Procedure for determination of elemental sulphur bio-oxidation rate

A procedure is described for measuring the rate of biooxidation of elemental sulphur in nutrient solutions. Results of preliminary measurements of sulphur bio-oxidation rate in a dynamic system are presented. The rate of sulphur bio-oxidation has been determined at the level of 0.02–0.05 g of sulphur per m² of sulphur per h.List of Symbols C g/dm³ concentration of sulphate ions - C ₂ g/dm³ concentration of sulphate ions in withdrawn solution - C g/dm³ C difference between solution outlet and inlet to sulphur bed - F m² sulphur surface exposed to bacteria action - m g mass of elemental sulphur - V dm³ volume of solution - V ₀ dm³/h volume of fresh solution supplied to the set - V ₁ dm³/h circulating solution flow rate - V ₂ dm³/h volume of solution withdrawn - h time Abbreviations RBES rate of bio-oxidation of elemental sulphur     

Mathematical models for mixing in deep-jet bioreactors: Calculation of parameters

The macroscopic mathematical model based on compartments with ideal mixing zones and tanks-in series was evaluated. Based on the experimental data obtained in a 300 dm³ pilot reactor and the dependence of mixing time on the volume of liquid phase, we have found mathematical relations between the ratio of vessel diameter to liquid level, adjustable parameters of model and the mixing time.List of Symbols V dm³ total volume of bioreactor - V _g dm³ total volume of liquid - V ₁ dm³ volume of ideally mixed zone in the vessel - V ₂ dm³ volume of macromixer in inner circulation flows - V ₃ dm³ volume of liquid phase in the pump - V ₄ dm³ volume of liquid phase in the pipe between the vessel and the pump - V ₅ dm³ volume of liquid phase in the pipe between the pump and air input system included falling jet - V _LT dm³ volume of liquid in the tank - V _LC dm³ volume of liquid in the circulation system - F _E dm³/s inner volumetric circulation flow rate across the macromixers - F _cir dm³/s external volumetric circulation flow rate, pumping capacity - t _A s time interval of the pulse application - t _AA s time point of the pulse application related to the free choosen starting point of the experiment - t _m s mixing time - t _c s circulation time - t _end s end time of simulation - C _*,* kg/m³ concentration of tracer in the indicated compartment - C ₀ kg/m³ concentration of the tracer before the injection - C _t kg/m³ concentration of the tracer at the indicated time - C kg/m³ theoretical concentration of the full mixed tracer - C _sim kg/m³ calculated concentration of tracer during numerical integration method - i index of an arbitrary tank - D _T m diameter of bioreactor - D 1/s dilution rate - H _L m level of liquid in the unaerated vessel - vector of inhomogenities     

Mathematical models for mixing in deep jet bioreactors: analysis

A mathematical model for single and multi step deep-jet bioreactors is presented. A stagewise approach based on macroscopic mechanistic model which divides the reactor into compartments with good quality of mixing and plug flow regions (macromixer), was used. For the mathematical representation of this model a system of differential equations, describing the concentration of tracer in structural elements based on mass balance, and the Runge-Kutta-Fehlberg numerical method of integration, was applied. The mixing time in a 300 dm³ tank was determined by conductivity method with NaCl as tracer.List of Symbols V _g dm³ total volume of liquid - V ₁; V ₆ dm³ volumes of ideally mixed compartments in the vessel - V ₂; V ₇ dm³ volumes of macromixer in the inner circulation flows - V ₃; V ₉ dm³ volumes of liquid phase in the pump - V ₄; V ₈ dm³ volumes of liquid phase in the pipe between the vessel and the pump - V ₅; V ₁₀ dm³ volumes of liquid phase in pipes between the pump and the air input system, including falling jet - F _E; F _E,1; F _E,2 dm³/s the inner volumetric circulation flow rates accross the macromixers - F _E,3; F _E,4 dm³/s exchanges volumetric flow rates between two ideally mixed compartments in the vessel - F _cir; F _1,cir; F _2,cir dm³/s external volumetric circulation flow rates (pumping capacity) - t _A s time interval of puls application - t _AA s time point of impuls application related to the free chosen point of simulation - t _end s end time of simulation - F _qu g²/dm⁶ sum of quadratic error - C _*,* kg/m³ concentration of the tracer in the indicated compartment - C ₀ kg/m³ concentration of the tracer before the injection - C _t kg/m³ concentration of the tracer at the indicated time - C kg/m³ theoretical concentration of full mixed tracer - i index of an arbitrary tank - C _sim kg/m³ calculated concentration of the tracer by numerical integration method     

