PETE%20411%20Well%20Drilling

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PETE 411Well Drilling
Lesson 12 Laminar Flow - Slot Flow
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Lesson 12 - Laminar Flow - Slot Flow

• The Slot Flow Approximation
• Shear Rate Determination
• Pressure Drop Calculations
• Laminar Flow
• Turbulent Flow
• Transition Flow - Critical Velocity

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ReadApplied Drilling Engineering Ch.4 to p. 145
Homework 6On the WebDue Friday, October 4, 2002
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Representing the Circular Annulus as a Slot
Equal Area and Height
Simpler Equations-yet accurate
slot approximation is OK if (d1/d2 gt 0.3
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Free body diagram for fluid element in a narrow
slot
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Representing the Annulus as a Slot
Consider - pressure forces - viscous forces
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Representing the Annulus as a Slot
Summing forces along flow
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Representing the Annulus as a Slot
Evaluate t0 at wall where y 0
But,
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Representing the Annulus as a Slot
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Representing the Annulus as a Slot
Hence, substituting for v0 and t0
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Representing the Annulus as a Slot
The total flow rate
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Representing the Annulus as a Slot
In field units,
psi/ft, cp., ft/sec, in
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Example 4.22

• Compute the frictional pressure loss for a 7 x
  5 annulus, 10,000 ft long, using the slot flow
  representation in the annulus. The flow rate is
  80 gal/min. The viscosity is 15 cp. Assume the
  flow pattern is laminar.

6 p
1
7
5
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Example 4.22

• The average velocity in the annulus,

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Example 4.22

• A somewhat more accurate answer, using an exact
  equation for a circular annulus, results in a
  value of 50.9792 psi.
• Difference 0.0958 psi i.e., within
  0.2

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Determination of Shear Rate...(why?)

• If shear rate in well is known
• 1. Fluid can be evaluated in viscometer at
  the proper shear rate.
• 2. Newtonian equations can sometimes give
  good accuracy even if fluid is
  non-Newtonian.

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Determination of Shear Rate

• The maximum value of shear rate will occur at the
  pipe walls.
• For circular pipe, at the pipe wall,

from (Eq. 4.51)
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Determination of Shear Rate

• From Eq. 4.54b,

(at the wall)
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Determination of Shear Rate (why?)

• Using the Newtonian Model,

Changing to field units,
(circular pipe)
sec-1, ft/sec, in
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Annulus

• From the slot flow approximation,

But,
Eq. 4.60 c
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Shear Rate in Annulus
In field units
(annulus)
Where,
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Power - Law Example 4.24

• A cement slurry has a flow behavior index of 0.3
  and a consistency index of 9,400 eq. cp. The
  slurry is being pumped in an 8.097 4.5 - inch
  annulus at 200 gal/min.
• (i) Assuming the flow pattern is laminar,
  compute the frictional pressure loss per
  1,000 ft of annulus.
• (ii) What is the shear rate at the wall?

n 0.3 K 9,400
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Example 4.24
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Example 4.24
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Example 4.24 contd

• (ii) Shear rate at pipe wall,

75 RPM
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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
PUMP
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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