Mathematical modeling of citric acid production by repeated batch culture

A mathematical model has been created for the process of citric acid biosynthesis by yeast (mutant strain Yarrowia lipolytica) cultivated by the repeated batch (RB) method on ethanol under conditions of nitrogen limitation. The model accounts for cell growth as a function of nitrogen concentration in the culture liquid; nitrogen uptake by growing cells; citric acid production; pH control in the fermentor by means of NaOH addition; and changes in system volume. The model represents a system of five nonlinear differential equations. Experimental measurements of cell concentration, citric acid concentration, and cultivation broth volume were used with the least squares method to determine the values of eight model parameters. The parameter values obtained were consistent with literature data and general concepts of cell growth and citric acid biosynthesis. The model has been used to predict optimum RB culture conditions.     

Analyzing the dynamics of cell growth and protein production in mammalian cell fed-batch systems using logistic equations

The logistic modeling approach was used to describe experimental viable cell density (X) and product concentration (P) data from two industrial fed-batch mammalian cell culture processes with maximum product concentrations in the 3.0-9.4 g/l range. In both cases, experimental data were well described by the logistic equations and the resulting specific growth rate and protein productivity profiles provided useful insights into the process kinetics. Subsequently, sensitivity equations for both the X and P models were analyzed which helped characterize the influence of model parameters on X and P time courses. This was augmented by conventional sensitivity analyses where five values of each model parameter, 25% apart, were used to generate X and P time courses. Finally, results from sensitivity analysis were used to simulate X and P time courses that were reflective of typical early- and late-stage fed-batch cell culture processes. Different combinations of the logistic model parameters were used to arrive at the same final product concentration demonstrating the ability of the logistic approach to describe the multitude of process paths that result in the same final product concentration. Overall, the capability of the logistic equations to well describe X and P data from fed-batch cultures, coupled with their ability to simulate the multitude of paths leading up to the desired cell density and product concentration profiles, make them a useful tool during mammalian cell fed-batch process development.     

Effect of operational conditions on the rate of citric acid production by rotating disk contactor using Aspergillus niger

The effect of operational conditions such as the specific biofilm area, oxygen concentration, and rotation speed on citric acid production by a rotating disk contactor (RDC) was examined. The overall productivity for a repeated batch culture was also compared with that for a non-repeated batch culture. The citric acid production rate per unit biofilm area (P) was almost constant regardless of the value of the specific film area. The rotation speed of the disks had no effect on P in the range of 5–20 rpm. The apparent saturation constant of dissolved oxygen concentration was 2.05 mg/l. Overall citric acid productivity for a 3-times-repeated batch culture was 1.7 times higher than that for the non-repeated batch culture.     

Optimizing medium constituents and fermentation conditions for citric acid production from palmyra jaggery using response surface method

The quantitative effects of pH, temperature, time of fermentation, sugar concentration, nitrogen concentration and potassium ferrocyanide on citric acid production were investigated using a statistical experimental design. It was found that palmyra jaggery (sugar syrup from the palmyra palm) is a suitable substrate for increasing the yield of citric acid using Aspergillus niger MTCC 281 by submerged fermentation. Regression equations were used to model the fermentation in order to determine optimum fermentation conditions. Higher yields were obtained after optimizing media components and conditions of fermentation. Maximum citric acid production was obtained at pH 5.35, 29.76 °C, 5.7 days of fermentation with 221.66 g of substrate/l, 0.479 g of ammonium nitrate/l and 2.33 g of potassium ferrocyanide/l.     

