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 (-)     

On the appropriateness of use of a continuous formulation for the modelling of discrete multireactant systems following Michaëlis–Menten kinetics

The possibility of solving the mass balances to a multiplicity of substrates within a CSTR in the presence of a chemical reaction following Michaelis-Menten kinetics using the assumption that the discrete distribution of said substrates is well approximated by an equivalent continuous distribution on the molecular weight is explored. The applicability of such reasoning is tested with a convenient numerical example. In addition to providing the limiting behavior of the discrete formulation as the number of homologous substrates increases, the continuous formulation yields in general simpler functional forms for the final distribution of substrates than the discrete counterpart due to the recursive nature of the solution in the latter case.List of Symbols C{N. M} mol/m³ concentration of substrate containing N monomer residues each with molecular weight M - {N, M} normalized value of C{N. M} - C {M} mol/m³ da concentration of substrate of molecular weight M - _in normalized value of C {M} at the i-th iteration of a finite difference method - {M} normalized value of C {M} - C ₀{N.M} mol/m³ inlet concentration of substrate containing N monomer residues each with molecular weight M - {N ·M} normalized value of C₀{N. M} - _{0 i} normalized value of C ₀ {M} at the i-th iteration of a finite difference method - C ₀ {M} mol/m³ da initial concentration of substrate of molecular weight M - C _tot mol/m³ (constant) overall concentration of substrates (discrete model) - C _tot mol/m³ (constant) overall concentration of substrates (continuous model) - D deviation of the continuous approach relative to the discrete approach - i dummy integer variable - I arbitrary integration constant - j dummy integer variable - k dummy integer variable - K _m mol/m³ Michaëlis-Menten constant for the substrates - l dummy integer variable - M da molecular weight of substrate - M normalized value of M - M da maximum molecular weight of a reacting substrate - N number of monomer residues of a reacting substrate - N maximum number of monomer residues of a reacting substrate - N total number of increments for the finite difference method - Q m³/s volumetric flow rate of liquid through the reactor - S inert product molecule - S _i substrate containing i monomer residues - V m³ volume of the reactor - v _max mol/m³ s reaction rate under saturating conditions of the enzyme active site with substrate - v _max{N. M} mol/m³ s reaction rate under saturating conditions of the enzyme active site with substrate containing N monomer residues with molecular weight M - _max{N · M} dimensionless value of v_max{N. M} (discrete model) - _max{M} dimensionless value of v _max {M} (continuous model) - mol/m³ s molecular weight-averaged value of v_max (discrete model) - mol.da/m³s molecular weight-averaged value of v_max (continuous model) - v _max {M} mol.da/m³s reaction rate under saturating conditions of the enzyme active site with substrate with molecular weight M - _max {M} dimensionless value of v_max{M} - _{max, (i)} dimensionless value of v_max{M} at the i-th iteration of a finite difference method - v _max mol/m³ s reference constant value of v _max Greek Symbols dimensionless operating parameter (discrete distribution) - dimensionless operating parameter (continuous distribution) - M da (average) molecular weight of a monomeric subunit - M selected increment for the finite difference method - auxiliary corrective factor (discrete model)     

