Xanthan batch fermentations: compared performances of a bubble column and a stirred tank fermentor

Fermentations of Xanthomonas campestris, NRRL B-1459, were carried out in a bubble column fermentor (BCF) and in a stirred tank fermentor (STF) to allow comparison of representative variables measured during the microbial growth and the gum production. The microbial growth phase was described by a logistic rate equation where maximum cell concentration was provided by nitrogenous compounds balance. The average value of the maximum specific growth rate was higher in the bubble column (μ _M =0.5 h^?1) than in the stirred reactor (μ _M =0.4 h^?1). The upper values of xanthan yield (Y _g-x =0.65 kg xanthan/kg glucose; Y _{O 2?x} xanthan/kg oxygen) and specific production rate (q _x =0.26 kg xanthan/kg biomass · h) were measured when the oxygen transfer coefficient was kept up above 80 h^?1 in the STF fermentor. In the bubble column the fermentation achieved in the same culture medium lasts two times longer than in the stirred aerated tank; this was attributed to the low value of the oxygen transfer coefficient (K _L a =20 h^?1) at the beginning of the gum synthesis phase. The results obtained in the stirred tank were the basis to estimate the optimal biomass concentration which enables to achieve a culture in non-limiting oxygen transfer conditions. Nevertheless, the transfer characteristics were more homogeneous in the bubble column than in the stirred tank where dead stagnant zones were observed. This is of primary importance when establishing fermentation kinetics models.     

Protein mass transfer studies on a spray column using the PEG-Reppal PES 100 aqueous two-phase system

The characterization of Bovine Serum Albumin mass transfer mechanisms in a spray column using an aqueous two-phase system composed of poly(ethylene glycol) and a modified starch-Reppal PES 100-is done. The poly(ethylene glycol) rich phase is used as the dispersed phase and protein transfer takes place from the dispersed phase to the continuous phase. The effect of dispersed phase superficial velocity, system composition, continuous phase height and distribution system design on either overall protein mass transfer coefficient or column hold-up is described. It is shown that continuous phase superficial velocity and phase composition are the main controlling factors for protein transfer. It is also observed that, with the tested system, only at very low dispersed phase superficial velocities is it possible to operate the spray column as an extraction column. In this system the upper operating limit of the dispersed phase velocity is ten times smaller than in other aqueous two-phase systems.List of Symbols ATPS Aqueous Two-Phase System - BSA Bovine Serum Albumin - C _i kg m^–3 inlet dispersed phase protein concentration - C ₀ kg m^–3 outlet dispersed phase protein concentration - C _d kg m^–3 dispersed phase protein concentration - C _c kg m^–3 continuous phase protein concentration - D m column internal diameter - H hold-up - h, h _d m dispersion height - h ₀ m initial dispersion height (initial continuous phase height) - k _da s^–1 overall mass transfer coefficient - m protein partition coefficient - n number of holes of distribution system - PEG Poly(ethylene glycol) - Q m³ s^–1 dispersed phase volumetric flow rate - S m² column internal area - V m³ dispersion volume A. Venâncio was supported by a JNICT (Junta Nacional de Investigaçäo Científica e Tecnológica) grant.     

Removal of benzene in a hybrid bioreactor

A novel hybrid bioreactor was designed to remove volatile organic compounds from wastewater and its performance was investigated. The bioreactor was composed of a biofilter section and a bubble column bioreactor section. Benzene was used as a model compound and the influent benzene was removed by immobilized cells in a bubble column bioreactor. Gas phase benzene stripped by air injection was removed in a biofilter. When the superficial air flow rate was 21.1 m h⁻¹ (0.76 min of residence time in a biofilter), up to 2.2 ppm of benzene in gas phase was removed completely in a biofilter and the maximum removal rate was 4.71 mg day⁻¹ cm⁻³. The concentration profile of benzene along the biofilter column was dependent on the superficial air flow rate and the degree of microbial adaptation. Air flow rate and residence time were found to be the most important operation parameters for the hybrid bioreactor. By manipulating these operational parameters, the removal efficiency and capacity of the hybrid bioreactor could be enhanced. The organic load on the hybrid bioreactor could be shared by the biofilter and bubble column bioreactors and the fluctuation of load on the hybrid bioreactor could be absorbed by changing the distribution of benzene between biofilter and bubble column bioreactors. The maximum removal capacity of the hybrid bioreactor in the experimental range was obtained when the biofilter took 50.3% of influent benzene while 100% of removal efficiency was achieved when the biofilter took 72.3% of influent benzene.     