Citric acid production by a novel Aspergillus niger isolate: II. Optimization of process parameters through statistical experimental designs

In this work, sequential optimization strategy, based on statistical designs, was employed to enhance the production of citric acid in submerged culture. For screening of fermentation medium composition significantly influencing citric acid production, the two-level Plackett-Burman design was used. Under our experimental conditions, beet molasses and corn steep liquor were found to be the major factors of the acid production. A near optimum medium formulation was obtained using this method with increased citric acid yield by five-folds. Response surface methodology (RSM) was adopted to acquire the best process conditions. In this respect, the three-level Box-Behnken design was applied. A polynomial model was created to correlate the relationship between the three variables (beet molasses, corn steep liquor and inoculum concentration) and citric acid yield. Estimated optimum composition for the production of citric acid is as follows pretreated beet molasses, 240.1g/l; corn steep liquor, 10.5g/l; and spores concentration, 10(8)spores/ml. The optimum citric acid yield was 87.81% which is 14 times than the basal medium. The five level central composite design was used for outlining the optimum values of the fermentation factors initial pH, aeration rate and temperature on citric acid production. Estimated optimum values for the production of citric acid are as follows initial pH 4.0; aeration rate, 6500ml/min and fermentation temperature, 31.5 degrees C.     

Simplified Modeling of Simultaneous Reaction Kinetics of Carbon Oxidation and Nitrification in Biofilm Processes

Batch experiments with varying initial substrate concentrations and biomass volumes were performed in a three‐phase fluidized bed biofilm reactor treating simulated domestic wastewater to study the simultaneous carbon oxidation and nitrification in the biofilm process. A simplified mass balance equation for the biofilm was proposed and five different kinetic rate equations were used to match the actual data. The kinetic parameters were obtained by nonlinear regression analysis on a set of two differential equations representing the simultaneous carbon oxidation and nitrification. The competitive inhibition model incorporating the effects of total organic carbon (TOC) concentrations on nitrification rates was the best‐suited model based on the average r². In this model, oxygen concentration and its affinity constants were not included. Instead, it was assumed that the rate of carbon oxidation is independent of the NH₄⁺‐N, while nitrification is affected by TOC. The number of parameters was successfully minimized without reducing its ability to accurately predict the bulk concentration time course, which would reduce computational complexity and possibly enhance the availability for an actual wastewater treatment process.     

Modeling biocide action against biofilms

A phenomenological model of biocide action against microbial biofilms was derived. Processes incorporated in the model include bulk flow in and out of a well-mixed reactor, transport of dissolved species into the biofilm, substrate consumption by bacterial metabolism, bacterial growth, advection of cell mass within the biofilm, cell detachment from the biofilm, cell death, and biocide concentration-dependent disinfection. Simulations were performed to analyze the general behavior of the model and to perform preliminary sensitivity analysis to identify key input parameters. The model captured several general features of antimicrobial agent action against biofilms that have been observed widely by experimenters and practitioners. These included (1) rapid disinfection followed by biofilm regrowth, (2) slower detachment than disinfection, and (3) reduced susceptibility of microorganisms in biofilms. The results support the plausibility of a mechanism of biofilm resistance in which the biocide is neutralized by reaction with biofilm constituents, leading to a reduction in the bulk biocide concentration and, more significantly, biocide concentration gradients within the biofilm. Sensitivity experiments and analyses identified which input parameters influence key response variables. Each of three response variables was sensitive to each of the five input parameters, but they were most sensitive to the initial biofilm thickness and next most sensitive to the biocide disinfection rate coefficient. Statistical regression modeling produced simple equations for approximating the response variables for situations within the range of conditions covered by the sensitivity experiment. The model should be useful as a tool for studying alternative biocide control strategies. For example, the simulations suggested that a good interval between pulses of biocide is the time to minimum thickness. (c) 1996 John Wiley & Sons, Inc.     

