1. PETE 203 DRILLING ENGINEERING
Drilling Hydraulics

2. Drilling Hydraulics Energy Balance Flow Through Nozzles
Hydraulic Horsepower
Hydraulic Impact Force
Rheological Models
Optimum Bit Hydraulics

3. 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

4. Average Fluid Velocity Pipe 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.

6. 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

7. 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.

8. Determine the pressure at the bottom of the drill collars, if
(bottom of drill collars)
(mud pits)

9. Velocity in drill collars
Velocity in mud pits, v1

10. Pressure at bottom of drill collars = 7,833 psig
NOTE: KE in collars
May be ignored in many cases

12. Fluid Flow Through Nozzle
Assume:

13. This accounts for all the losses in the nozzle.If
This accounts for all the losses in the nozzle.
Example:

15. 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.
&

16. Hydraulic Horsepower In field units:
HHP of pump putting out 400 gpm at 3,000 psi = ?
Power
In field units:

17. Hydraulic Impact Force
What is the HHP Developed by bit?
Consider:

18. Impact = rate of change of momentum

19. Shear stress = viscosity * shear rate
Newtonian Fluid Model
Shear stress = viscosity * shear rate

20. Laminar Flow of Newtonian Fluids

21. 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. .

22. Viscosity may be expressed in poise or centipoise.
Newtonian Fluid Model .
Viscosity may be expressed in poise or centipoise.

23. Shear Stress vs. Shear Rate for a Newtonian Fluid
Slope of line = m

24. Example - Newtonian Fluid

25. Example 4.16 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?

26. Example 4.16

27. Bingham Plastic Model

28. t and ty are often expressed in lbf/100 sq.ft
Bingham Plastic Model
t and ty are often expressed in lbf/100 sq.ft

29. Power-Law Model

30. n = flow behavior index K = consistency index
Power-Law Model
n = flow behavior index
K = consistency index

31. 1. Newtonian Fluid: 2. Bingham Plastic Fluid:
Rheological Models
1. Newtonian Fluid:
2. Bingham Plastic Fluid:
What if ty = 0?

32. 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

33. Velocity Profiles (laminar flow)
Fig Velocity profiles for laminar flow: (a) pipe flow and (b) annular flow

34. 3D View of Laminar Flow in a pipe
- Newtonian Fluid
“It looks like concentric rings of fluid
telescoping down the pipe at different velocities”

35. Summary of Laminar Flow Equations for Pipes and Annuli

38. Fig 4.33: Critical Reynolds number for Bingham plastic fluids.

39. Fig 4.34: Fraction Factors for Power-law fluid model.

41. 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)

42. Total Pump Pressure

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

44. 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.

45. Types of Flow Flow pattern is random (flow in all directions)
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…

46. Turbulent flow, cont’d Types of flow
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

47. 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,

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

49. Pressure Drop Calculations
PPUMP
Q = gal/min
r = lb/gal
PPUMP = DPDP + DPDC
+ DPBIT NOZZLES
+ DPDC/ANN + DPDP/ANN
+ DPHYD

50. DRILLPIPE DRILL COLLARS BIT NOZZLES ANNULUS
2103
DRILL COLLARS
BIT NOZZLES
ANNULUS

51. 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.

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

53. 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

54. 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.

55. 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

56. 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.

57. 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).

58. Maximum Bit Hydraulic Horsepower
The parasitic pressure loss in the system,
In general, where

59. Maximum Bit Hydraulic Horsepower

60. Maximum Bit Hydraulic Horsepower

61. Maximum Jet Impact Force
The jet impact force is given by Eq. 4.37:

62. Maximum Jet Impact Force
But parasitic pressure drop,

63. 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,