Mathematical modeling of production of microbial lipids

As a part of the investigations on the microbial lipid production using the yeast Rhodotorula gracilis, CFR-1, kinetics of the biomass synthesis has been studied using shake flask experiments. Using a medium containing a carbon to nitrogen ratio of 701, the rates of biomass production were followed at different initial substrate concentrations in the range of 20–100 kg/m³. A logistic model was found to be reasonably adequate to describe the kinetics of the growth of biomass; the maximum specific growth rate of 0.105 h^–1 was applicable for substrate concentrations less than 60 kg/m³, which gave reasonable agreement between predicted and actual biomass concentration values.List of Symbols S ₀, X ₀ kg/m³ Initial concentrations of sugar, non lipid biomass respectively - X, X(t) kg/m³ Concentrations of non lipid biomass at any time t - dX/dt kg/(m³ · h) Rate of biomass growth - h^–1 Specific growth rate - _max h^–1 Maximum specific growth rate - K _s mol/dm³ Monods constant - X _max kg/m³ Maximum biomass reached in a run     

Intraparticle mass-transfer resistance and apparent time stability of immobilized yeast alcohol dehydrogenase

The stability and, consequently, the lifetime of immobilized enzymes (IME) are important factors in practical applications of IME, especially so far as design and operation of the enzyme reactors are concerned. In this paper a model is presented which describes the effect of intraparticle diffusion on time stability behaviour of IME, and which has been verified experimentally by the two-substrate enzymic reaction. As a model reaction the ethanol oxidation catalysed by immobilized yeast alcohol dehydrogenase was chosen. The reaction was performed in the batch-recycle reactor at 303 K and pH-value 8.9, under the conditions of high ethanol concentration and low coenzyme (NAD⁺) concentration, so that NAD⁺ was the limiting substrate. The values of the apparent and intrinsic deactivation constant as well as the apparent relative lifetime of the enzyme were calculated.The results show that the diffusional resistance influences the time stability of the IME catalyst and that IME appears to be more stabilized under the larger diffusion resistance.List of Symbols C _A, C_B, C_E mol · m^–3 concentration of coenzyme NAD⁺, ethanol and enzyme, respectively - C _p mol · m³ concentration of reaction product NADH - d _p mm particle diameter - D _eff m² · s^–1 effective volume diffusivity of NAD⁺ within porous matrix - k _d s^–1 intrinsic deactivation constant - K _A, K_A, K_B mol · m^–3 kinetic constant defined by Eq. (1) - K _A ^x mol · m^–3 kinetic constant defined by Eq. (5) - r _A mol · m^–3 · s^–1 intrinsic reaction rate - R m particle radius - R _v mol · m^–3 · s^–1 observed reaction rate per unit volume of immobilized enzyme - t _E s enzyme deactivation time - t _r s reaction time - V mol · m^–3 · s^–1 maximum reaction rate in Eq. (1) - V ^x mol · m^–3 · s^–1 parameter defined by Eq. (4) - V _f m³ total volume of fluid in reactor - w _s kg mass of immobilized enzyme bed - factor defined by Eqs. (19) and (20) - kg · m^–3 density of immobilized enzyme bed - unstableness factor - effectiveness factor - Thiele modulus - relative half-lifetime of immobilized enzyme Index o values obtained with fresh immobilized enzyme     

Modelling continuous culture of Rhodospirillum rubrum in photobioreactor under light limited conditions

Rhodospirillum rubrum was grown continuously and photoheterotrophically under light limitation using a cylindrical photobioreactor in which the steady state biomass concentration was varied between 0.4 to 4 kg m^–3 at a constant radiant incident flux of 100 W m^–2. Kinetic and stoichiometric models for the growth are proposed. The biomass productivities, acetate consumption rate and the CO₂ production rate can be quantitatively predicted to a high level of accuracy by the proposed model calculations. Nomenclature: C _X, biomass concentration (kg m^–3) D, dilution rate (h^–1) Ea, mean mass absorption coefficient (m² kg^–1) I , total available radiant light energy (W m^–2) K, half saturation constant for light (W m^–2) R _W, boundary radius defining the working illuminated volume (m) r _X, local biomass volumetric rate (kg m^–3 h^–1) <r _X>, mean volumetric growth rate (kg m^–3 h^–1) V _W, illuminated working volume in the PBR (m^–3). Greek letters: , working illuminated fraction (–) _M, maximum quantum yield (–) bar, mean energetic yield (kg J^–1).     

