Biotechnol. prog. 1991, 7, 534-539
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Filtration Properties of Mycelial Microbial Broths Timothy Oolman' and Tuan-Chi Liu Department of Chemical Engineering, University of Utah, Salt Lake City, Utah 84112
The filtration properties of three mycelial cultures (Streptomyces griseus, Streptomyces tendae, and Penicillium chrysogenum) have been measured and quantified in terms of standard filtration equations. Three of the filtration parameters, the hyphal density, the index of compressibility, and the Kozeny constant, were found to vary systematically with broth age and with the visually observed morphology (i.e., pellets VI filaments). Since broth age and mycelial morphology both have a strong influence on bioreactor productivity, it is suggested that filtration could be used for on-line monitoring of mycelial fermentations.
Introduction
medium is commonly correlated by Darcy's equation:
Filtration is an important unit operation in the initial processing of microbial products. Thus, characterization of the filtration properties of commercially important microbial species is of significance. However, filtration has additional potential as a method for monitoring the morphological development of a microbial broth. The morphology of a mycelial microbial broth has a strong influence on broth rheology, mass-transfer rates, and overall productivity of suspension cultures as well as on the filtration properties of the broth. It is well documented (1-9) that there is a strong correlation between the morphology of mycelial cultures, the rheological properties of the broth, heat-transfer and mass-transfer efficiency in the reactor, and the rates of product synthesis. Although sophisticated optical methods have been proposed (IO),there are no simple methods for quantitatively characterizing mycelial morphology. Thus, the influence of mycelial morphology on process efficiency has not been systematically investigated. Nestaas and Wang (11) and Cagney et al. (12) have previously developed filtration as a probe of mycelial morphology. Furthermore, Nestaas and Wang (11)stated that a filtration probe may prove valuable for the characterization and the control of fermentations. However, they limited their application to the measurement of a single parameter, an apparent hyphal density. In the present study it was found to be simpler and more accurate to measure the hyphal density directly and utilize this information to calculate values of the Kozeny constant, which the earlier investigators assumed to have an arbitrary constant value. We have also investigated the compressibility of the filter cake, which has proven to be a sensitive measure of mycelial morphology.
Theory Filtration is a hydrodynamic process. In an incompressible filter cake, the volumetric flow rate of fluid is proportional to the pressure drop across the filter medium and inversely proportional to the flow resistance generated by the filter cake. For a compressible cake, the pores of the cake are constricted, resulting in an increase in resistance, with increasing pressure drop. Flow of an incompressible fluid through a porous
* Corresponding author. 8756-7938/9 1/3007-0534$02.50/0
where Vf is the volume of fluid flowing through the media, pf is the fluid viscosity, H a n d A are the depth and crosssectional area, respectively, of the porous medium, A p is the pressure drop across the medium, and K is the empiricallydefined permeability of the medium. The lefthand side of eq 1represents the superficial velocity of the fluid through the porous medium. If the medium is incompressible, it will have a permeability independent of the pressure drop or the fluid flow rate. For a compressiblemedium, both the depth and the permeability of the medium will change with Ap. Nestaas and Wang (11)and Cagney et al. (12)integrated eq 1 for the case of single-pass filtration of microbial slurries, with the filter cake developingduring the filtration process. In so doing, they assumed that the permeability of the cake, K, remained constant. However, with a developing cake Ap/H will vary significantly with time, and due to the compressibility of the cake, the cake permeability, K , could vary substantially as the cake develops. Nestaas and Wang (11)recognize this limitation but do not correct for it. By conducting the experiments with a constant cake thickness, the cake compressibility can be accounted for. If the filtrate is recirculated through a filter cake which had been previously formed, the thickness of the cake and Ap/H will remain constant for constant Ap, and eq 1can be integrated directly to obtain (2)
