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     

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     

Integration of continuous production and recovery of solvents from whey permeate: use of immobilized cells of Clostridium acetobutylicum in a flutilized bed reactor coupled with gas stripping

An investigation was performed into the operation of an integrated system for continuous production and product recovery of solvents (acetone-butanol-ethanol) from the ABE fermentation process. Cells of Clostridium acetobutylicum were immobilized by adsorption onto bonechar, and used in a fluidized bed reactor for continuous solvent production from whey permeate. The reactor effluent was stripped of the solvents using nitrogen gas, and was recycled to the reactor. This relieved product inhibition and allowed further sugar utilization. At a dilution rate of 1.37 h^–1 a reactor productivity of 5.1 kg/(m³ · h) was achieved. The solvents in the stripping gas were condensed to give a solution of 53.7 kg/m³. This system has the advantages of relieving product inhibition, and providing a more concentrated solution for recovery by distillation. Residual sugar and non-volatile reaction intermediates are not removed by gas stripping and this contributes to high solvent yields.List of Symbols C kg/m³ Lactose concentration in reactor effluent - C _b kg/m³ Lactose concentration in bleed stream - C _c kg/m³ Lactose concentration in whey permeate feed - C _i kg/m³ Lactose concentration at reactor inlet - C _p kg/m³ Lactose concentration in condensed solvent stream (=0) - C _r kg/m³ Lactose concentration in recycle line (C _b=C _r) - C kg/h Amount of lactose utilized during certain time period - D h¹ Dilution rate of reactor, F _i/D=F/D - F dm³/h, m3/h F _i = Rate of feed flow to the reactor - F _b dm ³/h, m³/h Rate of bleed - F _c dm³/h, m³/h Rate of feed of whey permeate solution - F _p dm³/h, m³/h Rate of concentrated product removal - F _r dm³/h, m³/h Rate of recycle of stripped effluent to the reactor - P _l % Percent lactose utilization - R _l kg/(m³ · h) Overall lactose utilization rate - R _p kg/(m³ · h) Overall reactor (solvent) productivity - R _sl kg/h Rate of solvent loss - S kg/m³ Solvent concentration in reactor effluent - S _b kg/m³ Solvent concentration in bleed - S _c kg/m³ 0; Solvent concentration in concentrated whey permeate solution - S _i kg/m³ Solvent concentration at inlet of reactor - S _p kg/m³ Solvent concentration in concentrated product stream - S _r kg/m³ Solvent concentration in stripped effluent, S _r=S_b - S kg/h Amount of solvent produced from C amount of lactose in a particular time - ds/dt kg/(m³ · h) Rate of accumulation of solvents in the stripper - t h Time - V dm³, m³ Total reactor volume - V ¹ dm³, m³ Liquid volume in stripper - Y _P/S Solvent yield     

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     

Performance of cell immobilized packed bed bioreactor for continuous fermentation of alcohol

Experiments were conducted in a packed bed bio-reactor consisting of entrapped yeast cells in alginate matrix for continuous production of alcohol. The variables include initial substrate level, reactor diameter, diameter of the bead and residence time. The influence of these parameters on the conversion of substrate was studied. The film and pore diffusional effects were observed by varying the column and bead diameters, respectively. The pseudo first order reaction rate constant was calculated and correlated with the bead diameter. The effectiveness factor and the Thiele modulus were estimated. A correlation was proposed for fractional conversion in terms of operating variables. It is possible to predict the residence time required and volumetric productivity achieved in a bioreactor for any given initial substrate concentration at any fractional conversion obtained.List of Symbols a _m m²/kg surface are per unit mass of catalyst particle - D m diameter of the reactor - D _e m²/s effective diffusivity - d m particle diameter - h m bed height - k m/s first order reaction rate constant - k m³/(kg · s) pseudo first order reaction rate constant - k _in m³/(kg · s) intrinsic reaction rate constant, (=K/gh) - k _m m/s mass transfer coefficient - P kmol/(m³ · s) volumetric productivity - Q m³/s flow rate of the feed - S kmol/m³ substrate concentration at any time - S _o kmol/m³ initial substrate concentration - S _p kmol/m³ substrate concentration on the gel bead surface - t s reaction time - T (kg · cat · s)/m³ space time (weight of the biocatalyst/flow rate of the feed) - v kmol/(kg · cat · s) reaction rate - V _pfr m³ volume of the packed bed reactor - X [1-(S/S _o)] fraction of the substrate converted in to product Greek Symbols effectiveness factor - Thiele modulus - kg/m³ density of the catalyst particle - s residence time, (= D² h/4Q) - voidage     

