Adaptive on-line simulation of bioreactors: Fermentation monitoring and modeling system

Summary In order to study and control fermentation processes, indirect on-line measurements and mathematical models can be used. Here an on-line model for fermentation processes is presented. The model is based on atom and partial mass balances as well as on stability equations for the protolytes. The model is given an adaptive form by including transport equations for mass transfer and expressions for the fermentation kinetics. The state of the process can be estimated on-line using the balance component of the model completed with measurement equations for the input and the output flows of the process. Adaptivity is realized by means of on-line estimation of the parameters in the transport and kinetic expressions using recursive regression analysis. On-line estimation of the kinetic and mass transfer parameters makes model-based predictions possible and enables intelligent process control while facilitating testing of the validity of the measurement variables. A practical MS-Windows 3.1 model implementation called FMMS—Fermentation Monitoring and Modeling System is shown. The system makes it easy to configure the operating conditions for a run. It uses Windows dialogs for all set-ups, model configuration parameters, elemental compositions, on-line measurement devices and signal conditioning. Advanced on-line data analysis makes it possible to plot variables against each other for easy comparison. FMMS keeps track of over 100 variables per run. These variables are either measured or estimated by the model. Assay results can also be entered and plotted during fermentation. Thus the model can be verified almost instantly. Historical fermentation runs can be re-analyzed in simulation mode. This makes it possible to examine different signal conditining filters as well as the sensitivity of the model. Combined, the data analysis and the simulation mode make it easy to test and develop model theories and new ideas.     

Monitoring of recombinant protein production using bioluminescence in a semiautomated fermentation process

On-line optimization of fermentation processes can be greatly aided by the availability of information on the physiological state of the cell. The goal of our "BioLux" research project was to design a recombinant cell capable of intracellular monitoring of product synthesis and to use it as part of an automated fermentation system. A recombinant plasmid was constructed containing an inducible promoter that controls the gene coding for a model protein and the genes necessary for bioluminescence. The cells were cultured in microfermenters equipped with an on-line turbidity sensor and a specially designed on-line light sensor capable of continuous measurement of bioluminescence. Initial studies were done under simple culture conditions, and a linear correlation between luminescence and protein production was obtained. Such specially designed recombinant bioluminescent cells can potentially be applied for model-based inference of intracellular product formation, as well as for optimization and control of recombinant fermentation processes.     

Structured modeling and state estimation in a fermentation process: Lipase production by Candida rugosa

A simple structured mathematical model coupled with a methodology of state and parameter estimation is developed for lipase production by Candida rugosa in batch fermentation. The model describes the system according to the following qualitative observations and hypothesis: Lipase production is induced by extracellular oleic acid present in the medium. The acid is transported into the cell where it is consumed, transformed, and stored. Lipase is excreted to the medium where it is distributed between the available oil-water interphase and aqueous phase. Cell growth is modulated by the intracellular substrate concentration. Model parameters have been determined and the whole model validated against experiments not used in their determination. The estimation problem consists in the estimation of three state variables (biomass, intra- and extracellular substrate) and two kinetic parameters by using only the on-line measurement provided by exhaust gas analysis. The presented estimation strategy divides the complex problem into three subproblems that can be solved by stable algorithms. The estimation of biomass (X) and the specific growth rate (mu), is achieved by a recursive prediction error algorithm using the on-line measurement of the carbon dioxide evolution rate. mu is then used to perform an estimation of intracellular substrate and the other kinetic parameter related to substrate transport (A) by an adaptive observer. Extracellular substrate is then evaluated by means of the estimated values of intracellular substrate and biomass through the material balance of the reactor. Simulation and experimental tests showed good performance of the developed estimator, which appears suitable to be used for process control and monitoring. (c) 1995 John Wiley & Sons, Inc.     

