Scale-up on basis of structured mixing models: A new concept

A new scale-up concept based upon mixing models for bioreactors equipped with Rushton turbines using the tanks-in-series concept is presented. The physical mixing model includes four adjustable parameters, i.e., radial and axial circulation time, number of ideally mixed elements in one cascade, and the volume of the ideally mixed turbine region. The values of the model parameters were adjusted with the application of a modified Monte-Carlo optimization method, which fitted the simulated response function to the experimental curve. The number of cascade elements turned out to be constant (N = 4). The model parameter radial circulation time is in good agreement with the one obtained by the pumping capacity. In case of remaining parameters a first or second order formal equation was developed, including four operational parameters (stirring and aeration intensity, scale, viscosity). This concept can be extended to several other types of bioreactors as well, and it seems to be a suitable tool to compare the bioprocess performance of different types of bioreactors. (c) 1994 John Wiley & Sons, Inc.     

Discrete particle simulations predicting mixing behavior of solid substrate particles in a rotating drum fermenter.

A soft-sphere discrete particle model was used to simulate mixing behavior of solid substrate particles in a slow rotating drum for solid-state fermentation. In this approach, forces acting on and subsequent motion of individual particles can be predicted. The (2D) simulations were qualitatively and quantitatively validated by mixing experiments using video and image analysis techniques. It was found that the simulations successfully predicted the mixing progress as a function of the degree of filling and size of the drum. It is shown that only relatively large, straight baffles perpendicular to the drum wall (67% of the drum radius) increase the mixing performance of the rotating drum. Considering the different aspects of mixing dealt with in this work, it is concluded that the soft sphere discrete particle model can serve as a valuable tool for investigating mixing of solid substrate particles. Finally, it is expected that this model may evolve into a potential tool for design and scale-up of mixed solid-state fermenters.     

Modeling and scale-up of the unsterile scleroglucan production process with Sclerotium rolfsii ATCC 15205

An empirical model was applied to describe the growth related formation of scleroglucan in batchwise cultivation of Sclerotium rolfsii. In this case, the level of oxygen supply controls the carbon flux into glucan, biomass, and CO₂ evolution and therefore determines the yield coefficients Y_Glucan/BDM and Y_BDM/O2. It was observed that scleroglucan formation is enhanced under microaerobic conditions. However, as the empirical model and data of actual batch cultivations show, different maxima exist for product end concentration [g/l] and volumetric productivity [g/ld] depending on the total oxygen uptake during cultivation. A sufficient bulk mixing of the highly viscous culture suspension becomes particularly important during large-scale cultivations. In addition, the scleroglucan production process proved to be shear sensitive. A correlation between the attainable molecular weight of the glucan and the stirrer tip velocity in bioreactors of different sizes is presented. For all these reasons, a scale-up of this process is very complex. Large-scale cultivations under microaerobic conditions, aiming for maximum product end concentration, were slowed down by poor bulk mixing leading to a lower carbon flux into glucan formation. On the other hand, a scale-up designed for maximum volumetric productivity using high oxygen supply was successfully conducted up to a reactor volume of 1.500 l. To minimize the loss in product quality (molecular weight of the glucan) due to high stirrer tip velocities, a mixing concept was developed employing reduced agitation combined with maximum aeration to secure a sufficient axial bulk mixing in the reactor.     

Modelling of the process yields of a whey fermentation

Summary The biomass yields (y) and COD reduction efficiencies (η) of a whey fermentation by Kluyveromyces fragilis were studied in a 100-1 fermenter at various stirrer speeds and lactose concentrations, and compared to those obtained in 10-1 and 15-1 fermenters at constant values of the oxygen transfer coefficient (k_La) and air velocity. The empirical models previously constructed by using the 15-1 fermenter data could be used to predict the yields on the other scales by calculating for each run the 15-1 fermenter which would provide the same oxygen transfer coefficient measured by the sulphite method on each fermenter under study. To make this model independent of stirrer speeds used in each generic fermenter, the effect of aeration and mixing was incorporated into an overall parameter (k_La) and the values of y and η were correlated only with temperature, lactose level and k_L a, since these variables were approximately orthogonal. The validity of this model was finally checked against the yields reported by Wasserman et al. (1961) in a 6-m³ fermenter, thus confirming the capability of the model to provide a reliable basis for further scale-up on the production scale.     

