Prediction of the diffusion of discharged brine by a simulation analytical method

D~Iizatin.22(1977)91--100 0E&vierScientifichb~ingCompmy,

91 Amderdam-RintisIinTheNetheriands

PREDICTEOB OF THE DIFFUSION OF DISCHARGED BY A SIHUGiTION ANALI-TICAI,,METHOD Akira

Naoaki

WADA**,

and

KATANO*

Tztaro

BRINE

GOTz**

Central Research Institute of Electrfc fowzr Industry, 1646 Abiko, Abiko City, Chiba Pref., Japan ** National Chemical Laboratory for Industry, Ministry of International Trade and Industry *

As one of the countermeasures brine on the surrounding be adopted

for the purpose

and surrounding brine

water.

fn order

the mixing

to grasp

outfall

the effect

in the sea. sutnerged

of promting

in case of subnerged

oceanographical

for minimizing

environment

action

the nixing

system,

the nixing

in reference

to different

is also necessary

to establish

the predictive

systexz may

of discharged

process

condition

of the discharged

outfall

water

of the discharged

processes

discharge

under

various

conditions

uust

be grasped.

It range

caused

models

and

outfall

by discharged

to examine

systen

salinity brine

change.

of the hydraulic The content and continuity

of numerical

of matter

can be changed

the 4sfluenced

range

pipe

method

analysis

govern

of the equations

the flow phenomena

the heat and

system

with

the

that

It MS

concluded

brine

of notion and the equa-

the salinity.

vas adopted

as a drain method.

brine at the plant where

Vito the fresh uater of 100,000

by the discharged

has been

rise and

for the discharged

of the predictfve

value of the discharged

was conducted.

models

temperature

the field surveys.

regarding

discharge

in the submerged

using numerical

is couposed

which

diffusion

and hydraulic

countermeasures.

range of mter

and

mdel

of hydrodynmics

analysis

analysis

the results

rzodel expertients

of the project

concrete

of the

mdels

for the facilities

of the prediction

comparing

The mono-vertical

the sea rater

various

the diffusion

Adaptability

tion of conservation

On the basis

guidance

a nev simulation

for predicting

is discussed

skwlation

a project

so as to establish

In this paper, developed

method

brine on the basis of nunerial

&/day.

fron the results

a that

was not wide but very local-

Generally,

the behaviour

called

the jet or plme,

source

3.23called

initial

spsren

2nd

descrfbed

compared

in this paper

belongs

(posftive fluid)

ambient

fluid,

vater

pattern

the mmentum

ambient

called

acts

or negative

density

As regards taken

certain

the vertical

against

and horizontal

theoretical

of entrainzeat

Since

the plume

computation

In fundamental

reaches

the static

step to carry fundaneutal

calculations,

it reached Mter

tion of tmtion,

region

fluid and in the con-

jet,

the water

to increase

discharge

cmditions

vfth a

the dilu-

there are vertical.

in a uniform

and water

out

surface

of flow on

of a similarity bottom

three-dimensional

can be

only

or water

were

the

(or density)

can be applied

calculations

fluid,

the velocity

on the basis

surface

vater

numerical

the outlet

analysis

up to

bottom.

In

dlffus5on

conducted

to establish

density

of

daiaanc

Results of

and

the

of the equa-

of conservation

equations,

with

to obtain

consisted

was conducted

experitlents.

and concentration

of discharge

or sea-bottom,

as an object, mdels

and the equation

of hydraulic

on the bs~s

to the behavior surface

Eiucericdl analysis

by the use of these

of velocity

paid

The numerical

equation

vas made

I MS

to the rater

a uniform

of jet.

salinity,

the results

distributions

the plume

hypothesis.

having

continuity

on ht?at +

radial

from

characteristics

Eade with

in

buoyancy

method.

