# The Ability to Control VOC Emissions from Multilayer Building Materials
## 1 Introduction
### State of Knowledge-Emission Modelling
Consequently, it is crucial to establish a simple and practical model to predict building material emissions. Research on the development of analytical models for engineering applications was carried out assuming constant values of the emission rate of pollutants or assuming that the concentration of TVOCs at the boundary of building material is exponentially decaying (adopted constantly, e.g., concerning formaldehyde HCHO emissions). The ASTM D 5116-06 Standard Guide [36] is important in this group of publications (Small-Scale Environmental Chamber Determinations of Organic Emissions From Indoor Materials/Products) based on a study by [PERSON], [PERSON] and [PERSON] [39] (of which the emission profile is cited in Figure 11), which proposes an analytical model useful in calculating the VOC chamber concentration during an emission test. The model includes the exponential equation to calculate the emission factor \(EF\) and the chamber concentration \(C_{i}\) of the VOC emitting from a material/product sample in a small, normalised chamber used in the standard chamber test. This model, called the first-order decay source model, is one of the most frequently used models of empirical emission processes carried out in a ventilated chamber (small-scale Environmental Test Chamber). The ASTM 5116-06 Standard Guide [36] presents the first-order decay source model \(C(t)\) with the following solution under the condition of \(t=0\) and \(C=0\):  
\[C=L(EF_{o})(e^{-kt}-e^{-Nt})/(N-k) \tag{4}\]  
where \(C\) is chamber VOC concentration (mg m\({}^{-3}\)), \(N\) is air change rate (h\({}^{-1}\)), \(L\) is chamber loading factor (m\({}^{2}\cdot\)m\({}^{-3}\)) and \(k\) is first-order decay rate constant (h\({}^{-1}\)). \(EF_{0}\) is the initial emission factor from the equation (in mg m\({}^{-2}\) h\({}^{-1}\)) calculated in the formula:  
\[EF(t_{i})=(\Delta C_{i}/\Delta t_{i}+NC_{i})/L \tag{5}\]  
where \(EF\) (\(t_{i}\))-emission factor at time \(t_{i}\) and \(\Delta C_{i}/\Delta t_{i}\)--the slope/gradient of the time concentration curve at time \(t_{i}\) (h). This model was also adopted in a simplified form. As a result of the research carried out at the LBNL in Berkeley ([PERSON] [40] and [PERSON] et al. [41]) on the optimisation of the strategy of removing air pollutants in residential residences, it was found for most VOC compounds (except, e.g., formaldehyde) that if the emission factor \(EF\) (\(t\)) was constant, the emitted VOC concentration in rooms/chambers was inversely proportional to the time-averaged air-change rate. Therefore, the equation simplified by [PERSON] et al. [40] for constant source is adopted in the following form:  
\[\frac{dC}{dt}=\frac{EF(A)}{V}+N(C_{out}-C) \tag{6}\]  
where \(EF\) is emission factor mg m\({}^{-2}\) h\({}^{-1}\); \(A\) is floor surface m\({}^{2}\); \(V\)-is chamber volume m\({}^{3}\); \(N\) is air change rate h\({}^{-1}\), \(C_{out}\) is outdoor VOC concentration mg m\({}^{-3}\) and \(C\) is chamber VOC concentration mg m\({}^{-3}\); \(t\)-time h.  
Two recently published analytical models of emissions were developed in 2020 by two Chinese scientists' teams with a very similar composition [PERSON], [PERSON], [PERSON] et al. [42] and [PERSON], [PERSON], [PERSON] et al. [43]. These are exponential mass transfer models that eliminate some of the disadvantages of the empirical model, and their parameters have a justified reference to the parameters of physical models. Efforts were made to develop a practical and straightforward model to simulate the VOC emission characteristics in an environmental chamber, taking into account convective mass transfer and equalising mass balance in the indoor environment. The mass transfer model considers the release characteristics of formaldehyde and VOCs from the following three aspects: (1) VOCs diffuse in materials, (2) diffusion from the surface of building materials to the air boundary layer, and (3) convection and diffusion of the air layer.