Design of Muds for Carrying Capacity
Authors: Walker R.E. , Mayes T.M. 
Published: December 2007

The ability to predict the degree of hole cleaning possible with a given mud and flow rate is an advantage in successfully planning and completing a drilling operation. A simple, reasonably accurate, mathematical-prediction technique is developed that can be used in the field.

Introduction
Hole cleaning is an important function of a drilling liquid. The ability to predict the degree of cleaning possible for a given mud and flow rate is a definite advantage in planning and completing a successful drilling operation. The prediction is nominally made by calculating the transport prediction is nominally made by calculating the transport velocity, the difference in the annular velocity and the slip velocity of the particles, by assuming the slip velocity is equal to the terminal settling velocity of the particle in a stationary liquid. The settling velocity is easily calculated if the annular flow is turbulent or the particle settles in the turbulent regime. Under these conditions, the slip velocity depends on the density difference between the mud and the particle and on the particle shape and size. The slip velocity is not a function of the liquid viscosity. However, these settling velocities may be high, up to 74 ft/min for a shale sphere 1/8 in. in diameter, and high annular velocities are needed to clean the hole.
There are many cases where high annular velocities are unavailable and/or undesirable. Annular velocities may be low because of pump limitations or an enlarged hole, or may be low where risers are used. Also, it may be necessary to restrict annular velocity to minimize the equivalent circulating density or to maintain laminar flow opposite drill collars. If turbulent-regime slip velocities are too high for the annular velocities, the viscous properties of the liquid must be increased until the particle properties of the liquid must be increased until the particle falls in a transition or laminar regime where slip velocities are influenced by viscous forces. Unfortunately, none of the methods proposed in the literature for predicting terminal settling velocities in the transition or laminar regimes are suitable for field application. Most of the theoretical and experimental work is with spheres or with liquids that are almost Newtonian. In work using non-Newtonian liquids, the rheological measurements are not sufficient for defining properties in the experimental range, or the prediction properties in the experimental range, or the prediction equations use rheological models with constants defined in a shear-rate range different than that of the experimental work. One study's uses viscosities not associated with that of the liquid surrounding the particle, while another study provides a solution so complex that it is impractical for field use.
An assumption that the terminal settling velocity will be the same as the slip velocity is questionable because of the complex motion of the particle in the annulus. The moving liquid has a velocity profile, near parabolic in form, that is affected by hole geometry, liquid flow properties, and pipe rotation. The particles tilt with the properties, and pipe rotation. The particles tilt with the velocity profile, which in turn affects their settling velocity. Drillpipe rotation introduces a centrifugal force causing radial migration, and some particles are also trapped near the pipe. If the mud is non-Newtonian, the viscosity of the liquid around the particle is dependent on the settling velocity and the flowing-velocity profile. An additional complication is the various shapes a cutting or caving may have.
Improvement in methods for predicting successful hole cleaning is dependent on a better understanding of how viscous forces retard particle settling.
JPT
P. 893