similarity

substance

=S

in which

however,

solution

the

In numerical computation, attention

diffusion

the direction

discharged

in order

obtained

of the water

the analytical

as the first

the aforementioned

jet until

with

of discharging

of

are generally

and computation,

the so-called

The plume,

jet,

of varm water

direction,

pipe

a large density

from the jet source , concentration

no boundary

in which

this research, prediction

having

stratification

and is %tatroduccd, f

coefficient

in this theory,

the prdcess

between

direction

development

with a distance

and the width of the plume

considered

As far as

dfscharge

the direction

direction

discharge

jet.

besides

directions.

the plt~~e axis

hypothesis.

difference

into the method

As a typical

In the usual concept

jet varies

direction),

is

in the jet

In the jet condition.

of flow and density

sS.deratfon is usuaLfy engle

the fluid

of the gravitational

the discharge

the fluid

the plume has buoyancy

by the underwater

of gravftationaf

(discharge

into

has no buoyancy

the gravitat%.onal

brine

is discharged

or the existence

tion efficiency.

discharged

is concerned,

to t,he category

The diffusion

acts

also

is

of discharged

with ambient

therefore,

which

it

pattern

flov which

On the otfter hand,

the let.

momentum,

the discharge

of a rapid

The jet street

of

on various cor;parison

for axFaX

the savitatfonal .

end pkmo

93

showed

exceLlent

agreeuent

tith

tzhere are sane exceptions. are

finally

produced

in flow velocity,

to obtafn

and salfnity

hydraulic

experinents,

generai-purpose

along

ceneral

of

approxCm%tion

though

cafcullatim

and Che values

for the calcuIarion

technique

is an Euletian finite-difference

flow

of

t&x,

the jeC trajectory

tmperaruro-

The fundamntal

the results

At the same

charts

of reduction

axis of the jet.

incanpressibfe

turbufent

to the Hav@r-stokes

equa-

tions

*+

acd the uass

where

is the density,

P

= 0 *

- g $G+J~ 0

i

+ Ah

Kj

ratio

(= P/p>,

zero,

t

equation

g is the gravity

irz the j

respectively,

state

S is salinity

LIP is

point

primarily used

is

tenperature.

dtiference

which

the he.?t and tile salinity

equations

m order

governing

convection

+up$za_(_iFi_Lj the

density, cozsma

corresponds

P

ax3

3

K.J are

Emundary

my

of

an

in which

of conserva-

be stiultaneously

the effects

density.

plune,

buoyancy.

salved The

of teuperatttre T and

and diffusfon

are ass-d

to

eddy therrml

to a nonconducting

cons&srs

equations

~fl.u.encc

of
cttc

the addition

(3)

%

condition

3s heat caa be uided at the outfet

the

reference

is

s

The most

&$ch

td simulate

undisturbed

has the form, p = p(S,T)

regarding

equation

between

In this case, an equation

the fluid

differential

conportent

for i=3, otherwise

uith disci-mrged brine

of atter

p is

(1)

and the vertical

p. is the effluent

in the plume,

for sea water

add T ater

the density

t&m

-35

-e

and directfon

631 is unity

with

saltiiry

A,

th dfrectioa, Q is the pressure

deceleration,

this r;;ork is concerned

af

+

3

Uf and XI are the i th velocity

are the eddy flux

aad an afiitrary

Since

vhich

Ui

is tine, Ab and AZ are the lateraf eddy viscosity

eddy viscosity

vhese

V2

equation

respectively,

ubient

(Ui Uj)

$&

diffusivities.

on the density

vafl sectfa.

or a pfane

of

The effect

fluid rzotions through of bzroyancy tefdls

is that oP zero syzzetr~of

flux,

Sources such

densflty vartitfon

a Boussfnesq

to the right

approx&ation, hand sides of

94

the turbulent

Since

are functions mean

coefficients

field,

these quantities

of the flow

Here,

flov properties. The coefficient

for wncntuq

trausport

Prandtl's

nust

hypothesis

for eddy viscosity

Ai (i = 1,2,3),

be related

to appropriate

to pbme-

is applied

is set as follovs.