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     

Production of glutamine by micro-gel bead-immobilized Corynebacterium glutamicum 9703-T cells in a stirred tank reactor

The effectiveness of using micro-gel bead-immobilized cells for aerobic processes was investigated. Glutamine production by Corynebacterium glutamicum, 9703-T, cells was used as an example. The cells were immobilized in Sr-alginate micro-gel beads 500 m in diameter and used for fermentation processes in a stirred tank reactor with a modified impeller at 400 min^–1. Continuous production of glutamine was carried out for more than 220 h in this reactor and no gel breakage was observed. As a result of the high oxygen transfer capacity of this system, the glutamine yield from glucose was more than three times higher, while the organic acid accumulation was more than 24 times lower than those obtained with 3.0 mm-gel bead-immobilized cells in an airlift fermentor under similar experimental conditions. During the continuous fermentations there was evolution and proliferation of non-glutamine producing strains which led to a gradual decrease in the productivity of the systems. Although a modified production medium which suppresses cell growth during the production phase was effective in maintaining the productivity, the stability of the whole system was shortened due to high cell deactivation rate in such a medium.List of Symbols C kg/m³ glutamine concentration - C _A mol/m ³ local oxygen concentration inside the gel beads - C _AS mol/m ³ oxygen concentration at the surface of the gel beads - De m²/h effective diffusion coefficient of oxygen in the gel bead - DO mol/m³ dissolved oxygen concentration - F dm³/h medium flow rate - K h^–1 glutamine decomposition rate constant - Km mol/m³ Michaelis Menten constant - QO _2max mol/(kg · h) maximum specific respiration rate - R m radius of the gel beads - r m radial distance - t h time - V _C dm ³ volume of the gel beads - V _L dm ³ liquid volume in the reactor - Vm mol/(m³ · h) maximum respiration rate - X kg/m³ cell concentration - x r/R - y C _A /C_AS - h^–1 cell deactivation rate constant - Thiele modulus defined by R(Vm/De Km) ^1/2 - C _AS /Km - _C kg/(m³-gel · h) specific glutamine formation rate - _c dm³-gel/dm³ V _C /V _L      

Ethanol production with Zymomonas mobilis with synthetic medium in batch operation

Ethanol was produced with Zymomonas mobilis Z6 (ATCC 29191), in batch culture with synthetic medium on glucose as substrate and in the presence of aspartate. The concentrations of glucose, phosphate, ammonium, ethanol and dissolved O₂ and CO₂ in the medium and O₂ and CO₂ in the outlet gas as well as the cell mass by culture fluorescence were measured on-line. Cell mass, glucose and aspartate concentrations were measured off-line. In the presence of a sufficient amount of aspartate, the ethanol inhibition effect can be reduced considerably. However, the improvement with yeast extract is more incisive. The relationship between the intensity of culture fluorescence and cell mass concentration is linear, if sufficient aspartate is present.List of Symbols ASP kg/m³ aspartate concentration - CTR kg/(m³ · h) CO₂ transfer rate - N, NH₄ kg/m³ nitrogen concentration from NH ₄ ⁺ - P kg/m³ product (ethanol) concentration - p% product (ethanol) yield - PO₄ kg/m³ phosphate concentration - Q _E kg/(kg · h) specific ethanol production rate - kg/(kg · h) specific nitrogen uptake rate from NH ₄ ⁺ - Q _P kg/(kg · h) specific phosphate uptake rate - Q _s kg/(kg · h) specific substrate (glucose) uptake rate - S kg/m³ glucose concentration - S _O kg/m³ initial glucose concentration - Y _x/s kg/kg yield coefficient - h^–1 specific growth rate     

Fed-batch culture of hybridoma cells: comparison of optimal control approach and closed loop strategies