In-situ recovery of butanol during fermentation

End-product inhibition in the acetone-butanol fermentation was reduced by using extractive fermentation to continuously remove acetone and butanol from the fermentation broth. In situ removal of inhibitory products from Clostridium acetobutylicum resulted in increased reactor productivity; volumetric butanol productivity increased from 0.58 kg/(m³h) in batch fermentation to 1.5 kg/(m³h) in fed-batch extractive fermentation using oleyl alcohol as the extraction solvent. The use of fed-batch operation allowed glucose solutions of up to 500 kg/m³ to be fermented, resulting in a 3.5- to 5-fold decrease in waste water volume. Butanol reached a concentration of 30–35 kg/m³ in the oleyl alcohol extractant at the end of fermentation, a concentration that is 2–3 times higher than is possible in regular batch or fed-batch fermentation. Butanol productivities and glucose conversions in fed-batch extractive fermentation compare favorable with continuous fermentation and in situ product removal fermentations.List of Symbols C _g kg/m³ concentration of glucose in the feed - C _w dm³/m³ concentration of water in the feed - F(t) cm³/h flowrate of feed to the fermentor at time t - V(t) dm³ broth volume at time t - V _i dm³ initial broth volume - V _si dm³ volume of the i-th aqueous phase sample - effective fraction of water in the feed Part 1. Bioprocess Engineering 2 (1987) 1–12     

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     

Adsorption studies for the separation ofl-tryptophan froml-serine and indole in a bioconversion medium

l-tryptophan was produced froml-serine and indole by immobilized Escherichia coli cells in organic-aqueous systems. Selective adsorption was the method chosen to enable both product separation andl-serine reutilization. Amongst various adsorbents tested activated carbons and neutral polymeric resins (XAD-4 and XAD-7) showed good performance. The neutral resins could selectively concentrate thel-tryptophan from dilute aqueous solutions and adsorbed only 5% of the unconvertedl-serine. High separation factors (l-tryptophan/l-serine and indole/l-tryptophan) were obtained with these adsorbents. Despite a lower capacity, the XAD-7 resin had the advantage of desorbingl-tryptophan with basic or acidic solutions, while organic solvents were required to desorb, at the same concentration levels, this compound from XAD-4.In a packed bed column filled with XAD-4 resin or activated carbon, totall-tryptophan adsorption and recovery were achieved at linear velocities up to 5.0 cm/min and 3.2 cm/min respectively. Successive sorbent reutilization, following continuous sorption and elution steps, was carried out in packed bed columns with the neutral resins and activated carbon.Thel-form of tryptophan, after crystallization, was identified by HPTLC.List of Symbols HPLC High Performance Liquid Chromatography - HPTLC High Performance Thin Layer Chromatography - Trp tryptophan - Ser Serine - A amount of sorbent(g) - c equilibrium solute concentration in the aqueous phase (g/dm³) - c _i initial (before adding the sorbent) liquid phase concentration (g/dm³) - C _T tryptophan concentration in the inlet solution (g/dm³) - C _To tryptophan concentration in the outlet solution (g/dm³) - E _z axial dispersion coefficient (m²/s) - k experimental constant (Eq. 1, 2 and 3) - K ₁ rate constant of adsorption (min^–1) - L column length(m) - n experimental constant (eq. 1, 2 and 3) - q equilibrium solid phase concentration (g solute/g sorbent) - q _max maximum capacity of sorbent (g solute/g sorbent) - t time(s) - v liquid velocity (m/s) - V volume of liquid phase(dm³) - V _e eluted volume(dm³) - V _r volume needed to saturate the column (dm³)     

