Estimation of Parameters for Non-Equilibrium Phase Transitions during the Flow of Oil and Gas Mixtures

Problems of unsteady gas-liquid flows in wellbores with phase transitions are common for hydrocarbon production and well drilling. Typically, flow in wellbores is sufficiently fast which requires taking into account the non-equilibrium nature of phase transitions. The set of equations describing conservation of mass for components and momentum conservation for the mixture is supplemented by the relaxation equation for concentration of gas dissolved in the liquid. It is known that the characteristic times of gas evolution from the liquid and gas dissolution in the liquid differ significantly and depend on fluid properties, thermobaric conditions, and the flow pattern. Therefore, obtaining estimates of relaxation times for real flows turns to be a difficult problem. In this study, we propose a method for estimating the characteristic relaxation times for gas evolution and dissolution during the gas-liquid flow in a well. The method combines the solution of the convective diffusion equation for the growth/collapse of a vapor bubble in a liquid with the current parameters of the gas-liquid flow. Estimates of the relaxation times for the bubbly flow (small bubbles, gas evolution predominates) and slug flow (large bubbles, dissolution predominates), as functions of time from the beginning of the process, are obtained for the parameters of a real flow in a wellbore. It is shown that the obtained dependencies are consistent with the typical scaling of the diffusion process with respect to the size of bubbles. The results are important for mathematical simulation of gas-liquid flows in wellbores during hydrocarbon production, as well as for calculation of the gas-kick process during well drilling with oil-based muds.