A new model for the biodegradation kinetics of oil droplets: application to the Deepwater Horizon oil spill in the Gulf of Mexico
© Vilcáez et al.; licensee BioMed Central Ltd. 2013
Received: 20 December 2012
Accepted: 9 October 2013
Published: 20 October 2013
Oil biodegradation by native bacteria is one of the most important natural processes that can attenuate the environmental impacts of marine oil spills. Existing models for oil biodegradation kinetics are mostly for dissolved oil. This work developed a new mathematical model for the biodegradation of oil droplets and applied the model to estimate the time scale for oil biodegradation under conditions relevant to the Deepwater Horizon oil spill in the Gulf of Mexico. In the model, oil is composed of droplets of various sizes following the gamma function distribution. Each oil droplet shrinks during the microbe-mediated degradation at the oil-water interface. Using our developed model, we find that the degradation of oil droplets typically goes through two stages. The first stage is characterized by microbial activity unlimited by oil-water interface with higher biodegradation rates than that of the dissolved oil. The second stage is governed by the availability of the oil-water interface, which results in much slower rates than that of soluble oil. As a result, compared to that of the dissolved oil, the degradation of oil droplets typically starts faster and then quickly slows down, ultimately reaching a smaller percentage of degraded oil in longer time. The availability of the water-oil interface plays a key role in determining the rates and extent of degradation. We find that several parameters control biodegradation rates, including size distribution of oil droplets, initial microbial concentrations, initial oil concentration and composition. Under conditions relevant to the Deepwater Horizon spill, we find that the size distribution of oil droplets (mean and coefficient of variance) is the most important parameter because it determines the availability of the oil-water interface. Smaller oil droplets with larger variance leads to faster and larger extent of degradation. The developed model will be useful for evaluating transport and fate of spilled oil, different remediation strategies, and risk assessment.
KeywordsModeling Biodegradation Oil droplets Size distribution Shrinking core model Gulf of Mexico oil spill Deepwater horizon oil spill
Oil spills can cause serious environmental problems and ecological consequences. The Deepwater Horizon oil spill in the Gulf of Mexico occurred in April 2010 is a recent example. This spill led to the accidental release of over 4.9 million barrels of oil  at a depth of 1500 m  below the water surface. After and during the oil spill it is a common practice to introduce chemical dispersants near the spill region. Under these conditions, spilled oil can not only dissolve in sea water, but also form oil droplets of various sizes. Although large oil droplets can rise to the sea surface due to the buoyancy effect, previous studies suggest that small oil droplets would remain underwater [3–5]. As such, spilled oil can exist in both dissolved form and as oil droplets in deep water.
Spilled oil is subject to various natural attenuation processes, including, for example, mixing, dilution, transport through advection with the sea water currents , dissolution, evaporation, and biodegradation . Among these, biodegradation can play a major role in ultimately transforming the spilled oil. In marine environments, many oil degrading microorganisms can use oil as their electron and carbon source and oxygen as their electron acceptor to ultimately degrade oil to carbon dioxide [8–10].
With documentation that spilled oil can occur in tiny droplets in deep water and that natural biodegradation can indeed occur, it is critical to estimate how fast oil droplets can be biodegraded. Oil is in general a complex mixture of various organic compounds, including chained and aromatic hydrocarbons, which can differ significantly in their biodegradation kinetics . In addition, the biodegradation kinetics can also be affected by the initial oil concentration, the abundance of oil degrading microbe, the concentration of dissolved oxygen, and the availability of the oil-water interface. It has been reported that the greater the oil-water interface, the faster the oil degradation by microbes [9, 12, 13]. As such, their size distribution can play a critical role in determining the biodegradation kinetics of oil spills.
Various models have been proposed to quantify the biodegradation kinetics of spilled oil. The majority of existing models assume that spilled oil is in soluble form [14–16]. Few biodegradation models have also been proposed to take into account the presence of oil droplets [17–19]. Among these, oil droplets have been assumed of uniform size with the presence of abundant oil degrading microbes, which is not applicable for most cases. For instance, in the Gulf of Mexico oil spill, the high pressure at 1500 m underwater and the addition of a chemical dispersant immediately broke the oil into tiny oil droplets of various sizes not much bigger than the size of a microbe (1 μm approximately), with typical mean oil droplet size between 20 – 30 μm [20, 21]. The background oil degrading microbe concentration was approximately 2.73 × 104 cells/ml . The oil concentration was approximately 0.4 mg/L . If all 0.4 mg/L of oil was assumed to exist in the form of 20 μm diameter oil droplets, the oil droplets concentration is approximately 1 × 105 droplets/ml. There is a significant lack of understanding on the oil degradation under these conditions where oil is highly dispersed with small oil droplets.
