Separation process of binary protein solution by ultracentrifuge

Separation process of a binary protein solution by ultracentrifuge with an angle rotor was discussed by considering the calculated distribution of concentration in an ultracentrifugal tube. The weight fraction of the desired protein and the recovery index after the ultracentrifugation were calculated from the distribution of the concentration. When the weight fraction after the ultracentrifugation is given, the optimal ultracentrifugal time was determined so as to maximize the recovery index.List of Symbols c _B kg/cm³ concentration of Bovine serum albumin - c _L kg/cm³ concentration of Lysozyme - D cm²/s diffusion coefficient - d cm diameter of ultracentrifugal tube - R dimensionless collecting range - r ^* dimensionless radial coordinate - r ₁ cm minimum radius of ultracentrifugal tube - r ₂ cm maximum radius of ultracentrifugal tube - s s sedimentation constant - t s ultracentrifugal time - X _L weight fraction of Lysozyme - X _LO initial weight fraction of Lysozyme - Y _L recovery index of Lysozyme - inclination of ultracentrifugal tube - s^–1 angular velocity of rotation     

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

Biotransformation of cephalosporin C (CPS-C) to 7-aminocephalosporanic acid (7-ACA) was carried out with coimmobilized permeabilized cells of Trigonopsis variabilis and Pseudomonas species entrapped in Ca-pectate gel beads. Good aeration and stirring during the process was assured. The analysis of this complicated biochemical process in a heterogeneous system was based on the identification of individual effects (internal diffusion, reaction) running simultaneously. A spectrophotometric method was proposed for the determination of 7-(-ketoadipyl amido) cephalosporanic acid (CO-GL-7-ACA) and 7-ACA. The reaction-diffusion model containing dimensionless partial differential equations was solved by using the orthogonal collocation method. A good agreement between experimental values and values predicted by the mathematical model was obtained. Numerical simulations were performed on the basis of following the two assumptions:- several times higher activity of both cells,- hydrogen peroxide was continuously supplied in the bioreactor.List of Symbols A m² surface of the bead - c _i mol/dm³ concentration of component in the bead and/or in the solution - c _i0 mol/dm³ initial concentration of component in the solution - c _l0 mol/dm³ initial concentration of CPS-C in the solution - C _jl orthogonal collocation weights of the first derivation - D _ei m²/s effective diffusion coefficient of the components - D _jl orthogonal collocation weights of the second derivation - k ₅ dm³/(mol · s) kinetic parameter of non-enzyme reaction - K _inh mol/dm³ inhibition parameter for the first enzyme reaction - K _i dimensionless Michaelis constant for the first and second enzyme reaction, defined in Eq. (7) - K _l dimensionless inhibition parameter for the first enzyme reaction, defined in Eq. (7) - K _mi mol/dm³ Michaelis constant for the first and second enzyme reaction - n number of beads - P( _i ) symbol of dimensionless reaction rate, defined in Eq. (13) - r m radial coordinate inside the bead - R m radius of the bead - R(c _i ) mol/(dm³ · s) symbol for reaction rate, defined in Eq. (6) - t s time - V _max mol/(dm³ · s) max. reaction rate for the first and second enzyme reaction - V _L dm³ volume of solution excluding the space occupied by beads - voidage in batch bioreactor - _P porosity of the bead - i dimensionless effective diffusion coefficient of the components, defined in Eq. (7) - dimensionless time, defined in Eq. (7) - _mi Thiele modulus, defined in Eq. (7) - _i dimensionless concentration, defined in Eq. (7) - dimensionless radial position inside the bead, defined in Eq. (7) - _l0 initial dimension concentration of CPS-C, defined in Eq. (9), (10) - _i0 initial dimension concentration of component, defined in Eq. (9), (10) 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).     

