This document summarizes key concepts from a drilling engineering course, including: - Types of fluid flow such as laminar, turbulent, and transitional and how the Reynolds number distinguishes these. - Rheological models for fluids including Newtonian, Bingham plastic, and power-law models. These describe the relationship between shear stress and shear rate. - Determining rheological properties of drilling fluids using a rotational viscometer at different speeds. - Factors that influence rheological properties like rotation, vibration, pulsing of mud pumps, and solid content.

1. Drilling Engineering 2 Course (1st Ed.)

2. 1. Mud Weight Planning
2. drilling hydraulics:
A. the hydrostatic pressure

3. 1. drilling hydraulics:
A. types & criteria of fluid flow
B. fluid Rheology and models
a.
Bingham plastic & Power-law models

5. Parameters influence rheological
properties of drilling fluid
Since multiple aspects of drilling and completion
operations require the understanding of how fluid
moves through pipes, fittings and annulus, the
knowledge of basic fluid flow patterns is essential.
Generally, fluid movement can be described as laminar,
turbulent or in transition between laminar and
turbulent.
It should be understood that rotation and vibrations
influence the rheological properties of drilling fluids.
Also the pulsing of the mud pumps cause variations in
the flow rates as well as the mean flow rates.
Furthermore changing solid content influences the
actual mud density and its plastic viscosity.
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
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6. Laminar vs. turbulent flow
Fluid movement, when laminar flow is present, can
be described as in layers or “laminae”.
Here at all times the direction of fluid particle movement
is parallel to each other and along the direction of flow.
In this way no mixture or interchange of fluid particles
from one layer to another takes place.
At turbulent flow behavior,
which develops at higher average flow velocities,
secondary irregularities such as vortices and eddys are
imposed to the flow.
This causes a chaotic particle movement and
thus no orderly shear between fluid layers is present.
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
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7. Ideal laminar flow (animation)
Ideal laminar
flow in a tube
(note that the
particles to
the center of
the tube
move faster,
as affected to
a lesser extent
dissipative
effect of the
walls)
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Drilling Engineering 2 Course (1st Ed.)
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8. Laminar, transitional, and turbulent
flow
Laminar vs. turbulent flow
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Laminar, transitional, and turbulent flow from a faucet
Drilling Engineering 2 Course (1st Ed.)
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9. Laminar vs. turbulent flow
Laminar and turbulent water flow
Fall 13 H. AlamiNia
Laminar vs. turbulent flow of smoke
Drilling Engineering 2 Course (1st Ed.)
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10. Reynolds number
The so called “Reynolds number” is often used to
distinguish the different flow patterns.
After defining the current flow pattern,
different equations are applied
to calculate the respective pressure drops.
For the flow through pipes, the Reynolds number is
determined with:
and for the flow through annuli:
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Drilling Engineering 2 Course (1st Ed.)
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11. Reynolds number range
The different flow patterns are then characterized
considering the Reynolds number.
Normally the Reynolds number 2,320 distinguishes
the laminar and turbulent flow behavior,
for drilling purposes a value of 2,000 is applied instead.
Furthermore it is assumed that turbulent flow is fully
developed at Reynolds numbers of 4,000 and above,
thus the range of 2,000 to 4,000 is named transition flow:
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
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14. Rheological Classification of Fluids
All fluids encountered in drilling and production
operations can be characterized as either
“Newtonian” fluids or “Non-Newtonian” ones.
Newtonian fluids,
like water, gases and thin oils (high API gravity)
show a direct proportional relationship between
the shear stress and the shear rate,
assuming pressure and temperature are kept constant.
They are mathematically defined by:
• 𝜏 [dyne/cm2] ... shear stress
• 𝛾[1/sec] ... shear rate for laminar flow within circular pipe
• μ [p] ... absolute viscosity [poise]
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
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15. Newtonian flow model
A plot of
−𝑑𝑣 𝑟
𝜏 vs.
𝑑𝑟
produces a
straight line
that passes
through the
origin and has
a slop of μ.
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
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16. Non-Newtonian fluids
Most fluids encountered at drilling operations
like drilling muds, cement slurries, heavy oil and gelled
fracturing fluids do not show this
direct relationship between shear stress and shear rate.
They are characterized as Non-Newtonian fluids.
To describe the behavior of Non-Newtonian fluids,
various models like
“Time-independent fluid model” including
the “Bingham plastic fluid model”,
the “Power law fluid model” and
“Time-dependent fluid models” were developed
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
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17. Non-Newtonian fluids
time depended models
The time dependence mentioned here concerns
the change of viscosity by the duration of shear.
It is common to subdivide the time depended
models into
“Thixotropic fluid models” and
The “Rheopectic fluid models”.
It shall be understood that all the models
mentioned above are based on
different assumptions that are
hardly valid for all drilling operations,
thus they are valid to a certain extend only.
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Drilling Engineering 2 Course (1st Ed.)
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19. Bingham plastic fluid model
Bingham plastic fluid
model
𝜏y [lbf/100 ft2]
yield point
μp [cp]
plastic viscosity
Sketch of Bingham fluid model
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Drilling Engineering 2 Course (1st Ed.)
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20. Bingham fluids
In contrary to Newtonian fluids,
Bingham fluids do have a yield point 𝜏 𝑦 and
it takes a defined shear stress (𝜏 𝑡 ) to initiate flow.
Above 𝜏 𝑦 , 𝜏 and 𝛾 are proportional defined by the
viscosity, re-named to plastic viscosity μp
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Drilling Engineering 2 Course (1st Ed.)
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21. Power-law fluid model
Power-law fluid model
n [1]
flow behavior index
K [1]
consistency index
Sketch of Power-law fluid model
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Drilling Engineering 2 Course (1st Ed.)
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22. Power-law fluid model
When the characteristics of the Power-law fluid model
is done on a log-log scale, the results is in a straight line.
Here the slope determines the flow behavior index n and
the intercept with the vertical,
the value of the consistency index (logK).
The flow behavior index (n), that ranges
from 0 to 1.0 declares the degree of Non-Newtonian behavior,
where n = 1.0 indicates a Newtonian fluid.
The consistency index K on the other hand
gives the thickness (viscosity) of the fluid where,
the larger K, the thicker (more viscous) the fluid is.
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
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23. rheological properties determination
To determine the rheological
properties of a particular fluid,
a rotational viscometer with
six standard speeds and variable
speed settings is used commonly.
In field applications, out of these
speeds just two are normally used
(300 and 600 [rpm])
since they are sufficient to
determine the required properties.
rotational Viscometer
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Drilling Engineering 2 Course (1st Ed.)
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24. individual fluid parameters
determination
Newtonian fluid model
Bingham plastic fluid model
Power-law fluid model
r2 [in] rotor radius, r1 [in] bob radius, r [in] any radius between
r1 and r2, θN [1] dial reading of the viscometer at speed N,
N [rpm] speed of rotation of the outer cylinder
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25. 1. Dipl.-Ing. Wolfgang F. Prassl. “Drilling
Engineering.” Master of Petroleum
Engineering. Curtin University of Technology,
2001. Chapter 4