1.7 pressure drop calculations

7/30/2019 1.7 Pressure Drop Calculations

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Pressure Drop Calculations

1.7-1


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1.7-2


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1.7-3 For multiple nozzles in

parallel

Vn is the same for each nozzleeven if thedn varies!

This followssince Dp is the sameacross each nozzle.

t

nA117.3

qv

2

2

t

2

d

-5

bitAC

q10*8.311p

10*074.8

pcv

4dn D

&

Cd = 0.95


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1.7-4 Hydraulic Horsepower

of pump putting out 400 gpm at 3,000 psi = ?

Power, in field units:

1714

000,3*400HHP

1714

pqHHP

D

Hydraulic Horsepower of Pump = 700 hp


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1.7-5 What is Hydraulic Impact

Force

developed by bit?

If:

psi169,1p

lb/gal12

gal/min400q

95.0C

n

D

pqc01823.0F dj D


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1.7-6 Laminar Flow

Rheological Models

Newtonian

Bingham Plastic

Power-Law (ADE & API)

Rotational Viscometer

Laminar Flow in Wellbore

Fluid Flow in Pipes

Fluid Flow in Annuli


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Laminar Flow of Newtonian Fluids

A

F

L

V

Experimentally:

1.7-7


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1.7-8 Newtonian Fluid Model

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.

sec

12

cm

dyne


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1.7-9 Newtonian Fluid Model

Viscosity may be expressed in poise orcentipoise.

poise0.01centipoise1

scm

g

1cm

s-dyne

1poise1 2

2cmsecdyne


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1.7-10 Shear Stress vs. Shear Rate for aNewtonian Fluid

Slope of line

.


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1.7-11 Typical Drilling Fluid Vs. Newtonian,

Bingham and Power Law Fluids

0


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1.7-12 Rheological Models

1. Newtonian Fluid:

2. Bingham Plastic Fluid:

viscosityplastic

pointyield

p

y

What ify 0?

py

rateshear

viscosityabsolute

stressshear


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1.7-13Rotating

Sleeve

Viscometer


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1.7-14 Figure 3.6Rotating

Viscometer Rheometer

We

determinerheological

properties

of drilling

fluids inthis device

Infinite

parallel

plates


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1.7-15 Rheometer

(Rotational Viscometer)

Shear Stress = f (Dial Reading)

Shear Rate = f (Sleeve RPM)

Shear Stress = f (Shear Rate)

)(f BOB

sleeve

fluid

RateShearthe(GAMMA),ofvalue

theondependsStressShearthe),TAU(


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1.7-16 Example

A rotational viscometer containing a Bingham plastic

fluidgives a dial reading of 12 at a rotor speed of 300RPM and a dial reading of 20 at a rotor speed of 600 RPM

Compute plastic viscosity and yield point

12-20

300600p

cp8p

600 = 20300 = 12

See Appendix A


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1.7-17 Example

8-12

p300y

2

y ftlbf/1004

600 = 20300 = 12

(See Appendix A)


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1.7-18 Gel Strength


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1.7-19 Gel Strength

= shear stress at which fluid movement begins

The yield strength, extrapolated from the

300 and 600 RPM readings is not a good

representation of the gel strength of the fluid

Gel strength may be measured by turning the

rotor at a low speed and noting the dial

reading at which the gel structure is broken

(usually at 3 RPM)


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1.7-20 Gel Strength

In field units,

In practice, this is often approximated to

06.1g 2ft100/lbf

2ft100/lbf

The gel strength is the maximum dial readingwhen the viscometer is started at 3 rpm.

g = max,3


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1.7-21 Velocity Profiles

(laminar flow)

Fig. 4-26. Velocity profiles for laminar flow:

(a) pipe flow and (b) annular flow


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It looks like concentric rings of fluid

telescoping down the pipe at different velocities

3D View of Laminar Flow in a pipe

- Newtonian Fluid

1.7-22


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1.7-23 Table 4.3 - Summary of

Equations for Rotational Viscometer

Newtonian Model

NaN

300

Nr

066.52

300a

or


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1.7-24 Table 4.3 - Summary of Equationsfor Rotational Viscometer

300

N

or

1pNy 1

rpm3atmaxg

Bingham Plastic Model

300600p )(NN

300

or

12 NN

12

p

p300y

or

or


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1.7-25 Total Pump Pressure

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 ( varies)


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1.7-26 Pressure losses for laminar

flow.

2

500,1 d

V

dL

dP

2

12000,1 dd

V

dL

dP

dd

V

dL

dP yp

225500,1 2

122

12 200000,1 dddd

V

dL

dP yp

Newtonian Fluid Bingham Plastic Fluid


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1.7-27 Types of flow

Laminar

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

1 7 28 Turbulent


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1.7-28 Turbulent

Flow - Newtonian

Fluid

We often assume that fluid flow is

turbulent if Nre > 2100

cp.fluid,ofviscosity

inI.D.,piped

ft/svelocity,fluidavg.v

lbm/galdensity,fluidwhere

_

dv928N

_

Re


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Turbulent Flow -

Newtonian Fluid

25.1

25.075.1_

75.0f

d1800

v

dL

dp

Turbulent Flow -

Bingham Plastic Fluid

25.1

25.0

p

75.1_75.0

fd1800

v

dL

dp

25.112

25.0

p

75.1_75.0

f

dd396,1

v

dL

dp

25.112

25.0

75.1_75.0

f

dd396,1

v

dL

dp

In Annulus

In Pipe

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1.7 pressure drop calculations

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