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Admissible Discharge Model


Dynamic Control of Maximum Allowable Discharge (MAD) Depending on River Overall State and Taking into Account Economic Interest of Water Users

Tech Area / Field

  • ENV-WPC/Water Pollution and Control/Environment

3 Approved without Funding

Registration date

Leading Institute
Republican Center of Environmental Monitoring, Georgia, Tbilisi


  • European Commission / ESSOR EUROPE, France, Paris\nGeorgia State Department of Hydrometeorology, Georgia, Tbilisi\nUnited Nations Development Programme, Georgia, Tbilisi\nUniversity of Athens, Greece, Athens\nUniversity of Sciences and Technologies of Lille, France, Lille\nInstituto "GUIDO CASTELNUOVO", Italy, Rome

Project summary

The objective of the presented project is to develop new approaches to the problem of calculation of maximum allowable discharges(MAD), that is to develop such models, methods, algorithms and programs that will allow correct and operative calculation of MAD with due regard for the river water level, the pollution level at the entrance of a certain river section, the impact of pollution sources acting within this section, and the economic interests of these pollution sources (enterprises).

This problem is particularly urgent for the rivers in which the volume of flowing water and the pollution level change greatly with time. This necessitates a dynamic calculation of MAD depending on the state of the controlled river.

Of course, there are some scientific and practical works concerning MAD calculations (see e.g.: Methods of Calculation of Maximum Allowable Discharges of Pollutants into Water Systems with Waste Water. - All-Union Scientific-Research Institute on water Protection (VNIIVO), Kharkov, 1990, p.112), but, in most cases, they are only suitable for certain particular cases, since they study some aspects of the general problem. In fact, for the time being, there exists no universal method taking into account all the pollution sources simultaneously as well as parameters characterizing the river flow, pollutants transfer, economic capacities and technical limitations of enterprises. Consequently, there exists no program package enabling correct calculation of optimal MAD values with allowances for specific features of a certain river and technical and economical resources of enterprises.

It should be emphasized that the dynamic MAD control has not been considered before and is posed for the first time. Due to importance of the posed problem and destination of the expected results, it is necessary to fill in the gaps in knowledge. To do that, it's necessary to develop new methods and approaches for solution of concrete associated subproblems in different fields. Namely, mathematical models describing pollutants transfer in a river will be developed with allowances for: river flow dynamics; specific features of pollutants transfer and of a river bed; locations of points at which different pollution sources discharge their waste water. Target function describing material costs of water users will be elaborated in such a way that, while providing the necessary level of water quality, perse economic interests of all river pollution sources on a certain river section will be taken into consideration (see e.g.: Primak A.V., Kafarov V.V., Kachiashvili K.J. System Analysis of Control and Management of Air and Water Quality. -Kiev: Naukova Dumka,1991, -358p.). For solution of the optimization problem, special fast algorithms will be developed to ensure real-time application of the developed program package. For numerical solution of partial differential equations describing river flow dynamics and pollutants transfer, special fast and efficient numerical algorithms will be developed on the basis of adaptive grid methods. These adaptive numerical methods are relatively new and have been intensively studied in numerical analysis and computational fluid dynamics.

At present, ISTC project G-047 "Identification of River Water Pollution Sources by Means of Automated Control Systems" is being completed under leadership of this project manager prof. Kachiashvili K.J. The project is being carried out without any problems, in compliance with the approved Work Plan. All the main programs of the package are developed and brought into accord with each other, and they function, solving the problem stated in the project. Some interesting and original scientific results were received, and these results were reflected in 14 published papers and theses of the conference. Besides, three papers are prepared for publication and will, be published in scientific reviews in the nearest future. Scientists involved in the project have experience in control and management of river pollution level. In particular, they developed different automated systems for control of river polution level, which operated in Moscow, Odessa, Kemerevo, Riga, Tbilisi. They developed algorithms for control, estimation and prediction of river pollution level, mathematical models of processes and measurement equipment, filtration and processing of measurement information, they developed methods of decision making and so on, created packages and special software realizing the problems mentioned above. Each of them has numerous published scientific works. Project manager, Dr. of Tech. Sciences, Pr. Kachiashvili K.J., has more than 90 scientific publications in this field.

The following results will be received in this project:

- formalization of the problem of MAD calculation in the form of a multidimensional nonlinear conditional optimization problem in which economic interests of pollution sources and their technical limitations are interrelated with real state of the river in given time interval;

- mathematical models that maximally take into account specific features of pollution and pollutant transfer in the river as well as hydrodynamic features of the river;

- clear, robust and efficient numerical methods speeding up computations of pollution ingredients values by factor between 2 and 10 in comparison with the existing ones;

- simple, robust and efficient methods for solution of multidimensional nonlinear optimization problems, ensuring real-time MAD computation with a given accuracy;

- models, methods and algorithms realized in the form of an application package enabling to compute MAD in dynamic regime on personal IBM-compatible computers with minimum runtime, computer memory and user friendly interface.

