The present invention provides a process for fractionating lignocellulosic biomass, comprising: digesting a biomass feedstock in the presence of a solvent for lignin, an acid, and water, to produce cellulose-rich solids; separating and washing the cellulose-rich solids with a wash solvent; washing the cellulose-rich solids with water, to generate washed cellulose-rich solids and a wash liquor comprising fines, wherein the wash liquor is introduced to or in contact with a classifier to remove the fines; and separating the fines and recycling the remaining water. The classifier may include a screen with mesh size in the range of 10 to 500, such as 200. The washed cellulose- rich solids will typically have a lower Kappa number (lignin content) and ash content compared to cellulose-rich solids from a process without a classifier that removes fines.