Estimation of multiple biomass growth rates and biomass concentration in a class of bioprocesses

In this paper, an approach to the estimation of multiple biomass growth rates and biomass concentration is proposed for a class of aerobic bioprocesses characterized by on-line measurements of dissolved oxygen and carbon dioxide concentrations, as well as off-line measurements of biomass concentration. The approach is based on adaptive observer theory and includes two steps. In the first step, an adaptive estimator of two out of three biomass growth rates is designed. In the second step, the third biomass growth rate and the biomass concentration are estimated, using two different adaptive estimators. One of them is based on on-line measurements of dissolved oxygen concentration and off-line measurement of biomass concentrations, while the other needs only on-line measurements of the carbon dioxide concentration. Simulations demonstrated good performance of the proposed estimators under continuous and batch-fed conditions.     

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.     

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.     

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.     

Respirometric assay for biofilm kinetics estimation: parameter identifiability and retrievability

Currently, no fast and accurate methods exist for measuring extant biokinetic parameters for biofilm systems. This article presents a new approach to measure extant biokinetic parameters of biofilms and examines the numerical feasibility of such a method. A completely mixed attached growth bioreactor is subjected to a pulse of substrate, and oxygen consumption is monitored by on-line measurement of dissolved oxygen concentration in the bulk liquid. The oxygen concentration profile is then fit with a mechanistic mathematical model for the biofilm to estimate biokinetic parameters. In this study a transient biofilm model is developed and solved to generate dissolved oxygen profiles in the bulk liquid. Sensitivity analysis of the model reveals that the dissolved oxygen profiles are sufficiently sensitive to the biokinetic parameters-the maximum specific growth rate coefficient (insertion markμ) and the half-saturation coefficient (Ks)-to support parameter estimation if accurate estimates of other model parameters can be obtained. Monte Carlo simulations are conducted with the model to add typical measurement error to the generated dissolved oxygen profiles. Even with measurement error in the dissolved oxygen profile, a pair of biokinetic parameters is always retrievable. The geometric mean of the parameter estimates from the Monte Carlo simulations prove to be an accurate estimator for the true biokinetic values. Higher precision is obtained for insertion markμ estimates than for Ks estimates. In summary, this theoretical analysis reveals that an on-line respirometric assay holds promise for measuring extant biofilm kinetic parameters. Copyright 1998 John Wiley & Sons, Inc.     

Application of mass and energy balance regularities in fermentation. Reprinted from Biotechnology and Bioengineering, Vol. XX, No. 10, Pages 1595-1621 (1978)

Material and energy balances for fermentation processes are developed based on the facts that the heat of reaction per electron transferred to oxygen for a wide variety of organic molecules, the number of available electrons per carbon atom in biomass, and the weight fraction carbon in biomass are relatively constant. Mass-energy balance equations are developed which relate the biomass energetic yield coefficient to sets of variables which may be determined experimentally. Organic substrate consumption, biomass production, oxygen consumption, carbon dioxide production, heat evolution, and nitrogen consumption are considered as measured variables. Application of the balances using direct and indirect methods of yield coefficient estimation is illustrated using experimental results from the literature. Product formation is included in the balance equations and the effect of product formation on biomass yield estimates is examined. Application of mass-energy balances in the optimal operation of continuous single-cell protein production facilities is examined, and the variation of optimal operating conditions with changes in yield are illustrated for methanol as organic substrate.     

Application of mass and energy balance regularities in fermentation

Material and energy balances for fermentation processes are developed based on the facts that the heat of reaction per electron transferred to oxygen for a wide variety of organic molecules, the number of available electrons per carbon atom in biomass, and the weight fraction carbon in biomass are relatively constant. Mass–energy balance equations are developed which relate the biomass energetic yield coefficient to sets of variables which may be determined experimentally. Organic substrate consumption, biomass production, oxygen consumption, carbon dioxide production, heat evolution, and nitrogen consumption are considered as measured variables. Application of the balances using direct and indirect methods of yield coefficient estimation is illustrated using experimental results from the literature. Product formation is included in the balance equations and the effect of product formation on biomass yield estimates is examined. Application of mass–energy balances in the optimal operation of continuous single-cell protein production facilities is examined, and the variation of optimal operating conditions with changes in yield are illustrated for methanol as organic substrate.     