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      

Convenient experimental determination of adsorption isotherms in a Hydrophobic Interaction Chromatography system

Summary HPLC was combined with a packable microbore guard column to obtain the adsorption isotherm of lysozyme in a Hydrophobic Interaction Chromatography system. The equipment configuration enabled isotherm determination of the protein on a relatively low pressure chromatographic media (TosoHaas 650M Phenyl).Notation C_m,i is the mobile phase concentration of protein. (M/L³ _(liquid)) - C_m,0 =0 - C_s,i is the stationary phase concentration of protein. It is the concentration of protein on the chromatographic media. (M/L³ _(solid)) - C_s,0 =0 - M,L is the dimensions mass and length - V_r,i is the retention volume of the peak front that corresponds to a mobile phase protein on the concentration C_m,i. (L³ _(liquid)) - i i is a counter that is used to keep track of C_m, C_s, and V_r.For example, i=1 in the term C_m,i denotes the first, and lowest, mobile phase protein concentrations are described by higher values of i. - V_d is the system dead volume. It consists of all of the system volume that the mobile phase "sees" or contacts, includingchromatographic media interparticle and pore volume. (L³ _liquid) - V_s the stationary phase volume. V_s is the nonporous bead volume. For porous beads, V_s is the bead volume - the porevolume. (L³ _(solid)) - V_e is the empty column volume. (L³ _liquid) - V_m is the packed column mobile phase volume and consists of the pore volume and the excluded volume. (L³ _(liquid)) - V_{e system} is the empty column system volume. (L³ _(liquid)) - V_frit the volume of mobile phase that fills the column frits. (L³ _(liquid)) - V_woc the system volume without the column connected. (L³ _(liquid))     

Studies on RTD and continuous culture (SCP) in cylindrical and tapered reactors

The performance of a tapered reactor for the continuous cultivation of bakers' yeast (SCP) from cane molasses has been compared with that of a conventional cylindrical reactor. It is found that the tapered reactor has less non-idealities (bypass and deadspace).Using the experimentally evaluated bypass and deadspace values, a model for predicting conversions of substrate (cane molasses), based on the RTD model proposed by Cholette and Cloutier has been developed. The experimental substrate conversions are found to match the model satisfactorily.List of Symbols D h^–1 dilution rate - E() exit age distribution function - K _s kg/m³ Monod's saturation constant - -r _sa kg/(m³ · h) rate of substrate utilization - S kg/m³ substrate concentration expressed as dextrose equivalent (DE) - S _a kg/m³ substrate concentration in active zone - S ₀ kg/m³ initial substrate concentration - S/S ₀ dimensionless substrate concentration - v _a dm³/h volumetric flow through active zone - v _b dm³/h volumetric flow through bypass stream - u _l dm³/h substrate feed rate - v _g dm³/min air-flow rate - V dm³ total working volume of the reactor - V _a dm³ volume of active zone in reactor - V _d dm³ volume of dead zone in reactor - X kg/m³ biomass concentration Greek Letters fraction of bypass of feed, v _b /v _l - fraction of deadspace, V _d /V - dimensionless residence time - _m h^–1 maximum specific growth rate - h mean residence time, V/v _l      

