# A Study on a Modified Model for the Hold Time of a Clean Extinguishing Agent
## 1 Introduction  
Water is the most widely used extinguishing agent to control, suppress, and extinguish fires. However, although water is used most efficiently, it is difficult to use in places where water damage is a concern. Therefore, in these places, water mist, gaseous agents, and a hybrid system combining water mist and inert gases are used. The water mist system extinguishes a fire by spraying very fine water droplets into the fire like water fog. That is, the sprayed water mist cools the frame and surrounding gases, displacing oxygen through evaporation, and attenuating radiant heat with the fine droplets [1, 2, 3]. The hybrid system adds the extinguishing effect of the inert agent to the extinguishing effect of the existing water mist by including inert gases in the water mist [4, 5, 6]. However, water mist has disadvantages such as high installation costs and limitations in actual discharge testing. On the other hand, a clean extinguishing agent (CEA) can limit water damage, and its performance can be evaluated without an actual discharge test through an evaluation of the theoretical model. Therefore, a CEA is one of the most widely used extinguishing agents in places where water damage is a concern. A CEA is a gas suppressant that is used in fire areas. It is discharged with a concentration above the extinguishing concentration in a sealed enclosure and prevents combustion from occurring for more than a certain period of time through physical and chemical mechanisms. This time is called the hold time or retention time. Because the hold time secures the time required to extinguish a firemanually, the longer this time is, the more the fire damage can be minimized [7]. Therefore, it is only possible to obtain approval from relevant authorities when evidence of a hold time exceeding the standard is secured. Evidence of hold time in an enclosure in which a CEA is installed cannot be measured by direct discharge of an applied CEA, which can be predicted using leakage characteristics obtained from an enclosure integrity test (EIT). Theoretical models for the prediction of hold times are provided in the National Fire Protection Association (NFPA) 2001 Annex C and the International Standards Organization (ISO) 14520-1 Annex E [8; 9]. The theoretical models provided are divided into _the continuous mixing models_ and _the descending interface models. The continuous mixing model_ is a model that is applied when the air flowing in from the outside of the enclosure and the agent-air mixture inside the enclosure are completely mixed by the bias pressure and other relevant factors. In this case, bias pressure can be generated by stack effect, wind, or a mechanical HVAC system. This model is offered by both NFPA and ISO. However, _the descending interface models_ are different between NFPA and ISO. NFPA provides _the sharp model_ that considers only advection, and ISO provides _the wide model_ that considers advection and diffusion at the same time. The difference between these two models is whether or not they consider the effect of diffusion on the prediction of hold time. Therefore, compared to _the sharp model_, which does not consider diffusion, _the wide model_ predicts a conservative hold time [10; 11]. This difference can be more than doubled depending on the conditions. As such, theoretical models for hold time inevitably have different predicted values depending on diffusion analysis. [PERSON] proposed _the thick model_ combined with _the sharp model_ and _the wide model_, which reduced the prediction error of the extreme hold time of these models [11; 12]. _The descending interface models_ are divided into three types based on differences in the interpretation of diffusion, but the interpretation of advection is the same [7; 8; 9; 10; 13]. In other words, the analysis of the advection for _the wide model_ and _the thick model_ is the same as in _the sharp model_. This analysis method, proposed by [PERSON] and [PERSON], is still applied today [14].