The goal of this study is to assess the biodegradation rates of dispersed oil droplets of mixed composition through developing and implementing a new mathematical model. The model takes into account the size distribution of oil droplets, microbial activity as a function of the available oil-water interface, as well as the shrinking and conversion process of oil droplets. We used the developed model to examine how various factors affect the time scale of oil droplet biodegradation, including the droplet size distribution, initial oil and microbial concentration, maximum microbial density at the water-oil interface, and the chemical composition of the oil droplets.
Conceptual model of the system
Kinetic parameters for representative hydrocarbon compounds
Oil biodegradation reactions
Half reactions for individual hydrocarbon compounds
C10H8 + 20H2O → 10CO2 + 48H+ + 48e-
C11H10 + 22H2O → 11CO2 + 54H+ + 54e-
C11H10 + 22H2O → 11CO2 + 54H+ + 54e-
C12H12 + 24H2O → 12CO2 + 60H+ + 60e-
C14H10 + 28H2O → 14CO2 + 66H+ + 66e-
C14H10 + 28H2O → 14CO2 + 66H+ + 66e-
C16H10 + 32H2O → + 16CO2 + 74H+ + 74e-
C6H6 + 12H2O → + 6CO2 + 30H+ + 30e-
C7H8 + 14H2O → + 7CO2 + 36H+ + 36e-
C8H10 + 16H2O → + 8CO2 + 42H+ + 42e-
Oxidation reactions of hydrocarbon compounds without including microbial growth
C10H8 + 12O2 → 4H2O + 10CO2
C11H10 + 13.5O2 → 5H2O + 11CO2
C11H10 + 13.5O2 → 5H2O + 11CO2
C12H12 + 14O2 → 6H2O + 12CO2
C14H10 + 16.5O2 → 5H2O + 14CO2
C14H10 + 16.5O2 → 5H2O + 14CO2
C16H10 + 18.5O2 → 5H2O + 16CO2
C6H6 + 7.5O2 → 3H2O + 6CO2
C7H8 + 9O2 → 4H2O + 7CO2
C8H10 + 10.5O2 → 5H2O + 8CO2
Calculated coefficients for individual hydrocarbons
Biodegradation kinetics for dissolved oil
where rb is the rate of microbial growth (cells/L - h), roil and are the rates of oil degradation (mg-oil/L - h) and oxygen consumption (mg-O2/L - h), respectively, μmax is the maximum rate coefficient (h-1), Coil is the total oil concentration (mg/L), Ks is the half saturation constant (mg/L), and B is the concentration of microbes (cells/L) in the bulk fluid. The Monod equation is widely used to describe microbial growth and substrate consumption . The Monod parameters here, including μmax and Ks, can represent the rate parameters not only due to regular oil biodegradation, but also those affected by other degrading mechanisms such as co-metabolism [31, 32]. In this case, the degradation of the co-metabolized compound should still follow the degradation kinetics of the primary compound. Therefore, the effects of co-metabolism will be reflected in the values of these parameters however will not change the general form of the formulation.
By using the sole-substrate model, it is assumed that there are no interactions, including inhibition, among different substrates. This represents one of the simplifications of the model, the validity of which may need to be determined by experimental work in the future. Ideally, the rate equation should include a term to represent the microbial decay. Although its incorporation in the kinetic model is straightforward, it is not done here because experimental data on the decay rate of oil degrading microbes at oil concentration levels relevant to marine oil spills are yet to be available. As such, the rates of bacterial growth here represent rates under relatively optimum conditions.
where Y O2 is the microbial biomass produced per mass of oxygen consumed from the biodegradation of hydrocarbon type i, and x i is the mass fraction of the hydrocarbon type i. All other terms with the subscript i represent the corresponding parameters for each individual hydrocarbon i. Table 1 summarizes kinetic parameters for representative recalcitrant hydrocarbons. The yield coefficient for oxygen is usually not reported. Therefore, its value has been estimated following the procedure described in previous sections.
The shrinking-core model (SCM) for the biodegradation of one oil droplet
here Bs is the concentration of microbes at the oil droplet surface.
The term X1-droplet quantifies the fraction of oil conversion into CO2 for a single oil droplet.
The model for a distribution of oil droplets with varying size
Here P(D) is the oil droplet size distribution function.
where oil droplets of size greater than Dt are partially reacted.
