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Mechanistic analysis of xanthan gum production in a stirred tank
[J. Ferment. Technol., Vol. 66, No. 3, 355-364. 1988]
Mechanistic Analysis of Xanthan Gum Production in a Stirred Tank HITOSHI FUNAHASHII, KOH-IcHI HIRAI2~ TOSHIOMI YOSHIDA.2, a n d HISAHARU TAGUCHII
Department of Fermentation Technology1, International Center of Cooperative Research in Biotechnology2, Faculty of Engineering, Osaka University, 2-1, Yamada-oka, Suita-shi, Osaka 565, Japan The overall effect of agitation on xanthan gum production by Xanthomonas campestris ATCC13951 in a stirred vessel was mechanistically analyzed considering local variation of the specific production rate due to variation of shear stress in the vessel. The whole liquid volume in a fermentor was roughly divided into three regions; the micromixing region around the impeller with high shear stress, the macromixing region dominated by a circulating flow and the stagnant region. The value of the shear rate was first ascertained by experiments in order to obtain a picture of shear rate variation in a radial direction from the impeller, and the equivalence between the volumes of the high shear stress region and micromlxing region was confirmed. The shear stress obtained using a correlation between the shear rate at the impeller tip and Reynolds number of Wichterle et al. was used as a representative of the shear stress in the micromixing region, and the shear stress estimated by use of an empirical correlation between the average shear rate in a fermentor and agitation speed derived by Metzner et al. was adopted as a representative of the shear stress in the macromixing region. The information about the circulation time distribution was also used to take into account oxygen deficiency during circulation of liquid elements in the macromixing region, considering that oxygen from the gas phase was supplied mainly in the high shear region. The calculated values ofxanthan gum concentrations which were obtained by the proposed simulation method agreed well with the experimental data in the time course of xanthan gum production at various agitation speeds. Experimental results of the relationship between the overall specific production rate and ND (N, agitation speed, and D, impeller diameter) was also verified by the proposed method.
X a n t h a n g u m is a n extracellular heteropolysaccharide p r o d u c e d b y Xanthomonas campestris. I t is used i n food a n d i n d u s t r i a l applications, X,2) a n d m a y be useful i n secondary oil recovery.2, 8) Weiss a n d Ollis 4) have reported that the changes i n cell c o n c e n t r a t i o n , x a n t h a n g u m , a n d substrate d u r i n g c u l t i v a t i o n u n d e r constant a g i t a t i o n conditions c a n be simulated b y a logistic, the L u e d e k i n g - P i r e t e q u a t i o n , a n d a modified L u e d e k i n g - P i r e t e q u a t i o n , respectively. Pinches a n d P a l l e n t 5) have also reported that the oxygen u p t a k e rate * Corresponding author
c a n be estimated b y use of these equations. T h e effects of a g i t a t i o n o n the m i c r o b i a l p r o d u c t i o n of x a n t h a n g u m have not yet b e e n analyzed, b u t M o r a i n e a n d RogovinS) have suggested that the a g i t a t i o n speed is a n i m p o r t a n t o p e r a t i o n a l factor. T h e specific rate of x a n t h a n g u m p r o d u c t i o n by X. campestris ATCC13951 depends o n N D , where N a n d D are the a g i t a t i o n speed a n d the impeller diameter, respectively; a n d shear stress is one of the most i m p o r t a n t factors relevant to agitation. 7) X a n t h a n g u m solution is a n o n - N e w t o n i a n fluid with pseudoplastic behavior, a n d the shear flow caused b y the i m p e l l e r is l i m i t e d to the area
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near the impeller itself.
Therefore, changes
M e a s u r e m e n t o£ s h e a r s t r e s s The shear rate at each part of a stirred tank was obtained from the distribution of the fluid velocity by measurement of the limiting diffusion current.9,10) The shear stress was estimated by substitution of the shear rate into the power law equation. The electrode used was one in which a platinum wire 0.2 mm in diameter was embedded in the center of a glass rod (diameter, 5 mm), with the tip of the wire exposed at the end of the rod. A solution containing 0.025 M potassium ferrocyanide, 0.025 M potassium ferricyanide, and 0.1 M potassium sulfate was used as the electrolyte and the xanthan gum (Taiyo Kagaku Co., Ltd.) was dissolved at a concentration of 9×10 -3, 1.7×10 -2 , or 2.7x10-2kg/kg broth. The electrode was inserted horizontally from the side wall of the fermentor at half of the depth of the liquid. The distribution of fluid velocity near the impeller was measured by sliding the electrode, which passed laterally through the wall of the fermentor, and shifting the impeller vertically 5 or 10 ram, making sure that aeration did not hinder the measurement of fluid velocity by this method.
in the mixing conditions during cultivation a r e c l e a r l y i m p o r t a n t for t h e p r o d u c t i o n o f xanthan gum. We have reported that the volume of each mixing region and the circulation time distribution at various xanthan gum concentrations can be estimated empirically from the impeller diameter, the impeller width, and the consistency coefficient of the x a n t h a n g u m s o l u t i o n , s)
In this report, we describe a method to show the effects of agitation on the production o f x a n t h a n g u m by using an empirical model for the expression of mixing states and by considering the effects of shear stress on the specific production rate of xanthan gum. Materials and Methods Fermentor and impeller The fermentor was the same as that used in a previous study, 7) with a diameter of 200 mm and capacity of 10 I. The total liquid volume was 6 l, and air was supplied at 1 vvm. The vessel was equipped with three baffle plates. A turbine impeller having six flat blades, 100 mm in diameter and 20 mm in width, was used. Tile agitation speed was from 5 to 16.7 rps.
A
Stagnant region
[J. Ferment. Technol.,
Results and Discussion Estimation of overall specific prod u c t i o n rate o f x a n t h a n g u m in a s t i r r e d tank The specific production rate of Cmicro - Q02 X tp = 0
B
,
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s
~
]
~..j~^
2 °Xtl>O
(i=l-P-1)
~mixing ~ , - ~ - - ~ , w z ~regio~ l~/TJ~'~.1 . Fluid element Cmicro =
C*- (Qo2X/kLa')
(~" Spa g .=r -
~LJ
without oxygen limitation O " with oxygen limitation
Fig. 1. Mixing state of culture broth of xanthan gum production in a stirred tank. A. The three regions in a stirred tank. The whole liquid volume in a stirred tank was divided into three regions. The micromixing region was dominated by the radial flow near the impeller, the macromixing region was the region of a slow circulating flow, and the stagnant region was where the fluid was stagnant, s) B. Model for oxygen consumption in the macromixing region• Oxygen might be supplied mainly in the micromixing region, with little going to the macromixing region. When the dissolved oxygen concentration in the micromixing region is not 0, the dissolved oxygen at a certain concentration in the fluid element left from the micromixing region would be consumed by the respiration of cells during circulation in the macromixing region, and places with limited oxygen might exist in the macromixing region.
Vol. 66, 1988]
Mechanistic Analysis of X a n t h a n Gum Production
xanthan g u m depended on the shear stress, that is the mixing state in each region. 7) T h e specific production rate at a particular place in a stirred tank might be different because of differences in the shear stress and oxygen supply at that place. A d i a g r a m of the mixing state is shown in Fig. 1-A. The whole liquid volume in the tank was divided into three regions. T h e micromixing region was dominated by the radial flow near the impeller, the macromixing region was the region of a slow circulating flow, and the stagnant region was where the fluid was stagnant, s) The overall specific production rate in a stirred tank, SPR, was calculated by the following equation, with the volume in each mixing region and the specific production rate therein taken into consideration.
