We present a semi-numerical modeling approach to analyzing the role of surface renewal during bubble-free devolatilization in vented single-screw extruders. To demonstrate the significance of surface renewal in the mass transport of volatiles, we derived approximate analytical solutions for the two-dimensional circulatory flow in a partially filled screw channel, placing special emphasis on the melt pool that forms in front of the active flight. By applying the resulting velocity field to the governing conservation equation for the volatile concentration in the polymeric phase, the convective influence of the polymer flow on mass transport is taken into account. The resulting convection-diffusion equation, which is solved numerically using the finite-volume method, provides both qualitative and quantitative insights into how volatile depletion in the melt pool is related to the flow field developed. Thus, we clearly demonstrate that surface renewal improves mass transport efficiency considerably, even at very low screw speeds.