Oxygen Concentration Profiles Research Articles

Prediction of acid rock drainage in waste rock piles Part 1: Water film model for geochemical reactions and application to a full-scale case study

Geochemical reactions taking place at the rock surface and pore water interface, and rapid preferential water flow through waste rock piles are identified as two primary steps for acid rock drainage (ARD) and metal leaching (ML) processes. This paper (Part I) develops a water film model to describe the interactions among sulphide minerals, pore water and oxygen, which considers the reactive surface areas as the primary sites to capture geochemical reactions including sulphide oxidation and neutralization reactions, and also considers acid and metal ion storage in pore water. In addition, the proposed water film model is further coupled with a pile-scale mass transport model to investigate a specific case of the main waste rock pile at the Equity Silver mine, Canada. Overall, the simulated profile of oxygen concentration matches the historical monitoring data. The modeling results revealed potential controlling mechanisms for ARD generation inside the waste rock pile and provided insights into the impact of an engineered cover on the waste rock pile.

Measuring effective diffusivity in porous media with a gasket-free, radial arrangement

A simple technique for measuring the effective diffusivity, and ultimately tortuosity, in porous media is presented. The method uses a custom-built apparatus, based on a radial geometry, which eliminates the need for any gaskets to seal the edge of the sample. This makes it particularly well suited for thin media such as films and layers. The experiment is based on the transient response of the oxygen concentration at the center of the sample as oxygen diffuses into an initially nitrogen filled domain from the sample perimeter. The analytical solution of Fick’s law for transient diffusion in cylindrical coordinates is fitted to the measured oxygen concentration profile to obtain the effective diffusivity. To validate the method, binary diffusion coefficients of N2-Air system were measured and the results show a close match and are consistent for a range of experimental parameters like flow rate and domain thickness. The classical study of diffusion in porous media based on sphere packing is revisited for further validation of the technique. The results show good agreement to the well-known Bruggeman correlation as well as to the experimental values reported in the literature. The new technique is further applied to other types of thin porous materials and the results indicate that the Bruggeman correlation generally underestimates the effective diffusivity of non-sphere packing.

Modelling the depletion of atmospheric fuzzy plankton-oxygen dynamics in a lake due to photosynthetic activity of ecosystem under Climate change

This paper proposes a new approach to the depletion of plankton-oxygen dynamic systems that deal with non-spatial processes in fuzzy environment. In this paper, an approximate analytical method to solve the non-linear fuzzy differential equations in a plankton-oxygen dynamics is presented. This kinetic mechanism is based on the system of non-linear reaction diffusion equations. An approximate fuzzy analytical expression of concentration profiles of oxygen, phytoplankton and zooplankton has been derived using the Homotopy perturbation method for all hypothetical values of the parameters. Analytical results are compared with the numerical results and graphical representation of previous result, a satisfactory agreement.

Mathematical Modeling of the Mesophilic and Thermophilic Stages of a Composting Tubular Reactor for Sewage Sludge Sanitization

A tubular composting reactor was constructed to study the physical phenomenology of the two first stages of a typical composting process; the mesophilic and thermophilic phases. The insulated reactor, with a height of 2.7 m and a diameter of 0.254 m, was filled with a mixture of aerobically digested sewage sludge from a local municipal wastewater treatment plant, wood chips, and grass. The present study consisted in the analyses of the heat and mass transfer processes, considering dispersion and convection processes coupled with a modified Contois kinetics model. The mathematical model was solved using the method of lines employing second-order finite differences to discretize the radial and axial coordinates and a fourth-order Runge Kutta method to integrate in time. Several physical parameters were estimated using a multivariable optimization routine after measuring temperature and oxygen concentration profiles. The reactor reached temperatures above 60 °C in the first 40 h and kept its temperature above or close to 50 °C for the next 80 h, thus maintaining conditions necessary to sanitize the sludge; fecal coliforms were reduced from 43,000 to 75 MPN/g 25 days after the end of sanitization. The mathematical model was able to predict temperature and oxygen concentration profiles, after running an experiment and fitting the model to obtain the value of selected parameters, for a change in length and gas velocity.