Bioreactor hydrodynamic effect on Escherichia coli physiology: experimental results and stochastic simulations

A microorganism circulating in a bioreactor can be submitted to hydrodynamic conditions inducing a significant effect on its physiology. The mixing time exhibited by the stirred bioreactor and the circulation of microorganisms are both involved in this reacting system. The mixing component determines the intensity of the concentration gradient and the circulation component determines the way in which the microorganism is exposed to this gradient. These two components linked to the experimental evaluation of microbial physiology can be analysed by a structured stochastic model in the case of a partitioned or “scale-down” reactor (SDR). A stochastic model indeed enables to simulate the mixing process as well as the circulation of microorganisms in SDRs. The superimposition of mixing and circulation processes determines the concentration profile experienced by a microorganism in the reactor. In the present case, the glucose concentration experienced by Escherichia coli has been modelled during a fed-batch culture. In this context, the use of a stochastic hydrodynamic model has permitted to point out an interesting feed pulse retardant effect in the SDRs. Nevertheless, the metabolic response of E. coli is not easy to interpret because of the possible simultaneous developments of overflow metabolism and mixed acid fermentation induced by the strong glucose concentration in the reactor.     

Optimization and scale up of industrial fermentation processes

To increase product yields and to ensure consistent product quality, key issues of industrial fermentations, process optimization and scale up are aimed at maintaining optimum and homogenous reaction conditions minimizing microbial stress exposure and enhancing metabolic accuracy. For each individual product, process and facility, suitable strategies have to be elaborated by a comprehensive and detailed process characterization, identification of the most relevant process parameters influencing product yield and quality and their establishment as scale-up parameters to be kept constant as far as possible. Physical variables, which can only be restrictedly kept constant as single parameters, may be combined with other pertinent parameters to appropriate mathematical groups or dimensionless terms. Process characterization is preferably based on real-time or near real-time data collected by in situ and on-line measurements and may be facilitated by supportive approaches and tools like neural network based chemometric data analysis and modelling, clarification of the mixing and stream conditions through computational fluid dynamics and scale-down simulations. However, as fermentation facilities usually are not strictly designed according to scale-up criteria and the process conditions in the culture vessels thus may differ significantly and since any strategy and model can only insufficiently consider and reflect the highly complex interdependence and mutual interaction of fermentation parameters, successful scale up in most cases is not the result of a conclusive and straight-lined experimental strategy, but rather will be the outcome of a separate process development and optimization on each scale. This article gives an overview on the problems typically coming along with fermentation process optimization and scale up, and presents currently applied scale-up strategies while considering future technologies, with emphasis on Escherichia coli as one of the most commonly fermented organisms.     

Scaling-up of a batch whey fermentation by Kluyveromyces fragilis

Summary A whey fermentation by Kluyveromyces fragilis was scaled-up to a 1000-dm³ stirred fermentor, by varying the stirrer speed, the air-flow rate and the initial concentration of lactose. Its evolution was simulated by applying the same unstructured model (consisting of a microbial specific growth rate of pseudo-first order with respect to the COD concentration and constant biomass yield per unit COD removed) set up in previous experiments using 8- to 80-dm³ fermentors. Despite the great scale-up ratios, very different operating conditions, and geometric dissimilarity, a series of empirical regressions previously developed allowed approximate, but acceptable prediction of the stoichiometric and kinetic coefficients of the above mathematical model, thus confirming the capability of this model to provide a reliable basis for further scale-up of this fermentation process to a production scale.     

Temperature control in a continuously mixed bioreactor for solid-state fermentation

A continuously mixed, aseptic paddle mixer was used successfully for solid-state fermentation (SSF) with Aspergillus oryzae on whole wheat kernels. Continuous mixing improved temperature control and prevented inhomogeneities in the bed. Respiration rates found in this system were comparable to those in small, isothermal, unmixed beds, which showed that continuous mixing did not cause serious damage to the fungus or the wheat kernels. Continuous mixing improves heat transport to the bioreactor wall, which reduces the need for evaporative cooling and thus may help to prevent the desiccation problems that hamper large-scale SSF. However, scale-up calculations for the paddle mixer indicated that wall cooling becomes insufficient at the 2-m(3) scale for a rapidly growing fungus like Aspergillus oryzae. Consequently, evaporative cooling will remain important in large-scale mixed systems. Experiments showed that water addition will be necessary when evaporative cooling is applied in order to maintain a sufficiently high water activity of the solid substrate. Mixing is necessary to ensure homogeneous water addition in SSF. Automated process control might be achieved using the enthalpy balance. The enthalpy balance for the case of evaporative cooling in the paddle mixer was validated. This work shows that continuous mixing provides promising possibilities for simultaneous control of temperature and moisture content in solid-state fermentation on a large scale.     