SPR=(Vmt:~oSPRmI~o -k V . . . . . SPR . . . . . )IV
(1)
where V, Vmi.... and V . . . . . are the total volume of liquid, and the volumes of the micromixing and macromixing regions, respectively. SPRmicro and SPR . . . . . are the m e a n specific production rates in the micromixing and macromixing regions, respectively. Production of xanthan g u m in the stagnant region was neglected because of no oxygen supply in the region. T h e relationship between the specific production rate of an individual cell, spr, and the shear stress, % was obtained from data reported before 7) to be as shown in the following equation:
spr=2.5 × 10-' × ~-/(48-k,), or
sprmax, when 2 . 5 × lO-4×~'/(48-t-~')>sprma~
(2)
T h e value of spr~az was 1 . 1 × 1 0 - 4 k g xanthan/(kg dry cell.s) when oxygen was unlimited. T h e shear stress influences the transfer of materials such as glucose, oxygen etc. from the m e d i u m into the cells. 7) O n the other hand, the oxygen supply from bubbles into the m e d i u m was also important for the estimation of the specific
357
production rate. Oxygen might be supplied mainly in the micromixing region, with little going to the macromixing region. When the dissolved oxygen concentration in the micromixing region is not 0, the dissolved oxygen at a certain concentration in the fluid element left from the micromixing region would be consumed by the respiration of the cells during circulation in the macromixing region, and places with limited oxygen might exist in the macromixing region as shown in Fig. 1-B. When the oxygen supply was limited in the micromixing region, xanthan g u m would no longer be produced in the macromixing region, and sprma~ m a y be limited by the oxygen supply. Consequently, the mean specific production rate in each mixing region might depend on the mean shear stress in that region and on the oxygen supply from bubbles into the m e d i u m when the concentration of glucose or other substrates do not limit the production. Effects o f s h e a r s t r e s s o n t h e m e a n specific p r o d u c t i o n rate in e a c h m i x i n g region In order to estimate the m e a n specific production rate in each mixing region, it is necessary to consider the effects of the m e a n shear stress and oxygen supply from bubbles into the medium. Here, we discuss the m e a n shear stress in each mixing region, and show a method for the estimation of the mean specific production rate in each region, provided there is no limitation of the oxygen supply from bubbles into the medium. Shear stress is particularly important for xanthan g u m production, v) The specific production rate increases with increasing shear stress as long as the shear stress is less than 40 Pa, but it is constant at the m a x i m u m value when the shear stress is more than 40 Pa. T h e xanthan g u m solution is a nonNewtonian fluid with pseudoplastic behavior, and the region of high shear is limited to the area near the impeller. T h e volume of the high shear region m a y be important for xanthan g u m production. T h e velocity distribution near the impeller was obtained by use of a method to measure the limiting diffusion current. There was
358
[J. Ferment. Technol.,
F U N ~ A S m et al.
cellulose, carbopol and attasol : ~,av= k W
c 4 .2 .= o~3 ¢.x
o
'
I
'
i
I
I
/ #,
/
/
B
1
m
/ 0
,
I
,
I
,
I
(3)
I //
i
4 1 2 3 Volume of high shear region ( [ )
Fig. 2. Relationship between volumes of the micromixing region and high shear region at various
agitation speeds. A, O, and m; data for xanthan gum concentrations of 9× 10-3, 1.7 × 10-% and 2.7 × 10-* kg/kg broth, respectively. a critical point at which the velocity decreased sharply with distance from the impeller tip, and the shear rate inside the boundary region was more than 20 1/s. Figure 2 shows the correlation between the volume of the micromixing region and the volume of the high shear region, in which the shear rate was more than 20 l/s, at various agitation speeds, for xanthan g u m concentrations of 9 × 1 0 -3 , 1.7×10-*, and 2 . 7 × 1 0 -2kg/kg broth. The volumes of the high shear region were almost equal to the volume of the micromixing region at various agitation speeds. T h e results suggested that the micromixing region corresponded to the high shear region. I n a xanthan g u m solution of 1.7× 10-3 and 2.7× 10-3kg/kg broth, the shear stress in the kigh shear region was 40 Pa or more, and the specific production rate in the region might be maximized. Metzner and Otto ix) have proposed the following equation for the relationship between the mean shear rate in a stirred tank, ~,v, and the agitation speed, N, within the range of the l a m i n a r flow region not only for Newtonian but also for non-Newtonian fluids, i.e., for solutions of carboxymethyl
where k is a constant that depends on the shape of impeller used. Calderbank and Moo-Young x*) have reported that the value o f k is 11.6 within the range of 0.08 to 1,000 of the generalized Reynolds n u m b e r when a turbine impeller with six fiat blades is used. 13) In our investigation, the generalized Reynolds n u m b e r was from 150 to 1,100. Based on these results, the shear stress, ~'~v, that was calculated by use of Eq. (3) and a power law equation, was adopted as the mean shear stress in the stirred tank. Wichterle et al. lo) have reported that the shear rate at the tip of the impeller, ~M can be estimated by the following equations: (1 -[-5.3 n) I/"ReM1/~1+", Re~ ~- N c~-,)D~p/K
~[N=
(4) (5)
where K is the consistency coefficient. T h e flow behavior index, n, was 0.12 at the concentration of xanthan g u m more than 9 × 10-8 kg/kg broth. Rex is the Reynolds n u m b e r defined by Eq. (5). T h e shear stress at the tip of the impeller, ~'M, can be estimated by substitution of the value for the shear rate obtained by these equations into the power law equation. The shear stress thus estimated would be m a x i m u m in the stirred tank. I f it was less than 40 Pa, no region in the stirred vessel has shear stress more than 40 Pa. When the shear stress at the tip of the impeller is more than 40 Pa, the high shear region, with 40 Pa or more of shear stress, and the low shear region, with less than 40 Pa, would probably exist together in the stirred tank. From the results shown in Fig. 2, the high shear region might correspond to the micromixing region, and the low shear region to the macromixing region. Based on this information about the mean shear stress in each mixing region, the mean specific production rate in the micromixing, SPRmi .... and macromixing regions, S P R . . . . . . was estimated as follows: 1) When ~'M< 4 0 P a , there is no region in which shear
Vol. 66, 1988]
Mechanistic Analysis of Xanthan Gum Production
stress is 40 Pa or more, and the m e a n specific production rate, estimated by substitution of ~-~v into Eq. (2), SPRay, was adopted as SPRmic~o and SPR ......
SPR~icro=SPR,~, SPR . . . . . =SPRav
and (6)
T h e overall specific production rate was obtained as follows by substitution of Eq. (6) into Eq. (1).
SPR=SPR, v×(V=~¢~o+V . . . . . )IV
(7)
2) W h e n ZM_~ 4 0 P a , we assumed that SPR~¢ro was equal to the m a x i m u m of the specific production rate, spr. . . . because the micromixing region corresponded to the high shear region, and the shear stress in the high shear region at a xanthan g u m concentration more than 1.7× 10-2kg/kg broth was more than 40 Pa. SPR . . . . . depended on the mean shear stress in the macromixing region. However, the distribution of the shear stress in the stirred tank has not been investigated in detail, because it is difficult to measure it thoroughly in a tank. ~-~ was used as the m e a n shear stress in the macromixing region.
