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Biotechnol. Prog. 1995, 1 1, 498-509
TOPICAL PAPER Design of Gas-Treatment Bioreactors G. F. Andrews” and K. S. Noah Biotechnology Department, Idaho National Engineering Laboratory, P.O.Box 1625, Idaho Falls, Idaho 83415-2203
Bioreactors are employed increasingly to remove undesirable components from gas streams and to carry out bioprocesses with gaseous nutrients. The problem is to match the type and detailed design of the bioreactor to the characteristics of the component and the microbial metabolism, in order to meet a given set of process requirements a t the lowest possible total cost. The higher the specified fractional removal, the greater the advantage of packed-bed and bubble-column reactors in which the gas approaches plug flow. The variation of the gasAiquid interfacial area with gas flow rate makes bubble columns unsuitable for relatively dilute, insoluble componehts (e.g., hydrocarbons), but the complete mixing of the liquid is a n advantage with more concentrated, soluble components, particularly those (e.g., H2S, S02) that dissociate in contact with water and may be inhibitory a t their equilibrium concentrations. When the component is the carbodenergy source or electron acceptor for metabolism, the amount of viable biomass in the reactor a t steady state is limited to the rate of component removal divided by the maintenance requirement of the biomass for the component. However, the volume of water in which this biomass is suspended is a variable to be fixed by the process designer or operator. Thus, a packed-bed bioreactor may be run as a minimum-water biofilm reactor (given a film-forming organism) or as a trickle-bed reactor containing a dilute cell culture (better when the metabolism requires a soluble nutrient or produces a nonvolatile and inhibitory product). In either case, the optimum operating point, close t o the onset of mass-transfer limitation, can be identified by setting the appropriate definition of the Thiele modulus equal to 1. An analysis based on interpolation between these limiting cases suggests a general definition of the modulus. It can be used in conjunction with mass-transfer and liquid-holdup correlations as a guide for selecting the type and size of packing material, operating strategies, and scale-up procedures, which can then be tested by experiment on particular gas streams.
Contents Introduction General Considerations in Bioreactor Design GasLiquid Mass Transfer Mass Conservation Equations Yield and Rate Equations The Biofilter The Water-Film Problem Optimum Biofilm Thickness Steady-State Biofilm Thickness Bubble Columns The Trickle-BedBioreactor The Design Problem The Trickle-Bed/Biofilm Reactor Theory Results Conclusions
498 499 500 500 501 501 502 503 503 504 505 505 506 506 507 508
Introduction It has been known for many years that air streams contaminated with low levels of hydrocarbons, malodor-
ous gases, carbon monoxide, nitrogen oxides, etc., can be effectively treated in soil biofilters (Bohn, 1975; Inman et al., 1971;Abeles et al., 1971). These consist of simple beds of soil through which the air is blown, the contaminants being removed by a combination of adsorption and degradation by the soil’s natural microflora. This idea has recently been extended, with more sophisticated microbiology and bioreactor technology, to treating air contaminated with the vapors of chlorinated solvents that must be degraded by cometabolic pathways (Kampbell et al., 1987;Apel et al., 1993; Shields et al., 1994;Ensley, 1992). Biological processes have also been proposed for removing hydrogen sulfide from fuel gases and nitrogen oxides from stack gases (Dasu et al., 1993; Lizama and Sankey, 1993; Apel and Turick, 1993), nor is this trend toward the biological processing of gases limited to environmental cleanup. Klasson et al. (1993)have shown that ethanol and acetic acid can be produced by the fermentation of synthesis gas, and various enzymatic and whole-cell bioconversions have been carried out in gasphase bioreactors (Lamare and Legoy, 1993). The design of all of these gas-treatment bioprocesses presents many similar problems, yet no standard design procedures appear in bioprocess engineering texts. “Design” means specifying values for the process variables, defined as any quantity under the direct control of the
8756-7938/95/3011-0498$09.00/00 1995 American Chemical Society and American Institute of Chemical Engineers
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process designer or operator (type, size, and shape of the bioreactor, liquid flow rates, nutrient addition, cell wastage, etc). The difficulty is that many combinations of these process variables will work, in the sense that they will meet the given set of process requirements (gas flow, contaminant concentration, fractional removal, etc.). Proper engineering design is concerned less with the many process configurations that will work than with finding the single configuration that works best, satisfying the process requirements at the lowest possible total cost. It is a complex economic optimization problem that can only be solved, and then only approximately, by means of a careful combination of mathematical modeling and experiments at different scales. The objective of this paper is to show how modeling can provide important quantitative insights at the start of the scale-up process. It uses some elementary, but often overlooked, considerations to provide guidelines for the selection of bioreactor type and the optimization of process variables, such as the size and type of the support particles in packed-bed biofilters. Since economic calculations necessarily are based on some uncertain economic assumptions, the paper focuses on the related, but purely technological, objective of minimizing the size of the bioreactor needed to meet the process requirements. The reader should not overlook the.obvious fact that a small stainless steel tank (for example) may be more expensive than a much larger bed of soil. An important preliminary question is whether the composition of the microbial culture qualifies as a process variable, as defined earlier. Some feed gases are sterile (stack gases, synthesis gas) or sterilizable, so that the bioreactor can contain a pure culture of a strain chosen by the process designer. This is, however, the exception. Most gas-treatment bioreactors will contain a mixed culture that develops by competition between those strains naturally present in the reactor, any inoculum added at start-up, and those strains entering with the gas. The outcome of this competition is usually beneficial when the contaminant is a major growth nutrient (hydrocarbons, NO,, etc.) because the selection pressure tends to favor those strains that can consume the contaminant fastest (characteristics like the ability to attach to surfaces and sensitivity to high concentrations may complicate matters in some cases). The outcome will not be as good when,the contaminant is one (chlorinated solvents)that must be degraded cometabolically. To the cell, cometabolic degradation represents a waste of enzymatic activity, so that natural selection pressure tends to favor strains incapable of the required degradation. Considerable ingenuity may be needed to set process variables like temperature, pH, nutrient addition, etc., to favor the growth of the desired strains.
