Modelling, Optimization and Optimal Control of Small Scale Stirred Tank Bioreactors

Models of the mass-transfer in a stirred tank bioreactor depending on general indexes of the processes of aeration and mixing in concrete simplifications of the hydrodynamic structure of the flows are developed. The offered combined model after parameters identification is used for optimization of the parameters of the apparatus construction. The optimization problem is solved by using of the fuzzy sets theory and in this way the unspecified as a result of the model simplification are read. In conclusion an optimal control of a fed-batch fermentation process of E. coli is completed by using Neuro-Dynamic programming. The received results after optimization show a considerable improvement of the mass-transfer indexes and the quantity indexes at the end of the process

Modeling and Use of Inter-Criteria Decision Analysis for Selecting Growth Rate Models for Batch Cultivation of Yeast Kluyveromyces marxianus var. lactis MC 5

Ten unstructured models of Monod, Mink, Tessier, Moser, Aiba, Andrews, Haldane, Luong, Edward, and Han-Levenspiel are considered in this paper to explain the kinetics of cell growth for batch cultivation of the yeast Kluyweromyces marxianus var. lactis MC 5. For the first time, two independent kinetic models are used to model the process for the two basic substrates—lactose and oxygen. The selection of the most appropriate growth rate models has been made through a new multi-criteria decision-making approach called the Inter-Criteria Decision Analysis (ICDA) method. The application of ICDA to the growth rate of lactose and oxygen alone has shown that there have been many correlations between the studied models. Thus, the models for the growth rate, depending only on lactose, are reduced to one—Monod model and there are two models—Monod and Mink—depending on oxygen only. Separate kinetic process models have been developed for the combination of Monod–Monod and Monod–Mink models. For the first time, in addition to the multiplicative form, the additive form of a specific growth rate has been studied. The comparison of the obtained results has shown that the additive form has shown better results than the multiplicative one. For this reason, the additive form of the Monod–Monod model will be used to model the process

A Combined Algorithm for Optimization: Application for Optimization of the Transition Gas-Liquid in Stirred Tank Bioreactors

A combined algorithm for static optimization is developed. The algorithm includes a method for random search of optimal an initial point and a method based on fuzzy sets theory, combined in order to be found for the best solution of the optimization problem. The application of the combined algorithm eliminates the main disadvantage of the used fuzzy optimization method, namely decreases the number of discrete values of control variables. In this way, the algorithm allows problems with larger scale to be solved. The combined algorithm is used for optimization of gas-liquid transition in dependence on some constructive and regime parameters of a laboratory scale stirred tank bioreactor. After the application of developed optimization algorithm significant increase of mass-transfer effectiveness, aeration and mixing processes in the bioreactor are observed

Modelling and Multi-Criteria Decision Making for Selection of Specific Growth Rate Models of Batch Cultivation by Saccharomyces cerevisiae Yeast for Ethanol Production

This study is focused on using multi-criteria decision making (MCDM) for selecting specific growth rate models of batch cultivation by the Saccharomyces cerevisiae. Ten specific growth rate models—Monod, Mink, Tessier, Moser, Aiba, Andrews, Haldane, Luong, Edward, and Han-Levenspiel—were investigated in order to explain the cell growth kinetics by the dependence on glucose. By using the preference ranking organization method (PROMETHEE) II, it was found that the Andrews model was the highest of rank and was the most appropriate one for modelling

Multi-objective parameter estimation on cultivation of yeast Kluyveromyces marxianus var. lactis MC5

AbstractIn this study, the most appropriate form of the specific growth rate of the yeast Kluyweromyces marxianus var lactis MC5 was determined by a multi-criteria decision-making method (PROMETHEE II). Then, based on experimental data from a total of six batch processes, the simultaneous estimation of the kinetic parameters for four batch processes was made. The remaining two experiments were used to test the model. The parameter estimation problem was designed as a multi-objective optimisation problem. The method of scalarisation of the weighted sum was used. In this way, the multi-objective optimisation problem was converted to a single-objective one. The direct search method was used to solve the problem of obtaining the Pareto solution. In order to test the resulting solution, two batches of experimental data were additionally used. The obtained results showed that the model satisfactorily described the test data. The validated kinetic model can be used for optimal control of batch and fed-batch fermentation

