1. THE METHOD OF FIRST INTEGRALS OF DIFFERENTIAL SYSTEM APPLIED TO BATCH ALCHOHOL FERMENTATION WITH IMMOBILIZED CELLS
Silvia B. Popova*, Georgi A. Kostov**
* Institute of System Engineering and Robotics, Bulgarian Academy of Science, Sofia, Bulgaria
**University of Food Technologies, Plovdiv, Bulgaria
INTRODUCTION: An important moment in the control of the batch and continuous fermentation processes is the estimation of population state. There are different methods for observers design. They need large computational resources.
The use of biofuels as an alternative energy source is motivated from: (1) the high petrol prices, the need for reduction of carbon emissions, leading to climate change, (2) water solubiliy of plant fuels, which helps avoiding the environmental pollution, caused by oil spills. The bioethanol is produced from sugar plants, as well as from starch and cellulose containing raw materials.
While in the process with free cells the biomass concentration can be estimated directly (by spectrophotometer), in the process with imobilized cells the estimation procedure is more difficult. Usually a mechanical or chemical distriction of the support is required, which delays the process of estimation of the concentration of the biomass, and even can lead to missleading conclusions, due to the incurred errors. As a consequence, the rapid and precise definition of the microorganisms’ concentration in the work volume of the bioreactor is of vital importance for the taking of quick decisions during the process´ control.
The aim of the present research is to elaborate a method for estimation of the concentration of the biomass, based on the ethanol and substrat concentration data, performed in a batch process of alchohol fermentation with imobilized cells. For this purpose are used the data dynamics of similar processes, obtained in earlier studies.
The main idea of the method consists of analytical derivation of the first integrals of the differential system, which describes the process (Popova, 2008). A theorem of theory of differential equations exists according to which for every system of n ordinary equations there exist n-1 first integrals. These integrals are locally defined (in a neighborhood of every non singular point for the system). We can use the experimental data to find the constants obtained by integration. Because of the type of systems describing the biotechnological process, the first integrals can be easily found.
(5)
4. METHOD OF FIRST INTEGRALS OF DIFFERENTIAL SYSTEM
To determine the biomass concentration by concentrations of ethanol and substrate we integrate the thirty equation of system (1) and receive:
In this way for biomass concentration X we obtain:
where the C and C1 are constants.
2. MATERIALS AND METHODS
 2.1.Yeast strain
The used strain-producer was dry yeasts Saccharomyces cerevisiae 46 EVD provided by
the company “Martin Vialatte OEnologie”, France. The amount of inoculating material
was 1% from the bioreactor working volume because the aim was to achieve
107 CFU/ml. During the immobilization the amount of used biomass was determined
such that we achieved 107 CFU/g preparations.
 2.2. Nutrition media (g/dm3)
glucose – 118,40; (NH4)2SO4 – 2; KH2PO4 – 2,72; MgSO4х7Н2О – 0,5; yeasts extract – 1.
  2.3. Yeast cells immobilization
For yeasts cell immobilization 2% solution of Na-alginate was used. The detailed
Description of that immobilization method is given in (Kostov, 2007).
 2.4. Bioreactors and cultivation conditions
The laboratory bioreactor is glass cylinder with geometrical volume of 2 dm3 and
Working volume of 1.7 dm3 (Kostov, 2007).
 2.5. Analysis
  Determination of concentration of ethanol and glucose into cultural medium
The accumulated ethanol and glucose concentrations are determined by a specialized
apparatus type „Anton Paar DMA 4500”, Austria (  
Determination of biomass concentration in cultural medium
The biomass concentration in cultural medium was determined spectrophotometrically
By „Spekol 221”, Germany using wave length of 620 nm (Kostov, 2007).
  Determination of biomass concentration in immobilized preparatory
The biomass concentration in immobilized preparatory was determined using the
Following methodology: 1 g of preparatory was put into 1% solution of sodium citrate;
for the control probe 1g of pure alginate pearls were put into 1% sodium citrate; after
full dissolving.
The constant C we may calculate by initial values and the coefficients YX/S и YP/S by parameter identification(Kostov G., S. Popova, 2012). The data for the parameters are given in table 1.
Table 1
The values of Parameters and constant C
3. MATHEMATICAL MODEL
The mathematical model of the batch alchohol l fermentation with immobilized cells has the following form:
(1)
Figure 1. Dynamics of the biomass estimation Monod’s model
It is based on the assumption that the substrate denoted by S is consumed with rate proportional to the increase rates of the cells X and product P concentrations. The constants Yx/s and Yp/s are called yield coefficients and μ and q denote the specific biomass growth and ethanol production rates respectively.
The specific growth rate μ and specific production rate q are main kinetic parameters in fermentation process. For their description the different equations are used After parameter identification(Kostov G., S. Popova, 2012) in previous investigation the best equations for the main kinetic parameters were chosen:.
Monod Andrews and Noack
Figure 2. Dynamics of the biomass estimation Andrews and Noack’s model
Figure 3. Dynamics of the biomass estimation Hinshelwood’s model
Figure 4 Dynamics of the biomass estimation Aiba’s model
CONCLUSIONS: The method of first integrals of differential system is applied for biomass estimation of batch process of ethanol production. The concentration of substrate and product are used as input data. For the process with immobilized cells this estimation is very important because of the biomass is inside of support.
Hinshelwood Aiba
REFERENCES:
Kostov.,G.(2007) Investigation of systems for ethanol fermentation, PhD Thesis, UFT, Plovdiv.
Kostov G., S. Popova, M. Angelov, P. Koprinkova-Hristova (2012), “Modeling of batch alcohol fermentation with free and imobilized yeasts Sacharomyces cerevisiae 46 EVD” J. Biotechnology & Biotechnological Equipment-26 /2012/3, pp
Popova S., (2008) Observers design for biotechnological processes, J. Biotechnology
& Biotechnological Equipment-4/2008/22-pp
Acknowledgments: This work was supported by Bulgarian National Fund “Scientific Researches” under contract No DTK – 02/27/