用于红霉素生产的500m3生物反应器的理性设计

红霉素(erythromycin)是由绛红色糖多胞菌(Saccharopolyspora erythraea)发酵生产的次级代谢产物,其生产水平不仅受发酵工艺的影响,也受反应器结构影响。为解决红霉素发酵过程放大问题,本研究采用时间常数法和计算流体力学(computational fluid dynamics,CFD)数值模拟验证相结合的方法设计了500m³超大规模红霉素耗氧发酵生物反应器。首先,通过对50L反应器红霉素发酵过程研究,发现溶氧是关键性限制因素,通过氧消耗速率(oxygen uptake rate,OUR)等参数分析计算得到设备的氧供应时间常数t_mt需小于6.25s。然后,基于时间常数法和经验关联式理性设计500m³反应器搅拌桨叶组合方式,即底层BDT8桨叶+两层MSX4桨叶的搅拌桨组合,并通过经验公式及CFD方法对设计结果进行了模拟验证。两种验证方法结果均表明500m³反应器采取底层BDT8桨叶+两层MSX4桨叶的组合方式时设备的氧供应时间常数小于6.25s,且反应器内流场特性(如持气率、剪切率和速度矢量等)均能满足红霉素大规模发酵的需要。经实际发酵验证,设计的生物反应器能够满足红霉素的工业规模发酵应用。     

Ethanol from hydrolyzed whey permeate using Saccharomyces cerevisiae in a membrane recycle bioreactor

A diauxic fermentation was observed during batch fermentation of enzyme-hydrolyzed whey permeate to ethanol by Saccharomyces cerevisiae. Glucose was consumed before and much faster than galactose. In the continuous membrane recycle bioreactor (MRB), sugar utilization was a function of dilution rate and concentration of sugars. At a cell concentration of 160 kg/m³, optimum productivity was 31 kg/(m³ · h) at ethanol concentration of 65 kg/m³. Low levels of acetate (0.05–0.1 M) reduced cell growth during continuous fermentation, but also reduced galactose utilization.     

Optimization of the microbial synthesis of dihydroxyacetone from glycerol with <Emphasis Type="Italic">Gluconobacter oxydans</Emphasis>

An optimized repeated-fed-batch fermentation process for the synthesis of dihydroxyacetone (DHA) from glycerol utilizing Gluconobacter oxydans is presented. Cleaning, sterilization, and inoculation procedures could be reduced significantly compared to the conventional fed-batch process. A stringent requirement was that the product concentration was kept below a critical threshold level at all times in order to avoid irreversible product inhibition of the cells. On the basis of experimentally validated model calculations, a threshold value of about 60 kg m^-3 DHA was obtained. The innovative bioreactor system consisted of a stirred tank reactor combined with a packed trickle-bed column. In the packed column, active cells could be retained by in situ immobilization on a hydrophilized Ralu-ring carrier material. Within 17 days, the productivity of the process could be increased by 75% to about 2.8 kg m^-3 h^-1. However, it was observed that the maximum achievable productivity had not been reached yet.Abbreviations K _O Monod half saturation constant of dissolved oxygen (kg m^-3) - K _S Monod half saturation constant of substrate glycerol (kg m^-3) - O Dissolved oxygen concentration (kg m^-3) - P Product concentration (kg m^-3) - P _crit Critical product concentration constant (kg m^-3) - S Substrate concentration (kg m^-3) - t Time (s) - X Biomass concentration (dry weight) (kg m^-3) - Y _P/S Yield coefficient of product from substrate - Y _X/S Yield coefficient of biomass from substrate - Growth dependent specific production rate constant (kg m^-3) - Growth independent specific production rate constant (s^-1) - Specific growth rate (s^-1) - _max Maximum specific growth rate constant (s^-1)     

