Bulk Oxygen Concentration Research Articles

The anaerobic soil volume as a controlling factor of denitrification: a review

AbstractDenitrification is an important component of the nitrogen cycle in soil, returning reactive nitrogen to the atmosphere. Denitrification activity is often concentrated spatially in anoxic microsites and temporally in ephemeral events, which presents a challenge for modelling. The anaerobic fraction of soil volume can be a useful predictor of denitrification in soils. Here, we provide a review of this soil characteristic, its controlling factors, its estimation from basic soil properties and its implementation in current denitrification models. The concept of the anaerobic soil volume and its relationship to denitrification activity has undergone several paradigm shifts that came along with the advent of new oxygen and microstructure mapping techniques. The current understanding is that hotspots of denitrification activity are partially decoupled from air distances in the wet soil matrix and are mainly associated with particulate organic matter (POM) in the form of fresh plant residues or manure. POM fragments harbor large amounts of labile carbon that promote local oxygen consumption and, as a result, these microsites differ in their aeration status from the surrounding soil matrix. Current denitrification models relate the anaerobic soil volume fraction to bulk oxygen concentration in various ways but make little use of microstructure information, such as the distance between POM and air-filled pores. Based on meta-analyses, we derive new empirical relationships to estimate the conditions for the formation of anoxia at the microscale from basic soil properties and we outline how these empirical relationships could be used in the future to improve prediction accuracy of denitrification models at the soil profile scale.

Modeling and simulation study of simultaneous nitrification–denitrification in membrane aerated bioreactor

This study introduces a two-dimensional multi-species biofilm model to investigate the mechanisms of simultaneous nitrification–denitrification (SND) in membrane aerated bioreactors. We focus here on the effect of bulk concentration of oxygen, ammonium, and acetate on the SND performance, biofilm composition, and SND mechanism. The simulation results revealed that the oxygen distribution within the biofilm plays a determining role in achieving simultaneous nitrification and denitrification in MABR. The distribution of the autotrophs and heterotrophs within the biofilm is not clearly stratified due to the combined impact of cell diffusion and cross-diffusion of different species. The nitrification rate increases with the increase in bulk ammonium and oxygen concentrations while remaining relatively steady when the biofilm thickness increases. Biofilm thickness and acetate concentration have been substantiated as two regulating factors affecting the denitrification of MABR biofilm. High bulk oxygen and ammonium concentrations can significantly delay the establishment of the denitrification capacity of the biofilm but their impact on the denitrification rate drastically diminishes after the biofilm grows to a certain thickness. According to the modeling results, to achieve a quick establishment of denitrification capacity of the MABR biofilm, the bulk ammonia nitrogen and acetate concentrations should be in a range greater than 25 and 12 [gm−3], respectively, while the oxygen partial pressure on the gas side should be less than 0.342 bar. Thus, this study provides extensive insight into the impact of the bulk oxygen, ammonium, and acetate on the SND performance and biofilm composition and structure of MABR.

An optimized numerical method on corrosion in the non–isothermal lead–bismuth eutectic loops with solid–phase oxygen control system

In the present work, a new calculation method for oxygen and iron concentration parameters that can be used to calculate corrosion was proposed for a non–isothermal liquid lead–bismuth eutectic (LBE) loop with solid–phase oxygen control system. We aimed to optimize the prediction of one–dimensional distribution of the bulk oxygen and iron concentrations, as well as the dissolution/precipitation rates of corrosion products along the entire LBE loop by incorporating the dissolution process of PbO particles and the oxygen mass transfer process. In numerical terms, three mass transfer models were simultaneously applied. The simulation results indicated that the iron concentration dissolved in the liquid LBE was negatively related to oxygen concentration, and correlation between dissolution/precipitation rate and temperature clearly revealed that dissolution and precipitation areas corresponded respectively to hot region and cold region in the LBE loop. Dissolved corrosion products were transported by the flowing liquid to the cold region of the loop and re–precipitates there. These regulars were consistent with previous reports. Comparisons of calculated and experimental results from CRAFT and DELTA loops indicated that the optimized calculation method and corrosion model were applicable to other LBE loops.

