In the long term, along with the growth of nuclear power and related changes in the fuel and energy balance of the country, natural gas will retain an important place in the national economy, including in the production of heat and electricity. Accordingly, the importance of gas distribution networks, which directly supply fuel to the Republic's consumers, will remain for a long time. According with the Concept of the National Strategy for Sustainable Development of the Republic of Belarus for the period until 2035, the main task in the gas sector is to maintain production assets at a level ensuring safe energy supply. Practice shows that corrosion factor has the greatest potential to influence the technical condition of steel underground distribution gas pipelines. To compensate for corrosion processes, steel underground pipelines are equipped with special protective means, in particular, insulation coatings. One of the key operational characteristics of insulation is its integrity, which is controlled through periodic (comprehensive) instrumental technical inspection. Based on the inspection results, statistics of identified defects of protective coatings is formed. The work examines the issues of ensuring the reliability of operational data, and highlights the experience of implementing specialized software packages in gas supply organizations of the Beltopgaz State Production Association for recording and processing the results of instrument surveys of gas distribution pipelines. The issue of the influence of organizational and production aspect (features of technology, local practice of planning and performing specific types of work on technical operation) on the structure of operational data, which requires separate study and accounting for their further statistical processing and use, has been considered in the paper.

Steel underground gas pipelines occupy a significant share of the total length of gas distribution pipelines, and therefore their maintenance in proper condition is a constant and very urgent task. Due to its global nature, the main influencing factor affecting the technical condition of any steel underground pipelines, including gas pipelines, is corrosion, primarily soil corrosion. To protect against it on pipeline networks, along with insulating coatings, electrochemical protection (ECP) is applied, that is, following the definition of STO [Standard of Organization] 17330282.27.060.001–2008, protection of metal against corrosion in an electrolytic environment, carried out by establishing a protective potential on it or eliminating the anodic potential shift from the stationary potential. In the gas distribution industry of the country, methods and means of electrochemical protection have been applied since the beginning of gasification and the construction of the first gas pipelines. All gas supplying organizations of the State Production Association for Fuel and Gasification “Beltopgaz” (six regional and Minsk city), which operate gas distribution facilities, have specialized corrosion protection services. These services provide maintenance of available ECP equipment, conduct electrical measurements on gas pipelines and corrosion studies of soils, and have certified laboratories. This paper is devoted to the analysis of domestic experience in organizing electrochemical protection of steel underground gas distribution pipelines, searching for promising directions for its improvement and increasing efficiency through the implementation of a unified industry technical policy, automation and telemechanization of ECP equipment in the general context of digital transformation, optimization of the timing and volume of maintenance.

One of the main types of maintenance of steel underground gas distribution pipelines is periodic instrument inspection. This inspection is a kind of operational control, which includes detection of defects of insulation coating and gas leaks by instrumental methods, without opening the pipeline. This simultaneously controls two different levels of failure of the gas pipeline’s serviceability, one of which fully preserves its operability, but creates the possibility of a chain of events threatening to cause a failure in the future (insulation defect), while the other level of failure is, in fact, the case when the failure has already occurred (loss of tightness of the gas pipeline), but before the examination was not detected. All underground gas distribution pipelines are subjected to an instrument inspection with a certain regulatory frequency. The identified damages are subject to mandatory elimination, the serviceability and operability of the gas pipeline are being restored. Thus, periodic instrument inspection is a key technical measure that ensures the management of the technical condition of steel underground gas distribution pipelines. It should be mentioned that the work carried out during the inspection and further repair of gas pipelines is the most extensive and labor-consuming of all those performed on the linear part of the gas distribution system. Accordingly, adequate planning in this area is very important from the point of view of both the reliability and safety of the gas distribution network and the economic and economic one. At the same time, it is quite difficult to ensure the required adequacy of operational control planning and maintenance of engineering facilities in practice, since the maintenance process itself combines regulated and unregulated components and has significant inertia of management. The present article is devoted to the issues of reasonable forecasting of the scope of work on the instrument inspection of steel underground gas pipelines, taking into account a specially identified complex organizational and logistical factor reflecting the influence of existing production practices and management approaches in the field of gas distribution. The forecast is based on the currently relevant time series analysis methods.