The effect of antifoam agents on mass transfer in bioreactors

The influence of antifoam agents on the liquid-phase mass transfer coefficient in stirred tank and bubble column bioreactors is studied. A physical model based on a surface-renewal concept and additional data in 40-dm³ bubble column bioreactor are presented. Comparisons between the physical model and the data indicate that the model predicts the maximum influence of antifoam agents on the liquid-phase mass transfer coefficient.List of Symbols a 1/m specific surface area - D m²/s diffusivity - D _c m bubble column diameter - d _vs m bubble diameter - g m/s² gravitational acceleration - k _L m/s liquid-phase mass transfer coefficient - k _LO m/s liquid-phase mass transfer coefficient for clean surface - N 1/s impeller speed - Sc Schmidt number (v/D) - U _sg m/s superficial gas velocity Greek Letters W/kg energy dissipation rate per unit mass - _g gas hold-up - Pa s viscosity - v m²/s kinematic viscosity - kg/m³ density - N/m surface tension     

Development of a new commercial-scale airlift fermentor for rapid growth of yeast

To grow yeast rapidly, it is necessary to supply sufficient oxygen to the yeast and to effectively remove the heat of the fermentation. We succeeded in developing a commercial-scale fermentor for growing a food yeast (Candida utilis) to produce RNA rapidly. This fermentor is an internal-loop airlift type with vertical heat transfer tubes between inner and the outer columns. The volume of the fermentor is 145 m³ (working volume 75 m³). The oxygen transfer rate (OTR) was 9.9 kg-O₂/m³/h using a superficial gas velocity of 30 cm/s based on the outer column. Much of the heat of fermentation and the energy resulting from aeration could be removed effectively by the heat transfer tubes. This unique airlift fermentor was driven at a dilution rate of 0.43 h⁻¹ for about 70 d, with the yeast concentration being maintained at 22.8 kg-dry cell/m³. The yeast production rate was 9.79 kg-dry cell/m³/h. Compared with a traditional stirred-type fermentor, two Vogelbush-type fermentors and another airlift fermentor, our fermentor was far superior with respect to OTR and yeast productivity.     

The effect of cultivation conditions on the penicillin production using a urethane foam-supported Penicillium chrysogenum

Urethane foam was applied to immobilize the fungus Penicillium chrysogenum in order to accelerate penicillin fermentation. Various operational conditions, such as cultivation temperature, initial pH value, composition of substrate and inoculum size of spores, which might influence penicillin fermentation significantly, were studied in a shaking flask culture system. The results are summarized as follows:

1. The maximum production amount of penicillin was achieved when cultivation temperature and initial pH were kept at 25±1°C and 4, respectively.
2. The maximum production yield of penicillin for substrate was obtainable when the concentration of lactose and that of cornsteep liquor in the basal medium were adjusted at 60 kg/m³ and 30 kg/m³, respectively.
3. It was found in this cultivation system that the optimum region concerning inoculum size was enlarged from 7.0·10⁵ to 1.0·10⁷ spores/dm³ while that of the traditional mehtod was very narrow around 1.0·10⁷ spores/dm³. Moreover, the production amount of penicillin produced by this new method was about twelve times as high as that produced by the traditional method.

     

Effect of serum concentration on production of monoclonal antibodies and on shear sensitivity of a hybridoma

The effect of serum content of culture medium on the specific production rate of monoclonal antibodies (Mab's) and on shear sensitivity has been studied with hybridoma's, cultured in a continuous stirred tank reactor (CSTR). No decrease in specific Mab-production was found when the serum concentration was reduced from 10 to 2.5%, while steady state cell concentrations were hardly affected as well. In contrast the cell death rate in a bubble column strongly increased when the serum concentration was lowered, which could be ascribed to a reduced physical protective effect by the serum.List of Symbols k _d s^–1 death-rate constant - k _g s^–1 growth-rate constant - D m diameter of bubble column - d m diameter of air bubble - H m height of bubble column - X m³ hypothetical killing volume - X (m³/m³) specific hypothetical killing volume - F m³/s volumetric air-flow rate - C cells/m³ number of viable cells - C₀ cells/m³ number of viable cells at t=0 - t s time     

Theoretical analysis of the baker's yeast production: An experimental verification at a laboratory scale