Evaluating Microbial Interactions of Autotrophs and Heterotrophs in Partial Nitritation/Anammox (PN/A) Process by Experimental and Simulation Analyses

The microbial interactions between autotrophs and heterotrophs by the exchange of microbial products in a partial nitritation/anammox (PN/A) bioreactor were evaluated with both experimental and simulation analyses. Real-time quantitative PCR analysis showed that anammox bacteria (AMX) and ammonium oxidizing bacteria (AOB) made up 56.59% and 8.35% of total bacteria, respectively, while heterotrophs identified as Chloroflexi also constituted a large portion (32.76%) in the reactor, even without an external organic carbon supply. Furthermore, a mathematical model was developed to describe the growth of heterotrophs on soluble microbial products (SMP), which were released from the metabolism of autotrophs. After model calibration and validation, the simulation results were consistent with the experimental observations of the microbial composition and the nitrogenous transformations. According to the model analysis, the bulk oxygen concentration was determined to be the dominant factor governing the reactor performance and biomass fractions in the granule. Increasing granular size could decrease heterotrophic growth, but has little effect on the effluent concentration of SMP. Results of this study could establish a better understanding of eco-physiological interactions of autotrophs and heterotrophs in PN/A process.

Prediction of nano/micro aluminum particles ignition in oxygen atmosphere

Ignition prediction of aluminum particle is of great significance for a variety of propulsion and power systems to achieve optimal energy release within a limited residence time. In this study a heat transfer model employing temperature dependent coefficients was developed and validated to describe the heat exchange between quiescent/flow gas and aluminum particles from nano- to micro-size, covering the free-molecular to continuum regimes. By coupling heat transfer and aluminum oxidation, a theoretical model has been proposed to accurately capture ignition properties of both aluminum nanoparticle and microparticle (ANP and AMP) burning in hot oxygen atmosphere. Two formulas were obtained to predict the ignition temperature and ignition delay time for nano/micro particles, which show good agreements with experimental results, providing a convenient and accurate method for practical application. A parametric study illustrates that AMP ignition is affected by bulk flow velocity, radiation and oxygen concentration, particularly for AMP over 100 μm in diameter; in contrast, ANP is more sensitive to alumina thickness which generally raises both ignition temperature and ignition delay time. The present study not only deepens the fundamental understanding of aluminum combustion but also provides a guideline for prompting ignition.

Achieving nitratation repression in an SBR at mainstream conditions through inorganic carbon limitation

This study investigated the effects of the influent inorganic carbon (IC) availability on nitrifying microbial activity of a sequencing batch reactor (SBR) operated for partial-nitritation (PN) at mainstream conditions (temperature of 15 °C and low influent N concentration). By operating the reactor with influent ammonium to inorganic carbon centration ratio (NH4+-N/IC) of 0.40 ± 0.01 mg N·mg C−1, which results in an excess of IC for full nitritation, the oxidized ammonium fully nitrified, and nitrite accumulation was not reached. Limiting influent IC (influent NH4+-N/IC of 0.73 ± 0.03 mg N·mg C−1) favored nitrite-oxidizing bacteria (NOB) suppression while nitritation was maintained, leading to nitrite accumulation of over 80%. Low bulk liquid IC reduced pH values and this one also favored the achievement of higher free nitrous acid (FNA) levels, but it did not stop nitrite oxidation to nitrate. PN control was also favored by keeping low bulk oxygen concentration during all the aeration phase (below 0.5 mg O2·L−1). Results obtained by batch assays showed that the ratio between the ammonium (rNH4+batch) and nitrite oxidation rates (rNO2−batch) dropped from 0.92 (without IC limitation) to 0.04 (with IC limitation). The results obtained highlight the critical IC role in the microbial interactions of the partial-nitritation process and present new insights in the direction of obtaining NH4+/NO2− for mainstream nitrite short-cut nitrogen removal process.

Lattice Boltzmann simulation of biofilm clogging and chemical oxygen demand removal in porous media

AbstractUnderstanding mechanisms of controlling the bacteria growth and degradation of pollutants is critical for effective improvements in water treatment and bioremediation in porous media. In this study, we developed an integrated model of individual‐based model and multicomponent lattice Boltzmann method to study interactions of oxygen, bioclogging, chemical oxygen demand (COD) removal, and their influence on growth and permeability of microbial biofilms. We found biofilm growth to be very heterogeneous on the surface of the solid matrix and pores. There is a biofilm porosity threshold. Beyond this threshold, the porosity of biofilm has no obvious influence on the flow rate and COD removal. We also studied the influence of initial cell populations, bulk oxygen concentration and biofilm permeability on the flow rate and COD removal. It demonstrated the capability of the present model to investigate biofilm growth, clogging and contaminants degradation in porous media, and its potential applications in water treatment.