Evaluation of sensors for the control of a continuous ethanol fermentation

A method is presented for the evaluation of sensors used in the control of continuous fermentations. Simulations of open-loop response to input disturbance provided a starting point for the choice of sensor type. This was evaluated quantitatively through a sensitivity ratio. It was shown that in the case of ethanol fermentation, there existed three regions where different sensors could be used for the process control depending on the inlet sugar concentration. Sugar sensors were preferable above an inlet sugar concentration of 50 kg/m³, while ethanol sensors were preferable below 25 kg/m³. In the intermediate region, sugar and ethanol sensors demonstrated equally good performance. A controllability study of a continuous ethanol fermentation was also made. A single-stage continuous stirred-tank fermentor was simulated operating at a dilution rate of 0.1 1/h and inlet glucose concentration of 160 kg/m³. The outlet glucose concentration was controlled with a PI controller. Mean square error of the controller input signal during the first five hours after introducing input disturbance was taken as a measure of the controllability. This was studied in the relation to the two key sensor characteristics, sampling time and accuracy.List of Symbols c _p kg/m³ ethanol concentration - c _p kg/m³ fermentor ethanol concentration corresponding to c _si and D - c _s kg/m³ substrate (glucose) concentration - c _s kg/m³ fermentor glucose concentration corresponding to c _si and D - c _si kg/m³ inlet substrate (glucose) concentration - c _si kg/m³ inlet glucose concentration value used for sensitivity evaluation - c _sm kg/m³ glucose concentration — measured value - c _ss kg/m³ glucose concentration setpoint value - c _x kg/m³ biomass concentration - D 1/h dilution rate - D 1/h dilution rate value used for sensitivity evaluation - D _i 1/h dilution rate at ith sampling interval - D ₀ 1/h dilution rate at steady state - K _c m³/kgh controller gain - K _p kg/m³ product inhibition constant - K _s kg/m³ Monod constant - n ₁, n ₂ random numbers - r _p kg/m³ h ethanol production rate - r _s kg/m³ h substrate (glucose) consumption rate - r _x kg/m³ h biomass growth rate - vector of independent variables - y _i ith dependent variable - Y _ps ethanol yield - Y _xs biomass yield - parameter vector - _j jth parameter - _ij sensitivity of y_i with respect to _j - _p sensitivity of fermentor ethanol concentration - _s sensitivity of fermentor glucose concentration - sensitivity ratio - c _p kg/m³ ethanol concentration difference corresponding to a change of c _si by 5% - c _s kg/m³ glucose concentration difference corresponding to a change of c _si by 5% - c _si kg/m³ concentration difference added to c _si - _i kg/m³ error at ith sampling interval - 1/h specific growth rate - _m 1/h maximum specific growth rate - _s kg/m³ standard deviation of monitored glucose concentration - _I h min kg/m³ integral time - _s min sampling period The Swedish Ethanol Foundation and the National Board for Technical Development (NUTEK) are kindly acknowledged for the financial support of this project. The authors wish to thank Peter Warkentin for the linguistic advice.     

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     

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

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

Analysing the responses of photosynthetic CO2 assimilation to long-term elevation of atmospheric CO2 concentration

