A solids supply systems having a solids deaeration zone and a solids pump zone, and to methods for supplying the solids e.g., pulverized dry coal, to an application, e.g., gasification process. The solids deaeration zone includes a roller system containing a plurality of porous roller assemblies, or a belt system containing a plurality of porous belt assemblies. The solids deaeration zone is operable to deaerate and convey the solids to the solids pump zone. In the solids deaeration zone, the solids become sufficiently compacted prior to and upon entry into the solids pump zone to be effectively conveyed through the solids pump zone.