Mathematical modeling of production of microbial lipids

In the microbial lipid production system using the yeast Rhodotorula gracilis, CFR-1, kinetics of lipid accumulation and substrate utilisation at initial substrate concentrations in the range of 20–100 kg/m³ were investigated using shake flask experiments. A mathematical representation based on logistic model for biomass and Luedeking-Piret model for lipid accumulation gave reasonably good agreement between the theoretical and experimental values for substrate concentration less than 60 kg/m³. The kinetic expressions and parameters obtained through shake flask studies were directly applied to experiments in the laboratory fermentors also and the models were found to hold good for the prediction of the change of biomass, product as well as substrate with time. The attainment of a saturation in the intracellular lipid accumulation with time, however, was not predicted by the model which was shown to be an inherent feature of the Luedeking-Piret model.List of Symbols S ₀, P ₀ kg/m³ Initial concentrations of sugar and lipid respectively - S, S(t) kg/m³ Concentrations of sugar and lipid respeclively at any timet - p,p(t) L kg/m³ Maximum concentration of lipid produced - E % Maximum sugar utilised - dP/dt kg/(m³ · h) Rate of lipid production - -dS/dt kg/(m³ · h) Rate of sugar utilisation - _max h^–1 Maximum specific growth rate - X _max kg/m³ Maximum biomass reached in a run - P _max kg/m³ Maximum product concentration - m, n Constants used in Luedeking-Piret model in eq. (7) - , Constants used to predict residual sugar - k _e maintainance coefficient - Y _x g/g Biomass yield based on sugar consumed - Y _p g/g Lipid yield based on sugar consumed - (dP/d t)_stat kg/(m³ · h) Rate of lipid production at stationary phase - (dS/dt)_stat kg/(m³ · h) Rate of sugar utilisation at stationary phase     

Process engineering aspects of the bioleaching of copper ores

The bioleaching of minerals is a complex process that is affected by a number of biological, mineralogical, electrochemical and engineering factors. This work presents and discusses the most significant process engineering aspects involved in the bacterial leaching of copper ores, i.e. bacterial population, type of mineral and particle size, nutrients and inhibitors, oxygen and carbon dioxide, temperature and pH, leaching kinetics and operation mode.It is concluded that more work is needed in this area in order to gain a deeper insight in the many factors that govern this process. This would allow to significantly improve its overall productivity.List of Symbols C _L kg/m³ dissolved oxygen concentration - C ^* kg/m³ equilibrium oxygen concentration - d, e, f, g % percentage of C, H, O and N in the cell - D m impeller diameter - K consistency index - K _S, K₁, K_c constants - k _La h^–1 volumetric oxygen transfer coefficient - M _b mol/kg biomass apparent molecular weight - N s^–1 rotation frequency - n behavior index - P kg/m³ ungassed agitation power, product concentration - P _g kW/m³ gassed agitation power - p % pulp density - Q m³/h air flow rate - S kg/m³ limiting substrate concentration - W kg/(m³ · h) mass transfer rate per unit volume - X cells/cm³ biomass concentration - Y _o g cells/g Fe oxygen cell yield - Y _x g cells/g Fe substrate cell yield - h^–1 specific growth rate - _m h^–1 maximum specific growth rate     

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     

Phytoplankton and zooplankton (Cladocera,Copepoda) relationship in the eutrophicated River Danube (Danubialia Hungarica,CXI)

The seasonal variation in primary production, individual numbers, and biomass of phyto- and zooplankton was studied in the River Danube in 1981. The secondary production of two dominant zooplankton species (Bosmina longirostris and Acanthocyclops robustus) was also estimated. In the growing season (April–Sept.) individual numbers dry weights and chlorophyll a contents of phytoplankton ranged between 30–90 × 10⁶ individuals, l^–1, 3–12 mg l^–1, and 50–170 µg l^–1, respectively. Species of Thalassiosiraceae (Bacillariophyta) dominated in the phytoplankton with a subdominance of Chlorococcales in summer. Individual numbers and dry weights of crustacean zooplankton ranged between 1400–6500 individuals m^–3, and 1.2–12 mg m^–3, respectively. The daily mean gross primary production was 970 mg C m^–3 d^–1, and the net production was 660 mg C m^–3 d^–1. Acanthocyclops robustus populations produced 0.2 mg C m^–3 d^–1 as an average, and Bosmina longirostris populations 0.07 mg C m^–3 d^–1. The ecological efficiency between phytoplankton and crustacean zooplankton was 0.03%.     