The scale-down procedure seems an adequate tool in the design, optimization and scale-up fermentation processes. The first step in this procedure is a theoretical analysis, called process analysis, which is based on characteristic times of the mechanisms which may influence the performance of the bioreactor. This analysis must give information about the behaviour of large and small scale fermentation processes. At a small scale a verification of the results of such an analysis of the fed-batch baker's yeast production is carried out.In this paper a comparison of calculated and measured characteristic times of liquid mixing and mass transfer is presented. It was concluded that the literature correlations give a rough estimation of the characteristic times and can be used in the process analysis. Depending on the kind of sparger, the medium and the scale of the reactor, more knowledge is needed about bubble coalescence in fermentation media.The volumetric oxygen transfer coefficient increased when the biomass concentration increased. Probably this is caused by the interaction between biomass and the anti-foaming agent used.List of Symbols C kg/m³ concentration - D m diameter - m²/s effective dispersion coefficient - d m holes of the sparger - g m/s² gravitational acceleration - H m height - k _L a s^–1 volumetric mass transfer coefficient based on the liquid volume - L m length - m kg/kg gas liquid distribution coefficient - OTR kg/(m³ · s) oxygen transfer rate - OUR kg/(m³ · s) oxygen uptake rate - t s time - ^s m/s superficial gas flow rate - m length - s time constant - _g m³/s gas flow rate Indices 0 value at t=0 - cal calculated - e value at t=t (end) - g gas phase - in flow going to the fermentor - l liquid phase - m mixing - mt mass transfer - O ₂ oxygen - out flow coming out the fermentor     

Physical and physiological impacts of different foam control strategies during a process involving hydrophobic substrate for the lipase production by Yarrowia lipolytica

The potentialities for the intensification of the process of lipase production by the yeast Yarrowia lipolytica on a renewable hydrophobic substrate (methyl oleate) have to be investigated. The key factor governing the lipase yield is the intensification of the oxygen transfer rate, considering the fact that Y. lipolytica is a strict aerobe. However, considering the nature of the substrate and the capacity for protein excretion and biosurfactant production of Y. lipolytica, intensification of oxygen transfer rate is accompanied by an excessive formation of foam. Two different foam control strategies have thus been implemented: a classical chemical foam control strategy and a mechanical foam control (MFM) based on the Stirring As Foam Disruption principle. The second strategy allows foam control without any modifications of the physico-chemical properties of the broth. However, the MFM system design induced the formation of a persistent foam layer in the bioreactor. This phenomenon has led to the segregation of microbial cells between the foam phase and the liquid phase in the case of the bioreactors operated with MFM control, and induced a reduction at the level of the lipase yield. More interestingly, flow cytometry experiments have shown that the residence time of microbial cells in the foam phase tends to induce a dimorphic transition which could potentially explain the reduction of lipase excretion.     

Effect of surface contaminants on oxygen transfer in bubble column reactors

Gas hold-up (ɛ_g), sauter mean bubble diameter (d₃₂) and oxygen transfer coefficient (k_La) were evaluated at four different alkane concentrations (0.05, 0.1, 0.3 and 0.5 vol.%) in water over the range of superficial gas velocity (u_g) of (1.18–23.52) × 10⁻³ m/s at 25 °C in a laboratory-scale bubble column bioreactor. Immiscible hydrocarbons (n-decane, n-tridecane and n-hexadecane) were utilized in the experiments as impurity. A type of anionic surfactant was also employed in order to investigate the effect of addition of surfactant to organic-aqueous systems on sauter mean bubble diameter, gas hold-up and oxygen transfer coefficient. Influence of addition of alkanes on oxygen transfer coefficient and gas hold-up, was shown to be dependent on the superficial gas velocity. At superficial gas velocity below 0.5 × 10⁻³ m/s, addition of alkane in air–water medium has low influence on oxygen transfer coefficient and also gas hold-up, whereas; at higher gas velocities slight addition of alkane increases oxygen transfer coefficient and also gas hold-up. Increase in concentration of alkane resulted in increase in oxygen transfer coefficient and gas hold-up and roughly decrease in sauter mean bubble diameter, which was attributed to an increase in the coalescence-inhibiting tendency in the presence of surface contaminant molecules. Bubbles tend to become smaller with decreasing surface tension of hydrocarbon, thus, oxygen transfer coefficient increases due to increasing of specific gas–liquid interfacial area (a). Empirical correlations were proposed for evaluating gas hold-up as a function of sauter mean bubble diameter, superficial gas velocity and interfacial surface tension as well as evaluating Sherwood number as a function of Schmidt, Reynolds and Bond numbers.     