Reactor design for the enzymatic isomerization of glucose to fructose

A comprehensive methodology is presented for the design of reactors using immobilized enzymes as catalysts. The design is based on material balances and rate equations for enzyme action and decay and considers the effect of mass transfer limitations on the expression of enzyme activity. The enzymatic isomerization of glucose into fructose with a commercial immobilized glucose isomerase was selected as a case study. Results obtained are consistent with data obtained from existing high-fructose syrup plants. The methodology may be extended to other cases, provided sound expressions for enzyme action and decay are available and a simple flow pattern within the reactor might be assumed.List of Symbols C kat/kg specific activity of the catalyst - D m²/s substrate diffusivity within the catalyst particle - Dr m reactor diameter - d d operating time of each reactor - E kat initial enzyme activity - E _i kat initial enzyme activity in each reactor - F m³/s process flowrate - F _i m³/s reactor feed flowrate at a given time - F ₀ m³/s initial feed flowrate to each reactor - H number of enzyme half-lives used in the reactors - K mole/m³ equilibrium constant - K _S mole/m³ Michaelis constant for substrate - K _P mole/m³ Michaelis constant for product - K _m mole/m³ apparent Michaelis constant f(K, K _s, K_p, s₀) - k mole/s · kat reaction rate constant - k _d d^–1 first-order thermal inactivation rate constant - L m reactor height - L _r m height of catalyst bed - N _R number of reactors - P _i kg catalyst weight in each reactor - p mole/m³ product concentration - R m particle radius - R _P ratio of minimum to maximum process flowrate - r m distance to the center of the spherical particle - s mole/m³ substrate concentration - s _0i mole/m³ substrate concentration at reactor inlet - s ₀ mole/m³ bulk substrate concentration - s mole/m³ apparent substrate concentration - T K temperature - t d time - t _i d operating time for reactor i - t _s d time elapsed between two successive charges of each reactor - V m³ reactor volumen - V _m mole/m³ s maximum apparent reaction rate - V _p mole/m³ s maximum reaction rate for product - V _R m³ actual volume of catalyst bed - V _r m³ calculated volume of catalyst bed - V _S mol/m³ s maximum reaction rate for substrate - v mol/m³ s initial reaction rate - v _i m/s linear velocity - v _m mol/m³ s apparent initial reaction rate f(K_m, s,V_m) - X substrate conversion - X _eq substrate conversion at equilibrium - =s/K dimensionless substrate concentration - ₀=s₀/K bulk dimensionless substrate concentration - _eq=s_eq/K dimensionless substrate concentration at equilibrium - local effectiveness factor - mean integrated effectiveness factor - Thiéle modulus - =r/R dimensionless radius - _s kg/m³ hydrated support density - substrate protection factor - s residence time     

Oxygen transfer in a stirred loop fermentor with dilute polymer solutions

Oxygen transfer in a 0.35 m diameter stirred loop fermentor (a stirred tank with a concentric draft tube) has been studied with water containing a small amount of polymer(polyethylene oxide) as a drag-reducing additive.Power consumption was measured. It was found that the addition of polyethylene oxide causes an increase of power consumption. This is contrary to the results reported in the literature.Volumetric mass transfer coefficients (K _La) were measured. In water the introduction of the draft tube increased the K _La coefficient. The increase in K _La became larger with impeller speed. On the other hand, mass transfer in dilute polymer solutions decreased due to the presence of the draft tube. An empirical correlation has been proposed for the volumetric mass transfer coefficient in stirred loop fermentors. It has a general applicability.List of Symbols a 1/m specific surface area - C constant in Eq. (6) - g m/s² gravitational acceleration - K _L m/s overall liquid-phase mass transfer coefficient - n 1/s impeller speed - P W aerated power input by mechanical agitation - P _g W power input by sparged air - Q m³/min volumetric gas flow rate - U _sg m/s superficial gas velocity - V m³ liquid volume Greek Symbols exponents in Eq. (3) - exponent in Eq. (6) - kg/m³ density     

Viscous media in tower bioreactors: Hydrodynamic characteristics and mass transfer properties

Studies in tower reactors with viscous liquids on flow regime, effective shear rate, liquid mixing, gas holdup and gas/ liquid mass transfer (k _La) are reviewed. Additional new data are reported for solutions of glycerol, CMC, PAA, and xanthan in bubble columns with diameters of 0.06, 0.14 and 0.30 m diameter. The wide variation of the flow behaviour index (1 to 0.18) allows to evaluate the effective shear rate due to the gas flow. New dimensionless correlations are developed based on the own and literature data, applied to predict k _La in fermentation broths, and compared to other reactor types.List of Symbols a(a) m^–1 specific interfacial area referred to reactor (liquid) volume - Bo Bond number (g D _c ² _L/) - c _L(c _L ^* ) kmol m^–3 (equilibrium) liquid phase oxygen concentration - C coefficient characterising the velocity profile in liquid slugs - C _s m^–1 coefficient in Eq. (2) - d _B(d_vs) m bubble diameter (Sauter mean of d _B) - d ₀ m diameter of the openings in the gas distributor plate - D _c m column diameter - D _L m²s^–1 diffusivity - E _L(E_W) m² s^–1 dispersion coefficient (in water) - E ² square relative error - Fr Froude number (u _G/(g D_c)^0.5) - g m s^–2 gravity acceleration - Ga Gallilei number (g D _c ³ _L ² / _eff ² ) - h m height above the gas distributor the gas holdup is characteristic for - k Pasⁿ fluid consistency index (Eq. 1) - k _L m s^–1 liquid side mass transfer coefficient - k _La(k_La) s^–1 volumetric mass transfer coefficient referred to reactor (liquid) volume - L m dispersion height - n flow behaviour index (Eq. 1) - P W power input - Re liquid slug Reynolds number ( _L(u _G +u _L) D _c/_eff) - Sc Schmidt number ( _eff/( _L D _L )) - Sh Sherwood number (k _La D _c ² /D_L) - t s time - u _B(u_sw) m s^–1 bubble (swarm) rise velocity - u _G(u_L) m s^–1 superficial gas (liquid) velocity - V(V_L) m³ reactor (liquid) volume Greec Symbols W m^–2 K^–1 heat transfer coefficient - y(y _eff) s^–1 (effective) shear rate - _G relative gas holdup - s relaxation time of viscoelastic liquid - _L(_eff) Pa s (effective) liquid viscosity (Eq. 1) - _L kg m^–3 liquid density - N/m surface tension     