A steady-state analytical profile method for determining methane oxidation in landfill cover

Gas concentration profiles of carbon dioxide (CO2), oxygen (O2), methane (CH4) and nitrogen (N2) are usually measured during tests investigating microbial aerobic methane oxidation in landfill cover. However, only qualitative/limited information can be obtained from gas concentration profiles by existing methods. A new method is proposed to determine methane oxidation in soil quantitatively and comprehensively, including methane oxidation efficiency, stoichiometry, gas transfer mechanism, methane generation rate and gas reaction rate distributions. Governing equations are established based on mass balance for O2, CO2, CH4 and N2 at one-dimensional and steady-state condition. Gas transfer mechanisms considered include gas diffusion, advection and gas reaction. The method utilizes gas concentration profiles to determine gas diffusion for each gas component according to Fick's law. Then gas advections and reactions can be determined by mass balance. The method is validated by (i) published soil column tests investigating methane oxidation and (ii) a calibrated numerical model based on a selected soil column test. The new method is capable of determining methane oxidation efficiency, stoichiometry, gas transfer mechanism, methane generation rate and gas reaction rate distributions for CH4, CO2 and O2.

Novel Method for Measuring in-Plane Effective Diffusivity of Ultrathin Catalyst Layer for PEMFC

Fuel cells are being increasingly deployed in various applications, however like all emerging technologies, its cost still needs to be lowered for wider commercialization. The most expensive component is the noble platinum (Pt) catalyst, so reducing the amount of Pt remains an ongoing effort. There are two ways to approach this problem: find a cheaper alternative1,2 or use less Pt.3,4 Regarding the former, most candidates are less active than Pt, so require higher loading and thicker catalyst layers, while the latter case, the lower loading must be compensated by higher accessibility and utilization. In both cases it is essential to design improved catalyst layer (CL) structures to provide maximum accessibility of reactant to the catalytic sites.5 Characterizing the nanoporous structure of the CL in terms of transport processes is essential to understanding how to design a better layer. The key transport parameter in fuel cell operation is the effective diffusivity through the CL structure since diffusion is the primary mode of reactant transport. Despite the importance of characterizing the effective diffusivity of the CL, the thinness of the CL combined with the fact that it’s not self-supporting, has hindered the development of well-established, easy to apply, and standardized tool and only a limited number of technique is available.6 There are several requirements in designing the proper ex-situ effective diffusivity measurement experiment for the CL. First, any surface in contact with the sample must be scratch-free to eliminate additional diffusion pathways. Second, the need for sealing should be avoided as it is nearly impossible to properly seal such thin (~10µm) layer. Lastly, the experiment should be designed so that it is performed within a reasonable time. This work presents a new method building on previous work7,8, but using a radial geometry instead. The main advantage of the method is that it requires no sealing around the edge of the sample, therefore easily applied even to ultrathin porous layers. Inside a cylindrical chamber, the catalyst layer sample is placed between two circular pedestals and the oxygen concentration is measured at the center as shown in Figure 1(a). The sample is initially flushed with air, then nitrogen gas is flowed past the sample perimeter at high flow rate to ensure instant change in boundary condition. The depletion of the oxygen concentration at the center of the sample is measured and recorded as a function of time. The effective diffusivity is determined by fitting the analytical solution of the Fick’s second law in cylindrical coordinates to the transient oxygen concentration profile.9 The technique was validated against open air and known GDL materials.7,8 In the present study, this novel experimental technique was applied to ultrathin porous layers fabricated with different ink formulae to explore the impact of morphology, and strong differences were seen.

Analytical solutions of an isothermal two-dimensional model of a cathode flow channel in a proton exchange membrane fuel cell

Two key assumptions are usually made while deriving analytical solutions of coupled kinetics and transport equations in a single channel on the cathode plate of a proton exchange membrane fuel cell (PEMFC). These are: plug flow and uniform oxygen concentration along the depth of the channel. However these assumptions are not always valid under typical operating conditions of a PEMFC, and particularly so at high current density. In this article we relax these two assumptions and present approximate analytical solutions of the governing equations using the methodology of separation of variables followed by power series solution. Spatial profiles of oxygen concentration and current density were derived, which led to the final derivation of a comprehensive current-potential relationship (polarization curve) in the reaction-controlled regime of an operational PEMFC. We compare polarization curves predicted by the present model with predictions of the earlier analytical model and also with a complete 3D-simulation of the same flow geometry and operation conditions. The local profiles of oxygen concentration and the polarization curve predicted by the present model compare far better with the 3D simulations than the earlier analytical model. While this comparison highlights the importance of the effects of finite oxygen diffusion rate and velocity profile in the channel on the polarization curves, it also points to other important factors that affect the current-potential relation.

