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

2. Lesson 12 - Laminar Flow - Slot Flow
The Slot Flow Approximation
Shear Rate Determination
Pressure Drop Calculations
Laminar Flow
Turbulent Flow
Transition Flow - Critical Velocity

3. Read: Applied Drilling Engineering Ch.4 to p. 145
Homework #6 On the Web Due Friday, October 4, 2002

4. Representing the Circular Annulus as a Slot
Equal Area and Height
Simpler Equations-yet accurate
{ slot approximation is OK if (d1/d2 > 0.3 }

5. Free body diagram for fluid element in a narrow slot

6. Representing the Annulus as a Slot
Consider:
- pressure forces
- viscous forces

7. Representing the Annulus as a Slot
Summing forces along flow:

8. Representing the Annulus as a Slot
Evaluate t0 at wall where y = 0
But,

9. Representing the Annulus as a Slot

10. Representing the Annulus as a Slot
Hence, substituting for v0 and t0 :

11. Representing the Annulus as a Slot
The total flow rate:

12. Representing the Annulus as a Slot
In field units,
psi/ft, cp., ft/sec, in

13. 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”

14. The average velocity in the annulus,
Example 4.22
The average velocity in the annulus,

15. Example 4.22
A somewhat more accurate answer, using an exact equation for a circular annulus, results in a value of psi.
Difference = psi i.e., within 0.2%

16. 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.

17. 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)

18. Determination of Shear Rate
From Eq. 4.54b,
(at the wall)

19. Determination of Shear Rate (why?)
Using the Newtonian Model,
Changing to field units,
(circular pipe)
sec-1, ft/sec, in

20. From the slot flow approximation,
Annulus:
From the slot flow approximation,
But,
Eq c

21. Shear Rate in Annulus
In field units:
(annulus)
Where,

22. 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 * 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

23. Example 4.24

24. Example 4.24

25. (ii) Shear rate at pipe wall,
Example cont’d
(ii) Shear rate at pipe wall,
= 75 RPM

26. 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)

27. Total Pump Pressure
PUMP

28. Types of Flow Laminar Flow Flow pattern is linear (no radial flow)
Velocity at wall is ZERO
Produces minimal hole erosion

29. 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.

30. 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 cleaning…but…

31. Types of flow 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 Laminar and turbulent flow patterns in a circular pipe: (a) laminar flow, (b) transition between laminar and turbulent flow and (c) turbulent flow

32. 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,

33. Turbulent Flow - Newtonian Fluid
We often assume that fluid flow is
turbulent if Nre > 2,100