# The Ability to Control VOC Emissions from Multilayer Building Materials
## 3 Results and Discussion
### Notes on Comparison of the Experimental Emission Profiles and Proposed Model  
To fit the Equation \(C(t)\) (17), the authors had to numerically determine for each experimental set the coefficients \(k_{1}\) and \(k_{2}\) and the value of the delay coefficient X (18). Factor X accounts for the time delay of emissions from the floor system and is necessary to fit the model of the experimental points. X = \(a\)\(\times\) log (t) + \(b\) (18) is a function of time t(h). The values of \(a\) are determined numerically with the use of the obtained experimental results. In most cases, parameter \(b\) is 0. The value of X depends on the number of layers, the type of the top coat, layer thickness, chemical composition, porosity, humidity and other factors. The value of X is therefore a kind of simplification while fitting the experimental results in the best way to the adopted \(C(t)\) model. To give an idea of the values of the X coefficient depending on the parameter \(a\) as a function of the number of layers, authors present the Table 10 with example values. X reaches the value of 1 in the maximum C(t) concentration in the test chamber. In our cases, the value of parameter \(a\) of the delay element was 0.45-0.55. Increasing the layer thickness or the number of layers delays the occurrence of the VOC concentration peak in time (h).  
Finding the optimal solution for a function \(C(t)\) (17) with its parameters \(k_{1}\) and \(k_{2}\) is a task requiring numerical technique. The numerical method that the authors used assumes the search for \(k_{1}\) and \(k_{2}\) that would give the highest R\({}^{2}\) coefficient for the comparison of the \(C(t)\) model and VOC concentration experimental points. The determined coefficients \(k_{1}\) and \(k_{2}\) for each tested floor system (in dry and wet conditions) are presented in Table 11.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(a\) = 1 For & \(a\) = 0.7 For & \(a\) = 0.6 For & \(a\) = 0.5 For \\ \hline
**Time of Test t(h)** & **1 Layer** & **2 Layers** & **3 Layers** & **4 Layers** \\ \hline  & & & X = \(a\)\(\cdot\)log(t) & & \\
1 & 0 & 0 & 0 & 0 \\  
\\ \hline \hline \end{tabular}
\end{table}
Table 10: Illustrative values of the X coefficient of the \(C(t)\) model (17) as a function of time and the number of layers of the heated floor system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **1-Butanol** & **Ethylbenzene** & **Butyl Acetate** & **m-p-Xylene** \\ \hline  & & C\({}_{max}\) values from the emission profiles & & \\ D1 & 340 & 600 & 1200 & 700 \\ W3 & 630 & 110 & 340 & 180 \\  & & C\({}_{480\,h}\) values from the emission profiles & & \\ D1 & 160 & 450 & 400 & 450 \\ W3 & 380 & 30 & 40 & 60 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparing the \(C_{max}\) (ug/m\({}^{3}\)) and C\({}_{480\,h}\) observed from the emission profiles of the four selected VOCs emitted from samples D1 tested in t = 29 \({}^{\circ}\)C and samples W3 tested in t = 33 \({}^{\circ}\)C (ACH \(n\) = 1.0 h\({}^{-1}\)).  
The authors, ina statistical representative sample, determined the influence of the change of \(k_{1}\) and \(k_{2}\) (in%) parameters on the coefficient R\({}^{2}\) of model curve \(C(t)\) (17) fittingto the VOC concentration points obtained experimentally in the chamber (Table 12). For example, a change of the \(k_{2}\) parameter by \(\pm\) 100% reduces the model curve fit by 14%.  
Comparing model-based VOC concentration values \(C_{480\,h}\) after 480 h (17) and experimental are rather corresponding (Table 13). This was also confirmed by Figures 9-17. There is a large difference in the diffusion coefficients of emission through oak parquet and the ceramic tile layer and can be useful for IAQ estimation, calculating the weights of \"difficult contaminants\" [47; 48; 49]. It was noted that some contaminants (such as 1-butanol) are difficult to be removed by ventilation.