The relevance of solving the problem of energy saving, today, is enhanced by the requirements of an environmental nature, united by the term “green energy”. Solving the problems of climate conservation is inseparable from solving the problem of energy saving. Green, hydrogen energy, about which there has been a powerful and aggressive debate over the past decade, turned out to be directions far from solving the problems of both energy saving and environmental protection. The solution of both problems of energy saving and environmental protection at the present time and in the foreseeable future is being solved on the basis of the use of traditional primary energy resources, primarily natural gas. In this regard, the need to solve the problem of quantifying the thermodynamic perfection of heat-technological process for producing an asphalt concrete mixture becomes extremely relevant. This assessment is most simply carried out on the basis of the exergy method of thermodynamic analysis with the determination of the exergy structure of the asphalt concrete mixture flow, including thermomechanical, concentration and reaction components. The value of the concentration component of the exergy of the asphalt concrete mixture allows us to assess the energy efficiency of its production at asphalt concrete plants based on the modern exergy method of thermodynamic analysis; gives a quantitative estimate of the energy consumption for the process of mixing the ingredients of the asphalt concrete mixture in the mixing unit of asphalt concrete plants. The paper defines the structure of the exergy of the asphalt concrete mixture, in which the transit reaction component dominates, which determines the specificity of the exergy of the asphalt concrete mixture. The value of the specific mass concentration component of the exergy of the asphalt concrete mixture in comparison with the thermal component is small and the error in determining the concentration component, which cannot be objectively eliminated, does not affect the results of thermodynamic analysis.

One of the most widespread technical systems in the world is underground steel pipeline communications (heat pipelines, main and distribution oil and gas pipelines, etc.). Accordingly, reliability assessment of such technical systems and their components is of great theoretical and practical interest. At the modern level of development, reliability calculation has become a mandatory stage in the design and diagnostics (during operation) of any technical systems in ge-neral, and in particular pipeline systems. A reliable calculation, either explicitly or implicitly, is always based on the model of the object being calculated. It is the adequacy of the model to the real physical relations and processes inside the technical object that determines the accuracy and practical value of calculation methods. It is proposed to consider a single linear section of an underground steel pipeline as a complex technical system of unequal elements from the point of view of reliability – the main element (steel pipe) and auxiliary protective elements combined into subsystems (blocks). The algorithm for calculating the reliability of the object is based on the method of block diagrams, taking into account the influence of the aftereffect of the failure of an auxiliary element (elements) on the reliability parameters of the main element, which more adequately reflects the specific features of the design and operation of steel pipelines compared with the applied static models. The variants of structural design of a steel underground gas pipeline with a protective insulation coating and with complex corrosion protection (insulation and electrochemical protection) are considered, for which refined formulas are obtained for calculating the main reliability (failure-free) indicators.

At industrial CHP plants which are characterized, in particular, by steam supply to industrial consumers, in cases with significant condensate losses, it is proposed to develop a system of feed water regenerative heating by utilizing low-temperature waste heat flows those are available directly at the CHP plant. The regenerative use of low-temperature heat flows within the CHP that is proposed is possible only on the basis of heat pumps use. In this context, the use of electrically-driven heat pumps (EHP) and absorption heat pumps (AHP) is considered. It is shown that, despite the higher heating coefficient of the EHP, the thermodynamic (exergetic) efficiency and economic efficiency of the AHP are higher. Furthermore, the latter also has operational advantages. It is possible to use heat flows with various heat carriers as AHP drive, those are required for the transfer of thermal energy from a cold source to a hot receiver. In this paper, using the example of the “PT-60” steam turbogenerator unit, which is the most common type for CHP plants of the Belarusian power system, the indicators of the primary fuel use efficiency growth at the CHP plant for the AHP with a steam drive are determined. Three scenarios of the use of AHP as part of the thermal scheme of the CHP are considered, viz. with an increase in generation, with the maintenance of generation or with a decrease in the generation of electric energy. The latter is relevant in the current situation with the Unified Energy System of Belarus. In this case, while maintaining the minimum steam flow into the condenser of 12 t/h, the following increase in the plant efficiency has been obtained: electrical efficiency increased by 0.90 %, energy efficiency – by 0.55 %, and exergetic efficiency – by 0.23 %.

