Hydraulic transport of solids in horizontal pipelines - predictive methods for pressure gradients

Chemical Engineering Science, Printed in Great Britain.

OOW-2509/87 $3.00 + 0.00 Pergamon Journals Ltd.

Vol. 42, No. 4. pp. 767-778, 1987.

HYDRAULIC TRANSPORT OF PREDICTIVE METHODS

SOLIDS IN RORIZONTAL PIPELINES FOR PRESSURE GRADIENTS

-

* A.R.

Khan,

R.L.

Department University Swanses,

Pirie

and

.T.F.

of Chemical College, SA2 SPP, TJ.K.

Richardson

Engineering

ABSTRACT The published methods for calculating pressure gradients for the flow of coarse particles in suspension in a horizontal pipeline have been critically examined and have been Experimental techniques have been developed found to show considerable inconsistencies. for the measurement of two in-line parameters, particle concentration and liquid velocity, in order to obtain a better understanding of the transport mechanism.

Introduction Transportation Overa

long

consumption groups

to

of

between in

occur

with

but

be

measured

result

dependent

on

Transport

Mechanisms

For treated of

50

pressure

flow,

gradients

when

velocity

and

importance

within

solid

friction

with

water

required, et

alc3),

solids

in

the with

as

the

for

instance,

suspended to

by

factor

falling

for of

flow the

was them

as

between

Fluid

is

to

In

the

formation

Some

flow

where on

the

turbulent

does

not

additional

Pressure

which

was

needed

settle

out

at

case

particles

767

of

bed and

flow, the

tube

the

have

over drop to

the

work

wall.

done

has

carried

For

out

Newitt

range.

on

to the

the Particles

approximating was

sus-

when

normally

attributable

velocities

relative

mainly

pipe

been

a wide

be

flow

the

are

conditions

work

the

of

is

tur-

modelling

Particles

flow

the

to

and

studies

vary

in

concentration

simplified

bottom

be

situation

properties,

pattern

the

the

Most

important.

flow

be

shearcan

the

vertical

particle

the

tended

the

of

and

can

properties

differently (1.2)

stress.

suspension.

under

liquid

nature

conditions

bed

and,

that

velocities.

friction

significant

the

with

the

they

shear

show

for

pipe

related

wall

fluid bulk

shows

flow

behave

high

the

flow

highly

large.

predictions

turbulent

may

in is

are

the

often

reliable

for

differences

behaviour

on

suspension

rheology

4-fold

diameters

based

which

particle

medium for

but

flow

power

several

Instabilities

pipe

be

and

by

discrepancies

to

suspensions,

can

the

up

and

where

drop

serious

solids.

pipeline

pipelines.

both

considered

flow

resuspend

solid

wall

transporting

friction

terminal

occasioned

the

and

fluid,

of

influence of

the

homogeneous

flow

are

industrially

drops

studied

later,

circumstances,

those

horizontal

workers,

the

conditions,

as

all

to

practiced

pressure been

there

shown

occurs,

conditions

mechanisms

several

the

continually their

by

in

near

laminar

regarded

diameter

different out

pended

be

be

pressure

these

flow

similar

transported

of

to of

flocculation

laminar

has

particularly

plant,

rise

in

been

subject but

will

has enable

years

as

place

In

under

can

pipeline

carried

give

liquid which

attributable

takes the

if

with

particularly

forty

calculations

for

carrier

The

and,

properties.

drops

solids

past

drops

of

which and

Fluids

Coarse

the

surging

Particularly

clear.

bulent

been

particles continuum

a

procedures

confidence.

pressure

layout

non-Newtonian

of

not

a

over

of

design

correlations

that

exact

system.

thinning made

fine

as

the

the

means

no

with

and

excess

by

are

workers

results

the

solids

there

calculated

research

their

exist

of

period

related flows

to to

with

that a

bed

A. R. KHAN

768

established

that

and,

in

of

the

case

=Fr

@(s-l) V. to mixture

V.

i-i,

For

bed

flow:

For

heterogeneous

It will flow

it

is

same

time,

larger

be

dent

on

drag

coefficient

20

a wide

size

to

i-i, _ Ci w flow,

bed

for

on

their

>

-1

=

. . . (1)

const.