A-C&bx

where

;4,

2 is the nixing

length,

This

radius-

mdeling

sax

is the plme length

The nlxitg

constant equal to 0.0256.

seems

2

a f+rst

to be only

centerline is

equal

velocity

to

y+.

to

approximation

and C is a

the plune

half-

the real

situations. The nuaaericai procedure with

the auxiliary The density

salinity. of

sea

water

at

Do,

gravity

O”

CUO)

the specific

of solving

appropriate

p is related

result,

(I), (2) and

turbulent

oodel

the temperature relation

(3). along to evaluate.

and

between

the

the density

CR (&,) holds.

CE - 0.001570

gravity

with

the following

and chlorinfty

+ 1.4708

anomaly,

CR2 c 0.0000398

is defined

CR3

in terms

(5)

of the specific

So by U,J = 103 (So - 1).

On the other

hand,

s = 0.030 + 1.8050

my

is consisted (41, and

of the water

From Kuudsen's

ug = -0.069

vhere

equation

be used generally

the following

sFnple

eqxatlon

CR

(6)

for the calculation

of the salimity

(s)

for

the

chlorine

content.

The specific

gravity

znonaly

IS= is

expressed in terms of tmperature

and

up in the form

uT = CT + ((Jo+ 0.1324)[1 - SL,+ BT (~0 - 0.1324)] where

AT and BT are functions &T'

(T5-33;g)* .

CT

=

+

= T (4.7867

BT

c

T-f- 283 T + 67.26

- 0.098185

= T (15.030 - 0.8164

of temperature.

T + 0.00108G3

T f 0.01667

T2) x lO-3

T2) x 10-6

(7)

95 The

set

of

ia

region

sjlall

respecr to this

at cell

faces

set of

A tirco-dependent

and the previous does

in stage

leGd to a velocfty ;in each cell is

temperature

eo acquire NuzieriuL

research

is

and high

salinity

vere nade pipe

the

under

arrangeraent

nenrioned

above

Ln the hydraulic to cowuttig

pk!ne

nuzlerfcnl

was perfamed

mdel

the maIlytical

of

to obmin of

space,

S-D as

to say,

uater

on

conducted

be

where

vertical

discharge

flow-rate.

&he dhcharged

region

the single

horizontal

sfnu~tion

matter,

there should

pipe

the nozzle the discharge

on the approxinate

experkents

the diffusion

sme

pipe

conditions

before. briae,

pftne

amlysf~

vim.2 vaterexpe-Srzents have beer\ so far conducred

of discharged

to etie

That is

were made in the discbarg& The

tbt

3.n the still

1s uniform.

depth.

dinensiom~%

the assumption

plaque) and the single

results

the

dfffusion.


becueen

constitusiag

and the salinity

were made S.SX the following

ehe water

variatfons

tenperamre

$.n the three

of

cxpericents

-As a lot of hydraulic

uenta2

plme

characteristics

was made on the discharged

made

density

of

the water

of

gravitat&mal

no net OMSS

sS.rzulacion. the m&n purpose velocity,

and the water

Prior

of

is (3)

pipe

arrangeclents

Thus,

This is done

there

the field

by

a&ance-

dfvergence.

equation

tva ttfnds OZ Ghe discharge

appropriate

zero

conservation.

of

skmlatiun,

the density

caused

accelerations

on the basis

of flow

conputations

discharge

FtiSlZ

distributfon

the flow.

&he total

En this

determlnaj

stages.

the denoity

field with

stage,

variables

of duration

Wowever, this the

etc.

mass

f i&i

steps

in such a way that

In the third

are located

rshe flow tfne

in three

the

body forces,

Is nade ta insure

of

short

calculated

not necessarfly

state

of

of the flow co calculate

the pressure

cunponents

fnto a

With

ceazcets.

bmh

gradienrs,

In this nmerfcal

as those

is

is divided

o^y and 62.

by advancing

two, adjuscnents

the distributions

diameter

vefocity

cell

a sequence step

6x,

using

ing of heat and salinity

Ngh

at

,111 advanced

in or out of the cell-

previous

cetfs.

is obtained

one tine are

to be perfamzcd

edge lengths

ate

through

for

state

pressure

by adjusting flow

values

solution

cmponents

convect ion,

are

having

conputaciunai

variables

The advancenent

the velocity

neat

celk

and pressure

and ctre density 6t.

cmputations

uhfch

rectangular

uzma water

results

obtatied

the adaptability

of

at C.R.I.E.P.X., this

on the

caparison

tiEIe and existing

the numerical

Eyxlels.