A Multiple-objective Optimization of Whey Fermentation in Stirred Tank Bioreactors

A multiple-objective optimization is applied to find an optimal policy of a fed-batch fermentation process for lactose oxidation from a natural substratum of the strain Kluyveromyces marxianus var. lactis MC5. The optimal policy is consisted of feed flow rate, agitation speed, and gas flow rate. The multiple-objective problem includes: the total price of the biomass production, the second objective functions are the separation cost in downstream processing and the third objective function corresponds to the oxygen mass-transfer in the bioreactor. The multiple-objective optimization are transforming to standard problem for optimization with single-objective function. Local criteria are defined utility function with different weight for single-type vector task. A fuzzy sets method is applied to be solved the maximizing decision problem. A simple combined algorithm guideline to find a satisfactory solution to the general multiple-objective optimization problem. The obtained optimal control results have shown an increase of the process productiveness and a decrease of the residual substrate concentration

Multi-objective parameter estimation on cultivation of yeast <i>Kluyveromyces marxianus var. lactis</i> MC5

In this study, the most appropriate form of the specific growth rate of the yeast Kluyweromyces marxianus var lactis MC5 was determined by a multi-criteria decision-making method (PROMETHEE II). Then, based on experimental data from a total of six batch processes, the simultaneous estimation of the kinetic parameters for four batch processes was made. The remaining two experiments were used to test the model. The parameter estimation problem was designed as a multi-objective optimisation problem. The method of scalarisation of the weighted sum was used. In this way, the multi-objective optimisation problem was converted to a single-objective one. The direct search method was used to solve the problem of obtaining the Pareto solution. In order to test the resulting solution, two batches of experimental data were additionally used. The obtained results showed that the model satisfactorily described the test data. The validated kinetic model can be used for optimal control of batch and fed-batch fermentation.</p

An Approach for Analysis and Assessment of the Pollution Indices of the Struma River in the Bulgarian Section

In this work, 13 pollution indices in 10 stations of the Struma river in the Bulgarian section are investigated: temperature (T°C), pH, dissolved oxygen (DO), oxygen saturation (SO2), electrical conductivity (EC), biological oxygen demand (BOD), permanganate oxidation (KMn3O4), ammonia nitrogen (NH3-N), nitrite nitrogen (NO2-N), nitrate nitrogen (NO3-N), orthophosphates (PO4), dissolved substances (DS), and unsolved substances (US). The analysis and assessment of the studied indices of pollution of the Struma river in the Bulgarian section is carried out by means of a recently proposed multi-criteria decision-making method called intercriteria decision analysis (ICDA). Application of ICDA showed that we have a degree of agreement for T°C for all stations with very few exceptions. This also applies to DO, KMn3O4, SO2 and EC. We had a degree of disagreement for all other indices. From the conducted research, it can be concluded that for all indicators, it is necessary to develop mathematical models in the studied stations according to the studied indicators of the Struma river in Bulgaria. The application of ICDA allows us to examine the correlations between individual indicators and eliminate those that are highly dependent on each other

Comparative Analysis of Two Models of the Strouma River Ecosystem

A modified method of regression analysis for modelling of the water quality of river ecosystems is offered. The method is distinguished from the conventional regression analysis of that the factors included in the regression dependence are time functions. Two type functions are tested: polynomial and periodical. The investigations show better results the periodical functions give. In addition, a model for analysis of river quality has been developed, which is a modified method of the time series analysis. The model has been applied for an assessment of water pollution of the Strouma river. An assessment for adequately of the obtained model of the statistical criteria - correlation coefficient, Fisher function and relative error is developed and it shows that the models are adequate and they can be used for modelling of the water pollution on these indexes of the Strouma river. The analysis of the river pollution shows that there is not a materially increase of the anthropogenic impact of the Strouma river in the Bulgarian part for the period from 2001 to 2004