# Hydraulic Horsepower – How To Calculate It?

This time we will discuss about hydraulic horsepower.Units of power which are often used in drilling engineering are horsepower and the hydraulic power generated by the mud pumps is therefore generally referred to as the hydraulic horsepower (HHP) of the pumps. Mud pumps are generally  rated in terms of the hydraulic horsepower that they are able to generate, and 1600 horsepower pumps are very common on modern drilling rigs. Higher pressures and flow rates require more power, and increase operating costs.

## The hydraulic horsepower (HHP) delivered by a pump is given by:

HHPt = Pt x Q /1714
Equation 1 Total Hydraulic Horsepower
where,
Pt = Total pressure (psi)
Q = flow rate (gpm)
The total discharge pressure is sometimes limited for operational reasons and seldom exceeds 3500 psi. The flow rate is determined by the cylinder size and the pump speed. Information on discharge pressures, pump speeds, etc. is given in
manufacturers’ pump tables. This expression for hydraulic horsepower is a general expression and can also be used to express the power which is expended in sacrificial losses and the power that is used to pump the fluid through the nozzles of the bit.
HHPs = Ps x Q / 1714
HHPb = Pb x Q /1714
where,
HHPs : Sacrificial Hydraulic Horsepower (hp)
HHPb : Bit Hydraulic Horsepower (hp)
Ps : Sacrificial Pressure Losses (psi)
Pb : Bit Pressure Losses (psi)
Q : Flowrate (gpm)

As stated above, it is desirable to optimise the pressure losses through the nozzles (and therefore the cleaning of the bit face) and minimise the sacrificial losses in the drillstring and annulus. There is, for all combinations of drillstring, nozzle size and
hole size, an optimum flow rate for which the hydraulic power at the bit is maximised (Figure 2).

Horsepower Used in Drillstring and Across Nozzles of Bit

The analysis and optimization of these pressure losses is generally referred to as, optimising the hydraulic power of the system. The design of an efficient hydraulics programme is an important element of well planning.
Optimization of the hydraulics of the system is a very important aspect of drilling operations. However, as stated above, the primary function of the drilling fluid is to carry the drilled cuttings to the surface. In order to do this the velocity of the fluid
in the annulus will have to be high enough to ensure that the drilled cuttings are efficiently removed. If these cuttings are not removed the drillstring will become stuck and theoretical optimization will be fruitless. Considerations with respect to optimization should therefore only be addressed once the minimum annular velocity for which the cuttings will be removed is achieved. Only then, should any further increase in fluid flowrate be used to improve the pressure loss across the nozzles
of the bit and therefore the hydraulic power at the bit face. If the drilled cuttings are not removed from the bit face, the bit wastes valuable effort in regrinding them instead of making new hole. This results in a significant reduction in penetration
rate (Figure below).

Impact of Horsepower at the Bit on Rate of Penetration for Given Weight
on Bit

Once the cuttings are removed from the face of the bit they must then be transported, via the drillpipe/wellbore annulus, to surface. To ensure that the cuttings are removed from the annulus the annular velocity must never be allowed to fall below a certain minimum value. This minimum annular velocity is dependent on the properties of the mud and cuttings for any particular well, and is usually between 100 – 200 ft/min.

The techniques used to optimise the hydraulics of the system will be described at the next article. However, optimizing the use of the hydraulic horsepower generated by the mud pumps requires the ability to quantify the pressure losses in the drillstring, across the nozzles and in the annulus between the drill string and well bore. The principal factors which influence the magnitude of the pressure losses in the system are:
• The geometry of circulating system (e.g. I.D. of drillpipe, length of drillpipe)
• The flowrate through the system
• The flow regime in which the fluid is flowing (laminar/turbulent)
• The rheological properties of the circulating fluid
The geometry of the system and the flowrate through the system are generally fixed by a wide range of considerations. The geometry of the system is determined by well design and drilling operational considerations. Whilst the minimum flowrate
through the system is dictated primarily by the annular velocity required to clean the drilled cuttings from the annulus. The maximum flow rate will be limited by the maximum power output by the mud pumps and the maximum pressures which can
be tolerated by the pumping system. It is therefore only necessary to understand the nature of the flow regime and rheological properties of the fluid and their influence on the pressure losses in the system.

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