E

particle

results

They

therefore

small

particles

the

particle

D of particle v2 6 give ~ gD(s-1)

range

number

that

mm.

C

for

2 V gD(s-1)

at

sizes

but its

By

of

is

less

the

carrying

particles

of

for

of

by

JC, at

pipes

very

They

and

found

into

the

the of

particle?3

be

particles.

balance

in for

would

suspended

about

gravel

which

incorporating

a force

At

size

condition

for

but

Vo.

particle

large

falling

out

. ..(2)

involved,

a parameter

so

correlated

2

transportation

for

terminal

]-l

not

independent

looked

were

.

were

v2 gD(s-1)

size

terminal falling velocity (41 , who worked on the Condolios

and

particle

1

the

found

about

const

that,

in

Durand

=

suspension:

noted

sizes, than

Froude

ciw

involved

different

for

- V2

i-i, would be a function of the modified Froude Group, Ciw of the ratio of terminal falling velocity suspended flow,

they

velocity

eral.

depen-

chose that

the

results

the

modified

terminal

falling

velocity

c

4 3

2R= 2

=

D

dg

2

(s-1)

OVO

=

dg

K

small

on

particle

particles

proportional

to

Results as

is

no

C

longer

been of

between in

of

given

Figs.

in

V2 gD(s-1) should

line

(25mm

used

only

(SRC) to

work

give

?zz C noted

diam.) one and

a wide

is

as

as the

cover

material

of

the

Solids

liquid

the

cases

of

(3)

. . .

<4)

a very

wide

Abbott

the data

noted

that

the

range

by

different were

sizes

with

after

of

Ci, this

simplified

so

far

model by and

or

no of

discharged

whereas relation

shows

is

that

incorporating this

account

procedure

has

been

taken

theaonsequentdifferences

mixtures.

discharged

and

and

from

For the

results

pipe-line.

i-iw as c

and

ranges

which, their

their

are

refer

diameters. the

(= $1

as

a

W

of

results

is

to gain access to the i-i as J (=Y) as a function iW

shown

Turtle")

particle

on

is

Water

sizes)

use

V.

that

formation,

v= 6 ____

operating

coal

dependent

i-i, as -

shown

is obtained

solids,

the

suspension

The (8)

is and

CgD
recalculated

(5-11). of

of (12)

bed

expressed their results V2 = and a selection gD
been

CD

(5,S,7)

have Fr

Figs.

particle

with

though

in

and

been

evidence

versus

to

and

in

results

work

be

dL

applicable

frequently

l-iw iW

Transported

have

(limestone

Gaessler's

should

workers

in

even

to is

considerable

plotting

measured

results

(=X)

. . .

size.

transportation

pipeline

number,

that but

range

for

region

have

. .

It of

particle

is

of

proportional law

representation

and

the

is

solids

flow,

better

In those

data,

for

paper.

Froude

(l-4).

C

number

previous

modified

be

there

heterogeneous

Results

cases,

experimental

However,

velocity

C

of

coarse

to

Vo

Newton's

of

within


most

function

It

relative

Workers'

In

of

this

region

independent

much

Froude

in

Figs.

Previous

raw

for

concentrations

shown

law

particles,

is

v2 Jc3

modified

the

Stokes

___ gD(s-1)' proportional

A very

adopted

0

transportation

so.

for non-spherical particles characteristic dimension d

v 2

large CD

applicable

the

either

of

be

into

has

&and

directly

it would

the

For

for

a function

i-i,

in

size.

a sphere

v0

(s-1) For

for

given

only

to

James

Saskatchewan

because equipment.

of

its

in Table

2.

a small

pipe(10)

and

Broad

Research

Council
friability,

The

results

degraded! of

Transport

Chhabra

and in

pipe; Some

addition,

they

consideration The

i-i to 2 Ci Richardson(5)w approximately slope

that

X = 40 The

a slope is

of

value

note

low

not

with

and

that

were

of

mean

slope bed

results.

difficulty

of

at values

flow

is

at

X =

raises

knowing

10%

of

the

(10)

results show

flow

1.

