The relevance of this work is determined by the current active implementation of alternative energy sources, one of which is the development and operation of bioenergy complexes. These systems not only provide energy and heat but also protect the environment from methane emissions, which naturally occur during the decomposition of biowaste from agriculture and the food industry. To ensure the widespread use of these technologies, it is necessary to develop an effective system for managing and predicting the technological processes occurring in these systems [1].

The novelty of the work is related to the creation of a computer program and a mathematical model for describing the technological parameters of a bioreactor during anaerobic fermentation under production, industrial-scale conditions in real time. Currently used models, such as the Konto, Mono, Chen-Hashimoto models, the international model of anaerobic fermentation ADM1, etc., are general and of little usage in production, since they describe the biochemical, physicochemical and kinetic processes of reproduction of anaerobic bacteria and their inhibition under laboratory conditions. Therefore, such mathematical models are difficult to use in practice. Furthermore, parameters such as bacterial concentration and inhibition coefficient are immeasurable in real-world production conditions. An analysis of the work of scientists from around the world shows that a scientific methodology for calculating bioreactor parameters for anaerobic fermentation in industrial settings has not previously been studied or applied [2].

Our research to develop a mathematical model for more accurately predicting biogas yield during anaerobic digestion used statistical data from a biogas plant in Kurma, Karaganda region, and data from a biogas plant in Manitoba, Canada. The proposed mathematical model included more than 20 different parameters that significantly affect the quality of anaerobic fermentation and, accordingly, the biogas yield. These parameters include indicators of the amount of macro- and microelements, as well as the main process factors: K – potassium, Na – sodium, Ca – calcium, Mg – magnesium, Fe – iron, Cu – copper, Zn – zinc, Ni – nickel, Co – cobalt, Mo – molybdenum, Cr – chromium, Cd – cadmium, C – carbon, N – nitrogen, P – phosphorus, C/N – carbon to nitrogen ratio, L – nutrient concentration, n – degree of grinding, VFA – fatty acid content, τ – fermentation period, m – substrate mass, t – temperature, pH – acidity index, φ – humidity, S – sulfur, H4N+ – ammonium [3, 4].

Experimental researches have shown that the influence of various parameters on biogas yield is linear. Therefore, the resulting mathematical model is a linear equation of empirical relationships between parameters, obtained through regression analysis.

Based on statistical data, a number of mathematical models were created, differing in the number of factors taken into account, which were included based on the level of correlation with the biogas yield indicator [5].

The best result was shown by a model in the form of a linear regression equation with twenty factors:

The calculation results are presented in figure 1. The multiple correlation coefficients between V and the factors under consideration were 0.84, and the average relative error of the constructed model was 5.47% [7, 11].

Figure 1: Biogas output.

To create the computer program, the hypertext markup languages HTML, CSS, scripting languages PHP, Javascript, and the MySQL database were used. This web technology was not chosen by chance, as its concept is based on the visualization of statistical data using the Internet and mobile devices, which allows experts to obtain information remotely in real time. To implement this concept, a website was developed that allows online transfer of measured values to a database (DB) and obtaining calculation results (see fig. 2, 3) [6, 8].

Figure 2: Computer program architecture.

Figure 3: website home page.

All statistical data obtained during the operation of the bioenergy plant are collected and stored in a database. Next, using a computer program, we can process all this data and display it on the screen in the form of infographics. All data in the database can be displayed on the screen as shown in figure 4. [9, 10]

Figure 4: Diagram of the dependence of the output parameter on the input parameters.

As a result of the research conducted, the following results were obtained:

- A comparative analysis of various mathematical models used in anaerobic fermentation research was performed, and their advantages and disadvantages were examined;

- The universal mathematical model for predicting anaerobic fermentation processes at an industrial scale was developed;

- The correlation coefficient R, the determination coefficient R², and the average relative error A were determined, which suggest that the proposed model is sufficiently accurate and universal;

- Based on the constructed model, a computer program was created for predicting the operating results of bioenergy plants using HTML, CSS, PHP, JavaScript, and the MySQL database;

- The website was developed that allows for online transfer of measured values to a database and the necessary calculations.

Thus, the proposed mathematical model allows for more precise prediction of biogas yield during anaerobic fermentation on an industrial scale. This model can be applied not only to agriculture but also to other areas of human activity involving the processing of biowaste. It is designed taking into account parameters measured in real time at the production site using various biosensors. A computer program created based on the proposed mathematical model, using an analytical database and machine learning technologies, will eventually enable forecasting the operation of a bioenergy plant and calculating its efficiency and productivity, taking into account various influencing factors.

Funding

This study was funded by the Scientific Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (grant no. AP25794135).

References

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