Understanding how photosynthetic capacity acclimatises when plants are grown in an atmosphere of rising CO₂ concentrations will be vital to the development of mechanistic models of the response of plant productivity to global environmental change. A limitation to the study of acclimatisation is the small amount of material that may be destructively harvested from long-term studies of the effects of elevation of CO₂ concentration. Technological developments in the measurement of gas exchange, fluorescence and absorption spectroscopy, coupled with theoretical developments in the interpretation of measured values now allow detailed analyses of limitations to photosynthesisin vivo. The use of leaf chambers with Ulbricht integrating spheres allows separation of change in the maximum efficiency of energy transduction in the assimilation of CO₂ from changes in tissue absorptance. Analysis of the response of CO₂ assimilation to intercellular CO₂ concentration allows quantitative determination of the limitation imposed by stomata, carboxylation efficiency, and the rate of regeneration of ribulose 1:5 bisphosphate. Chlorophyll fluorescence provides a rapid method for detecting photoinhibition in heterogeneously illuminated leaves within canopies in the field. Modulated fluorescence and absorption spectroscopy allow parallel measurements of the efficiency of light utilisation in electron transport through photosystems I and IIin situ.Abbreviations A net rate of CO₂ uptke per unit leaf area (µmol m^–2 s^–1) - A_sat light-saturated A - A₈₂₀ change in absorptance of PSI on removal of illumination (OD) - c CO₂ concentration in air (µmol mol^–1) - c_a c in the bulk air; c_i, c in the intercellular spaces - ce carboxylation efficiency (mol m^–2 s^–1) - E transpiration per unit leaf area (mol m^–2 s^–1) - F fluorescence emission of PSII (relative units) - F_m maximal level of F - F_o minimal level of F upon illumination when PSII is maximally oxidised - F_s the steady-state F following the m peak - F_v the difference between F_m and F_o - F'_m maximal F' generated after the m peak by addition of a saturating light pulse - F'_o the minimal level of F' after the m peak determined by re-oxidising PSII by far-red light - g₁ leaf conductance to CO₂ diffusion in the gas phase (mol m^–2 s^–1) - g'₁ leaf conductance to water vapour diffusion in the gas phase (mol m^–2 s^–1) - k_c and k_o the Michaelis constants for CO₂ and O₂, respectively, (µmol mol^–1); - J_max the maximum rate of regeneration of rubP (µmol m^–2 s^–1) - l stomatal limitation to CO₂ uptake (dimensionless, 0–1) - LCP light compensation point of photosynthesis (µmol m^–2 s^–1) - o_i the intercellular O₂ concentration (mmol mol^–1) - Pi cytosol inorganic phosphate concentration - PSI photosystem I - PSII photosystem II - Q photon flux (µmol m^–2 s^–1) - Q_abs Q absorbed by the leaf - rubisCO ribulose 1:5 bisphosphate carboxylase/oxygenase; rubP, ribulose 1:5 bisphosphate; s, projected surface area of a leaf (m²) - V_c,max is the maximum rate of carboxylation (µmol m^–2 s^–1) - W_c the rubisCO limited rate of carboxylation (µmol m^–2 s¹) - W_j the electron transport limited rate of regeneration of rubP (µmol m^–2 s^–1) - W_p the inorganic phosphate limited rate of regeneration of rubP (µmol m^–2 s^–1) - absorptance of light (dimensionless, 0–1) - _a of standard black absorber ₁, of leaf - _s of integrating sphere walls - , CO₂ compensation point of photosynthesis (µmol mol^–1) - the specificity factor for rubisCO carboxylation (dimensionless) - , convexity of the response of A to Q (dimensionless 0–1) - the quantum yield of photosynthesis on an absorbed light basis (A/Q_abs; dimensionless) - the quantum yield of photosynthesis on an incident light basis (A/Q; dimensionless) - _app the maximum - _m the maximum - _m,app the photochemical efficiency of PSII (dimensionless, 0–1) - _PSII,m the maximum      

A graphical method of determining the Michaelis-Menten constant free of external mass transfer resistance for immobilized enzymes in a packed bed reactor

Summary A graphical method of determining the Michaelis-Menten constant free of the external mass transfer resistance for a packed bed immobilized enzyme system was illustrated with examples from 3 different enzyme reactions. The intercept at the ordinate obtained by the straight line extrapolation of data points in the plot of apparent K_m value vs. the reciprocal of superficial velocity in column allowed an easy calculation of K_m free of external mass transfer resistance. An asymptotic value of apparent K_m value at infinite zero superficial velocity was ascribed to the fact that the mass transfer coefficient k_L, approached a definite value at this condition.Nomenclature K_m Michaelis-Menten constant, M/L³ - K_m' K_m free of external mass transfer resistance in a given ionic strength, M/L³ - Km" apparent K_m with external mass transfer resistance, M/L³ - S substrate concentration, M/L³ - S_o initial substrate concentration, M/L³ - k₂ rate constant, t^-1 - E enzyme concentration in support, M/L³ - void volume per unit volume of reactor, dimensionless - u superficial velocity of substrate, L/t - K_L mass transfer coefficient in liquid film, L/t - a external surface area of support per unit volume of reactor, L^-1 - ratio of average channeling length to particle diameter, dimensionless - d_p diameter of support particle, L - X fractional conversion of substrate, dimensionless - H partition coefficient, dimensionless - k a constant, 3 k₂E(1-)d_p/4 - T space time, t - N molecular flux, M/L²t - r radius of immobilized enzyme particle, L     

