## 1 Introduction  
In the last 30 years, strict government policies have been developed to restrict the emission levels of pollutants that mainly affect the emission of nitrogen oxides (NOxs), carbon monoxide (CO), hydrocarbons (HCs), and particulate matter (PM). Implementing these environmental policies is also intended to reduce the consumption of fossil fuels and encourage the use of alternative low carbon fuels, such as biodiesel, gas-to-liquid, hydrotreated vegetable oil, and farresane, which also contribute to reducing pollutant emissions. Manufactures of fuel injection systems develop these systems focusing on the improvement of the combustion process for reducing pollutant emissions according to the requirements of environmental regulations, increasing their efficiency and, therefore, the brake engine efficiency. Numerous researchers have shown that fuel injection parameters significantly impact pollutant emissions [1; 2; 3; 4]. Research on the efficiency of injection systems focuses on improving fuel atomization and optimizing the injection process to achieve the best possible combustion in the cylinder. The rate of fuel injection (RoI) is closely related to the heat release rate of the fuel; therefore, analyzing the parameters that directly or indirectly affect the injection rate makes it possible to know how the fuel heat will be released during the combustion process. Alternative fuels are one of the most promising ways to reduce pollutant emissions, along with modern catalytic aftertreatment systems [5; 6; 7; 8; 9; 10]. Traditional biodiesels have been a promising substitute for diesel because of their good thermal efficiency and low CO and SOx emissions [8]. However, other aspects related to crop and food availability have led to the search for alternative fuels, including third-generation synthetic fuels such as farresane or hydrotreated vegetable oil (HVO). These synthetic fuels have high thermal efficiency and lower emissions than traditional biodiesel [11; 12; 13; 14]. The influence of biodiesel properties on injection parameters has been extensively studied in traditional biodiesel [2; 3; 15; 16; 17], although it has been studied to a lesser extent on these synthetic fuels [18; 19; 20]. Varying injection parameters such as injection timing, injection pressure, and fuel spray duration is one of the strategies to improve engine performance [2; 21; 22; 23; 24] that can be combined with the use of alternative fuels to reduce emissions. In injection systems, the fuel injection rate depends on different control variables, such as injector nozzle geometry and injector type, engine load, properties of the fuel used, and injection characteristics (multiple injections, injection pressure, injection duration, etc.) [25; 26; 27; 28]. This large variability of study parameters complicates experimentation. Most researchers use robust test benches and fuel injection rate indicator equipment [29] to reproduce the operating situations of injection systems in vehicles. However, these facilities are costly and complex to maintain, making it difficult for universities or companies with fewer resources to access this type of facility. Injection rate simulations are a valuable tool for the reduction of experimental time and error reduction, allowing the simulation of operating conditions that would be dangerous for the experimental equipment. Simulations of injection rates can be performed with zero-dimensional (0D) models [30; 31], or multidimensional models in combination with other mathematical and software tools [32; 33; 34]. 0D models are simple to implement and require limited experimental trials [29]. In 0D models, the injection time variation is the most commonly used parameter for studies focused on combustion behavior, emissions, and fuel consumption [29]. Although other injection parameters, such as injection pressure, injector energizing time [29; 35; 36; 37], or injector nozzle geometry [38; 39] have also been varied.