Drilling in small diameters is not new : the mineral industry currently drills slim holes in hard rocks. In this context, the drill string rotates at high speed very close to the hole wall, which is in general of good stability.To transfer that drilling method to the oilfield and keeping high rotation speed and small annulus, many problems occur due to the sedimentary type of formations drilled, and hydraulics become crucial for following points of view : the lifting up of cuttings in the annulus (no ball i i up), the well bore stability, the cleaning of the bit, the differential mud pressure in the annulus, the hydrodynamic lubrication between rods and the well bore.Therefore, it is essential in slimhole to investigate drilling hydraulics, using basic theoretical equations derived from fluid mechanics.The developed model takes into account mud rheology, drill string rotation -and eccentric position of drill string. Outputs are annulus thickness, drilling parameters (including mud flow), and mud characteristics, all to be respected to reduce slimhole drilling problems. The final output is the compromise which integrates all these requirements for a successful operation. SPE 24596R. DELWICHE, M. LEJEUNE, P. MAWET, R. VIGHETTO Nomenclature AP annular pressure (bars), DP pressure losses (bars), ECD equivalent circulatin density (kg/m3>,

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