PETE 203 DRILLING ENGINEERING. Drilling Hydraulics. Drilling Hydraulics. Energy Balance Flow Through Nozzles Hydraulic Horsepower Hydraulic Impact Force Rheological Models Optimum Bit Hydraulics. Nonstatic Well Conditions. Physical Laws: Conservation of Mass Conservation of energy
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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.
States that as a fluid flows from point 1 to point 2:
In the wellbore, in many cases Q = 0 (heat)
r = constant
p1andp2 are pressures in psi
ris 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.
(bottom of drill collars)
Velocity in mud pits, v1
NOTE: KE in collars
May be ignored in many cases
This accounts for all the losses in the nozzle.
Vn is the same for each nozzle even if the dn varies!
This follows since Dp is the same across each nozzle.
HHP of pump putting out 400 gpm at 3,000 psi = ?
In field units:
What is the HHP Developed by bit?
Shear stress = viscosity * shear rate
In a Newtonian fluid the shear stress is directly proportional to the shear rate (in laminar flow):
The constant of proportionality, is the viscosity of the fluid and is independent of shear rate.
Viscosity may be expressed in poise or centipoise.
Slope of line = m
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?
tand tyare often expressed inlbf/100 sq.ft
n = flow behavior index
K = consistency index
1. Newtonian Fluid:
2. Bingham Plastic Fluid:
What ifty = 0?
K = consistency index
n = flow behavior index
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).
Fig. 4-26. Velocity profiles for laminar flow: (a) pipe flow and (b) annular flow
- Newtonian Fluid
“It looks like concentric rings of fluid
telescoping down the pipe at different velocities”
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)
Flow pattern is linear (no radial flow)
Velocity at wall is ZERO
Produces minimal hole erosion
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.
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…
Turbulent flow, cont’d
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
The onset of turbulence in pipe flow is characterized by the dimensionless group known as the Reynolds number
In field units,
We often assume that fluid flow is
turbulent ifNre > 2,100
Pressure Drop Calculations fluids.
Q = 280 gal/min
r = 12.5 lb/gal
PPUMP = DPDP + DPDC
+ DPBIT NOZZLES
+ DPDC/ANN + DPDP/ANN
Both these items increase when the circulation rate increases.
However, when the circulation rate increases, so does the frictional pressure drop.
Proper bottom-hole cleaning
Will eliminate excessive regrinding of drilled solids, and
Will result in improved penetration rates
Through nozzle size selection, optimization may be based on maximizing one of the following:
Bit Nozzle Velocity
Bit Hydraulic Horsepower
Jet impact force
From Eq. (4.31)
so the bit pressure drop should be maximized in order to obtain the 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.
The hydraulic horsepower at the bit is maximized when is maximized.
where may be called the parasiticpressure loss in the system (friction).
The parasiticpressure loss in the system,
In general, where
The jet impact force is given by Eq. 4.37:
But parasitic pressure drop,
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,