Flash Calculation

The isothermal flash calculation is one of the most important and most common calculations in any PVT calculation. The term flash is nothing more than taking some mixture (\(z_i\)) and equilibrating it at a specified pressure (\(p\)) and temperature (\(T\)). The resulting single or multi-phase mixtures (vapor \(y_i\) and liquid \(x_i\)), K-values (\(K_i=y_i/x_i\)) and the resulting volume(s) (or Z-factors) are the main outputs of the flash calculation.

The flash calculation is divided into three main parts: (1) the material balance, (2) calculating the component fugacities and (3) updating the K-values to try and reach thermodynamic equilibrium. The first part requires that the molar balance of each component is concerved. This is solved using the Rachford-Rice or Muskat-MacDowell equation. Part (2) requires the fugacities for each component in each phase to be calculated. This calculation is EOS dependent. The goal is to find a set of K-values that result in the equal fugacity constraint: \(f_{Vi}=f_{Li}\). The last part of the flash calculation considers how to update the estimate of K-values based on the current set of K-values and the fugacities.

The material balance equation, for which the Rachford-Rice and Muskat-MacDowell equations are based, can be written as \(z_i=y_i \cdot F_V + x_i \cdot (1-F_V)\), where \(z_i\) is the total composition, \(y_i\) is the vapor composition, \(x_i\) is the liquid composition, and \(F_V\) is the vapor molar fraction (\(F_V = \frac{n_G}{n_G+n_L}\)). The solution space for the flash calculation is divided into three regions: positive flash where \(F_V\) is between 0 and 1, negative flash where \(F_V\) is between 0 and \(-\infty\) or 1 and \(\infty\), and the third region is the trivial region where all K-values are equal to 1 and the value of \(F_V\) is arbitrary.