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PETE 203 DRILLING ENGINEERING. Drilling Hydraulics. Drilling Hydraulics. Energy Balance Flow Through Nozzles Hydraulic Horsepower Hydraulic Impact Force Rheological Models Optimum Bit Hydraulics. Nonstatic Well Conditions. Physical Laws: Conservation of Mass Conservation of energy

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Pete 203 drilling engineering l.jpg


Drilling Hydraulics

Drilling hydraulics l.jpg
Drilling Hydraulics

  • Energy Balance

  • Flow Through Nozzles

  • Hydraulic Horsepower

  • Hydraulic Impact Force

  • Rheological Models

  • Optimum Bit Hydraulics

Nonstatic well conditions l.jpg
Nonstatic Well Conditions

  • Physical Laws:

    • Conservation ofMass

    • Conservation ofenergy

    • Conservation ofmomentum

  • Rheological Models

    • Newtonian

    • Bingham Plastic

    • Power – Law

    • API Power-Law

  • Equations of State

    • Incompressible fluid

    • Slightly compressible fluid

    • Ideal gas

    • Real gas

Average fluid velocity pipe flow annular flow l.jpg
Average Fluid VelocityPipe Flow Annular Flow


v = average velocity, ft/s

q = flow rate, gal/min

d = internal diameter of pipe, in.

d2 = internal diameter of outer pipe or borehole, in.

d1=external diameter of inner pipe, in.

Law of conservation of energy l.jpg
Law of Conservation of Energy

States that as a fluid flows from point 1 to point 2:


In the wellbore, in many cases Q = 0 (heat)

r = constant

In practical field units this equation simplifies to l.jpg
In practical field unitsthis equation simplifies to:

p1andp2 are pressures in psi

ris density in lbm/gal.

v1 and v2 are velocities in ft/sec.

Dpp is pressure added by pump

between points 1 and 2 in psi

Dpf is frictional pressure loss in psi

D1 and D2 are depths in ft.


Determine the pressure at the bottom of the drill collars if l.jpg
Determine the pressure at the bottom of the drill collars, if

(bottom of drill collars)

(mud pits)

Velocity in drill collars l.jpg
Velocity in drill collars if

Velocity in mud pits, v1

Slide10 l.jpg

Pressure at bottom of drill collars = 7,833 psig if

NOTE: KE in collars

May be ignored in many cases

Slide13 l.jpg
If if

This accounts for all the losses in the nozzle.


For multiple nozzles in l.jpg
For multiple nozzles in if//

Vn is the same for each nozzle even if the dn varies!

This follows since Dp is the same across each nozzle.


Hydraulic horsepower l.jpg
Hydraulic Horsepower if

HHP of pump putting out 400 gpm at 3,000 psi = ?


In field units:

Hydraulic impact force l.jpg
Hydraulic Impact Force if

What is the HHP Developed by bit?


Newtonian fluid model l.jpg

Newtonian Fluid Model if

Shear stress = viscosity * shear rate

Newtonian fluid model21 l.jpg

Newtonian Fluid Model if


In a Newtonian fluid the shear stress is directly proportional to the shear rate (in laminar flow):


The constant of proportionality, is the viscosity of the fluid and is independent of shear rate.

Newtonian fluid model22 l.jpg

Newtonian Fluid Model if


Viscosity may be expressed in poise or centipoise.

Example 4 16 l.jpg

Example 4.16 if

Area of upper plate = 20 cm2

Distance between plates = 1 cm

Force req’d to move upper plate at 10 cm/s = 100 dynes.

What is fluid viscosity?

Bingham plastic model28 l.jpg

Bingham Plastic Model if

tand tyare often expressed inlbf/100 sq.ft

Power law model l.jpg

Power-Law Model if

n = flow behavior index

K = consistency index

Rheological models l.jpg

Rheological Models if

1. Newtonian Fluid:

2. Bingham Plastic Fluid:

What ifty = 0?

Rheological models32 l.jpg

Rheological Models if

K = consistency index

n = flow behavior index

3. Power Law Fluid:

When n = 1, fluid is Newtonian and K = m

We shall use power-law model(s) to calculate pressure losses (mostly).

Velocity profiles laminar flow l.jpg

Velocity Profiles if(laminar flow)

Fig. 4-26. Velocity profiles for laminar flow: (a) pipe flow and (b) annular flow

Slide34 l.jpg

3D View of Laminar Flow in a pipe if

- Newtonian Fluid

“It looks like concentric rings of fluid

telescoping down the pipe at different velocities”

Total pump pressure l.jpg

Total Pump Pressure fluids.