Glutamic acid production in an airlift reactor with net draft tube

Cultivation of Brevibacterium divaricatum for glutamic acid production in an airlift reactor with net draft tube was developed. Cell concentration gave an index for adding penicillin G. On-line estimation of total sugar concentration yielded an identified model which was used for determination of the substrate addition. Fermentation for glutamic acid production requires high oxygen concentration in the broth. The proposed reactor has the capability to provide sufficient oxygen for the fermentation. Since the reactor is suitable for fed-batch culture, the cultivation of B. divaricatum for glutamic acid production in the proposed reactor is successfully carried out.List of Symbols a system parameter - b system parameter - C _c,in mole fraction carbon dioxide in the gas inlet - C _c,out mole fraction carbon dioxide in the gas outlet - C _L mole/dm³ oxygen concentration in liquid phase - C _L ^* mole/dm³ saturated oxygen concentration in liquid phase - C _0,in mole fraction of oxygen in the gas inlet - C _0,out mole fraction of oxygen in the gas outlet - CPR mole/h/dm³ carbon dioxide production rate based on total broth - E(t) error signal - F _in mole/h inlet gas flow rate - k ₁ constant defined by Eq. (4) - k ₂ constant defined by Eq. (5) - k _L a 1/h volumetric mass transfer coefficient of gas-liquid phase - OUR mole/h/dm³ oxygen uptake rate based on total broth - P atm pressure in the reactor - t h time - TS _c g total sugar consumption - TS _s g/dm³ set point of total sugar concentration - TS _* g/dm³ reference value of total sugar concentration - TS(t) g/dm³ total sugar concentration in the broth at timet - u(t) cm³/min feed rate at timet - V dm³ total broth volume - VVM (dm³/min)/dm³ flow rate per unit liquid volume - a negative constant defined by Eq. (7)     

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 effect of micro- and macromixing on enzyme reaction in a real CSTR

The effect of micromixing and macromixing on enzyme reaction of Michaelis-Menten type in a real continuously stirred tank reactor (CSTR) is considered. The effect of bypassing of a fraction of feed stream, dead space, initial enzyme concentration and Michaelis-Menten constant on substrate conversion is evaluated. Bypass reduces the substrate conversion significantly compared with other parameters in the case of micro and macromixing. Micromixing predicts higher substrate conversions compared with macromixing. The effect of micro and macromixing on substrate conversion is negligible at low and high conversions.List of Symbols C kmol/m³ concentration of reactant - ¯C kmol/m³ average concentration of reactant - C_A kmol/m³ exit concentration of reactant A - C_Aa kmol/m³ exit concentration of reactant A from active zone - C_AO kmol/m³ initial concentration of reactant A - C_EO kmol/m³ initial enzyme concentration - C_O kmol/m³ initial concentration of reactant - E(t) 1/s exit age distribution function - k 1/s reaction rate constant - M kmol/m³ Michaelis-Menten constant - r kmol/(m³s) rate of reaction - –r_A kmol/(m³s) rate of reaction with respect to A - t s time - v m³/s volumetric feed rate - v_a m³/s volumetric feed rate entering the active zone - v_b m³/s volumetric feed rate entering the bypass stream - V m³ total volume of the vessel - V_a m³ active volume of the vessel - V_d m³ volume of dead space - X_A conversion of A Greek Letters fraction of feed stream bypassing the vessel (v_b/v) - fraction of the total volume as dead space (V_d/V) - (t) 1/s Dirac delta function, an ideal pulse occurring at time t = 0 - s life expectancy of a molecule - 1/s intensity function or escape probability function - s space time or mean residence time     

Mass transfer and liquid mixing in an airlift reactor with a net draft tube

Mass transfer and liquid mixing in an airlift reactor with a net draft tube were experimentally investigated. Four different column diameters were considered. The mass transfer was measured using the volumetric gas-liquid mass transfer coefficient which was determined by the dynamic method. The mass transfer coefficients in the airlift reactors with different column diameters were not always higher than those in the bubble columns. The liquid mixing was measured using mixing time which was determined by a pulse technique. Under the same superficial gas velocity, the mixing times of the airlift reactors with a net draft tube were always less than those of the bubble columns.List of Symbols C mol·dm^–3 bulk concentration of dissolved oxygen - C ₀ mol·dm^–3 initial concentration of dissolved oxygen - C _e mol·dm^–3 saturated concentration of dissolved oxygen - ¯C dimensionless dissolved oxygen concentration - D _c cm diameter of column - D _N cm diameter of the nozzle hole - D _T cm diameter of the net draft tube - H _L cm static liquid height - H _T cm height of the net draft tube - k _L a hr^–1 volumetric mass transfer coefficient - L _T cm length of the net draft tube - t _M sec mixing time of the liquid phase - t ₀ sec mixing time of the liquid phase in a bubble column - V _L dm³ volume of the liquid phase - U _g cm/s superficial air velocity     

To what extent is a constant volume design worse than a minimum volume design for a series of CSTR's?