Control of fed-batch culture of hybridoma cells was investigated based on two approaches optimal control theory and feedback control. Experiments were conducted for both approaches-with a feed enriched in glutamine. The optimal feed trajectory, a decreasing one, yielded a final monoclonal antibody (MAb) concentration of 170 mg/l, a three-fold increase compared to a typical batch operation.The feedback strategy relied on the on-line estimation of the net specific growth rate of cells from the measurement of the CO₂ production rate with a mass-spectrometer. A PI controller was then used to maintain the growth rate at a desired value by adjusting the dilution rate to the reactor. For the chosen set-point (0.1 d^–1), the final MAb concentration achieved was about 100 mg/1. It was found that there was a delay in the assimilation of the glutamine that should be included in the model to explain the lower MAb production in feedback mode. A higher production can be expected also for a lower set-point in feedback operation.List of Symbols Amm mM ammonia concentration - CPR l/(ld) carbon dioxide production rate - D _t l/d dilution rate - e _t l/d control error - F L/d feed flow rate - Glc mM glucose concentration - Gln mM glutamine concentration - Lac mM lactate concentration - I mg performance index - k _d l/d specific death rate - K _damm l/(mM · d) kinetic parameter for death rate - K _dgln mM kinetic parameter for death rate - K _dlac l/(mM·d) kinetic parameter for death rate - K _c l controller gain - K _glc mM kinetic parameter for growth rate - K _gln mM kinetic parameter for growth rate - K _tr L/(cell·d) transport coefficient - K l/d kinetic parameter for Mab production - m _glc mM/(cell·d) maintenance coefficient - M _Ab mg/l monoclonal antibody concentration - P _t covariance matrix - q _glc l/(l·cell·d) specific CO₂ production rate - q _glc mM/(cell·d) specific glucose uptake rate - q _gln mM/(cell·d) specific glutamine uptake rate - q _Mab mg/(l·cell·d) specific monoclonal antibody production - t _f d final culture time - T d sampling rate - u control input - V l reactor volume - X cell/l total cells concentration - X _v cell/l viable cells concentration - Y yield coefficient Greek mg/cell variable yield coefficient - ₀ mg/(cell·d) growth-associated kinetic parameter - mg/(cell·d) non growth-associated kinetic parameter - _t+1 defined by Eq. (19) - forgetting factor - l/d specific growth rate - _max l/d specific growth rate - _i d controller integral time constant     

Process kinetic analysis of pleuromulin fermentation

The industrial production of pleuromulin, an example for the production of secondary metabolites, has been carried out of the corporation Biochemie Kundl/Austria. The results of the experiments, especially the process kinetics are analyzed following the principles of the integrating strategy, which has been developed by the authors.Experiments on technical and laboratory scale were carefully designed and evaluated in order to allow an adequate insight in to this complex bioprocess. Typical plots are presented to illustrate the general macroscopic behaviour which serve as a reliable basis for process quantification.Mathematic modelling of this bioprocess will be presented in a following paper.List of Symbols n l/min rotational speed - P kg/m³ pleuromulin concentration - q _P h^–1 specific production rate - q _S1 h^–1 specific rate of glucose consumption - q _S2 h^–1 specific rate of oil consumption - r _P kg/m³ · h product formation rate - r _S1 kg/m³ · h glucose consumption rate - r _X kg/m³ · h growth rate - S ₁ kg/m³ glucose concentration - S ₂ kg/m³ oil concentration - T °C temperature - t h, d time - _g m³/h gas flow rate - X kg/m³ mycelium dry weight - Y _i/j yield coefficient - _app mPa s apparent viscosity - h^–1 specific growth rate The authors extend their gratitude to Biochemie Kundl Gmbh, where the experimental work has been carefully carried out     

Dynamics of production oftrans-zeatin andtrans-zeatin riboside by immobilized cytokinin-autonomous and cytokinin-dependent tobacco cells