The effect of bulk gas diffusivity on apparent pulverized coal char combustion kinetics

Apparent char kinetic rates are commonly used to predict pulverized coal char burning rates. These kinetic rates quantify the char burning rate based on the temperature of the particle and the oxygen concentration at the external particle surface, inherently neglecting the impact of variations in the internal diffusion rate and penetration of oxygen. To investigate the impact of bulk gas diffusivity on these phenomena during Zone II burning conditions, experimental measurements were performed of char particle combustion temperature and burnout for a subbituminous coal burning in an optical entrained flow reactor with helium and nitrogen diluents. The combination of much higher thermal conductivity and mass diffusivity in the helium environments resulted in cooler char combustion temperatures than in equivalent N2 environments. Measured char burnout was similar in the two environments for a given bulk oxygen concentration but was approximately 60% higher in helium environments for a given char combustion temperature. To augment the experimental measurements, detailed particle simulations of the experimental conditions were conducted with the SKIPPY code. These simulations also showed a 60% higher burning rate in the helium environments for a given char particle combustion temperature. To differentiate the effect of enhanced diffusion through the external boundary layer from the effect of enhanced diffusion through the particle, additional SKIPPY simulations were conducted under selected conditions in N2 and He environments for which the temperature and concentrations of reactants (oxygen and steam) were identical on the external char surface. Under these conditions, which yield matching apparent char burning rates, the computed char burning rate for He was 50% larger, demonstrating the potential for significant errors with the apparent kinetics approach. However, for specific application to oxy-fuel combustion in CO2 environments, these results suggest the error to be as low as 3% when applying apparent char burning rates from nitrogen environments.

Relationship between Dislocation Density and Oxygen Concentration in Silicon Crystals during Directional Solidification

This paper reports the relationship between oxygen concentration and dislocation multiplication in silicon crystals during directional solidification using numerical analysis. Based on the Alexander–Haasen–Sumino model, this analysis involved oxygen diffusion from the bulk to dislocation cores during crystal growth and annealing processes in a furnace. The results showed that the dislocation density mainly increased during cooling process, rather than crystal growth, when the effect of oxygen diffusion to dislocation cores was ignored. On the contrary, the dislocation density increased during both crystal growth and cooling processes when the effect of interstitial oxygen diffusion was considered. At a dislocation density larger than 1.0 × 105 cm−2, the interstitial oxygen concentration in bulk decreased due to the diffusion process, if interstitial oxygen atoms were between dislocations, whereas the concentration at dislocation cores increases.

Anoxic microsites in upland soils dominantly controlled by clay content

Recent evidence suggests that oxygen limitations are a critical regulator of soil organic matter mineralization rates, even within seemingly well-drained upland soils. Oxygen limitations may arise in otherwise well-aerated soils when oxygen consumption (via microbial respiration) in soil microsites outpaces oxygen supply (through diffusion). Due to analytical limitations, attempts to parameterize oxygen limitations in models have so far been limited to measures of bulk oxygen concentrations or cm-scale gradients within larger soil structural units (e.g., aggregates or peds). Smaller anoxic microsites may thus have gone undetected, limiting our ability to accurately model and predict anoxic pore volume. Here we quantify the extent of anoxic microsites in soils held at moderate moisture and identify the soil properties that dictate their formation and persistence. Using a planar optode imaging system, we monitored oxygen dynamics during incubations of a range of soils spanning natural and artificial gradients in texture and organic matter availability. While bulk oxygen concentrations ranged from 40 to 100% of saturation, we observed significant micro-scale variability resulting in the formation of anoxic microsites, here defined as soil spaces showing less than 5% saturation. Anoxic microsites comprised 2 and 9% of the total soil volume, or 14–85% of the total pore volume. Bulk oxygen concentrations showed a strong negative correlation with bioavailable organic matter, presumably due to its influence on microbial oxygen consumption. In contrast, the extent of anoxic microsites was negatively correlated to clay content, an effect attributed to limited oxygen supply in clay-rich microstructures. Our results demonstrate that texture-dependent diffusion limitations at moderate moisture conditions cause an abundance of anoxic domains, not only in cm-sized macro-aggregates as current modeling approaches assume, but also within micro-aggregates. Anoxic domain size within these microstructures is at least partially decoupled from bulk oxygen concentrations, challenging the use of bulk oxygen concentrations for predicting microbially available oxygen levels and resulting OM mineralization rates and pathways in upland soils.