The balance equations for substrate in a cascade of CSTR's undergoing an enzyme-catalyzed reaction following Michaelis-Menten kinetics are developed in dimensionless form. Analytical expressions relating the intermediate concentrations are independently obtained for the cases of minimum overall volume and constant volume. The fractional deviations between the overall volumes following these two design criteria are calculated and presented for several values of the relevant parameters. For situations of practical interest, the fractional deviation is below 10%. Increasing values of the Michaelis-Menten parameter, K _m(or decreasing values of the number of reactors in the cascade, N) lead to lower values of the maximum deviation; this maximum deviation is attained at lower conversions of substrate when K _mis increased or N decreased.List of Symbols C _{S, i}mol.m^–3 concentration of substrate at the outlet of the i-th reactor - C _* ^{S, i} normalized concentration of substrate at the outlet of the i-th reactor - C _* ^{S, i, eq} normalized concentration of substrate at the outlet of the i-th reactor using the design criterion of constant volume - C _* ^{S, i, opt} normalized concentration of substrate at the outlet of the i-th reactor using the design criterion of minimum overall volume - C _{S, 0} mol.m^–3 concentration of substrate at the inlet to the first reactor - Da _i Damköhler number for the i-th reactor - Da _eq constant Damköhler number for each reactor of the cascade - Da _{tot, eq} overall Damköhler number for the cascade assuming equal-sized reactors - Da _{tot, min} minimum overall Damköhler number for the cascade - Er fractional deviation between the overall volumes using the two different design criteria - K _mmol. m^–3 Michaelis-Menten constant - K _* ^M dimensionless Michaelis-Menten constant - N number of reactors of the cascade - Q m³. s^–1 volumetric flow rate - V _im³ volume of the i-th reactor - v _max mol. m^–3. s^–1 reaction rate under saturation conditions of the enzyme with substrate - V _{tot, opt} m³ minimum overall volume of the cascade - V _{tot, eq} m³ overall volume of the cascade assuming equal-sized reactors     

Gas-exchange of ears of cereals in response to carbon dioxide and light

Data for the maximum carboxylation velocity of ribulose-1,5-biosphosphate carboxylase, V_m, and the maximum rate of whole-chain electron transport, J_m, were calculated according to a photosynthesis model from the CO₂ response and the light response of CO₂ uptake measured on ears of wheat (Triticum aestivum L. cv. Arkas), oat (Avena sativa L. cv. Lorenz), and barley (Hordeum vulgare L. cv. Aramir). The ratio J_m/V_m is lower in glumes of oat and awns of barley than it is in the bracts of wheat and in the lemmas and paleae of oat and barley. Light-microscopy studies revealed, in glumes and lemmas of wheat and in the lemmas of oat and barley, a second type of photosynthesizing cell which, in analogy to the Kranz anatomy of C₄ plants, can be designated as a bundle-sheath cell. In wheat ears, the CO₂-compensation point (in the absence of dissimilative respiration) is between those that are typical for C₃ and C₄ plants.A model of the CO₂ uptake in C₃–C₄ intermediate plants proposed by Peisker (1986, Plant Cell Environ. 9, 627–635) is applied to recalculate the initial slopes of the A(p^c) curves (net photosynthesis rate versus intercellular partial pressure of CO₂) under the assumptions that the J_m/V_m ratio for all organs investigated equals the value found in glumes of oat and awns of barley, and that ribulose-1,5-bisphosphate carboxylase is redistributed from mesophyll to bundle-sheath cells. The results closely match the measured values. As a consequence, all bracts of wheat ears and the inner bracts of oat and barley ears are likely to represent a C₃–C₄ intermediate type, while glumes of oat and awns of barley represent the C₃ type.Abbreviations A net photosynthesis rate (mol·m^-2·s^-1) - J_m maximum rate of whole-chain electron transport (mol·e^-·m^-2·s^-1) - p^c (bar) intercellular partial pressure of CO₂ - PEP phosphoenolpyruvate - PPFD photosynthetic photon flux density (mol quanta·m^-2·s^-1) - RuBPCase ribulose bisphosphate carboxylase/oxygenase - RuBP ribulose bisphosphate - V_m maximum carboxylation velocity of RuBPCase (mol·m^-2·s^-1) - T^* CO₂ compensation point in the absence of dissimilative respiration (bar)     