SPR~i¢~o=sprmax and SPR . . . . . =SPR~v
(8)
The overall specific production rate was obtained as follows by substitution of Eq. (8) into Eq. (1).
SPR= ( s p r ~ Vm~o~o-kSPR., V
. . . . .
)IV
(9) T h e overall specific production rate when there is no limitation of the oxygen supply can be estimated from Eqs. (7) or (9). T h e volume of each mixing region was estimated from the conditions of agitation: namely, the agitation speed, impeller diameter, impeller width, and also the consistency coefficient of the culture broth. T h e consistency coefficient was estimated empirically from the xanthan g u m concentration by the use of the following equation: K = 4 . 9 × l0 s × XG 1.3
(I0)
where XG is the xanthan gum concentration.
359
This relationship held between concentrations of xanthan g u m of 9 × 10 -3 and 4 . 6 × 10 -2 kg/kg broth. Effects of oxygen supply to the medium on xanthan gum production X.
campestris is an aerobic microorganism, and oxygen is necessary for the production of xanthan gum.7~ When the oxygen supply from bubbles into the m e d i u m was not limited, the value of Sprmax was 1.1 × 10 -4 kg xanthan/(kg dry cell.s). When the oxygen supply was limited, however, sprm,~ would be less than 1.1 x 10-4kg xanthan/(kg dry cell.s). Some ceils in the macromixing region do not produce xanthan g u m because of oxygen deficiency in a liquid element traveling for a long time from the micromixing region where most of oxygen is supplied. In fact, the m e a n circulation time is sometimes of the order of a few seconds, is) during which time cells m a y consume the dissolved oxygen. Here, we discuss the effects of oxygen supply on the mean specific production rate in each mixing region. In this cultivation, the dissolved oxygen tension might not be the same throughout the fermentor, and it is very difficult to obtain, experimentally, a complete picture of the local distribution of dissolved oxygen tension. The oxygen transfer from the bubbles into the medium would depend on the intensity of the shear flow. When a highly viscous solution is used, the oxygen carried from the macromixing region into the micromixing region might be negligible in the early period of the measurement of the volumetric oxygen transfer coefficient by the dynamic method. 14) Therefore, the oxygen balance in the micromixing region could be shown by the following equations; dC micro/dt =kLamtcro ( C * --Cmiero) --qCmtero/Vmiero =kLat(C ~ --Cmiero)
(l l)
where Cml¢,o is the dissolved oxygen concentration in the micromixing region, C* is the concentration saturated with the air, Vmier o is the volume of the micromixing region, and q is the exchange rate between the
360
Fu~a-~asm et al.
micromixing and macromixing regions. kLamicro and kLa' are the actual and apparent volumetric oxygen transfer coefficients, respectively, in the micromixing region, and k~a' was measured under various agitation conditions and at various concentrations of xanthan gum in a previous study. 7) The oxygen conveyed from the macromixing into the micromixing region in a fermentor would be small compared with the oxygen supply in the micromixing region, because the oxygen is consumed by respiration during circulation in the macromixing region. The concentration of the dissolved oxygen in the micromixing region at a quasi-steady state during cultivation, C=i .... could be calculated by use of following equation:
[J. Ferment. Technol.,
SPR . . . . . = N',{R(O~)SPR~XI/[{~R(O~)IX] =~{R(O~)SPRd/~R(O 0 (14)
where R(Oi) is the relative frequency of the circulating flow at 0i of circulation time and can be estimated by the agitation speed and impeller diameter.S) Thus, the value of SPR . . . . . estimated by Eq. (14) was substituted into Eq. (1). On the other hand, when the oxygen supply limits the xanthan gum production in the micromixing region, xanthan gum would no longer produced in the macromixing region, and the mean specific production rate in the micromixing region may be affected by the oxygen supply. The specific production rate, spr, corresponded to the specific oxygen uptake rate, SOUR, as shown in Fig. 3. The correlation Cmicro-~-C*--( Q,o,X/kLa') (12) between the specific production rate and the The specific oxygen uptake rate at 40 Pa specific oxygen uptake rate is described by or more of shear stress reported elsewhere 7) the following equation for 3.0×10 -5 to was adopted for Qo~, and the value of kLa' 1.1 x 10-4 kg xanthan/(kg dry cell.s). under each agitating condition was described s p r = 2 . 7 8 × S O U R - - 5 . 0 9 × 10-n (15) in the same study. 7) When the dissolved oxygen concentration in the micromixing region is not 0, the dissolved oxygen at a certain concentration in the fluid element left from the micromixing region would be consumed by the respiration of cells during circulation in the macromixing region, as shown in Fig. 1-B. Therefore, when the circulation time is longer than the time for complete consumption of the dissolved oxygen in the fluid element, production would cease because of the oxygen limitation before the fluid element returned to the micromixing region. Based on this idea, the mean specific production rate in a circulating flow, SPRy, was estimated as follows: SPRt = S P R ~ × t p/0i
The maximum specific production rate, spry,a× in the micromixing region could be estimated by substitution of the maximum specific oxygen uptake rate, SOUR . . . . into "01
'
I
'
I
'
I0 '
o ::~l-
(13)
where t p is the time for complete consumption T.#I , I , I , I , "r" of oxygen for xanthan gum production in 0 2 3 4 5 6 a circulating flow, which equals C=~¢~o/ S p e c i f i c o x y g e n u p t a k e rate (Qo~ X), and 0~, the circulation time in the X I O s ( k g 0 2 / ( k g dry c e l l . s ) ) macromixing region. SPR,, was obtained Fig. 3. Relationship between the specific oxygen by substitution of ~-,, into Eq. (6). SPR . . . . . uptake rate and the specific production rate of would be estimated considering the SPR~ of xanthan gum. Data from a previous studyT) each circulating flow as follows: were used in the calculations.
Vol. 66, 1988]
Mechanistic Analysis of Xanthan Gum Production
Eq. (15). sprm~x= 2 . 7 8 × SOURma,--5.09 × 10 -5 (16)
spr=~, estimated from Eq. (16) was less than 1.1 x 10 -4 kg xanthan/(kg dry cell.s), and was adopted as Sprm** in Eq. (8). T h e m a x i m u m of the specific oxygen uptake rate in the micromixing region is equal to the specific oxygen supply rate, and could be calculated by the following equation: SO URm, ~=kLa'C*/X
(17)
Consequently, the overall specific production rate under various agitation conditions was estimated by consideration of the m e a n shear stress in each mixing region and the oxygen supply from bubbles into the m e d i u m in accordance with a flow chart, as shown in Fig. 4. Comparison experimental
between calculated and data T o check the meth-
od described above for the estimation of xanthan g u m production, the calculated values were compared with the experimental values obtained before. 7> The estimation was carried out for the case of corresponding
,/N, D, W, XG, ,It,kLa,X/ [Vmicro and V . . . . .