The tuning of a model-based estimator for the specific growth rate of Candida utilis

Control of microbial conversion processes is frequently inhibited by the infeasibility of measuring important process variables. In order to circumvent this lack of measurements, an accurate or valuable and conveniently measurable on-line hardware measurement can be combined with the balance equations describing the process to obtain estimates of less easily measurable variables. In this article the on-line estimation of the specific growth rate of Candida utilis is evaluated. The observer-based estimator requires a hardware measurement of the biomass during fermentations in conjuction with a model of the process; therefore the Biomass Monitor, giving an on-line measurement of viable biomass, is used in the bioreactor experiments described. The optimal tuning of the estimation for the experimental conditions is described and several alternative adaptations of the design of the estimator are presented. The influence of implemented time intervals for discretization of the estimator on the reliability of the estimated growth rate values is discussed. Additionally, the necessary choice of an initial value of the estimated specific growth rate has proven to be of great importance in practice.     

Modeling of heat and mass transfer for solid state fermentation process in tray bioreactor

A mathematical model is developed to simulate oxygen consumption, heat generation and cell growth in solid state fermentation (SSF). The fungal growth on the solid substrate particles results in the increase of the cell film thickness around the particles. The model incorporates this increase in the biofilm size which leads to decrease in the porosity of the substrate bed and diffusivity of oxygen in the bed. The model also takes into account the effect of steric hindrance limitations in SSF. The growth of cells around single particle and resulting expansion of biofilm around the particle is analyzed for simplified zero and first order oxygen consumption kinetics. Under conditions of zero order kinetics, the model predicts upper limit on cell density. The model simulations for packed bed of solid particles in tray bioreactor show distinct limitations on growth due to simultaneous heat and mass transport phenomena accompanying solid state fermentation process. The extent of limitation due to heat and/or mass transport phenomena is analyzed during different stages of fermentation. It is expected that the model will lead to better understanding of the transport processes in SSF, and therefore, will assist in optimal design of bioreactors for SSF.     

Metabolism analysis and on-line physiological state diagnosis of acetone-butanol fermentation

Fermentation equations for acetone-butanol (AB) were applied in a metabolic analysis of the reaction network under various conditions; that is, at different pHs and a high NADH2 turnover rate using methyl viologen, in a Clostridium acetobutylicum culture. The results disclosed variations in the pattern of rate changes that reflected changes in the physiological state. A linear relationship was found to exist between NADH2 generation and butanol production rate. By coupling an automated measurement system with the fermentation model, on-line estimation of the culture state was accomplished. Based on the AB fermentation model, new parameters were defined for on-line diagnosis of the physiological state and determination of the best timing for amplifying NADH2 generation by the addition of methyl viologen to obtain a high level of butanol productivity. A potential means of achieving optimal control for a high level of solvent production, involving the correlation of certain rates, is proposed.     

Application of spectrofluorometry to the prediction of PHB concentrations in a fed-batch process

On-line estimation of biopolymer production during fermentation would be a useful adjunct to the development of strategies for process control and optimization. This study examined the applicability of spectrofluorometry, along with other on-line measurements, for the prediction of poly-ß-hydroxybutyric acid (PHB) concentrations in a high-cell density fed-batch fermentation of Ralstonia eutropha. Models previously used for modelling PHB evolution with time are not sufficiently accurate for situations where transient intermediate accumulations or PHB degradation occur. Thus, the mass balance in the model was modified to account for these situations. An estimation algorithm was developed that is based on a hybrid model consisting of a dynamic mass balance of PHB where the main reaction coefficient was regressed with respect to spectrofluorometric data. The regression between the kinetic parameter and the spectrofluorometric data was accomplished using partial least squares (PLS) regression to avoid high sensitivity to noise expected from highly correlated data, such as the spectrofluorometric readings. The model accounts for dynamics of intermediates and in this way allows the prediction of dynamic behaviour in PHB concentrations that cannot be predicted with other reported mathematical models.     