Two strains of cultured tobacco cells (Nicotiana tabacum L. cv. Wisconsin 38) differing in their requirement for exogenous cytokinins (cytokinin-dependent and cytokinin-autonomous) were immobilized on polyphenylenoxide (Sorfix) activated with glutaraldehyde. Columns packed with immobilized cells were continually eluted with diluted Murashige and Skoog's medium lacking or supplemented with synthetic cytokinin (6-benzylaminopurine; BA). Purified samples of column eluates were fractionated by HPLC, andtrans-zeatin (t-Z) andtrans-zeatin riboside (t-ZR) content was estimated by enzyme immunoassay. Both cytokinin-autonomous and cytokinin-dependent tobacco cells produced and excretedt-Z and its riboside, and there were significant quantitative differences between the strains. The steady-state excretion rate oft-Z was 19.8 ng · g^–1 dw · h^–1 and 4 ng · g^–1 dw · h^–1, respectively, and that oft-ZR 4 ng · g^–1 dw · h^–1 and 1 ng · g^–1 dw · h^–1, respectively. Exposure of cytokinin-dependent cells to BA after 72 h of starving for this synthetic cytokinin caused temporary increase in excretion of both zeatin and its riboside. After the application of 5 M BA for 24 h, the excretion rate oft-ZR reached 5 ng · g^–1 dw · h^–1 (5-fold increase), and that oft-Z achieved 12 ng · g^–1 dw · h^–1 (3-fold increase). The elevation oft-Z excretion was delayed about 13 h compared witht-ZR excretion, which started increasing almost immediately after BA application. A pulse of BA in lower concentration (1.5 M for 30 h) provoked lower response.     

Biotransformation of cephalosporin C to 7-aminocephalosporanic acid with coimmobilized biocatalyst in a batch bioreactor

The permeabilized cells of Trigonopsis variabilis CCY 15-1-3 having D-amino acid oxidase (DAAO) activity were used to convert cephalosporin C (CPS-C) into 7-(-ketoadipyl amido) cephalosporanic acid (CO-GL-7-ACA) in a batch bioreactor with good aeration and stirring during the process. The deacylation of 7--(4-carboxybutanamido)-cephalosporanic acid (GL-7-ACA) to 7-cephalosporanic acid (7-ACA) by permeabilized cells of Pseudomonas species 3635 having 4--(4-carboxybutamido)-cephalosporanic acid acylase (GL-7-ACA acylase) activity was performed in a batch bioreactor. A spectrophotometric method for the determination of CO-GL-7-ACA and 7-ACA was proposed. Experimental data were fitted by non-linear regression with parameters optimization. The sorption method (without reaction) was applied for the determination of cephalosporin effective diffusion coefficients in Ca-pectate gel beads. These beads were prepared by dropping a potassium pectate gel suspension of inactive permeabilized cells of Trigonopsis variabilis and Pseudomonas species, crosslinked with glutaraldehyde, into a stirred 0.2 M calcium chloride solution. Concentrations of appropriate cephem components were measured by the refractive method. Values of effective diffusion coefficients were calculated by the Fibbonacci optimization method.List of Symbols c _L mol/dm³ concentration on the surface of a bead - c _L0 mol/dm³ initial cephalosporin concentration - c _L mol/dm³ equilibrium cephalosporin concentration in the solution - c _s1 mol/dm³ concentration of CPS-C - c _s2 mol/dm³ concentration of GL-7-ACA - D _ei m²/s effective diffusion coefficient of the components - K _i mol/dm³ inhibition parameter in Eq. (2) - K _{m i} mol/dm³ Michaelis constant in Eq. (1) - K _{m 2} mol/dm³ Michaelis constant in Eq. (2) - n number of beads - q _n nonzero positive roots in Eq. (7) - r ₁ mol/(dm³·s) rate of the conversion of CPS-S to CO-GL-7-ACA - r ₂ mol/(dm³·s) rate of the conversion of GL-7-ACA to 7-ACA - R m radius of the bead - S( ) symbol for total residual sum of squares in Eq. (1) - t s time - V _{m 1} mol/(dm³·s) max. reaction rate in Eq. (1) - V _{m 2} mol/(dm³·s) max. reaction rate in Eq. (2) - V _L dm³ volume of the solution excluding the space occupied by beads - V _s dm³ volume of beads - y _i mol/(dm³ · s) symbol for experimental data in Eq. (1) - _i mol/(dm³· s) symbol for calculated data in Eq. (1) - _P porosity, defined by Eq. (5) - dimensionless parameter, defined by Eq. (6) The authors wish to thank Dr. P. Gemeiner of Slovak Academy of Sciences for rendering of pectate gel. This work is supported by Ministry of Education (Grant No. 1/990 935/93)     