On-line estimation of biodegradation in an unsaturated soil

The objective of this study was to develop a model-based estimator of biodegradation in unsaturated soil. This would allow real-time assessment of the efficiency of treatment bioprocesses, such as bioventilation and biopile, and eventually permit optimization through the implementation of control strategies. Based on a reduced-order model, an asymptotic observer was designed to estimate on-line the contaminant concentration, using carbon dioxide measurement. Two observer-based estimators were built to approximate: (1) the specific microbial growth rate; and (2) the biocontact kinetics representing the soil resistance to contaminant biodegradation. State observers and parameter estimators were confronted with the experimental results of biodegradation in microcosms. Hexadecane was used as the model compound, representing petroleum hydrocarbons. Three water contents, corresponding to 20%, 50% and 80% of the water-holding capacity, were tested. The asymptotic observer is able to predict hexadecane depletion with an error on the overall time trajectories of 13%, 8% and 4% for the dry, intermediate and wet soils, respectively, which is acceptable given that all the biokinetic parameters were identified from a biodegradation experiment in liquid phase. The observer-based estimator of the specific microbial growth rate, based on the CO₂ measurement, was successfully calibrated using the off-line measurements of hexadecane as validation data, and allowed estimation of the time when biodegradation switched from a microbial to a biocontact limitation. The biocontact kinetics was also identified on-line, using an estimator based on the hexadecane not in biocontact. These results are very encouraging with respect to the potential for on-line assessment of the performance of treatment bioprocesses in unsaturated soils.     

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.     

Data consistency,yield, maintenance,and hysteresis in batch cultures of Candida lipolytica cultured on n-hexadecane

Candida lipolytica was cultured batchwise using n-hexadecane as the main carbon source. Biomass production, n-hexadecane consumption, oxygen consumption, and carbon dioxide evolution were measured to follow the fermentation. The consistency of the measured data was examined using integrated and instantaneous available electron and carbon balances. Values of the “true” growth yield, η_max, and maintenance coefficient, m_e were estimated using three different sets of data (biomass and n-hexadecane, oxygen and biomass, and CO₂ and biomass), and the results were compared with estimates obtained from literature data. Hysteresis patterns were observed in plots of specific rates of oxygen consumption and carbon dioxide evolution versus specific growth rate.     

Combining yield coefficients and exit-gas analysis for monitoring of the baker's yeast fed-batch fermentation

Baker's yeast is one of the micro-organisms that is studied most in literature. Therefore, a lot of knowledge on the biochemical pathways and corresponding yield coefficients is available. This knowledge is combined with measurements of oxygen and carbon dioxide in the exit-gas to determine the coefficients appearing in the stoichiometric equations. In this manner, two measurements are sufficient to yield on-line estimates for biomass, glucose, ethanol and the specific growth rate, and information about the (ill-defined) nitrogen source NH_q. This is not possible if the yield coefficients are not included in the estimation procedure. A sensitivity analysis illustrates that this estimation scheme is rather insensitive to uncertainties on the yield coefficients.     

An adaptive state estimator for detecting contaminants in bioreactors

An algorithm is presented for detecting the appearance of contaminants during batch or fed-batch fermentations, using only presently available on-line measurements. Its adaptive nature enables it to rely on almost no prior knowledge of the real process. The necessary on-line measurements are total biomass and its production rate; it is also shown how a physical variable such as oxygen uptake can be used alone instead. The algorithm's properties are studied theoretically and through simulations. These were confirmed by on-line experimental results, obtained with a Yeast culture, both pure and contaminated by a Bacteria. The algorithm does not detect contaminants when none are there, and it also provides a convergent estimate of a pure culture's specific growth rate. Contaminated cultures are recognized by the algorithm, and this detection can be made more or less conservative. After detection, the various estimates may diverge, due to general observability difficulties, though this divergence can itself be monitored. Moreover, the algorithm is easy to tune and its qualitative behavior is quite insensitive to its adjustable parameters. A practical criterion and scheme for implementation are proposed. The generality of the approach, which far exceeds the experimental system used, is finally discussed.     