A model for treating isopropyl alcohol and acetone mixtures in a trickle-bed air biofilter

A mathematical model that incorporates mass transfer process and biofilm reactions is presented to predict the performance of a trickle-bed air biofilter (TBAB) for treating isopropyl alcohol (IPA) and acetone (ACE) mixtures. The model consists of a set of mass balance equations for IPA, ACE and oxygen in the bulk gas phase and within the biofilm. The effluent gas phase IPA and ACE concentrations predicted by the present model were in good agreement with the measured data available in a previous study. The important parameters were evaluated by sensitivity analysis to determine their respective effects on model performance. Four parameters were identified that strongly influenced model performance: surface area of the biofilm per unit volume of packing material (A_S), empty-bed residence time (EBRT), maximum specific growth rate of microorganism (μ_m), and microbial yield coefficient (Y). Practical applications of the model to derive the performance equation of TBAB for treating different inlet IPA and ACE concentrations were also demonstrated.     

Linearized kinetic model of<Emphasis Type="Italic"> Listeria monocytogenes</Emphasis> biofilm growth

In this study the dynamics of biofilm formation on aluminum has been investigated. The process of cell growth has been observed using fluorescence microscopy. It has been confirmed that the process of biofilm formation can be represented as a sum of two separate processes: cell adhesion and colony proliferation. The derived set of equations describes kinetics of surface population growth and characteristic times for adsorption and combined growth processes, including characteristic time for the nutrient supply depletion. All equations contain variables based on the fundamental characteristics of bacterial population and can be easily determined from the experimental data or estimated theoretically. The developed theoretical model allows obtaining realistic values for population growth time and characteristic time for nutrient limitation occurrence during the biofilm development. Resulting equations qualitatively describe the biofilm formation process, and allow predicting microbial kinetics in the batch reactor system and determining critical values of the process parameters.     

Optimization of citric acid production from a carrot juice-based medium by <Emphasis Type="Italic">Yarrowia lipolytica</Emphasis> using response surface methodology

In this study, diluted and fortified carrot juice was used for modelling and optimization of citric acid production by a new mutant strain, Yarrowia lipolytica K-168. Protein concentrate obtained from fine flour -a byproduct of semolina production- was used as a nitrogen source in the fermentation medium. Interactive effects of selected independent variables, initial total sugar concentration, initial pH, initial concentration of protein concentrate obtained from fine flour of semolina and temperature, on the growth and citric acid production of the yeast were investigated. An experimental design including 30 experiments was conducted by using the method of central composite design. Modelling the effects of these independent variables on maximum citric acid concentration, maximum citric acid production rate, citric acid yield, the ratio of maximum citric acid concentration to maximum isocitric acid concentration and specific growth rate were performed by response surface methodology. The variations of all of the responses with the independent variables were defined by a quadratic model. Numeric optimization was performed by using the desireability function. The conditions with 190.83 g/L initial sugar concentration, 5.90 initial pH, 0.07 g/L initial concentration of fine flour protein concentrate and 27.86 °C were determined as optimal conditions for citric acid production. The maximum citric acid concentration reached to 80.53 g/L in optimal conditions.     

Oxygen uptake and citric acid production by Candida lipolytica Y 1095

The rates of oxygen uptake and oxygen transfer during cell growth and citric acid production by Candida lipolytica Y 1095 were determined. The maximum cell growth rate, 1.43 g cell/L . h, and volumetric oxygen uptake rate, 343 mg O(2)/L . h, occurred approximately 21 to 22 h after inoculation. At the time of maximum oxygen uptake, the biomass concentration was 1.3% w/v and the specific oxygen uptake rate was slightly greater than 26 mg O(2)/g cell . h. The specific oxygen uptake rate decreased to approximately 3 mg O(2)/g cell . h by the end of the growth phase.During citric acid production, as the concentration of dissolved oxygen was increased from 20% to 80% saturation, the specific oxygen uptake and specific citric acid productivity (mg citric acid/g cell . h) increased by 160% and 71%, respectively, at a biomass concentration of 3% w/v. At a biomass concentration of 5% w/v, the specific oxygen uptake and specific citric acid productivity increased by 230% and 82%, respectively, over the same range of dissolved oxygen concentrations.The effect of dissolved oxygen on citric acid yields and productivities was also determined. Citric acid yields appeared to be independent of dissolved oxygen concentration during the initial production phase; however, volumetric productivity (g citric acid/L . h) increased sharply with an increase in dissolved oxygen. During the second or subsequent production phase, citric acid yields increased by approximately 50%, but productivities decreased by roughly the same percentage due to a loss of cell viability under prolonged nitrogen-deficient conditions. (c) 1994 John Wiley & Sons, Inc.     