Fermentation ofCandida utilis for uricase production

Summary Conditions for the production of microbial uricase byCandida utilis were studied. For the selected strain, hypoxanthine proved to be the most effective inducer of uricase formation. The highest values of biomass as well as uricase activity in the mechanically agitated fermentor were obtained under the following conditions: 50 h, rotation impeller speed 7 s^–1, air flow rate 1.25×10^–5 m³s^–1, concentration of inducer 0.1%.List of symbols b width of baffle, m - c length of baffle, m - D diameter of cylindrical fermentor, m - d diameter of impeller, m - d ₁ diameter of impeller disc, m - Fr _m impeller Froud number - g gravitional acceleration, ms^–2 - H height of batch surface above bottom, m - H ₂ height of impeller disc above bottom, m - h height of impeller blade, m - Kp _g flow rate number - L length of impeller blade, m - N rotational speed of impeller, s^–1 - Re _m impeller Reynolds number - T time, h - V volume of batch, m³ - V _g air (gas) flow rate, m³s^–1 - x mass fraction of the dry matter of cells - x ₀ initial value of the mass fraction of the dry matter of cells - _r volume fraction of the dry matter of cells - <eta<₁ viscosity of pure liquid, Pa s - viscosity of batch (suspension of microbial suspension), Pa s - density of batch, kg m^–3     

The effect of pH on kinetic and yield parameters during the ethanolic fermentation of D-xylose with Pachysolen tannophilus

We have studied the ethanolic fermentation of D-xylose with Pachysolen tannophilus in batch cultures. We propose a model to predict variations in D-xylose consumed, and biomass and ethanol produced, in which we include parameters for the specific growth rate, for the consumption of D-xylose and production of ethanol either related or not to growth.The ideal initial pH for ethanol production turned out to be 4.5. At this pH value the net specific growth rate was 0.26 h^–1, biomass yield was 0.16 g.g^–1, the cell-maintenance coefficient was 0.073 g.g^–1.h^–1, the parameter for ethanol production non-related to growth was 0.064 g.g^–1,h^–1 and the maximum ethanol yield was 0.32 g.g^–1.List of Symbols A _c Carbon atomic weight - a _d1/h Specific cell-maintenance rate defined in Eq. (8) - c Mass fraction of carbon in the biomass - E g/l Ethanol concentration - f _x Correction factor defined in Eq. (13) - f _x Correction factor defined in Eq. (13) - f _xi Correction factor defined in Eq. (14) - k _d1/h Death constant - M _E Ethanol molecular weight - M _s Xylose molecular weight - M _xi Xylitol molecular weight - m g xylose/g biomass Maintenance coefficient for substrate - m _dg xylose/g biomass Maintenance coefficient when k _d - q _Eg ethanol/g biomass. Specific ethanol production rate - s g/l Residual xylose concentration - s ₀ g/l Initial xylose concentration - t h Time - x g/l Biomass concentration - x ₀ g/l Initial biomass concentration - Y _E/sg ethanol/g xylose Instantaneous ethanol yield - ¯Y _E/sg ethanol/g xylose Mean ethanol yield - Y _E ^s/T g ethanol/g xylose Theoretical ethanol yield - Y _E ^s/* g ethanol/g xylose Corrected instantaneous ethanol yield - ¯Y _E ^s/* g ethanol/g xylose Corrected mean ethanol yield - Y _x/sg biomass/g xylose Biomass yield - ¯Y _xi/sg xylitol/g xylose Mean xylitol yield Greek Letters g ethanol/g biomass Growth-associated product formation parameter - g ethanol/g biomass.h Non-growth-associated product formation parameter - _dg ethanol/g biomass.h Non-growth-associated product formation parameter when k _d0 - h Variable defined in Eq. (6) or Eq. (7) - 1/h Specific growth rate - _m1/h Maximum specific growth rate     