Scale-up of Escherichia coli growth and recombinant protein expression conditions from microwell to laboratory and pilot scale based on matched k(L)a

Fermentation optimization experiments are ideally performed at small scale to reduce time, cost and resource requirements. Currently microwell plates (MWPs) are under investigation for this purpose as the format is ideally suited to automated high-throughput experimentation. In order to translate an optimized small-scale fermentation process to laboratory and pilot scale stirred-tank reactors (STRs) it is necessary to characterize key engineering parameters at both scales given the differences in geometry and the mechanisms of aeration and agitation. In this study oxygen mass transfer coefficients are determined in three MWP formats and in 7.5 L and 75 L STRs. k(L)a values were determined in cell-free media using the dynamic gassing-out technique over a range of agitation conditions. Previously optimized culture conditions at the MWP scale were then scaled up to the larger STR scales on the basis of matched k(L)a values. The accurate reproduction of MWP (3 mL) E. coli BL21 (DE3) culture kinetics at the two larger scales was shown in terms of cell growth, protein expression, and substrate utilization for k(L)a values that provided effective mixing and gas-liquid distribution at each scale. This work suggests that k(L)a provides a useful initial scale-up criterion for MWP culture conditions which enabled a 15,000-fold scale translation in this particular case. This work complements our earlier studies on the application of DoE techniques to MWP fermentation optimization and in so doing provides a generic framework for the generation of large quantities of soluble protein in a rapid and cost-effective manner.     

Three-dimensional simulation of grain mixing in three different rotating drum designs for solid-state fermentation

A previously published two-dimensional discrete particle simulation model for radial mixing behavior of various slowly rotating drums for solid-state fermentation (SSF) has been extended to a three-dimensional model that also predicts axial mixing. Radial and axial mixing characteristics were predicted for three different drum designs: (1) without baffles; (2) with straight baffles; and (3) with curved baffles. The axial mixing behavior was studied experimentally with video- and image-analysis techniques. In the drum without baffles and with curved baffles the predicted mixing behavior matched the observed behavior adequately. The predicted axial mixing behavior in the drum with straight baffles was predicted less accurately, and it appeared to be strongly dependent on particle rotation, which was in contrast to the other drum designs. In the drum with curved baffles complete mixing in the radial and axial direction was achieved much faster than in the other designs; that is, it was already achieved after three to four rotations. This drum design may therefore be very well suited to SSF. It is concluded that discrete particle simulations provide valuable detailed knowledge about particle transport processes, and this may help to understand and optimize related heat and mass transfer processes in SSF.     

Dependence of mycelial morphology on impeller type and agitation intensity

The influence of the agitation conditions on the morphology of Penicillium chrysogenum (freely dispersed and aggregated forms) was examined using radial (Rushton turbines and paddles), axial (pitched blades, propeller, and Prochem Maxflow T), and counterflow impellers (Intermig). Culture broth was taken from a continuous fermentation at steady state and was agitated for 30 min in an ungassed vessel of 1.4-L working volume. The power inputs per unit volume of liquid in the tank, P/V(L), ranged from 0.6 to 6 kW/m(3). Image analysis was used to measure mycelial morphology. To characterize the intensity of the damage caused by different impellers, the mean total hyphal length (freely dispersed form) and the mean projected area (all dispersed types, i.e., also including aggregates) were used. [In this study, breakage of aggregates was taken into account quantitatively for the first time.]At 1.4-L scale and a given P/V(L), changes in the morphology depended significantly on the impeller geometry. However, the morphological data (obtained with different geometries and various P/V(L)) could be correlated on the basis of equal tip speed and two other, less simple, mixing parameters. One is based on the specific energy dissipation rate in the impeller region, which is simply related to P/V(L) and particular impeller geometrical parameters. The other which is developed in this study is based on a combination of the specific energy dissipation rate in the impeller swept volume and the frequency of mycelial circulation through that volume. For convenience, the function arising from this concept is called the "energy dissipation/circulation" function.To test the broader validity of these correlations, scale-up experiments were carried out in mixing tanks of 1.4, 20, and 180 L using a Rushton turbine and broth from a fed-batch fermentation. The energy dissipation/circulation function was a reasonable correlating parameter for hyphal damage over this range of scales, whereas tip speed, P/V(L), and specific energy dissipation rate in the impeller region were poor. Two forms of the energy dissipation/circulation function were considered, one of which additionally allowed for the numbers of vortices behind the blades of each impeller type. Although both forms were successful at correlating the data for the standard impeller designs considered here, there was preliminary evidence that allowing for the vortices would be valuable. (c) 1996 John Wiley & Sons, Inc.     