MS

expetiks Par

as the Qdraulfc of decrease

These copputatiou

taperature

results

It is, therefore,

merits.

on the plume

expzrkzents

in mter

almost

are concerned,

along

the plume axis

agree

with

concluded

the characteristics

have been exanined.

the results

of hydraulic

that the analytfcal

method

herein is applicable to prediction of diffusion of discharged

DIFFUSION

OF

DISCHARGED BRINE FRW

by discharged

of prediction

developed

brine,

THE 100,000 m3/day DESALINATION PLA&T

As an ejcvlple of the desalination on the results

expori-

plant,

on the diffusion

herein

of salinity

and vater

vi11

be made

temperature

sea water

of 100,000

~3 per day.

1 shows a flov chart for conposition of intaken

sea water,

producing

water

brine when deszljnating

description

and discharged

In this

case,

fresh

sea water. the dischareed Elow rate, teaperature and salinity of the

dishcarged brine is a3 shown belo> nhen the temperature environmental

Figure

vafer

in the sea region

and salinity

of natural

zre 25°C and 32.52X, (Ca = 182,)

respectively.

(1)

flou‘rate

Discharged

(2) Water temperzture =

5 4,200

f 1,500 f 11,000

= 16,700 &/hr.

(= 4.64 m3/s)

35 x 1,500 + 34 (11,000 + 4,200)

16,700

f 34.1°C (AT, = 34.1 - 25.0 = 9-1°C) (3) Salinity concentration ratio = Then, ASO

=

the salinity

is 40.7 f,, resulting

l6 20,300 700 9.

= 1.2515

in the salinity

excess

of

40.7 - 32.52 = 8.18 Z,. Zn order to keep the temperature

and discharged

vater

Vdlmr~,

aS

Qb,

32=

iS

PC 7OC, by-pass

difference, dilution

AT,,

between

is conducted.

intaken

By-pass

water

dilution

fO~Oh’S.

34 x16,700+25x@ (Qb I- 16,700)

(- 1.33 or%) + Qb = 4,770 c13/hr,

Then.

DLshcarged flaw rate, Q. = 16,700 Salinity density. So =

l

4,770 = 21,470 m3/hr. (= 5.96 n3/s)

16,700 x 40.7 + 4,770 x 32.52 21,470

_ 38 88x l

0

the difference between

Accordingly, salinity

volume

can be expressed

38.88 - 32.52

Using

discharge

are set as shorn

pipe system.

ii3 Fig.

and

Is located

3 show

axfs

civd

and

y.

at the position

the distribution

central

of cite pfme

discharged

s&Znity water

for numxfcaf

plant

values

the vertical

across

there

is a negative

density

wfer

and

Figs. 2

the section

distribution

by simutition

for

The discharge

c

of z = 2.7 u on the SGl botco3,

uete obtained

of' high density

is discharged

upward

and dischzzrged

of the

of desities

analysis

respec-

an the basis

(f)-(4).

Lo this case, betkeen

conditions

desalinaticn

of flau velocities aad

these values

of equations

volume

2 OR the basis of design

n3/day outlet

salinity

= 6.367,,

a cone-vertical

simulation

intaken

as fol.lous:

difference

surrounding mter-

is contained

This

ti the discharged

at LZ high tfznperarure difference

flaw by discharged

brine

is, therefore,

of Ap = 2.7 x 1W3

is attx9_butable mter

that

The verc ical

of 7°C.

subjected

t&c

to

despite

to the effect

of

negative buoyancy, preventing the flov from rising up to the V;lter surface. That

is, the velocity

Then,

along

discharged

vith water

starts

simvs a tendency of horizontal and salinity brine,

and

of vertical

the surrounding going

along

shcwn

2n Fig.