where tf is the time required to collect a filtrate volume of Vf. The permeability of a filter cake, K , can be related to properties of the cake (13,141. If the cake porosity were made up of uniform, straight, cylindrical pores, the permeability could be expressed as (3)
where d, is the diameter of the pores and t is the porosity (cakevoid fraction). For noncylindricalpores it is common to substitute an equivalent pore diameter, de, defined as
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de = (void volume)/(solid surface area)
(4)
and introduce an empirical shape factor, K”, commonly known as the Kozeny constant and defined by (5) The Kozeny constant is a shape factor which should reflect the morphology and packing of the microbial filaments. If it is assumed that the hyphae are uniform cylindrical filaments, the equivalent diameter of the pore space can be expressed as h‘
de = 4(1- t) where dh is the diameter of the hyphae. Finally, substituting eq 6 into eq 5, the permeability can be written as
16Kr’(1- e)’ If E, dh, and K can be independently determined, then K” can be calculated. In the present study, K values were determined by fitting eq 2 to experimental data and dh was measured microscopically. The void fraction, E, was determined from ”
Table I. Nutrient Medium Composition Utilized for All Cultures
concn, nutrient g/L component corn steep liquid 15 mannitol 25 yeast extract 20 soy bean meal 5 correlated in the form (15)
nutrient component soy bean oil glucose lactose distilled water
concn, g/L 5 15 5 910
where pe is the density (grams of dry hyphae per cubic centimeter of cake) of the filter cake at the prevailing Ap, n’ and KO’ are empirical constants, andg is the gravitational acceleration. For an incompressiblecake n’ will equal zero, and for a compressible cake n’ will be positive. Ap is expressed in dimensionless form, thereby allowing KO’ to have the units of permeability. Note that p a is the dry weight of cake per unit area of the filter medium, which is independent of Ap. A more direct method to determine the cake compressibility is to measure the thickness of the filter cake as a function of Ap. It will be shown that such data can be effectively correlated by the empirical formula
H O
E=l--(l-to)
H where HO and €0 are the depth and the void fraction, respectively, of the developed cake when Ap equals zero. EO was calculated from where Ph is the hyphal density (grams of dry hyphae per cubic centimeter of hyphae) and p d is the density (grams of dry hyphae per cubic centimeter of cake) of the filter cake when Ap is equal to zero (no induced flow through the cake), expressed by
For a compressible cake n* should be a positive number between zero and one. Equations 13and 14 are both empirical equations whose justification will come from demonstrated consistencywith experimentaldata. Although both equations will be shown to have applicability, eq 13 has an obvious limitation, in that it predicts the permeability will approach infinity as the pressure drop approaches zero, which is clearly not realistic. Equation 14 correctly predicts H = HOwhen Ap = 0. Thus, reasonable predictions of cake permeability at Ap below the experimental range can be obtained by combining eqs 7, 8, 12, and 14 to yield (1- II)’ 16K”(1 -
where V , is the volume of slurry initially filtered to develop the cake and w is the concentration (grams of dry weight/ liter) of cells in the original slurry. Since H,Ph, and all of the parameters in eq 10 are experimentally measurable, eqs 8-10 can be applied to determine the porosity of a filter cake under any experimental pressure drop. Thus, eq 7 can be systematically applied to calculate K” for a filter cake. The compressibility of the cake strongly reflects the morphology of the hyphae, as will be shown subsequently. The approaches used to characterize the compressibility of the cake are outlined below. I t is convenient to account for all effects of compressibility in terms of a permeability, K ’ , defined by
where Ho,the depth of the filter cake at A p equal to zero, is independent of Ap. By comparing eqs 2 and 11, it is seen that = (H,/H)K (12) The variation of permeability with Ap can be empirically K’
(15) E ~ ) ~
where II = Cy(Ap/gpfl”’. Equation 15 can be used to extrapolate from experimentally measured values of K’ to pressure drops below the experimental range of data.