Process of penicillin G hydrolysis catalyzed by penicillin acylase immobilized on acylic carrier

The usefulness of penicillin acylase immobilized onto butyl acrylate — ethyl glycol dimethacrylate (called in this paper acrylic carrier) in penicillin G hydrolysis performed in a stirred tank reactor is shown. The enzyme-acrylic carrier preparation does not deteriorate its own properties in the mixing condition of slurry reactor. The experiments were carried out in a batch and a continuous stirred tank reactor as well as continuous stirred tank reactors in series. It was found to be a satisfactory agreement between experimental and predicted results. It also indicated the optimal substrate concentration range which provides the most effective enzyme operation. A superiority of the three reactors in series over the batch reactor is shown.List of Symbols C_E g/m³ equivalent enzyme concentration - C_SO mol/m³ initial penicillin G concentration - K_A mol/m³ substrate affinity constant - K_iS mol/m³ substrate inhibitory constant - K_iP mol/m³ PhAA inhibitory constant - K_iQ mol/m³ 6-APA inhibitory constant - k₃ mol/g min constant rate of dissotiation of the active complex - r mol/m³ rate of reaction - t min. reaction time - t_j min. maintenance time - degree of conversion - _B, _F dimensionless time - min. residence time - PA penicillin acylase - PG penicillin G - PhAA phenylacetic acid - 6-APA 6-aminopenicillanic acid     

Adsorption equilibrium and dynamics of lactase/CM-Sephadex system

Summary Partitioning behaviour and adsorption isotherms of lactase/CM-Sephadex system at equilibrium were investigated together with the adsorption kinetics in this study. Maximum adsorption was obtained at the pH values between 5.5–6.0. Adsorption isotherm was a close fit to the Langmuir model.Nomenclature a specific mass transfer area - D_m molecular diffusion coefficient (m²/sec) - e₁, e₂ charge of the protein and the gel - k apparent mass transfer coefficient (s^-1) - ka global mass transfer coefficient - f partition coefficient - K_p dissociation constant for adsorbent-adsorbate complex, (mg/mL solvent) - p equilibrium concentration of free enzyme, (mg free enzyme/mL solution) - q equilibrium concentration of adsorbed enzyme, (mg ads./mL gel) - q_m maximum adsorption capacity, (mg ads./ml gel) - Re particle Reynolds number - Sh Sherwood number - V_g/V gel volume (mL)/bulk solvent volume (mL) - Z dimensionless extent of adsorption - K_p/P_o , model parameter - (/) +1 , model parameter - V_g q_m / V P_o , model parameter     

Gas holdup and mass transfer characteristics of carboxymethyl cellulose solutions in a bubble column with a radial gas sparger