General Considerations in Bioreactor Design The starting point for the design of any bioreactor is the autocatalytic nature of microbial kinetics. Bacteria not only catalyzethe desired reactions but will also, given sufficient nutrients, reproduce themselves as part of the process. By recycling or immobilizing these growing cells in the reactor, the cell concentration and thus the volumetric reaction rate (grams degraded per hour per unit reactor volume) can be increased to very high levels. Andrews (1994a)has shown that the concept of mean cell residence time, M , originally developed for biological wastewater treatment, applies equally well to gas-treatment bioreactors. Large M means a high cell concentration in the reactor, which is what allows gases to be treated with a residence time of minutes, despite the fact that the time scale for the inherent kinetics of microor-
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Graham F. Andrews received his M.S. and Ph.D. (1979) degrees in chemical engineering from Syracuse University. He worked on the faculty of the Department of Chemical Engineering at the State University of New York a t Buffalo before moving in 1988 to the Idaho National Engineering Laboratory, where he is Technical Leader for Bioprocess Engineering in the Center for Industrial Biotechnology and Process Engineering. His main research interests are in bioremediation, desulfurization of fossil fuels, and control of bioprocesses. He has authored several reviews on the modeling and design of bioreactors.
I
Karl S. Noah received his B.S. degree in chemical engineering from North Carolina State University in 1983 and his M.S. degree in chemical engineering from Colorado State University in 1987. In his 8 years at the Idaho National Engineering Laboratory, he has conducted research in biohydrometallurgy and the desulfurization of fossil fuels.
ganisms (i.e., the specific rates: grams degraded per hour per gram of cells) is usually on the order of hours. In the analyses given here, the cells are seen as part of the biophase, which may be a suspension of cells in water, a packed mass of cells in a biofilm or even individual cells attached to a moist surface. A major difference between wastewater-treatment bioreactors and gas-treatment bioreactors is that the amount of water in the latter, and thus the volume of the biophase, is a process variable totally under the control of the process designer. It may vary from just sufficient to maintain humidity in a soil biofilter to the large amount found in bubble-column-type bioreactors. Note also that, in the common situation where the contaminant is dilute and provides the main electron donor or acceptor for the cells’ energy metabolism, there is a definite upper limit to the number of viable cells in the reactor. It happens when M = (i.e., no loss of viable cells from the reactor) and corresponds to the situation where all of the contaminant is used to satisfy the cells’ maintenance energy requirements. The total cell mass is then given by the contaminant feed rate (gramshour) divided by the maintenance coefficient (grams per hour per gram of biomass). However, since we control the amount of water, this biomass may be distributed at low concentrations through a large
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bioreactor or, more sensibly, at high concentrations in a small bioreactor. If the only upper limit on the concentration of the biophase is the number of cells that will fit into unit volume (as in a biofilm), it may well be asked what limits the volumetric reaction rate in a real, well-designed bioreactor. The answer is the purely physical processes of gashquid mass transfer and mixing that move the contaminant from the gas to the cells in the biophase. As the cell concentration increases, these processes become increasingly restrictive until, in the limit of the biofilm, mixing disappears and all mass transfer is by molecular diffusion, a notoriously slow process. The design of a gas-treatment bioreactor can be summarized in one sentence: choose an efficient gashiophase contacting device and provide it with sufficient cells so that it operates at the mass-transfer limit. GasLiquid Mass Transfer. The experience of most bioprocess engineers with mixing and mass transfer comes from aeration and can be misleading. The objective in aeration is to transfer oxygen at the maximum possible rate, which can best be accomplished with a high airflow in a mechanically agitated tank. The fraction of oxygen in the air that is actually transferred to the liquid and consumed by the microorganisms is irrelevant and is typically 1-2%. Contrast this with the gas-treatment bioreactor where the objective is to achieve some specified, high value (usually >go%) of fractional removal of the contaminant from the gas, and the rate, although still important in determining the size of the bioreactor, is a secondary consideration. This very different objective is best achieved not by mechanical mixing but by a reactor in which the gas approximates plug flow (a series of mechanically agitated tanks remains a possibility). The difference in reactor configuration requires a change in the definition of the driving force for mass transfer. In a stirred tank both the gas and liquid phases are assumed to be completely mixed, so that the driving force is (S,* - S) where S is the dissolved concentration in the liquid and S,* is the dissolved concentration in equilibrium with the exit gas composition. This explains the ineffectiveness of the stirred tank; as the contaminant concentration in the exit gas approaches zero, so does S,* and the mass-transfer rate. When the gas moves in plug flow, the partial pressure of the contaminant in the gas (and thus S") decreases through the reactor, and the appropriate definition is the log-mean concentration difference:
Subscript i shows the inlet conditions and e the exit conditions. This approaches the stirred-tank driving force only if the liquid is completely mixed (Si = S,) and there is little change in pressure and contaminant concentration in the gas phase through the reactor. The effect of gasfliquid mass-transfer resistances is that the Concentration to which most of the cells are actually exposed, S, is less than the solubility of the contaminant, S*. On the basis of the aeration precedent this is normally considered detrimental, but there are two situations in which it is actually beneficial. The first involves soluble, inhibitory gases (Klasson et al., 1993). For example, a gas stream containing 1%SO2 at 20 "C and 1 atm has an equilibrium solubility S* = 1.8 g;lL, which is sufficient to inhibit many microorganisms. A reactor operating in the mass-transfer-limited regime may therefore remove SO2 faster because the biomass it
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contains is exposed to a dissolved concentration S -= S* and, consequently,is not inhibited. This applies as much to the design of laboratory experiments as to that of fullscale bioreactors. It is easy to fill a flask with an inhibitory gas mixture, add a dilute suspension of cells, and conclude, when nothing happens, that the contaminant cannot be treated biologically. Very different conclusions may be reached by exposing a more concentrated cell suspension with appropriate levels of agitation to steadily increasing gas-phase contaminant concentrations, so that the dissolved concentration to which the cells are actually exposed is always at a noninhibitory level. Bioprocess design always requires collaboration between engineers trained in mass-transfer effects and microbiologists trained in metabolic requirements, and this collaboration should start in the laboratory. Cometabolic degradation is the other area in which mass-transfer resistances may be beneficial. Consider, for example, the degradation of chlorinated solvent vapors by methanotrophic bacteria. A high volumetric rate requires a high concentration of viable bacteria in the biophase, with high levels of induced methane monooxygenase (MMO) enzyme. Unfortunately, the contaminants must compete with the methane for the active site of this enzyme, so that a high contaminant degradation rate can onlybe achieved if the concentration of dissolved methane to which the cells are exposed is vanishingly small. How can high concentrations of cells and enzymes