Materials and Methods Suspension cultures of Streptomyces griseus (ATCC 10137), Streptomyces tendae (ATCC 31160), and Penicillium chrysogenum (ATCC 10106) were grown in 750mL shake flasks and a 2-L New Brunswick Bioflo benchtop chemostat. The nutrient medium used for all cultures is given in Table I. Variations in morphology were obtained by varying the inoculum size and the mixing intensity. Filtration experiments were conducted in 25-mL disposable pipets, as depicted in Figure 1. The filter medium on which the mycelial cake was collected is a thin layer of cotton supported by a short column of glass beads. Before each filtration experiment, the resistance of the filter medium was measured by flowing water through the medium at constant pressure. In all cases, the measured medium resistance, quantified as the effective value of H / Kin eq 2, was small in comparison to the subsequently measured cake resistance. Cake permeabilities, K ’ , were determined by filtering 20-30 mL of broth to collect a cake and subsequently
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0.5
Mycelial s l u r r y
1 0
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Mycelial cake Cotton
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25
50
75
100
125
150
Fermentation time (hours) Manometer
Figure 1. Schematic drawing of the filtration probe.
recycling the filtrate over the cake and measuring filtrate flow rate as a function of pressure drop. The cake depth, H , was manually measured through the side of the pipet during and after each filtration. The small cross-sectional area of the pipet allowed for the development of a deep filter cake from a small volume of slurry, thereby giving better sensitivity in determining the cake depth and permeability. The hyphal density, Ph, was measured directly. Filter cakes were rinsed with 10 mL of pure ethanol to displace interstitial water, and the alcohol was evaporated for 1h at room temperature. The dewatered cakes were weighed and their volume was measured by water displacement in a pycnometer. Hyphal diameters, d h , were measured microscopically. Diluted mycelial slurries were observed under 1OOOX magnification with an oil-immersionlens, and the hyphal diameters were measured using a calibrated grid. The reported hyphal diameters are averages of 5-10 measurements for each sample.
Results In the followingdiscussion, filtration data are presented for both filamentous and pelleted cultures of the three organisms mentioned above. In all cases, the batch cultures reached maximum cell concentrations of 20-25 g of dry weight/L after approximately 100 h of growth and subsequently declined. Values of hyphal density vs broth age are reported in Figure 2 for batchwise growth of filamentous cultures of the three species. The data points represent the averages of two or three measurements at each broth age. It is observed that the data are repeatable within 3% of the measured values, whereas the hyphal densities vary by 30-35% over the course of these batch fermentations. Similar data for filamentous and pelleted morphologies of all three microbial species are reported in Table 11. The single-pass-filtrationmethod of Nestaas and Wang (11) and Cagney et al. (12) was also conducted with six microbial slurries in the present study. Details of the procedures are given in those references. That filtration method yielded calculated hyphal densities which were consistently 5-6 % higher than the directly measured hyphal densities.
Figure 2. Hyphae density versus fermentation time for filamentoussuspensioncultures of P. chrysogenum (opencircles), S. griseus (filled circles), and S. tendae (open squares).
Several mycelial-cake permeabilities were measured as a function of broth age and applied pressure drop. From experimental values of Vf/A vs tf for known Ho, pf, and Ap, values of K' were calculated accordingto eq 11. Typical data are reported in Figure 3, for the case of a filamentous culture of P. chrysogenum,as a function of pressure drop and broth age. It is seen that for individual broth samples the permeability is well correlated by the functionality given by eq 13; the negative slopes of the lines determine the values of n', which reflects the compressibility of a cake. Table I1 reports values of n' for several samples. Cake compressibility was also directly determined by measuring the depths of individual cakes as a function of applied pressure drop. Typical data are presented in Figure 4, for the same filamentous culture of P. chrysogenum as represented in Figure 3. Values of HO(cake depth at zero Ap) were 2-3 cm in all cases; the depths of individual cakes repeatedly recovered to within 1mm of the same HOvalues when Ap was returned to zero after permeability measurements. For individual broth samples, the data are well correlated by the functionality given by eq 14. The exponent, n*, should also reflect the compressibility of a cake. Measured values of n* are plotted against measured values of n' in Figure 5 for a wide variety of broth samples. The two independently measured properties of cake compressibility show a very strong cross correlation. Although n* may inherently seem to be a more direct measure of compressibility, n' appears to have the same information content and is easier to measure experimentally, since it does not require a precise measurement of variations in cake thickness. Values of the Kozeny constant, K", were calculated by application of eqs 7-10. Plots of observed K" values are presented in Figure 6 as a function of void fraction of the cake, for the same filamentous culture of P. chrysogenum represented in Figure 3. Previous authors (15) have reported consistent correlations between the observed Kozeny constant and void fraction for beds of uniform solids. The linearity of the data in Figure 6 allows for easy extrapolation outside the range of experimental conditions. The plus signs on the figure represent extrapolations to zero pressure drop, with eq 9 used to predict €0. It is difficult to measure permeabilities as low pressure drops.