The gas phase holdup and mass transfer characteristics of carboxymethyl cellulose (CMC) solutions in a bubble column having a radial gas sparger have been determined and a new flow regime map has been proposed. The gas holdup increases with gas velocity in the bubbly flow regime, decreases in the churn-turbulent flow regime, and increases again in the slug flow regime. The volumetric mass transfer coefficient (k _La) significantly decreases with increasing liquid viscosity. The gas holdup and k _La values in the present bubble column of CMC solutions are found to be much higher than those in bubble columns or external-loop airlift columns with a plate-type sparger. The obtained gas phase holdup ( _g) and k _La data have been correlated with pertinent dimensionless groups in both the bubbly and the churn-turbulent flow regimes.List of Symbols a m^–1 specific gas-liquid interfacial area per total volume - A _d m² cross-sectional area of downcomer - A _r m² cross-sectional area of riser - d _b m individual bubble diameter - d _vs m Sauter mean bubble diameter - D _c m column diameter - D _L m²/s oxygen diffusivity in the liquid - Fr Froude number, U _g/(g D_c)^1/2 - g m/s² gravitational acceleration - G _a Galileo number, gD _c ^{3 2}/² _app - H _a m aerated liquid height - H _c m unaerated liquid height - K Pa · sⁿ fluid consistency index - k _L a s^–1 volumetric mass transfer coefficient - n flow behavior index - N _i number of bubbles having diameter d _bi - Sc Schmidt number, _app/( D _L) - Sh Sherwood number, k _L a D _c ² /D_L - U _sg m/s superficial gas velocity - U _gr m/s superficial riser gas velocity - V _a m³ aerated liquid volume - V _c m³ unaerated liquid volume - N/m surface tension of the liquid phase - _g gas holdup - _app Pa · s effective viscosity of non-Newtonian liquid - kg/m³ liquid density - ý s^–1 shear rate - Pa shear stress     

Hydrodynamics and mass transfer in an airlift loop fermentor

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

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     

A theoretical and experimental evaluation of a novel radial-flow hollow fiber reactor for mammalian cell culture

A hollow fiber perfusion reactor constructed from pairs of concentric fibers forming a thin annular space is analyzed theoretically in terms of mass transfer resistances, and is shown experimentally to support the growth of an anchorage-dependent cell line in high-density culture. Hollow fiber perfusion reactors described in the literature typically employ a perfusion pathlength much greater than the distance that could be supported by diffusion alone, and analyses of these reactors typically incorporate the assumption of uniform perfusion throughout the cell mass despite many reported observations of inhomogeneous cell growth in perfusion reactors. The mathematical model developed for the annular reactor predicts that the metabolism of oxygen, carbon substrates, and proteins by anchorage-dependent cells can be supported by the reactor even in the absence of perfusion. The implications of nonuniform cell growth in perfusion reactors in general is discussed in terms of nutrient distribution. In the second part of the paper, the growth and metabolism of the mouse adrenal tumor line Y-1 in flask culture and in the annular reactor are compared. The reactor is shown to be a promising means for culturing anchorage-dependent cells at high density.List of Symbols c mol/dm³ substrate concentration - D _mm²/s effective diffusivity of substrate in the membrane - D _tm²/s effective diffusivity of substrate in the cell region - L _pm²s/kg hydraulic permeability of fiber - Pe _m Peclet number for membrane transport, _wR₁/D _m - Pe _t Peclet number for transport through cell mass, v _wR₂/D _t - Q mol/m³s zero-order consumption rate of substrate per unit volume of cell mass - r m radial distance from centerline of fiber lumen - R ₁, R ₂ m inner and outer radii of inner annular fiber (Fig. 1) - R ₃, ₄ m inner and outer radii of outer annular fiber (Fig. 1) - v _wm/s fluid velocity through the fiber wall at R ₁ - fraction of shell side filled with cells - dimensionless radial distance, R ₃/R₁ - dimensionless radial distance, R ₂/R ₁ - cm² hydraulic conductivity - viscosity - ², Thiele modulus - dimensionless radial distance, R ₄/R ₁     

Determination of the overall volumetric mass transfer coefficient kLa,by a temperature dependent change of gas solubility

Summary The solubility of oxygen in the liquid phase of a bioreactor was changed by a ramp change of temperature, and k_La was determined from the resulting return to equilibrium of dissolved oxygen activity. The maximum k_La that can be measured by this method in a standard laboratory scale bioreactor is 145 h^–1 corresponding to a temperature change rate of 320°C h^–1.Nomenclature p Difference between p_G and p_L (% saturation) - T Ramp change of temperature (°C) - E Temperature-compensated output from the oxygen electrode (A) - E_u Uncompensated output from the oxygen electrode (A) - k_La Overall volumetric mass transfer coefficient (h^–1) - k_La_Tm Overall volumetric mass transfer coefficient at temperature T_m (h^–1) - P_G Dissolved oxygen activity in equilibrium with the gas phase (% saturation) - p_L Dissolved oxygen activity (% saturation) - p_Lm Dissolved oxygen activity at time t_m (% saturation) - t Time (h) - t_m Time of maximum p (h) - T Temperature (°C) - T_cal Calibration temperature of the oxygen electrode (°C) - T_m Final temperature after a temperature shift (°C) - T_n Temperature at time t_n     