be combined with low dissolved methane? Pulsing of methane in the gas feed to the reactor is one possible solution. Operating under conditions of methane mass-transfer limitation is another. It is possible, in principle, because most of the chlorinated solvents have a higher solubility than methane, which helps to compensate for the higher affinity of the MMO enzyme for methane. Another often unstated assumption from aeration is the idea that all of the mass-transfer resistance occurs on the liquid side of the gashquid interface. This is true for most gases since diffusivities in a gas are some 4 orders of magnitude higher than those in water, but it may not be true for very soluble gases, particularly those that dissociate upon contact with water (NO2, C02, H2S, NH3, SO5 the dissolved SO2 discussed earlier is mainly HS03- and H+). Mass transfer of these gases is extremely fast, and what little resistance exists may be on the gas side of the interface (Lizama and Sankey, 1993). Analysis of these situations is complicated by enhancement effects resulting from the dissociation reactions [see, for example, the analysis by Counce and Perona (1983)of the abiotic stripping of NO,], and they must be treated on a case-by-casebasis. In all of the analysis that follows, the L subscript (meaning liquid side) is dropped from the mass-transfer factor, k ~ aand , it is assumed that the contaminant solubility follows Henry's law: S* =p/H, where p is the partial pressure of the contaminant in the gas and H is the Henry's law constant. Mass ConservationEquations. At steady state, the mass conservation equation for the reactor states that the rate of contaminant removal from the gas phase equals the rate of mass transfer to the biophase and the rate of consumption by the microorganisms. The terms are written per unit volume of bioreactor, so that they are independent of scale. For plug flow of gas the equations are JX = J
- G&),
= k a k - S)lm = kS,"Q dy
(2)
J is the loading, the mass of contaminant fed per hour
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per unit volume and is inversely proportional to the reactor size for a given application. x is the fractional removal of contaminant, a specified process requirement. G is the volumetric gas flow rate per unit reactor volume, evaluated at the exit temperature, Te, and pressure (usually atmospheric). G is the reciprocal of the gas residence time. Q is the volumetric reaction rate (grams consumed by the biomass per hour per unit reactor volume) at any point in the reactor. It can be expressed in various equivalent ways depending on the bioreactor type:
sufficient to satisfy the maintenance requirement m:
- (actual reaction rate)/(rate if all
When S > S,, the biomass grows (given the required nutrients), and when S < S,, it is an endogenous state and slowly declines, even though scavenging of the low levels of available contaminant continues. It is accepted in biological wastewater treatment that S , sets a lower limit on the effluent concentration from many bioreactor configurations (Andrews, 1994a). This rarely matters in practice because mlij, the fraction of contaminant uptake required for maintenance under ideal conditions, is a very small number and S , is a minuscule concentration (at least for aerobic metabolism). However, when low concentrations of relatively insoluble (large H)gas-phase contaminants are treated, the corresponding equilibrium partial pressure, HS,, may be significant, and these minimum concentration effects can influence bioreactor selection. Note that the analysis of cometabolism necessarily involves an extra rate, the consumption of the carbod energy source, and an extra rate equation that may include phenomena like the competition for enzyme sites between the contaminant and the natural substrate (Andrews, 1994b). Conclusions based on eq 4 should not be applied to cometabolic metabolism.
biomass were exposed to equilibrium concn; p / H )
The Biofilter
E is the biophase holdup, the fraction of the reactor volume occupied by the biophase, and X is the cell concentration in the biophase. The biomass per unit reactor volume, Ex, can also be expressed as, a,, where X,is the mass of cells per unit area of gashquid interface. q(S) is the specific consumption rate (grams consumed per hour per gram of biomass) evaluated at the concentration, S , to which the cells are exposed. q is the effectiveness factor, a dimensionless number defined by
q(S)
q=4(pIH)-
q shows the significance of mass-transfer resistance, whose effect is to make S < @/HI. Clearly, 17 = 1in the absence of such resistance and is usually 1for inhibitory contaminants. Since E , X,S , and 9 may all vary through a bioreactor, Q must be integrated, as in the final term of eq 2, in order to obtain the average volumetric reaction rate. Our objective can now be restated as the choice of all process variables (including bioreactor type) in order to maximize this average rate, thus maximizing the loading, J,and minimizing the reactor size to achieve the specified removal, x . As a formal mathematical problem this is impossibly difficult, so that a more intuitive and semiquantitative procedure is employed. If Q can be kept large at all points in the reactor by careful choice of the quantities in eq 3, then its average must also be large. This is the basis for subsequent discussion of the process variables. Yield and Rate Equations. In the preceding equations, all of the complexities of microbial metabolism are contained in the function q(S),and more detailed analysis requires that the form of this function be specified. It is assumed that the contaminant is the carbodenergy source or electron acceptor for the biomass and is needed for both growth and maintenance metabolism and also that the process is sufficientlywell operated (i.e., all other nutrients are available) so that the contaminant is the limiting nutrient. The yield and rate equations are then best written in the form suggested by Lawrence and McCarty (1980): q(S) = p./Y
+ m = @3/(K+ S )
(4)
An advantage of this formulation for the low-concentration regime found in gas-treatment bioreactors is that it predicts a non-zero stationary-phase concentration, S,, at which p = 0 and the contaminant uptake is just
The oldest and simplest type of gas-treatment bioreactor is the biofilter, a packed bed of support particles through which the gas is blown (Leson and Winder, 1991). The biophase consists of individual attached cells, which may develop into a biofilm, and just sufficient moisture is added to prevent the bed from drying out. In terms of the quantities in eq 3, the biofilter is the large alsmall Xalq = 1approach to process optimization. Two major process variables are the type and size of the support particles. They must be small enough to provide a large surface area, but not so small that the bed becomes plugged with excess biofilm or waterlogged by excess moisture. The particles can perform several functions besides simple support. Some, like soil and compost (Ape1et al., 1994))provide a huge natural variety of microorganisms, as well as some nutrients for their growth. They can also adsorb contaminant, which has several advantages, including the removal of sudden slugs of contaminant from the feed stream for later biodegradation. When air contaminated with, say, hydrocarbons is first blown through a bed of soil or compost, those organisms capable of metabolizing hydrocarbons grow, while others may die and lyse, providing nutrients for the growth of the hydrocarbon degraders. During this bed-ripening period, the volumetric reaction rate increases dramatically until X,(the mass of hydrocarbon degraders per unit area) reaches the steady-state value discussed in the following. A similar start-up period is, of course, required to develop a concentrated, acclimated microbial culture in any continuous bioprocess. Biofilters are the only bioreactors known to the authors that are commonly sized to provide the desired contaminant removal from the instant they are switched on. The development of a rational start-up procedure could greatly reduce the size of commercial-scale biofilters. The addition of highly adsorptive particles such as activated carbon to the bed may provide sufficient contaminant removal until the bed has ripened sufficiently to provide adequate removal by biodegradation.
