## Dy

The "stoichiometric coefficients" on the other components in equation 5 then provide the y values needed to calculate the concentrations of nutrients and products from the last term in equation 3. These simple calculations can provide a surprising amount of approximate information about process design and development. A feature of the example in equation 5 is the large amount of acid (H+) produced by the metabolism. Even with the high liquid flow rate allowed by cell immobilization or recycle (29,37) its neutralization requires a high pH in the liquid inflow, so the biophase must be very well mixed if metabolism is not to be inhibited by pH gradients, suggesting some type of bubble-gasified bioreactor. If all of the NO— and OH" are provided by their sodium salts, then the salinity in the biophase would be high, suggesting a need for halophilic strains of bacteria. A reasonable alternative would be to explore the use of calcium salts, which would precipitate some of the product sulfate as gypsum, reducing inhibitory effects.

Like all the previous analyses, equation 6 applies only to steady-state operation. Gas treatment bioreactors, like any other bioprocess, are generally started with a relatively small inoculum of acclimated microorganisms, the objective of the start-up period being to increase the population to the steady-state value, Sx. This requires additional growth nutrients, and the initial feed concentration, Sji, can be calculated as above, but with setting the observed cell yield, y, equal to the growth yield coefficient, Y. These concentrations can then be decreased slowly as steady state is approached. Start-up of biofilters is sometimes called ripening of the bed, and it is not always necessary to add growth nutrients, because the microorganisms capable of growth on the contaminant may obtain nutrients from the support material (compost, soil, etc.), or may grow at the expense of cells that die and lyse under conditions in the biofilter. If these sources are not sufficient to produce the biofilm thickness needed for maximum contaminant removal, some nutrient addition after steady-state contaminant removal has been reached will further improve performance. However, excessive nutrient addition must be avoided because modeling (38) suggests that, under contaminant limited conditions, a biofilm will grow much thicker than is needed. The inlet end of the biofilter may plug with useless biofilm.

Just because a steady state exists in theory, it does not follow that it can be reached by any start-up procedure. Of particular concern are those contaminants that are so concentrated (high ni) and soluble (low H) that they will cause substrate inhibition of the microbial metabolism if their dissolved concentration in the biophase ever reaches equilibrium with the feed (ni/H). The steady state analyzed above still exists, but S < nJH only as a consequence of the metabolism of the large numbers of microorganisms present. Starting with a small inoculum, the dissolved concentration in the biophase will be much higher, metabolism will be inhibited, and the biomass may wash out. For similar reasons, batch experiments may produce the erroneous conclusion that the gas cannot be treated biologically. A proper start-up procedure may involve dilution of the feed gas and careful control of the dilution rate and nutrient addition, until a dense, well-acclimated microbial culture has developed.

### Gas-Biophase Mass Transfer

Figure 2 shows that high levels of contaminant removal require high values of the dimensionless mass-transfer factor, G, which is actually the product of two dimensionless numbers: H/RT, an inverse measure of the contaminant solubility, and k1a/g, a measure of the efficiency with which the gas flow generates mass transfer. This is not usually a difficulty for biofilters with their thin biophase and very large a but how can it be achieved for other bioreactor types? Measurements of gas-liquid mass transfer factors (28) are often given as correlations of the form k a = AUcg

The superficial gas velocity Ug is related to the flow rate g by Ug = gL, where L is the bioreactor height. Consider first an idealized bubble column, a hypothetical device in which all the bubbles are the same size, and doubling Ug simply doubles their number. The exponent c must then be 1, making k1a/g = AL, a constant dependent upon scale but independent of gas-flow rate. In real bubble columns, with their imperfect bubble dispersion, c is closer to 0.7, but this still implies that G varies only slightly with g. The copious data available for oxygen transfer from air (28) shows that, at normal gas flows (g on the order of 1 VVM), k1a/g is on the order of 1 at the laboratory scale, rising toward 10 in commercial-scale equipment. Assuming for the purposes of illustration that k1 for a gas is proportional to its diffusivity in water raised to the 2/3 power (strictly valid only for relatively insoluble gases, for which most of the mass-transfer resistance is on the liquid side of the gas-biophase interface), this can be used to estimate G and the maximum possible fractional removal, 1 — e"G, (equation 4 with S r 0) for contaminant gases of low, medium, and high solubility. The results shown in Table 1 suggest that bubble columns would be useless for insoluble contaminants like carbon monoxide, but worth consideration for moderately soluble contaminants like hydrogen sulfide. Most hydrocarbon vapors fall into the former category, but many alcohols and chlorinated aliphatic solvents are in the latter (30). For very soluble contaminants, such as sulfur dioxide, G tends to be unnecessarily large in bubble columns, and while acceptable removal with a moderate pressure drop could be achieved in very short, wide columns, this configuration has not been explored in practice.

The addition of a mechanical agitator can increase k1a by roughly one order of magnitude, mainly by breaking up the gas flow into many small bubbles with a large interfacial area. Equation 7 still applies, but the A parameter becomes a function of the mechanical power input per unit reactor volume. Unfortunately, agitation also undermines the assumption that the gas moves though the reactor in plug flow. In a mechanically agitated tank, the gas bubbles are assumed to recirculate several times so that the gas phase is completely mixed; a sample of gas containing many bubbles taken from anywhere in the tank would have the same composition as the outlet gas. The effect on the driving force for mass transfer can be seen by comparing the concentration profiles shown in Figure 3a and b. Mathematically, the long-mean concentration difference used in equation 3 must be replaced by the more familiar effluent partial pressure driving force (p/H — S), which makes the maximum possible removal not (1 — e—G), but G/(1 + G). These two functions are virtually identical at small G, which explains why the exact definition of the driving force is not an issue for aeration (oxygen is an insoluble gas, H/RT = 30 at 20 °C, and its small fractional removal from the air stream in conventional fermenters is

Table 1. Performance of Bioreactors for which k1atg = 1-10 for O2

Maximum possible removal

Contaminant gas

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