Organic reduction of tapioca wastewaters using modified RBC

A modified Rotating Biological Contactor (RBC) was used for the treatability studies of synthetic tapioca wastewaters. The RBC used was a four stage laboratory model and the discs were modified by attaching porous nechlon sheets to enhance biofilm area. Synthetic tapioca wastewaters were prepared with influent concentrations from 927 to 3600 mg/l of COD. Three hydraulic loads were used in the range of 0.03 to 0.09 m³·m^–2·d^–1 and the organic loads used were in the range of 28 to 306 g COD· m^–2·d^–1. The percentage COD removal were in the range from 97.4 to 68. RBC was operated at a rotating speed of 18 rpm which was found to be the optimal rotating speed. Biokinetic coefficients based on Kornegay and Hudson models were obtained using linear analysis. Also, a mathematical model was proposed using regression analysis.List of Symbols A m² total surface area of discs - d m active depth of microbial film onany rotating disc - K _s mg ·l^–1 saturation constant - P mg·m^–2·^–1 area capacity - Q l·d^–1 hydraulic flow rate - q m³·m^–2·d^–1 hydraulic loading rate - S ₀ mg·l^–1 influent substrate concentration - S _e mg·l^–1 effluent substrate concentration - w rpm rotational speed - V m³ volume of the reactor - X _f mg·l^–1 active biomass per unit volume ofattached growth - X _s mg·l^–1 active biomass per unit volume ofsuspended growth - X mg·l^–1 active biomass per unit volume - Y _s yield coefficient for attachedgrowth - Y _A yield coefficient for suspendedgrowth - Y yield coefficient, mass of biomass/mass of substrate removed Greek Symbols hr mean hydraulic detention time - (_max)_A d^–1 maximum specific growth rate forattached growth - (_max)_s d^–1 maximum specific growth rate forsuspended growth - _max d^–1 maximum specific growth rate - d^–1 specific growth rate - _v mg·l^–1·hr^–1 maximum volumetric substrateutilization rate coefficient     

Kinetics of inhibition in propionic acid fermentation

The inhibitory effect of propionic acid P and biomass concentration X is studied in batch and continuous fermentations with cell recycle.In batch fermentations, the specific growth rate decreases and cancels out at a critical propionic acid concentration Pc ₁; the formerly decreasing specific production rate becomes constant after Pc ₁ and cancels out when a second critical propionic acid concentration Pc ₂ is reached.In continuous fermentation with cell recycle, a similar inhibition is observed with biomass. The specific rates decrease and become constant at a critical biomass concentration Xc. They cancel out at different high biomass concentrations.In both cases, the specific production rate can be related to the specific growth rate by the Luedeking and Piret expression: =+, [1], where the constants and are determined by the fermentation parameters.List of Symbols t h time - X kg/m³ biomass concentration - P kg/m³ propionic acid concentration - A kg/m³ acetic acid concentration - S kg/m³ lactose concentration - dX/dt kg/(m³h) instantaneous rate of cell growth - dP/dt kg/(m³h) instantaneous rate of propionic acid production - h^–1 specific growth rate - h^–1 specific propionic acid production rate - D h^–1 dilution rate     

Model for the production of L-tryptophan from L-serine and indole by immobilized cells in a three-phase liquid-impelled loop reactor

