Introduction

The calculation of flow rate from pump strokes is based on pump specifications. It is effectively a computation of the maximum internal volume of the pump, without any corrections for fluid compressibility. This calculation requires the pump type as well as the specifications of the pump because the pump type determines the geometry of the fluid volume. There are two commonly used pump types: duplex and triplex. Duplex pumps have two reciprocating pistons and have generally been replaced by Triplex (three pistons) for oil field usage in all but developing countries. Recently two new styles of pumps have been developed: Hex pumps (six vertical pistons driving a rotating plate) and Quintuplex pumps (five horizontal pistons). The advantage of the new style pumps over the triplex pump is multiple, smaller pressure surges which result in lower mud noise for MWD/LWD measurements as well as better pressure management for the borehole annulus. At this time we will present the calculations for duplex/triplex pumps, as these are well defined. Calculations for the Hex/Qintuplex pumps will depend upon the geometry and configuration of the specific pump. From experience, Hex pumps report an equivalent bore and stroke to use the Triplex computation, although the computation should be based on the pump geometry.

Calculation Approaches

The first step in the calculation is to compute the volume of fluid contained in the cyclinder(s) of the pump. A Duplex pump requires one additional piece of information, the rod diameter of the reciprocating piston. Other pumps styles may require different specification data/metadata.

Presented here are the computations for Duplex and Triplex pumps. The fluid volume of an individual pump stroke is multiplied by the number of strokes to determine flow rate at 100% pump efficiency. To determine real flow rates the efficiency of the pump must be determined. Traditionally, the efficiency of the pump is expressed as a fixed number – this pump is 95% efficient. With an independent measurement of flow in (i.e. via a Coriolis meter, a weir, wedge meter, or some device that is more accurate than a paddle meter), efficiency can be computed by calibrating the stroke counter with the flow-in measurement. This can then be used over time to monitor pump performance/maintenance.

For these calculations, US based oil-field (API?) units have been used and factored into the constants. These include gallons per minute for flow rate and inches for the specifications of the pump parts.

Finally, many rigs have multiple pumps. Total flow-in will be the sum of the flow from each pump that contributes fluids to the wellbore. Pumps which are used for other purposes, such as a riser, should not be included to the flow-in totals. This requires an additional piece of metadata, a flag which states where the pumps output is going. With an automated system, this flag can be determined by the state of a valve on the output of the pump.

Duplex Pump

The fluid volume of a duplex pump is determined by the liner diameter and stroke length of the piston. The physical volume of the rod is subtracted from the overall volume of the cylinder.

• FlowIn = 0.00680386 x (2 x Liner Diameter^2 - RodDiameter^2 ) x StrokeLength x PumpStrokes x PumpEfficency

* FlowIn is in gallons/minute
* LinerDiameter is in inches
* RodDiameter is in inches
* StrokeLength is in inches
* PumpStrokes is in strokes/minute
* Efficiency is a percentage

Triplex Pump

The fluid volume of a trilex pump is determined by the liner diameter and stroke length of the piston.

• FlowIn = 0.010206 x LinerDiameter^2 x StrokeLength x PumpStokes x PumpEfficiency

* FlowIn is in gallons/minute
* LinerDiameter is in inches
* StrokeLength is in inches
* PumpStrokes is in strokes/minute
* Efficiency is a percentage

Total Flow In

The total flow in is the sum of the outputs of the active (connected to the wellbore) pumps.

Flow(i) = Pump flow calculation for pump(i)

If the individual pump is active (connected to the wellbore) then add that pumps contribution to flowIn

• FlowIn = 0
• Foreach( pump(i) in allPumps)
• {
  • If (pump(i) isActive)
  • { * FlowIn = FlowIn + Flow(i)
  • }
• }

Note: pump efficiencies need to be determined for each individual pump or through linear algebra

Metadata Required

• Pump Type - pump type determines the geometry framework for the pump
• Activity flag – Is the pump output going into the wellbore
• Efficiency flag – Is the pump efficiency calculated/calibrated or an assumed number

Digitization

Data collection at the wellsite from each pump is generally provided via WITS0. The data stream is a series of (value, time) data points which are nearly evenly sampled in time. They can contain data gaps, null values, and noise. As such, they are not suitable for direct usage. The individual, discreet data points for pump flow (stroke counter) should therefore be converted to a continuous function, then evenly sampled at a user specified time interval for usage in calculations.

References

Formulas and Calculations for Drilling, Production and Workover 2nd Edition, Norton Lapeyrouse, Gulf Professional Publishing, 2002

Website: Drilling Formulas.com
http://www.drillingformulas.com/pump-output-calculation-for-duplex-pump-and-triplex-pump/