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Table 11. Filtration Properties of P.chrysogenum, S. griseus, and S. tendae at Various Broth Ages morphological broth hyphal density, index of species form age, h g of dry hyphae/mL of wet hyphae compressibility (n’) P. chrysogenum filament 48 0.323 0.37
pellet
S. griseus
filament
pellet
S. tendae
filament
pellet
Pressure drop (-)
6.8 6.1 5.1 5.3 4.9 4.1 9.0 7.5 6.5 5.6
72 84 96 108 120 24 48 72 84
0.270 0.253 0.246 0.239 0.228 0.301 0.254 0.227 0.211
0.34 0.33 0.33 0.31 0.28 0.54 0.50 0.46 0.41
36 60 72 96 120 36 60 84 96
0.431 0.399 0.381 0.361 0.345 0.332 0.272 0.241 0.222
0.30 0.26 0.24 0.22 0.19 0.50 0.46 0.43 0.39
5.8 5.3 4.4 3.5 2.1
36 48 60 84 96 108 36 48 60 84
0.461 0.440 0.426 0.386 0.372 0.355 0.326 0.280 0.259 0.226
0.24 0.21 0.19 0.19 0.18 0.16 0.49 0.44 0.40 0.38
5.9 5.3 4.7 3.8 2.9 2.2 7.1 5.7 4.9 3.8
1.7
6.1 5.0 4.5
1 ,
I
I-
Kozeny constant at 20 cmHa
AP
/
Pressure drop
(E) @cH
BPCH
Figure 3. Permeability of the filter cake versus pressure drop at various broth ages (open circles, 24 h; filled circles, 48 h; open squares, 72 h; filled squares, 84 h) for P.chrysogenum broths with a filamentous mycelial morphology. The negative slope is an index of compressibility,n’ (defined by eq 13).
Figure 4. Filter-cakedepthversus pressure drop for filamentous samples of P. chrysogenum at various broth ages (open circles, 36 h; filled circles, 60 h; open squares, 84 h; filled squares, 108 h). The slope is an index of compressibility, n* (defined by eq
However, since the void fraction at low Ap is easily measured and is close to the reported range where filtration data were collected, a straight-line extrapolation should give a good estimate of filtration behavior at low Ap. Figure 7 reports the values of the Kozeny constant for a given pressure drop as a function of batch fermentation time for filamentous growth of the three microbial species. It is clearly observed that the Kozeny constant decreases steadily with broth age. The two species of Streptomyces show essentially identical behavior. Data for filamentous and pelleted morphologies of the three microbial species are reported in Table 11.
Discussion
14).
The filtration characteristics of mycelial slurries have been shown to be effectively correlated by standard filtration equations. Figures 3,4, and 6 demonstrate good consistency between the experimental data and the filtration model presented by eqs 7 and 11 and eq 13 or 14 for the filamentous culture of P.chrysogenum. Similar agreement between the experimental data and the filtration model were observed for filamentous and pelleted broths of the three mycelial species. Table I1 reports the
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0.4
0
0
0 0
0.2
1
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.