Production of L-tryptophan from L-serine and indole catalyzed by Escherichia coli, immobilized in k-carrageenan gel beads, is technically feasible in the liquidimpelled loop reactor (LLR), using an organic solvent, e.g. n-dodecane.With L-serine in large excess intrinsic reaction kinetics is approximately first order with respect to indole, with a reaction constant of 8.5×10^–5 m³ kg _dw ^–1 s^–1.The overall process kinetics is jointly controlled by intrinsic kinetics and by intraparticle mass transfer resistance, which can be quantified using an effectiveness factor.Mass transfer of indole from the organic to the aqueous phase and from the aqueous to the gel phase are relatively fast and thus have negligible influence in the overall process kinetics, under the operational conditions tested. However, they may become important if the process is intensified by increasing the cell concentration in the gel and/or the gel hold-up in the reactor.A simple model which includes indole mass balances over the aqueous and organic phases, mass transfer and reaction kinetics, with parameters experimentally determined in independent experiments, was successful in simulating L-tryptophan production in the LLR.List of Symbols a, b, c coefficients of the equilibrium curve for indole between organic and aqueous phases - A, B, C, D, E, F auxiliary variables used in liquid-liquid mass transfer studies - a _x specific interfacial area referred to the volume of the aqueous phase (m^–1) - A _x interfacial area (m²) - a _Y specific interfacial area referred to the volume of the organic phase (m^–1) - A _Y interfacial area (m²) - C _b substrate concentration in the bulk of the aqueous phase (kg m^–3) - C _e substrate concentration in exit stream (kg m^–3) - C _E biocatalyst concentration referred to the aqueous phase (kg m^–3) - C _{E s} biocatalyst concentration referred to the volume of gel (kg m^–3) - C _s substrate concentration at the gel surface (kgm^–3) - d, e, f coefficients of the equilibrium curve for indole between aqueous and organic phases - dp particle diameter (m) - K ₂ kinetic constant (s^–1) - K ₁ kinetic constant K₂/K_M (kg^–1 m³ s^–1) - K _M Michaälis-Menten constant (kgm^–3) - K _X mass transfer coefficient referred to the aqueous phase (ms^–1) - K _Xa_X volumetric mass transfer coefficient based on the volume of the aqueous phase (s^–1) - k _Y mass transfer coefficient referred to the organic phase (ms^–1) - K _Ya_Y volumetric mass transfer coefficient based on the volume of the organic phase (s^–1) - N _X mass flux of indole from organic to aqueous Phase (kg m^–2s^–1) - N _Y mass flux of indole from aqueous to organic phase (kg m^–2s^–1) - Q _e volumetric flow rate in exit stream (m³s^–1) - Q _f volumetric flow rate in feed stream (m³s^–1) - _obs observed reaction rate (kg s^–1 m^–3) - intrinsic reaction rate (kg s^–1 m^–3) - Re Reynolds number - Sc Schmidt number - Sh Sherwood number - t time (s) - u superficial velocity (m s^–1) - V _max maximum reaction rate (kg s^–1m^–3) - V _S volume of the support (m³) - V _X volume of aqueous phase (m³) - V _Y volume of the organic phase (m³) - X indole concentration in the aqueous phase (kgm^–3) - Y indole concentration in the organic phase (kg m^–3 Greek Letters overall effectiveness factor - _e external effectiveness factor - _i internal effectiveness factor - Thiele module A fellowship awarded to one of us (D.M.R.)by INICT is gratefuly acknowledged.     

Model aided design of repeated fed-batch penicillin fermentation

Structured models of antibiotic fermentation that quantify maturation and aging of product forming biomass are fitted to experimental data. Conditions of superiority of repeated fed batch cultivation are characterized on the basis of a performance criterion that includes penicillin productivity and costs of operation. Emphasis is placed on the relevance of such research to the model aided design of optimal cyclic operation.List of Symbols c IU/mg cost factor - D s^–1 dilution rate - J IU · cm^–3 · h^–1 net productivity - k _p IU · mg^–11 · h^–1 specific product formation rate - k _pm IU · mg^–1 · h^–1 maximum specific product formation rate - p IU/cm³ concentration of penicillin - T s final time of fermentation - t s fermentation time - X kg/m³ concentration of biomass dry weight - X ₁kg/m³ concentration of young, immature biomass - X ₂ kg/m³ concentration of mature product forming biomass - X _c kg/m³ biomass concentration of the end of growth phase - X _mkg/m³ maximum biomass concentration Greek Letters s^–1 specific maturation rate - s^–1 specific aging rate - s^–1 specific growth rate - _m s^–1 maximum specific growth rate - _p s^–1 specific growth rate during the product formation phase - s cycle time - % volume fraction of draw-off Abbreviations CC chemostat culture - RFBC repeated fed batch culture - RBC repeated batch culture     

Determination of the inherent kinetics of immobilized glucose oxidase using a diffusion cell