New solution method for equations of reaction and mass transfer in biocatalyst particles

Summary For numerical solution of the reaction-mass transfer equations for immobilised biocatalysts it may be better to start integration at the particle surface and proceed inwards: calculations are targetted on the region to which practically interesting changes are often confined (because concentrations are effectively zero in the interior); and during iterative solution wrong initial estimates may be rejected after detecting anomalies early in the integration.Symbols C_b substrate concentration in bulk (mol m^–3) - c dimensionless substrate concentration (C/C_b) (-) - D_e effective diffusion coefficient (m²s^–1) - Da Damkohler number (V.r_o ²/D_e.K_s) (-) - K_s substrate concentration kinetic coefficient (mol m^–3) - k_e external mass transfer coefficient (ms^–1) - r_o bead radius (m) - Sh Sherwood number (k_e.r_o/D_e) (-) - V maximum rate per unit volume in beads (mol m^–3s^–1) - x dimensionless distance from bead centre (r/r_o) (-) - dimensionless kinetic coefficient (K_s/C_b) (-) - _o effectiveness factor (-)     

Simulation of the dynamics in the Baker's yeast process

Simulation of the dynamics in a fed batch process for production of Baker's yeast is discussed and applied. Experimental evidences are presented for a model of the energy metabolism. The model involves the concept of a maximum respiratory capacity of the cell. If the sugar concentration is increased above a critical value, corresponding to a critical rate of glycolysis and a maximum rate of respiration, then all additional sugar consumed at higher sugar concentrations is converted into ethanol.In a fed batch process with constant sugar feed the sugar concentration declines slowly. If ethanol is present when the sugar concentration declines below the critical value of 110 mg/dm³ fructose +glucose the metabolism switches rapidly into combined oxidation of sugar and ethanol. Thus, no diauxic growth is involved under process conditions. The rate of ethanol consumption is determined by the free capacity of respiration under these conditions. The invertase activity of the cells was found to be so high that mainly fructose and glucose were present in the medium, typically in the concentration range around 100 mg/dm³. These components are consumed at the same rate but with fructose at a higher concentration, indicating a higher K _s for fructose consumption.The model was used in simulation experiments to demonstrate the dynamics of the Baker's yeast process and the influence of different process conditions.List of Symbols DOT % air sat dissolved oxygen tension - F dm³/h rate of inlet medium flow - H kg/(dm³ % air sat.) oxygen solubility - K kg/m³ saturation constant specified by index - K _L a 1/h volumetric oxygen transfer coefficient - m g/(g · h) maintenance coefficient specified by index - P kg/(m³ · h) mean productivity of biomass in the process - q g/(g · h) specific consumption or production rate - S kg/m³ concentration of sugar in reactor - S ₀ kg/m³ concentration of inlet medium sugar medium t h process time - V dm³ medium volume - X kg/m³ concentration of biomass - Y g/g yield coefficient specified by index - 1/h specific growth rate Index aa anaerobic condition - c critical value - e ethanol - ec ethanol consumption - ep ethanol production - max maximum value - o oxygen - oe oxygen for growth on ethanol - os oxygen for growth on sugar - s sugar - x biomass     

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.     