Updated SABER Night Atomic Oxygen and Implications for SABER Ozone and Atomic Hydrogen

AbstractUpdated night atomic oxygen concentration (O) profiles from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument on the National Aeronautics and Space Administration TIMED satellite are presented. These are derived from measurements of the OH(υ = 9 + 8) volume emission rates and photochemical balance relationships. The new night O concentrations are smaller than those originally derived in 2013 and yield physically realistic global annual mean energy budgets in the upper mesosphere and lower thermosphere. The update to the night O atom profiles is motivated by recent discovery and verification of large rates of collisional quenching of OH(υ) by atomic oxygen. The kinetic model relating the SABER‐observed OH emission rates to atomic oxygen is now consistent with these larger quenching rates and other literature values. The new, smaller SABER night O also confirms that SABER daytime ozone is too large. The new night O and OH(υ) model impacts the inference of day and night atomic hydrogen.

Design of Bioartificial Pancreases From the Standpoint of Oxygen Supply

A bioartificial pancreas (BAP), in which islets of Langerhans (islets) are enclosed in a semipermeable membrane, has been developed to realize islet transplantation without the use of immunosuppressive drugs. Although recent progress in induced pluripotent stem (iPS) and embryonic stem (ES) cells has attracted attention owing to the potential applications of these cells as insulin-releasing cells, concerns about the safety of implantation of these cells remain. The use of the BAP has the advantage of easy removal if insulin-releasing cells derived from iPS/ES cells undesirably proliferate and form tumors in the BAP. Oxygen supply is a crucial issue for cell survival in BAPs as insufficient oxygen supply causes central necrosis of cell aggregates. In this study, we derived several simple equations considering oxygen supply in BAPs in order to provide insights into the rational design of three different types of BAPs (spherical microcapsules, cylindrical capsules, and planar capsules). The equations give (i) the thickness of a capsule membrane leading to no central necrosis of encapsulated cell aggregates as a function of the original size of the cell aggregate; (ii) the oxygen concentration profiles in BAPs; (iii) the effects of encapsulation of a cell aggregate on insulin release; (iv) the amount of encapsulated cells required to normalize blood glucose levels of a patient; and (v) the total volumes and sizes of BAPs. As an example, we used the equations in order to design three different types of BAPs for subcutaneous implantation.

Oxidation behaviour of zirconium hydride and its influence on the thermal desorption kinetics

The oxidation kinetics of zirconium hydride powder in air was studied over the temperature range of 100–300 °C. The oxidation kinetic parameters were obtained and a controlling mechanism was proposed. The XPS depth profile analysis was consistent with a layered structure of the oxide film. The evolution of oxygen concentration profile allowed to estimate the diffusion coefficient of oxygen in zirconium oxide. Thermal desorption behaviours of pre-oxidized ZrH2 were studied using simultaneous thermogravimetry and thermal desorption spectroscopy (TG-TDS). The phase transformation sequence during dehydrogenation process of pre-oxidized ZrH2 was established and a corresponding shrinking core model was proposed.

Mathematical modeling, simulation and validation for co-fermentation of glucose and xylose by Saccharomyces cerevisiae and Scheffersomyces stipitis

Hydrolysis of pretreated lignocellulosic biomass releases pentoses and hexoses. Ethanol production incorporating co-culture of hexose and pentose fermenting microorganisms in lignocellulose hydrolysates is gaining importance. However, very few models are available to predict the fate and the interaction between these microorganisms during fermentation. In this study, mathematical models are proposed to predict the dynamics involved in the co-culture of wild strain of hexose fermenting Saccharomyces cerevisiae (NRRL Y-132) and pentose fermenting Scheffersomyces stipitis (NCIM 3507) in fermentation media containing glucose and xylose, under microaerophilic conditions. The model equations consider the dissolved oxygen dependence of Scheffersomyces stipitis's growth rate. The model predictions were statistically validated conducting t-test and evaluating indices of agreement. Willmott's index of agreement for the models predicting the concentration profiles of Saccharomyces cerevisiae, Scheffersomyces stipitis, glucose, xylose, ethanol and oxygen were 0.867, 0.929, 0.980, 0.995, 0.910 and 0.850, respectively, satisfying the criteria for ‘very high’ agreement between model-predicted and experimental values.