Concentration of microbes on the water-oil interface
Controlling parameters on biodegradation kinetics
In microcosm experiments, a typical oil concentration is in the order of tens of mg/L. In marine oil spills like in the Gulf of Mexico, reported oil concentrations are between 0.1 to 1.0 mg/L [2, 7]. Oil droplet size and its distribution have been reported to vary significantly at different sampling points . Furthermore, concentrations of biodegrading microbes can differ extensively depending on the location of the spill. The goal of this section is to use the formulated model to assess the biodegradation time scale and its sensitivity to various factors, including initial oil and microbe concentration, maximum microbial density on oil droplets, oil droplet size distribution, and oil composition. For comparison, we also show the biodegradation kinetics of dissolved oil. The simultaneous biodegradation of dissolved and dispersed oil droplets are not included in this work. Except for the evaluation of the effect of chemical composition, the composition of dissolved oil and dispersed oil droplets in mole fraction used for calculations in all cases is 0.2 for Naphthalene, 0.2 for 1-Methylnaphthalene, 0.1 for 2-Methylnaphthalene, 0.1 for 2-Ethylnaphthalene, 0.1 for Phenanthrene, 0.1 for Anthracene, 0.05 for Pyrene, 0.05 for Benzene, 0.05 for Toluene, and 0.05 for Xylene.
Biodegradation of dissolved oil
It is important to note that oxygen uptake under conditions relevant to oil spills in marine environments does not result in high levels of oxygen depletion . Assuming that the initial oxygen concentration is 6 mg/L, oxygen levels after complete biodegradation of 0.4 mg/L of spilled oil with the given composition (Figure 2B2) will not go lower than 5 mg/L. As such, we confirm that the effect of oxygen concentration in the biodegradation kinetics of spilled oil in marine environments can be assumed negligible.
Effect of initial oil concentration
Effect of initial microbe concentration
Effect of oil droplet size distribution
Effect of maximum microbial density at the water-oil interface
In this section we assess the effect of maximum microbial density at the water-oil interface. For all previous cases we assumed the maximum microbial density to be 1 cell/μm2 using the average diameter of bacterial cell of 1 μm. In reality, the maximum microbial density on water-oil surface may be higher than 1 cell/μm2, because the oil degrading microbes may have a small size (<1 μm diameter), or because they may only need to be partially in contact with the water-oil interface to effectively biodegrade oil droplets. For example, typically bacteria can form biofilms which consist of layers of bacterial cells with only the most inner layer in direct 100% contact with the interface . Microscopic electron images have demonstrated that biofilms are often composed of swarms of bacteria with extracellular polysaccharides serving as the adhesive agent . As an alternative, it is also possible that nanofilaments (such as bacterial pili or some other mobile devices) are used in respiration of the oil rather than requiring that a single bacterium be in constant contact with the surface . In these cases, the maximum microbial density at the interface can be higher than 1 cell/μm2. Here we compare three cases with the maximum microbial densities of 1, 5, and 10 cell/μm2 and with the initial concentrations of oil degrading microbes and oil droplets of 2.73 × 103 cells/ml and 0.4 mg/L, respectively. Results revealed that at these typical oil and microbial concentration levels, higher maximum microbial density at the interface can result in higher rates of biodegradation only if the mean diameter of oil droplets is larger than 100 μm.
Effects of chemical composition
Oil is in general a complicated mixture of various types of organic chemicals. For the oil leaked in the Gulf of Mexico, it has been reported that the majority of the oil (approximately 80%) are alkanes, while the rest being other types of chemicals such as BTEX and PAHs [41, 42]. Although alkanes are much easier to degrade, chemicals such as PAHs and BTEX are recalcitrant. These chemicals are also more toxic and carcinogenic. During the biodegradation the easily biodegradable chemicals will be depleted first, which leaves the recalcitrant components in the oil droplets. As such, it is important to evaluate the biodegradation kinetics of the oil droplets of different chemical composition.
Here we compare the degradation kinetics of three different chemical groups: alkanes, BTEX, and PAH. For alkanes, μmax and Ks values of 0.6 h-1 and 86.0 mg/L were used based on literature values for heneicosane . For BTEX, a μmax value of 0.32 h-1 and a Ks value of 129.2 mg/L was used based on averaged values from literature data [16, 43–47]. For PAHs, μmax and Ks values of 0.053 h-1 and 28.65 mg/L were used, respectively [32, 48]. From the initial and final concentrations reported for the biodegradation of oil spilled in the Gulf of Mexico , we calculated the yield coefficient to be equeal to1.25 × 108 cells/mg-oil. This yield coefficient was assumed to be the same for alkenes, BTEX, and PAHs.
