameter k is obtained from eq. (2). (iii) The calculated value of us,,, together with VW, U,, and a suitable value of C, are substituted in eq. (8) to solve for E,. Initially, Co is assumed to have a value close to unity. (iv) The value of the gas holdup obtained from (iii) is compared with the assumed value from (i), and if necessary the procedure is repeated until the calculated .z#is equal to the assumed value. (v) Steps (Q-o-(v)are repeated for a range of values of the superficial gas velocity, U,. In the following section, the application of the proposed model is demonstrated with reference to data for fermentations of baker’s yeast, Saccharomyces cereuisiae, and Saccharopolyspora erythraea obtained from experiments carried out in a concentric cylinder airlift bioreactor operating under bubbly flow regime.

EXPERIMENTAL Boreactor configuration Experiments were carried out in a pilot-scale concentric tube airlift fermenter manufactured by Chemap AG (Volketswil, Switzerland). The column was constructed from three cylindrical stainless steel sections, each with a diameter of 0.31 m. All work presented in this paper was performed with a working volume of 250 I which had an unaerated liquid height of 3.24 m. The draft tube height was 2.77 m (Fig. 1). The column was equipped with a range of draught tubes of 0.217 m outside diameter and 0.211 m internal diameter, giving a ratio of AR/A,, of 0.83. The tubes were constructed from straight pipes cut into a various lengths. These tube sections could be joined together to give draught tube heights from 1.17 to 3.22 m. The tubes were fitted with support rods which enabled the tubes to be positioned firmly and centrally in the column. The bottom draught tube was also fitted with three legs of 0.06 m length so as to allow an annular passage for the circulating liquid. Aeration was achieved by using either a perforated plate disc or a ring sparger. The perforated plate sparger had a diameter of 0.13 m with 120 holes of 0.001 m in diameter whereas the ring sparger diameter was 0.16 m and had 30 holes of 0.002 m diameter. In the experiments reported in this work, the gas was sparged up the draught tube and the annulus acted as the downcomer. Each section of the fermenter was jacketed and fully instrumented for the purpose of sterilization. Additionally, a variety of probes could be mounted in the side ports of the column to monitor the state of the fermentation broth. Liquid circulation was measured by a pH pulse tracer technique. A standard Ingold pH probe was used for this purpose. Gas holdups were measured by two methods. The “mean” gas holdup

Gas holdup and liquid circulation rate

in concentric-tubeairlift bioreactors

307

was obtained from measurements of aerated and unaerated liquid heights by using a graduated rod suspended from the top plate into the top section of the column. A sight glass in the head plate permitted visual observation of the graduations on the rod. The average volumetric gas holdup in the downcomer was measured separately using the well-established differential pressure measurement technique used widely by previous researchers and reviewed extensively elsewhere (Chisti, 1989). In the present study, the downcomer gas holdup was measured by using two “Druck” pressure transducers positioned at two points in the downcomer. The distance between the probes was 1.59 m. The operating conditions during the experiments were such that wall shear stresses had a negligible effect on the holdup. The gas holdup and liquid circulation in the riser were calcualted using basic mass balances around the column (Russell, 1989). Air flow rate was measured by using a HITEC thermal mass flow sensor calibrated specifically for this purpose. Saccharomyces cerevisiae fermentation The airlift reactor was inoculated with baker’s yeast, Saccharomyces cereuisiae (Distillers Company Ltd., Surrey, U.K.) at a concentration of 9 g dry cell weight (DCW) per litre into a non-sterile medium containing (g/l): glucose, 10; yeast extract, 10; ammonium sulphate, 5; potassium dihydrogen orthophosphate, 2.5; polypropylene glycol, 0.25ml/l. The temperature was kept constant at 26°C. pH was not controlled but remained constant at 7.

-7

Schematic diagram Airlift resctor.

of the

Key. i=Air inlet line 2= Vessel outside crting 3 - i nsulation cledi nq 4= temperature circulation jacket 5= iwide vessel wall 6= draft tube 71 ring 3perpcr Ii I = height of the ve$scl,4.1 1m HZ= height of the draft tubt.2.77m P = pressure probe poritions PZ= pH probe position A = addition port Fig. 1. Pilot-plant

CES 49:3-C

scale airlift fermenter used in

this work.

