Barite Sag is the settling of barite particles (or other weighting materials), which results in the undesirable fluctuations in drilling fluid density. A variety of major drilling problems including lost circulation, well control difficulties, poor cement jobs and stuck pipe can result from uncontrolled barite sag. Study of this phenomenon and how to mitigate its effects has long been of interest. This paper describes a fundamental mathematical approach to analyze the settling of barite particles in shear flow of Newtonian fluids. A set of four coupled partial differential equations to describe dynamic barite sag in Newtonian fluids in pipe flow is obtained by applying mass and momentum conservation for solid and liquid phase. Solid concentration in axial and radial directions as a function of time is calculated by using an explicit numerical method to solve these equations. A number of experiments in a flow loop were conducted to verify the mathematical model. A method proposed by Bern et. al.4,8 to measure the fluid density during circulation was modified to measure the change of circulating density in the test section. Two mass flow meters were installed at the inlet and outlet of the flow loop's test section. Differences in the density measurements over time were converted to the solid accumulation, which was compared with results from the modeling. In addition, based on the experimental results, three different stages of barite accumulation due to the settling and bed pickup of barite particles during circulation will be presented. The proposed methodology and results of this study will help drillers have a better understanding in terms of undesirable density fluctuations and barite bed characteristics. Introduction During drilling operations, control of sub surface pressure is of utmost importance. High density minerals such as barite and hematite are used to increase the density of drilling fluids in order to control these pressures. However, contributing factors such as gravitational force will cause the weighting material particles to settle out of the suspension. This is designated as "sag" within the drilling industry. Under normal operating conditions, the drilling fluid is pumped through the drillpipe and returns to the surface in the annular region formed by the drillpipe and the hole. The settling of barite particles occurs in shear flow and may appear in both pipe and annulus. In this case, it is necessary to recognize that one is dealing with a two-phase mixture: solid (barite particles) and liquid (base fluid). Each phase has its own density, velocity and volume fraction. Nunziato1 introduced an approach to model the mixture as a continuum, and accounted for the interaction between phases through the exchange of momentum and energy. One advantage of the continuum approach is that it provides the theoretical structure by which models can be extended to high concentrations. The author considered the behavior of a Newtonian two-phase mixture of small solid particles in a viscous fluid flow in pipe. He also assumed that the mixture is sufficiently dilute and the particles sufficiently small that Brownian motion may be important, but that the collisions between particles are negligible. The result in this case is a solid concentration profile corresponding to a radial direction.

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Barite Sag is the settling of barite particles in the wellbore (or other weighting materials), which results in undesirable fluctuations in drilling fluid density. A variety of major drilling problems including lost circulation, well control difficulties, poor cement jobs, and stuck pipe can result from uncontrolled barite .^ag. Study of this phenomenon and how to mitigate its effects has long been of interest. This paper describes a fundamental mathematical approach to analyze the settling of barite particles in shear flow of Newtonian fluids. A set of four coupled partial differential equations to de.<:cribe dynamic barite sag in Newtonian fluids in pipe flow is obtained by applying mass and momentum conservation for solid and liquid phase. Solid concentration in axial and radial directions as a function of time is calculated by using an explicit numerical method to solve these equations. A number of experiments in a flow loop were conducted to verify the mathematical model. Two mass flow meters were installed at the inlet and outlet of the flow loop's test section. Differences in the density measurements over time were converted to the solid accumulation, which was compared with results from the modeling. In addition, based on the experimental results, three different stages of barite accumulation due to the settling and bed pickup of barite particles during circulation will be presented. The propo.sed methodology and results of this study will help drillers have a better understanding in terms of undesirable density fluctuations and barite bed characteristics.

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