State and parameter estimation of microalgal photobioreactor cultures based on local irradiance measurement

Local photosynthetic photon flux fluence rate (PPFFR) determined by a submersible 4pi quantum micro-sensor was used in developing a versatile on-line state estimator for stirred-tank microalgal photobioreactor cultures. A marine micro-alga Dunaliella salina was used as a model organism in this study. On-line state estimation was realized using the extended Kalman filter (EKF), based on a state model of the photobioreactor and on-line local PPFFR measurement. The dynamic state model for the photobioreactor was derived based on mass-balance equations of the relevant states. The measurement equation was established based on an empirical correlation between the microalgal biomass concentration and the local PPFFR measured at a fixed point inside the photobioreactor. An internal model approach was used to estimate the specific growth rate without the need of state-based kinetic expression. The estimator was proven to be capable of estimating biomass concentration and specific growth rate, as well as phosphate and dissolved oxygen concentrations in a photobioreactor illuminated with either fixed or time-varying incident radiation. The quantum sensor was shown to be robust and able to quickly respond to dynamic changes in local PPFFR. In addition, the quantum sensor outputs were not affected by bubble aeration or agitation within the typical operating range. The strong filtering capacity of EKF gives the state estimator superior performance compared to direct calculation from the empirical biomass/local PPFFR correlation. This state estimation system makes use of inexpensive and reliable sensor hardware to report key process dynamics of microalgal photobioreactor cultures on-line, enabling improved operation of such a process.     

An algorithmic approach to constructing the on-line estimation system for the specific growth rate

The objective of this article is to propose an algorithm for the on-line estimation of the specific growth rate in a batch or a fed-batch fermentation process. The algorithm shows the practical procedure for the estimation method utilizing the macroscopic balance and the extended Kalman filter. A number of studies of the on line estimation have been presented. However, there are few studies discussing about the selection of the observed variables and for the tuning of some parameters of the extended Kalman filter, such as covariance matrix and initial values of the state.The beginning of this article is devoted to explain the selection of the observed variable. This information is very important in terms of the practical know-how for using technique. It is discovered that the condition number is a practically useful and valid criterion for number is a practically useful and valid criterion for choosing the variable to be observed.Next, when the extended Kalman filter in applied to the online estimation of the specific growth rate, which is directly unmeasurable, criteria for judging the validity of the estimated value from the observed data are proposed. Based on the proposed criterial, the system equation of the specific growth rate is selected and initial value of the state variable and covariance matrix of the system noises are adjusted. From many experiments, it is certified that the specific growth rate in the batch or fed -batch fermentation can be estimated accurately by means of the algorithm proposed here. In these experiments, that is, when the cell concentration is measured directly, the extended Kalman filter using the convariance matrix with a constant element can estimate more accurately values of the specific growth rate than the adaptive extended Kalman filter does.     

Sliding-mode control of fermentation processes

Continuous fermentation processes described by two nonlinear differential equations with uncertain parameters are considered. Sliding mode control design for these processes is proposed. The control design is carried out with direct use of nonlinear model, expert knowledge and on-line measurement of output variable only. Chattering phenomena are avoided by realizing the sliding mode with respect to the control input derivative. The excellent performance of presented control is proved through simulation investigations.     

Indirect measurement of water content in an aseptic solid substrate cultivation pilot-scale bioreactor

A lack of models and sensors for describing and monitoring large-scale solid substrate cultivation (SSC) bioreactors has hampered industrial development and application of this type of process. This study presents an indirect dynamic measurement model for a 200-kg-capacity fixed-bed SSC bioreactor under periodic agitation. Growth of the filamentous fungus Gibberella fujikuroi on wheat bran was used as a case study. Real data were preprocessed using previously reported methodology. The model uses CO2 production rate and inlet air conditions to estimate average bed water content and average bed temperature. The model adequately reproduces the evolution of the average bed water content and can therefore be used as an on-line estimator in pilot-scale SSC bioreactors. To obtain a reasonable fit of the bed temperature, however, inlet air humidity measurements will have to be adjusted with a data reconciliation algorithm. Good estimation of temperature is important for the future design of improved water content estimation using state observers. The model also provides insight into understanding the complex behavior of the dynamic system, which could prove useful when establishing advanced model-based operational and control strategies.     