Suspension culture of gametophytes of transgenic kelp in a photobioreactor

Transgenic Laminaria japonica gametophytes producing a recombinant tissue-type plasminogen activator (rtPA) protein, which is an effective third-generation thrombolytic agent for acute myocardial infarction (AMI), were cultured in an illuminated bubble column bioreactor. A maximum final dry cell weight of 1120 mg l⁻¹ was obtained in batch culture with an initial dry cell weight of 126 mg l⁻¹ and with aeration rate of 1.2 l air min⁻¹ l⁻¹ culture, nitrate at 1.5 mM and phosphate at 0.17 mM. The yield of rtPA was 56 μg g⁻¹ dry cell wt. This is the first report regarding cultivation of a transgenic macroalga in a bioreactor.Revisions requested 27 January 2005 and 14 April 2005; Revisions received 6 April 2005 and 17 May 2005     

Oxalic acid production by Aspergillus niger

Aspergillus niger is able to produce a quite high concentration of oxalic acid using sucrose as carbon and energy source. Operating at pH higher than 6 and an enriched N and P medium is necessary in order to conduct the fermentation towards oxalic acid production. A pH?shift technique, operating at acid pH?in the first two days and then setting pH?to 6, allowed the productivity to slightly increase in shaking flasks cultures up to 3.0?kg/m³?·?d, with a final oxalic acid concentration of 29?kg/m³. When operating at more controlled conditions, in a stirred tank, both productivity and oxalic acid concentration were improved (4.1?kg/m³?·?d and 33.8?kg/m³, respectively). However the main drawback of this fermentation is the low yield attained (about 0.3?kg oxalic acid/kg sucrose) because most of glucose, resulting from the hydrolysis of sucrose by the extracellular enzymes secreted at the beginning of the fermentation, is very quickly oxidised to gluconic acid, a process which is favoured at a pH?close to 6. Milk whey was proved to be a very good substrate as it allows oxalic acid to be produced with a similar productivity (2.5?kg/m³?·?d in shaking flasks) giving excellent yields of almost 0.6?kg oxalic acid/kg lactose.     

Theoretical analysis of the baker's yeast production: An experimental verification at a laboratory scale

The scale-down procedure can be used to optimize and scale up fermentation processes. The first step in this procedure, a theoretical analysis of the process at a large scale, must give information about the regime, or bottle necks, ruling the process. In order to verify the theoretical results the process analysis has been applied to the fed-batch baker's yeast production at a laboratory scale. The results of this analysis are compared with results from fed-batch experiments. It was concluded that if only one mechanism is ruling the process, for instance mass transfer, the results of the analysis are quite clear. If more than one mechanism is important, for example mass transfer and liquid mixing, additional knowledge is needed to predict the behaviour of the process.Concerning the baker's yeast production, it was concluded that if oxygen limitation occurs, liquid mixing is of little importance.List of Symbols C kg/m³ concentration - C ^* kg/m³ saturation concentration - D m diameter - D _E m²/s effective dispersion coefficient - d m holes of the sparger - F _sm³/s substrate flow to the fermentor - g m/s² gravitational acceleration - H m height - k _La s^–1 volumetric mass transfer coefficient based on the liquid volume - L m length - m _skg/(kg·s) maintenance coefficient - OTR kg/(m³·s) oxygen transfer rate - OUR kg/(m³·s) oxygen uptake rate - r kg/(m³·s) reaction rate - t s time - V m³ volume - v m/s velocity - v _sm/s superficial gas flow rate - y _ijkg/kg yield of componentj oni - s^–1 specific growth rate - s time constant - _gm³/s gas flow rate Indices 0 value att=0 - cir liquid circulation - e ethanol - f feed concentration - g gas phase - in flow going to the fermentor - l liquid phase - m mixing - mt mass transfer - o, O₂ oxygen - oc oxygen consumption - out flow coming out the fermentor - s substrate - sa substrate addition - sc substrate consumption - x biomass     

