The present invention refers to the separation of cellulose pulp into distinct fractions with different draining and morphological characteristics, as well as the use of part of these fractions for the production of nanocellulose. The process in reference combines the unitary operations of fiber separation, thickening to a certain consistency, draining and drying of the cellulosic pulp with the high drainage ability and production of nanocellulose from high primary fines content pulp. The process may consider any cellulosic pulp fiber derived from short or long fiber woods such as Eucalyptus, Corymbia, Birch, Aspen, Pinus, recycled fibers, etc., their residues such as bark, sawdust, etc.