This invention relates to water-based well drilling fluids. It has been found that cellulose based particles, which comprise cell wall material and their networks of cellulose based fibers and nanofibrils can be used to produce suspensions having viscosity and rheological properties particularly suitable for use as a drilling fluid. It is assumed that the organization of the cellulose fibrils, as it exists in the parenchymal cell walls, is at least partly retained in the cellulose based particles of the invention, even though part of the pectin and hemicellulose is removed there from. Breaking plant-based pulp down into this kind of cellulose based particles involves fewer and gentler processes than to break the pulp down further into cellulose nanofibrils, and therefore the present cellulose based particles can be produced much faster and at lower cost than completely unraveled cellulose nanofibrils. The well drilling fluids based on the cellulose material of this invention are stable over a wide range of operating temperatures.