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# Drill bit hydraulics

## Hydraulic energy

Energy is the rate of doing work. A practical aspect of energy is that it can be transmitted or transformed from one form to another (e.g., from an electrical form to a mechanical form by a motor). A loss of energy always occurs during transformation or transmission. In drilling fluids, energy is called hydraulic energy or commonly hydraulic horsepower.

The basic equation for hydraulic energy is

where *H* = hydraulic horsepower, *p* = pressure (psi or kPa), *q* = flow rate (gal/min or L/min), and 1,714 is the conversion of (psi-gal/min) to hydraulic horsepower
[
or (kPa•L/min) = 44 750]
. Rig pumps are the source of hydraulic energy carried by drilling fluids. This energy is commonly called the total hydraulic horsepower or pump hydraulic horsepower:

where *H*_{1} = total hydraulic energy (hydraulic horsepower) and *p*_{1} =actual or theoretical rig pump pressure (psi). (See prior equation for metric conversion.) Note that the rig pump pressure (*p*_{1}) is the same as the total pressure loss or the system pressure loss. *H*_{1} is the total hydraulic energy (rig pump) required to counteract all friction energy (loss) starting at the Kelly hose (surface line) and Kelly, down the drillstring, through the bit nozzles, and up the annulus at a given flow rate (*q*).

Bit hydraulic energy, *H*_{b}, is the energy needed to counteract frictional energy (loss) at the bit or can be expressed as the energy expended at the bit:

See prior equation for metric conversion.

### Fluid velocity

The general formula for fluid velocity is

where *v* = velocity (ft/min or m/min), *q* = flow rate (gal/min or L/min), and *A* = area of flow (ft^{2} or m^{2}).

The average velocity of a drilling fluid passing through a bit
’
s jet nozzles is derived from the fluid velocity equation:
where *v*_{j} = average jet velocity of bit nozzles (ft/sec or m/s) and *A*_{n} = total bit nozzle area (in.^{2} or cm^{2 }).

Nozzle sizes are expressed in ^{1}/_{32}-in. (inside diameter) increments. Examples are ^{9}/_{32} and ^{12}/_{32} in. The denominator is not usually mentioned; the size is understood to be in 32nds of an inch. For example, ^{9}/_{32}- and ^{12}/_{32}-in. nozzles are expressed as sizes 9 and 12.

The impact force of the drilling fluid at velocity *v*_{j1} can be derived from Newton
’
s Second Law of Motion: force equals mass times acceleration. Assuming that all the fluid momentum is transferred to the bottomhole,
where *I*_{j} = impact force of nozzle jets (lbf or kPa), *W* = mud weight (lbm/gal or kg/L), *q* = flow rate (gal/min or L/min), and *v*_{j} = average jet velocity from bit nozzles (ft/sec or m/s).

### System pressure loss

Pressure losses inside the drillstring result from turbulent conditions. Viscosity has very little effect on pressure losses in turbulent flow. At higher Reynold
’
s numbers, a larger variation results in only a small variation in friction factor. The calculated pressure loss equations are based on turbulent flow and are corrected for mud weight instead of viscosity:
where *A*_{n} = total combined area of the bit nozzles (in.^{2} or cm^{2}), *W* = mud weight (lb/gal or kg/L), *p*_{b} = bit nozzle jets pressure loss (psi or kPa), and *q* = flow rate (gal/min or L/min).

## Roller cone bit hydraulic features

### Nozzles and flow tubes

Drilling fluids circulate through a drillstring to nozzles at the bit and back to the surface via the system annulus. They provide three crucial functions to drilling:

- Cleaning of the cutting structure.
- Cuttings removal from the hole bottom.
- Efficient cuttings evacuation to the surface.

The hydraulic energy that causes fluid circulation is one of only three variable energy inputs (wob, rotary speed, and hydraulic flow) available on a drill rig for optimization of drilling performance.

Hydraulic performance can be optimized by roller-cone bit options, such as:

- Nozzle selection.
- Flow tubes.
- Vectored flow tubes.
- Center nozzle ports.

These features provide alternatives for precise placement of hydraulic energy according to well bottom needs.

Generating cuttings is the first step needed to achieve high ROPs; cleaning those cuttings from the cone and hole bottom and lifting them through the annulus to the rig surface is the remaining part of a hydraulic solution. Computer modeling supported by laboratory testing is the most common approach to development and verification of hydraulic designs. Efficient velocity profiles deliver hydraulic energy to the most needed points, even in cases for which drilling flow rates are compromised.

Normally, several different nozzles can be used interchangeably on a particular bit. Nozzles are commonly classified into standard, extended, and diverging categories. Extended nozzles release the flow at a point closer than standard to the hole bottom. Diverging nozzles release the flow in a wider-than-normal, lower-velocity stream. They are designed primarily for use in center jet installations.^{[1]}

### Asymmetric nozzle configurations and crossflow

A bit has a symmetric nozzle configuration when three nozzles of the same size and type, at the same level on the periphery of a bit, are installed 120° from each other. An asymmetric nozzle configuration has two or more different nozzle sizes and/or types.

When the fluid from a nozzle impinges on the well bottom, it moves away from the point of impingement in a 360°, fan-like, spray. A boundary forms at which fluids from two different jets meet. Fluids at these boundaries create stagnant zones known as dead zones. In the case of a symmetric nozzle configuration, dead zones occur under the middle part of the cone’s asymmetric nozzle configurations; dead zones are moved away from the impingement zone of the larger jet and toward that of the smaller jet (i.e., away from the middle of the cone). Asymmetric flows resist entrapment of cuttings under a bit and help prevent the inefficiencies of regrind, lower ROPs, and erosive wear on the bit. **Fig. 1** shows typical flow patterns.

Crossflow is a subset of asymmetric nozzle sizing in which one jet is blocked by nozzle blank. The blanked side of the bit leaves a natural exit path for the fluid from the opposing two jets. The flow from the two jets sweeps under two of the cones to improve bottomhole cleaning and chip removal.

### Practical hydraulic guidelines

**Table 1** is a summary of accepted starting hydraulics configurations for roller-cone bits.

## References

- ↑ Chia, R. and Smith, R. 1986. A New Nozzle System To Achieve High ROP Drilling. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 5-8 October. SPE-15518-MS. http://dx.doi.org/10.2118/15518-MS.

## See also

PEH:Introduction to Roller-Cone and Polycrystalline Diamond Drill Bits