Mud Pump-Related Calculations

Mud Pump Capacity

As shown under (Working principles), the theoretical output per stroke is given by:

Theoretical output per stroke for a single-acting triplex  pump :

Theoretical output per stroke for a double-acting duplex pump: All in consistent units

Multiplying the theoretical output per stroke by the recorded strokes per minute and adjusting for the volumetric efficiency (ηv) will give the effective output, Qe.

Thus, the Theoretical output for a single-acting triplex pump Qe =

In Liters/Min

But in BBls/Min, the equation will be:

In the two equations where units are given, L, D, and d are expressed in inches, the unit normally used for this purpose. Similarly, the Theoretical output for a double-acting duplex pump Qe:

In Liters/Min

But in BBls/Min, the equation will be:

Pump Stroke Counters

Mud  pumps are normally equipped with pump stroke counters. There are two types of stroke counters: one to indicate the pump rate (spm) and one to record the cumulative number of strokes. The latter type of counter monitors jobs such as chasing Casing Cementing Jobs, spotting slugs, and during well control.

Such counters are generally needed to follow the volumes pumped when volumetric control is essential. However, it is also necessary to know the pump efficiency to determine the delivered volume. Since this efficiency is pressure-related, it should always be checked when pumping with reasonable pressure.

Volumetric Efficiency (ηv)

As stated in the previous paragraphs, volumetric efficiency is the relationship between a pump’s theoretical and effective output.

Loss of volumetric efficiency is mainly caused by the delay in valve shutdown. When the plunger motion reverses, the valves are not yet completely closed due to the mass inertia of the valves, and some of the liquid has the opportunity to flow back.

Major Causes Of Mud Pump Efficiency Drop

The following losses are recognized:

• Leakage losses of the discharge valve: As long as the discharge valve does not close completely during the suction stroke, a small amount of liquid will flow back from the discharge line into the cylinder.

• Leakage losses of the suction valve: As long as the suction valve does not close completely during the discharge stroke, a small amount of liquid will flow back from the cylinder into the suction line.

Other causes of loss in efficiency are:

• Losses due to a leaking stuffing box: During the suction stroke air is sucked in through the stuffing box. This air reduces the overall suction volume of the pump. During the discharge stroke, the liquid will leak through the stuffing box to reduce the quantity discharged.

• Leakage losses between piston and liner: The seal between the piston and liner may not be perfect. Consequently, some liquid may leak past the piston during the discharge stroke. It is also possible that some air is drawn in past the piston during the suction stroke of a single-acting pump.

• Leakage losses in suction lines: Leaks in the suction line may result in air being pulled into the drilling fluid flow during the suction stroke.

• Air or gas absorbed in liquids: The liquid may contain gas or air either dissolved or transported as small bubbles. One of the most common causes of suction aeration is mixing drilling fluid or adding chemicals through the hopper.

The highest practical efficiency should be maintained by regularly checking and servicing the  pump.