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
4.
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.)
5
5.
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.)
6
6.
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)
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
7
7.
Laminar, transitional, and turbulent
flow
Laminar vs. turbulent flow
Fall 13 H. AlamiNia
Laminar, transitional, and turbulent flow from a faucet
Drilling Engineering 2 Course (1st Ed.)
8
8.
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.)
9
9.
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:
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
10
10.
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.)
11
11.
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.)
14
12.
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.)
15
13.
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.)
16
14.
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.
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
17
15.
Bingham plastic fluid model
Bingham plastic fluid
model
𝜏y [lbf/100 ft2]
yield point
μp [cp]
plastic viscosity
Sketch of Bingham fluid model
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
19
16.
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
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
20
17.
Power-law fluid model
Power-law fluid model
n [1]
flow behavior index
K [1]
consistency index
Sketch of Power-law fluid model
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
21
18.
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.)
22
19.
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
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
23
20.
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
Fall 13 H. AlamiNia
Drilling Engineering 2 Course (1st Ed.)
24
21.
1. Dipl.-Ing. Wolfgang F. Prassl. “Drilling
Engineering.” Master of Petroleum
Engineering. Curtin University of Technology,
2001. Chapter 4
A particular slide catching your eye?
Clipping is a handy way to collect important slides you want to go back to later.
Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.
Be the first to comment