# CFD-Based Metamodeling of the Propagation Distribution of Styrene Spilled from a Ship
## 1 Introduction  
Hazardous and noxious substances (HNSs), often transported by ships, are harmful to living resources, marine life, and even human health when spilled into the sea [1; 2; 3]. Because most HNSs, unlike oil, are transparent, the HNSs are difficult to recognize directly after leakage. In general, the HNS can be classified into gases (G), evaporates (E), floaters (F), dissolvers (D), and sinkers (S), as they float, evaporate, or dissolve [4]. For instance, the levoli Sun, a chemical tanker, sank in the English Channel and released approximately 4000 tons of styrene [5]. In this accident, high-intensity currents caused significant dilution, spreading styrene in the seawater, and styrene was detected in the gill tissues of crabs in the vicinity of the wreck. More than 2000 HNSs are being transported by ships currently; thus, a robust and quick response strategy for spill accidents should be developed. According to the literature, there are many reports on oil spill problems. [PERSON] et al. [6] performed a numerical analysis of the leakage from an oil container ship in the Istanbul Strait and provided information on the oil propagation. [PERSON] et al. [7] developed a combined model using the hydrodynamic and oil-spill models. They also conducted a numerical simulation of the oil-spill propagation in the case of real accidents in the Arabian Gulf region, showing that the simulated results agreed well with the observed spill trajectories. As mentioned above, the oil spill was not difficult to visualize in the experiment because the oil was not transparent. However, because HNSs are optically transparent and very dangerous it is very difficult to conduct experiments in a real marine environment. Hence, many experimental works have been conducted in restricted areas and conditions. For example, [PERSON] et al. [8] released a floating cell containing a small amount of styrene into the sea and monitored the residual concentration over time. They reported that only 50% of the initial amount of spilled styrene remained just after one hour. Furthermore, experimental data have been reported in the Standard European Behavior Classification (SEBC) code. However, these data have limitations because the experiments were mostly conducted for pure products under atmospheric conditions in a laboratory. It turns out that these conditions significantly differ from those in the case of incidents at sea. Consequently, actual propagation behavior is different from the experimental results reported previously. Another issue in carrying out the experiments is about the safety caused by the lethal toxicity of the HNSs. When the real experiment is conducted in the sea, the marine ecosystem and living resources will be at risk and eventually destroyed. Thus, doing a real experiment is strictly limited. Computational works are a promising alternative for the detailed investigation of HNS propagation behavior under various conditions. Even if the computational fluid dynamics (CFD) approach yields a lot of information on HNS propagation for various scenarios, it requires a huge amount of time to obtain the final solutions. Practically, we should make specific responses as quickly as possible just after HNS spill accidents. In this regard, CFD simulation cannot be used practically; however, a direct prediction tool, such as a metamodel, can be a powerful way to suggest how to respond to the HNS accident quickly. Indeed, the metamodel is a surrogate model, which includes the mathematical relationship between inputs and outputs [9; 10; 11]. To develop the metamodel, we needed to gather a lot of information on the related physics. Hence, the present study extensively conducted CFD simulations for different cases and it suggested important parameters that can be used to mathematically connect inputs and outputs. Previously, a regression model was reported and tested with the CFD simulation results [12; 13]. The current study aimed to construct the metamodel with the simulation results for 80 scenarios.