Abstract
A mixed inverse problem for determining the biochemical oxygen demand of water ( L 0 ) and the rate of biochemical oxygen consumption ( k 0 ), which are important indicators of water quality, has been formulated and numerically solved based on real experimental data. The inverse problem is reduced to the optimization problem consisting in minimization of the deviation of the calculated values from the experimental data, which is solved numerically using the Nelder–Mead method (zero order) and the gradient method (first order). A number of examples of processing both model experimental data and field experimental data provided by hydrological stations monitoring pollutants in the Kazakhstani part of the Ili River basin are presented. A mathematical model that adequately describes the processes in the river system has been constructed.
Highlights
Many models describing the processes of pollution and purification of water resources are based on the work of Streeter and Phelps published in 1925 [1], where a simple model was proposed, which for many years satisfied the needs of engineers and other practitioners in the field of monitoring of water pollution in many countries
CðtÞÞ, Here, t is the time, LðtÞ is the concentration of dissolved organic substance, CðtÞ is the concentration of dissolved oxygen, k0 is the rate of biochemical oxygen consumption, Cs is the concentration of oxygen saturation, and k2 is the rate of reaeration
Kazakhstani part of the Ili River, which is the main tributary of lake Balkhash basin, was chosen as the object of modeling
Summary
Many models describing the processes of pollution and purification of water resources are based on the work of Streeter and Phelps published in 1925 [1], where a simple model (considered classical in our time) was proposed, which for many years satisfied the needs of engineers and other practitioners in the field of monitoring of water pollution in many countries. As shown in the work of Gotovtsev [4], the classical Streeter-Phelps model does not guarantee physically correct solutions for any input data, i.e., a rather difficult process of data calibration leads to a Modelling and Simulation in Engineering separately posed problem that requires separate consideration [2]. With development of more powerful computers, the capabilities of calculators have increased significantly and works have appeared where application of the modified Streeter-Phelps models is considered solutions to some inverse problems, for example [6]. The general tendency to consider some problems as inverse to direct ones, which appeared in the 20th century [7, 8], was reflected in the implementations of models describing the processes of pollution and purification of water resources
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