The fermentation of hexose and pentose sugars by Candida shehatae and Pichia stipitis

Summary The fermentation by Candida shehatae and Pichia stipitis of xylitol and the various sugars which are liberated upon hydrolysis of lignocellulosic biomass was investigated. Both yeasts produced ethanol from d-glucose, d-mannose, d-galactose and d-xylose. Only P. stipitis fermented d-cellobiose, producing 6.5 g·l^-1 ethanol from 20 g·l^-1 cellobiose within 48 h. No ethanol was produced from l-arabinose, l-rhamnose or xylitol. Diauxie was evident during the fermentation of a sugar mixture. Following the depletion of glucose, P. stipitis fermented galactose, mannose, xylose and cellobiose simultaneously with no noticeable preceding lag period. A similar fermentation pattern was observed with C. shehatae, except that it failed to utilize cellobiose even though it grew on cellobiose when supplied as the sole sugar. P. stipitis produced considerably more ethanol from the sugar mixture than C. shehatae, primarily due to its ability to ferment cellobiose. In general P. stipitis exhibited a higher volumetric rate and yield of ethanol production. This yeast fermented glucose 30–50% more rapidly than xylose, whereas the rates of ethanol production from these two sugars by C. shehatae were similar. P. stipitis had no absolute vitamin requirement for xylose fermentation, but biotin and thiamine enhanced the rate and yield of ethanol production significantly.Nomenclature _max Maximum specific growth rate, h^-1 - Q _p Maximum volumetric rate of ethanol production, calculated from the slope of the ethanol vs. time curve, g·(l·h)^-1 - q _p Maximum specific rate of ethanol production, g·(g cells·h) - Y _p/s Ethanol yield coefficient, g ethanol·(g substrate utilized)^-1 - Y _x/s Cell yield coefficient, g biomass·(g substrate utilized)^-1 - E Efficiency of substrate utilization, g substrate consumed·(g initial substrate)^-1·100     

Immobilization of lactase for the continuous hydrolysis of whey permaete

The production of lactose-based sweeteners is considered very promising. Fungal lactase has been immobilized on crosslinked chitin to develop a process for the continuous hydrolysis of demineralized whey permaete. The optimization of lactase immobilization on chitin and chitosan was performed, activities of 4 · 10⁵ and 2.2 · 10⁵ u/kg at yields of 33 and 23% were obtained for both supports, respectively. The chitin based catalyst was selected for further studies and a procedure was developed for in-situ enzyme immobilization. The kinetic behaviour of the catalyst was determined to propose a kinetic model for the initial rate of lactose hydrolysis. Pseudo steady-state and long term operation of packed bed reactors with chitin-immobilized lactase ranging from small laboratory to pre-pilot unit was carried out. The results are discussed and compared with commercial immobilized lactases. Preliminary economic evaluation for the production of ultrafiltered whey protein and hydrolyzed lactose syrup, within a dairy industry in Chile, was satisfactory in terms of profitability, both for the chitin immobilized lactase developed and for a commercial immobilized lactase.List of Symbols a moles/m³ glucose concentration in Eq. (1) - C _i US$ total annual cost (without considering plant depreciation) - D US$ annual depreciation - F m³/h flowrate - h m³/h volumetric mass transfer coefficient - i moles/m³ galactose concentration in Eqs. (1) and (2) - K _A moles/m³ dissociation constant for glucose in Eq. (1) - K _A moles/m³ dissociation constant for glucose in Eq. (1) - K _I moles/m³ inhibition constant for galactose in Eqs. (1) and (2) - K _m moles/m³ Michaelis constant for substrate in Eqs. (1) and (2) - k _D h^–1 first-order thermal deactivation constant - P kg dry weight of catalyst - PV US$ net present value - R % discounted cash-flow rate of return - s moles/m³ substrate concentration - s₀ moles/m³ feed substrate concentration - S _n US$ annual sales income - TC US$ total capital income - t _1/2 h catalyst half-life - v moles/h · kg initial rate of reaction - V _MAX moles/h · kg maximum reaction rate in Eqs. (1) and (2) - V _MAX moles/h · kg maximum reaction rate in Eq. (1) - ¯V _max moles/h initial rate of reaction - V _R m³ reaction volume free of catalyst particles - X substrate degree of conversion = s₀–s/s₀ - Damkoehler number = ¯V _MAX /h k _m - moles/(m³ · h) reactor productivity in Eq. (3)     