I
361
experimental data obtained during the production phase, in which the cell concentration was constant, and the xanthan g u m concentration was between 1.0× 10 -2 and 2.8× 10-2 kg/kg broth. Figure 5 shows the relationship between the calculations and the experimental data at various agitation speeds. T h e results agreed well. The difference between the calculated values and the experimental data observed at the agitation speed of 13.3 rps might be due to over-estimation of the shear stress in the macromixing region. An overestimation arises because the mean shear stress estimated from Eq. (4) and the power law equation was the m e a n value in the stirred tank, and would be larger than the real mean shear stress in the macromixing region when the concentration of xanthan g u m was 1 . 7 × 1 0 - 2 k g / k g broth or more. When the xanthan g u m concentration is less than 1.7 x 10-2kg/kg broth, the contribution by cells in the macromixing region to the overall production might be small, because the volume of the macromixing region was small compared with that of the micromixing region. Figure 6 compares the production in the macromixing region with the overall production in a stirred tank. A, B, C, and D are the results at agitation speeds of 6.7, 8.3, 10.0, and 13.3rps, respectively. The pro._~
31
'
I
'
I
.....
I SPR=vlIkg xanthan/(kgdry I I ~ 'R=vl ImatedbyEq. I ~2:liilme c~istri.i I'
"1(16)[_...__]
I
"
I O
~PR.X.4tl Fig. 4. Flow chart for the estimation of xanthan gum production.
10 Time (h)
20
Fig. 5. Comparison of calculated values and experimental data for xanthan gum production at various agitation speeds. O, B, ©, and A; experimental data at 6.7, 8.3, 10.0, and 13.3 rps, respectively. , , .-., and - . - ; calculated values at 6.7, 8.3, I0.0, and 13.3 rps, respectively.
362
FUNAHASHIet al.
9 A
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0.4 0.8 1.2 1.6 (/)~ 0 Fig. 6. Comparison between the production in the ND ( m / s ) macromixing region and the overall production in a stirred tank. A, B, C, and D are results Fig. 7. Effects of N D on the specific production rate calculated at 6.7, 8.3, 10.0, and 13.3rps, reof xanthan gum. Calculated values were comspectively. -- and ---; production in the whole pared with experimental data.v) The symbols of the stirred tank and in the macromixing region, stand for different sizes of impeller diameter: respectively. A, D=0.087 m; O, D:0.100 m; II, D=0.120 m; O, D =0.140 m; and --, calculated values.
duction in the macromixing region as Consequently, xanthan gum production a fraction of the overall production increased under various agitation conditions could be with increasing agitation speed. However, estimated by consideration of the shear stress the contribution by cells in the macromixing in each mixing region and the mixing state region to the overall production was smaller in a fermentor. We found that the volume than that in the micromixing region. The of the high shear region was important for highest value of the fraction of production in xanthan gum production, and it is suggested the macromixing region vs overall production that xanthan gum production is promoted was 42%, which was obtained in the case of by application of an agitation condition that 24 h cultivation as shown in the figure. gives a large volume for the micromixing These results suggested that the overall region. Basic information for the developspecific production rate was influenced by ment of agitation systems and scale-ups was the volume of the micromixing region with obtained from this investigation, although a high shear stress and by short circulation the effects of scale on the mixing condition in times in the macromixing region to avoid a stirred tank should be investigated in order oxygen deficiency. to carry out scale-up production. Figure 7 shows the effects of N D on the specific production rate in terms of the Nomenclature calculated values and experimental data : concentration of dissolved obtained in a previous study. 7) The specific Cmicro oxygen in the micromixing production rate was obtained by the linear region, kg/kg broth regression analysis of experimental data, : concentration of dissolved and the calculated value was obtained from C* oxygen saturated with air, the time course o f x a n t h a n gum concentration kg/kg broth simulated by the flow chart shown in Fig. 4. D : impeller diameter, m The calculated values agreed well with the k : proportional constant in Eq. experimental data, and the overall effects (3), -of agitation on the specific production rate • consistency coefficient, Pa's n of xanthan gum were satisfactorily verified K kLamicro : volumetric oxygen transfer by this method.
Vol. 66, 1988]
kLa'
n N q
QO~ ReM
R(0i)
SOUR SOURm,x
spr
Sprmax
SPR
SPRy,
SPRi
SPR .....
SPRm~o
t tp
V
Mechanistic Analysis of Xanthan Gum Production coefficient in the m i c r o m i x i n g region, 1/s : a p p a r e n t volumetric oxygen transfer coefficient, 1/s : flow b e h a v i o r index, - : agitation speed, s : e x c h a n g e rate between the m i c r o m i x i n g and m a c r o m i x ing region, l/s : s p e c i f i c respiration rate, kg O2/(kg d r y cell.s) : Reynolds n u m b e r defined by Eq. ( 4 ) , : relative frequency of a circulating flow with a circulation time of 0i, -: specific oxygen uptake rate, kg O2/(kg d r y cell-s) : m a x i m u m of specific oxygen uptake rate, kg O2/(kg d r y cell.s) : specific production rate estim a t e d from Eq. (2), kg x a n t h a n / ( k g dry cell.s) :maximum of specific production rate, kg x a n t h a n / ( k g d r y cell.s) : overall specific production rate in a stirred tank, kg x a n t h a n / ( k g d r y cell.s) : m e a n specific production rate in the entire stirred tank, kg x a n t h a n / ( k g dry cell-s) : m e a n specific production rate in a circulating flow, kg x a n t h a n / ( k g dry cell.s) : specific production rate in the macromixing region, kg x a n t h a n / ( k g dry cell-s) : specific p r o d u c t i o n rate in the micromixing region, kg x a n t h a n / ( k g d r y cell.s) : time, s : time for complete consumption of oxygen during circulation in the m a c r o m i x i n g region, s : t o t a l volume of liquid in a stirred tank, l
V..... Vmicro
X XG ~,av
~'M z ray
rM p 0i
363
: volume of the m a c r o m i x i n g region, l : volume of the m i c r o m i x i n g region, l : d r y cell concentration, kg/kg broth : x a n t h a n g u m concentration, kg/kg b r o t h : m e a n shear rate in a stirred tank, 1/s : shear rate at the tip of impeller, 1/s : shear stress, Pa : a v e r a g e shear stress calculated by Eq. (3) and a power law equation, Pa : s h e a r stress at the tip of impeller, Pa : fluid density, k g / m 3 : circulation time in the macromixing region, s Acknowledgments
This research was partly supported by a grant from the Komori Memorial Foundation. References
1) Andrew, T.R. : ExtraceUular Microbial Polysaccharides, (Sandford, P.A., Laskin, A.), Series No. 45, 231, ACS, Washington, D. C. (1977). 2) Wells, J.: Extracellular Microbial Polysaccharides, (Sandford, P. A., Laskin, A.), Series No. 45, 231, ACS, Washington, D. C. (1977). 3) Sandvic, A.I., Maerker, J.W. : ExtraceUular Microbial Polysaccharides, (Sandford, P.A., Laskin, A.), Series No. 45, 231, ACS, Washington, D. C. (1977). 4) Weiss, R.M., Ollis, D.F.: Biotechnol. Bioeng., 22, 859 (1980). 5) Pinches, A., Pallent, L.J.: Biotechnol. Bioeng., 28, 1484 (1986). 6) Moraine, R. A., Rogovin, P.: Biotechnol. Bioeng., 15, 225 (1973). 7) Funahashi, I~., Maehara, IV[., Taguchi, H., Yoshida, T.: J. Chem. Eng. Japan, 20, 16 (1987). 8) Funahashi, 1~., Hirai, K., Yoshida, T., Taguchi, I'L: J. Ferment. Technol., 66, 108 (1988). 9) Ito, S., Urusiyama, S." Kagaku Kogaku, 32, 267 (1968). 10) Wichterle, K., Kadlec, M., Zac, L., Mitschka, P.: Chem. Eng. Commun., 26, 25 (1984).