The enzyme glucose oxidase (GO) was covalently immobilized onto a poly(vinyl alcohol) hydrogel, cross-linked with glutardialdehyde and a polyazonium salt. To compare the kinetic parameters of immobilized GO with the known kinetic parameters of soluble GO, the diffusion cell method was used.Between two compartments, containing solutions with different glucose concentrations, a GO-containing hydrogel membrane was placed. Simultaneous diffusion through and enzymatic reaction in the membrane occurred. In this way diffusional effects of the membrane could be eliminated from the effective kinetic parameters to yield the inherent kinetic parameters.It appeared that the enzymatic reaction is independent of the oxygen concentration at oxygen concentrations 0.22 mol m^–3 (Michaelis constant for oxygen < 0.22 mol m^–3). Further, the Michaelis constant for glucose does not change dramatically after immobilizing the enzyme. The maximal reaction rate is depending on the enzyme concentration. As the enzyme concentration in the membrane is not exactly known (mainly due to leakage of enzyme out of the membrane during membrane preparation), only an estimation of the turnover number can be made.The diffusion cell method is easy to carry out. Still, some recommendations can be made on the performance.List of Symbols _g , _0x partition coefficient of glucose and oxygen, respectively - thickness of the wetted membrane (m) - A _m surface area of membrane (m^–2) - C constant (mol² m^–3) - c _g , c _0x concentration of glucose and oxygen, respectively (mol m^–3) - c _g,0 c _g, glucose concentration at the filter-paper/membrane interface next to compartment A and B, respectively (mol m^–3) - c _{g, A} c _{g, B} glucose concentration in compartment A and B, respectively (mol m^–3) - c _GO glucose oxidase concentration (mol m^–3) - D _eff effective diffusion coefficient (m² s^–1) - D _m , D _sl diffusion coefficient in, respectively, the membrane and the solution layer (m² s^–1) - d _dl , d _df , d _sl thickness of, respectively, the diffusion layer, the filter-paper and the solution layer (m) - h _B initial slope of concentration versus time curve of compartment B (mol m^–3 s^–1) - J flux (mol m^–2 s^–1) - J ₀ flux in the membrane at membrane/filter-paper interface next to compartment A and B, respectively (mol m^–2 s^–1) - J _A , J _B flux leaving compartment A and entering compartment B, respectively (mol m^–2 s^–1) - J _m flux through the membrane (mol m^–2 s^–1) - k total mass transfer coefficient (m s^–1) - k ₁ , k ₂ rate constant of a particular reaction step (m³ mol^–1 s^–1) - k_–1, k_–2 rate constant of a particular reaction step (s^–1) - k _cat (intrinsic) catalytic constant of turnover number (s^–1) - k _cat ^* inherent catalytic constant, determined by inserting D _m (s^–1) - k _cat ^** inherent catalytic constant, determined by inserting D _eff (s^–1) - k _m (g) (intrinsic) Michaelis constant for glucose (mol m^–3) - k _m (o) (intrinsic) Michaelis constant for oxygen (mol m^–3) - k _m ^* (g) inherent Michaelis constant for glucose (mol m^–3) - k _m ^* (o) inherent Michaelis constant for oxygen (mol m^–3) - m _GO number of moles of GO present (mol) - P _m permeability of glucose in the mebrane (m s^–1) - P _eff effective permeability (m s^–1) - V volume (m³) - v ₀ initial reaction velocity (mol m^–3 s^–1) - V _max ^** inherent maximal reaction velocity, determined by inserting D_eff (mol m^–3 s^–1) - x distance (m)     

Analysis of continuous fermentation processes in aqueous two-phase systems

Simulations of continuous ethanol or acetonobutylic fermentations in aqueous two-phase systems show that at high substrate feed concentrations it is possible to obtain solvent productivities about 25–40% higher than in conventional systems with cell recycle if the biomass bleed rate is kept about one tenth of the value of D.List of Symbols a Volumetric fraction of dextran rich phase - B h^–1 Bleed rate - D h^–1 Dilution rate - P kg m^–3 Product concentration - PD kg m^–3 h^–1 Productivity - S kg m^–3 Substrate - X kg m^–3 Biomass - Partition coefficient     

Ulva rigida (Ulvales,Chlorophyta) tank culture as biofilters for dissolved inorganic nitrogen from fishpond effluents