Effects of dissolved oxygen concentration on lipase production by Rhizopus delemar

Summary The influence of the concentration of oxygen on lipase production by the fungus Rhizopus delemar was studied in different fermenters. The effect of oxygen limitation ( 47 mol/l) on lipase production by R. delemar is large as could be demonstrated in pellet and filamentous cultures. A model is proposed to describe the extent of oxygen limitation in pellet cultures. Model estimates indicate that oxygen is the limiting substrate in shake flask cultures and that an optimal inoculum size for oxygen-dependent processes can occur.Low oxygen concentrations greatly negatively affect the metabolism of R. delemar, which could be shown by cultivation in continuous cultures in filamentous growth form (D_optimal=0.086 h^-1). Continuous cultivations of R. delemar at constant, low-oxygen concentrations are a useful tool to scale down fermentation processes in cases where a transient or local oxygen limitation occurs.Symbols and Abbreviations CO Oxygen concentration in the gas phase at time = 0 (kg·m^-3) - C_{O 2i} Oxygen concentration at the pellet liquid interface (kg·m^-3) - C_{O 2i} Oxygen concentration in the bulk (kg·m^-3) - D Dilution rate (h^-1) - ID_{O 2} Diffusion coefficient for oxygen (m²·s^-1) - dw Dry weight of biomass (kg) - f Conversion factor (rs _{O 2} to oxygen consumption rate per m³) (-) - k Radial growth rate (m·s^-1) - K Constant - kla Volumetric mass transfer coefficient (s^-1) - klA Oxygen transfer rate (m^-3·s^-1) - kl Mass transfer coefficient (m·s^-1) - K _{O 2} Affinity constant for oxygen (mol·m^-3) - K _w Cotton plug resistance (m^-3·s^-1) - M Henry coefficient (-) - NV Number of pellets per volume (m^-3) - R Radius (m) - RO Radius of oxygen-deficient core (m) - RQ Respiration quotient (mol CO₂/mol O₂) - rs _{O 2} Specific oxygen consumption rate per dry weight biomass (kg O₂·s^-1[kg dw]^-1) - rX Biomass production rate (kg·m^-3·s^-1) - SG Soytone glucose medium (for shake flask experiments) - SG ₄ Soytone glucose medium (for tower fermenter and continuous culture experiments) - V Volume of medium (m^-3) - X Biomass (dry weight) concentration (kg·m^-3) - XR _o Biomass concentration within RO for a given X (kg·m^-3) - Y _{O 2} Biomass yield calculated on oxygen (kg dw/kg O₂) - Thiele modulus - Efficiency factor =1-(RO/R)³ (-) - Growth rate (m^-1·s^-1·kg^1/3) - Dry weight per volume of pellet (kg·m^-3)     

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     

A mathematical model for solid state fermentation in tray bioreactors

A simple mathematical model for the interaction of mass transport with biochemical reaction in solid state fermentations (SSF) in static tray type bioreactors under isothermal conditions has been developed. The analysis has enabled scientific explanations to a number of practical observations, through the concept of critical substrate bed thickness. The model will be most useful in the prediction of the concentration gradients as also in efficient design of these bioreactors.List of Symbols C g/cm³ Oxygen concentration in the bed - C _g g/cm³ Atmospheric oxygen concentration - C ^* Dimensionless oxygen concentration, C/C _g - D _e cm²/h Effective diffusivity - H cm Bed thickness or height - H _c cm Critical bed thickness or height - H _m cm Maximum height of zone of zero oxygen concentration - p _i mg/(g · h) Productivity (Eq. 13) - R g/(cm³ · h) Biochemical reaction rate - t h Fermentation time - t ^* Dimensionless time, D _e t/H² - X mg/cm³ Biomass concentration - X _max mg/cm³ Maximum biomass concentration - y Dimensionless thickness or height, (y = z/H) - y cm Thickness of zone of zero oxygen concentration (Eq. 12) - Y Yield coefficient - z cm Bed thickness or height along tray axis - Bed void fraction - _max h^–1 Specific growth rate - Thiele modulus      