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11) Metzner, A.B., Otto, R.E.: AIGhE J., 3, 3 (1957). 12) Calderbank, P.H., Moo-Young, M.B.: Trans. Instn. Chem. Engrs., 39, 337 (1961). 13) Funahashi, H., Harada, H., Taguchi, H., Yoshida,
[J. Ferment. Technol.,
T.: J. Chem. Eng. Japan, 20, 277 (1987). 14) Taguchi, H., Humphrey, A.H.: J. Ferment. Technol., 44, 881 (1966). (Received September 18, 1987)
Mechanistic Analysis of Xanthan Gum Production in a Stirred Tank HITOSHI FUNAHASHII, KOH-IcHI HIRAI2~ TOSHIOMI YOSHIDA.2, a n d HISAHARU TAGUCHII
Department of Fermentation Technology1, International Center of Cooperative Research in Biotechnology2, Faculty of Engineering, Osaka University, 2-1, Yamada-oka, Suita-shi, Osaka 565, Japan The overall effect of agitation on xanthan gum production by Xanthomonas campestris ATCC13951 in a stirred vessel was mechanistically analyzed considering local variation of the specific production rate due to variation of shear stress in the vessel. The whole liquid volume in a fermentor was roughly divided into three regions; the micromixing region around the impeller with high shear stress, the macromixing region dominated by a circulating flow and the stagnant region. The value of the shear rate was first ascertained by experiments in order to obtain a picture of shear rate variation in a radial direction from the impeller, and the equivalence between the volumes of the high shear stress region and micromlxing region was confirmed. The shear stress obtained using a correlation between the shear rate at the impeller tip and Reynolds number of Wichterle et al. was used as a representative of the shear stress in the micromixing region, and the shear stress estimated by use of an empirical correlation between the average shear rate in a fermentor and agitation speed derived by Metzner et al. was adopted as a representative of the shear stress in the macromixing region. The information about the circulation time distribution was also used to take into account oxygen deficiency during circulation of liquid elements in the macromixing region, considering that oxygen from the gas phase was supplied mainly in the high shear region. The calculated values ofxanthan gum concentrations which were obtained by the proposed simulation method agreed well with the experimental data in the time course of xanthan gum production at various agitation speeds. Experimental results of the relationship between the overall specific production rate and ND (N, agitation speed, and D, impeller diameter) was also verified by the proposed method.
X a n t h a n g u m is a n extracellular heteropolysaccharide p r o d u c e d b y Xanthomonas campestris. I t is used i n food a n d i n d u s t r i a l applications, X,2) a n d m a y be useful i n secondary oil recovery.2, 8) Weiss a n d Ollis 4) have reported that the changes i n cell c o n c e n t r a t i o n , x a n t h a n g u m , a n d substrate d u r i n g c u l t i v a t i o n u n d e r constant a g i t a t i o n conditions c a n be simulated b y a logistic, the L u e d e k i n g - P i r e t e q u a t i o n , a n d a modified L u e d e k i n g - P i r e t e q u a t i o n , respectively. Pinches a n d P a l l e n t 5) have also reported that the oxygen u p t a k e rate * Corresponding author
c a n be estimated b y use of these equations. T h e effects of a g i t a t i o n o n the m i c r o b i a l p r o d u c t i o n of x a n t h a n g u m have not yet b e e n analyzed, b u t M o r a i n e a n d RogovinS) have suggested that the a g i t a t i o n speed is a n i m p o r t a n t o p e r a t i o n a l factor. T h e specific rate of x a n t h a n g u m p r o d u c t i o n by X. campestris ATCC13951 depends o n N D , where N a n d D are the a g i t a t i o n speed a n d the impeller diameter, respectively; a n d shear stress is one of the most i m p o r t a n t factors relevant to agitation. 7) X a n t h a n g u m solution is a n o n - N e w t o n i a n fluid with pseudoplastic behavior, a n d the shear flow caused b y the i m p e l l e r is l i m i t e d to the area
356
FtrNAriASI~Zet al.
near the impeller itself.
Therefore, changes
M e a s u r e m e n t o£ s h e a r s t r e s s The shear rate at each part of a stirred tank was obtained from the distribution of the fluid velocity by measurement of the limiting diffusion current.9,10) The shear stress was estimated by substitution of the shear rate into the power law equation. The electrode used was one in which a platinum wire 0.2 mm in diameter was embedded in the center of a glass rod (diameter, 5 mm), with the tip of the wire exposed at the end of the rod. A solution containing 0.025 M potassium ferrocyanide, 0.025 M potassium ferricyanide, and 0.1 M potassium sulfate was used as the electrolyte and the xanthan gum (Taiyo Kagaku Co., Ltd.) was dissolved at a concentration of 9×10 -3, 1.7×10 -2 , or 2.7x10-2kg/kg broth. The electrode was inserted horizontally from the side wall of the fermentor at half of the depth of the liquid. The distribution of fluid velocity near the impeller was measured by sliding the electrode, which passed laterally through the wall of the fermentor, and shifting the impeller vertically 5 or 10 ram, making sure that aeration did not hinder the measurement of fluid velocity by this method.
in the mixing conditions during cultivation a r e c l e a r l y i m p o r t a n t for t h e p r o d u c t i o n o f xanthan gum. We have reported that the volume of each mixing region and the circulation time distribution at various xanthan gum concentrations can be estimated empirically from the impeller diameter, the impeller width, and the consistency coefficient of the x a n t h a n g u m s o l u t i o n , s)
In this report, we describe a method to show the effects of agitation on the production o f x a n t h a n g u m by using an empirical model for the expression of mixing states and by considering the effects of shear stress on the specific production rate of xanthan gum. Materials and Methods Fermentor and impeller The fermentor was the same as that used in a previous study, 7) with a diameter of 200 mm and capacity of 10 I. The total liquid volume was 6 l, and air was supplied at 1 vvm. The vessel was equipped with three baffle plates. A turbine impeller having six flat blades, 100 mm in diameter and 20 mm in width, was used. Tile agitation speed was from 5 to 16.7 rps.
A
Stagnant region
[J. Ferment. Technol.,
Results and Discussion Estimation of overall specific prod u c t i o n rate o f x a n t h a n g u m in a s t i r r e d tank The specific production rate of Cmicro - Q02 X tp = 0
B
,
I ~ #t I t
s
~
]
~..j~^
2 °Xtl>O
(i=l-P-1)
~mixing ~ , - ~ - - ~ , w z ~regio~ l~/TJ~'~.1 . Fluid element Cmicro =
C*- (Qo2X/kLa')
(~" Spa g .=r -
~LJ
without oxygen limitation O " with oxygen limitation
Fig. 1. Mixing state of culture broth of xanthan gum production in a stirred tank. A. The three regions in a stirred tank. The whole liquid volume in a stirred tank was divided into three regions. The micromixing region was dominated by the radial flow near the impeller, the macromixing region was the region of a slow circulating flow, and the stagnant region was where the fluid was stagnant, s) B. Model for oxygen consumption in the macromixing region• Oxygen might be supplied mainly in the micromixing region, with little going to the macromixing region. When the dissolved oxygen concentration in the micromixing region is not 0, the dissolved oxygen at a certain concentration in the fluid element left from the micromixing region would be consumed by the respiration of cells during circulation in the macromixing region, and places with limited oxygen might exist in the macromixing region.