Growth simulation ofHansenula polymorpha

Summary Using the model presented in part I, the measured time and spacial variations of process variables were simulated with satisfactory accuracy. Especially the experimentally found minima of the longitudinal dissolved oxygen concentration profiles in the substrate limiting growth range, which are caused by the transition from oxygen transfer limited to substrate limited growth along the tower, can be simulated with great accuracy.Symbols L length - M mass - T time - K temperature - M_M mole mass - a Specific gas/liquid interfacial area with regard to the liquid volume in the tower (L^–1) - DS_R Substrate feed rate (ML^–3T^–1) - K_O Saturation constant of Monod kinetics with regard to oxygen (ML^–3) - K_S Saturation constant of Monod kinetics with regard to the substrate (ML^–3) - K_ST Constant - K_L Mass transfer coefficient (LT^–1) - k_La Volumetric mass transfer coefficient (T^–1) - k_La^E Volumetric mass transfer coefficient at the entrance (T^–1) - k_La Volumetric mass transfer coefficient at large distances from the entrance (T^–1) - k_La ₀ Volumetric mass transfer coefficient in the absence of substrate (ethanol) (T^–1) - L_R Gas-liquid layer height in the tower (L) - L_R Height of the loop (L) - - O_B Dissolved oxygen concentration in the loop liquid (ML^–3) - O_F Dissolved oxygen concentration in the tower liquid (ML^–3) - O _F ^* Saturation value of O_F (ML^–3) - OTR Oxygen transfer rate (ML^–3T^–1) - P Pressure - Oxygen transfer rate (ML^–3T) - S_B Substrate concentration in the loop liquid (ML^–3) - S_D Substrate concentration at which k_La=2 k_La ₀ (ML^–3) - S_F Substrate concentration in the tower liquid (ML^–3) - T Absolute temperature - t Time (T) - u_Go Superficial gas velocity in the tower - V_R Reactor volume (L³) - V_G Volumetric gas flow rate in the tower (L³T^–1) - V_B Volumetric liquid flow rate in the loop (L³T^–1) - V_F Volumetric liquid flow rate in the tower (L³T^–3) - V_u Liquid recycling rate (L³T^–1) - X_B Biomass concentration in the loop liquid (ML^–3) - X_F Biomass concentration in the tower liquid (ML^–3) - x Longitudinal coordinate in the tower (L) - x^* Longitudinal coordinate in the loop (L) - x_OG O₂ mole fraction in the gas phase - Y_X/O Yield coefficient of biomass with regard to oxygen - Y_X/S Yield coefficient of biomass with regard to substrate - z=x/L_R Dimensionless longitudinal coordinate in the tower - z^*=x^*/L_B Dimensionless longitudinal coordinate in the loop - Constant (L_R is the distance from the aerator on which k_L a is space dependent) - Liquid recirculation ratio - _G Mean relative gas holdup in the tower - _exp Experimentally determined (T^–1) - _max Maximum specific growth rate (T^–1) - _F Liquid density (ML^–3) - A At the exit - E At the inlet     

The influence of temperature on glucose-6-phosphate dehydrogenase and 6-phosphogluconate dehydrogenase and the regulation of these enzymes in a mesophilic and a thermophilic cyanobacterium