Microbiota dysbiosis in inflammatory bowel diseases: in silico investigation of the oxygen hypothesis

BackgroundInflammatory bowel diseases (IBD), which include ulcerative colitis and Crohn’s disease, cause chronic inflammation of the digestive tract in approximately 1.6 million Americans. A signature of IBD is dysbiosis of the gut microbiota marked by a significant reduction of obligate anaerobes and a sharp increase in facultative anaerobes. Numerous experimental studies have shown that IBD is strongly correlated with a decrease of Faecalibacterium prausnitzii and an increase of Escherichia coli. One hypothesis is that chronic inflammation induces increased oxygen levels in the gut, which in turn causes an imbalance between obligate and facultative anaerobes.ResultsTo computationally investigate the oxygen hypothesis, we developed a multispecies biofilm model based on genome-scale metabolic reconstructions of F. prausnitzii, E. coli and the common gut anaerobe Bacteroides thetaiotaomicron. Application of low bulk oxygen concentrations at the biofilm boundary reproduced experimentally observed behavior characterized by a sharp decrease of F. prausnitzii and a large increase of E. coli, demonstrating that dysbiosis consistent with IBD disease progression could be qualitatively predicted solely based on metabolic differences between the species. A diet with balanced carbohydrate and protein content was predicted to represent a metabolic “sweet spot” that increased the oxygen range over which F. prausnitzii could remain competitive and IBD could be sublimated. Host-microbiota feedback incorporated via a simple linear feedback between the average F. prausnitzii concentration and the bulk oxygen concentration did not substantially change the range of oxygen concentrations where dysbiosis was predicted, but the transition from normal species abundances to severe dysbiosis was much more dramatic and occurred over a much longer timescale. Similar predictions were obtained with sustained antibiotic treatment replacing a sustained oxygen perturbation, demonstrating how IBD might progress over several years with few noticeable effects and then suddenly produce severe disease symptoms.ConclusionsThe multispecies biofilm metabolic model predicted that oxygen concentrations of ∼1 micromolar within the gut could cause microbiota dysbiosis consistent with those observed experimentally for inflammatory bowel diseases. Our model predictions could be tested directly through the development of an appropriate in vitro system of the three species community and testing of microbiota-host interactions in gnotobiotic mice.

Effect of Char Particle Size on NO Release during Coal Char Combustion

In this study, the effect of particle size on the release of NO during the char combustion under particle packed-layer conditions was investigated at combustion temperatures of 900 °C~1400 °C. The results show that after pyrolysis, the small size char favored more pores and specific surface area. No significant variations of the intrinsic reactivity of O2 and NO with char particle size were measured. By increasing char particle size, more NO conversion from nitrogen in char (char-N) was found regardless of the combustion temperature and bulk oxygen concentration. This can be explained as follows. By increasing char particle size, less O2 penetrated into the pores and more NO formed because of a less accessible pore surface area and a decreased NO reduction time. The effects of reaction temperature and bulk oxygen concentration were also discussed. A quantified description using a first-order reaction model shows that the char particle size will finally influence the accessible pore surface area and depth ...

Tunable electron affinity with electronic band alignment of solution processed dielectric

We report the tunability of the electronic band structure, especially the electron affinity, of an all-inorganic precursor processed sol-gel aluminium oxide phosphate dielectric by the influence of processing temperature. The dielectric offers tunable electron affinity ranging from 1.42 eV to 0.72 eV with the change in processing temperature from as-prepared to 1000 °C, respectively. The remarkable change in electron affinity is ascribed to the variation in the bulk oxygen concentration in solution processed oxide. As a result, the leakage current of the dielectric is affected significantly by a factor of ∼103.