A multikinetic model approach to predict gluconic acid production in an airlift bioreactor

This paper uses a multikinetic approach to predict gluconic acid (GA) production performance in a 4.5 L airlift bioreactor (ALBR). The mathematical model consists of a set of simultaneous firstorder ordinary differential equations obtained from material balances of cell biomass, GA, glucose, and dissolved oxygen. Multikinetic models, namely, logistic and contois equations constitute kinetic part of the main model. The main model also takes into account the hydrodynamic and mass transfer parameters. These equations were solved using ODE solver of MATLAB v6.5 software. The mathematical model was validated with the experimental data available in the literature and is used to predict the effect of change in initial biomass and air sparging rate on the GA production. It is concluded that the mathematical model incorporated with multikinetic approach would be more efficient to predict the change in operating parameters on overall bioprocess of GA production in an ALBR.     

Modeling of oleaginous fungal biofilm developed on semi-solid media

An oleaginous fungus, Mortierella isabellina, able to transform efficiently sugar to storage lipid, was used as a model microorganism which develops a biofilm structure during the semi-solid fermentation process for the production of biodiesel from sweet sorghum. A mathematical model was developed to describe the fungal oil production in M. isabellina biofilm. The model describes diffusion and consumption of sugars and nitrogen of sweet sorghum and single cell oil production in a biofilm, which grows according to the kinetics of double-substrate limitation (sugars and nitrogen) with sugar inhibition. Experimental data from a previous experimental study were used to determine the kinetic parameters of the model. Maximum biofilm thickness and the percentage of lipid inside the biofilm were estimated using the model at 1892 μm and 15%, respectively. The proposed mathematical model could prove a useful tool for designing semi-solid fermentation processes.     

Citric acid production by Candida lipolytica Y 1095 in cell recycle and fed-batch fermentors

The effect of dissolved oxygen on citric acid production and oxygen uptake by Candida lipolytica Y 1095 was evaluated in cell recycle and fed-batch fermentation systems. The maximum observed volumetric productivity, which occurred at a dilution rate of 0.06 h(-1), a dissolved oxygen concentration of 80%, and a biomass concentration of 5% w/v, in the cell recycle system, was 1.32 g citric acid/L . h. At these same conditions, the citric acid yield was 0.65 g/g and the specific citric acid productivity was 24.9 mg citric acid/g cell . h. In the cell recycle system, citric acid yields ranged from 0.45 to 0.72 g/g. Both the volumetric and specific citric acid productivities were dependent on the dilution rate and the concentration of dissolved oxygen in the fermentor. Similar productivities (1.29 g citric acid/L . h) were obtained in the fed-batch system operated at a cycle time of 36 h, a dissolved oxygen concentration of 80%, and 60 g total biomass. Citric acid yields in the fed-batch fermentor were consistently lower than those obtained in the cell recycle system and ranged from 0.40 to 0.59 g/g. Although citric acid yields in the fed-batch fermentor were lower than those obtained in the cell recycle system, higher citric:isocitric acid ratios were obtained in the fed-batch fermentor. As in the cell recycle system, both the volumetric and specific citric acid productivities in the fed-batch fermentor were dependent on the cycle time and dissolved oxygen concentration. (c) 1995 John Wiley & Sons, Inc.     