Gas distribution system is a production complex, which is part of the gas supply system and consists of organizational and economically interconnected facilities designed to organize the supply of gas directly to consumers. On the national basis of the gas distribution system is formed by about 67.0 thousand km of external distribution gas pipelines, 28.0 thousand km of which are underground steel pipelines. As potentially hazardous objects, steel underground distribution pipelines are subject to higher requirements for corrosion protection. As a rule, they are provided with complex anticorrosion protection, an obligatory component of which is insulation coatings. Taking into account the above mentioned, the definition of general indicators characterizing condition of insulation, the degree of its wear is an actual task. To solve it, for the first time, we have analyzed an array of long-term statistical data on defects of protective coatings of distribution gas pipelines, detected by instrumental method. The values of specific defect density Dd and damageability Ad have been determined for all types of applied protective coatings. The best values have been found for insulation on the basis of heat-shrinkable tapes. The characteristic damage of the protective coating on the basis of bituminous mastics (microcracks), which can be used as an indicator of aging of this type of insulation, has been determined. It has been shown that defect formation in the insulation coatings of gas pipelines up to the present time is, as a rule, a low-intensive process, which has been confirmed, among other things, for gas pipelines operated for a long time. The obtained results were included into the justification of abolition of the previously used 40-year normative service life of steel gas pipelines in the new edition of the Rules of Technical Safety in the Field of Gas Supply of the Republic of Belarus.

The energy system is a structure that is among the most complex artificial objects, the successful functioning and development of which is absolutely necessary to ensure the livelihoods of a modern state. In this regard, its continuous monitoring with obtaining reliable and objective performance indicators is undoubtedly in demand. Traditional key energy indicators (specific consumption of conventional fuel for electricity generation and heat release) do not give a complete picture of the operation of the power system for such complex structures and in some cases are calculated incorrectly. The present paper proposes to add a well-known, but practically unused exergetic efficiency coefficient to the range of traditional characteristics. Its application expands the monitoring capabilities and increases the objectivity of the evaluation. For the first time, the analysis of various periods (annual, heating and inter-heating) was carried out on the example of thermal power plants (CHP) of the Unified Energy System of Belarus. The relative power generation of the CHP before the commissioning of the Belarusian NPP was estimated at ≈45 %, and after commissioning it decreased to ≈39 %. More than half of the annual consumption of thermal energy in Belarus is accounted for by heat-generating sources, while thermal power plants provide up to 88 % of heat output. The installed electric capacity utilization factor, the extraction factor and the average annual specific generation of electricity on thermal consumption for each CHP separately have been determined. The results are presented graphically, which makes the content more informative and facilitates the perception. Solutions have been proposed to improve the efficiency of the CHP.

. The results of numerical studies carried out on the basis on a mathematical model developed by the authors of this paper devoted to the investigation of the influence of various factors on the characteristics of the process of heat treatment of composite products in industrial heat technology installations in the presence of internal heat emissions distributed over the volume of individual layers of the product are presented. The formulation of boundary conditions for this model is proposed, considering the multilayer structure of products and the peculiar properties of the organization of their heat treatment process in a heat technology installation. A detailed description of the mathematical model was presented in the previous works. In this study, the functions of temperature distribution and the coefficient (degree) of hydration in the spatial regions that make up the product have been studied as characteristics of the heat treatment process. Model composite products of the same shape and structure but of different volume, consisting of two layers of material in which an exothermic hydration reaction takes place separated by a layer of expanded polystyrene were considered. The temperature-time regime of heat treatment was assumed to be close to that used in industrial conditions in the production of three-layer external wall panels. The boundary and initial conditions corresponded to the conditions of heat treatment on flat stands with water heating and sheltering products from above. It has been determined that the presence of a thermal insulation layer in the core of the product separating the layers that have an internal heat source, changes the distribution of temperature values and the hydration coefficient in the upper and lower layers significantly. An increase in the characteristic volume of the product leads to an increase in the influence of internal volumetric heat release on the processes of heating and hydration, while heat release caused by the course of the hydration reaction begins to have a decisive influence on them.

The experience of developed countries shows that the development of the road network and transport infrastructure determines the intensity of economic ties and is one of the most important conditions for the development of the state’s economy. Optimization of the composition and production technology of asphalt concrete mixture – the basis of paved roads, is of great importance, both from an economic and environmental point of view. The production of asphalt concrete mixture directly (during the production process at asphalt concrete plants) and indirectly (during delivery from the plant to the place of installation) determines the energy costs for the production of asphalt concrete. At asphalt-concrete plants the specific energy consumption per ton of hot asphalt concrete mixture varies from 0.3 to 0.7 GJ. The range in energy costs is large. This situation indicates the presence of a significant energy-saving potential of asphalt concrete mixture thermal technology. The exergy analysis of technical systems proposed in this paper, which are operated in the asphalt concrete mixture production processes, makes it possible to judge the efficiency of energy use in their thermal units. This approach is expedient not only in the primary production of asphalt concrete mixture, but also for more environmentally friendly, energy- and resource-saving production processes for the operation of equipment during the regeneration of road asphalt concrete.