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WATER
GAS
i
PARTIAL PRESSURE OF CONTAMINANT = p
DISSOLVED CONTAMINANT CONC. = p/H
F lbl
OF
CONCENTRATION PROFILE OF DISSOLVED CONTAMINANT
lo-' 10-1
I C 1 THICK TRICKLINQ FILM OF CELL S U-
MASS TRANSFER FILM, THICKNESS
CELL SUSPENSION
10'
100
= 1
0
Figure 2. Conventional gashquid mass-transfer model. = pIHK = dimensionless gas-phase concentration, is
- - - - - - _ - - - - -- 0 Figure 1. Simplified models for gas-treatmentbioreactors. Biofilters are o h n referred to as gas-phase bioreactors, implying that the cells are directly in contact with the gas rather than water. It has even been suggested that this situation changes the inherent microbial kinetics: that the specific consumption rate is larger than that for the same cell attached to the same surface (to cancel out adsorptionhiodegradation interactions) and covered with water containing a dissolved concentration plH. This seems unlikely. A microbial cell is itself an aqueous phase, and if it is coated with a water layer, even a few molecules thick, the contaminant must first dissolve (at concentration plH) before reaching even those enzymes in the cell envelope. In the absence of definitive experimental data, which is difficult to obtain, the application of aqueous-phase kinetics to gas-phase bioreactors remains the best available assumption. The Water-FilmProblem. The following analysis is given for two reasons. It provides a simple example of the meaning of mass-transfer resistance and the effectiveness factor concept upon which later, more complex analyses are based. It also illustrates the importance of humidity control in biofilters. Consider the picture in Figure l a with cells attached to a support particle surface in a film of water. The film is either stagnant or moving downward 80 slowly that the flow remains laminar. In either case, the transfer of contaminant across the film occurs only by molecular diffusion. The steady-state conservation of mass then requires that the rate of diffusion across the liquid film equals the rate of consumption by the microorganisms:
This is a quadratic equation for S, the dissolved contaminant concentration a t the base of the film where the cells are located. The solution for the dimensionless concentration S' = SIK in the range 0 5 S' 5 P,where P
where
e=
Lx,q KD(1
+P)
(8)
8 is a dimensionless number called the Thiele modulus, whose definition is critically dependent on the physical situation. Its general form is the maximum possible rate of metabolism [here Xa$.pIH)I(K plH) when S = pIK1 divided by the maximum possible rate of mass transfer (here DpIHL when S = 0). The effectiveness factor, from the general definition given previously, can be written (the final equality follows from eq 6) as
+
Elimination of S' from eqs 7 and 9 gives 77 as a function of 8 with P as a parameter, as shown in Figure 2. An important feature of this graph is that all of the lines from P = 0 (first-order kinetics: in practice a low partial pressure of a relatively insoluble contaminant for which the cells have a low affinity) to P = = (zero-order kinetics: a high partial pressure of a soluble contaminant for which the cells have a high affinity) are sufficiently close together to be treated as a single line. This is a consequence of the correct definition of the Thiele modulus, 8, and allows some general conclusions to be made about the relationship between the rate of consumption of contaminant, the cell concentration X,,and the liquid film thickness L. There are two limiting cases. When 8 * 1,eq 7 gives S' = P,and the first form of eq 9 gives 77 = 1(the second form becomes indeterminate at this limit). This is the metabolism-limited case with a negligible concentration gradient through the liquid film and the biomass exposed to the equilibrium dissolvedgas concentration, plH. What 8 * 1 means in practice is that the liquid film in Figure l a is thinner than the diameter of the cells, the gas-phase bioreactor case. The
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consumption rate per unit area is X&lH) and can always be increased by adding more cells. The water fdm may even disappear altogether ( 8 = 01, in which case the metabolic activity, q, is a function not only of the contaminant partial pressure, p , but also of the water activity in the reactor (Lamar and Legoy, 1993). When 8 >> 1, the concentration to which the biomass is exposed S’ 0 (eq 7). This is the mass-transfer-limited situation, and the consumption rate per unit area is given by the rate DpIHL (the left-hand side of eq 6 with S’ F is the masstransfer-limited, thick-film regime in which the cells at the base of the biofilm never see any contaminant, are in an endogenous state, and represent wasted space in the reactor. Steady-State Biofilm Thickness. Setting 8 = F gives a design goal by showing how the biofilm thickness would vary with contaminant concentration through an ideal bioreactor. The relationship is shown in dimensionless variables by the “optimum thickness” line in Figure 3. With the expected orders of magnitude of X cm21s),and K (-100 mglcms), Q (-0.1 glg-h), D (-0.5 m a ) , the desired thicknesses are a few hundred micrometers. (Note that this is for a bioflm whose pores are full of water; a gas-phase biofilm with its pores full of air could be 100 times thicker.) The next question is how this compares with the natural thickness to which a biofilm will develop without outside intervention. While the bed is ripening during the start-up period, the rate of contaminant uptake per unit area is vXaijPl(l P),of which an amount mX, is needed for maintenance, and the rest can be used (given the availability of all other nutrients) for the growth of new biofilm. The biofilm keeps growing until all the contaminant uptake is needed for maintenance:
+
r P = m 1+P
d2C C DT=qX-
K+C
dz
with boundary conditions
C = p / H at z = O d C
dz
= ~a t
Z = L
where C is the local contaminant concentration in the film and z is the distance from the gadfilm interface. The effectiveness factor is now given by the rate of diffusion into the film divided by the maximum possible consumption rate in the absence of mass-transfer resistances:
q
(13)
This can be solved simultaneously with the general solution for 11 as a function of 8 and P discussed earlier to obtain the steady-state dimensionless film thickness as a function of P for any value of mlq. It must be emphasized that there are several uncertainties in this analysis and that the results, plotted in Figure 3, should be thought of only as general guides to bioreactor operation. What Figure 3 suggests is that, near the bed inlet, where P is large, the steady-state biofilm thickness is much larger than what is needed. Indeed it is so thick that the bed may become plugged. At the other extreme, near the bed exit where P 0, the steady-state biofilm is too thin. The theory actually predicts that no biofilm will grow for P < m/(p - mj, because eq 13 then has no solution for 7 5 1. This corresponds to the stationaryphase concentration given by eq 5 and establishes a
-
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5
4
I 2 =
E
3
E
-3 ,E e
2
E
a 1
0 Dimensionlessgas-phase concentration P
N94 0038
Figure 3. Comparison of optimum and steady-state biofilm thicknesses. theoretical lower limit for the effluent concentration from a packed-bed biofilter. What design and operating strategies can be adopted in order to bring the steady-state biofilm thickness closer to the optimum profile? Growth nutrients may be injected at different points in the bed during the startup period, or they may be introduced in a liquid flowing countercurrent to the gas. It may be possible to use larger particles near the inlet to accommodatethe thicker film and to wash the excess biomass down from the inlet toward the effluent where it is needed. Various movingbed strategies may be able to achieve the same goals of reducing the biofilm thickness near the bed inlet and increasing it near the outlet. In the small P regime where biofilm growth may be inadequate, support particles like compost or activated carbon that can adsorb the contaminant should be considered. Adsorption and biodegradation have a number of complex, mutually beneficial interactions, the most important of which is that adsorption concentrates the contaminant in the environment of an attached cell. The resulting enhancement of cell growth, which is not included in the theory given here, probably accounts for the observed ability of biofilters to reduce contaminant concentrations down to vanishingly small levels.