Growth of Thermoanaerobium brockii in batch and continuous culture at supraoptimal temperatures

Summary Thermoanaerobium brockii was grown in batch and continuous culture at supraoptimal temperatures (>65° C). Specific growth rates were lower in batch (_max>1.0 h^-1) than in continuous cultures (_max1.2–1.4 h^-1). Acetone addition to the medium did not increase critical dilution rate significantly. The media used contained significantly less organic material and sulfide than previously reported media; however, yeast extract requirements were shown to be exceptionally high (60% of the glucose concentration used). Organic substrates inhibited growth and product formation in chemostat cultures whereas the slow formation of acetic acid was observed in batch cultures, but also with virtually no growth. The inhibiting concentration was found to be approximately 15 g organic carbon·l^-1. The maintenance requirements of T. brockii were in the same range as expected of aerobic extreme thermophiles (m_s0.5 g·g^-1·h^-1) and could be met only by glucose and not by yeast extract. Maintenance was obviously not independent of specific growth rate. Production of the stereospecific alcohol-aldehyde/ketone oxidore-ductase was strictly growth associated and its formation was not affected by acetone added to medium.     

Verification studies of a simplified model for the removal of dichloromethane from waste gases using a biological trickling filter

The removal of dichloromethane from waste gases in a biological trickling filter was studied experimentally as well as theoretically within the concentration range of 0–10,000 ppm. A stable dichloromethane elimination performance was achieved during two years of operation, while the start-up of the system only amounted to several weeks at constant inlet concentrations. The trickling filter system was operated co-currently as well as counter-currently.However, experimental and theoretical results revealed that the relative flow direction of the mobile phases did not significantly affect the elimination performance. Moreover, it was found that the gas-liquid mass-transfer resistance in the trickling filter bed applied was negligible, which leaves the biological process inside the biofilm to be the rate limiting step.A simplified model was developed, the Uniform-Concentration-Model, which showed to predict the filter performance close to the numerical solutions of the model equations. This model gives an analytical expression for the degree of conversion and can thus be easily applied in practice.The dichloromethane eliminating performance of the trickling filter described in this paper, is reflected by a maximum dichloromethane elimination capacity EC _max=157 g/(m³ · h) and a critical liquid concentration C _lcr=45 g/m³ at a superficial liquid velocity of 3.6 m/h, inpendent of the gas velocity and temperature.List of Symbols a _s m²/m³ specific area - a _w m²/m³ specific wetted area - A m² cross-sectional area - C _g g/m³ gas phase concentration - C _go g/m³ inlet gas phase concentration - C _gocr g/m³ critical gas phase concentration - C _g ^* C_g/C_go dimensionless gas concentration - C _l g/m³ liquid concentration - C _lcr g/m³ critical liquid concentration - C _lcr ^* mC_lcr/C_go dimensionless critical concentration - c _li g/m³ substrate concentration at liquid-biofilm interface - C _l ^* mC_l/C_go dimensionless liquid concentration - C _o g/m³ oxygen concentration inside the biofilm - C _oi g/m³ oxygen concentration at liquid-biofilm interface - C_s g/m³ substrate concentration inside the biofilm - C _si g/m³ substrate concentration at liquid-biofilm interface - D _eff m²/h effective diffusion coefficient in the biofilm - D _o m²/h effective diffusion coefficient for oxygen in the biolayer - E mu_g/u_l extraction factor - E _act kJ/mol activation energy for the biological reaction - EC g/(m³· h) K _o a _w : elimination capacity, or the amount of substrate degraded per unit of reactor volume and time - EC _max g/(m³ · h) K _o a_w: maximum elimination capacity - f degree of conversion - h m coordinate in height - H m height of the packed bed - K ₀ g/(m³ · h) _maxX_b/Y zeroth order reaction defined per unit of biofilm volume - k _og m/h overall gas phase mass transfer coefficient - K ^* dimensionless constant given by Eq. (A.5) - K _l ^* dimensionless constant given by Eq. (A.6) - K ₂ ^* dimensionless constant given by Eq. (A.6) - m C _g /C_l gas liquid distribution coefficient - N g/(m² · h) liquid-biofilm interfacial flux of substrate - N _og k_oga_wH/u_g number of gas phase transfer units - N _r k_o a_w H/u_g C_go number of reaction units - OL g/(m³· h) u _g C _go /H organic load - r _s g/(m³ ·h) zeroth order substrate degradation rate given by Eq. (1) - R _s g/(g TSS ·h) specific activity - T K absolute temperature - u _g m/h superficial gas velocity - u _t m/h superficial liquid velocity - X _b g TSS/m₃ biomass concentration inside biofilm - X _s g TSS/m₃ liquid suspended biomass concentration - x m coordinate inside the biofilm - Y g TSS/(g_DCM) yield coefficient Greek Symbols dimensionless parameter given by Eq. (2) - m averaged biofilm thickness - biofilm effectiveness factor given by Eqs. (7a)–(7c) - m penetration depth of substrate into the biofilm - _max d^–1 microbiological maximum growth rate - v _o stoichiometric utilization coefficient for oxygen - v _s stoichiometric utilization coefficient for substrate - dimensionless height in the filter bed - h H/u _g superficial gas phase contact time - _o (K ₀ /DC _ii )^1/2 - _o C _o /C _oi dimensionless oxygen concentration inside the biofilm - _s C _s /C _si dimensionless substrate concentration inside the biofilm Experimental results, verifying the model presented will be discussed Part II (to be published in Vol. 6, No. 4)     

