Migration of Particles to a Hole Wall in a Drilling Well

The rate at which a particle will migrate from the rotating drill pipe to the hole wall was calculated as functions of the mud properties, pipe rotational speed, and hole size. The information can be used to estimate the relative carrying capacity of one mud compared to another Then the changes that need to be made when a hole. is not cleaning can be determined. An adaptive control process for field use is suggested Two major simplifying assumptions are that axial flow does not influence the liquid viscosity and that the viscous resistance to particle movement in the radial direction is proportional to the particle's velocity. The calculations assume a power model liquid, spherical cuttings, and concentric pipe in a round hole. A concept of "theoretical zones" where the calculations are valid interspersed with areas where the particles are uniformly redistributed, is used to relate the simplified theory to actual hole conditions. Introduction This theoretical study was conducted to improve the understanding of hole cleaning and how various drilling conditions and muds influence the ability to lift cuttings to the surface. The primary object of the study was to see how fast a particle might move from the drill pipe to the hole wall and how factors of drilling and liquid properties influence the rate of radial movement. The rate of movement may be important as the centrifugal force set up by the rotating drill pipe tends to force the particle toward the hole wall, an area of low vertical mud velocity and, therefore, poor lifting. PRIOR WORK Removal of cutting from a drilling well by circulating a structured liquid such as bentonite-water is a physically complex operation. Explicit prediction of the path of a cutting requires the ability to calculate the velocity of the particle relative to the liquid and the velocity field of the liquid. Various phases have been investigated. Williams and Bruce showed experimentally the path of particles in a laboratory wellbore and developed slip correlations for turbulent flow. Many investigations have been made for drag coefficients of particles settling in stationary Newtonian liquids under conditions of laminar and turbulent flow. The only work with inclined discs is with very low Reynolds numbers, an area of little interest in hole cleaning. Some investigations with drag coefficients in non-Newtonian liquids and the only work with structured liquids indicates the drag coefficient is different in stationary liquid from the drag coefficient in moving liquid. Various methods of predicting slip velocities are available, as well as correlations of hole cleaning based on experimental well tests. Bentonite drilling muds are generally a shear thinning liquid in which stress-rate relation at a fixed time depends on past history. Most rheological work is done under steady-state conditions to show the influence of chemical additives and temperature changes. There has been little work on dynamic response such as has been done with viscoelastic liquids to select time dependent constitutive equations or experiments with shear in two directions. Most pressure drop calculations for field use are based on annular flow without rotating drill pipe, and radial migration of particles and angular liquid velocities are neglected. Savins and Wallick calculated annular pressure drops, including rotating drill pipe, for a liquid described by a three constant Oldroyd model. The calculations were based on a viscosity relation for one-dimensional flow but used the vector sum of the longitudinal and angular components of stress to calculate the viscosity. This procedure was shown correct for a viscoelastic liquid. SPEJ P. 147ˆ