Hydrodynamics and mass transfer in an airlift loop fermentor

Summary The hydrodynamics and mass transfer behaviour of an airlift fermentor with an external loop (height 10m) has been investigated by measuring gas and liquid velocities, gas hold-up, liquid mixing and oxygen transfer coefficients. Liquid phase properties, i.e., ionic strength, viscosity and surface tension have been varied by altering the fermentation media. Results are compared with those from bubble column experiments performed in the same unit. It is shown, that more uniform two-phase flow in the airlift leads to advantages in scale-up and operation.Nomenclature a Specific interfacial area per volume of dispersion (m²/m³) - c Local concentration of tracer (kmol/m³) - c Concentration of tracer at infinite time (kmol/m³) - C_L Concentration of oxygen in the liquid bulk (kmol/m³) - C_L ^* Concentration of oxygen in the interface (kmol/m³) - D_ax Axial dispersion coefficient (cm²/s) - I Ionic strength (kmol/m³) - i Inhomogeneity [defined in Eq. (2)] - Rate of oxygen transfer (kmol/s) - t_c Circulation time (s) - t_M Mixing time (s) - V_R Volume of gas-liquid dispersion (m³) - V_SG Superficial gas velocity in up-flow column (m/s) Greek letter symbols _L Oxygen transfer coefficient (m/s) - Dynamic viscosity (m Pa s) - Surface tension (m N/m) Presented at the First European Congress on Biotechnology, Interlaken, September 25–29, 1978     

Modelling of alcohol fermentation in a tubular reactor with high biomass recycle

Fermentation in tubular recycle reactors with high biomass concentrations is a way to boost productivity in alcohol production. A computer model has been developed to investigate the potential as well as to establish the limits of this process from a chemical engineering point of view. The model takes into account the kinetics of the reaction, the nonideality of flow and the segregation in the bioreactor. In accordance with literature, it is shown that tubular reactors with biomass recycle can improve productivity of alcohol fermentation substantially.With the help of the computer based reactor model it was also possible to estimate the detrimental effects of cell damage due to pumping. These effects are shown to play a major role, if the biomass separation is performed by filtration units which need high flow rates, e.g. tangential flow filters.List of Symbols Bo d Bodenstein number - c kg/m³ concentration of any component - CPFR continuous plug flow reactor - CSTR continuous stirred tank reactor - d _h m hydraulic diameter - D _eff m²/s dispersion coefficient - f residence time distribution function - K _s kg/m³ monod constant for biomass production - K _s kg/m³ monod constant for alcohol production - p kg/m³ product concentration - P _i kg/m³ lower inhibition limit concentration for biomass production - p _i kg/m³ lower inhibition limit concentration for alcohol production - p _m kg/m³ maximum inhibition limit concentration for biomass production - p _m kg/m³ maximum inhibition limit concentration for alcohol production - q _p h^–1 specific production rate - q _p,max h^–1 maximum specific production rate for alcohol production - q _s h^–1 specific substrate consumption rate - Q _L m _gas ³ /m³h specific gas rate - r _p , r _s , r _x kg/(m³ · h) reaction rate for ethanol production substrate consumption and cell growth, respectively - S _F kg/m³ substrate concentration in feed stream - s kg/m³ substrate concentration - t h time - x kg/m³ biomass concentration - x _max kg/m³ maximum biomass concentration for biomass production - Y _p/s yield coefficient - h^–1 specific growth rate - _max h^–1 maximum specific growth rate - dimensionless time (t/) - h mean residence time - _s glucose conversion     

Improvement of lipase production by addition of catalase during fermentation

A batch fermentation process for lipase production with the recombinant strain Staphylococcus carnosus (pLipMut2) was studied in a bubble column. The rates of growth and lipase production in this type of fermentor were compared with results from shakeflasks. It was seen that cultivation in the bubble column resulted in a prolonged lag time and a reduced lipase activity in comparison to flask cultures. However, by addition of catalase during the fermentation in the bubble column this different behaviour could be avoided. Correspondence to: E. Wenzig     

High yeast concentration in continuous fermentation with cell recycle obtained by tangential microfiltration

Summary Continuous fermentation fed by 150 kg/m³ of glucose with total cell recycling by tangential microfiltration enabled yeasts concentration of 300 kg/m³ (dry weight) to be reached with a dilution rate of 0,5h^–1 and a cell viability greater than 75%. The stability of this system was tested for 50 residence times of the permeate. The method can be used both for the production of cell concentrates and for high rates of metabolite production.Nomenclature D. W. dry weight - X_T (kg/m³) total cell concentration D.W. - X_V (kg/m³) viable cell concentration D.W. - V viability of cell culture in per cent of total cell concentration - S (kg/m³) glucose concentration - P (kg/m³) ethanol concentration - D (h) dilution rate - R (kg/kg) fermentation yield - (h) specific growth rate - vp(kg/kg/h) specific alcohol production rate - (m) yeast size - (kg/kg) kg of intracellular water per kg of dry cells