Fig. 3 shows

20-25

tines,

to what

recognized because

and

are almost

extent

that

there

Then,

will

from the neighborhood of water

taperatures

effect

of discharged

is diluted.

water

of

That

is diluted

of the discharged

As describled above,

local.

brine cz&t%

is given

environzlent vhen

operation

the power

plant of S~~,~~~

difference

and

diffusion

along

of 2-7 x 10-3 bctveen

is,

nearly water

on

it cat be

the sea bo&tcm dischargaf

water

water.

consitieration

for condensers

the

layer,

the plum

to the distribution

uater

that &he effect

density

cxeanophysical tith

stiflar

the discharged

be kept

the discharged is a negative

and surrounding

layer

the discharged

that

ft oan be judged

environcent

the bottom

edge of

3.

at r/D = 10, it is considered

surrounding

&he outer

to the addvective

subjected

these distributions

densities

from the upper

rlD = 3.0. The distributions

are directly

the sea surface.

is lost below

entraining

dove along

of dispersing

distance,

upv;lrd flov mter

plant.

to 6U~,~~

this pomx

betweea

to the effect

carrying When

takfng

kW, it fs assumed plant

dkscharged

uses MU

&ater

of discharged

out a desalimtion

uater on project

into consideration that the amrvrt

be zbout

and natural

by joine

the power of cooling

vater

30 c13/s and the teslpcrature

enviromental

water

will

be

When

AT = 7aC. and

the

the

tenperatute

the density

to be 25oc,

densiry

of

PO = 1.019,196,

of

natural.

of dzscharged

environmental

water

water

(p,)

envirozmeatat

water

($3,) by diSCharged are

respectfvi&y

is

presrned

Wamz

vater

onfy

as foLLows;

And.,its density difference is 2,299 x IO'.

and ps = 1.021,495.

fn this case, fzhedischarged water is assaxmedCO spread on the surface Layer

with

positive

brine

into

the discharged

On

bouyancy.

tenperature and salinity density

FIOW

rate

the

other

warm E*ater of the

the discttarged

the flow rate,

pfant,

of the discharg&

water = 3Q.0 f

of discharged

when n5xfng pOW4X

vater

are as follovs:

5,96 = 35.96 m31’s

Temperature rise = 7.0°C Rise in salinfty density =

30x0+5.96x6,36 35.96

_loS4y *

*

when the:salinity density of environmental water is assumed EU be 32.52X, the density 5I> = 1,513 siiter*

of discharged wter rts caused

x m-3

is p. = l,Of9,982,

between

and

a densPty difference of

the environmental.water and the discharged

ALthough the value is sraallerthan that of discharged warm water

there is positive

only.

houyancy.

Sinufation analysis was conducted by the use of comrentionaf numerical mdels

to predict

the

diffusion of discharged warm uater

thkkness

charged 6iffus3.m

of

the

in the surface layer.

the power piant the layer of discharged water becomes greater than that by dis-

As a result, it is considered that in joint

operation

xdth

warm water only with an increase of salinfty of density but the af discharged

br2ne

shows

the Saue behavior as the diffusion of

discharged warm water.

The realization af this research was deoendent on many persons, not onlv because

active

collaboration

all the inconvenience

caused

was often needed. but also because by the investigation

A3.fthese persons deserve our gratitude

endurance

programs was necessary,

and respect,

of

99

35oc

&!jaiDt/fu.

-

To waste uotcr tank

Distt~bufion af ffaw velocity across the section of centraJ axis of the plume (Q = 5.6 m3/s, dS = 6.36”/cro , LIT= 7°C )

Fig. 3

Verfrcol

distribution

( Q =5.6mq/s,

oi fhe densfies

AS=6.36°/ko,

AT=7T

)