Pressure Drop Calculations

1
Pressure Drop Calculations

• 1.7-1

2
1.7-2
3
1.7-3 For multiple nozzles in parallel

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

Cd 0.95
4
1.7-4 Hydraulic Horsepower

• of pump putting out 400 gpm at 3,000 psi ?
• Power, in field units

Hydraulic Horsepower of Pump 700 hp
5
1.7-5 What is Hydraulic Impact Force

• developed by bit?
• If

6
1.7-6 Laminar Flow

• Rheological Models
• Newtonian
• Bingham Plastic
• Power-Law (ADE API)
• Rotational Viscometer
• Laminar Flow in Wellbore
• Fluid Flow in Pipes
• Fluid Flow in Annuli

7
1.7-7
Laminar Flow of Newtonian Fluids
Experimentally
8
1.7-8 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.

9
1.7-9 Newtonian Fluid Model

• Viscosity may be expressed in poise or centipoise.

10
1.7-10 Shear Stress vs. Shear Rate for a
Newtonian Fluid
.
Slope of line m
11
1.7-11 Typical Drilling Fluid Vs. Newtonian,
Bingham and Power Law Fluids
0
12
1.7-12 Rheological Models

• 1. Newtonian Fluid
• 2. Bingham Plastic Fluid

What if ty 0?
13
1.7-13 RotatingSleeveViscometer
14
1.7-14 Figure 3.6
Rotating Viscometer
Rheometer
We determine rheological properties of drilling
fluids in this device
Infinite parallel plates
15
1.7-15 Rheometer (Rotational Viscometer)

• Shear Stress f (Dial Reading)
• Shear Rate f (Sleeve RPM)
• Shear Stress f (Shear Rate)

16
1.7-16 Example

• A rotational viscometer containing a Bingham
  plastic fluid gives a dial reading of 12 at a
  rotor speed of 300 RPM and a dial reading of 20
  at a rotor speed of 600 RPM
• Compute plastic viscosity and yield point

q600 20 q300 12
See Appendix A
17
1.7-17 Example
q600 20 q300 12
(See Appendix A)
18
1.7-18 Gel Strength
19
1.7-19 Gel Strength shear stress at which
fluid movement begins

• The yield strength, extrapolated from the
  300 and 600 RPM readings is not a good
  representation of the gel strength of the fluid
• Gel strength may be measured by turning the
  rotor at a low speed and noting the dial
  reading at which the gel structure is broken
• (usually at 3 RPM)

20
1.7-20 Gel Strength
The gel strength is the maximum dial reading when
the viscometer is started at 3 rpm.

• In field units,

In practice, this is often approximated to
tg qmax,3
21
1.7-21 Velocity Profiles(laminar flow)
Fig. 4-26. Velocity profiles for laminar flow
(a) pipe flow and (b) annular flow
22
1.7-22
3D View of Laminar Flow in a pipe - Newtonian
Fluid
It looks like concentric rings of fluid
telescoping down the pipe at different
velocities
23
1.7-23 Table 4.3 - Summary of Equations for
Rotational Viscometer

• Newtonian Model

or
24
1.7-24 Table 4.3 - Summary of Equations for
Rotational Viscometer
Bingham Plastic Model
or
or
25
1.7-25 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)

26
1.7-26 Pressure losses for laminar flow.
Newtonian Fluid
Bingham Plastic Fluid
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1.7-27 Types of flow
Laminar
Turbulent
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
28
1.7-28 Turbulent Flow - Newtonian Fluid

• We often assume that fluid flow is
• turbulent if Nre gt 2100

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Turbulent Flow - Newtonian Fluid
Turbulent Flow - Bingham Plastic Fluid
In Pipe
In Annulus
1.7-29