Chuong 5h cuttings transport slip velocity

Petroleum Engineering 405 Drilling Engineering * Well Drilling Engineering Lifting Capacity of Drilling Fluids & Particle Slip Velocity Dr DO QUANG KHANH * Fluid Velocity in Annulus Particle Slip Velo[.]

Well Drilling Engineering

Lifting Capacity of Drilling Fluids

& Particle Slip Velocity

Dr DO QUANG KHANH

 Fluid Velocity in Annulus

 Particle Slip Velocity

 Particle Reynolds Number

 Friction Coefficient

 Example

 Iterative Solution Method

 Alternative Solution Method

 API RP 13D Method

Applied Drilling Engineering, Ch 4

HW #

ADE 4.55, 4.56

Lifting Capacity of Drilling Fluids

Historically, when an operator felt that

the hole was not being cleared of cuttings

at a satisfactory rate, he would:

Increase the circulation rate

Thicken the mud

(increase YP/PV)

Lifting Capacity of Drilling Fluids

More recent analysis shows that:

 Turbulent flow cleans the hole better

 Pipe rotation aids cuttings removal.

 With water as drilling fluid, annular

velocities of 100-125 ft/min are generally adequate (vertical wells)

Lifting Capacity of Drilling Fluids

 A relatively “flat” velocity

profile is better than a highly pointed one

 Mud properties can be

modified to obtain a flatter profile in laminar flow

e.g., decrease n

Drilled cuttings typically

have a density of about 21 lb/gal

Since the fluid density is

less than 21 lb/gal the cuttings will tend to

settle, or ‘slip’ relative

to the drilling mud

V V

V

Velocity Profile

The slip velocity can be reduced by

modifying the mud properties such that the velocity profile is flattened:

Increase the ratio (YP/PV)

(yield point/plastic viscosity) or

Decrease the value of n

Plug Flow

 Plug Flow is good for hole

cleaning Plug flow refers

to a “completely” flat velocity profile

 The shear rate is zero

where the velocity profile

is flat

Participle Slip Velocity

Newtonian Fluids:

The terminal velocity of a small

spherical particle settling

(slipping) through a Newtonian

fluid under Laminar flow

conditions is given by STOKE’S

s

v

Particle Slip Velocity - small particles

Where

cp viscosity,

fluid

in particle,

of diameter

d

lbm/gal fluid,

of density

lbm/gal particle,

solid of

density

ft/s velocity,

slip v

s

f s s

Particle Slip Velocity

Stokes’ Law gives acceptable accuracy for a particle Reynolds number < 0.1

For Nre > 0.1 an empirical friction factor

What forces act

Sphericities for Various Particle Shapes

Shape Sphericity

0.87

2r h

0.83

r h

0.59

r/3 h

0.25

r/15 h

Cylinders

0.73

3

* 2

*

0.77

2

*

*

Prism

0.81

Cube

0.85 Octahedron

1.00

particle

Particle Reynolds Number, fig 4.46

) d 104

4 (

Eq

1 f

d 89 1

Slip Velocity Calculation using Moore’s graph (Fig 4.46)

1 Calculate the flow velocity

2 Determine the fluid n and K values

3 Calculate the appropriate viscosity

(apparent viscosity)

4 Assume a value for the slip velocity.

5 Calculate the corresponding

Particle Reynolds number

Slip Velocity Calculation (using Moore’s graph)

6 Obtain the corresponding drag coeff., f,

from the plot of f vs Nre

7 Calculate the slip velocity and compare

with the value assumed in step 4 above

8 If the two values are not close enough,

repeat steps 4 through 7 using the calculated Vs as the assumed slip velocity

in step 4

Use (the modified) Moore’s method to

calculate the slip velocity and the net particle velocity under the following assumptions:

Drill pipe: 4.5”, 16.6 #/ft Density of Particle: 21 lbm/gal Mud Weight: 9.1 #/gal Particle diameter: 5,000 m Plastic viscosity: 7 cp Circulation rate: 340 gal/min Hole size: 7-7/8”

_ Re

Re

d82.87v

;N

40f

:3N

2 Intermediate;

; N

22

f

: 300 N

s

s s

_

)(

)(

d

2.90v

μρ

3 Fully Turbulent:

f s

s s

Re

ρ

)ρ(ρ

d1.54

v

1.5;

f

:300N

For the above calculations:

d)q.(4.104

E

1f

d1.89

v

dv

928N

f

s

s s

a

s s

f Re

μρ

Slip Velocity - Alternate Method

Slip Velocity - Alternate Method_2

If the flow is fully laminar, cuttings transport is not likely to be a problem

Slip Velocity - API RP 13D

Iterative Procedure

Calculate Fluid Properties, n & K

Calculate Shear Rate

Calculate Apparent Viscosity

Calculate Slip Velocity

Example

Calculation Procedure

1 Calculate ns for the settling particle

2 Calculate Ks for the particle

3 Assume a value for the slip velocity, Vs

4 Calculate the shear rate, s

5 Calculate the corresponding apparent viscosity, es

6 Calculate the slip velocity, Vs

7 Use this value of V and repeat steps 4-6 until the

Slip Velocity - Example

ASSUMPTIONS:

3 RPM Reading R3 3 lbf/100 ft2

100 RPM Reading R100 20 lbf/100 ft2

Particle Density p 22.5 lb/gal

Mud Density  12.5 lb/gal

Particle Dia = Dp 0.5 in

Slip Velocity - Example

V s = 0.8078 ft/sec

4 Shear rate: s = 19.386 sec -1

Second Iteration - using

4 Shear rate: s = 18.849 sec -1

Third Iteration - using V s = 0.7854 ft/sec

Slip Velocity - Example

V s = 0.7823 ft/sec

4 Shear rate: s = 18.776 sec -1

Fourth Iteration - using

Slip Velocity, V s = 0.7819 ft/sec

{ V = 1.0, 0.808, 0.782, 0.782 ft/sec }

Transport Ratio

? Efficiency

Transport

ft/min 120

velocity

Fluid

ft/min 90

velocity

Particle

: Example

100%

* velocity

fluid

velocity

particle Efficiency

Transport

velocity fluid

velocity

particle

Ratio Transport

Transport Ratio

%75

%100

*)120/

efficiency Transport

A transport efficiency of 50% or higher is desirable!

Note: Net particle velocity = fluid velocity - slip velocity.

Potential Hole-Cleaning Problems

1 Hole is enlarged This may result in

reduced fluid velocity which is lower than the slip velocity

2 High downhole temperatures may

adversely affect mud properties downhole

[ We measured these at the surface.]

Potential Hole-Cleaning Problems

3 Lost circulation problems may preclude

using thick mud or high circulating

velocity Thick slugs may be the

answer

4 Slow rate of mud thickening - after it has

been sheared (and thinned) through the bit nozzles, where the

shear rate is very high.

The End