In the present-day conditions, the issue of energy saving is becoming increasingly acute and permanently relevant. This situation is caused by rapid growth in prices for primary energy resources and by the need to reduce the share of natural gas in the incoming part of the energy balance of Belarus. According to available statistics, with the commissioning of the Belarusian NPP, the share of natural gas in the incoming part of the energy balance decreases from 97 to 59 %. In the economic complex, the share of this primary energy resource is projected at 70 %. The problem of energy saving is solved most rationally and with the least investment only by increasing the efficiency of natural gas use, especially due to the commissioning of the Belarusian NPP, the issue of preserving the possibility of using centralized heating facilities is acute. It is necessary to increase the thermodynamic efficiency of the cycles of steam turbine plants, both heating and condensing, which form the basis of the generation of the Belarusian power system, in order to restore the energy characteristics of the power system, which have somewhat decreased with the commissioning of the NPP. In the limit, the share of natural gas in the incoming part of the energy balance should be reduced to values not exceeding 50 %, in accordance with the requirements of energy security. The article considers examples of utilization of low-temperature secondary energy flows occurring at thermal power plants: the heat of the cooling processes of the generator, lubrication systems, as well as the heat of condensation of turbine exhaust steam and deeper cooling of flue gases. On the basis of this review, it is expected to identify promising areas of relevant research in relation to the energy system of Belarus.

This article is the second part of the research devoted to the exergetic analysis of heat treatment processes of concrete products in heat technology installations. In the first part, the issues of calculating the exergy of a concrete mixture and hardening concrete have been considered, taking into account all the components of the exergy, viz. reaction, concentration and thermomechanical ones. In the present part of the study, exergetic criteria are proposed that make it possible to evaluate the energy efficiency of the operating modes of heat-technological equipment for the heat treatment of concrete products. These include the degree of thermodynamic perfection of a heat-power system, which is used to evaluate the completeness of the use of the exergetic input; thermodynamic efficiency of the system of heat treatment of concrete products in heat technology installations, representing the degree of thermodynamic perfection of the heat power system that is calculated without taking into account all the components of the sum of transit exergies; thermodynamic efficiency of the heat treatment system, taking into account the exergetic efficiency of the system of heat energy production and transportation; the degree of technological perfection that indicates at the portion of the exergy supplied to the heat technology installation for the heat treatment of concrete products is intended to obtain a technological result. To calculate the listed indicators and characteristics, a mathematical apparatus is proposed that takes into account the mass of the concrete product, the specific mass exergy of cement and hardening concrete, the specified degree of hydration of cement in concrete at the end of heat treatment, the exergetic flows supplied to the product in a heat technology installation during its heat treatment, and numerical indicators characterizing the incompleteness of the cement hydration process. The results obtained in this paper are discussed from the viewpoint of their applicability in the selection of heat treatment modes. They can be used in the selection of energy-saving modes of heat-technological equipment for industrial heat treatment of concrete products.

Production of concrete and reinforced concrete products in the conditions of the Republic of Belarus and in the countries with similar climatic conditions requires heat treatment in heat-technological installations in order to achieve the desired strength of the products at the appointed time, which consumes a great amount of thermal energy. In this case, the purpose of equipment operating modes is associated with a number of difficulties when it comes to new products of complex spatial configuration and structure. The optimality criteria of such modes are, as a rule, the duration and temperature limits of processing, providing the required strength with minimal energy consumption. In the conditions of serial production in the case of structurally simple objects, the assignment of heat treatment modes is carried out empirically. As the analysis shows, the modes obtained in this way do not meet the above criteria, especially from the standpoint of energy saving. The paper, using a mathematical model previously developed by the authors, proposes dependencies for calculating the optimal modes of heat treatment of concrete products that are distinguished by a complex spatial shape and multi-component structure. The method is based on three-dimensional transfer equations, taking into account internal sources of heat release due to the ongoing hydration reaction of the active components of the cement clinker, and the boundary conditions corresponding to the structure of the processed product, as well as the type of heat technology device for accelerated hydration. Equations are proposed for calculating the amount of heat energy supplied to the processed product providing a given strength at a specified time. On the example of a manufactured industrial concrete product and for the conditions of an actually used device for accelerated hydration, a comparison has been made between two limiting modes of heat treatment: with isothermal exposure and in its absence. As a result of the performed calculations, the dependences of energy consumption, temperature fields and the degree of hydration in the product for both modes have been obtained and an energy-saving mode of heat treatment corresponding to the case under consideration has been developed. It is shown that the used numerical method allows to solve problems of this type and to achieve thermal energy savings.