Bubble Columns Biofilters usually are not designed for a continuous flow of water. Yet some processes need such a flow either to bring in fresh nutrients (e.g., a carbodenergy source for denitrifying or cometabolic processes) or to wash out nonvolatile metabolic products (e.g., H+, C1-) that would otherwise accumulate to inhibitory levels. Bioreactors in which the gas is bubbled through a microbial suspension (Ensley, 1992; Dasu et al., 1993)represent the high dsmall X approach to maximizing the rate (see eq 3) and have some obvious advantages for these processes. They are not restricted to microbial strains that attach to surfaces and form biofilms. The large water volume provides useful pH buffering for processes like NO, and SO2 absorption, and it is relatively easy to control other aspects of the cell’s physicochemical environment (temperature, nutrient concentrations,etc.). The gas sparger and deep liquid do give a large pressure drop and relatively high compression costs, but this is offset to some extent by the enhanced mass transfer resulting from the higher pressure at the bottom of the reactor.
The complete mixing of the biophase in these reactors greatly simplifies their analysis. Just as in the complete mix-activated sludge system, the mass conservation equation for biomass gives the specific growth rate as p = 1/M, where M is the mean cell residence time [(cells in reactor)/(celloutflow from reactor)]. When there is a continuous flow of water to bring in nutrients and wash out metabolic products and excess biomass, M equals the hydraulic residence time, although it may need correcting for the loss of cells in mist in the effluent gas. Equation 4 now gives the specific consumption rate as q = m 1MM and the dissolved contaminant concentration as
+
(14) The problem can be simplified further by ignoring variations in temperature and pressure through the reactor. Then the loading J = GpiIRT and eqs 1 and 2 give the fractional removal as
x = ( 1 - H S / p J ( l - ePA)
(15)
A = kaRT1GH The first process variable to be fured is the liquid flow rate. It is poor practice to make this zero since dead cells and metabolic products may then accumulate in the reactor. It must, however, be kept small (M -1, so that S approaches its minimum, stationary-phase value given by eq 5. Under this condition, virtually all of the contaminant is used for maintenance metabolism, so that Q = dim (eq 3) and eq 2 gives the viable cell concentration as
-
X = Jxlmc
(16)
This is the maximum number of cells that can be maintained in a viable state using the amount of contaminant being removed from the gas. Equation 15 illustrates two major problems in attempting to achieve high values of the fractional removal, x , in this type of bioreactor: (1)Even if it were a perfect mass-transfer device (A = m), x does not approach 100% even with M = -, This happens because the concentration, S , approaches not zero but S,, given by eq 5. It is similar to the minimum P problem illustrated by Figure 3 for biofilters, but without the possibility of a solution
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based on the interactions between adsorption, cell growth, and biodegradation. (2) Even without problem 1,it may not be possible to achieve the desired removal with a reasonable gas flow rate. For example, if HS e pi, then eq 15 shows that 99% removal requires A = 4.6. This can only be achieved by adjusting the gas flow rate per unit reactor volume, G, but in a bubble column a reduced G means less bubbles and a lower mass-transfer factor, ka. Mass-transfer correlations for these reactors have the form ka = b(GhY, where h is the column height (Gh is the gas superficial velocity) and b and c are constants. If c = 0.75, a reasonable value, then doubling A involves reducing G by a factor of 16, possibly producing a completely unrealistic value. Correct reactor design with a high aspect ratio and efficient gas sparging may alleviate this problem, but it cannot completely eliminate it. Furthermore, the values of the constants b and c are scale-dependent and tend to be smaller in larger scale equipment (Wang et al., 19791, so that prediction of removals in commercial-scale equipment from pilot-plant results is very uncertain. Both of the problems described in the preceding paragraph disappear for very soluble gases. If H is very small (NO2, S02, etc., do not actually obey Henry's law but have very small effective H values), thenA is always large, HSh,is always small, and x can approach 100%. Bubble columns should be limited to these applications. Finally, note that, in a stirred-tank reactor, the masstransfer driving force is (S,* - SI,and the (1 - e-A)in eq 15 is replaced by Al(1 A). Removal at 99% now requires not A = 4.6 but A = 99, which illustrates the superiority of plug-flow-type reactors despite the higher ka values created by mechanical agitation.
