Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 110, Issue 1 (2023) 104-120 104 Journal of Advanced Research in Fluid Mechanics and Thermal Sciences Journal homepage: https://semarakilmu.com.my/journals/index.php/fluid_mechanics_thermal_sciences/index ISSN: 2289-7879 The Foundation and Validation of Sigmoid-Typed Functions for Fouling Formation Modelling of Crude Oil Flows Gunawan Nugroho 1, , Novandion R. Kurniawan 1 , Totok R. Biyanto 1 , Purwadi A. Darwito 1 , Titik Budiati 2 1 Department of Engineering Physics, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Surabaya, 60111, Indonesia 2 Department of Food Engineering, Politeknik Negeri Jember, Jl. Mastrip, Jember, 68121, Indonesia ARTICLE INFO ABSTRACT Article history: Received 17 June 2023 Received in revised form 10 September 2023 Accepted 20 September 2023 Available online 9 October 2023 The phenomenological model of fouling formation is investigated in this research which, the parametrization method based on the species and energy equation is implemented. It is shown that the previous empirical sigmoid-typed correlation can also be generated from the species equation as a special solution. Meanwhile, the fouling heat resistance is obtained from the phenomenological energy equation. Correlating these two solutions, it is shown that the proposed model generates key parameters of fouling formation characteristics of crude preheat train within all operational conditions. Thus, it generalizes the previous models as it covers wider operational range. Keywords: Heat Exchanger; fouling formation; sigmoid function; crude oil flows 1. Introduction Heat exchanger has a crucial role as heat transfer equipment in many industrial processes. Various designs have the flexibility to adapt into many industrial processes based on thermodynamics properties, temperature, pressure, fluids, stream phase, density, chemical composition and viscosity [1]. As a preheat train in crude oil refining process, it is fed by heating fluid in the network coming from downstream products, which the recovered heat can be considered as energy saving [2]. However, fouling is the main problem in this specific application because details of physical and chemical mechanisms in fouling formation are not clear and depend on several conditions. Operational and financial from refinery unit are affected by formation of fouling as it causes losses in thermal efficiency, constriction of pipe cross-section, increasing pressure drop as well as increasing maintenance cost, which are major impacts from fouling formation [3]. Fouling formation occurs in various forms, such as chemical reaction, corrosion, crystallization, particulate, biological, solidification and combine fouling. It is pointed that variation of heat transfer surface and bulk fluid  Corresponding author. E-mail address: gunawan@ep.its.ac.id https://doi.org/10.37934/arfmts.110.1.104120