Vol. 66, 1988]
Mechanistic Analysis of X a n t h a n Gum Production
xanthan g u m depended on the shear stress, that is the mixing state in each region. 7) T h e specific production rate at a particular place in a stirred tank might be different because of differences in the shear stress and oxygen supply at that place. A d i a g r a m of the mixing state is shown in Fig. 1-A. The whole liquid volume in the tank was divided into three regions. T h e micromixing region was dominated by the radial flow near the impeller, the macromixing region was the region of a slow circulating flow, and the stagnant region was where the fluid was stagnant, s) The overall specific production rate in a stirred tank, SPR, was calculated by the following equation, with the volume in each mixing region and the specific production rate therein taken into consideration.
SPR=(Vmt:~oSPRmI~o -k V . . . . . SPR . . . . . )IV
(1)
where V, Vmi.... and V . . . . . are the total volume of liquid, and the volumes of the micromixing and macromixing regions, respectively. SPRmicro and SPR . . . . . are the m e a n specific production rates in the micromixing and macromixing regions, respectively. Production of xanthan g u m in the stagnant region was neglected because of no oxygen supply in the region. T h e relationship between the specific production rate of an individual cell, spr, and the shear stress, % was obtained from data reported before 7) to be as shown in the following equation:
spr=2.5 × 10-' × ~-/(48-k,), or
sprmax, when 2 . 5 × lO-4×~'/(48-t-~')>sprma~
(2)
T h e value of spr~az was 1 . 1 × 1 0 - 4 k g xanthan/(kg dry cell.s) when oxygen was unlimited. T h e shear stress influences the transfer of materials such as glucose, oxygen etc. from the m e d i u m into the cells. 7) O n the other hand, the oxygen supply from bubbles into the m e d i u m was also important for the estimation of the specific
357
production rate. Oxygen might be supplied mainly in the micromixing region, with little going to the macromixing region. When the dissolved oxygen concentration in the micromixing region is not 0, the dissolved oxygen at a certain concentration in the fluid element left from the micromixing region would be consumed by the respiration of the cells during circulation in the macromixing region, and places with limited oxygen might exist in the macromixing region as shown in Fig. 1-B. When the oxygen supply was limited in the micromixing region, xanthan g u m would no longer be produced in the macromixing region, and sprma~ m a y be limited by the oxygen supply. Consequently, the mean specific production rate in each mixing region might depend on the mean shear stress in that region and on the oxygen supply from bubbles into the m e d i u m when the concentration of glucose or other substrates do not limit the production. Effects o f s h e a r s t r e s s o n t h e m e a n specific p r o d u c t i o n rate in e a c h m i x i n g region In order to estimate the m e a n specific production rate in each mixing region, it is necessary to consider the effects of the m e a n shear stress and oxygen supply from bubbles into the medium. Here, we discuss the m e a n shear stress in each mixing region, and show a method for the estimation of the mean specific production rate in each region, provided there is no limitation of the oxygen supply from bubbles into the medium. Shear stress is particularly important for xanthan g u m production, v) The specific production rate increases with increasing shear stress as long as the shear stress is less than 40 Pa, but it is constant at the m a x i m u m value when the shear stress is more than 40 Pa. T h e xanthan g u m solution is a nonNewtonian fluid with pseudoplastic behavior, and the region of high shear is limited to the area near the impeller. T h e volume of the high shear region m a y be important for xanthan g u m production. T h e velocity distribution near the impeller was obtained by use of a method to measure the limiting diffusion current. There was
358
[J. Ferment. Technol.,
F U N ~ A S m et al.
cellulose, carbopol and attasol : ~,av= k W
c 4 .2 .= o~3 ¢.x
o
'
I
'
i
I
I
/ #,
/
/
B
1
m
/ 0
,
I
,
I
,
I
(3)
I //
i
4 1 2 3 Volume of high shear region ( [ )
Fig. 2. Relationship between volumes of the micromixing region and high shear region at various
agitation speeds. A, O, and m; data for xanthan gum concentrations of 9× 10-3, 1.7 × 10-% and 2.7 × 10-* kg/kg broth, respectively. a critical point at which the velocity decreased sharply with distance from the impeller tip, and the shear rate inside the boundary region was more than 20 1/s. Figure 2 shows the correlation between the volume of the micromixing region and the volume of the high shear region, in which the shear rate was more than 20 l/s, at various agitation speeds, for xanthan g u m concentrations of 9 × 1 0 -3 , 1.7×10-*, and 2 . 7 × 1 0 -2kg/kg broth. The volumes of the high shear region were almost equal to the volume of the micromixing region at various agitation speeds. T h e results suggested that the micromixing region corresponded to the high shear region. I n a xanthan g u m solution of 1.7× 10-3 and 2.7× 10-3kg/kg broth, the shear stress in the kigh shear region was 40 Pa or more, and the specific production rate in the region might be maximized. Metzner and Otto ix) have proposed the following equation for the relationship between the mean shear rate in a stirred tank, ~,v, and the agitation speed, N, within the range of the l a m i n a r flow region not only for Newtonian but also for non-Newtonian fluids, i.e., for solutions of carboxymethyl
where k is a constant that depends on the shape of impeller used. Calderbank and Moo-Young x*) have reported that the value o f k is 11.6 within the range of 0.08 to 1,000 of the generalized Reynolds n u m b e r when a turbine impeller with six fiat blades is used. 13) In our investigation, the generalized Reynolds n u m b e r was from 150 to 1,100. Based on these results, the shear stress, ~'~v, that was calculated by use of Eq. (3) and a power law equation, was adopted as the mean shear stress in the stirred tank. Wichterle et al. lo) have reported that the shear rate at the tip of the impeller, ~M can be estimated by the following equations: (1 -[-5.3 n) I/"ReM1/~1+", Re~ ~- N c~-,)D~p/K
~[N=
(4) (5)
where K is the consistency coefficient. T h e flow behavior index, n, was 0.12 at the concentration of xanthan g u m more than 9 × 10-8 kg/kg broth. Rex is the Reynolds n u m b e r defined by Eq. (5). T h e shear stress at the tip of the impeller, ~'M, can be estimated by substitution of the value for the shear rate obtained by these equations into the power law equation. The shear stress thus estimated would be m a x i m u m in the stirred tank. I f it was less than 40 Pa, no region in the stirred vessel has shear stress more than 40 Pa. When the shear stress at the tip of the impeller is more than 40 Pa, the high shear region, with 40 Pa or more of shear stress, and the low shear region, with less than 40 Pa, would probably exist together in the stirred tank. From the results shown in Fig. 2, the high shear region might correspond to the micromixing region, and the low shear region to the macromixing region. Based on this information about the mean shear stress in each mixing region, the mean specific production rate in the micromixing, SPRmi .... and macromixing regions, S P R . . . . . . was estimated as follows: 1) When ~'M< 4 0 P a , there is no region in which shear
Vol. 66, 1988]
Mechanistic Analysis of Xanthan Gum Production
stress is 40 Pa or more, and the m e a n specific production rate, estimated by substitution of ~-~v into Eq. (2), SPRay, was adopted as SPRmic~o and SPR ......
