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# PETE 203 DRILLING ENGINEERING - PowerPoint PPT Presentation

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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### PETE 203DRILLING ENGINEERING

Drilling Hydraulics

• Energy Balance

• Flow Through Nozzles

• Hydraulic Horsepower

• Hydraulic Impact Force

• Rheological Models

• Optimum Bit Hydraulics

• Physical Laws:

• Conservation ofMass

• Conservation ofenergy

• Conservation ofmomentum

• Rheological Models

• Newtonian

• Bingham Plastic

• Power – Law

• API Power-Law

• Equations of State

• Incompressible fluid

• Slightly compressible fluid

• Ideal gas

• Real gas

Average Fluid VelocityPipe 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.

States that as a fluid flows from point 1 to point 2:

{

In the wellbore, in many cases Q = 0 (heat)

r = constant

In practical field unitsthis equation simplifies to:

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.

where

(bottom of drill collars)

(mud pits)

Velocity in mud pits, v1

NOTE: KE in collars

May be ignored in many cases

Assume:

If if

This accounts for all the losses in the nozzle.

Example:

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 = ?

Power

In field units:

What is the HHP Developed by bit?

Consider:

### Newtonian Fluid Model if

Shear stress = viscosity * shear rate

### Newtonian Fluid Model if

.

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.

### Newtonian Fluid Model if

.

Viscosity may be expressed in poise or centipoise.

### Shear Stress vs. Shear Rate for a Newtonian Fluid if

.

Slope of line = m

### Example 4.16 if

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?

### Bingham Plastic Model if

tand tyare often expressed inlbf/100 sq.ft

### Power-Law Model if

n = flow behavior index

K = consistency index

### Rheological Models if

1. Newtonian Fluid:

2. Bingham Plastic Fluid:

What ifty = 0?

### Rheological Models if

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).

### Velocity Profiles if(laminar flow)

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”

### Total Pump Pressure fluids.

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)

### Types of Flow fluids.

Laminar Flow

Flow pattern is linear (no radial flow)

Velocity at wall is ZERO

Produces minimal hole erosion

### Types of Flow - fluids.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.

### Types of Flow fluids.

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…

Types of flow fluids.

Turbulent flow, cont’d

• 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. 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

### Turbulent Flow - Newtonian Fluid fluids.

The onset of turbulence in pipe flow is characterized by the dimensionless group known as the Reynolds number

In field units,

### Turbulent Flow - Newtonian Fluid fluids.

We often assume that fluid flow is

turbulent ifNre > 2,100

Pressure Drop Calculations fluids.

PPUMP

Q = 280 gal/min

r = 12.5 lb/gal

PPUMP = DPDP + DPDC

+ DPBIT NOZZLES

+ DPDC/ANN + DPDP/ANN

+ DPHYD

DRILLPIPE fluids.

2103

DRILL COLLARS

BIT NOZZLES

ANNULUS

Optimum Bit Hydraulics fluids.

• 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.

• Nozzle Size Selection for Optimum Bit Hydraulics:

• Max. Nozzle Velocity

• Max. Bit Hydraulic Horsepower

• Max. Jet Impact Force

### Jet Bit Nozzle Size Selection fluids.

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

### Jet Bit Nozzle Size Selection fluids.- 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.

### Maximum Nozzle Velocity fluids.

From Eq. (4.31)

i.e.

so the bit pressure drop should be maximized in order to obtain the maximum nozzle velocity

### Maximum Nozzle Velocity fluids.

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.

### Maximum Bit Hydraulic Horsepower fluids.

The hydraulic horsepower at the bit is maximized when is maximized.

where may be called the parasiticpressure loss in the system (friction).

### Maximum Bit Hydraulic Horsepower fluids.

The parasiticpressure loss in the system,

In general, where

### Maximum Jet Impact Force fluids.

The jet impact force is given by Eq. 4.37:

### Maximum Jet Impact Force fluids.

But parasitic pressure drop,

### Maximum Jet Impact Force fluids.

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,