Permeating air is known to have a negative impact on the roller compaction process, because the feed is destabilized by the flow of escaping gas, causing pressure to build-up and potentially damage compacts at release. Airflow during powder roller compaction and its effect on the rolling process are investigated in the rolling direction (1D), using an extension of the Johanson model for the solid. Fluid transport obeys Darcy's law, with permeability being a function of both material density and particle size, through the Kozeny-Carman relationship. In this modeling, the effect of the air pressure on the solid is neglected in the compaction zone. Assuming air at atmospheric pressure at the feeding angle and ignoring airflow through the gap, predictions of air pressure as a function of the rolling angle for bentonite material powder are presented and discussed. Results suggest the existence of two different stability zones within the operating conditions, where industrial systems could function without being affected by airflow effects. The model highlights the importance of the permeability/rotation speed ratio, which governs the proportion of air trapped in the compacts to the portion evacuated through the feed. We also investigate the effect of particle fragmentation during the rolling process. Finally, we provide guidelines for the scale-up of roller presses subjected to air flow issues, through a study of the effect of the system dimensions and rotation speed on the elimination of air. In spite of the lack of available experimental data, this model allows for a better understanding of how air escapes by diffusing through the material during the rolling process, and opens interesting perspectives for the mitigation of its effect on the process. (C) 2013 Elsevier Ltd. All rights reserved.