Filamentous fermentation erythraea (NRRL B-2338) Saccharopolyspora spores were harvested from a tap water agar medium after incubation at 29°C for 11 d. 2 ml of a spore solution (IO6 spores/ml) was inoculated into a 2 I shake flask containing 500 ml sterile medium. The medium contained (g/l): bacteriological peptone, 4 (Oxoid Ltd, Basingstoke); yeast extract, 6 (Yeatex, Bovril Foods Ltd., Burton-on-Trent); glycine, 2, magnesium sulphate, 0.5; glucose, 10; potassium diorthophosphate, 1.36. All reagents were analar grade unless specified. The medium was adjusted to pH 7.0 and sterilised at 121°C for 20 min. The glucose and potassium diorthophosphate were sterilised separately and aseptically added following sterilisation. Flasks were inoculated and cultures grown for 40 h in order to provide an 8% (v/v) inoculum for the following seed stage. The fermenter (LH Fermentation Ltd, Reading) contained 25 I of sterile medium and was agitated at 500 rpm by three Rushton turbine impellers. The air flow rate was set at 0.5 vvm and the temperature held constant at 29°C. Foam control was by addition of polypropylene glycol as required. The seed culture was grown for 19 h and then transferred to the airlift bioreactor via a sterile flexible tubing by overpressure in the seed fermenter. The airlift bioreactor was sterilised prior to inoculation at 121°C for 45 min. The medium was identical to that used in the

308

P. AVAZI SHAMLOU

seed fermenter except that the glucose concentration was higher (35 g/l). Carbon dioxide evolution rate, oxygen uptake rate, dissolved oxygen tension, pH, and temperature were monitored throughout the fermentation. Samples were taken every four hours for viscosity and DCW measurements. The hydrodynamic studies were carried out when the cell mass had reached 10 g DCW/I. Rheological measurements were carried out at room temperature using a coaxial cylinder viscometer (Bohlin Reologi AB, Lund, Sweden).

etal.

In Figs 2 and 3, mode1 predictions are compared with data for the aerated yeast fermentation used in the present investigation. Rheological measurements performed on samples of the yeast suspension in the airlift indicated a Newtonian-flow behaviour with a viscosity practically equal to water. Data shown in Fig. 2 are for two different spargers, namely a ring sparger used as part of the present study and a disc sparger employed previously by Russell (1989) in the same airlift configuration. For both spargers, the value of the loss coefficient, KF, was assumed to be constant and equal to 5 (Chisti et al., 1989). The data in Fig. 2 suggest that the type of sparger can have RESULTSANDDISCUSSION a strong influence on the gas holdup in the column. The experimental data examined as part of the The effect can be explained adequately by the propresent study were chosen to test the predictions of posed model in terms of the distribution parameters, the mode1 equations derived above. Numerous re- Cc, which characterises the shape of the liquid velosearchers have reported data on gas holdups for city profile in the column. It is generally accepted that air-water operations and some workers have also the liquid velocity profile is sensitive to changes in the measured liquid circulation velocities in the riser flow and distribution of bubbles across the column, and/or in the downcomer (Chisti, 1989). Only a few both of which are affected by the type and design of researchers appear to have studied the fluid dynamics the sparger. In Fig. 2, the solid curves were obtained of airlifts containing moderately viscous Newtonian from the model equations by using the operating and non-Newtonian liquids (Miyahara et al., 1986; conditions in the riser section of the column. In the Philip et al., 1990; Wachi et al., 1991). There is hardly case of the disc sparger, the value of the distribution any information on the hydrodynamics of airlift parameter, Co, used in the model was equal to unity. bioreactors containing highly viscous non-Newtonian For comparison, the curve for C,, = 1.2 is also shown. fermentation broths. For the ring sparger, a value of Co equal to 0.7 was Available techniques for the measurements of these found to give better agreement between prediction parameters have been extensively reviewed by others and experimental observations. This infers a liquid (Heijnen and van? Riet, 1984, Chisti, 1989), and a fact flow profile in the riser with the velocity higher nearer that clearly emerges from these reviews is that there the draft tube than at the ccntre of the riser. As the are many experimental difficulties associated with the ring sparger discharges air close to the draft tube, such measurements and interpretation of data relating to a liquid velocity profile is not surprising at least in the these parameters in bubble columns and airlifts. For region close to the sparger. There will be a gradual example, it is well recognised that the presence of even change in the velocity profile as liquid moves up the small traces of impurities in water causes the slip riser. The value of Co represents, therefore, the avervelocity to change significantly. Heijnen and van? age of the liquid velocity profiles in the riser. Riet (1984) concluded, for example, that, for otherwise Higher holdups than those predicted by the mode1 identical conditions, the addition of salt can increase were observed for superficial gas velocities greater gas holdup by anything between 20 and 200%. than approximately 0.2 m/s. The degree of deviation Equally important are the experimental observations between predictions and experimental data increases that slip velocity is a function of liquid temperature as gas velocity increases beyond this value. This is and gas density (Grover et al., 1986; Clark, 1990; attributed to a change in the hydrodynamics of the Wilkinson et al., 1990). Other factors that are known Bow in the column. Verlaan et al. (1986) suggest that to influence gas holdup include the type. and the slug flow occurs at gas holdups above about 0.3. location of the sparger (Chisti, 1989), the presence of Experimental data indicate that there is no sharp baffles and internals in the column, the size. of point at which flow changes from one regime to angas-liquid disengagement region at the top of the other. As gas velocity is gradually increased, gas holdcolumn (Russell, 1989) and the ratio of the cross up and liquid circulation become progressively less sectional area of the riser to that of the downcomer sensitive to gas flow rate indicating a change in flow (Wachi et aI., 1991). There is little information on the regime. The available data suggest that the value of combined effect of all these factors on gas holdup and superficial gas velocity at which slug flow begins is liquid circulation rate in the column. Inevitably, approximately in the range 0.15-0.25 m/s. For this therefore, variations in reported values of these para- reason, measurements were made below 0.15 m/s as meters exist between researchers. For these reasons, depicted in Fig. 2. models and equations which are capable of predicting The experimental gas holdup and liquid circulation gas holdup and liquid circulation rate with an ac- data shown in Figs 4 and 5 are for fermentation of S. curacy of + 30% are normally considered adequate erythraea after 29 h. The measurements were made by (Chisti et al,, 1988), and predictions of & 20% appear stopping the normal mode of operation of the column, making measurements of gas holdup for a series of gas to be acceptable (Chisti, 1989; Garcia et al., 1991).