SPR~icro=SPR,~, SPR . . . . . =SPRav
and (6)
T h e overall specific production rate was obtained as follows by substitution of Eq. (6) into Eq. (1).
SPR=SPR, v×(V=~¢~o+V . . . . . )IV
(7)
2) W h e n ZM_~ 4 0 P a , we assumed that SPR~¢ro was equal to the m a x i m u m of the specific production rate, spr. . . . because the micromixing region corresponded to the high shear region, and the shear stress in the high shear region at a xanthan g u m concentration more than 1.7× 10-2kg/kg broth was more than 40 Pa. SPR . . . . . depended on the mean shear stress in the macromixing region. However, the distribution of the shear stress in the stirred tank has not been investigated in detail, because it is difficult to measure it thoroughly in a tank. ~-~ was used as the m e a n shear stress in the macromixing region.
SPR~i¢~o=sprmax and SPR . . . . . =SPR~v
(8)
The overall specific production rate was obtained as follows by substitution of Eq. (8) into Eq. (1).
SPR= ( s p r ~ Vm~o~o-kSPR., V
. . . . .
)IV
(9) T h e overall specific production rate when there is no limitation of the oxygen supply can be estimated from Eqs. (7) or (9). T h e volume of each mixing region was estimated from the conditions of agitation: namely, the agitation speed, impeller diameter, impeller width, and also the consistency coefficient of the culture broth. T h e consistency coefficient was estimated empirically from the xanthan g u m concentration by the use of the following equation: K = 4 . 9 × l0 s × XG 1.3
(I0)
where XG is the xanthan gum concentration.
359
This relationship held between concentrations of xanthan g u m of 9 × 10 -3 and 4 . 6 × 10 -2 kg/kg broth. Effects of oxygen supply to the medium on xanthan gum production X.
campestris is an aerobic microorganism, and oxygen is necessary for the production of xanthan gum.7~ When the oxygen supply from bubbles into the m e d i u m was not limited, the value of Sprmax was 1.1 × 10 -4 kg xanthan/(kg dry cell.s). When the oxygen supply was limited, however, sprm,~ would be less than 1.1 x 10-4kg xanthan/(kg dry cell.s). Some ceils in the macromixing region do not produce xanthan g u m because of oxygen deficiency in a liquid element traveling for a long time from the micromixing region where most of oxygen is supplied. In fact, the m e a n circulation time is sometimes of the order of a few seconds, is) during which time cells m a y consume the dissolved oxygen. Here, we discuss the effects of oxygen supply on the mean specific production rate in each mixing region. In this cultivation, the dissolved oxygen tension might not be the same throughout the fermentor, and it is very difficult to obtain, experimentally, a complete picture of the local distribution of dissolved oxygen tension. The oxygen transfer from the bubbles into the medium would depend on the intensity of the shear flow. When a highly viscous solution is used, the oxygen carried from the macromixing region into the micromixing region might be negligible in the early period of the measurement of the volumetric oxygen transfer coefficient by the dynamic method. 14) Therefore, the oxygen balance in the micromixing region could be shown by the following equations; dC micro/dt =kLamtcro ( C * --Cmiero) --qCmtero/Vmiero =kLat(C ~ --Cmiero)
(l l)
where Cml¢,o is the dissolved oxygen concentration in the micromixing region, C* is the concentration saturated with the air, Vmier o is the volume of the micromixing region, and q is the exchange rate between the
360
Fu~a-~asm et al.
micromixing and macromixing regions. kLamicro and kLa' are the actual and apparent volumetric oxygen transfer coefficients, respectively, in the micromixing region, and k~a' was measured under various agitation conditions and at various concentrations of xanthan gum in a previous study. 7) The oxygen conveyed from the macromixing into the micromixing region in a fermentor would be small compared with the oxygen supply in the micromixing region, because the oxygen is consumed by respiration during circulation in the macromixing region. The concentration of the dissolved oxygen in the micromixing region at a quasi-steady state during cultivation, C=i .... could be calculated by use of following equation:
[J. Ferment. Technol.,
SPR . . . . . = N',{R(O~)SPR~XI/[{~R(O~)IX] =~{R(O~)SPRd/~R(O 0 (14)
where R(Oi) is the relative frequency of the circulating flow at 0i of circulation time and can be estimated by the agitation speed and impeller diameter.S) Thus, the value of SPR . . . . . estimated by Eq. (14) was substituted into Eq. (1). On the other hand, when the oxygen supply limits the xanthan gum production in the micromixing region, xanthan gum would no longer produced in the macromixing region, and the mean specific production rate in the micromixing region may be affected by the oxygen supply. The specific production rate, spr, corresponded to the specific oxygen uptake rate, SOUR, as shown in Fig. 3. The correlation Cmicro-~-C*--( Q,o,X/kLa') (12) between the specific production rate and the The specific oxygen uptake rate at 40 Pa specific oxygen uptake rate is described by or more of shear stress reported elsewhere 7) the following equation for 3.0×10 -5 to was adopted for Qo~, and the value of kLa' 1.1 x 10-4 kg xanthan/(kg dry cell.s). under each agitating condition was described s p r = 2 . 7 8 × S O U R - - 5 . 0 9 × 10-n (15) in the same study. 7) When the dissolved oxygen concentration in the micromixing region is not 0, the dissolved oxygen at a certain concentration in the fluid element left from the micromixing region would be consumed by the respiration of cells during circulation in the macromixing region, as shown in Fig. 1-B. Therefore, when the circulation time is longer than the time for complete consumption of the dissolved oxygen in the fluid element, production would cease because of the oxygen limitation before the fluid element returned to the micromixing region. Based on this idea, the mean specific production rate in a circulating flow, SPRy, was estimated as follows: SPRt = S P R ~ × t p/0i
The maximum specific production rate, spry,a× in the micromixing region could be estimated by substitution of the maximum specific oxygen uptake rate, SOUR . . . . into "01
'
I
'
I
'
I0 '
o ::~l-
(13)
where t p is the time for complete consumption T.#I , I , I , I , "r" of oxygen for xanthan gum production in 0 2 3 4 5 6 a circulating flow, which equals C=~¢~o/ S p e c i f i c o x y g e n u p t a k e rate (Qo~ X), and 0~, the circulation time in the X I O s ( k g 0 2 / ( k g dry c e l l . s ) ) macromixing region. SPR,, was obtained Fig. 3. Relationship between the specific oxygen by substitution of ~-,, into Eq. (6). SPR . . . . . uptake rate and the specific production rate of would be estimated considering the SPR~ of xanthan gum. Data from a previous studyT) each circulating flow as follows: were used in the calculations.
Vol. 66, 1988]
Mechanistic Analysis of Xanthan Gum Production
Eq. (15). sprm~x= 2 . 7 8 × SOURma,--5.09 × 10 -5 (16)
spr=~, estimated from Eq. (16) was less than 1.1 x 10 -4 kg xanthan/(kg dry cell.s), and was adopted as Sprm** in Eq. (8). T h e m a x i m u m of the specific oxygen uptake rate in the micromixing region is equal to the specific oxygen supply rate, and could be calculated by the following equation: SO URm, ~=kLa'C*/X
(17)
Consequently, the overall specific production rate under various agitation conditions was estimated by consideration of the m e a n shear stress in each mixing region and the oxygen supply from bubbles into the m e d i u m in accordance with a flow chart, as shown in Fig. 4. Comparison experimental
between calculated and data T o check the meth-
od described above for the estimation of xanthan g u m production, the calculated values were compared with the experimental values obtained before. 7> The estimation was carried out for the case of corresponding
,/N, D, W, XG, ,It,kLa,X/ [Vmicro and V . . . . .
