The minimum volume required to dilute solids remaining after processing by the solids-control equipment depends on the drilled solids concentration in the drilling fluid. If all of the drilled solids are removed from the system, the clean drilling fluid added to return the pit levels back to the original level will dilute the solids already in the drilling fluid. As noted earlier, more clean drilling fluid will be needed to return the pits to the original level with 100% removal than 90% removal of drilled solids.

The smallest volume required will occur when the system is balanced, as previously defined. The same solids-removal efficiency that provides the minimum quantity of new drilling fluid to be built will also be the removal efficiency that generates the minimum discard volume. This would be a condition in which the volume of clean drilling fluid required to dilute the solids remaining after processing through the removal equipment is exactly the volume discarded by the equipment.

## Equation Derivation

volume of discard=(solids removal efficiency)(solids to surface)/(drilled solids concentration in discard)

♥Volume of clean drilling fluid:

*volume of new drilling fluid built=volume of clean drilling fluid+volume of retained drilled solids.*

♥The volume of new drilling fluid built and the volume of retained drilled solids may be expressed in terms of the discard concentration and the targeted drilled-solids concentration in the drilling fluid.

♥ The volume of new drilling fluid built requires that the drilled-solids concentration in the new fluid be the targeted concentration, or

*drilled solids volume=(targeted drilled-solids concentration)×(new drilling fluid built).*

♥The second term on the right side of the equation relates to the volume of retained drilled solids, which is determined by the solids-removal efficiency:

*volume of retained drilled solids=(1−solids removal efficiency)×(drilled solids to the surface).*

♥These expressions may now be substituted into the expression for the volume of clean drilling fluid that needs to be added to the drilling fluid system, which is:

♥Solving this equation for the volume of clean drilling fluid that must be added to dilute drilled solids remaining in the system:

## Discarded Solids

Solids discarded by the solids-removal equipment contain some of the original resident drilled solids and the new drilled solids that have just entered the system. For example, in the case of 70% removal efficiency, 70% of the newly drilled solids are discarded in a slurry of drilling fluid. The target drilled-solids concentration in the preceding examples was 4%vol. For the case of 70% removal efficiency (Figure 15.4), 70 bbl of drilled solids will be discarded in a 200-bbl slurry that contains 130 bbl of drilling fluid. The 130 bbl of drilling fluid will contain 5.2 bbl of resident

solids. The total quantity of drilled solids will be 75.2 bbl. The SREE relates only to removed solids that decrease the solids concentration in the system. If a volume of 130 bbl of drilling fluid is dumped from the system, the remaining drilling fluid still has 4%vol drilled solids, whereas the removal of 70 bbl by the equipment reduces the total solids concentration in the system.

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