Gas holdup and liquid circulation rate in concentric-tube

flow rates and then reverting back to normal operation. These measurements were taken sufficiently rapidly so as to minim& any effect on the growth rate and antibiotic production of the fermentation. Rheological’measurements carried out on samples of the fermentation broths removed periodically from the bioreactor were analysed using a two parameter power-law relationship (T = K$J”).Figure 6 shows the change in the flow behaviour index, n, and the consistency coefficient, K, of the culture broth during the fermentation period. It is evident from Fig. 6 that the non-Newtonian behaviour of the broth changes dramatically during the growth period, and more importantly the effect of this change on gas holdup is significant, as shown in Fig. 4.

airlift bioreactors

309

The concept of an average shear rate in the bubble columns can be used to examine the effect of nonNewtonian properties on flow regime in the column. The average shear rate in a bubble cotumn and the riser of an airlift device can be defined using * = k,Lr,. Y.”

m

The shear rate constant, k,, in eq. (22) has a value of 5000 for bubble columns according to Nishikawa (1977), which is applicable for U., in the range of 0.04-0.1 m/s. Equation (22) has been used by many other researchers in this field (Deckwer et al., 1982; Godbole et al., 1984 and Kelkar and Shah, 1985), although the magnitude of the shear rate constant, k., appears to be dependent upon the geometrical system and the range of operating conditions (Chisti, 1989).

Fig. 2. Comparison between mode1 predictions and experimental observations for riser gas voidage, Ed,as a function of superficial gas velocity, U, (m/s). Data are for air-yeast experiments and refer to two types ring sparger, 0, (this work); disc sparger, l , (Russell, 1989). Model predictions were obtained with KP = 5 and with Co = 0.7 for ring spargcr and Co = 1 and 1.2 (broken line) for disc sparger.

0

L 0

1 0.1

kg

[m/s)

0.2

Fig. 3. Model predictions vs experimental measurements for riser superticial liquid velocity, U, (m/s), against superficial gas velocity, U, (m/s). Data are for the aerated yeast experiments and the ring sparger.

310

P.

AYAZI SHAMLOU

et al.

0.1

%I

Fig. 4. Comparison between measurements and model predictions for changes in riser gas voidage. es, as a function of superficial gas velocity, U, (m/s). The data am for Saccharopolyspora erythmea, 0 (n = 0.55) and yeast fermentation (n = l.O), 0. Model predictions were obtained using K, = 30 and Co = 1.0 for S. erythraea and K,J = 5, Cc = 0.7 for yeast fermentation.

0

03

kg

bvs)

0.2

Fig. 5. Model predictions vs experimental measurements of superficial riser liquid Row velocity as a function of superficial gas velocity for S. erythrnea fermentation; parameters used for prediction are given in Fig. 4.

For example, Schumpe and Deckwer (1987) recommend a value of 2800 for k., while Henzler (1980) suggests that k is equal to 1500. For a power-law fluid, the apparent viscosity, pa., can be defined as cc. = T/jr,” = K(k,Uw)“ml

= K(5ooOV,)“-‘.