Calculation errors of time-varying flux control coefficients obtained from elasticity coefficients by means of summation and connectivity theorems in metabolic control analysis

This paper investigates the accuracy of a matrix method proposed by other researchers to calculate time-varying flux control coefficients (dynamic FCCs) from elasticity coefficients by means of summation and connectivity theorems in the framework of metabolic control analysis. A mathematical model for the fed-batch penicillin V fermentation process is used as a case example for discussion. Calculated results reveal that this method produces significant calculation errors because the theorems are essentially valid only in steady state, although it may provide rough time-transient behaviors of FCCs. Strictly, therefore, dynamic FCCs should be directly calculated from the differential equations for metabolite concentrations and sensitivities.     

基于傅里叶变换近红外光谱实时分析1,3-丙二醇发酵过程生物量的在线监测方法

生物量是反映生物发酵过程进展的重要参数,对生物量进行实时监测可用于对发酵过程的调控优化。为克服目前主要采用的离线方法检测生物量时间滞后和人工测量误差较大等缺点,本研究针对1,3-丙二醇发酵过程设计了一个基于傅里叶变换近红外光谱实时分析技术的生物量在线监测实验平台,通过对实时采集光谱预处理以及敏感光谱段分析,应用偏最小二乘算法,建立了1,3-丙二醇发酵过程生物量变化的动态预测模型。以底物甘油浓度为60 g/L和40 g/L的发酵过程作为外部验证实验,分析得到模型的预测均方根误差分别为0.341 6和0.274 3,结果表明所建立的模型具有较好的实时预测能力,能够实现对1,3-丙二醇发酵过程中生物量的有效在线监测。     

Fermentation fault management and on-line state estimation using methods of cluster analysis

The results of the cluster analysis of fermentation data are used for the supervision and on-line state estimation. The results of the classification are presented as the average over all fermentation runs belonging to the class as well as the standard deviation. With the help of the class information the on-line fermentation is associated with the best suiting class. Faults in the data such as spikes or total failure of the sensors are detected as the class information automatically supplies tolerance regions for the measurements. In case of a fault a reliable extrapolation for the time of the fault can be calculated. The approach is implemented in the real-time expert system tool G2 and is applied to data of the carbon dioxide evolution rate (CER) of an industrial antibiotic fermentation process.     

Nonlinear estimation of specific growth rate for aerobic fermentation processes

The specific growth rate of the biomass, a very important parameter of almost every fermentation process, cannot be measured directly or estimated from related variables, as the concentrations of biomass, substrates, or products, due to the lack of reliable and cheap sensors. In this article a stable adaptive estimator of the specific growth rate is designed for those aerobic processes where the measurement of the oxygen uptake rate is available on-line. This particular approach can be applied also for other reaction rates if the model of the process satisfies some very general assumptions, which make the dynamics of the measured reaction rate a nonlinear function only of two unknown parameters, the specific growth rate and its time derivative. With respect to a previous similar approach, the new estimator has one additional parameter and a different nonlinear structure. From the analysis of the dynamics of the estimation error, a tuning criterion is derived, by which the two different algorithms can be compared under similar conditions. Simulation results show a good performance of both estimators for various kind of processes and disturbances. (c) 1995 John Wiley & Sons, Inc.     

