PETE 203 DRILLING ENGINEERING

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PETE 203DRILLING ENGINEERING

• Drilling Hydraulics

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Drilling Hydraulics

• Energy Balance
• Flow Through Nozzles
• Hydraulic Horsepower
• Hydraulic Impact Force
• Rheological Models
• Optimum Bit Hydraulics

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Nonstatic Well Conditions

• Physical Laws
• Conservation of Mass
• Conservation of energy
• Conservation of momentum
• Rheological Models
• Newtonian
• Bingham Plastic
• Power Law
• API Power-Law
• Equations of State
• Incompressible fluid
• Slightly compressible fluid
• Ideal gas
• Real gas

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Average Fluid VelocityPipe Flow
Annular Flow

• WHERE
• 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.

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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
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In practical field units this equation
simplifies to

where

• p1 and p2 are pressures in psi
• r is 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.

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Determine the pressure at the bottom of the drill
collars, if
(bottom of drill collars)
(mud pits)
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Velocity in drill collars

Velocity in mud pits, v1
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Pressure at bottom of drill collars 7,833 psig
NOTE KE in collars May be ignored in
many cases
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Fluid Flow Through Nozzle
Assume

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If
This accounts for all the losses in the nozzle.
Example
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For multiple nozzles in //

• Vn is the same for each nozzle even if the
  dn varies!
• This follows since Dp is the same across
  each nozzle.

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Hydraulic Horsepower

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

In field units
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Hydraulic Impact Force

• What is the HHP Developed by bit?
• Consider

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Impact rate of change of momentum
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Newtonian Fluid Model

• Shear stress viscosity shear rate

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Laminar Flow of Newtonian Fluids
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Newtonian Fluid Model

• In a Newtonian fluid the shear stress is directly
  proportional to the shear rate (in laminar flow)
• i.e.,
• The constant of proportionality, is the
  viscosity of the fluid and is independent of
  shear rate.

.
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Newtonian Fluid Model
.

• Viscosity may be expressed in poise or centipoise.

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Shear Stress vs. Shear Rate for a Newtonian Fluid
.
Slope of line m
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Example - Newtonian Fluid
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Example 4.16

• Area of upper plate 20 cm2
• Distance between plates 1 cm
• Force reqd to move upper plate at 10 cm/s
  100 dynes.
• What is fluid viscosity?

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Example 4.16
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Bingham Plastic Model
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Bingham Plastic Model
t and ty are often expressed in lbf/100 sq.ft
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Power-Law Model
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Power-Law Model

• n flow behavior index
• K consistency index

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Rheological Models

• 1. Newtonian Fluid
• 2. Bingham Plastic Fluid

What if ty 0?
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Rheological Models

• 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).

K consistency index n flow behavior index
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Velocity Profiles(laminar flow)
Fig. 4-26. Velocity profiles for laminar flow
(a) pipe flow and (b) annular flow
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3D View of Laminar Flow in a pipe - Newtonian
Fluid
It looks like concentric rings of fluid
telescoping down the pipe at different
velocities
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Summary of Laminar Flow Equations for Pipes and
Annuli
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Fig 4.33 Critical Reynolds number for Bingham
plastic fluids.
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Fig 4.34 Fraction Factors for Power-law fluid
model.
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Total Pump Pressure

• 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)

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Total Pump Pressure
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Types of Flow

• Laminar Flow
• Flow pattern is linear (no radial flow)
• Velocity at wall is ZERO
• Produces minimal hole erosion

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Types of Flow - 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.

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Types of Flow

• 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 cleaningbut

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Types of flow
Turbulent flow, contd

• 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
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Turbulent Flow - Newtonian Fluid

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

In field units,
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Turbulent Flow - Newtonian Fluid

• We often assume that fluid flow is
• turbulent if Nre gt 2,100

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Pressure Drop Calculations
PPUMP
Q 280 gal/min r 12.5 lb/gal
PPUMP DPDP DPDC DPBIT NOZZLES
DPDC/ANN DPDP/ANN DPHYD
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DRILLPIPE
2103
DRILL COLLARS
BIT NOZZLES
ANNULUS
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Optimum Bit Hydraulics

• 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.

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Jet Bit Nozzle Size Selection

• Nozzle Size Selection for Optimum Bit
  Hydraulics
• Max. Nozzle Velocity
• Max. Bit Hydraulic Horsepower
• Max. Jet Impact Force

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Jet Bit Nozzle Size Selection

• 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

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Jet Bit Nozzle Size Selection- 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.

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Maximum Nozzle Velocity

• From Eq. (4.31)
• i.e.
• so the bit pressure drop should be maximized in
  order to obtain the maximum nozzle velocity

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Maximum Nozzle Velocity

• 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.

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Maximum Bit Hydraulic Horsepower

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

where may be called the parasitic
pressure loss in the system (friction).
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Maximum Bit Hydraulic Horsepower
The parasitic pressure loss in the system,
In general, where
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Maximum Bit Hydraulic Horsepower
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Maximum Bit Hydraulic Horsepower
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Maximum Jet Impact Force

• The jet impact force is given by Eq. 4.37

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Maximum Jet Impact Force

• But parasitic pressure drop,

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Maximum Jet Impact Force

• 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,