Stokes’ Law and Drilling Fluids

Drilling fluids normally contain two categories of solids: (1) commercial clays and drilled solids, both low gravity, with specific gravities (SGs) of about 2.6, and (2) weighting agents, usually barite, with an assumed SG of 4.2. If all of the solids particles were of the same size, decanter centrifuges could be used to separate the weighting agent from the low-gravity solids, because the barite particles, due to their higher SG, would be heavier. Drilling fluids, of course, are not slurries of particles of equal size. Weighted drilling fluids always contain solids of both categories, ranging from colloidal particles too fine to settle, even in pure water, to particles 70 microns () in size and larger. Consequently, the centrifuge cannot separate barite from low-gravity solids. What it does, when operated properly, is separate larger barite particles from smaller ones and larger low-gravity-solids particles from smaller ones. Failure to recognize this very important fact frequently leads to the misuse of centrifuges.

Stokes’ law shows that the terminal velocities of barite and low gravity- solids particles are equal when they have equal mass. This equality exists when the low-gravity particle is approximately 50% larger than the barite particle. This leads to the conclusion that if a centrifuge is achieving a D50 cut point of, for example, 4 on barite, it will be making a D50 6 cut on low-gravity solids. In other words, most of the barite particles larger than 4 and the low-gravity-solids particles larger than 6 are routed to the underflow, while the smaller particles remain with the centrate.

Separation Curves and Cut Points

Solids-separation performance is often described using cut points. The cut point is the size at which a stipulated percentage of the feed solids are separated. If a percentage is not stated, it is usually assumed to be 50%. For example, if a shale shaker is removing 50% of the 100µ particles and 50% remain in the mud, the D50 cut point is said to be 100µ. If it is removing 90% of the 120µ particles, its D90 cut point is 120µ.

Picture 1 and 2 indicate the importance of this concept and also the significance of the ‘‘sharpness’’ of cuts. When interpreting these graphs, note that the solids particles of the size range represented by the area to the right of the curve are separated, while those in the area to the left remain in the fluid. Note also that in the shaker screen example (Picture 1), there is little difference between the cut points at 10% and at 90%. The closer the cut point curve is to vertical, the ‘‘sharper’’ the cut is considered to be. With an ideal screen and perfect screening (neither of which exist in the real world), the cut point curve would be a vertical line and all solids smaller than the designed opening size would remain in the fluid, while all of those larger than that size would be separated. Typically, cut point curves for hydrocyclones are far from vertical, which is to say that if the D50 cut point is, for example, 25, significant quantities of material larger than 25 will remain in the system, while significant quantities of finer material will be separated. This is also true of centrifuges operated under less than ideal conditions, as they usually are.

Picture 1. Shale shaker separation curve   
Picture 2. Desander separation curve.

Ideal conditions include maximum pool depth, maximum retention time, maximum difference between particle and liquid densities, minimum solids content, and minimum viscosity. Under these ideal conditions, many centrifuges are capable of achieving a D50 cut point of 2µ on barite. Under the conditions typically encountered in drilling applications, actual cut points can be expected to be significantly higher.

Drilling-Fluids Solids

Commercial solids are used in drilling fluids to provide desired density, viscosity, and filtration control. Additional drilled and sloughed solids become part of the fluid during the drilling process. These formation solids, as well as colloidal barite particles, when present in excessive concentrations, are detrimental to drilling-fluid performance and are considered to be contaminants. The coarser solids, though they can be troublesome, are ordinarily the least injurious to drilling-fluid performance and are the most easily separated.

Barite and bentonite are the most widely used commercial solids in drilling fluids. Current American Petroleum Institute (API) specifications (API 13A, 1996) permit as much as 30% of barite to be finer than 6µ in size, and much of this 30% can be assumed to be colloidal when purchased. Pure barium sulfate is a very soft mineral, but the hardness of commercial barite depends on the impurities associated with it. Much of it is rather soft, and particle size can diminish rapidly with use. After several hours, days, or weeks in the mud system, more of the finer material can be expected to become colloidal. Bentonite is ground much finer than barite and can be assumed to be colloidal when purchased.

Drilled solids are unavoidably incorporated into the drilling fluid while drilling. In softer sediments drilled with water-based muds, significant proportions of the drilled material are dispersed and can first reach the surface as colloidal particles, too fine to be separated from the base fluid. Coarser particles, if recirculated, can be expected to break up before returning to the surface. Drilled and sloughed solids that are not removed during their first passage through the surface mud system are unlikely to be separated later.

The solids particles that cause solids problems in oil well drilling are those that create viscosity problems and contribute to poor hole conditions. These are the finest solids, the colloids and ultra-fine solids that, because of their small size and great number at any given solids concentration, have a disproportionate amount of surface area per unit of volume. These solids, which are generally considered to be the most detrimental to drilling-fluid performance, are too fine to be separated by screens or hydrocyclones. Their concentration can be reduced only by dilution or centrifuging.

Note that solids surface area and the concentration of solids particles per unit of liquid volume, rather than the solids volume itself, are the usual sources of solids problems. Consequently, while retort solids can provide clues to the possible causes of drilling-fluid problems, solids problems can arise due to decreasing particle size even though the concentration of solids in the fluid remains unchanged. As particle size decreases, the resultant increase in solids area and number of particles increases plastic viscosity and can create or exacerbate hole problems, even though the solids concentration has not increased. Pictures 3 and 4 illustrate the increase of surface area and number of particles corresponding to a reduction in average particle size of a given volume of solids.

Picture 3. One barrel of drilled solids: Surface area versus particle size.
Piuture 4. One barrel of drilled solids: Number of particles versus particle size.