Numerical study of substrate assimilation by a microorganism exposed to fluctuating concentration

In most modelling works on bioreactors, the substrate assimilation is computed from the volume average concentration. The possible occurrence of a competition between the transport of substrate towards the cell and the assimilation at the cell level is generally overlooked. In order to examine the consequences of such a competition, a diffusion equation for the substrate is coupled with a specific boundary condition defining the up take rate at the cell liquid interface. Two assimilation laws are investigated, whereas the concentration far from the cell is varied in order to mimic concentration fluctuations. Both steady and unsteady conditions are investigated. The actual uptake rate computed from the interfacial concentration is compared to the time-averaged uptake rate based on the mean far-field concentration. Whatever the assimilation law, it is found that the uptake rate can be correlated to the mean far-field concentration, but the actual values of the parameters are affected in case of transport limitation. Moreover, the structure of the far-field signal influences the substrate assimilation by the microorganism, and the mean interfacial uptake rate depends on the ratio between the characteristic time of the signal and the diffusional time scale, as well as on the amplitude of the fluctuations around the mean far-field concentration in substrate. The present work enlightens some experimental results and helps in understanding the differences between the concentration measured and that present in the microenvironment of the cells

Piv study of mixing characteristics in a stirred vessel with a non-Newtonian fluid

PIV is used to analyze the flow induced by a Rushton turbine in a shear-thinning fluid, at constant input power, constant impeller velocity but different concentrations. The rheology of each shear-thinning fluid is first addressed. The mean velocity fields are compared. POD methodology is applied to estimate coherent structures and turbulence levels. Finally, the heterogeneity of shear rate is estimated and the spatial distribution of dissipation rate of total kinetic energy is addressed

A photosynthetic rotating annular bioreactor (Taylor–Couette type flow) for phototrophic biofilm cultures

In their natural environment, the structure and functioning of microbial communities from river phototrophic biofilms are driven by biotic and abiotic factors. An understanding of the mechanisms that mediate the community structure, its dynamics and the biological succession processes during phototrophic biofilm development can be gained using laboratory-scale systems operating with controlled parameters. For this purpose, we present the design and description of a new prototype of a rotating annular bioreactor (RAB) (TayloreCouette type flow, liquid working volume of 5.04 L) specifically adapted for the cultivation and investigation of phototrophic biofilms. The innovation lies in the presence of a modular source of light inside of the system, with the biofilm colonization and development taking place on the stationary outer cylinder (onto 32 removable polyethylene plates). The biofilm cultures were investigated under controlled turbulent flowing conditions and nutrients were provided using a synthetic medium (tap water supplemented with nitrate, phosphate and silica) to favour the biofilm growth. The hydrodynamic features of the water flow were characterized using a tracer method, showing behaviour corresponding to a completely mixed reactor. Shear stress forces on the surface of plates were also quantified by computer simulations and correlated with the rotational speed of the inner cylinder. Two phototrophic biofilm development experiments were performed for periods of 6.7 and 7 weeks with different inoculation procedures and illumination intensities. For both experiments, biofilm biomasses exhibited linear growth kinetics and produced 4.2 and 2.4 mg cm-2 of ash-free dry matter. Algal and bacterial community structures were assessed by microscopy and T-RFLP, respectively, and the two experiments were different but revealed similar temporal dynamics. Our study confirmed the performance and multipurpose nature of such an innovative photosynthetic bioreactor for phototrophic biofilm investigations

New developments of the Extended Quadrature Method of Moments to solve Population Balance Equations

Population Balance Models have a wide range of applications in many industrial fields as they allow accounting for heterogeneity among properties which are crucial for some system modelling. They actually describe the evolution of a Number Density Function (NDF) using a Population Balance Equation (PBE). For instance, they are applied to gas–liquid columns or stirred reactors, aerosol technology, crystallisation processes, fine particles or biological systems. There is a significant interest for fast, stable and accurate numerical methods in order to solve for PBEs, a class of such methods actually does not solve directly the NDF but resolves their moments. These methods of moments, and in particular quadrature-based methods of moments, have been successfully applied to a variety of systems. Point-wise values of the NDF are sometimes required but are not directly accessible from the moments. To address these issues, the Extended Quadrature Method of Moments (EQMOM) has been developed in the past few years and approximates the NDF, from its moments, as a convex mixture of Kernel Density Functions (KDFs) of the same parametric family. In the present work EQMOM is further developed on two aspects. The main one is a significant improvement of the core iterative procedure of that method, the corresponding reduction of its computational cost is estimated to range from 60% up to 95%. The second aspect is an extension of EQMOM to two new KDFs used for the approximation, the Weibull and the Laplace kernels. All MATLAB source codes used for this article are provided with this article

An assessment of methods of moments for the simulation of population dynamics in large-scale bioreactors

A predictive modelling for the simulation of bioreactors must account for both the biological and hydrodynamics complexities. Population balance models (PBM) are the best approach to conjointly describe these complexities, by accounting for the adaptation of inner metabolism for microorganisms that travel in a large-scale heterogeneous bioreactor. While being accurate for solving the PBM, the Class and Monte-Carlo methods are expensive in terms of calculation and memory use. Here, we apply Methods of Moments to solve a population balance equation describing the dynamic adaptation of a biological population to its environment. The use of quadrature methods (Maximum Entropy, QMOM or EQMOM) is required for a good integration of the metabolic behavior over the population. We then compare the accuracy provided by these methods against the class method which serves as a reference. We found that the use of 5 moments to describe a distribution of growth-rate over the population gives satisfactory accuracy against a simulation with a hundred classes. Thus, all methods of moments allow a significant decrease of memory usage in simulations. In terms of stability, QMOM and EQMOM performed far better than the Maximum Entropy method. The much lower memory impact of the methods of moments offers promising perspectives for the coupling of biological models with a fine hydrodynamics depiction