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     

Comparison of three granular support materials for anaerobic fluidized bed systems

Summary Three different materials, kaolin, pozzolana and biolite (a material used in a commercial anaerobic fluidized bed treatment process) when tested as supports for an anaerobic fluidized bed system had similar physical and fluidization properties but behaved differently towards the biomass hold-up. However, all three systems attained similar removal efficiency rates.Nomenclature U Fluidization velocity (m/s) - U₁ Terminal fluidization velocity (m/s) - g Local acceleration due to gravity (m/s²) - _s Solid density (kg/m³) - _f Fluid density (kg/m³) - P Pressure drop (Pa) - HRT Hydraulic retention time (days) - H_mf Height of bed at minimum fluidization (m) - H Height of bed (m) - C_d Drag coefficient (dimensionless) - W Mass of solids in bed (kg) - dp Particle diameter (m) - A Cross-sectional area of column (m²) - h column height (m) - Rc_t Terminal Reynolds no. - Voidagc (fractional free volume, dimensionless) - _mf Voidage (fractional free volume) at minimum of fluidization (dimensionless)     

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))     

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     

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     

Flight of the honey bee VI: energetics of wind tunnel exhaustion flights at defined fuel content,speed adaptation and aerodynamics

To gain information on extended flight energetics, quasi-natural flight conditions imitating steady horizontal flight were set by combining the tetheredflight wind-tunnel method with the exhaustion-flight method. The bees were suspended from a two-component aerodynamic balance at different, near optimum body angle of attack and were allowed to choose their own speed: their body mass and body weight was determined before and after a flight; their speed, lift, wingbeat frequency and total flight time were measured throughout a flight. These values were used to determine thrust, resultant aerodynamic force (magnitude and tilting angle), Reynolds number, total flight distance and total flight impulse. Flights in which lift was body weight were mostly obtained. Bees, flown to complete exhausion, were refed with 5, 10, 15 or 20 l of a 1.28-mol·l^-1 glucose solution (energy content w=18.5, 37.0, 55.5 or 74.0 J) and again flown to complete exhaustion at an ambient temperature of 25±1.5°C by a flight of known duration such that the calculation of absolute and relative metabolic power was possible. Mean body mass after exhaustion was 76.49±3.52 mg. During long term flights of 7.47–31.30 min similar changes in flight velocity, lift, thrust, aerodynamic force, wingbeat frequency and tilting angle took place, independent of the volume of feeding solution. After increasing rapidly within 15 s a more or less steady phase of 60–80% of total flight time, showing only a slight decrease, was followed by a steeper, more irregular decrease, finally reaching 0 within 20–30 s. In steady phases lift was nearly equal to resultant aerodynamic force; tilting angle was 79.8±4.0°, thrust to lift radio did not vary, thrust was 18.0±7.4% of lift, lift was somewhat higher/equal/lower than body mass in 61.3%, 16.1%, 22.6% of all totally analysable flights (n=31). The following parameters were varied as functions of volume of feeding solution (5–20 l in steps of 5 l) and energy content. (18.5–74.0 J in steps of 18.5 J): total flight time, velocity, total flight distance, mean lift, thrust, mean resultant aerodynamic force, tilting angle, total flight impulse, wingbeat frequency, metabolic power and metabolic power related to body mass, the latter related to empty, full and mean (=100 mg) body mass. The following positive correlations were found: L=1.069·10^-9 f ^2.538; R=1.629·10^-9 f ^2.464; P _m=7.079·10^-8 f ^2.456; P _m=0.008v+0.008; P _m=18.996L+0.022; P _m=19.782R+0.021; P _m=82.143T+0.028; P _m=1.245·bm _f ^1.424 ; P _{mrel e}=6.471·bm _f ^1.040 ; =83.248+0.385. The following negative correlations were found: V=3.939–0.032; T=1.324·10^-4–0.038·10^-4. Statistically significant correlations were not found in T(f), L(), R(), f(), P _m(bm _e), P _{m rel e}(bm _e), P _{m rel f}(bm _e), P _{m rel f}(bm _f).Abbreviations A(m²) frontal area - bl(m) body length - bm(mg) body mass - c(mol·1^-1) glucose concentration of feeding solution - c _D (dimensionless) drag coefficient, related to A - D(N) drag - F _w(N) body weight - F _wp weight of paper fragment lost at flight start - f wingbeat frequency (s^-1) - g(=9.81 m·s^-2) gravitational acceleration - I(Ns)=R(t) dt total impulse of a flight - L(N) lift vertical sustaining force component - P _m(J·s^-1=W) metabolic power - P_{m ret} (W·g^-1) metabolic power, related to body mass - R(N) resultant aerodynamic force - Re v·bl·v ^-1 (dimensionless) Reynolds number, related to body length - s(m) v(t) dt virtual flight distance of a flight - s(km) total virtual flight distance - T (N) thrust horizontal force component of horizontal flight - T _a (°C) ambient temperature - t(s) time - t _tot (s or min) total flight time - v(m·s^-1) flight velocity - v(l) volume of feeding solution - W (J) energy and energy content of V - ( °) body angle of attack between body longitudinal axis and flow direction - ( °) tilting angle ( 90°) between R and the horizont in horizontal flight v(=1.53·10^-5m²·s^-1 for air at 25°) kinematic viscosity - (=1.2 kg·m^-3 at 25°C) air density     

