The level-set method is used to study the evolution of a bubble carried by a primary phase in (1) a straight channel, (2) a double-bend channel, and (3) a constricted channel. Special attention is given to the conservation of mass for the phases. A global mass correction scheme is proposed to ensure mass conservation. Surface tension effect is modeled using the continuum surface force approach. A finite-volume method is used to solve the governing equations. The CLAM schemes are used to model the convection of the level-set equations. The results compare well with the solutions of the volume-of-fluid (VOF) method.