Pressure loss in surf. equipment

Pressure loss in drill pipe

Pressure loss in drill collars

Pressure drop across the bit nozzles

Pressure loss in the annulus between the drill collars and the hole wall

Pressure loss in the annulus between the drill pipe and the hole wall

Hydrostatic pressure difference (r varies)

Types of flow l.jpg

Types of Flow fluids.

Laminar Flow

Flow pattern is linear (no radial flow)

Velocity at wall is ZERO

Produces minimal hole erosion

Types of flow laminar l.jpg

Types of Flow - fluids.Laminar

Mud properties strongly affect pressure losses

Is preferred flow type for annulus (in vertical wells)

Laminar flow is sometimes referred to as sheet flow, or layered flow:

* As the flow velocity increases, the flow type changes from laminar to turbulent.

Types of flow45 l.jpg

Types of Flow fluids.

Turbulent Flow

Flow pattern is random (flow in all directions)

Tends to produce hole erosion

Results in higher pressure losses (takes more energy)

Provides excellent hole cleaning…but…

Types of flow46 l.jpg
Types of flow fluids.

Turbulent flow, cont’d

  • Mud properties have little effect on pressure losses

  • Is the usual flow type inside the drill pipe and collars

  • Thin laminar boundary layer at the wall

Fig. 4-30. Laminar and turbulent flow patterns in a circular pipe: (a) laminar flow, (b) transition between laminar and turbulent flow and (c) turbulent flow

Turbulent flow newtonian fluid l.jpg

Turbulent Flow - Newtonian Fluid fluids.

The onset of turbulence in pipe flow is characterized by the dimensionless group known as the Reynolds number

In field units,

Turbulent flow newtonian fluid48 l.jpg

Turbulent Flow - Newtonian Fluid fluids.

We often assume that fluid flow is

turbulent ifNre > 2,100

Slide49 l.jpg

Pressure Drop Calculations fluids.


Q = 280 gal/min

r = 12.5 lb/gal





Slide50 l.jpg






Optimum bit hydraulics l.jpg
Optimum Bit Hydraulics fluids.

  • Under what conditions do we get the best hydraulic cleaning at the bit?

    • Maximum hydraulic horsepower?

    • Maximum impact force?

      Both these items increase when the circulation rate increases.

      However, when the circulation rate increases, so does the frictional pressure drop.

Jet bit nozzle size selection l.jpg
Jet Bit Nozzle Size Selection fluids.

  • Nozzle Size Selection for Optimum Bit Hydraulics:

    • Max. Nozzle Velocity

    • Max. Bit Hydraulic Horsepower

    • Max. Jet Impact Force

Jet bit nozzle size selection53 l.jpg

Jet Bit Nozzle Size Selection fluids.

Proper bottom-hole cleaning

Will eliminate excessive regrinding of drilled solids, and

Will result in improved penetration rates

  • Bottom-hole cleaning efficiency

    • Is achieved through proper selection of bit nozzle sizes

Jet bit nozzle size selection optimization l.jpg

Jet Bit Nozzle Size Selection fluids.- Optimization -

Through nozzle size selection, optimization may be based on maximizing one of the following:

Bit Nozzle Velocity

Bit Hydraulic Horsepower

Jet impact force

  • There is no general agreement on which of

  • these three parameters should be maximized.

Maximum nozzle velocity l.jpg

Maximum Nozzle Velocity fluids.

From Eq. (4.31)


so the bit pressure drop should be maximized in order to obtain the maximum nozzle velocity

Maximum nozzle velocity56 l.jpg

Maximum Nozzle Velocity fluids.

This (maximization) will be achieved when the surface pressure is maximized and the frictional pressure loss everywhere is minimized, i.e., when the flow rate is minimized.

Maximum bit hydraulic horsepower l.jpg

Maximum Bit Hydraulic Horsepower fluids.

The hydraulic horsepower at the bit is maximized when is maximized.

where may be called the parasiticpressure loss in the system (friction).

Maximum bit hydraulic horsepower58 l.jpg

Maximum Bit Hydraulic Horsepower fluids.

The parasiticpressure loss in the system,

In general, where

Maximum jet impact force l.jpg

Maximum Jet Impact Force fluids.

The jet impact force is given by Eq. 4.37:

Maximum jet impact force62 l.jpg

Maximum Jet Impact Force fluids.

But parasitic pressure drop,

Maximum jet impact force63 l.jpg

Maximum Jet Impact Force fluids.

Upon differentiating, setting the first derivative to zero, and solving the resulting quadratic equation, it may be seen that the impact force is maximized when,