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     

Packed-bed immobilized enzyme reactors for complex processes

Utilization of enzymic reactors for biotechnological-biomedical applications is currently developing at a sustained pace.Our present study concentrates on development of procedures for describing the performance of devices where enzyme-catalyzed reactions between two substrates take place, and for the rational design and optimization of the reactors considered. Within this context, an analytical model was developed for immobilized enzyme packed-bed reactors; it takes into account internal diffusion limitations for the cosubstrates, and hydrodynamic backmixing effects. In order to overcome the complex mathematical problems involved, the compartmental analysis approach was employed.Using this model, performance was simulated for various configurations of the enzymic unit, i.e. from a continuously operated stirred tank reactor (CSTR) to an essentially plug flow type. In addition, an experimental method is described for quantitatively assessing the backmixing effects prevailing in the reactor.The procedures established also provide the ground for further developments, particularly for systems where, in parallel to the enzymic reaction, additional processes (e. g. complexation) take place.List of Symbols C _j,i mM Concentration of substrate j in the pores of stage - iD _j cm²/s Internal (pore) diffusion coefficient of substrate j; defined in Eq. (7) - D _e cm²/s Axial dispersion diffusion coefficient - D _j, cm²/s cm²/s Bulk diffusion coefficient for substrate j - E mM Enzyme concentration inside the catalytic pores - J _j,immol/s/cm² Net flux of substrate j taking place from the bulk of stage i into the corresponding pores; defined in Eq. (6) - K _m,1, K _m,2 mM Michaelis-Menten constants for cosubstrates 1 and 2, respectively - k s ^–1 Catalytic constant - k _s cm/s Catalytic constant - n Total number of elementary stages in the reactor - Q cm³/s Volumetric flow rate throught the reactor - r cm Radius of the pore - R _j,i mM/s Reaction rate of substrate j in stage i, in terms of volumetric units - S cm² Internal surface of a pore - S _j,0 mM Concentration of substrate j in the reactor feed - S _j,i–1, S _j,i mM Concentration of substrate j in the bulk phase leaving stages i — 1 and i, respectivley - V _i cm³ Total volume of stage i (bulk phase + pore phase + inert solid carrier) - V cm³ Total volume of the reactor - V _m ^* mmol/s/cm² Maximal reaction rate in terms of surface units; defined in Eq. (8) - V _m mM/s Maximal reaction rate in terms of volumetric units; defined in Eq. (8) - V _p cm³ Volume of one pore - y cm Axial coordinate of the pores - y ₀ cm Depth of the pores - Z cm Axial coordinate of the reactor - Z ₀ cm Length of the reactor - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - Ratio between the radius of the enzyme molecule and the radius of the pore (dimensionless) - V₁ Dimensionless parameter; defined in Eq. (21) - v₂ Dimensionless parameter; defined in Eq. (21) - Q Volumetric packing density of catalytic particles (dimensionless) - Ø Porosity of the catalytic particles (dimensionless) - Ø Dimensionless concentration of substrate j in pores of stage i; defined in Eq. (16) - _j,i-1,_j,i Dimensionless concentration of substrate j in the bulk phase of stage i; defined in Eq. (18) - Dimensionless position; defined in Eq. (16) - ² s² Variance; defined in Eq. (33) - Mean residence time in the reactor; defined in Eq. (33)     

