Hydrostatic level measurement systems (HLMSs), applied to pressure vessels, loose their reliability during transient processes, if the depressurization of water that absorbed a certain amount of gases at high pressure initiates bubble formation and movement through the liquid in these systems. To simulate and predict the effect of migrating bubbles on the reliability of HLMS, a model was proposed taking bubble formation, motion and mass diffusion of dissolved multi-component gases through the supersaturated liquid into consideration. The one-dimensional flow model, which described the two-phase flow in tubes (5-10 mm) by use of Eulerian and Lagrangian coordinate systems, was applied to bubbly and slug flow through arbitrary inclined tubes without junctions. A transition criterion between the two flow regimes was defined. A homogenous nucleation model with pressure, temperature and fluid properties as parameters was developed for gas-in-liquid solions. The mass transfer rate by gas diffusion from the supersaturated liquid into the formed bubbles was calculated by numerical solution of an introduced differential equation. The quality of the proposed model was examined by the simulation of an experimental series where a binary gas-liquid solution was depressurized under variation of saturation pressure, release velocity and tubing geometry. The behavior of the water level, bubble size and velocity was observed by use of needle probes and a conductive sensor. The simulated data found confirmation by the experimentally obtained results.