Increased sediment oxygen flux in lakes and reservoirs: The impact of hypolimnetic oxygenation

AbstractHypolimnetic oxygenation is an increasingly common lake management strategy for mitigating hypoxia/anoxia and associated deleterious effects on water quality. A common effect of oxygenation is increased oxygen consumption in the hypolimnion and predicting the magnitude of this increase is the crux of effective oxygenation system design. Simultaneous measurements of sediment oxygen flux (JO2) and turbulence in the bottom boundary layer of two oxygenated lakes were used to investigate the impact of oxygenation on JO2. Oxygenation increased JO2 in both lakes by increasing the bulk oxygen concentration, which in turn steepens the diffusive gradient across the diffusive boundary layer. At high flow rates, the diffusive boundary layer thickness decreased as well. A transect along one of the lakes showed JO2 to be spatially quite variable, with near‐field and far‐field JO2 differing by a factor of 4. Using these in situ measurements, physical models of interfacial flux were compared to microprofile‐derived JO2 to determine which models adequately predict JO2 in oxygenated lakes. Models based on friction velocity, turbulence dissipation rate, and the integral scale of turbulence agreed with microprofile‐derived JO2 in both lakes. These models could potentially be used to predict oxygenation‐induced oxygen flux and improve oxygenation system design methods for a broad range of reservoir systems.

Properties and relevance of the volatile flame of an isolated coal particle in conventional and oxy-fuel combustion conditions

A model that accounts for the volatile matter release and its subsequent combustion in the surroundings of an isolated coal particle is presented and used to analyze the characteristics and relevance of the flame so generated in a broad range of conditions. The devolatilization kinetics were experimentally determined in a previous work; the volatile composition is given by the chemical percolation model; and the GRI 3.0 mechanism accounts for the homogeneous reactions. Both conventional and oxy-fuel combustion conditions are considered. In all the cases, three consecutive (although not fully independent) flames are identifiable around the particle, corresponding to the consumption of CH4 and C2H2, first, and the oxidation of CO, further on. A more intense chemistry is generally observed in N2 than in CO2-rich environments; in any case, those reactions result in significant heat transfer towards the particle, and thus in an acceleration of the devolatilization, more marked for higher bulk oxygen concentrations. The predictions of the model regarding devolatilization duration and peak flame temperature and position are in good qualitative agreement with the (rather scarce) experimental data available in the literature. Finally, simulations with different particle diameters from 30 to 120µm show that only for the finest particles an overlapping of the devolatilization and the char oxidation steps during combustion is foreseeable.

Impact of coexistence of flocs and biofilm on performance of combined nitritation-anammox granular sludge reactors

Nitrogen (N) removal from high-strength wastewater can be accomplished in single-stage combined nitritation-anammox reactors with suspended growth biomass composed of floccular sludge, granular sludge, or of any mix of these 2 different sludge fractions. To date, the influence of floccular biomass on granular sludge reactor performance and stability has not been investigated experimentally or numerically. To address this knowledge gap, two 1D multi-species models were developed in Aquasim to assess the importance of small levels of flocs in putatively granular sludge combined nitritation-anammox reactors for different bulk oxygen concentrations and organics loads. The models included the growth and decay of aerobic ammonium-oxidizing organism (AOO), nitrite-oxidizing organisms (NOO), heterotrophic organisms (OHO), and anammox organisms (AMO) in exclusively granular sludge reactors, and in granular sludge reactors with small levels (∼5% of total biomass) of flocs. While maximum N removal efficiencies were similar for both model structures, floc addition led to a lower optimal dissolved oxygen concentration (DO) as well as a narrower maximum N removal peak, suggesting that small levels of floccular material may decrease process robustness to bulk oxygen changes. For some DO levels, this led to drastic efficiency drops. Furthermore, floc addition also led to substantial segregation in activity and microbial population distribution, with AOO, NOO and OHO concentrated in flocs and AMO concentrated in granules. Increased organic loading (COD:N = 4:3) improved maximum N removal efficiency in both model structures, but yielded substantially different predictions for optimal DO setpoint and process robustness to variations in DO. Taken together, our results indicate that even small levels of floccular biomass in biofilm reactors can have profound implications for reactor performance and optimization and for segregation of linked microbial processes, and suggest that the common practice of neglecting small levels of floccular material in biofilm models and in practice may lead to erroneous predictions.