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     

A simple dynamic method for on-line and off-line determination of kLa during cultivation of animal cells

Summary A new, fast method is described to determine k_La either off-line, or on-line during animal-cell cultivation. Since it does not need the equilibrium concentration of oxygen in the liquid phase (C*), it is not required to await a new steady state. Furthermore, the results do not depend on the calibration value of the dissolved-oxygen probe. The method yielded accurate values for k_La, both for an oxygen-consuming and a non-consuming system.Nomenclature C _L Dissolved-oxygen concentration [mol·m^-3] - C ^* C _L in equilibrium with the oxygen concentration in the gas phase [mol·m^-3] - C _L, Equilibrium oxygen concentration at stationary conditions [mol·m^-3] - k_La Volumetric oxygen transfer coefficient [s^-1] - r Specific oxygen consumption of biomass [mol·cell^-1·s^-1] - X Cell concentration [cells·m^-3] - t Time [s] - Noise of dissolved-oxygen probe [mol·m^-3] - Absolute error of k_La-measurement [s^-1]     

Optimum temperature policy for batch reactors performing biochemical reactions in the presence of enzyme deactivation

A necessary condition is found for the optimum temperature policy which leads to the minimum reaction time for a given final conversion of substrate in a well stirred, enzymatic batch reactor performing an enzyme-catalyzed reaction following Michaelis-Menten kinetics in the presence of first order enzyme decay. The reasoning, which is based on Euler's classical approach to variational calculus, is relevant for the predesign steps because it indicates in a simple fashion which temperature program should be followed in order to obtain the maximum advantage of existing enzyme using the type of reactor usually elected by technologists in the fine biochemistry field. In order to highlight the relevance and applicability of the work reported here, the case of optimality under isothermal operating conditions is considered and a practical example is worked out.List of Symbols C _E mol.m^–3 concentration of active enzyme - C _E ^* dimensionless counterpart of C_E - C _E,0 mol.m^–3 initial concentration of active enzyme - C _E,b mol.m^–3 final concentration of active enzyme - C _E,opt ^* optimal dimensionless counterpart of C_E - C _smol.m^–3 concentration of substrate - C _S ^Emphasis>/* dimensionless counterpart of C_S - C _S,0mol.m^–3 initial concentration of substrate - C _S,bmol.m^–3 final concentration of substrate - E enzyme in active form - E ₃ ^* dimensionless counterpart of E_a,3 - E _a,1J.mol^–1 activation energy associated with k₁ - E _a,3J.mol^–1 activation energy associated with k₃ - E _d enzyme in deactivated form - ES enzyme/substrate complex - k ₁ s^–1 kinetic constant associated with the enzyme-catalyzed transformation of substrate - k _1,0 s^–1 preexponential factor associated with k₁ - k ₂ mol^–1.m³s^–1 kinetic constant associated with the binding of substrate to the enzyme - k _–2 s^–1 kinetic constant associated with the dissociation of the enzyme/substrate complex - K _2,0 mol.m^–3 constant value of K₂ - K _2,0 ^* dimensionless counterpart of K_2,0 - k ₃ s^–1 kinetic constant associated with the deactivation of enzyme - k _3,0 s^–1 preexponential factor associated with k₃ - k _3,0 ^* dimensionless counterpart of k_3,0 - P product - R J.K^–1.mol^–1 ideal gas constant - S substrate - t s time since start-up of reaction - T K absolute temperature - T ^* dimensionless absolute temperature - T _i,opt ^* optimal dimensionless isothermal temperature of operation - T _opt ^* optimal dimensionless temperature of operation - t _b s time of a batch - t _b ^* dimensionless counterpart of t_b - t _b,min ^* minimum value of the dimensionless counterpart of t_b Greek Symbols dimensionless counterpart of C_E,0 - dimensionless counterpart of C_E,b - dummmy variable of integration - dummy variable of integration - auxiliary dimensionless variable - ^* dimensionless variation of k₁ with temperature - _i ^* dimensionless value of k₁ under isothermal conditions - _opt ^* optimal dimensionless variation of k₁ with temperature     