+
The Trickle-Bed Bioreactor In a trickle bed, a microbial culture is recirculated continuously over a bed of Pall rings or similar packing designed to give a large gasAiquid interfacial area with a low gas-phase pressure drop and a low probability of plugging. In contrast to the biofilm reactor, the contaminant is distributed through the falling film by rapid turbulent mixing rather than slow molecular diffusion, so that the film can be much thicker before mass-transfer limitations set in. In terms of the quantities in eq 3, X, can be large while 7 = 1. Water may be added continuously to the recirculating culture to compensate for evaporation, bring in fresh nutrients, and wash out excess cells and products, but as in the bubble column, these flows are usually small, so that M -. There are, however, two important differencesthat make the trickle bed less prone to the two problems discussed earlier for bubble columns. First, in a trickle bed, the gasAiquid interfacial area, a , is the independent of the gas flow rate, G. The dependence of the mass-transfer coefficient, k , on G is also small, except for soluble gases where the gas-side mass-transfer resistance is significant. It follows that the dimensionless parameter, A, in eq 15 can be doubled, if necessary to achieve the required fractional removal, by simply halving G. Problem 2 is thus much less severe for a trickle bed than for bubble columns. The second difference is that the liquid in a trickle bed is not Completely mixed. The implications can be illustrated by the case of cocurrent gadiquid flow. The cells near the influent are exposed to high contaminant concentrations, their metabolism is active, and, given sufficient nutrients and time, they will multiply. Further down the bed there is a point where the dissolved concentration has been reduced to the value S,, given by
-
eq 5, at which growth stops. Below this point the cells are in an endogenous state, but most will not have time to die and lyse before reaching the base of the bed and being recycled. They can therefore continue to scavenge the low levels of contaminant present in this region. Thus, unlike in the biofilter (Figure 3) and the bubble column (problem 11, simple theory shows no reason why the contaminant partial pressure in the effluent of a trickle bed should not be reduced below HS,, toward zero. Simple theory, of course, contains many uncertainties, and this conclusion must be confirmed by experiments on each specific mimobelcontaminant combination. The preceding discussion suggests a flaw in the cocurrent mode of operation. The cells recirculated to the reactor influent are in an endogenous state and may go through a lag phase before starting to actively metabolize the contaminant. This may be avoided by countercurrent operation (gas upflow), where cells trickling down through the bed experience an ever-improving environment (Lizama and Sankey, 1993). The discussion also suggests that the single-passliquid residence time may be an important process variable. Given a reasonable liquid superficial velocity of 10 R/h, a laboratory-scale reactor a few feet high does not give sufficient time for significant growth or death of cells. The liquid phase is then effectivelycompletely mixed, and eq 16 provides a reasonable estimate of the steady-state cell concentration for large M. However, a commercialscale bed 20 ft high would have a single-pass residence time of 2 h, which is enough time for significant growth of some strains (eq 16 now gives an average viable cell concentration in the bed). If the ideal scale-up procedure of building the laboratory reactor 20 ft high and scaling only the diameter is not possible, simple projections of the performance of the commercial-scalereador from labscale data must be treated with caution. The Design Problem. Trickle beds are often designed by making a priori selections of three main process variables-the size and shape of the packing material and the liquid velocity-and then conducting experiments to determine the gas flow at which the desired removal can be achieved. While this procedure produces workable designs, it is not likely to produce the optimum design. Is it not possible to use effectiveness factor analysis to eliminate the guesswork and specify close-to-optimal values for all four process variables? Figure ICshows a cross section of a trickling film with a thin, mass-transfer film at the gasAiquid interface and a uniform, dissolved gas concentration, S , throughout the rest of the biophase. As long as the total film thickness, L, is much l a g & than the thickness of the mass-transfer film, I , the mass conservation equation states that the rate of consumption by the cells equals the rate of mass transfer: (17) The reader can confirm that this is identical to eq 6, with the mass-transfer coefficient, k , replacing DIL. The solution therefore is identical t o that for the water-film case (Figure 21, except that the modulus 8 is replaced by OISh, where Sh = kLlD, a Sherwood number, which can be thought of as a dimensionless mass-transfer coefficient. The design point that gives the maximum consumption rate without excessive mass-transfer resistance is now given by 8 = Sh. Since Sh, as defined here, is necessarily larger than 1,this is a larger value than those for the water film and the biofilm, where there was no transport by turbulent mixing.
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The design problem can now be solved, in principle, as follows: (1)Pick a packing material for which the specific surface area, a , is known and the liquid holdup ( E = aL) and gasAiquid mass transfer factor (ka) are available from correlations. (2) Calculate 6 and ka as functions of the liquid superficial velocity from the correlations. (3) The onset of mass-transfer limitation, 8 = Sh [&q = ka(K p/H)1, gives the desirable value of the cell concentration X. It should be evaluated at the average contaminant partial pressure in the bed. (4) Calculate Jx from eq 16. Choose the packing and liquid velocity that give the highest value of this product subject to some obvious constraints (no flooding of the bed; X small enough to make a pumpable cell suspension).
(a)
B< 1
;
LITTLE MASS-TRANSFER LIMITATION
GAS
ALL FIGURES DRAWN FORSh = L/1 3
+
lb) B e I ; ONSET OF MASS-TRANSFER LIMITATION GAS
The Trickle-Bed5iofilm Reactor The picture (Figure IC)upon which the analysis in the preceding section was based, a dilute microbial suspension trickling uniformly over a clean packing, is clearly an idealization. In practice the suspension is concentrated and may contain clumps of cells, and the packing has stagnant regions and patches of attached biofilm with water trickling over or around them. A suggestion made previously for biofilm reactors, that excess biofilm be washed down from the bed influent toward the effluent end where natural biofilm growth is insufficient, leads to a similar picture of events in a real bioreactor. The problem is to suggest a design procedure capable of dealing with this complexity. Jones et al. (1993) have analyzed the case of a microbial suspension trickling over a biofilm, but their model contains several parameters, including liquidmiofilm mass-transfer coefficients, that would be difficult to evaluate in practice. The procedure suggested here is based on the classical chemical engineering approach to problems of simultaneous mass transfer and reaction (Bischoff, 1965). Idealized pictures of the physical situation are analyzed, and each produces a slightly different definition for the Thiele modulus. The appropriate modulus is set equal to 1, establishing the design goal of operating just at the onset of mass-transfer limitation. For example, the pictures in Figure la-c produced definitions of the modulus 8,(81FP2,and 8/Sh, respectively, and setting them equal to 1 gave the optimum biofilm thickness shown in Figure 3 and the cell concentration in the trickle bed. The problem therefore is to specify a consistent definition of the Thiele modulus for the more complex picture in a real gastreatment bioreactor. The starting point is the relationship between the film thickness, L , and the thickness of the stagnant masstransfer film, 1, shown in Figure IC. The latter film does not actually exist, but is the basic hypothesis of the stagnant-film theory, which has been found to be useful in the understanding of many mass-transfer problems. The theory gives the thickness as I = D l k , so that if the gas-side mass-transfer resistance is negligible (k = k ~ ) , the Shenvood number can be written Sh = k&lD = LIZ. The analysis of Figure ICwas based on the assumption that virtually all of the cells are in the mixed, bulk-liquid region, that is, L >> 1 or Sh * 1. However, in a gas-treatment bioreactor, the thickness of the liquid film, L, may be quite small, and as 1 L , more and more of the cells are in the stagnant film rather than the wellmixed bulk liquid. The limit of this process is a very thin, laminar liquid film with no turbulent mixing (1 = L or Sh = 11, which is the picture in Figure lb. A similar thought-experiment involves starting from Figure ICand increasing the cell concentration. This increases the viscosity of the liquid and, thus, the stagnant-film thickness, 1, which is a function of the hydrodynamics.