Optimization of citric acid production from Candida lipolytica Y-1095 using n-paraffin

Currently, the majority of worldwide microbial production of citric acid utilizes Aspergillus niger in a carbohydrate based submerged fermentation. Due to their high carbon content, hydrocarbons also have the potential of producing high concentrations of citric acid. Initial lab experiments conducted using 1875 ml batch fermentations with n-paraffin found that Candida lipolytica NRRL-Y-1095 assimilated the feedstock and had a citric acid productivity of 47 mg l(-1) h(-1). To determine the optimum level of initial biomass concentration, n-paraffin concentration, iron concentration and temperature for the production of citric acid, a central composite design was developed using 200 ml batch fermentations. The design involved conducting 31 batch fermentations under various combinations of high and low values of these four parameters. From this investigation empirical models were developed describing the interactions between the experimental parameters and citric acid production. It was found that the maximum concentration of citric acid produced was 9.8 g l(-1) and the optimum levels of each parameter for citric acid production were, 10--12% volume for initial biomass concentration, 10--15% volume for n-paraffin concentration, 10 mg l(-1) for ferric nitrate concentration, and 26--30 degrees C for temperature.     

Prediction of average biofilm density and performance of a spherical bioparticle under substrate inhibition

In this article, a model was proposed to predict the average performance and biofilm density of a spherical bioparticle under substrate inhibition in a fluidized bed system. The average biofilm density and substrate consumption rates were predicted for a definite biofilm thickness and limiting substrate concentrations. A diffusion and reaction model was developed over the bioparticle with biofilm-density dependent effective diffusion coefficients for maximum substrate consumption theory. This theory predicts the optimum density of a biofilm to yield a maximum substrate consumption rate within the biofilm, developed for the first time with this study and experimentally verified. A good correlation was observed between the model prediction and experimental results for biofilm density and substrate consumption rates. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 319-329, 1997.     

Production of biodiesel by lipase-catalyzed transesterification of vegetable oils: a kinetics study

Kinetics of production of biodiesel by enzymatic methanolysis of vegetable oils using lipase has been investigated. A mathematical model taking into account the mechanism of the methanolysis reaction starting from the vegetable oil as substrate, rather than the free fatty acids, has been developed. The kinetic parameters were estimated by fitting the experimental data of the enzymatic reaction of sunflower oil by two types of lipases, namely, Rhizomucor miehei lipase (RM) immobilized on ion-exchange resins and Thermomyces lanuginosa lipase (TL) immobilized on silica gel. There was a good agreement between the experimental results of the initial rate of reaction and those predicted by the proposed model equations, for both enzymes. From the proposed model equations, the regions where the effect of alcohol inhibition fades, at different substrate concentrations, were identified. The proposed model equation can be used to predict the rate of methanolysis of vegetable oils in a batch or a continuous reactor and to determine the optimal conditions for biodiesel production.     

A model for treating toluene and acetone mixtures by a trickle-bed air biofilter

A mathematical model that incorporates mass transfer process and biofilm reactions is presented to predict the performance of a trickle-bed air biofilter (TBAB) for treating toluene (T) and acetone (ACE) mixtures. The model consists of a set of mass balance equations for T, ACE and oxygen in the bulk gas phase and within the biofilm. The gas phase T and ACE concentrations predicted by the model were in good agreement with the measured data available in a previous study. The important parameters were evaluated in the sensitivity analysis to determine their respective effects on the model performance. Four parameters were identified as strongly influencing the model performance, the surface area of the biofilm per unit volume of packing material (A _S), the empty-bed residence time (EBRT), the maximum specific growth rate of microorganism ( _m), and the microbial yield coefficient (Y). A practical application of the model to derive the performance equation of TBAB is also given.     

Kinetics of fermentation processes

Kinetic studies on fermentation processes were made and a general equation of production rate was newly presented applying the kinetic theory on mierobial cell growth which was reported previously by the authors.^l,2 Equations for product concentration in fermentation time courses were derived by developing mathematically the general equation of production rate, and characteristic properties of fermentation processes were clarified. Some examples of fermentations were analyzed kinetically using the new kinetic theory. The calculated values of product, and cell concentrations were in good agreement with the observed values.