Development of a structured model for biopolymer synthesis in the fungus Aureobasidium pullulans

Previous modelling of the pullulan fermentation is discussed and found to lack any mechanistic basis. It is concluded that predictive ability can only be conferred by a structured model with at least two compartments, based upon the best available knowledge of the physiology of the microorganism. Such a model is constructed and compared with experimental data.List of Symbols A (gdm^–3)(g/l) Ammonium ion concentration - B (gdm^–3)(g/l) Concentration of balanced growth compartment of biomass - G (gdm^–3)(g/l) Glucose concentration - k _A (gdm^–3)(g/l) Saturation constant for ammonium - k _G (gdm^–3)(g/l) Saturation constant for glucose - k _S (gdm^–3)(g/l) Saturation constant for sucrose - P (gdm^–3)(g/l) Pullulan concentration - Q Quality of biomass=U/(U+B) - r _G (gdm^–1h^–1)(g/l/h) Rate of removal of glucose from broth - r _GB (gdm^–3h^–1)(g/l/h) Rate of incorporation of glucose into balanced compartment - r _GB (gdm^–3h^–1)(g/l/h) Rate of utilisation of glucose for energy production and cell maintenance - r _GP (gdm^–3h^–1)(g/l/h) Rate of conversion of glucose to pullulan - r _GU (gdm^–3h^–1)(g/l/h) Rate of incorporation of glucose into unbalanced compartment - r _s (gdm^–3h^–1)(g/l/h) Rate of conversion of sucrose to glucose - S (gdm^–3)(g/l) Concentration of sucrose - U (gdm^–3)(g/l) Concentration of unbalanced growth compartment of biomass - X (gdm^–3)(g/l) Biomass concentration - Y _G/A Grams of glucose consumed per gram of ammonium consumed - Y _G/B Grams of glucose consumed per gram of balanced biomass produced - Y _G/U Grams of glucose consumed per gram of unbalanced biomass produced - Y _G/P Grams of glucose consumed per gram of pullulan produced - Rate constant for conversion of sucrose to glucose - Rate constant for uptake of glucose by the cells - Model parameter governing inhibition of sucrose conversion and glucose utilisation - Model parameter denoting fraction of glucose uptake devoted to cell maintenance and energy production - Model parameter governing apportionment of glucose between pseudo-growth and pullulan production This work was funded by the National Engineering Laboratory (NEL) through the Bioreactor Design Club. The authors would like to express their gratitude to the NEL for this generous support.