Understanding the Dynamics of the Oxic‐Anoxic Interface in the Black Sea

AbstractThe Black Sea, the largest semienclosed anoxic basin on Earth, can be considered as an excellent natural laboratory for oxic and anoxic biogeochemical processes. The suboxic zone, a thin interface between oxic and anoxic waters, still remains poorly understood because it has been undersampled. This has led to alternative concepts regarding the underlying processes that create it. Existing hypotheses suggest that the interface originates either by isopycnal intrusions that introduce oxygen or the dynamics of manganese redox cycling that are associated with the sinking of particles or chemosynthetic bacteria. Here we reexamine these concepts using high‐resolution oxygen, sulfide, nitrate, and particle concentration profiles obtained with sensors deployed on profiling floats. Our results show an extremely stable structure in density space over the entire basin with the exception of areas near the Bosporus plume and in the southern areas dominated by coastal anticyclones. The absence of large‐scale horizontal intrusive signatures in the open‐sea supports a hypothesis prioritizing the role of biogeochemical processes.

Invasive Macrophytes Control the Spatial and Temporal Patterns of Temperature and Dissolved Oxygen in a Shallow Lake: A Proposed Feedback Mechanism of Macrophyte Loss.

Submerged macrophytes can have a profound effect on shallow lake ecosystems through their ability to modify the thermal structure and dissolved oxygen levels within the lake. Invasive macrophytes, in particular, can grow rapidly and induce thermal gradients in lakes that may substantially change the ecosystem structure and challenge the survival of aquatic organisms. We performed fine-scale measurements and 3D numerical modeling at high spatiotemporal resolution to assess the effect of the seasonal growth of Potamogeton crispus L. on the spatial and temporal dynamics of temperature and dissolved oxygen in a shallow urban lake (Lake Monger, Perth, WA, Australia). Daytime stratification developed during the growing season and was clearly observed throughout the macrophyte bed. At all times measured, stratification was stronger at the center of the macrophyte bed compared to the bed edges. By fitting a logistic growth curve to changes in plant height over time (r2 = 0.98), and comparing this curve to temperature data at the center of the macrophyte bed, we found that stratification began once the macrophytes occupied at least 50% of the water depth. This conclusion was strongly supported by a 3D hydrodynamic model fitted to weekly temperature profiles measured at four time periods throughout the growing season (r2 > 0.78 at all times). As the macrophyte height increased and stratification developed, dissolved oxygen concentration profiles changed from vertically homogeneous oxic conditions during both the day and night to expression of night-time anoxic conditions close to the sediments. Spatially interpolated maps of dissolved oxygen and 3D numerical modeling results indicated that the plants also reduced horizontal exchange with surrounding unvegetated areas, preventing flushing of low dissolved oxygen water out of the center of the bed. Simultaneously, aerial imagery showed central dieback occurring toward the end of the growing season. Thus, we hypothesized that stratification-induced anoxia can lead to accelerated P. crispus dieback in this region, causing formation of a ring-shaped pattern in spatial macrophyte distribution. Overall, our study demonstrates that submerged macrophytes can alter the thermal characteristics and oxygen levels within shallow lakes and thus create challenging conditions for maximizing their spatial coverage.

Determination of oxygen diffusion coefficients of compacted asphalt mixtures

The oxidative aging of asphalt binder in asphalt mixture is a key factor that affects the long-term durability of asphalt pavement. The aging susceptibility of an asphalt mixture is dependent on oxygen transport and consumption in the mixture. In this study, an apparatus was developed to measure oxygen diffusion and consumption in compacted asphalt mixtures, and methods to compute oxygen diffusion and possible consumption of asphalt mixtures were evaluated and compared. Oxygen diffusion coefficients of samples prepared with different asphalt mixture designs and air void contents were determined, and correlations between the diffusion coefficients and samples’ volumetric characteristics were examined. The oxygen environment exposed by asphalt binders in pavements and its implication on pavement durability were also discussed based on simulated oxygen concentration profiles with time. The developed apparatus and test procedure were found to be suitable to measure the oxygen diffusion coefficients of compacted asphalt mixtures. It was also found that oxygen consumption during the diffusion test at room temperature is negligible, and both numerical and analytical methods perform equally well in calculating oxygen diffusion coefficients. The oxygen diffusion coefficients of the tested asphalt samples vary in orders of magnitude, dependent not only on air void contents but also on other volumetric characteristics. The traditional models to predict the oxygen diffusion coefficients of dry porous media are not fit for compacted asphalt mixtures. The oxygen diffusion coefficients of asphalt mixtures have significant implications on oxygen level exposed by asphalt binders inside of the pavements; therefore, they may be used as an indicator in asphalt mixture design and construction quality control.