Biodegradation of dissolved oil vs. oil droplets
The biodegradation of 5.0 μm size starts at the same rate of 100 μm size because there is sufficient oil-water interface at the beginning. However, over time the degradation rate of oil droplets of 100 μm size levels off at a conversion factor of approximately 50% due to the lack of interface, while the biodegradation of oil droplets with 5 μm continue to increase up to 80% of complete biodegradation due to the larger available interface. For the dissolved oil, the degradation rates are low at the beginning but increase quickly over time. It eventually ends up having 100% conversion factor that is higher than that of the oil droplets, because it is not limited by the availability of the oil-water interface.
The Deepwater spill in the Gulf of Mexico led to the formation of large subsurface plumes of oil droplets within several miles of the wellhead . This study formulated a new mathematical model and provided a framework to describe the biodegradation of spilled oil with complex chemical compositions in the form of oil droplets. We applied the model under conditions relevant to marine oil spills and estimated the time scale of oil droplets biodegradation. Our results suggest that under conditions relevant to marine oil spills where oil concentrations are lower than 1 mg/L and background bacteria concentrations are lower than 2.73 × 104 cells/ml, degradation of dispersed oil droplets with a mean diameter lower than 100 μm typically occur in two stages. The first stage is governed by the activity of oil degrading microbes reflected by high biodegradation rates. The second stage is governed by the water-oil interface availability where the oil droplets are susceptible to slower biodegradation. This is very different from the degradation of dissolved oil with no interface limitation and therefore can reach a much higher conversion factor. Compared to the dissolved oil, degradation rates of oil droplets are typically higher in early stages and slow down quickly in the second stage, resulting in a much lower ultimate conversion factor within much longer time duration.
Because water-oil interfaces play a key role in determining the oil droplet degradation, any factors that can lead to increase in water-oil interface increase the degradation rates. For example, the rates and extent of degradation are larger for oil droplets with smaller mean diameter and smaller coefficient of variation values because the oil-water surface is larger in these cases. This is consistent with observations regarding the life time of oil droplets. Venosa and Holder  suggested that different oil droplet size distributions that might have resulted from the addition of different types of chemical dispersants (Corexit 9500 and JD2000) can explain why biodegradation rate of the oil treated with JD2000 was several-fold higher than the biodegradation rate of the oil treated with Corexit 9500. The fact that the amount of “interface” among different phases or zones plays a key role in determining overall reaction rates is also similar to observations in other reaction systems, including mineral dissolution and microbe-mediated redox reactions in subsurface environments [52–55]. Another interesting observation is that initial bulk microbial concentration and maximum microbial density on water-oil interface have relatively smaller effects compared to dissolved oil. Besides the size distribution of oil droplets, initial oil concentrations also have an important role in determining the time scale for oil degradation.
The developed model will be useful for evaluating different remediation strategies after spill under marine environments and for predicting the timing and exposure risk of associated spills. This work provides the basis for future experimental work to evaluate the model and demonstrate its utility. This model can be incorporated into reactive transport models to explicitly evaluate the transport and fate of spilled oil in both dissolved and oil droplet form. A natural next step is to couple flow and transport processes with combined biodegradation of dissolved and dispersed oil droplets to explicitly simulate the evolution of oil composition with time to more accurately represent what occurs after the oil spill. This type of simulations should be done on case by case bases using field data on the fraction of dissolved and oil droplets, oil droplet size distribution, and initial oil degrading microbial concentrations.
It is also important to understand the results of this work in the context of the model limitations and assumption. Here we focus on the biodegradation itself without considering other processes. In the undersea or other natural environments, oil degradation typically occurs together with other processes such as flow and transport. Therefore it can be affected by these processes as well. Although we used averaged kinetic parameters to represent degradation of pseudo-compounds in each simulation, in reality the specific rate coefficient has a transient nature because the composition of oil droplets changes over time. With easily degradable compounds being transformed, the fraction of recalcitrant chemicals, such as PAH, will increase within the oil droplets of decreasing size. As such, it could take a longer time for the oil droplets to be completely degraded.
This work was supported by a subcontract from the University of California at Berkeley, Energy Biosciences Institute, to Lawrence Berkeley National Laboratory under its U.S. Department of Energy contract DE-AC02-05CH11231. The Energy Biosciences Institute is funded by BP.
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