Mathematical modeling of foamy-oil flow in a cyclic solvent injection process

Foamy-oil flow is one of the main mechanisms for cold heavy oil production with sand (CHOPS) and cyclic solvent injection (CSI) processes. The flow pattern of foamy oil was observed in previous experimental studies under reasonable reservoir conditions. This study aims to investigate the foamy-oil flow mechanisms through theoretical modeling. A mathematical model is developed, which couples a solvent concentration field and a pressure field through flow velocity and oil viscosity, in which a pseudo-chemical reaction is used to describe the release of gas. The model is numerically solved by the Newton-Raphson iterative method. Results show that, firstly, during the pressure drawdown process, propane concentration decreases and oil viscosity increases with solvent exsolution in the transition zone, which restricts the bubbles coalescence and conduces to the formation of foamy oil. Secondly, the existence of bubbles leads to the buildup of local pressure gradient and causes the spatial difference of flow velocity. Moreover, when the threshold velocity is reached, the bubbles coalesce rapidly to form free gas, pushing the oil in the foamy region forward to the gas zone. Finally, the total waves of foamy-oil flow are generally 2 to 4, depending on the initial solvent concentration, oil viscosity, and pressure depletion rate. Higher initial solvent concentration, faster pressure depletion, and lighter original heavy oil lead to the easier induction of foamy-oil flow.