I
361
experimental data obtained during the production phase, in which the cell concentration was constant, and the xanthan g u m concentration was between 1.0× 10 -2 and 2.8× 10-2 kg/kg broth. Figure 5 shows the relationship between the calculations and the experimental data at various agitation speeds. T h e results agreed well. The difference between the calculated values and the experimental data observed at the agitation speed of 13.3 rps might be due to over-estimation of the shear stress in the macromixing region. An overestimation arises because the mean shear stress estimated from Eq. (4) and the power law equation was the m e a n value in the stirred tank, and would be larger than the real mean shear stress in the macromixing region when the concentration of xanthan g u m was 1 . 7 × 1 0 - 2 k g / k g broth or more. When the xanthan g u m concentration is less than 1.7 x 10-2kg/kg broth, the contribution by cells in the macromixing region to the overall production might be small, because the volume of the macromixing region was small compared with that of the micromixing region. Figure 6 compares the production in the macromixing region with the overall production in a stirred tank. A, B, C, and D are the results at agitation speeds of 6.7, 8.3, 10.0, and 13.3rps, respectively. The pro._~
31
'
I
'
I
.....
I SPR=vlIkg xanthan/(kgdry I I ~ 'R=vl ImatedbyEq. I ~2:liilme c~istri.i I'
"1(16)[_...__]
I
"
I O
~PR.X.4tl Fig. 4. Flow chart for the estimation of xanthan gum production.
10 Time (h)
20
Fig. 5. Comparison of calculated values and experimental data for xanthan gum production at various agitation speeds. O, B, ©, and A; experimental data at 6.7, 8.3, 10.0, and 13.3 rps, respectively. , , .-., and - . - ; calculated values at 6.7, 8.3, I0.0, and 13.3 rps, respectively.
362
FUNAHASHIet al.
9 A
B
9~..
x X 3
I ~0 C
8
,~
~.. ~,
D
/
8~
C D:
~ o~ 46 ~.x
x 3 0
[J. Ferment. Technol.,
e~ .2~ 10
20 0 - Time (h)
10
20
"~ x ~..~
2 ,
I
i
I
I
I
.
I
0.4 0.8 1.2 1.6 (/)~ 0 Fig. 6. Comparison between the production in the ND ( m / s ) macromixing region and the overall production in a stirred tank. A, B, C, and D are results Fig. 7. Effects of N D on the specific production rate calculated at 6.7, 8.3, 10.0, and 13.3rps, reof xanthan gum. Calculated values were comspectively. -- and ---; production in the whole pared with experimental data.v) The symbols of the stirred tank and in the macromixing region, stand for different sizes of impeller diameter: respectively. A, D=0.087 m; O, D:0.100 m; II, D=0.120 m; O, D =0.140 m; and --, calculated values.
duction in the macromixing region as Consequently, xanthan gum production a fraction of the overall production increased under various agitation conditions could be with increasing agitation speed. However, estimated by consideration of the shear stress the contribution by cells in the macromixing in each mixing region and the mixing state region to the overall production was smaller in a fermentor. We found that the volume than that in the micromixing region. The of the high shear region was important for highest value of the fraction of production in xanthan gum production, and it is suggested the macromixing region vs overall production that xanthan gum production is promoted was 42%, which was obtained in the case of by application of an agitation condition that 24 h cultivation as shown in the figure. gives a large volume for the micromixing These results suggested that the overall region. Basic information for the developspecific production rate was influenced by ment of agitation systems and scale-ups was the volume of the micromixing region with obtained from this investigation, although a high shear stress and by short circulation the effects of scale on the mixing condition in times in the macromixing region to avoid a stirred tank should be investigated in order oxygen deficiency. to carry out scale-up production. Figure 7 shows the effects of N D on the specific production rate in terms of the Nomenclature calculated values and experimental data : concentration of dissolved obtained in a previous study. 7) The specific Cmicro oxygen in the micromixing production rate was obtained by the linear region, kg/kg broth regression analysis of experimental data, : concentration of dissolved and the calculated value was obtained from C* oxygen saturated with air, the time course o f x a n t h a n gum concentration kg/kg broth simulated by the flow chart shown in Fig. 4. D : impeller diameter, m The calculated values agreed well with the k : proportional constant in Eq. experimental data, and the overall effects (3), -of agitation on the specific production rate • consistency coefficient, Pa's n of xanthan gum were satisfactorily verified K kLamicro : volumetric oxygen transfer by this method.
Vol. 66, 1988]
kLa'
n N q
QO~ ReM
R(0i)
SOUR SOURm,x
spr
Sprmax
SPR
SPRy,
SPRi
SPR .....
SPRm~o
t tp
V
Mechanistic Analysis of Xanthan Gum Production coefficient in the m i c r o m i x i n g region, 1/s : a p p a r e n t volumetric oxygen transfer coefficient, 1/s : flow b e h a v i o r index, - : agitation speed, s : e x c h a n g e rate between the m i c r o m i x i n g and m a c r o m i x ing region, l/s : s p e c i f i c respiration rate, kg O2/(kg d r y cell.s) : Reynolds n u m b e r defined by Eq. ( 4 ) , : relative frequency of a circulating flow with a circulation time of 0i, -: specific oxygen uptake rate, kg O2/(kg d r y cell-s) : m a x i m u m of specific oxygen uptake rate, kg O2/(kg d r y cell.s) : specific production rate estim a t e d from Eq. (2), kg x a n t h a n / ( k g dry cell.s) :maximum of specific production rate, kg x a n t h a n / ( k g d r y cell.s) : overall specific production rate in a stirred tank, kg x a n t h a n / ( k g d r y cell.s) : m e a n specific production rate in the entire stirred tank, kg x a n t h a n / ( k g dry cell-s) : m e a n specific production rate in a circulating flow, kg x a n t h a n / ( k g dry cell.s) : specific production rate in the macromixing region, kg x a n t h a n / ( k g dry cell-s) : specific p r o d u c t i o n rate in the micromixing region, kg x a n t h a n / ( k g d r y cell.s) : time, s : time for complete consumption of oxygen during circulation in the m a c r o m i x i n g region, s : t o t a l volume of liquid in a stirred tank, l
V..... Vmicro
X XG ~,av
~'M z ray
rM p 0i
363
: volume of the m a c r o m i x i n g region, l : volume of the m i c r o m i x i n g region, l : d r y cell concentration, kg/kg broth : x a n t h a n g u m concentration, kg/kg b r o t h : m e a n shear rate in a stirred tank, 1/s : shear rate at the tip of impeller, 1/s : shear stress, Pa : a v e r a g e shear stress calculated by Eq. (3) and a power law equation, Pa : s h e a r stress at the tip of impeller, Pa : fluid density, k g / m 3 : circulation time in the macromixing region, s Acknowledgments
This research was partly supported by a grant from the Komori Memorial Foundation. References
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T.: J. Chem. Eng. Japan, 20, 277 (1987). 14) Taguchi, H., Humphrey, A.H.: J. Ferment. Technol., 44, 881 (1966). (Received September 18, 1987)