Is the cholesterol bilayer domain a barrier to oxygen transport into the eye lens?

In the eye lens, the oxygen partial pressure is very low and the cholesterol (Chol) content in cell membranes is very high. Disturbance of these quantities results in cataract development. In human lens membranes, both bulk phospholipid-Chol domains and the pure Chol bilayer domains (CBDs) were experimentally detected. It is hypothesized that the CBD constitutes a significant barrier to oxygen transport into the lens. Transmembrane profiles of the oxygen diffusion-concentration product, obtained with electron paramagnetic resonance spin-labeling methods, allow evaluation of the oxygen permeability (PM) of phospholipid membranes but not the CBD. Molecular dynamics simulation can independently provide components of the product across any bilayer domain, thus allowing evaluation of the PM across the CBD. Therefore, to test the hypothesis, MD simulation was used. Three bilayers containing palmitoyl-oleoyl-phosphorylcholine (POPC) and Chol were built. The pure Chol bilayer modeled the CBD, the 1:1 POPC-Chol bilayer modeled the bulk membrane in which the CBD is embedded, and the POPC bilayer was a reference. To each model, 200 oxygen molecules were added. After equilibration, the oxygen concentration and diffusion profiles were calculated for each model and multiplied by each other. From the respective product profiles, the PM of each bilayer was calculated. Favorable comparison with experimental data available only for the POPC and POPC-Chol bilayers validated these bilayer models and allowed the conclusion that oxygen permeation across the CBD is ~10 smaller than across the bulk membrane, supporting the hypothesis that the CBD is a barrier to oxygen transport into the eye lens.

Oxide Dissolution and Oxygen Diffusion in Solid-State Recycled Ti-6Al-4V: Numerical Modeling, Verification by Nanoindentation, and Effects on Grain Growth and Recrystallization

The oxide dissolution and oxygen diffusion during annealing of Ti-6Al-4V solid-state recycled from machining chips by equal-channel angular pressing (ECAP) have been investigated using nanoindentation and numerical modeling. The hardness profile from nanoindentation was converted into the oxygen concentration distribution using the Fleisher and Friedel model. An iterative fitting method was then employed to revise the ideal model proposed previously, leading to correct predictions of the oxide dissolution times and oxygen concentration profiles and verifying nanoindentation as an effective method to measure local oxygen concentrations. Recrystallization started at the prior oxide boundaries where local strains were high from the severe plastic deformation incurred in the ECAP recycling process, forming a band of ultrafine grains whose growth was retarded by solute dragging thanks to high oxygen concentrations. The recrystallized fine-grained region would advance with time to eventually replace the lamellar structure formed during ECAP.

Oxygen transport in hollow fibre membrane bioreactors for hepatic 3D cell culture: A parametric study

Hepatic cell cultures are exploited for different applications in liver disease studies, drug toxicity testing and bioartificial liver (BAL) devices. Despite the development of various 3D cell culture systems, mass transfer properties and limitations, especially oxygen supply, still remain a controversial topic. In this paper, oxygen transport in a convection-enhanced, crossed-configuration hollow fibre membrane bioreactor hosting hepatocyte spheroids has been investigated through coupled free/porous media flow hydrodynamics and mass transfer modelling using finite-element simulations. Starting from experimental measurements of the oxygen concentration in the bioreactor, a systematic parametric study was performed to evaluate the effect of different parameters – oxygen partial pressure, perfusion rate, hollow fibre spacing, spheroid size, Michaelis-Menten kinetics for oxygen uptake and porosities of the spheroid and the membrane – on dissolved oxygen concentration profile. These parameters were studied in relation to dimensionless groups and variables. Among the operational conditions, oxygen concentration was much more influential than perfusion rate. As for the Michaelis-Menten parameters, oxygen concentration profile inside the spheroids was strongly affected by the maximum consumption rate (Vmax) and weakly dependent on the constant KM. Culturing smaller spheroids minimized the exposure of cells to hypoxic conditions, owing to the short diffusive penetration depth of oxygen especially at low porosities (0.2). An in vivo-like microenvironment in terms of physiological oxygen concentration range was achieved in large spheroids (400µm diameter) at spheroid porosity of 0.47. Membrane porosity also affected the intra-spheroid oxygen concentration and an improvement in oxygen supply to the spheroids could be achieved by reducing the corresponding transfer resistances. The mechanical stress on the spheroid surfaces was found to be within the tolerated ranges. Overall, the most important parameters for optimization of the bioreactor were identified.