The activities and kinetics of the enzymes G6PDH (glucose-6-phosphate dehydrogenase) and 6PGDH (6-phosphogluconate dehydrogenase) from the mesophilic cyanobacterium Synechococcus 6307 and the thermophilic cyanobacterium Synechococcus 6716 are studied in relation to temperature. In Synechococcus 6307 the apparent K _m's are for G6PDH: 80M (substrate) and 20M (NADP⁺); for 6PGDH: 90M (substrate) and 25M (NADP⁺). In Synechococcus 6716 the apparent K _m's are for G6PDH: 550M (substrate) and 30M (NADP⁺); for 6PGDH: 40M (substrate) and 10M (NADP⁺). None of the K _m's is influenced by the growth temperature and only the K _m's of G6PDH for G6P are influenced by the assay temperature in both organisms. The idea that, in general, thermophilic enzymes possess a lower affinity for their substrates and co-enzymes than mesophilic enzymes is challenged.Although ATP, ribulose-1,5-bisphosphate, NADPH and pH can all influence the activities of G6PDH and 6PGDH to a certain extent (without any difference between the mesophilic and the thermophilic strain), they cannot be responsible for the total deactivation of the enzyme activities observed in the light, thus blocking the pentose phosphate pathway.Abbreviations G6PDH glucose-6-phosphate, dehydrogenase - 6PGDH 6-phosphogluconate dehydrogenase - G6P glucose-6-phosphate - 6PG 6-phosphogluconate - RUDP ribulose-1,5-bisphosphate - Tricine N-Tris (hydroxymethyl)-methylglycine     

Intensity of microcarrier collisions in turbulent flow

A model is developed, allowing estimation of the share of inelastic interparticle collisions in total energy dissipation for stirred suspensions. The model is restricted to equal-sized, rigid, spherical particles of the same density as the surrounding Newtonian fluid. A number of simplifying assumptions had to be made in developing the model. According to the developed model, the share of collisions in energy dissipation is small.List of Symbols b parameter in velocity distribution function (Eq. (28)) - c _K factor in Kolmogoroff spectrum law (Eq. (20)) - D _t(r _p ) m²/s characteristic dispersivity at particle radius scale (Eq. (13)) - E(k, t) m³/s² energy spectrum as function of k and t (Eq. (16)) - E _K (k) m³/s² energy spectrum as function of k in Kolmogoroff-region (Eq. (20)) - E _p dimensionless mean kinetic energy of a colliding particle (Eq. (36)) - E _cp dimensionless kinetic energy exchange in a collision (Eq. (37)) - G(x, s) dimensionless energy spectrum as function of x and s (Eq. (16)) - G _B(x) dimensionless energy spectrum as function of x for boundary region (Eq. (29)) - G _K(x) dimensionless energy spectrum as function of x for Kolmogoroff-region (Eq. (21)) - g m/s² gravitational acceleration - I _cp dimensionless collision intensity per particle (Eq. (38)) - I _cv dimensionless volumetric collision intensity (Eq. (39)) - k l/m reciprocal of length scale of velocity fluctuations (Eq. (17)) - K dimensionless viscosity (Eq. (13)) - n(2) dimensionless particle collision rate (Eq. (12)) - n(r) l/s particle exchange rate as function of distance from observatory particle center (Eq. (7)) - r m vector describing position relative to observatory particle center (Eq. (2)) - r m scalar distance to observatory particle center (Eq. (3)) - r _pm particle radius (Eq. (1)) - s dimensionless time (Eq. (10)) - SC kg/ms³ Severity of collision (Eq. (1)) - t s time (Eq. (2)) - u(r, t) m/s velocity vector as function of position vector and time (Eq. (2)) - u(r, t) m/s magnitude of velocity vector as function of position vector and time (Eq. (3)) - u _r(r, t) m/s radial component of velocity vector as function of position vector and time (Eq. (3)) - u _r (r, t) m/s magnitude of radial component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u _gsm/s superficial gas velocity - u(r) m/s root mean square velocity as function of distance from observatory particle center (Eq. (3)) - u_r(r) m/s root mean square radial velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s root mean square latitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s Root mean square longitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - w(x) dimensionless root mean square velocity as function of dimensionless distance from observatory particle center (Eq. (11)) - V _pm³ particle volume (Eq. (36)) - w(2) dimensionless root mean square collision velocity (Eq. (34)) - w ^* parameter in boundary layer velocity equation (Eq. (24)) - x dimensionless distance to particle center (Eq. (9)) - x ^* value of x where G _Band G _K-curves touch (Eq. (32)) - x _K dimensionless micro-scale (Kolmogoroff-scale) of turbulence (Eq. (15)) - volumetric particle hold-up - m²/s³ energy dissipation per unit of mass - m²/s kinematic viscosity - kg/m³ density - (r) m³/s fluid-exchange rate as function of distance to observatory particle center - Latitudinal co-ordinate (Eq. (5)) - Longitudinal co-ordinate (Eq. (5))     