As

how

to

it

apply

for

low

All

the

were

shown

a-fold.

is

noted

that

In to

the

for

suspensions and

constant for the

pipe,

particles

is in

in

and

Fig.

is

Chhabra

as and

seen;

to

35

for

the

(S),

authors

data

for

pressure

of

as

apparent

this

For

X <40

suggested

line

the

use

again

value

has

of

CD

a weighted

(shown

solids

by

pecked

line).

a wide

range

with

larger

drop

limestone

at

high

is

in

particles

values

many

at

of

cases

X.

This

only

that

the

show

slope

line

excess

occurs were

noticeable

the

a large

used,

the

5;2,6)

considerable

is

-1

at

drop

of was

the

less

X = 40. obtained

Abbott's which

but

proportion

pressure

both

in

scatter,

on

work,

the

and

is more

same

Turtle's

characteristic

of

of

method for (14)

high

X,

of

correlation,

similar

line

values

this

more

of

of

Y

but

can

slope show

because

conditions

confirms

so

viscosity pipe

pressure

coarse

s

be -1

said for

a spread

some

of

obtained

condition,

the

with

high

walls

than

X < 40

of

the

by

stating

Reynolds

water.

Shear-thinning

and

where

a wide

up

to

biggest

different

"each

the

settling

rates the

low

are

pipeline

a bed

formed

could

shear

approach

are

not

the

fluids

be

were taken

and

as

approx-

are

highly

near

the

Centre

of

the

suspended

viscosities

excessively pipeline:

shear

frequently

fluids

apparent not

of

solutions

numbers

region

velocity high,

in

range

polymer

factor

In the

in

in

friction

shear

gradients

conditions

The

particles. fluid

particles. is

particles shear-thinning

viscosities,

floculated

coarse

for

the

Little a

results"!

experiments

the

11. by

of

transported

of

the

the

in Fig.

represented

Fluids

fine

Near

low.

of

value

Verkerk

laminar,

in

not

best

results

set

liquids

transporting

shown

of

the

paper,

flow

at which

in

assembled

be

a given

because

consequence

It was

At

Richardson(')

thinning

the

to

Transporting

and

X

(Figs.

slope

are

data

a different

very

and

<40

particularly

excess

of

is

= 40,

The

results the

a recent

Newtonian

suitable

40

7)

X.

between

including

imately

of

not

Other

values

results

at X

X > 40.

is

give

Chhabra

low

X

value

mainly

scatter,

a transition

X > 40.

for

are

workers.

Results

to

high

Turtle's(')

values

Is

This

very

transition

for

discrepancies

appears

about

of

suspension. <13) have

the

interpret

obtained

a considerable

Again

available

trend

1, 1.5

at

and

all

of

results

(Fig.

Govatos

to

intercept


patterns.

However,

the

+

the

X of

and

diameter

section.

water

total.

The

the

in

a 42mm

a later -

heterogeneous

two

in

in

2

predominantly

size.

gravel

gDl;s_l)

of

Zandi

the

relate 15

to

-1.4.

between

particle

1) which

obtained

results

low

intercept

Table

when for

results

the

the

transition point (11) for coal all

and

Abbott's")

and

of

of

described

alone. (Figs. 3,9). (12) Gaessler's results with coal (Figs. 4, 10) also -3 the low density (1290 kg m ) and high concentrations

equipment.

that

from

Broad's

surprising of

results than

of

slope

an

set

as

769

sizes.

concentrations

lo-20%

a change

a Sauter

each

fluids,

as i-i, (Y) versus iw 1) is clearly seen
transition

has

the

to

transport

to

of

pipelines

results

X >40,

below

underlines

James

is

and

given

for

the

using

particle

(7)

relating range

the

results

-1

(see

This of

marks

SRC

be

V2 gD
In Fig.

and

those

a wide

plotting

versus

-1

calculated

now

of

marks

is

were

used

will

advantage

opposed

the

(5,6)

Richardson

of solids in horizontal

great.

Of coarse

are

A.

770

R.

KHAN

et al.

i-i w=

where

fL

. . . (5)

const. i

w

is

the

Some

results

best

represented

friction

are

factor

shown

in

by

equation

an

for

Fig.