Volumetric mass transfer coefficient in viscous liquid in mechanically agitated fermenters. Measurement and correlation

In the industrial fermentation processes, most liquids are non-coalescent and often exhibit increased viscosity. However, due to the limitations of most measurement methods, there is a lack of reliable data for predicting volumetric mass transfer coefficients (kLa) for viscous batches, especially under high dissipated energies, as the accurate determination of oxygen concentration profile in viscous liquids is not as easy as in low viscosity ones. Our goal is to develop reliable technique for kLa determination in viscous liquids and to establish suitable correlation shapes to describe kLa data. We used the dynamic pressure method (DPM), the experimental set-up of which has been modified for the measurement in viscous liquids. Dissolved oxygen (DO) probes were placed in bypass measuring cells. This set up brings well defined transient characteristics of DO probes, which is crucial for correct kLa evaluation. Measurements were conducted in two phase multiple-impeller fermenters with a non-coalescent viscous Newtonian batch under a wide range of experimental conditions and in the apparatuses of two scales. Using pure oxygen as gas phase, it was confirmed that DPM yields kLa’s independent of the driving force of absorption even in viscous batch. The improved set up of DPM enabled to use also optical DO probes as well as polarographic ones. It was confirmed that optical DO probe can be used for kLa values up to 0.4s−1. Based on the experimental data, correlations were developed to predict kLa in industrial fermenters. Standard correlation kLa=2.99⋅10−3⋅(Pg/VL)0.891vs0.556 with standard deviation, SD, 30%, based on gassed power input Pg and superficial gas velocity vs, has low standard deviation but it is scale specific. On the other hand, when the term of impeller tip speed (ND) is used instead of Pg, predicted data exhibit neither over- nor under-estimation of kLa for particular apparatus scale; so the effect of the vessel scale is properly described using this term. In addition, the impeller power number Po was found to be a reliable predictor of kLa in a common correlation for various impeller types, when used together with the impeller tip speed term. The correlation kLa=0.295⋅(ND)2.083vs0.461Po0.737 with SD 28% suggested in this work can be used for fairly accurate design of industrial fermenters. Both the experimental technique and the correlation shape are ready to be used to obtain the design tool for other batches with various viscosities.

Local investigations on the gas-liquid mass transfer around Taylor bubbles flowing in a meandering millimetric square channel

Gas-liquid mass transfer around Taylor bubbles moving in a meandering millimetric square channel was locally visualized and characterized in the present study. For that, the colorimetric technique proposed by Dietrich et al. (2013) was implemented. With this technique, the evolution of equivalent oxygen concentration fields in the liquid slugs passing through one and several bends was firstly described. In particular, it was observed how the flow structure (recirculation zones) inside the liquid slugs were twisted and split by the periodic bends (centrifugal effect), until reaching, after several bends, a uniform O2 concentration inside the liquid slugs. The influence of the “turning point”, joining two “straight” sections of meandering channel was also highlighted: a slowing down of the gas-liquid mass transfer was clearly shown. Volumetric mass transfer coefficients were determined at last by fitting the experimental axial profiles of averaged oxygen concentrations in the liquid slugs (before the turning point) with the ones predicted by a classical plug-flow model.

Mathematical modeling of a composting process in a small-scale tubular bioreactor

A mathematical model is presented to describe a composting process occurring in a tubular bioreactor. The mathematical model is based on heat and mass transfer phenomena under the continuum approximation. The bioreactor is divided into two phases: a gas phase and a solid–liquid phase. Between these phases, oxygen and heat are interchanged. In the solid–liquid phase, biomass growth occurs causing a change in substrate concentration as well as a change in temperature due to heat release from microbial activity. Thus the mathematical model is able to describe temperature and oxygen concentration profiles in the gas phase and temperature and biomass and substrate concentration profiles in the solid–liquid phase as a function of time and axial and radial positions. Useful information obtained from the model solution are the highest temperature that can be attained within the bioreactor and the length of high temperature conditions, which are important if sludge sanitization is the purpose of the composting process. Also a theoretical calculation of the logarithmic decimal reduction of Salmonella is presented. Using the model, a design analysis was performed to determine the effect of the main design variables in the temperature of the solid–liquid phase and the oxygen concentration in the gas phase.