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     

Cell recycling studies for α-amylase production by Bacillus amyloliquefaciens

Production of -amylase by a strain of Bacillus amyloliquefaciens was investigated in a cell recycle bioreactor incorporating a membrane filtration module for cell separation. Experimental fermentation studies with the B. amyloliquefaciens strain WA-4 clearly showed that incorporating cell recycling increased -amylase yield and volumetric productivity as compared to conventional continuous fermentation. The effect of operating conditions on -amylase production was difficult to demonstrate experimentally due to the problems of keeping the permeate and bleed rates constant over an extended period of time. Computer simulations were therefore undertaken to support the experimental data, as well as to elucidate the dynamics of -amylase production in the cell recycle bioreactor as compared to conventional chemostat and batch fermentations. Taken together, the simulations and experiments clearly showed that low bleed rate (high recycling ratio) various a high level of -amylase activity. The simulated fermentations revealed that this was especially pronounced at high recycling ratios. Volumetric productivity was maximum at a dilution rate of around 0.4 h^–1 and a high recycling ratio. The latter had to exceed 0.75 before volumetric productivity was significantly greater than with conventional chemostat fermentation.List of Symbols a proportionality constant relating the specific growth rate to the logarithm of G (h) - a ₁ reaction order with respect to starch concentration - a ₂ reaction order with respect to glucose concentration - B bleed rate (h^–1) - C starch concentration (g/l) - C ₀ starch concentration in the feed (g/l) - D dilution rate (h^–1) - D _E volumetric productivity (KNU/(mlh)) - e intracellular -amylase concentration (g/g cell mass) - E extracellular -amylase concentration (KNU/ml) - F volumetric flow rate (l/h) - G average number of genome equivalents of DNA per cell - k _l intracellular equilibrium constant - k ₂ intracellular equilibrium constant - k _s Monod saturation constant (g/l) - k ₃ excretion rate constant (h^–1) - k _d first order decay constant (h^–1) - k _gl rate constant for glucose production - k _st rate constant for starch hydrolysis - k _t1 proportionality constant for -amylase production (gmRNA/g substrate) - k ₁ translation constant (g/(g mRNAh)) - KNU kilo Novo unit - m maintenance coefficient (g substrate/(g cell massh)) - n number of binding sites for the co-repressor on the cytoplasmic repressor - Q repression function K₁/K₂Q1.0 - R ratio of recycling - R _s rate of glucose production (g/lh) - r _c rate of starch hydrolysis (g/(lh)) - R _eX retention by the filter of the compounds X: starch or -amylase - r intracellular -amylase mRNA concentration (g/g cell mass) - r _C volumetric productivity of starch (g/lh) - r _E volumetric productivity of intracellular -amylase (KNU/(g cell massh)) - r _r volumetric productivity of intracellular mRNA (g/(g cell massh)) - r _e volumetric productivity of extracellular -amylase (KNU/(mlh)) - r _s volumetric productivity of glucose (g/(lh)) - r _X volumetric productivity of cell mass (g/(lh)) - S ₀ free reducing sugar concentration in the feed (g/l) - S extracellular concentration of reducing sugar (g/1) - t time (h) - V volume (l) - X cell mass concentration (g/l) - Y yield coefficient (g cell mass/g substrate) - Y _E/S yield coefficient (KNU -amylase/g substrate) - Y _E total amount of -amylase produced (KNU) - substrate uptake (g substrate/(g cell massh)) - specific growth rate of cell mass (h^–1) - _d specific death rate of cells (h^–1) - _m maximum specific growth rate of cell mass (h^–1) This study was supported by Bioprocess Engineering Programme of the Nordic Industrial Foundation and the Center for Process Biotechnology, the Technical University of Denmark.