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.
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0.0
0.2
0.8
0.6
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150
Figure 7. Experimental variation of Kozeny constant with fermentation time at a pressure drop of 20 cmHg. The three speciesshown are P. chrysogenum (opencircles),S. griseus (filled circles), and S. tendae (open squares).
I
J,
0.5
50
Fermentation time (hours)
Figure 5. Cross correlation of the two indicesof compressibility, n' defined by eq 13 and n* defined by eq 14. The three species shown in the figure are P. chrysogenum (open circles),S. griseus (filled circles), and S. tendae (open squares). The straight line is a least-squares fit.
2
25
0.7
Void fraction
09 (E
)
10
100
loo0
10000
Pressure drop ( K ) gPcH
Figure 6. Kozeny constant versus void fraction of the filter cake for filamentoussamples of P. chrysogenumat various broth ages (open circles, 36 h; filled circles, 60 h; open squares, 84 h; filled squares, 108 h). Changes in void fraction were induced by varying pressure drop. The plus signs are extrapolated values at zero pressure drop.
Figure 8. Filter-cake permeability versus filtration pressure drop for a filamentous sample of P. chrysogenum. Circles designate experimentaldata. The solid line showsextrapolation of eq 15;the predicted permeability at zero pressure drop is 2.99 X lo4 cm2. The dashed line shows extrapolation based on eq 13; the predicted permeability at zero pressure drop is infinite.
experimentally determined values of three filtration parameters for varying broth ages of six representative cultures. In many situations it would be useful to predict permeabilities beyond the range of experimental data. Figure 8 demonstrates two methods for extrapolating beyond the data points for the filamentous culture of P. chrysogenum represented in Figure 3. The solid line represents eq 15, based on a linear fit of K" vs e, and the dashed line shows the extrapolation of eq 13. Equation 15 gives a more realistic prediction of filtration behavior a t low A p , since it predicts a finite permeability at A p equal to zero. Since industrial filtration equipment, such as filter presses, typically operate a t pressure drops in excess of 65 psia, extrapolation to higher pressure drops is of interest. However, without further experimental data it is difficult
to judge which expression is more appropriate for extrapolation to Ap/Ho values above the experimental range. Filtration has also been shown to be a sensitive measure of mycelial morphology. The data presented in Table I1 demonstrate that three of the filtration parameters, the hyphal density, the index of compressibility, and the Kozeny constant, vary systematically with the age and with the visually observed morphology (i.e., pellets vs filaments) of the cultures. Thus, the "condition" of the broth could be monitored by any one of these parameters. Since broth age and mycelial morphology both have a strong influence on broth rheology and transport phenomena in a biochemical reactor, on-line monitoring of the broth condition would be beneficial. The three filtration parameters listed in Table I1 all decrease with increasing broth age. However, these parameters vary uniquely with observed morphology.
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Blotechnol. Rag., 1991, Vol. 7, No. 6
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.*
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This work was supported by NSF Grant CTS-8908454.
Literature Cited
8
X
Kozeny constant, are sensitive indicators of the age and morphology of the mycelia, which are known to influence transport phenomena and overall productivity in biochemical reactors. It is proposed that simple filtration probes could be used to monitor commercial-scale fermentations with mycelial cultures.
Acknowledgment
pellets
O O
0
:
599
(1) Fatile, I. A. Rheological Characteristics of Suspension of
0
I
I
I
I
I
0.1
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0.3
0.4
0.5
Index
I
0.6
of Compressibility (n’)
Figure 9. Kozenyconstant,K” (eq71,vs indexof compressibility, n’ (eq 13), for filamentous (open symbols) and pelleted (filled symbols) broths of P. chrysogenum (circles), S. griseus (diamonds), and S. tendae (squares).