12

the

with

of

same

flow

rate

i-i _fL 2 C iul form:

the

of

the

plotted

liquid

alone v2 gD(s-1)

against

in

the The

.

pipe. results

are

i-i w i shown The

as

pecked

line

includes

some

order

in

a

Need

In

in

a

on

common -

given

inherently on

flow

where

in

the

the

situ

more,

the

able

under

for

that

rate. on

drag

which

thus

continuous

line

(15)

the

use

out

further

seem

of

.

a

drag

coefficient

study

appropriate

of

phase

two

that in drag

the

of to

the

CD

for

settling

express

conditions

In

pipeline

the

and

of

results

as

the

is

taken

of

the

have

been

made

taken

the

into

relates of

the

to

to

of

the

prevalent

account.

been

under the

installation

under

The

For in

cond-

flow.

used

is

been

the

particle

particles

and

effect

of

lower

that

applicnumber

to

energy

particle

than

Further-

Reynolds

relative the

the

be

the

has

liquid

Parameters

example,

general, of

the

substantial

has

occur.

nature

which

operating

-

gradient

layout

will, the

expressed

of

velocities

pressure

may

which

been

range

attributable

properties.

velocity on

of

of

determines

drag

a wide

particularly

particles

investigators have

and

partly

piPeline

be

therefore

hydrodynamic

account

is

the

mixture

is

and

values is

external

the

principal

cases

effect

which

which

it

the

to

the

interpretation

properties

actual

of

all

for

all

This

and

discharged

coefficient

the

the

needs

are

pipeline

in

four.

c:rcling

factor

of

liquid

flow

results

the

similar

to

of

capable

blockage

falling

no

up

for

in

results

form

between of

the

a

are

factor

important

determines

Furthermore,

by

carry

would

in

full-bore

of

the

terminal

the

transfer concentration

coefficient. Very

because

of

a

Kenchington

size to

Properties,

the.tendency

is

condition.

particles

a

concentration value

of

experimental

discrepancies

another

concentration

in

particle

by

correlation

solids

the

trenas

momentary

However, used

It

general

the

and

even

particle

were

nature

stability

itions

as

V2&D gD(s_l)C

section,

vary

results

necessary

fluid.

diameter,

unstable

is

gradients The

conditions

of

it

against

previous

pipe

shown

Measurements

pressure

However,

covered.

account

plotted

form.

variables

2

is

. ..<7)

fluid,

In-Pipeline

5 -1

gD(s-1) -1 I_ experimental

non-Newtonian

the

data

take

the

fL

for

equation V

to

in

i-i w i w

whose

with -

also In

The

conformity

0.30

particles

(6)

-

L

fL c=

particles

... gD(s-1)

line.

in

-1.25

0.55

i-i w i w 12

the

V

C

w

a

best

Fig.

f _=L

2-

of

few the

regarded

as

pressure

gradients. In

attempts

experimental

necessary

the

present

for

difficulties the

work,

development

the

following

previously involved, of

to and

practical

variables

measure partly formulae

were

the because for

measured:

in-pipe they the

parameters, have

estimation

not

partly been

of

Transport

1.

Mixture

2.

Liquid

3.

velocity

V,

using

an

velocity,

VL,

using

a salt-injection

In-line The

concentration

following

Cx,

dependent

electromagnetic

using

absorption

can

Superficial

liquid

velocity

VSL

=

2.

Superficial

solids

velocity

VSS

= V

3.

Mean

velocity

flowmeter method.

a y-ray

parameters

1.

then

be

Velocity

4.

of

Volumetric

5.

VS

liquid

relative

discharge

=

to

method.

calculated:-

(1 - C,)VL - VSL

= V

-

v solids

771

of solids in horizontal pipelines

vss'cx

the

(1 - C,)V,

=

. ..
cx

particles

VR

= VL

V SS C = -___

concentration

. . (9)

(1 - C,)VL

=

- VS

1 -

vLv ___ C.. n

=

(1 - C,)

. . . (11) ...

$

vss + vsL in

If, the

results

add,ition,

can

be

measured

by

and

then

draining

was

used

only

one

collecting

the

weighing

liquid

a check

dependent

In several

and

the

as

of

checked.

samples

before

of

variables

also

experiments of

weighing

consistency

the

the

and

the

not

is

mixture

residual

the

consistency

concentration

obtained

The

time

sampling

measurement

for

of

C was

a known

over

solids.

a primary

as

measured,

discharge

period

technique

the

following

reasons:1.

It

is

flow 2.

