Analysis of the Mathematical Models for Identifying the Thickness of the Fouling Layer in Natural Gas Coolers  
[PERSON]  
1 Department of Energy Engineering, Faculty of Mechanical Engineering, Technical University of Kosice, 04200 Kosice, Slovakia; [EMAIL_ADDRESS]  
[PERSON]  
2 Department of Thermal Engineering, Faculty of Materials Science and Technology, VSB-Technical University of Ostrava, 708 33 Ostrava-Poruba, Czech Republic; [EMAIL_ADDRESS]  
[PERSON]  
3 Department of Applied Mathematics and Informatics, Faculty of Mechanical Engineering, Technical University of Kosice, 04200 Kosice, Slovakia; [EMAIL_ADDRESS]  
[PERSON]  
1 Department of Energy Engineering, Faculty of Mechanical Engineering, Technical University of Kosice, 04200 Kosice, Slovakia; [EMAIL_ADDRESS]  
Footnote 12: email: {https:////www.mdpi. of the fouling layer formed on the internal heat-transfer surfaces in the pipes of a cooler. Therefore, this study includes a rather detailed analysis of mathematical equations. The proposed method brings relevant results that have been validated in experiments. Natural gas coolers are characterised by cooling surfaces of various sizes and shapes. The numbers of tubes and their arrangements inside the cooler block, as well as the methods of transporting gas through the tubes, may vary. Over a prolonged operation of a cooler, its cooling capacity decreases due to sediments accumulated on the internal and external surfaces of the tubes. Keeping the external heat-transfer surface clean is relatively easy; however, cleaning the internal surfaces is a complicated process. The cooler must be dismantled, all its tubes must be cleaned with the use of special technology, and then it must be re-assembled. As the cleaning technology is complicated and very long, the cooler must be removed from service for a long period of time; this causes a considerable financial loss to the gas transporter. The currently available analytical procedures for the identification of a cooling capacity of any equipment in which heat is transferred between the cooled medium and the cooling medium are rather complicated. In general, the key challenge is to exactly identify the heat transfer coefficient for both the cooled medium and the cooling medium, especially in cases where the internal or external heat-transfer surfaces are fouled and the external surface has a complex shape. Figure 1 shows the real condition of a natural gas cooler fouled with impurities of an unknown composition. The authors of paper [1] identified the heat-transfer coefficient of the fouling layer in an experiment. Expressing a cooling capacity is also difficult due to the fact that the temperatures of the cooled medium and of the cooling medium change on the heat-transfer surface along the entire tube length [2; 3; 4]. The basics of the process of cooling gas media by applying ventilation technology may be found in the literature [5; 6]. The analysed cooler was designed with the tubes arranged in several rows on top of each other. In each row, the temperatures of the gas and of the cooling air are different. As the temperatures change, the heat transfer coefficients for the internal and external sides also change, and so does the gas density and viscosity, as well as the thermal conductivity coefficient. The authors were searching for a procedure that would describe in the simplest possible way, but with sufficient accuracy, the process of formation of the fouling layer in natural gas coolers that are used in various compressor stations and have various shapes of the heat-transfer surface. In this article, two different methods for the identification of the fouling layer thickness were analysed: the balance method, and the procedure using dimensional analysis. When applying dimensional analysis, it is advisable to confront the obtained results with the results obtained by a physical experiment [7] or numerical modelling [8; 9], or a complicated analytical procedure [10; 11; 12].