(23)

First-order calculations based on eqs (22) and (23) suggest that as the culture broth becomes increasingly more non-Newtonian and viscous, the liquid flow Reynolds number in the riser changes from a value in the turbulent flow to a value in the laminar or lower transitional regime. The changes in the rheology of the broth and the consequential change in the flow regime in the column profoundly affect the gas holdup

and liquid circulation rate in the bioreactor as shown, respectively, in Figs 4 and 5. As far as the proposed model is concerned, the effects of changes in broth rheology and flow regime are reflected strongly in the value of the loss coefficient, KF, and to a lesser extent on the value of the distribution parameter, Co. Figures 4 and 5 show model predictions for S. erythruea obtained using the experimental value for the flow behaviour index, n = 0.55, distribution parameter, Co = 1.0, and loss coefficient, KF = 30. In Fig. 4, the data for the aerated yeast are also shown for comparison. The comparison between model predictions and experimental observation depicted in Figs 4 and 5 are considered to be good. Additionally, the data for liquid circulation shown in Fig. 5 are

Gas holdup and liquid circulation rate in concentric-tube airlift bioreactors

time

I hrs)

Fig. 6. Changes in flow behaviour index ( + ), n, and consistency coefficient (A), K (Pas”), as a function of time of fermentation for S. erythraea.

described adequately with KF = 30, suggesting that, compared with the aerated yeast data (KF = 5), energy losses due to the change in flow direction at the entrance to the riser are higher in the case of viscous non-Newtonian S. erythraea broth. Philip et al.. (1990) used an expression similar to eq. (11) for the estimation of the total superficial liquid velocity, &. The ratio of the liquid-wake volume to bubble volume, k, in their analysis was assumed constant and was fixed empirically for each liquid so as to get a good fit of experimental data. Philip et al. (1990) used values for this ratio in the range O-3 for liquids of viscosity between 0.115 and 2.85 Pas, and surface tension between 0.03 and 0.08 N/m. Their actual measurements of the liquid-wake volume indicated values for the ratio of liquid-wake volume to bubblewake volume between 0 and 2. However, no generalisation could be detected as to the effects of viscosity and surface tension on the ratio of the two volumes. Equation (2) predicts values for this ratio between 0.5 and 1.5 which falls in the range reported by Philip et al. ( 1990). The model equations described in this work assume that the effect of downcomer gas recirculation on the riser gas holdup is negligible, and the good agreement between the model and experimental data demonstrates that this assumption is reasonable. Verlaan et 01. (1986) concluded that, for air-water, the rate of gas carry over from the downcomer is approximately in the range l-8.5% of the riser gas flow. This is normally well masked by the natural scatter of experimental data, specially for operations in bubbly flow regime in which gas flow rate is relatively low. The experimental work described here was done using one particular configuration of the airlift fermenter. Further investigation of the validity of the proposed model will be made using different configurations which are possible with this bioreactor. NOTATION

A AD AR

cross-sectional area of column, mz cross-sectional area of downcomer. m2 cross-sectional area of riser, m2

311

distribution parameter, dimensionless energy dissipation in liquid motion, W energy dissipation resulting from change in flow direction, W energy input by the gas, W energy dissipation due to bubble wake, W acceleration due to gravity, m’/s liquid height in the column, m volumetric flux density, m/s gas drift flux, m/s ratio of liquid-wake volume to bubble volume, dimensionless shear rate constant, m-l consistency coefficient of the broth, Pa s“ loss coefficient, dimensionless flow behaviour index of the broth, dimensionless gas power input, w volumetric gas flow rate, m3/s volumetric liquid flow rate, m3/s radial position, m column radius, m equivalent bubble radius, m diameter of column and riser section, m primary liquid velocity along the column, m/s bubble rise velocity relatively to mean mixture velocity, m/s terminal velocity of an isolated bubble, m/s centre-line primary liquid velocity, m/s superficial gas velocity in the riser, m/s total superficial liquid velocity in the riser, m/s linear velocity of liquid-wake, m/s gas-liquid slip velocity, m/s volume of two-phase mixture, m3 Greek letters shear rate, (I/s) average shear rate, (l/s) gas-liquid density difference, kg/m3 gas holdup in the column, dimensionless liquid holdup in the column, dimensionless liquid-wake holdup, dimensionless gas holdup near vessel wall, dimensionless gas holdup at column centre, dimensionless Y kinematic viscosity, m2/s liquid density, kg/m3 PL surface tension, N/m U shear stress, N/m2 t REFERENCES

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