Analytical solutions for the specific activities of a traced substance within the component parts of a simulated kidney-ureter system

Two models for a kidney-ureter system are considered: one model of one vessel in which a traced substance, undergoing exchange between the vessel and an external compartment, is emptying into the ureter; the second model of two approximately parallel, identical vessels in which a traced substance, undergoing exchange between each vessel and an external compartment, is emptying into the ureter. A single impulsive input of label into a vessel is assumed. For mathematical simplicity, the major conditions imposed on each system are: (1) rapid mixing transverse to a vessel axis and no mixing longitudinal to a vessel axis within the plasma; (2) small variation of the specific activity within the plasma in the longitudinal direction to a vessel axis; (3) constant flow rate of urine into the ureter and (4) constant exchange coefficients, tubule flow velocity and traced substance concentrations within individual compartments.     

Stochastic models to study the impact of mixing on a fed-batch culture of Saccharomyces cerevisiae

The mechanisms of interaction between microorganisms and their environment in a stirred bioreactor can be modeled by a stochastic approach. The procedure comprises two submodels: a classical stochastic model for the microbial cell circulation and a Markov chain model for the concentration gradient calculus. The advantage lies in the fact that the core of each submodel, i.e., the transition matrix (which contains the probabilities to shift from a perfectly mixed compartment to another in the bioreactor representation), is identical for the two cases. That means that both the particle circulation and fluid mixing process can be analyzed by use of the same modeling basis. This assumption has been validated by performing inert tracer (NaCl) and stained yeast cells dispersion experiments that have shown good agreement with simulation results. The stochastic model has been used to define a characteristic concentration profile experienced by the microorganisms during a fermentation test performed in a scale-down reactor. The concentration profiles obtained in this way can explain the scale-down effect in the case of a Saccharomyces cerevisiae fed-batch process. The simulation results are analyzed in order to give some explanations about the effect of the substrate fluctuation dynamics on S. cerevisiae.     

Model-based bioreactor selection for large-scale solid-state cultivation of Coniothyrium minitans spores on oats

Non-mixed and mixed SSF reactors were evaluated for their applicability in large-scale spore production of the biocontrol fungus Coniothyrium minitans. The major problem to overcome in large-scale SSF is heat accumulation. Testing various cooling strategies in large-scale bioreactors would be very expensive and time consuming, therefore lab experiments in combination with mathematical simulations were used instead. The metabolic heat production rate, estimated from the oxygen consumption rate of C. minitans on oats in Erlenmeyer flasks, was about 500 Watt per m(3) bed. Conductive cooling in packed-bed reactors was insufficient to cool large reactor volumes (radius > 0.2 m). The poor thermal conductivity of the bed (lambda(b) = 0.1 W m(-2) K(-1)) resulted in steep radial temperature profiles. Adequate temperature control could be achieved with forced aeration, but concomitant water losses lead to significant shrinkage of the oats (30%) and critically low water activities, even though the bed was assumed to be aerated with water saturated air. Mixed systems, however, allowed heat removal without the need of evaporative cooling. Simulations showed that large volumes could be cooled via the wall at low mixing intensities and small temperature driving forces. Experimental studies showed no detrimental effect of mixing on spore production by C. minitans. The spore production yield in a continuously mixed scraped-drum reactor (0.2 rpm) was 5 x 10(12) spores per kg dry oats after 450 hours. Based on the scale-up potential of the mixed system and the absence of detrimental mixing effects it is believed that a mixed bioreactor is superior to a non-mixed system for large-scale production of C. minitans spores.     

Prelude to rational scale-up of penicillin production: a scale-down study

Penicillin is one of the best known pharmaceuticals and is also an important member of the β-lactam antibiotics. Over the years, ambitious yields, titers, productivities, and low costs in the production of the β-lactam antibiotics have been stepwise realized through successive rounds of strain improvement and process optimization. Penicillium chrysogenum was proven to be an ideal cell factory for the production of penicillin, and successful approaches were exploited to elevate the production titer. However, the industrial production of penicillin faces the serious challenge that environmental gradients, which are caused by insufficient mixing and mass transfer limitations, exert a considerably negative impact on the ultimate productivity and yield. Scale-down studies regarding diverse environmental gradients have been carried out on bacteria, yeasts, and filamentous fungi as well as animal cells. In accordance, a variety of scale-down devices combined with fast sampling and quenching protocols have been established to acquire the true snapshots of the perturbed cellular conditions. The perturbed metabolome information stemming from scale-down studies contributed to the comprehension of the production process and the identification of improvement approaches. However, little is known about the influence of the flow field and the mechanisms of intracellular metabolism. Consequently, it is still rather difficult to realize a fully rational scale-up. In the future, developing a computer framework to simulate the flow field of the large-scale fermenters is highly recommended. Furthermore, a metabolically structured kinetic model directly related to the production of penicillin will be further coupled to the fluid flow dynamics. A mathematical model including the information from both computational fluid dynamics and chemical reaction dynamics will then be established for the prediction of detailed information over the entire period of the fermentation process and thereby for the optimization of penicillin production, and subsequently also benefiting other fermentation products.     