Analyse locale et globale de l'hydrodynamique et du transfert de matière dans des fluides à rhéologie complexe caractéristiques des milieux de fermentation

La production d éthanol à partir de biomasse lignocellulosique est reconnue comme une des voies possibles de réduction des émissions de gaz à effet de serre et de remplacement partiel des énergies fossiles. Pour être compétitif, la production d'enzymes à bas coûts est nécessaire. Ces enzymes sont produites par le champignon filamenteux Trichoderma reesei, qui présente, à forte concentration, un comportement fortement rhéofluidifiant pouvant entrainer des limitations de mélange et de transfert de matière lors du changement d'échelle. Dans ce travail, il est proposé de compléter les données de la littérature concernant le temps de mélange, la puissance dissipée et le transfert de matière gaz-liquide (global et local) par des mesures à plusieurs échelles dans des fluides modèles de rhéologie similaire aux milieux biologiques visés. Les modèles et corrélations développés qui en résultent sont directement exploitables pour le design des fermenteurs industriels. Afin d étudier plus en détail le mélange, le taux de cisaillement et la turbulence, une étude par PIV a été menée sur des milieux transparents. La caractérisation fine de l'hydrodynamique repose sur la dissociation des différentes composantes du mouvement à l aide de la POD. L'évolution des grandeurs mesurées avec les conditions opératoires permet de fournir des indications précieuses pour l'extrapolation des fermenteurs mettant en œuvre des micro-organismes potentiellement sensibles au cisaillementEthanol made from cellulosic biomass is recognized as a promising substitute for fossil fuel and thus as a way to reduce greenhouse gas emissions. To be competitive, low cost cellulosic enzymes produced by the filamentous fungus Trichoderma reesei are required. At high biomass concentration, the culture broth becomes so highly shear-thinning that mixing and mass transfer limitations may be encountered when the process is scaled up.In this study, we propose to complete data available in the literature for mixing times, power draw, and mass transfer (local and global) with measurements at several scales in model fluids (shear thinning) that mimic the rheology of biological media. Models and correlations that derive from this work can be used directly for industrial fermentor design. In order to study mixing, local shear rate and turbulence in detail, PIV is performed in transparent model fluids. The refined hydrodynamic characterisation relies on the dissociation of instantaneous velocity by means of the POD method. The change of key parameters with operating conditions gives relevant information for the scale-up of shear-sensitive micro-organisms.TOULOUSE-INSA-Bib. electronique (315559905) / SudocSudocFranceF

Rate-based simulation of a high pressure counter-current packed column for supercritical CO 2 extraction of alcohol from dilute aqueous mixtures

In this work, the modeling and simulation of a fractionation packed column for the recovery of isopropanol from dilute aqueous mixtures using supercritical CO2 is presented. The model is based on the numerical resolution of differential mass balances for each component over the column height. The multicomponent mass transfer between phases is described using a “rate-based” approach and the concept of local mass transfer coefficients. The model was validated by reproduction of experimental steady-state results for the fractionation of 5% isopropanol aqueous solutions obtained in a bench scale counter-current column. The effect of process conditions on the separation performance was satisfactorily described by the model calculations, showing that operation pressure and CO2 flow rate enhance IPA recovery and extract purity, while operation temperature has a negative effect. Model deviations (AARD) were in all cases lower than 20%

A two-dimensional population balance model for cell growth including multiple uptake systems

Cell growth in a chemostat is a well-documented research topic. How cells uptake the avail-able substrate to gain weight and engage cell division is not generally taken into account inthe modelling bioreactors. In fact, the growth rate is related to a population doubling timewhereas the microorganisms’ growth in mass is due to the mass transfer of substrates fromthe liquid phase to the biotic phase. Clearly, growth in mass precedes growth in number.Similarly, the transport of substrates down to the cell scale precedes the mass transfer. Thisarticle’s main feature is a two-dimensional population balance model that allows to uncou-ple growth in mass and growth in number when the equilibrium between a cell populationand its environment is disrupted. The cell length and the rate of anabolism are chosen asinternal variables. It is proved that the hypothesis “growth in number = growth in mass” isvalid at steady-state or in exponential growth only. The glucose uptake is assumed drivenby two transport systems with a different affinity constant for the substrate. This combina-tion of two regulated uptake systems operating in parallel explains a 3-fold increase in theuptake following a glucose pulse, but can also predict substrate uptake rates higher thanthe maximal batch value as observed in some experiments. These features are obtainedby considering carbon fluxes in the formulation of regulation principles for uptake dynam-ics. The population balance’s implementation in a multi-compartment reactor is a naturalprospective work and allows extensions to industrial processes

Numerical tools for scaling up bioreactors

The present paper focuses on the development of a population balance model (PBM) accounting for microbial population dynamics in a fluctuating environment. Heterogeneity within the cell population has two origins: extrinsic/intrinsic noises (cell to cell variability due to biological processes) and external noise (due to fluctuations in the cell environment). Modelling the effects of concentration gradients on the population heterogeneity was addressed in previous works using a population balance model based on the specific growth rate. However that model was unable to predict the distribution of specific growth rates experimentally observed at steady state. Using recent experimental data, we now propose a suitable law for the probability that cells growing at a given specific rate produce daughter cells with a different growth rate. Characteristic times of substrate assimilation and mixing at the cell scale are then combined to produce a generic model for substrate uptake limited by micromixing. The simulated results compare favorably to experimental observations leading to a robust multiscale model for bioreactor dynamics combining liquid-cell mass transfer and population heterogeneit