# Development of a New Evaporation Exposure Model: Chemical Product Evaporation Model (CPEM)
## 5 Discussion  
In this study, a new evaporation model was developed to assess non-applied chemical products that reflect product mass reduction over time. Theoretically and experimentally, this study demonstrated the mass of the product decreased at a constant rate, under the assumption of a constant surface area in contact with the air. Under the assumption of a constant reduction rate of the product mass, we obtained three main results. The first was that the ConsExpo evaporation model underestimated the concentration of chemical  
Figure 5: Comparison of the estimated target substance concentrations in the air between the indirect estimation method (\(C_{air}^{ss}\)) and direct estimation method (CPEM). The graphs on the left show the air concentrations of the target substance at given times, and the graphs on the right show the time-averaged concentration of the target substance in the air over 1 year. The dotted line represents the product exhaustion time. (**a**) When the target substance in a product entirely evaporates until exhaustion time. (**b**) When the target substance in a product does not entirely evaporate until exhaustion time. evaporated in the room air from chemical products. Because the ConsExpo evaporation model assumed that the mass of the product does not change, the product mass would overestimate the mass of a product containing volatile solvents. Thus, the substance concentration in the product estimated by the ConsExpo evaporation model was lower than the substance concentration estimated by CPEM. The ConsExpo evaporation model considers only cases in which the concentration in the product decreases. However, in the CPEM, because the product mass was incorporated as a variable, it was possible for \(C_{prod}\) to increase depending on the measured product mass reduction rate. [PERSON] proposed two assumptions for the ConsExpo evaporation model (i.e., low concentrations and a pure substance) to obtain an approximate solution [10]. In terms of the assumption of low concentrations, it was assumed that the concentration of the substance in the product was low enough that \(P_{eq}=P_{vap}C_{prod}/\left(C_{prod}+C_{r}M/M_{r}\right)\approx P_{vap}C_{ prod}/(C_{r}M/M_{r})\). In terms of the pure substance assumption, it was assumed that the whole product consisted of a substance whose concentration was stable, and \(P_{eq}=P_{vap}\). A plateau stage may occur under the assumption of a pure substance but not in the case of low concentrations because the substance concentration of the product decreases. From our simulation results, it can be seen that the plateau stage does not occur, consistent with [PERSON]'s results. In this study, corresponding to the case of low concentrations, it was confirmed that if the evaporation of the target substance was slower than that of the other materials, the concentration of the substance in the product would increase. It was apparent that the predicted concentration of the target substance in the air was higher than that estimated in previous studies using the ConsExpo evaporation model. Therefore, the ConsExpo evaporation model should be applied when other materials do not volatilize, and the CPEM should be applied when other materials are volatilized. The third finding was that we can suggest new methods for screening the chemical risk of a product by considering evaporation. If the target substance in a product is predicted to completely evaporate by the product exhaustion time, the average air concentration of the target substance can be estimated using the steady-state solution of Equation (18). Therefore, in this case, only the product of the weight fraction and the product mass reduction rate coefficient is required, without the need for modeling using, for example, the ConsExpo model or the CPEM.