Figure 9 shows a cross correlation between the Kozeny constant and the index of compressibility, n’,for pelleted and filamentous morphologies of the three organisms. The data for the filamentous broths are consistently shifted toward lower compressibilitiesat all values of the Kozeny constant. A similar trend is observed when the hyphal density is cross correlated with the index of compressibility for the same broths (plot not shown). These observations indicate that a multiparameter analysis would provide more detailed information about the condition of the broth than any single parameter would provide. The above analysis, as well as most of the literature, classifies mycelial morphology in terms of a discrete, qualitative distinction between pelleted and filamentous morphologies. However, there is clearly a continuum of morphological structures which can occur, of which pellets and filaments represent two extremes. This fact has been overlooked in the past because of the limited ability to quantatively measure morphologies. The filtration methods outlined above provide one of the first simple, quantitative characterizations of mycelial morphologies.
Conclusions Several filtration parameters have been defined. For slurries of three mycelialorganisms,the filtration behavior was precisely and reproducibly correlated in terms of these parameters. It has been demonstrated that three filtration parameters, hyphal density, cake compressibility, and
Aspergillus niger: Correlation of RheologicalParameters with MicrobialConcentration and Shapeof the MycelialAggregate. Appl. Microbiol. Biotechnol. 1985,21,60-64. (2) Metz, B.; Kossen, N. W. F.; van Suijdam, J. C. The Rheology of Mould Suspensions. Adv. Biochem. Eng. 1979, 11, 104-
156. (3) Roels, J. A.; van den Berg, J.; Voncken,R. M. The Rheology of Mycelial Broths. Biotechnol. Bioeng. 1974, 16,181-208. (4) Blanch, H. W.; Bhavaraju, S. M. Non-Newtonian Fermen-
tation Broths: Rheology and Mass Transfer. Biotechnol. Bioeng. 1976,18,745-790. (5) Charles, M. Fermentation Scale-up: Problems and Possibilities. Trends Biotechnol. 1985,3, 134-139. (6) Kim, J. H.; Lebeault, J. M.; Reuss, M. Comparative Study on Rheological Properties of Mycelial Broth in Filamentous and PelletedForma Eur. J.Appl. Microbiol. Biotechnol. 1983, 18,ll-16. (7) Smith, J. J.; Lilly, M. D. The Effect of Agitation on the
Morphologyand Penicillin Production of Penicillium chrysogenum. Biotechnol, Bioeng. 1991,35, 1011-1023. (8) Oolman, T.; Blanch, H. W. Non-Newtonian Fermentation Systems. Crit. Rev. Biotechnol. 1986,4,133-184. (9) Blakebrough, N.; McManamey, W. J.; Tart, K. R. Heat Transfer to Fermentation Systems in an Air-Lift Fermenter. Trans. Zmt. Chem. Eng. 1978,56,127-135. (10) Packer, H. L.; Thomas, C. R. MorphologicalMeasurements of Filamentous Microorganisms by Fully Automatic Image Analysis. Biotechnol. Bioeng. 1990,35, 870-881. (11) Nestaaa, E.;Wang, D. I. C. A New Sensor, The “Filtration Probe,” for Quantitative Characterization of the Penicillin Fermentation. Biotechnol. Bioeng. 1981,23,2803-2813. (12) Cagney, J. W.; Chittur, V. K.; Lim, H. C. Use of Filtration Measurements for Estimation of Cellular Activityin Penicillin Production. Biotechnol. Bioeng. Symp. 1984, 14, 619-634. (13) Ingmanson, W. L. Filtration Resistance of Compressible Materials. Chem. Eng. Prog. 1953,49,577-584. (14) Harvey, M. A.; Bridger, K.; Tiller, F. M. Apparatus for Studying Incompressible and Moderately CompressibleCake Filtration. Filtr. Sep. 1988 (Jan/Feb), 21-29. (15) Ward, A. S.Liquid Filtration Theory. In Filtration; Matteson, M. J., Orr, C., Eds.; Marcel Dekker, Inc.: New York, 1987;p 138. Accepted September 10,1991.