-
0 (c)
B > > 1 ; SEVERE MASS-TRANSFER LIMITATION
Figure 4. Proposed model for gas-treatmentbioreactors.
The limiting picture is again Figure l b , a packed mass of cells in a biofilm with 1 = L. It must be emphasized that what is proposed here is not intended as an exact mathematical description of what goes on in a gas-treatment bioreactor. It is an approximate approach to the design problem involving interpolation between two limiting cases based on a consistent physical picture of the liquidmiomass film. The essential question is as follows. If Sh = 1 corresponds to a film through which the contaminant penetrates only by molecular diffusion (Figure lb), and Sh >> 1 corresponds to a thicker film in which turbulent mixing is the major transport mechanism (Figure IC),how should the Thiele modulus be defined in order to interpolate between these cases for the purpose of reactor design and optimization? An obvious advantage of this approach is that the value of the interpolation parameter, Sh, for many types of support particle is available from correlations of mass-transfer and liquid-holdup data. Numbers found from these correlations are themselves averages over the entire bed, so that much of the detailed hydrodynamic complexity of the trickle bed (dripping, channeling, pooling, etc.) is reflected in their values. Theory. The picture upon which the model is based (Figure 4a) is the standard one for predicting the enhancement of mass transfer by reaction (Andrews et al., 1984). It is identical to Figure IC,except that the stagnant mass-transfer film now occupies a significant fraction of the total film thickness. Transfer through this stagnant region is solely by molecular diffusion, but contaminant consumption by microorganisms in the film is now significant, so that the conservation of mass of the contaminant is given by eq 10. Below the stagnant mass-transfer film (z > 1) lies a bulk-liquid region of thickness L - 1, where turbulent mixing ensures a uniform dissolved concentration, S, of contaminant. The first boundary condition under eq 10 remains unchanged, but the secondary boundary condition must be changed
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to state that the diffusion rate of contaminant out of the base of the stagnant film equals the rate of consumption by microorganisms in the bulk-liquid region. dC
qs
dz
K+S
C = S and - D - = ( L - l ) X -
at z = l (18)
With these boundary conditions, eq 10 can only be solved numerically. However, for the present purposes, the complete solution is unnecessary and only the asymptotic solutions for low and high P are needed. When P 0 (a dilute, relatively insoluble contaminant for which the cells have a low affinity), then C *: K and the right-hand side of eq 10 becomes gXC/K, producing a linear differential equation that can be solved algebraically to give the concentration profile in the stagnant film. Substitution of this solution into the definition of the effectiveness factor (eq 9) gives
-
10-1
10-1
100
B
Figure 5. Complete model.
Results. The effectiveness factor calculated from the preceding equations is plotted in Figure 5 against a generalized Thiele modulus defined by
e
Note that when Sh = 1this reduces to v = (tanh (8)1/z)l (W2,the known first-order kinetics solution for a biofilm (Andrews, 19911, and when Sh * 1it reduces to 17 = 1/(1 8/Sh), the first-order kinetics solution for the trickle film. At the other extreme (concentrated, soluble contaminants for which the cells have a high affinity), P B. 1, C * K throughout the stagnant film, and the right-hand side of eq 10 reduces to a different linear form, qX. This zero-order kinetics solution must be divided into three regimes. Figure 4a shows the situation where 8 I2Sh2/ (2Sh - 1). There is dissolved contaminant throughout the fdm, so that all the cells are metabolizing it at the maximum possible rate, ij (a consequence of zero-order kinetics), and 7 = 1by definition. As 8 is increased (thicker film, high cell concentration, more dilute contaminant), the dissolved contaminant concentration in the well-mixed region, S, decreases until it reaches zero. When this first happens, the diffusion rate into the well-mixed region, -D(dC/dz)ll, is positive, as shown in Figure 4b. The ability of the cells to consume contaminant at some indeterminate rate between zero and a when its concentration, S, is zero is another consequence of the zero-order kinetics assumption. Replacement of boundary condition eq 18 (which is now indeterminate) with C = 0 at z = 1, solution of eq 10, and substitution of the resulting concentration profile into eq 11give
+
+
1 Sh for 2Sh2 < 8 I2Sh2: 17 = - - (20) 2Sh - 1 2Sh 8 As 8 increases further, or as Sh decreases (Le., the stagnant film gets thicker), the diffusion rate into the well-mixed region eventually becomes zero. This will be referred to as the thick stagnant film regime and is illustrated in Figure 4c. The well-mixed region is now irrelevant because it never receives any contaminant, and the situation is identical to that in a thick biofilm. We need not concern ouselves with the asymptotic (P* 1) solution in this situation because the general solution can be found by solving the complete form of eq 10 with the boundary condition C = 0 where dC1d.z = 0 (Andrews, 1991):
(21)
=
[( S h - 1 )”
+Fe]1’2
(22)
1 - 1/2Sh
No formal mathematical derivation of this definition is given here, but it is based on the ideas of Bischoff (1965). Note that it is consistent with the limiting cases discussed earlier. When Sh = 1, B = (8/F)1/z,the correct form of the Thiele modulus for a biofilm. The same applies whenever [(Sh- 1)/(1- 1/2Sh)I2 F8, a generalization of the thick stagnant film regime of Figure 4c. 8/Sh, the appropriate form of When Sh B. 1, then B the modulus for the trickle film. The form of the first term in the denominator of B comes from the finding (eq 20) that mass-transfer limitation sets in for zero-order kinetics (F = 2 ) when 8 = 2Sh2/(2Sh- 1). This point must correspond to B = 1. The main justification for eq 22 is that, with this definition of B , the lines for all possible contaminant concentrations (0 IP Iw) and all possible mass-transfer situations (1 ISh Iw) fall close together on Figure 5 . In fact, given the precision with which we normally know the parameter values and the accuracy with which we can control the film thickness in practice, the lines can be considered identical. Thus, B is a general parameter that allows important conclusions to be drawn about the onset of mass-transfer limitation in all situations. When B 1(small 8 and/or large Sh),the concentration profiles are roughly as shown in Figure 4a (the relative proportions of the well-mixed and stagnant-film regions obviously depend on Sh). This is the metabolism-limited regime. The volumetric reaction rate given by eq 3 can be increased simply by adding more cells, since increasing X and/or L (which increase B ) causes only a slight decrease in q (Figure 5). B * 1corresponds to the thick stagnant film regime of Figure 4c, a very undesirable operating condition. The film is far thicker than is necessary, which can only contribute to plugging or flooding of the bed. The cells at the base of the film never see any contaminant and, if the contaminant is an essential nutrient, must lose viability as a result (individual cells may be moved up to the gasAiquid interface by random mixing, but the average viability must be decreasing). The desirable situation is B close to 1,which gives the maximum contaminant uptake rate per unit area, while ensuring that all of the cells (whether in a biofilm or a trickle film) are exposed to non-zero concentrations of contaminant. Replacement of the condition
-
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9 = Sh with B = 1represents a useful generalization of the design procedure given in the preceding section.