It

removing

analysis

Methods

The

equipment

concentration) The

piezometric means

an

and

of

outlet

y-Ray

and

of

the

the

perticulsr3y

accurately,

at

high

large

solids

which

is

when

using

liquids

enough

to

upset

the

hold-up

in

solids"'). between relation through

permit (also

Centrifugal the

of

high

viscosities

media.

measurements delivered

of

mixture

flow

concentration

as

rates,

a check

mean

of

liquid

in-situ

in

and

with

over

Grit

electrical

13

Fig.

system,

consists

pressure

a 4.57m

Pump

with

long speed

Mixture

supply.

test

a 38 mm

diameter

measured

by

rates

could

means

were be

pipeline

using

a

Circulation

section.

controlled flow

concentrations

discharge

of

gradients

of

measured

obtained

by

was

a frequency by

means

sampling

of at

pipeline. has at

mean

now the

been mid

fitted

for

absorption

the The

flow

of

of

of

the

between

and

incident

a thickness

Measurement is

and

x

of

based

on

absorptivity

and

medium

system

absorption

section

that and

mixtures

therefore


a y-ray test

and

a salt

for

measuring

injection

method

in-situ for

liquid.

method

in

gas

the

Holdup

liquid-gas

difference

liquid

with

point

linearvelocity System

y-ray

to

manometers

flowmeter

equipment

The

passed

the

conveying

schematically

U-tube

on

the

circulating

a Vat-Seal

Absorption

that

out

gradients.

shown

concentration

measuring

The

pressure

(inverter)

solids

carry

difficult

as

designed

a continuous ring

The

of

was

electromagnetic

the

of

impracticably

concentrations,

apparatus

as

changer

to

a proportion

suspensions

in-situ

velocities,

by

is

particulate

Experimental

arranged

difficult

conditions.

Sample or

and

rates.

involves

flow 3.

time-consuming

used

subsequently

between a higher

for

solids

and

precision

of

emergent

(I)

is

by:-

given

previously

intensities

(16)

for

vertical

liquids

is

measurement after

the

the

determination

transport far iS

less

Of than

required.

radiation

has

A. R. KHAN

772

where

JJ is

a coefficient

An the

Americium

241

produces

pipe,

beam

passes

whose line

a beam

vertically

value

which

is

upwards

counter

(Harwell

counter

system

the

The covered

by

assumed. taken.

equipment

is

the

y-ray

beam

For

each

mixture

of

concentrations Using

tion. an

accuracy

A pulse in

velocity by

opening

of

solution

above

the

then

is

injected

was

distances

a

the

system pair

the

of

is

produced

to

peak'

as

the

first

of

to

height

settings.

cross-section

of

of

20s

for

iS

was

a particle/

a range function

could

pipe

duration,

containing

a linear

is

the

be

of

particle

of

concentra-

predicted

within

and

the

of

detected

The

ms

during

maintained

the

first

electrode

with

of the

the

time

been

pair

salt

electrodes

is

is

2 cm3

2.5

bar

to

0.46

solution

injected

about Of

found m

over

terminating

the

the

pulse

a pressure has

by

apart;

salt

which

at

configuration

dispersion

downstream

distance

pulse.

20

is

is

a known

be

such

and

between

the

cross-

at

different

in

a BBC

micro

every

10

a digital

each

electrode moment'

to

it was

The by

to

of

adopted

0.6%

for by

and

all

2%

the

calibrate

moment

3%

may

each

a func-

calculated

on

software. the

salt

injection

were

made,

as

between

solid

with

a value

present.

accuracy

of

and

method

consistent

with

solids

the

be

computer

results

but

been

converter

concentration

the

with

has

digital

salt

measurements

first

and

to

velocity

measurements

between

injection

interval

of

differential

necessary

of

time

means

Peak-to-peak

typically

the

analogue

A plot

pair.

the

once

An

form.

basis

obtain

values

and,

ms.

of

a

0.3%.

Results

the

flowmeter

had

been

used

previously

by

Newitt,

Richardson

and

Shook

(18) .

Their

scatter.

Results the

mixture

present

velocities of

mixture

experiments

difference

was

work

gravel

and

particle

velocity

carried

concentrations C

through

'first

flowmeter

considerable

In

(CX)

pulse

to

+2%.