A mathematical approach for the estimation of biomass production rate in solid state fermentation

The oxygen uptake rate (OUR) was studied in a solid state fermentation process of dried citrus peel with the strain Aspergillus niger QH-2 in order to obtain the growth estimation of the microorganism in the system. The relationship between OUR, the maintenance coefficient (m) and the yield for oxygen consumption Y_O2 allows the estimation of the biomass rate if we consider that both parameters are not constants in some periods of the process. It was estimated that in the first 24th the strain has an specific growth rate of 0.174 h^?1 with values for Y_O2 and m in the order of 2.84 g-cell/g-oxygen and 0.006 g-oxygen/g-cell ·h respectively.     

Soft sensors for on-line biomass measurements

One of the difficulties encountered in control and optimisation of bioprocesses is the lack of reliable on-line sensors for their key state variables. This paper investigates the suitability of using on-line recurrent neural networks to predict biomass concentrations. Input variables of the proposed recurrent neural network are feed rate, liquid volume and dissolved oxygen. Experimental results revealed that the proposed neural network is able to predict biomass concentrations with an accuracy of ±11%.     

Multirate state and parameter estimation in an antibiotic fermentation with delayed measurements

This article discusses issues related to estimation and monitoring of fermentation processes that exhibit endogenous metabolism and time-varying maintenance activity. Such culture-related activities hamper the use of traditional, software sensor-based algorithms, such as the extended kalman filter (EKF). In the approach presented here, the individual effects of the endogenous decay and the true maintenance processes have been lumped to represent a modified maintenance coefficient, m(c). Model equations that relate measurable process outputs, such as the carbon dioxide evolution rate (CER) and biomass, to the observable process parameters (such as net specific growth rate and the modified maintenance coefficient) are proposed. These model equations are used in an estimator that can formally accommodate delayed, infrequent measurements of the culture states (such as the biomass) as well as frequent, culture-related secondary measurements (such as the CER). The resulting multirate software sensor-based estimation strategy is used to monitor biomass profiles as well as profiles of critical fermentation parameters, such as the specific growth for a fed-batch fermentation of Streptomyces clavuligerus. (c) 1994 John Wiley & Sons, Inc.     

Computer-aided baker's yeast fermentations.

The economics of yeast production depend heavily upon the cellular yield coefficient on the carbon source and the volumetric productivity of the process. The application of an on-line computer to maximize these two terms during the fermentation requires a continuous method of measuring cell density and growth rate. Unfortunately, a direct sensor for biomass concentration suitable for use in industrial fermentations is not available. Material balancing, with the aid of on-line computer monitoring, offers an indirect method of measurement. Laboratory results from baker's yeast production in a 14-liter fermentor (with a PDP-11/10 computer for on-line analyses) show this indirect measurement technique to be a viable alternative. From the oxygen uptake and carbon dioxide production data, gas flow rate, and ammonia addition rate, the cell density during the fermentation has been estimated and found to compare well with actual fermentation data.     