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     

Diagnosing lactic acid fermentation based on specific rates of growth,substrate consumption and product formation

The on-line calculated specific rates of growth, substrate consumption and product formation were used to diagnose microbial activities during a lactic acid fermentation. The specific rates were calculated from on-line measured cell mass, and substrate and product concentrations. The specific rates were more sensitive indicators of slight changes in fermentation conditions than such monitored data as cell mass or product concentrations.List of Symbols 1/h specific rate of cell growth - 1/h specific rate of substrate consumption - 1/h specific rate of product formation - ^* dimensionless specific rate of cell growth - ^* dimensionless specific rate of substrate consumption - ^* dimensionless specific rate of product formation - _max 1/h maximum specific rate of cell growth - _max 1/h maximum specific rate of substrate consumption - _max 1/h maximum specific rate of product formation - X g/l cell mass concentration - S g/l substrate concentration - S ^* dimensionless substrate concentration - S ₀ g/l initial substrate concentration - P g/l product concentration     

Transport of branched-chain amino acids in Corynebacterium glutamicum

The transport of branched-chain amino acids was characterized in intact cells of Corynebacterium glutamicum ATCC 13032. Uptake and accumulation of these amino acids occur via a common specific carrier with slightly different affiniteis for each substrate (K _m[Ile]=5.4 M, K _m[Leu]=9.0 M, K _m[Val]=9.5 M). The maximal uptake rates for all three substrates were very similar (0.94–1.30 nmol/mg dw · min). The optimum of amino acid uptake was at pH 8.5 and the activation energy was determined to be 80 kJ/mol. The transport activity showed a marked dependence on the presence of Na⁺ ions and on the membrane potential, but was independent of an existing proton gradient. It is concluded, that uptake of branched-chain amino acid transport proceeds via a secondary active Na⁺-coupled symport mechanism.Abbreviations CCCP Carboxyl cyanide m-chlorophenylhydrazone - dw dry weight - MES 2[N-morpholino]ethanesulfonic acid - mon monensin - nig nigericin - TPP tetraphenylphosphonium bromide - Tris tris[hydroxymethyl]aminomethane - val valinomycin     

The dynamic performance of an immobilised-urease bioreactor in a recycle loop

Use of immobilised urease is a promising alternative for the removal of urea from blood plasma in association with an artificial kidney device. In such a device, carrier particles containing the immobilised enzyme are retained within an extracorporeal vessel through which blood perfuses. During the operation of the system, urea diffuses into the immobilisation matrix where it is hydrolysed by urease. This system is intrinsically dynamic, since the urea concentration changes continuously with time as the perfusing blood is progressively cleared of urea. Its design and optimisation is therefore a significant technical challenge. This paper presents a model for and a simulation study of the continuous operation of an immobilised urease artificial kidney device operating, in fluidized bed mode, in a recycle loop. The partial differential equations that describe the system account for axial backmixing, intraparticle and external mass transfer resistances and intraparticle urea hydrolysis. The performed simulations reveal the effect of key parameters, such as the liquid recirculation rate and the size of the enzyme carriers on the performance of the system. Based on those, optimum operating conditions for maximum efficiency have been determined. The presented mathematical model and methodology is of general nature and thus suitable for the design and optimisation of a variety of dynamic (batch or semi-batch) biochemical systems.List of Symbols B _m dimensionless number defined as B _m=k _eR/D_eff - C _L urea concentration in the bulk liquid - C _R urea concentration at the particle surface - C _R ^L urea concentration at the inner side of the stagnant film surrounding the particle; C _R=C _R ^L / - C _p intraparticle urea concentration - D _eff, D effective intraparticle diffusivity of urea - D _L axial dispersion coefficient in the bioreactor - F volumetric flowrate - k reaction rate constant - k _e external mass transfer coefficient - k _n parameter, k _n=D _eff(n/R)² - L bioreactor length - Pe Peclet number, defined as Pe=(uL/D _L) - R particle radius (2R=D _P) - R _h instantaneous urea hydrolysis rate - u axial superficial velocity in the reactor - V reactor volume - X dimensionless length Greek Letters partition coefficient - bed voidage - integration variable - dimensionless time; = tF/V