# Dynamic Response of Drill Floor Considering Propagation of Blast Pressure Subsequent to Blowout
## 3 Blowout Explosion Analysis
### FLACS Program  
Explosion simulation was carried out using FLACS program. FLACS is a finite volume solver that solves the Reynolds averaged mass, momentum, and energy balance equations, with special schemes for supersonic flows and a database of chemical kinetics [19]. There are several approaches to analyze explosion such as the Smoothed Partial Hydrodynamic (SPH) Method, Boundary Element Method (BEM) and Finite Volume Method (FVM). These methodologies are reviewed, and a validity check has been carried out [20]. This study utilizes FLACS which adopts FVM, since it is widely used and accepted for explosion analysis in offshore projects and petroleum industries. * Mixture fraction;
* Turbulent kinetic energy;
* Dissipation rate of turbulent kinetic energy. The equation of state is that of an ideal gas, and is presented in Equation (1):  
\[\mathrm{pW}=\ \mathrm{\rho RT} \tag{1}\]  
where \(\mathrm{p}\) is absolute pressure, \(W\) is the molar weight of the gas mixture, \(\mathrm{\rho}\) is density, \(\mathrm{R}\) is the universal gas coefficient and \(\mathrm{T}\) is absolute temperature. Conservation of mass (2):  
\[\frac{\partial}{\partial t}(\beta_{\mathrm{\
u}}\mathrm{\rho})+\ \frac{\partial}{ \partial x_{j}}\Big{(}\beta_{j}\mathrm{\rho}u_{j}\Big{)}=\ \dot{m}/V \tag{2}\]  
where \(\beta_{\mathrm{\
u}}\) is volume porosity, \(\beta_{j}\) is area porosity in \(j\)-direction, \(u_{j}\) is mean velocity component in \(j\)-direction, \(\dot{m}\) is mass rate and \(V\) is volume. The conservation of momentum (3) secures that the relation between pressure and flow velocities is representative. \[\frac{\partial}{\partial t}(\beta_{\mathrm{\
u}}\mathrm{\rho}u_{i})+\frac{ \partial}{\partial x_{j}}\Big{(}\beta_{j}\mathrm{\rho}u_{j}u_{i}\Big{)}=- \beta_{\mathrm{\
u}}\frac{\partial p}{\partial x_{i}}+\ \frac{\partial}{ \partial x_{j}}\Big{(}\beta_{j}\mathrm{\sigma}_{ij}\Big{)}+R_{i}+R_{\mathrm{ \
u}}+\beta_{\mathrm{\
u}}(\mathrm{\rho}-\mathrm{\rho}_{0})g_{i} \tag{3}\]  
where \(R_{i}\) represents flow resistance in \(i\)-direction due to obstruction, \(R_{\mathrm{\
u}}\) is flow resistance due to wall, \(\mathrm{\sigma}_{ij}\) is stress tensor and \(g_{i}\) is gravitational acceleration in \(i\)-direction (4) and (5). \[R_{i}=-f_{i}A_{i}\mathrm{\rho}|u_{i}|u_{i} \tag{4}\]  
\[A_{i}=\frac{1-\beta_{i}}{\Delta x_{i}} \tag{5}\]  
and \(f_{i}\) is a non-dimensional constant depending on type and orientation of the obstruction. Conservation of enthalpy (6):  
\[\frac{\partial}{\partial t}(\beta_{\mathrm{\
u}}\mathrm{\rho}t)+\frac{ \partial}{\partial x_{j}}\Big{(}\beta_{j}\mathrm{\rho}u_{j}\mathrm{\mu}\Big{)} =\frac{\partial}{\partial x_{j}}\Bigg{(}\beta_{j}\frac{\mathrm{\mu}_{eff}}{ \mathrm{\sigma}_{h}}\frac{\partial h}{\partial x_{j}}\Bigg{)}+\ \beta_{\mathrm{\
u}}\frac{Dp}{Dt}+\dot{Q} \tag{6}\]  
where \(h\) is enthalpy, \(\mathrm{\mu}_{eff}\) is effective viscosity, and \(\dot{Q}\) is heat flow rate. Conservation of fuel mass fraction (7):  
\[\frac{\partial}{\partial t}(\beta_{\mathrm{\
u}}\mathrm{\rho}Y_{\mathrm{fuel}})+ \frac{\partial}{\partial x_{j}}\Big{(}\beta_{j}\mathrm{\rho}u_{j}Y_{\mathrm{ fuel}}\Big{)}=\frac{\partial}{\partial x_{j}}\Bigg{(}\beta_{j}\frac{ \mathrm{\mu}_{eff}}{\mathrm{\sigma}_{fuel}}\frac{\partial Y_{\mathrm{fuel}}}{ \partial x_{j}}\Bigg{)}+R_{\mathrm{fuel}} \tag{7}\]  
where \(Y_{\mathrm{fuel}}\) is mass fraction and \(R_{\mathrm{fuel}}\) is reaction rate for fuel. Conservation of mixture fraction (8):  
\[\frac{\partial}{\partial t}(\beta_{\mathrm{\
u}}\mathrm{\rho}f)+\frac{ \partial}{\partial x_{j}}\Big{(}\beta_{j}\mathrm{\rho}u_{j}f\Big{)}=\frac{ \partial}{\partial x_{j}}\Bigg{(}\beta_{\mathrm{j}}\frac{\mathrm{\mu}_{eff}}{ \mathrm{\sigma}_{f}}\frac{\partial f}{\partial x_{j}}\Bigg{)} \tag{8}\]  
where \(f\) is mixture fraction.