Ulva rigida was cultivated in 7501 tanks at different densities with direct and continuous inflow (at 2, 4, 8 and 12 volumes d^–1) of the effluents from a commercial marine fishpond (40 metric tonnes, Tm, of Sparus aurata, water exchange rate of 16 m³ Tm^–1) in order to assess the maximum and optimum dissolved inorganic nitrogen (DIN) uptake rate and the annual stability of the Ulva tank biofiltering system. Maximum yields (40 g DW m^–2 d^–1) were obtained at a density of 2.5 g FW 1^–1 and at a DIN inflow rate of 1.7 g DIN m^–2 d^–1. Maximum DIN uptake rates were obtained during summer (2.2 g DIN M^–2 d^–1), and minimum in winter (1.1 g DIN m^–2 d^–1) with a yearly average DIN uptake rate of 1.77 g DIN m^–2 d^–1 At yearly average DIN removal efficiency (2.0 g DIN m^–2 d^–1, if winter period is excluded), 153 m² of Ulva tank surface would be needed to recover 100% of the DIN produced by 1 Tm of fish.Abbreviations DIN= dissolved inorganic nitrogen (NH _inf4 ^sup+ + NO _inf3 ^sup– + NO _inf2 ^sup– ); - FW= fresh weight; - DW= dry weight; - PFD= photon flux density; - V= DIN uptake rate     

Cost minimization in the predesign of an enzymatic CSTR: an overall approach

The balance equations pertaining to the modelling of a CSTR performing an enzyme-catalyzed reaction in the presence of enzyme deactivation are developed. Combination of heuristic correlations for the size-dependent cost of equipment and the purification-dependent cost of recovery of product with the mass balances was used as a basis for the development of expressions relating a (suitably defined) dimensionless economic parameter with the optimal outlet substrate concentration under the assumption that overall production costs per unit mass of product were to be minimized. The situation of Michaelis-Menten kinetics for the substrate depletion and first order kinetics for the deactivation of enzyme (considering that the free enzyme and the enzyme in the enzyme/substrate complex deactivate at different rates) was explored, and plots for several values of the parameters germane to the analysis are included.List of Symbols C _E mol m^–3 concentration of active enzyme - C _E,0 mol m^–3 initial concentration of active enzyme - C _p mol m^–3 concentration of product of interest - C _s mol m^–3 concentration of substrate - C _s,0 mol m^–3 initial concentration of substrate - I $ capital cost of equipment - k _d s^–1 deactivation constant of free enzyme - k _d s^–1 deactivation constant of enzyme in enzyme/substrate complex - K _m mol m^–3 Michaelis-Menten constant - K _m dimensionless counterpart of K _m - k _r s^–1 rate constant associated with conversion of enzyme/substrate complex into product - M _w kg mol^–1 molecular weight of product of interest - P $ kg^–1 cost of recovery of product of interest in pure form - Q m³s^–1 volumetric flow rate - V m³ volume of reactor - X $ kg^–1 global manufacture cost of product of interest in pure form - X dimensionless counterpart of X Greek Symbols ₁ $ m^–1.8 constant - ₂ $ m^–3 constant - t s useful life of CSTR - ₀ ratio of initial concentrations of enzyme and substrate - ratio of deactivation constant of free enzyme to rate constant of depletion of substrate - ratio of deactivation constants - univariate function expressing the dependence of the rate of enzyme deactivation on C _S - univariate function expressing the dependence of the rate of substrate depletion on C _S - dimensionless economic parameter     

Development of reactor model for glucose isomerization catalyzed by whole-cell immobilized glucose isomerase

Based on the kinetic constants determined and the mathematical model of the reactor system developed, the performance of axial flow packed bed continuous enzyme reactor system was studied experimentally and also simulated with the aid of a computer for ultimate objective of optimization of the glucose isomerase reactor system.A reactor model was established analogous to heterogeneous catalytic reactor model taking into account the effect of fluid mass transfer and reversible kinetics. The investigated catalyst system consists of immobilized Streptomyces bambergiensis cells containing the enzyme glucose isomerase, which catalyzes the isomerization of glucose to fructose.List of Symbols A ₀, A ₁, A ₂ parameters in axial dispersion reactor model - c _go, c_g, c_gemol m^–3 glucose concentration at time t=0, at any time and at equilibrium conditions - c _gsmol m^–3 glucose concentration at particle surface - C dimensionless glucose concentration - d _pm particle diameter - d _rm diameter of reactor tube - Da Damkohler number - D _eff m² s^–1 effective glucose diffusion coefficient in Ca-alginate gel beads - k _fm s^–1 film transfer coefficient - K _e equilibrium constant - K _mg, K_mfmol m^–3 Michaelis-Menten constant for glucose and fructose, respectively - K _mmol m^–3 modified Michaelis-Menten constant - K dimensionless parameter - K ^* dimensionless parameter - L m length of reactor tube - Pe Peclet number - Pe _p particle Peclet number - Q m³ s^–1 volumetric flow rate - (-r _g) mol m^–3 s^–1 reaction rate - Re _p Reynolds particle number - Sc Schmidt number - Sh Sherwood number - t s time - v ₀ m s^–1 linear superficial fluid velocity - V _mg, V_mfmol g^–1 s^–1 maximal reaction rate for glucose and fructose, respectively - V _mmol m^–3 s^–1 modified maximal reaction rate for glucose - V _mg ^x mol m^–2 s^–1 maximal reaction rate for glucose - X _g, X_ge glucose conversion and glucose conversion at equilibrium conditions - X normalized conversion - Y dimensionless glucose concentration - void fraction of fixed bed - effectiveness factor of biocatalyst - Pa s kinematic viscosity of substrate - ₁ s first absolute weighted moment - ₂ s² second central weighted moment - _gkg m^–3 substrate density - _pkg m^–3 particle density - ² dimensionless variance of RTD curve - s residence time     