An assessment is given to the problems of urban wastewater sludge utilization in our country and abroad, with determination of formation and usage level. Global trends in the reduction of carbon dioxide emissions exacerbate the urgency of solving the designated tasks. At the same time, recently, in connection with the EU’s plans to introduce a cross-border carbon levy, it has become necessary to reduce the carbon footprint from burning traditional fuels, which is an urgent problem of modern society. One of the directions that provide a solution to this problem is the replacement of part of the hydrocarbon fuel by the consumption of multicomponent solid fuel based on the use of combustible waste that is part of the multicomponent fuel. This solid fuel can be used to meet the needs of small consumers, for example, in the autumn-summer period to generate a drying agent for the preparation of grain on the threshing-floor, in small boiler houses, in sand drying plants of locomotive depots, heat installations of hangars and workshops, as well as in other heat-generating installations operating on solid fuels. At the same time, solving the problem of reducing the carbon footprint for Belarus is closely related to another urgent task – reducing the energy component of industrial products and the environmental consequences of storing accumulated and generated waste. The paper presents the results of joint scientific research in the field of application of modern technologies and equipment using electrohydraulic treatment to reduce and minimize the level of anthropogenic and polluting substances in wastewater sludge. The described technological equipment, technology and post-treatment modes reduce the content of harmful substances in the wastewater sludge composition even with short-term treatment. An assessment of the effectiveness of the developed technology for the use of sewage sludge is given, using the method of wet multicomponent briquetting to obtain a multicomponent fuel. The presented process flow diagram of multicomponent briquetting using sewage sludge and plant-wood waste directly shows the undeniable advantages of using watered wastewater sludge as a raw material for the production of solid fuel. At the same time, the optimally selected ratio of components and moisture content of the briquetted composition solves a number of technologically difficult problems that cannot be realized using traditional briquetting technologies. The presented data of the conducted research and the developed technology make it possible to expand the area of using wastewater sludge as a secondary renewable material resource.

In industrial heat-technological installations for accelerated hydration of concrete, which are the main element of the thermal power system of enterprises of concrete products, the modes of heat treatment and the organization of heat supply to the product processed in them are due to the required temperature distribution in the volume of the concrete body, providing a given product quality. In order to optimize the processes occurring in such thermal device, a nonstationary mathematical model of the hardening process of the concrete product subjected to heat treatment has been developed, which allows calculating the spatial distribution of its volume temperature and degree of hydration of the active part of the cement clinker. The proposed model is based on the use of a non-stationary three-dimensional heat equation that takes into account the internal heat release due to the exothermic reaction in a concrete body and determines the degree of its hydration and hardening. For a given mode of heat treatment with the use of the finite volume method, numerical simulation of the hardening process of a symmetric concrete object of cubic shape is performed. In the selected points of the object under study, depending on the time of heat treatment, the rates of temperature change and the degree of hydration were calculated and their analysis was carried out. When analyzing the graphs of the temperature change rate, the characteristic inflections consistent with the given thermal mode of the heater were revealed. By a given mode of heat treatment of the form of “temperature rise – isothermal exposure – temperature decrease” in the selected points of the object there is an increase in temperature compared with the specified maximum temperatures of isothermal exposure, which is associated with the exothermic effect of the hydration reaction. A temperature shift relative to the specified thermal mode of the heater due to the non-equilibrium of the concrete hardening process is observed. The proposed mathematical model allows determining the time of reaching a preset temperature for any point of the internal space of the product subjected to heat treatment that can be used in the when designing of new and modernizing of existing thermal technological installations of accelerated hydration of concrete, as well as systems for automated control of the concrete hardening process in these devices. The results obtained during the study are in satisfactory agreement with the experimental data of other authors.