Results of this project will essentially change state of the art in the field of river protection against inadmissible pollution. In particular, existing at present reality - calculation of MAD once in several years - provides lower than MAD concentration of pollutants in rivers on the average within this time period base. Whereas in separate time periods this concentration may exceed MAD significantly and inflict irreparable damage to the river natural medium, to say nothing of the optimality of MAD calculated by means of these techniques. In our case, dynamic recalculation of MAD for every necessary situation will ensure permanent maintenance of pollutants concentration at lower than MAD level and will greatly increase efficiency of water protection measures by operative taking into consideration both changes that take place in water management and economic and technical limitations of water users.

Large-scale introduction of the developed program package in corresponding water protection agencies and its reasonable use will give considerable ecological and economic effects. The latter is conditioned not only by the effect received from improvement of river ecological state, but also by simplification and improvement of MAD calculation process itself.

Commercial cost of the developed package will be about 200-250 thousand US Dollars. Besides, algorithms and programs developed in this project will be added into the automated system for control of environmental object pollution levels; this system was developed by the authors for IBM-compatible personal computers and has possibility of adding into it automatic pollution level analyzers produced by any instrument-making company of the world. Commercial price of this system, together with results of this project and those of project G-047, will amount to 750-800 thousand US Dollars at minimum.

They who will own the developed package, including, in the first place, of course, the developers themselves, will be able to make, on commercial basis, MAD calculations for different towns and populated areas. Cost of a single calculation will depend on sizes of populated areas, characteristic features of rivers and pollution processes, and the number of pollution sources. For instance, for a town with population of 50 thousand, river accounting length up to 10 kilometers, and the number of pollution sources up to 100, the cost of a single calculation will roughly amount to 5-7 thousand US Dollars.

To our opinion, this project is important for realization of ISTC aims, since its implementation solves the following problems:

- gives the scientists and specialists dealing with development of weapons and united in this project the opportunity to redirect their abilities to peaceful activity, especially on such important sphere of human activity as ecology;

- gives the above-mentioned specialists the opportunity to integrate more profoundly into the international scientific community, consolidate, extend and expand the scientific relations which they established within the bounds of ISTC project G-047 and project INTAS-GEORGIA 97-1738 "Pollutants Transfer into the Sea by Means of Minor Polluted Rivers";

- supports applied researches and development of technologies for peaceful purposes in such important field as protection of environment; the more so, as the results received in this project are also applicable to power engineering (mathematical models of pollutants transfer and methods of optimization);

- the problem solved in the project is not only national, but also international, since reliable, operative calculations of MAD optimal values are important not only for Georgia and CIS countries, but also for the developed countries;

- implementation of this project supports the change-over to market economy and answers civil needs, since it gives the project participants the opportunity to conclude in future commercial contracts with different municipal and water protection bodies for carrying out MAD dynamic calculations for rivers and pollution sources they are concerned about; besides, it gives them the opportunity to enter the world software market to sell the program package developed within the bounds of the project.

The project will be carried out according to the following plan.

The problem of MAD calculation for a set of pollution sources will be formalized in the form of nonlinear multidimensional optimization problem of target function minimization; this function characterizes discharged water quality costs of pollution sources, under restrictions allowing for their technological and economic limitations and the requirement that concentration of pollutants, in any point of the river, is less than MAC.

A set of mathematical models of pollutants transfer in river water, depending on specific character of water system, pollution sources and pollution processes, will be developed. Accordingly, one-, two- and three-dimensional diffusion models with different initial and boundary conditions will be developed.

The following algorithms will be developed: optimal, robust ensuring a given accuracy, numerical algorithms for calculation of concentration of pollutants in any point of the river; an algorithm for solution of multidimensional nonlinear optimization problem of nonlinear target function minimization, under restrictions imposed on solutions of differential equations describing pollutants transfer in the river.

Software realization of developed algorithms will be flexible in use, clear to user and simple to run. It will be shaped as program modules ready for both independent use and addition into different systems. The whole problem of MAD calculation will be shaped as a program package.

Obtained results set forth in quarterly progress reports and, in case need, additional information as well will be regularly sent to foreign collaborators. Their wishes and remarks will be taken into consideration in progress of the project. Their comments evaluating the project progress will be regularly sent to ISTC. This, undoubtedly, will improve the quality of results. Besides, the scientific results will be given to foreign collaborators for using these results in their investigations.

At the stage of development of methods, models and algorithms, the following theories will be used: mathematical statistics, mathematical programming (optimization theory), mathematical modeling, calculus mathematics, theory of differential equations and theory of identification.

At the stage realization of developed algorithms in programs, methods of system and application programming will be used. Programs will be written in programming language Delphi for IBM-compatible personal computers in operating system Windows.

When testing developed programs, methods of optimal experiment planning, simulation modeling and Monte-Carlo will be widely used.


The International Science and Technology Center (ISTC) is an intergovernmental organization connecting scientists from Kazakhstan, Armenia, Tajikistan, Kyrgyzstan, and Georgia with their peers and research organizations in the EU, Japan, Republic of Korea, Norway and the United States.


ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

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