Experimental

'which

to

a

was

showed

little

each pipe

be

the

axis

measured

to

line

of

optimum

of

for

mean

method

made

point

flowmeter.

A similar results

time

measurements

possible,

method

the

was

pipe

vertical

of

situated

which

uniformity

required as

the

moments from

only

was

the

the

by

The

long. connected

gatewidth

concentration

the

a period

The

injection

electromagnetic

error

differed

is

it

for

reservoir

making

into

travel

air.

stored

and

accurately

found

electrodes

alternately

be

time

standard

For

to

of the

the

operated

sampled

output

of

and

beneath

wall.

'peak

against

been

pipe is

is

Because liquid

pairs

The by

rate

1-1was

23.5mm

a detector

accepted

measurements,

count

and

on

situated

Determination

injected

valve

the

half

particle

Velocity

from

m.

ascertained

The

tion

two

from

from

in-line

is

compressed

2.75

from

electrode

both

by

pairs

enables

Liquid

solution at

one

length

and

volume.

determined

distance

section

of

for

salt

atmospheric

that

was

Method

threshold

medium.

block

wide

pulses

small

the

received

about

ten a

The

the

by

of

l.Smm

is

the

exactly

using

of alloy

The by

coefficient

a solenoid-operated

electrode

The

cent

a slit and

symmetry

a mean

calibration

conductance is

that

out

the

bed;

1 per

of

so

horizontal

carried

by

6000).

concentration.

the

this of

Salt-Injection

change

was

known

in

arranged

nature

a tungsten

pipe

controlled

determination

Calibration

water

Series are

and

the

the

by

collimated

through

a scintillation

upon

shielded

source,

analyser

in

depends

PI al.

measured

V,

out

at

between

V

should by

particles

concentrations. mean

high and

V

correspond

collecting

(3.5s~~)

liquid

In

velocity

velocities,

the

Under

these

L'

closely. a

sample

have

a

pipe

all

VL,

transported

in water

experiments

and

particles conditions

Several at

been

in-line are the

measurements concentration

fully

suspended

delivered

experiments

discharge

whilst

at

were Cx

(C)

carried was

a range have

C

X' and there and

in-line

out

in

obtained

Transport

simultaneously was

from

a maximum For

a furction tal

of

liquid-solid

be

of

also

of

_ V =

14,

dependence

c X that,


which

is

o.08

delivered

as

pipeline

in-line

increased would

the

solids

different

following

the

two

mean

liquid

values

velocity

concentration types

scales this

VL

cX

for

are

size

(1 - CX)

b were

of

C

so

obtained

VL

must

The

X'

equation,

the

negative

the

that

V

was

velocity and

be

experimen-

most

satis-

L

difference

c positive.

- V must

Gauss-Jordan(20)

relation

method

The

be

zero

when

to

determine

from

con-

the

obtained:

. . , (14)

equation

four

equa-

the

-1) (14)

different

are

compared

mixture

with

velocities

experimental is

seen

values.

in Fig.

15

used).

in water,

C

C

the

(ms

of

C X decreased,

if

condition

using

CXo.27

on

so

limiting

the

- V

and

be

By

concentration

C=l-

and

several

zero.

values

of

V

the

V-o.e4

VL

gravel

the

between

. ..<13)

satisfy

logarithmic

For

in

V

using

this

a,b,c,

of

system

analysed

predicted

The

difference

volume.

velocity

less;

solids

values

The

773

form, C

become then

vL

give

the

expected

centration

In Fig.

been

of

- V would

optimum

of

- V = aVb

would

by

mixture

being

It would

cent

a given

have

vL

"L tion

1 per

measurements.

only

results

factory

y-ray

of solids in horizontal pipelines

as

equation

a function

(1 + 0.08

V-1*64

14

can

._

of

C,

CX0.2T)

and

be

substituted

mixture

into

velocity

equation

12

to

V

...

1

(15)

i.e.

1-c -= l_CX

(1 + 0.08

This of

equation

delivered

ties ted

of

where

internal

13,

solids

a range

C

C X has

equation

the

for

permits

concentration

Chhabra('), In

v-l.64

not

the

for

calculation

and

mixture

been

the of

in-line

V

for

concentration

experimental

C

data,

as X such

a function as

that

of

experimentally. will,

density),

results

the

velocity

a,b,c,

systems

the

of

measured

shape,

different

parameters

the

constants

(size,

of

CX0.2T)

and

in

general,

liquid

results

(rheology

can

previous

be

then

be

a

function

and

of

the

density).

applied

to

proper-

When

evaluate

evalua-

the

workers.