Oxygen controlled batch cultivations of Schizophyllum commune for enhanced production of branched β-1,3-glucans

Oxygen and shear stress are the key factors for enhanced glucan production with Schizophyllum commune. During batch cultivation control of or (specific oxygen uptake rate) was achieved by variation of the impeller speed. Biomass was modelled by using the carbon and oxygen balance derived from exhaust data. At mycel growth a of 0.042 h^–1 presents just the border before oxygen limitation arises and is simultaneously the optimum operation condition for maximum glucan formation. Related to an overall cultivation time of 72 h a maximum of both productivity (4.3 kg m^–3 d^–1) and yield (13 kg m^–3) were obtained.List of Symbols C kg m^–3 concentration - k _L a h ^–1 volume related oxygen transfer coefficient - K _s mol m^–3 substrate saturation constant - N rpm impeller speed - % oxygen partial pressure of the liquid phase - kg m^–3h^–1 oxygen uptake rate - h^–1 specific oxygen uptake rate, kg O₂ (kg biomass h)^–1 - t h time - yield coefficient (biomass formed/oxygen consumed) Greek Symbols h^–1 specific growth rate Indices O ₂ oxygen - X biomass - L liquid phase - * gas/liquid interface - S substrate (glucose) Dedicated to the 65th birthday of Professor Fritz Wagner.This work was kindly supported in parts by B. Braun Biotech International. The authors are grateful to Prof. Dr. Fritz Wagner for scientific support and appreciate the technical assistance of Detlev Rasch     

Bacterial productivity and microbial biomass in tropical mangrove sediments

Bacterial productivity (³H-thymidine incorporation into DNA) and intertidal microbenthic communities were examined within five mangrove estuaries along the tropical northeastern coast of Australia. Bacteria in mangrove surface sediments (0–2 cm depth) were enumerated by epifluorescence microscopy and were more abundant (mean and range: 1.1(0.02–3.6)×10¹¹ cells·g DW^–1) and productive (mean: 1.6 gC·m^–2· d^–1) compared to bacterial populations in most other benthic environments. Specific growth rates (¯x=1.1) ranged from 0.2–5.5 d^–1, with highest rates of growth in austral spring and summer. Highest bacterial numbers occurred in winter (June–August) in estuaries along the Cape York peninsula north of Hinchinbrook Island and were significantly different among intertidal zones and estuaries. Protozoa (10⁵–10⁶·m^–2, pheopigments (0.0–24.1g·gDW^–1) and bacterial productivity (0.2–5.1 gC·m^–2·d^–1) exhibited significant seasonality with maximum densities and production in austral spring and summer. Algal biomass (chlorophylla) was low (mean: 1.6g·gDW^–1) compared to other intertidal sediments because of low light intensity under the dense forest canopy, especially in the mid-intertidal zone. Partial correlation analysis and a study of possible tidal effects suggest that microbial biomass and bacterial growth in tropical intertidal sediments are regulated primarily by physicochemical factors and by tidal flushing and exposure. High microbial biomass and very high rates of bacterial productivity coupled with low densities of meiofaunal and macroinfaunal consumers observed in earlier studies suggest that microbes may be a sink for carbon in intertidal sediments of tropical mangrove estuaries.