This section examines two quantitative models for predicting biodegradation: the kinetic rate expressions and the biofilm model. It also examines several qualitative models for describing biodegradation in the deep-well environment.

Kinetic rate expressions

When microorganisms use an organic compound as a sole carbon source, their specific growth rate is a function of chemical concentration and can be described by the Monod kinetic equation. This equation includes a number of empirical constants that depend on the characteristics of the microbes, pH, temperature, and nutrients.54 Depending on the relationship between substrate concentration and rate of bacterial growth, the Monod equation can be reduced to forms in which the rate of degradation is zero order with substrate concentration and first order with cell concentration, or second order with concentration and cell concentration.144

The Monod equation assumes a single carbon source. The difficulty in handling multiple carbon sources, which are typical in nature, has led to the use of an empirical biodegradation rate constant k^

where B = bacterial concentration, k1 = an empirical biodegradation rate constant. This equation is of the same form as Equation 20.6 for linear adsorption. Predicting biodegradation using such a rate constant is complicated when multiple biodegradable compounds are present. For example, phenol and naphthalene are both rapidly biodegraded in single-compound laboratory shake-flask experiments when seeded with bacteria from an oil-refinery settling pond, but when the two compounds are combined, naphthalene is not degraded until the phenol is gone.3

When a compound is cometabolized (degraded but not used as a nutrient), a second-order biodegradation coefficient can be used to estimate, kB:

where kB = first-order biodegradation coefficient, kB2 = second-order biodegradation coefficient, and B = bacterial concentration.

Mills and colleagues58 describe the use of these formulations to predict aerobic biodegradation in surface waters and present methods of adjusting for temperature and nutrient limitations. This approach to predicting biodegradation is problematic because it is difficult to obtain empirical coefficients in the deep-well setting.

Baughman and colleagues145 derive a second-order kinetic rate expression as a special case of the Monod kinetic equation. It appears to describe biodegradation of organics in natural surface waters reasonably well:

Paris and colleagues144 found that degradation of several pesticides in samples from over 40 lakes and rivers fits this second-order model of microbial degradation.

General degradation rate models of organics in soils have been described by Hamaker,146 Larson,147 and Rao and Jessup.148 In most instances, biodegradation is the major, but not necessarily the only, process affecting the rate of degradation.

Biofilm model

The most sophisticated model available for predicting biodegradation of organic contaminants in subsurface systems is the biofilm model, presented by Williamson and McCarty149,150 which has been refined over several years by researchers at Stanford University and the University of Illinois/Urbana.151157

The biofilm model is based on two important features of the groundwater environment:

1. The nutrient concentrations tend to be low.

2. The solid matrix has a high specific surface area.

These characteristics favor the attachment of bacteria to solid surfaces in the form of biofilm so that nutrients flowing in the groundwater can be used. The presence of low nutrient levels in the groundwater also implies that bacteria must regularly use many different compounds as energy sources and, consequently, may select organic contaminants more readily as nutrients.

The basic biofilm model149,150 idealizes a biofilm as a homogeneous matrix of bacteria and the extracellular polymers that bind the bacteria together and to the surface. A Monod equation describes substrate use; molecular diffusion within the biofilm is described by Fick's second law; and mass transfer from the solution to the biofilm surface is modeled with a solute-diffusion layer. Six kinetic parameters (several of which can be estimated from theoretical considerations and others of which must be derived empirically) and the biofilm thickness must be known to calculate the movement of substrate into the biofilm.

Rittmann and McCarty152,153 have developed equations for incorporating bacterial growth into the model, allowing the steady-state utilization of substrate materials to be predicted. They also show theoretically and verify experimentally that there is a substrate concentration threshold Smin below which no significant activity occurs. McCarty and colleagues154 introduce the idea of secondary substrate utilization by a biofilm, in which microbes can metabolize trace compounds (S < Smin) in the presence of another substrate that is in sufficient concentrations to support biofilm growth. Bouwer and McCarty155 incorporate steady-state utilization of secondary substrates into the model by coupling the biofilm mass (controlled by degradation of the primary substrate) with concentration and individually determine rate parameters for each secondary substrate. Laboratory tests of degradation on a variety of chlorinated benzenes, nonchlorinated aromatics, and halogenated ali-phatics as secondary substrates agree reasonably well with predicted values.155 The later refinement of the model incorporates the effects of adsorption of material substrate to the surface on which the biofilm is attached, but is restricted to biofilm on activated carbon.156,157

When water containing substrate concentrations greater than Smin is injected into the subsurface, the model predicts that biofilm development will occur only in the first meter or so of the injection zone.151 Low concentrations of hazardous compounds will be significantly degraded as secondary substrates only if they are readily biodegraded in the biofilm zone. Any amount not biodegraded in the biofilm zone will tend to persist once it leaves the zone of concentrated biological activity. When substrate concentrations are not sufficient to sustain biofilm development, Bouwer and McCarty155 suggest that a simple biodegradation coefficient such as that discussed earlier (Equation 20.11) is probably adequate.

Qualitative models

Several qualitative models for biodegradation in the deep-well environment have been suggested. They do not allow quantitative predictions to be made, but they do provide insight into the types of biodegradation processes that may occur. These models have not been expressed quantitatively to



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Observation well

Front (degradation)

FIGURE 20.10 Proposed geochemical model of waste after injection into the subsurface. (From U.S. EPA, Assessing the Geochemical Fate of Deep-Well-Injected Hazardous Waste: A Reference Guide, EPA/625/ 6-89/025a, U.S. EPA, Cincinnati, OH, June 1990.)

Observation well

Front (degradation)

FIGURE 20.10 Proposed geochemical model of waste after injection into the subsurface. (From U.S. EPA, Assessing the Geochemical Fate of Deep-Well-Injected Hazardous Waste: A Reference Guide, EPA/625/ 6-89/025a, U.S. EPA, Cincinnati, OH, June 1990.)

simulate degradation, although relatively simple codes using first-order biodegradation constants kB could probably be developed without much difficulty. In the absence of quantitative models for predicting biodegradation, laboratory simulations must be used to assess biodegradation potential.

The conceptual geochemical model of acidic waste after injection into the subsurface, proposed by Leenheer and Malcolm,102 involves a moving front of microbial activity with five zones as shown in Figure 20.10:

1. The dilute zone, controlled by diffusion

2. A zone where substrate concentrations are sufficiently high to allow significant microbial activity

3. The transition zone, where increasing waste concentrations create unfavorable conditions for microbial growth

4. The neutralization zone, where abiotic chemical reactions predominate

5. The waste storage zone where undiluted waste no longer reacts with the host rock.

This model implies that the rate of injection far exceeds the zone's capacity for biodegradation. Bouwer and McCarty155 suggest a qualitative model that represents nonbiofilm microbial biodegradation over increasing distances from the injection point. This model follows the redox reaction sequence. This model implies that most compounds not degraded in their appropriate zone will move through the groundwater system without significant additional degradation. The model also implies, however, that those compounds that are biodegraded by methanogenesis will continue to move through the groundwater until degradation is complete.

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