Modeling of electric field in silicon micro-strip detectors irradiated with neutrons and pions

Edge-TCT method was used to extract velocity profiles in heavily irradiated silicon micro-strip detectors. Detectors were irradiated up to 1016 c -2 with reactor neutrons, 200 MeV pions and a combination of both. A simple electric field model assuming two space charge regions at each side of the detector and neutral bulk in-between was found to describe the field profile. It was observed that after heavy irradiation a sizeable electric field is present in the entire detector volume. For pion-irradiated detectors strikingly different profiles were obtained and attributed to the large oxygen concentration in the detector bulk. The model parameters were also studied during the long term annealing. The space charge region near the strips was found to shrink which in turn leads to larger electric field and impact ionization. The model parameters extracted from the measurements were fed to the device simulation program which showed reasonable agreement between simulated and measured data at lower fluences.

Accuracy of the single-film model in the prediction of coal char conversion rates under oxy-fuel and conventional combustion conditions

The accuracy of the single-film model in the calculation of char burning rates and particle temperatures in conventional and oxy-fuel combustion conditions has been investigated taking as a reference the results obtained with a model with detailed gas-phase kinetics. Both models have been applied to subbituminous coal and anthracite char particles in different sizes (60–1000μm), in N2 and CO2-rich atmospheres with a low and a high oxygen concentration. For 120μm char particles, the models’ predictions have been also compared over an ample range of ambient gas temperatures (1373–1823K) and oxygen concentrations (4–50%). High particle diameters, bulk gas temperatures and oxygen concentrations result in CO-flames closer to the particle surface; however, the specific effects of the flame strongly depend on the coal rank and combustion conditions. In general, the single-film model accuracy is quite high in terms of burning rate predictions, except for fine anthracite particles burning at moderate bulk gas temperatures and high O2 concentrations; greater deviations have been found regarding particle temperatures, even in cases where the corresponding combustion rates are very similar. The oxy-combustion of the reactive coal char is found to be faster than its conventional combustion, except for the finest particles; although qualitatively similar, the difference in rates is overestimated if the single-film model is considered.

Oxygen consumption upon electrochemically polarised zinc

A Pt microelectrode was used to measure the oxygen consumption by redox reduction (ORR) on electrochemically polarised zinc in the redox competition mode. Zinc was polarised in the active and passive state, using a pH 7 and pH 13 solution, respectively. At pH 7, the oxygen concentration measured at a distance of 50 μm from the zinc surface, using the Pt microelectrode, is 15–60 % of the bulk oxygen concentration. Therefore, correspondingly, the oxygen consumption by zinc (due to ORR) is 40–85 % of the bulk oxygen concentration. At pH 13, where zinc undergoes passivation, the oxygen consumption by zinc is 70–80 % of the bulk oxygen concentration. The ORR rate on the surface of zinc passive films (ZnO/Zn(OH)2) is thus significant when compared to that on bare/actively corroding zinc. The influence of the electrode kinetics of zinc corrosion, on oxygen diffusion towards the metal surface has been investigated in this study.

Effect of heterotrophic growth on autotrophic nitrogen removal in a granular sludge reactor

This study deals with the influence of heterotrophic growth on autotrophic nitrogen removal from wastewater in a granular sludge reactor. A mathematical model was set-up including autotrophic and heterotrophic growth and decay in the granules from a partial nitritation-anammox process. A distinction between heterotrophic bacteria was made based on the electron acceptor (dissolved oxygen, nitrite or nitrate) on which they grow, while the nitrogen gas produced was ‘labelled’ to retrieve its origin, from anammox or heterotrophic bacteria. Taking into account heterotrophic growth resulted in a lower initial nitrogen removal, but in a higher steady state nitrogen removal compared with a model in which heterotrophic growth was neglected. The anammox activity is related with the fact that heterotrophs initially use nitrite as electron acceptor, but when they switch to nitrate the produced nitrite can be used by anammox bacteria. Increased anammox activity in the presence of heterotrophs, therefore, resulted in a marginally increased N2 production at steady state. Heterotrophic denitrification of nitrate to nitrite also explains why small amounts of organic substrate present in the influent positively affect the maximum nitrogen removal capacity. However, the process efficiency deteriorates once the amount of organic substrate in the influent exceeds a certain threshold. The bulk oxygen concentration and the granule size have a dual effect on the autotrophic nitrogen removal efficiency. Besides, the maximum nitrogen removal efficiency decreases and the corresponding optimal bulk oxygen concentration increases with increasing granule size.