Scale-down studies on the hydrodynamics of two-liquid phase biocatalytic reactors

The maintenance of constant interfacial area per unit volume is a key parameter for the successful scale-up of two-liquid phase bioconversion processes. To date, however, there is little published information on the hydrodynamics of such systems and a suitable basis for scale-up has yet to be defined and verified. Here we report power input and hydrodynamic data for a whole-cell bioconversion process using resting cells of Rhodococcus R312 to catalyse the hydration of a poorly water-soluble substrate 1,3-dicyanobenzene (1,3-DCB). Experiments were performed in geometrically similar 3-L and 75-L reactors, each fitted with a three-stage Rushton turbine impeller system. The two-phase system used comprised of 20% v/v toluene dispersed in 0.1 M aqueous phosphate buffer containing up to 10 g(ww) x L(-1) of resuspended biocatalyst and 20 g x L(-1) 1,3-DCB. The power input to the 3-L reactor was first determined using an air-bearing technique for both single-phase and two-phase mixing. In both cases, the power number attained a constant value of 11 at Re>10,000, while the measured power inputs were in the range 0.15-3.25 kW x m(-3). Drop size distributions and Sauter mean drop diameters (d(32)) were subsequently measured on-line in both reactors, using an in-situ light-backscattering technique, for scale-up on the basis of either constant power input per unit volume or constant tip speed. At both scales d(32) decreased with increasing agitation rate, while the drop size distributions obtained were log-normal. All the measured d(32) values were in the range of 30-50 microm, with the lowest values being obtained in systems with biocatalyst present. In all cases, constant power input per unit volume was found to be the most suitable basis for scale-up. This gave virtually identical d(32) values and drop size distributions at both scales. A number of correlations were also identified that would allow reasonable prediction of d(32) values for various agitation rates at each scale. While the results obtained are for a particular phase system, the scale-down methodology presented here would allow the rapid evaluation of other bioconversion processes in the 3-L reactor with a 25-fold reduction in scale. In this way, potential problems that might be encountered at the larger scale, such as the carryover of antifoam from the fermentation stage, could be quickly and efficiently identified.     

A methodology for the design of scale-down bioreactors by the use of mixing and circulation stochastic models

Scale-up is traduced in practice by an increase of the dimensions of the bioreactors, leading to a modification of the time scale and thus of the process dynamics. In the present work, a methodology to study the effect of scale-up on bioreactors hydrodynamics and to put in place scale-down reactors representative of the flow properties encountered in real scales bioreactors is detailed.In order to simplify the analysis, we have proposed the use of a stochastic model which is directly affected by the time scale. Indeed, to run simulations with such models, we have to specify the time taken to achieve a transition Δt. Stochastic models are thus reliable to study scale-up effect on stirred reactors hydrodynamics. In addition, these models permit to have an insight on the internal dynamic of the process.In the case of the circulation process, qualitative aspects have to be taken into account and induce a modification of the flow regions arrangement of the model. The stochastic analysis of large-scale bioreactors permits to propose a translating methodology into a scale-down context. Optimised scale-down reactors can be used further to carry out fermentation tests with the hydrodynamic conditions of the industrial scale. In a general rule, the performances of stochastic model allow to facilitate greatly the analysis of the scale-up effect and the hydrodynamic characteristics of both large-scale and scale-down reactors.     

Small-scale liquid mixing in a bioreactor column with xanthan-gum simulated filamentous media

Using the heat pulse technique, the local mean flow liquid velocity and the mixing conditions for twophase flow in the riser of an airlift bioreactor have been measured and analysed. Xanthan-gum solutions were used as the physical model to some filamentous broths reported in the literature. A two-fold decrease of liquid velocity and diffusional mixing regime are predicted for the course of a fermentation process proceeding in a non-Newtonian biomass growth circulation system.