Conclusions
It is sometimes argued that biological processes are inappropriate for large-scale processes like stack-gas scrubbing because their slow inherent kinetics would make the bioreactors impractically large. This argument overlooks the fact that bioprocess kinetics are autocatalytic. The microbial catalysts grow as part of the process and, by recycling these cells or immobilizing them in the bioreactor, during the start-up period, the catalyst concentration, and thus the rate of reaction, can be increased to very high steady-state levels. When an essential nutrient is a sparingly soluble gas, the process rate is limited not by the inherent kinetics of metabolism but by the rate of gaslliquid mass transfer, and the rate of mass transfer in a biological process can be similar to that in a chemical process. The maximum viable biomass in the reactor at steady state occurs when there is no outflow of cells (mean cell w) and equals the inflow rate of the residence time contaminant divided by the maintenance coefficient. The biomass is then, on the average, in a stationary-phase state, although some cells may be growing while others are dying and lysing. Since the amount of water in a gas-treatment bioreactor is a process variable under the control of the process designer, this biomass may be distributed as a small volume of very concentrated biophase (a biofilm) or as a larger volume of a more dilute cell suspension in a trickle-bed or bubble-column reactor. The former approach generally gives a smaller reactor, but the latter is favored when the process requires a liquid-phase nutrient or generates a product (e.g., Hf from the dissolution of acid gases) that would quickly reach inhibitory concentrationswhen dissolved in a small volume of water. Gas-treatment bioreactors should be designed to operate just at the onset of mass-transfer limitation. Below this point, in the metabolism-limitedregime, the reactor size can be reduced by increasing the cell concentration in the biophase. Above this point, in the mass-transfer limited regime, the reactor tends to get plugged or flooded with excess, nonviable biophase. For packed-bed reactors, this design point has been identified by defining a Thiele modulus, a dimensionless number whose exact form depends on of the details of the liquidmiomass film. Equation 22 provides a definition appropriate for many circumstances from a dilute, suspended-cell biophase, where transport is by turbulent mixing, to biofilms where the dominant mechanism is molecular diffusion. By setting this modulus close to 1,combined with correlations for mass transfer and liquid holdup in packed beds, reasonable estimates can be made of important process variables such as support particle size, liquid flow rate, cell concentration, and biofilm thickness. These estimates provide the starting point for experiments designed to find the best practical bioreactor design for any set of process requirements. When the equilibrium dissolved concentration of the contaminant inhibits microbial metabolism, which can happen with very soluble gases such as SOZ, masstransfer limitations are beneficial because they reduce the concentrations to which the cells are actually exposed. Bubble-column-typereactors are suitable for these situations but not for less soluble contaminants, because the dependence of the gasAiquid interfacial area on the gas flow rate makes it difficult to achieve high removals. Also, the complete mixing of the biophase implies, at least in
-
theory, a minimum contaminant concentration below which the gas stream cannot be treated. Many gas treatment processes could be improved by refining the nutrient addition, flow rates, etc., during the start-up period.
Notation gashiophase interfacial area per unit reactor a volume A dimensionless number defined by eq 15 B generalized Thiele modulus defined by eq 22 local dissolved concentration of contaminant in C a biofilm D diffisivity of component in the biophase dimensionless number defined by eq 12 F gas flow rate (volume per unit reactor volume G per hour) bioreactor height h H Henry's law constant for contaminant loading (grams of contaminant per hour per unit J reactor volume) gashiophase mass-transfer coefficient k K Monod half-velocity constant L biophase thickness 1 thickness of mass-transfer film in biophase m maintenance coefficient (grams per gram of biomass per hour) M mean cell residence time [(viablecells in reactor)/ (wastage rate of viable cells)] pIHK (dimensionlessgas-phase concentration) P partial pressure of contaminant in gas P volumetric reaction rate (grams consumed per 8 hour per unit reactor volume) specific consumption rate for cells exposed to a q(S) concentration S maximum specific consumption rate Q R gas constant dissolved concentration of contaminant S SIK (dimensionless dissolved concentration) s' dissolved concentration in equilibrium with gas S* phase Sh Shenvood number absolute temperature T fractional removal of contaminant X X biomass concentration in biophase biomass per unit area of interface X, distance along bioreactor Y cell yield coefficient Y z distance into biophase € biophase holdup effectiveness factor r biomass specific growth rate P 8 Thiele modulus defined by eq 8 Subscripts e effluent value i influent value lm log-mean value 8 stationary-phase value Acknowledgment This work was supported under Contract No. DEAC07-76ID01570 from the U.S.Department of Energy, Office of Advanced Research and Technology Develop-
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ment, Office of Fossil Energy, to the Idaho National Engineering Laboratory/ElG&GIdaho, Inc.
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