# SimEx: A Tool for the Rapid Evaluation of the Effects of Explosions
## 2 SimEx Capabilities
### Other Calculation Assistants
#### 2.2.1 Assistant for the Calculation of the Thermodynamic Properties of Explosives  
For the calculation of the theoretical thermodynamic properties of explosives and explosive mixtures, SimEx includes an extensive database of pure CHNO propellants and explosives extracted from [PERSON] and Graham [1], updated with data from [PERSON] [7] and [PERSON] [5] for more recent explosives. From the properties of pure explosives, the thermochemical assistant estimates the properties of explosive mixtures formed by two or more components by specifying the mass fractions and the density of the mixture. First, it computes the apparent chemical formula of the explosive mixture along with its molecular weight and maximum density. For the calculation of the decomposition reaction in nominal products, which provides the heat of explosion and the volume of gases generated, one can choose different calculation hypotheses: Kamlet-Jacobs (KJ), Kistiakowsky-Wilson (KW), Modified Kistiakowsky-Wilson (modified KW), Springall-Roberts (SR), or chemical equilibrium [5]. In the latter case, SimEx determines the composition of the product mixture following the chemical equilibrium approach considering a constant-volume explosion transformation that uses the ideal gas Equation of State (EoS) for the products according to the norm UNE 31-002-94 [42], as illustrated in Figure 3.  
More complex computations based on the European Standard EN 13631-15 [43], which use the semi-empirical Becker-Kistiakowsky-Wilson (BKW) EoS [44; 45; 46] or the Heuze (H9) EoS [47] for the products, are also supported in the last version of SimEx. As sample results of these computations, Table 1 shows the detonation properties obtained by SimEx for different explosive mixtures (see Table 2 for its composition) compared with the results  
Figure 3: Interface of the assistant for the calculation of the theoretical thermodynamic properties of explosives and explosive mixtures. reported in the European Standard EN 13631-15 [43], and obtained with the W-DETCOM code [48; 49], which computes directly the Chapman-Jouguet state. The equilibrium calculations are carried out using Combustion Toolbox (CT), an in-house thermochemical equilibrium package developed at UC3M [24; 50]. CT determines the equilibrium composition of the product mixture through the Gibbs free energy minimization method by using Lagrange multipliers combined with a multidimensional Newton-Raphson method. The thermodynamic properties (specific heat, enthalpy, and entropy) are \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Explosive** & **Source** & \(\mathbf{T}\) **[K]** & \(\mathbf{p_{\text{CJ}}}\) **[GPa]** & \(\mathbf{v_{\text{CJ}}}\) **[m/s]** & \(\mathbf{Q_{\text{CJ}}}\) **[kJ/kg]** & \(\mathbf{F_{e}}\) **[kJ/kg]** \\ \hline \multirow{4}{*}{ANFO} & CT & 2592 & 7.14 & 5353 & 3845 & 943 \\  & EN 13631-15 & 2586 & - & - & 3820 & 945 \\  & W-DETCOM 1  & 2919 & 6.62 & 5326 & 3849 & - \\ \hline \multirow{4}{*}{ANFO} & CT & 3026 & 7.38 & 5442 & 4666 & 1009 \\  & EN 13631-15 & 3060 & - & - & 4642 & 1020 \\  & W-DETCOM 1  & 3370 & 6.55 & 5215 & 4655 & - \\ \hline \multirow{4}{*}{Emulsion} & CT & 2112 & 15.3 & 6549 & 3263 & 766 \\  & EN 13631-15 & 2099 & - & - & 3236 & 771 \\  & W-DETCOM 1  & 2438 & 13.9 & 6758 & 3214 & - \\ \hline \multirow{2}{*}{Dinamite I} & CT & 4173 & 25.03 & 7960 & 6452 & 1147 \\  & EN 13631-15 & 4130 & - & - & 6338 & 1138 \\ \hline \multirow{2}{*}{Dinamite II} & CT & 3165 & 23.58 & 7729 & 5049 & 987 \\  & EN 13631-15 & 3151 & - & - & 4989 & 984 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of the calculated temperature at constant volume, \(T\), detonation pressure, \(p_{\text{CJ}}\), detonation velocity, \(v_{\text{CJ}}\), heat release at constant volume, \(Q_{\text{CJ}}\), and explosive force, \(F_{e}\), with the results provided by the European Standard EN 13631-15 [43] and by the thermochemical code W-DETCOM [49] for different explosive mixtures using the BKW–S EoS.