Discussion The tures when

in

review

pipes

obtained

of

mechanisms. absorption

results as

the

have

have

a function possible mixture eters models

of

of to

can

of

be

of

liquid

studied

mixture

as

of

the V

studied,

it

properties

conditions developed

will

flow of

of

liquid-solid

different

therefore

a better

decided

has

in-situ been

mix-

workers,

understanding

of

injection

and

be

possible of

of

the

in

their

studied

to

in

liquid

to

make

of

the

even

flow

concentration

established

express and

CX

the

the

in

and

concentration

solid

previous

conveying

solids

between

in-line

concentration

the

salt

lin.uids

and

results

applying for

It was obtain

the

results

measurements

difference

physical

delivered

to

direct by

for

between

by

under

the

far.

velocity

the

order

velocity so

gradients

conditions.

making

the

and

pressure

in

mixture

expressed

recalculate

the

discrepancies

been

velocity for

on

parameters

particular

been

a function

systems

and

work wide

similar

feasibility

conditions

For

very

nominally

in-pipe

The

particular

previous

shown

under

measurements

y-ray

of

has

parameters

who

order

evaluate

experiments. process.

At

research,

have

that

velocity

(equation

14). in

It will

liquid

workers, to

the

mixture

the (VL

equation then

- V)

When

other 14

be

usuallv

measured

only

all

in-line

param-

the

stage,

new

physical

as

774

A. R. The

sities

future

programme

conveyed

of

work

in Newtonian

includes

fluids

and

in

A.

Canad.

KHAN

et al.

a study

of

particles

shear-thinning

of

polymer

different solutes

sizes and

and

den-

suspensions.

References 1)

Wilson,

K.

C.

and

Thomas,

2)

Heywood, N. I. and Cheng, Trans. Inst. of Measurement

D.

D.,

C-H. and Control,

3)

Newitt, Trans.

D. M., Richardson, S. I. Chem. E. -33 (1955).

4)

Durand, R. and Condolios, E. Proceedings of a Colloquium on London (1952), Paper IV.

F.,

the

R.

P.

and

Richardson,

J.

6)

Chhabra,

R.

P.

and

Richardson,

J. F.,

7)

Babcock,
H. A. : in Advances Press, 1971).

8)

Abbott,

9)

Turtle,

Ph.D. Thesis, The Hydraulic

R.

B.,

in

F.,

Ph.D. Thesis, The Hydraulic

M.

539.

33.

Transport

Chem.

(1985)

Turtle,

and

R.

B.

of

Coal,

National

Eng.

Res.

Des.

-61

Cheat. Eng.

Res.

Des.

83.

(1985),

in Pipes

and

its

Solid-Liquid

University Conveying

(1984)

No.1

Hydraulic

Chhabra,

Em.%. -63

Chem.

5.

Abbott,

5)

M.,

J.

Flow

of London of Solids

University Conveying

10)

James, J. G. Supplementary

Transport and Broad, B. A., Report 635 (1980).

11)

Haas, D. B., Saskatchewan

Gillies, Research

(1955) in Pipe

313. 300.

Applications,

(1952) Material.

and

Research

R., Small, M. and Husband, W. H. W. Council publication No. E-835-l-CSO,

Laboratory,

March

1980.

12)

Gaessler, H., Experimentelle und theoretische Untersuchungen uber die gange beim Transport van Feststoffen in Pl&sigkeiten durch horizontale Dissertation Technische Hochschule, Karlsruhe, Germany. (1966).

13)

Zandi.

141

Verkerk,

15)

Kenchington, FRG) (May.

16)

Heywood,

17)

Al-Salihi,

18)

D. M.,Richardson, Newitt, Institution of Chemical London <1962), 87.

19)

Carnhan, "Applied

I.

and G.

N.

Govatos,

G.,

Bulk

J. M. 1978). I. L.

G.,

and

J.

Solids Paper

in

Div.

Handling, D7

Richardson,

Work

Hydr.

Amer.