Thermo-technical installations consuming significant amounts of thermal energy are used in order to intensify precast and reinforced concrete production processes under industrial conditions. Despite significant progress in the study of concrete hardening in accelerated hydration devices, a prominent lack of reliable and cost-effective research and optimization methods of their operation is observed. The methods used in real production processes are mainly based on empirical dependences obtained for specific technological conditions. These methods can not always be applied for other modes and technologies. The present paper develops calculation methods based on fundamental laws that make it possible to obtain functions for evolution of concrete product hydration process. Methods of mathematical modeling permit to develop new ways directed on improvement of modes for heat treatment of concrete products and accelerated hydration technologies. The paper describes a mathematical model for calculating a hardening process of a concrete product that includes a transient three-dimensional heat conductivity equation, a function of internal heat release due to behavior of exothermic reactions of cement hydration and also a system of initial and boundary conditions. A numerical simulation for temperature and hydration coefficient of a concrete product having shape of a 0.1´0.1´0.1 m cube has been performed in the paper. Verification of the non-stationary mathematical model for calculating temperature fields and hydration degree while using experimental data on concrete product strength obtained under industrial conditions. Investigations on hydration degree function of time have shown that experimentally obtained values of compressive strength correlate with hydration coefficient and hydration rate functions of heat treatment time which are calculated on the basis of the proposed non-stationary mathematical model of concrete product hardening. Satisfactory agreement of experimental and calculated data confirms adequacy of the proposed non-stationary mathematical model for calculating temperature fields and hydration degree with accelerated heat treatment of concrete products.

In the article the technique of an assessment of modes of operation of the heat engineering equipment used for heat treatment of concrete products in the conditions of programcontrolled heat supply according to the pattern of “heating – isothermal influence – cooling” has been developed. The method is based on the numerical solution of a non-stationary heat equation supplemented by equations describing the hydration process of a concrete product; also, it includes a system of initial and boundary conditions for its spatial structure. The method makes it possible to create tabulated functions of temperature and the degree of hydration of the time of heat treatment in any point of a 3D-product. The mathematical tools for calculating the functional dependencies of concrete hydration equipment with software-heated environment are presented. Numerical calculations of the concrete hydration process in the formwork are performed with respect to the symmetrical object. Based on the calculation of the temperature gradient across the minimal cross section of the product, a numerical analysis of the functions modeling heat supply mode depending on the processing time of a concrete product has been fulfilled. It is demonstrated that the maximum speed of the hydration process in a concrete product hardening is achieved at the maximum of time lag of isothermal cure. Additionally, with an increase in the duration of the product heating, the value of the maximum hydration rate decreases. It is concluded that the method of assessing the mode of heat treatment of concrete products being developed makes it possible to determine parameters for the calculation of the minimal useful heat required for the heat treatment of concrete products with spatially distributed parameters. The proposed method is applicable to calculate the temperature fields and the extent of hydration in the products of any geometric shape and volume in a software-controlled heating environment of industrial facilities for the accelerated hydration of concrete, and also affords the possibility of preliminary calibration prior to the assignment of relevant heat supply modes to the products being processed.

The development of methods for calculating the dynamics of the energy thermal characteristics of the accelerated hydration process is one of the most difficult tasks of heat power engineering. The article describes a new method of calculating the thermal characteristics of the process, focused on its application in the installations of accelerated hydration used for the production of 3D-reinforced concrete structures. The principles of cellular-automatic modeling of energy characteristics of concrete heat treatment process were used in the development of the method. The mathematical apparatus used in the method is based on the finite-difference three-dimensional heat equation, which allows taking into account, due to the system of boundary and initial conditions, the spatial dimensions of the concrete product, the spatial arrangement of the formwork, the spatial distribution of heating elements and other design features of the accelerated hydration system. The input parameters of the models used are the density, thermal conductivity, heat capacity of the concrete mixture and structural elements included in the tooling of the product. Boundary and initial conditions will make it possible to solve modeling problems for any 3D-design. The goal of the study is to develop a method for calculating the energy characteristics dynamics of the hardening of 3D-concrete products subjected to heat treatment, based on a grid non-equilibrium thermal model. The paper presents a mathematical equation apparatus that allows linking the geometric characteristics of the product and the finite-difference equations of thermal conductivity, including sources of heat. A numerical method for determining the energy characteristics of the hardening of 3D-concrete products subjected to heat treatment has been proposed consisting of, depending on the time of heat treatment, the calculation of the outside heat supplied to the concrete product, heat dissipated into the environment, the emitted heat of hydration and the heat accumulated in the concrete product during heat treatment, taking into account the geometry of the product. The method is based on a grid three-dimensional thermophysical model that takes into account the nonequilibrium and the system of boundary conditions that reflect the specifics of the process in the accelerated hydration of concrete. Calculations of the functions of the energy characteristics determining the heat treatment, depending on the time of heat treatment for cubic 3D-concrete products of different sizes have been performed. It is demonstrated that the rate of alteration of energy characteristics can be modeled for products of any spatial configuration.