Growth, death, and oxygen uptake kinetics of Pichia stipitis on xylose

Pichia stipitis NRRL Y-7124 has potential application in the fermentation of xylose-rich waste streams, produced by wood hydrolysis. Kinetic models of cell growth, death, and oxygen uptake were investigated in batch and oxygen-limited continuous cultures fed a rich synthetic medium. Variables included rates of dilution (D) and oxygen transfer (K(1)a) and concentrations of xylose (X), ethanol (E), and dissolved oxygen (C(ox)). Sustained cell growth required the presence of oxygen. Given excess xylose, specific growth rate (micro) was a Monod function of C(ox). Specific oxygen uptake rate was proportional to mu by a yield coefficient relating biomass production to oxygen consumption; but oxygen uptake for maintenance was negligible. Thus steady-state C(OX) depended only on D, while steady-state biomass concentration was controlled by both D and K(1)a. Given excess oxygen, cells grew subject to Monod limitation by xylose, which became inhibitory above 40 g/L. Ethanol inhibition was consistent with Luong's model, and 64. 3 g/L was the maximum ethanol concentration allowing growth. Actively growing cells died at a rate that was 20% of micro. The dying portion increased with E and X.     

Adaptive control of dissolved oxygen concentration in a bioreactor

A new adaptive DO (dissolved oxygen) concentration control algorithm considering DO electrode dynamics with response time delay has been developed. A system model with two time-varying parameters was used to relate the DO concentration with two control variables: air flow rate and agitation speed. Parameters of this model were estimated on-line using a regularized constant trace recursive least-squares method. An extended Kalman filter was used to remove the effect of noises from the DO concentration measurements and thus to improve control performance. A discrete one-step ahead control scheme was adopted to determine control actions based on the parameter estimation results. Experimental results showed that the new adaptive DO concentration control algorithm performed better than other algorithms tested, a PID controller and adaptive algorithms without the DO electrode dynamics.     

Oxygen enriched air supply in Escherichia coli processes: production of biomass and recombinant human growth hormone

In order to investigate the impact of high oxygen and carbon dioxide concentrations, Escherichia coli was grown in batch cultivations where the air supply was enriched with either oxygen or carbon dioxide. The effect of elevated concentrations of oxygen and carbon dioxide on stochiometric and kinetic constants was studied this way. The maximum growth rate was significantly reduced, the production of acetic acid and the biomass yield coefficient on glucose increased in cultures with carbon dioxide enriched air, compared to reference cultivations and cultivations with oxygen enriched air. The application of oxygen enriched air was studied in high cell density cultivations of Escherichia coli. Two production processes were chosen to investigate the impact of oxygen enrichment. Biomass concentration, specific growth rate, yield coefficient, respiration, mixed acid fermentation products and the product yield and quality for the recombinant product were investigated. First, a process for the production of biomass was investigated. Exponential growth could proceed for a longer time and higher growth rates could be maintained with oxygen enriched air supply. However, a higher specific oxygen consumption rate per glucose was measured after the start of the oxygen enrichment, indicating higher maintenance and consequently the growth rate and yield coefficient decreased drastically in the end of the process. Second, a process for the production of recombinant human growth hormone (rhGH) was investigated. Although the glucose feed rate and all medium components were doubled, the amount of produced biomass could only be increased by 77% when oxygen enriched air (40% oxygen) supply was applied. This was due to a decreased yield coefficient of biomass per glucose. The total amount of produced product was decreased by almost 50% compared to the control, although less proteolytically degraded variants were produced.     

On-line estimation of the biomass activity during animal-cell cultivations

A software sensor was developed to determine the volumetric biomass activity of animal cell cultivations on-line. It was based on the on-line estimation of the ATP-production rate from the oxygen uptake and the lactic-acid production rate. The sensor was verified for a batch culture of Vero cells, and a batch and a continuous culture of hybridoma cells. For the hybridoma cells, the sensor showed a good correlation with the biomass concentration. However, this was not the case for the Vero cells. As soon as glutamine was exhausted, the biomass activity stabilized, whereas the amount of biomass almost doubled. Because the sensor developed responds to nutrient limitations much faster than becomes visible through cell density measurements, and because the volumetric biomass activity can be related to the volumetric consumption rates and production rates of important metabolites, it shows excellent possibilities for control purposes. (c) 1996 John Wiley & Sons, Inc.