2

(4)

Hydrotransport

J. F.,

progress,

Chem.

Civ.

93,

801.

5

Fluids

Engineering,

(BHRA

Sci. of

C. A. 'Interaction

(1969).

-34

<1979),

145.

Hanover,

17.

Swansea.(for

between

StrzmungsvorRohrleitungen,

(19671,

19851,

College

S., Luther, H. A. and Wilkes, J. 0. Numerical Methods", John Wiley N.Y.

Engrs.,

(August

Eng.

University

J. F. and Shook, Engineers Symposium

Sot.

Board,

Lines.

of London of Granular Road

(19831,

Coal

Ph.D.,

Fluids

and

Univ.of

Wales).

Particles',

Transport

of solids

in horizontal

pipelines

775

Symbols Fractional

C

volumetric

concentration

8

Ratio

V

Velocity

of

solid

to

liquid

density

(delivered) cD

In-line

cX D

Pipe

d

Particle

*L

V

diameter diameter

Fanning

Friction

igD (-1 2v gravity

Acceleration

due

to

I

Intensity

of

transmitted incident

Io i

Intensity

of

Hydraulic

gradient

i

Hydraulic

gradient

K

Coefficient

n

Exponent

R'

Force per particle

in in

relation

relation

unit

vsL V

radiation

ss

Y = K Xn

velocity

Velocity

Superficial

liquid

velocity

Superficial

solids

velocity

JC D

V2

X

water

falling

Distance

x

radiation

for

Solid

mixture

velocity

Terminal

0

vS

Factor

of

Liquid

vL

concentration

g

w

(ZR’/pV2)

Drag coefficient for particle at terminal falling velocity

gD
c

Y

(i-i,)/i,

P

Fluid

p

Absorptivity

Fr

Modified

Y = K Xn

projected

area

of

density to

Froude

radiation V2

no.

gD
TABLE SUMMARY

OF

Y -

Worker8

Hewitt

Ref.

et

Turtle,

al. Abbott

Chhabra

and

inc.

I

PREVIOUB K.

Particle Range

1180-4500

3,839

*In

the

Size mm

Pipe Diameter8 mm

0.02-5.97

2650

30

2700

5,10,20,40

102,158,207

1200

1.75,3.2,4.2 5.2

80,115,160

11

1.8-2.8

110,100,ae0

1370

mixed fines

referencea.

37(S) 65(S) X<<4O)lb

X~(4O)llS

I

Rem.

K

25

3,5,S

I Saskatchewan Council

RESULTS

Xn

Particle Density Range kg m-3

5

Riahrrdmon

1

the

value

of

where CI,i 1~ the value corresponding coal degrade&, it '188 felt that the

C

D

calculated

for

554

X<<40)111 x~(401102

1%

with

the

35

multisized

system

from

to the veight fraction xi on each screen. fines were making too great a contribution

the

on

P

-1

-1 -1.4 -1.5

-1.0 9 -1.7 -1 -1

relation:

Becaune the thi8 basis.

A.

776

R.

KHAN

et al.

x

t

2.m

a/s

x

3.85

n/s !+rspax

10”

10-' Fig.

,

1

Results for

of

lo-”

a i

a

t

Q

i

d .

1,50”

x

1,1P,**

10”

J

y-,/8”

1oa

IO3

2 Results of Turtle (9) for 25mm pipeline for range of particle sizes and densities d

Chhabra and Richardson in 43 mm pipeline

p-rive1

Y

%

+

!

f

I

e

I

1OU Fig.3

10" Results

Of

limestone

Fig.5 Results

James

and

Broad (lo) for <5,10,20,4Omm)

(6)

in

particles

of

Abbott

IO”

lo-

25mm

pipeline

Fig.4

1 oz

(12) %eeults of Gaessler for particles (1.75,3.2,4.2,5.2mm)

Fig.6 Results pipeline

of

Turtle

G,

in

25mm

coal

Transport

Fig.7

Results

of

Chhabra

and

of solids in horizontal

Richardson

(5)

Fig.8

777

pipelines

Results coal in

of Haas et al'll) for 110,160,260mm pipelines

Results

for

70?

107

lo?

lo+ Fig.11

IO" Comparison different.

10% of results workers

lo=

of

Fig.12

non-Newtonian

fluids