Physiological state control of fermentation processes

In this article a novel approach to the control of fermentation processes is introduced. A "physiological state control approach" has been developed using the concept of representing fermentation processes through the current physiological state of the cell culture. No conventional mathematical model is required for the synthesis of such a control system.The main idea is based on the fact that during batch, feed-batch, or even continuous cultivation the physiological characteristics of the cell population, jointly expressed by the term "physiological state", are not constant but rather variable, which is reflected in expected or unexpected changes in the behavior of the control plant, and which requires flexible alteration of the current control strategy. The proposed approach involves decomposition of the physiological state space into several subspaces called "physiological situations." In every physiological situation the cell population expresses stable characteristics, and therefore an invariant control strategy can be effectively applied. The on-line functions of the physiological state control system consist of the calculation of physiological state variables, determination of the current physiological situation as an element of a previously defined set of known physiological situations, switching of the relevant control strategy, and calculation of the control action. Attention is focused on the synthesis of the novel and nonstandard part of the control system - the algorithm for online recognition of the current physiological state. To this end an effective approach, based on artificial intelligence methods, particularly fuzzy sets theory and pattern recognition theory, was developed. Its practical realization is demonstrated using data from a continuous fermentation process for single cell protein production.     

Model-based control of feed rate and illuminance in a photosynthetic fed-batch reactor for H2S removal

Traditional application of computer to fermentation processes has focused on the measurement and control of parameters such as temperature, pH, vessel pressure, sparge rate, dissolved oxygen, substrate concentration, and product concentration. In a fed-batch reactor with the photosynthetic green sulfur bacterium Chlorobium thiosulfatophilum which converts hydrogen sulfide to elementary sulfur or sulfate, separate measurement of cell mass concentration and sulfur particle concentration turbidimetrically was difficult due to their combined contributions to the total turbidity. Instead of on-line measurement of many process variables, a model-based control of feed rate and illuminance was designed. Optimal operation condition relating feed rate vs. light intensity was obtained to suppress the accumulation of sulfate and sulfide, and to save light energy in a 4-1 photosynthetic fed-batch reactor. This relation was correlated with the inreasing cell mass concentration. A model which describes the cell growth by considering the light attenuation effects due to scattering and absorption, and to crowding effect of the cells, was established beforehand with the results from the experiments. Based on these optimal operating conditions and the cell growth model, automatic controls of feed rate and illuminance were carried out alternatively to the traditional application of computer to fermentation with on-line measurement, realtime response and adjustment of process variables.List of Symbols F ml/min Flow rate of gas mixture - hV lux Average illuminance - Q mmol/(l h) Removal rate of hydrogen sulfide - X mg protein/l Cell mass concentration as protein - X ₀ mg protein/l Initial cell mass concentration - X _m mg protein/l Maximum cell mass concentration - _a h^–1 Apparent specific growth rate     

Coupling of microbial kinetics and oxygen transfer for analysis and optimization of gluconic acid production with Aspergillus niger

Gluconic acid fermentation has been widely used for the analysis of various aspects of kinetics and gas liquid transfer of oxygen. Most of these studies are, however, restricted to processes with bacteria. Mathematical models for industrially important productions with fungi have not been elaborated. In the experimental part of this work computer coupled fermentations of gluconic acid production with Aspergillus niger NRRL 3 have been performed. Knowledge of the stoichiometric relationship in the key reaction (glucose oxidase) provides an excellent opportunity for on-line estimation of glucose, biomass and product gluconate from oxygen uptake and carbon dioxide evolution rates. Starting then from experimental observations on the pH-depending oxygen kinetics of gluconic acid formation and influences of product concentrations on the growth of Aspergillus niger a mathematical framework is developed in which the kinetics of growth and production are coupled with gas liquid oxygen transfer. The model can be successfully applied to simulations of the experimental results of gluconic acid fermentations with cyclic addition of glucose. An important aspect in the coupling of transport and microbial reaction in this model is the incorporation of the influence of sugar and gluconate on the solubility of oxygen and k _La via changes of viscosities and molecular diffusivities. With the development of such a comprehensive model, it appears feasible to investigate the influence of various process conditions (sugar feeding, pressure, optimal pH profiles) and to study their possible impacts on the productivity of the overall process.