Flash calculations are used for the dynamic simulation of vapor-liquid phase equilibria (VLE) in many chemical processes. When used to predict the composition of mixtures in VLE, the repeated applicatino of these flash calculations, particularly in dynamic cases can cause small inaccuracies to cascade. One way to prevent this, is to have strong predictions and initial guesses for what a mixture in equilibrium will look like. For this, stability tests can be employed. Stability tests require the minimisation of the tangent plane distance, which is derived from the excess Gibbs Energy. The VLE problem and stability tests have been approached from a viewpoint based in mathematical optimisation, not one based in thermodynamics. As such, this work provides a slightly different description of flash calculations and stability tests, and can serve as both an introduction to the problems, as well as an approach to the problem in a different way than is traditionally done. In this report, the tangent plane distance function has been studied and applied to an example to gain intuition on the problem, and different optimisation methods were considered for minimising this function. A stochastic- and a deterministic method were applied to the stability problem to gain a better understanding of which type of method will work better for minimising the tangent plane distance. Both methods seem sufficient, but the scalability to higher dimensions is lacking, especially in the deterministic case.