Equilibrium and dynamic investigations of organic acids adsorption onto ion-exchange resins

The aim of the study was to determine properties of selected ion-exchange resins for citric and lactic acids recovery, to define sorption isotherms for these acids at different temperatures (in the range of 20–60°C) and to determine diffusion coefficients inside sorbent particles. A mathematical model of the ion-exchange process in the chromatographic column and its experimental verification is also presented. During investigations 18 types of ion-exchange resins were tested. It was found that weakly basic resins were more suitable for the recovery process than strongly basic ones. The best resin for the separation of citric acid was Amberlite IRA-67 and for lactic acid Amberlite IRA-92. As a result of transient-state sorption experiments diffusion coefficients of the citric acid inside the sorbent particle at different temperatures were obtained. It was found that D_p increased with the temperature by two times in the range of 20–60°C, and its value at 60°C was 7.2×10^–10 m²/s. The proposed mathematical model was applied to identify bed operation parameters in the column for the needs of the simulated moving bed chromatography method.List of symbols b Equilibrium constant in Langmuir equation, [dm³/g] - c Acid concentration in the liquid phase inside the particle pores, [g/dm³] - C Acid concentration in the liquid, [g/dm³] - D_L Axial dispersion coefficient, [m²/s] - D_p Intraparticle diffusion coefficient, [m²/s] - k_f Liquid film mass transfer coefficient, [m/s] - L Ion-exchanger bed height, [m] - q Acid concentration in the adsorbent phase, [g/dm³] - R_p Particle radius, [m] - U Volumetric flow rate of the feeding solution, [dm³/s] - V Volume of the solution, [dm³] - W Weight of the wet resin particles, [g] - The ion-exchanger bed porosity, [-] - _p Particle porosity, [-] - Linear liquid velocity, [m/s] - Apparent density of the wet resin, [g/dm³]     

Recycling ofd-glucose in collagenous cuticle: A means of nutrient conservation?

Summary Transport by an epithelium, possessing an accumulating, saturable transport system in the apical membrane as well as a finite Fick permeability to the transported solute, was considered in the steady state in the case of zerocis concentration, and in the presence of a peripheral diffusion resistance in a layer apposing thecis face of the tissue (unstirred solution or structural coating). Under suitable conditions, the combination of peripheral diffusion resistance and accumulating epithelial transport may lead to recycling of solute at thecis face of the epithelium. This causes a decrease of the effective permeability to diffusionaltrans-cis flow across the tissue. The phenomenon is discussed in terms of epidermald-glucose transport by the integument of aquatic animals with a collagenous cuticle, such as the seawater-acclimated polychaete wormNereis diversicolor. The recycling phenomenon may be of significance to other epithelia with the function of maintaining large concentration gradients of permeating substances.List of Symbols and Fixed Parameter Values C _m Bulk medium solute concentration,cis face of epidermisC _m=0 mol cm^–3 - C _i Concentration of solute at interface between cuticle and unstirred medium (mol cm^–3) - C _s Concentration of solute atcis face of apical epidermal membrane (mol cm^–3) - C _e Concentration of solute in extracellular fluid,trans-side of epidermisC _e=1.0×10^–6 mol cm^–3 - D _m Diffusion coefficient of solute in outside mediumD _m=6.7×10^–6 cm² sec^–1 - D _c Diffusion coefficient of solute in cuticleD _c=7.4×10^–9 cm² sec^–1 - _m Operative thickness of unstirred medium layer - _c Thickness of cuticle - J Steady-state net flux of solute through cuticle or unstirred layer (flux is positive indirectioncis-trans) (mol cm^–2 sec^–1) - J _i ^max Maximal influx through saturable transport system in apical membraneJ _i ^max =2.0×10^–12 mol cm^–2 sec^–1 - K _t Transport constant, saturable systemK _t=1.0×10^–7 mol cm^–3 - P Epithelial permeability (cm sec^–1)