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Mathematical modeling of the process of determining the standards for process losses in the transfer of thermal energy of the coolant

Currently the actual problem is a precise definition of the normative and actual heat loss. Existing methods - experimental, on metering devices, on the basis of mathematical modeling methods are not without drawbacks. Heat losses establishing during the heat carrier transport has an impact on the tariff structure of heat supply organizations. This quantity determination also promotes proper choice of main and auxiliary equipment power, temperature chart of heat supply networks, as well as the heating system structure choice with the decentralization. Calculation of actual heat loss and their comparison with standard values justifies the performance of works on improvement of the heat networks with the replacement of piping or its insulation. To determine the cause of discrepancies between normative and actual heat losses thermal tests on the magnitude of the actual heat losses in the 124 sections of heat networks in Kazan. As were carried out the result mathematical model of the regulatory definition of heat losses is developed and tested. This model differ from differs the existing according the piping insulation type. The application of this factor will bring the value of calculative normative losses heat energy to their actual value. It is of great importance for enterprises operating distribution networks and because of the conditions of their configuration and extensions do not have the technical ability to produce thermal testing.


Introduction
Over a long period of time, heat supply in Russia developed on the basis of combined energy production (heat and electricity). The result is the district heating predominance. The main load for thermal energy in large and medium-sized cities is carried by the CHP [1]. According to the data of [2] almost 72% of the heat energy from the total volume produced in Russia is generated at the CHPP. Combined generation of electrical and thermal energy is an economically more profitable way. However, the mass cogeneration process led to large-scale construction of extended and ramified heating networks [3].

The problem of determining thermal losses
The Russian heat supply infrastructure needs a global improvement. The level of losses in the country's heating networks reaches 20-30% [4] (Figure 1), which is approximately four times higher than in Europe (4-8% [5]). In Russia, there are a large number of governmental and industry acts regulating the country's the heat supply, however, they are not without shortcomings. There are three methods for heat losses evaluation. The first method [6][7][8][9][10][11] is the determination of losses based on experimental data. Undoubtedly, this method is the most reliable, but in practice it is not always possible to perform tests because of the difficulty of the necessary experimental requirements fulfilling [9]: consumers detachment from the tested ring, temperature provision with a drop of at least 8 ° C, constant maintenance of the flow regime during the test. Therefore, this method of heat losses determining is used extremely rarely and, mainly, on trunk heat pipes, while heat losses occurring in distribution networks have a greater specific weight [14].
The second method of heat losses determination is to remove the indicators for metering devices from the consumer. Several methods have been developed for this method [12][13][14][15][16]. However, according to the difference between the released thermal energy and fixed at the consumer, it is possible to estimate only the average losses along the heating main. This method does not allow to establish losses on a particular section of the heat network. This method does not represent practical interest, since it does not allow to identify the section of the heat pipe with the greatest losses.
The third method of thermal losses determination is based on the method of mathematical modeling of specific losses of thermal energy, when a its properties change occurs during the thermal insulation using [17][18][19][20][21][22][23][24][25]. However, the results of studies [26] showed that the increase in thermal losses is not affected by the problem of moisture insulation, as described in [17][18][19][20][21][22][23][24][25], but insulation faults associated with its physical degradation and integrity damage of the insulation layer.
Thus, today there is no universal method of heat losses establishment. But this task is one of the most important, since the establishment of heat loss during the coolant transportation affects the structure of the tariff for heat supply organizations. This value understanding also contributes to the correct selection of the main and auxiliary equipment power, the thermal schedule of the heating networks, and the choice of the heat supply system structure, with its possible decentralization. Determination of actual heat losses and their comparison with normative values justifies the effectiveness of carrying out works to improve heat networks with the replacement of pipelines or their insulation.
However, the greatest interest from our point of view is the definition of normative losses, since this value affects the size of the heat supply organization tariff. Today, the methodology of normative losses determination is regulated by the Order of the Ministry of Energy No. 325 of 30. 12 approval of the procedure for technological losses standard determination in the heat energy transfer coolant». Normative values of technological losses during the heat transfer must be determined for each heat supply organization in an individual order. The definition of standards is realized by calculation performation for the heat supply system.
An analysis of the methodology for indicator findation of losses in the thermal energy transfer, coolant showed that it does not take into account some important features, such as the type of insulation and its thickness.

Experimental research
Thermal tests were conducted using the example of heat networks in Kazan. As a result of the tests, thermal losses were determined for each of the test ring sections, and separately for the supply and return pipelines. Calculations of the thermal energy actual losses in the tested sections of the heat network were made.
For comparison with the normative values, the heat losses results for each tested section were recalculated into average annual operating conditions of the heat network.
In the standard heat losses calculation, a factor was introduced that takes into account the value of thermal losses for a thermal insulation specific type for new pipelines: where is k 1i -a coefficient that takes into account the type of insulation (mineral wadding, basalt, polyurethane foam, tilith, etc.).
In Table. 1 there are shows the values of the actual heat losses and the normative values given to the average annual operating conditions of the heat network as a result of thermal tests.
The conducted experiments made it possible to establish that the actual heat losses differ from the standard values even for new, newly laid pipelines, and the magnitude and the deviation sign depend on the used of thermal insulation type (Figure 2). Thus, a mathematical model for the standard heat losses determination has been developed and tested, which differs from existing ones taking into account the type of pipelines insulation. This coefficient using will make it possible to approximate the value of the calculated standard thermal energy losses to their actual value. This is of great importance for enterprises operating distribution networks and because of their configuration conditions and lengths it has no technical capability to perform thermal tests.

Results of the experiment
A block diagram of the calculation program and a list of used the initial data are shown in Tab. 1 and Fig. 3. .

Conclusions
The obtained results show that the boiler house standard thermal losses differ from the actual values by 36%. This is due to the fact that polyurethane foam is mainly used as thermal insulation in these areas. In case of using mineral wadding, the discrepancy would not be so significant. Since the tariff for thermal energy depends on the amount of normative losses, in the example of a boiler-house Vysotnaya, 30 it can be seen that this boiler-house did not receive a significant part of the money resources.