07z 2007 cee 5134 streeter phelps

7/21/2019 07z 2007 Cee 5134 Streeter Phelps

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CEE 5134 - 1 -

CEE 5134

Deoxygenation – Reaeration

and the

The Streeter-hel!" E#$ation

Tho%a" &' (ri))ard

25 *+toer, 2007



CEE 5134 - 2 -

Streeter-hel!" i"tory

. /odeling o oxygen dyna%i+" in loing ater" ha"

e+o%e a "o!hi"ti+ated di"+i!line in the 21"t +ent$ry

. /odern %odel" are $ilt on the or o Streeter and

hel!" on the *hio Rier in the ir"t #$arter o the 20th

+ent$ry 114 – 1256

. Deelo!ed a relation"hi! to !redi+t longit$dinal oxygen

!roile in loing ater" a" a $n+tion o

– Strength o degradale organi+ %atter

. Con"i"ting o %ix o a+gro$nd 8*D in "trea% and 8*Dintrod$+ed y a a"te di"+harge

– Rate o di$"ion o oxygen into the ater ro% the

at%o"!here



CEE 5134 - 3 -

9ho 9ere Streeter and hel!":

. 8eginning in 113, ;SS %aintained a laoratory in

Cin+innati dedi+ated to the "t$dy o <the %aniold!role%" o "trea% "anitation=

– Eent$ally %or!hed into the E> Cin+innati ?aoratory

. '9' Streeter Sanitary Engineer at the ;SS

Cin+innati ?a. E'8' hel!" roe""or o Sanitary S+ien+e at @n"tit$te o

$li+ ealth o the College o hy"i+ian" and S$rgeon"at Col$%ia ;nier"ity

. St$die" on the oxygen dyna%i+" o the *hio Rier ere+o%%i""ioned in 114 and 115 y S$rgeon (eneral9'' Fro"t

– @n 125, hel!" dedi+ate" hi" oo, Stream Sanitation, tothe %e%ory o Fro"t



CEE 5134 - 4 -

Aey i"tori+al $li+ation"

. $rdy, 9'C', <> St$dy o the oll$tion and Bat$ral $rii+ation o the

*hio Rier, ol' @, The lanton and Related *rgani"%",= PublicHealth Bulletin No. 133, U.S. Public Health Service, Washington,

D.C., 193.

. Streeter, '9' and 9'' Fro"t, <> St$dy o the oll$tion and Bat$ral$rii+ation o the *hio Rier, ol' @@, Re!ort on S$rey" and

?aoratory St$die",= Public Health Bulletin No. 1!3, U.S. Public

Health Service, Washington, D.C., 19!.

. Streeter, '9' and E' 8' hel!", <> St$dy o the oll$tion and

Bat$ral $rii+ation o the *hio Rier, ol' @@@, Fa+tor" Con+erned in

the heno%ena o *xidation and Reaeration,= Public Health Bulletin

No. 1!", U.S. Public Health Service, Washington, D.C., 19#.



CEE 5134 - 5 -

Ee+t o *rgani+ 9a"te" on Strea% E+o"y"te%"

. Streeter-hel!" /odel Di""oled *xygen Sag C$re

– The Streeter-Phelps Equation i" integral to %o"t o the

idely $"ed di""oled oxygen %odel" in $"e today

– >ddition o degradale organi+ %atter 8*D6 to a loingater+o$r"e +a$"e" a "lo de+rea"e in *2, +a$"ed y

heterotro!hi+ %etaoli"%

– *!!o"ing <deoxygenation= i" reaeration, hi+h !ro+eed" ata rate !ro!ortional to the +on+entration dei+it relatie to

the "at$ration +on+entration6



CEE 5134 - -

*xygen Sag Ee+t" on 8iologi+al Co%%$nitie"


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Co%!onent" o the *xygen Sag C$re


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Deinition" or the D* Sag C$re


http://slidepdf.com/reader/full/07z-2007-cee-5134-streeter-phelps 9/35CEE 5134 - -

Streeter-hel!" /odel >""$%!tion"

. Strea% ehae" a" an ideal !l$g lo rea+tor FR6

. Flo rate, "trea% +ro"" "e+tion and longit$dinal elo+ity

are +on"tant

. hy"i+al, +he%i+al, and io+he%i+al rea+tion" o intere"tare 8*D exertion and *2 tran"er a+ro"" air-ater

intera+e



Streeter-hel!" /odel ?i%itation"

. Con"ider" only one <"in= or D* – Degrading 8*D

– /i""ing B*D, S*D, non!oint "o$r+e", algal re"!iration,degradation o %i+roial !rod$+t"

. Con"ider" only one <"o$r+e= or D* – >t%' Reaeration – /i""ing >lgal !hoto"ynthe"i"

. Don"trea% %oe%ent i" y ade+tion only ideal FR6'

– /i""ing Di"!er"ionDi$"ion

. elo+ity, de!th, 8*D exertion, and reaeration are

inariant ith di"tan+e



1"t *rder 8*D Exertion Relation"hi!

. @t ha" een "hon that, $nder ex!eri%ental +ondition"

a!!roxi%ating tho"e !reailing in a "trea% +ontainingre"ere di""oled oxygen, thi" rea+tion an orderly and

+on"i"tent one, !ro+eeding at a %ea"$rale rate, and

a++ording to the olloing la

<$he rate o% biochemical o&i'ation o% organic matter is

(ro(ortional to the remaining concentration o% uno&i'i)e'

substance, measure' in terms o% o&i'i)abilit*.+

Phel(s, -arle B.



G$antitatiely Stating the 8*D Exertion Relation"hi!

. >" long a" oxygen i" !re"ent, the rate o io+he%i+al

oxidation o organi+ %atter i" !ro!ortional to the a%o$nto organi+ %atter re%ainingH'

( )

d

d

-1

d

d?I rate o 8*D exertion I - ?

dt

here ? I organi+ %atter re%aining at ti%e, t, oxygen +on+entration $nit", %g ?

I ir"t - order 8*D rate +oei+ient, t

Se!arate ar

d

d

0 0

- t

0

d?iale" I - dt?

@ntegrate J a!!ly o$ndary +ondition" ? I ? K t I t 6

? I? e



9hat doe" 8*D exertion loo lie:



S$%%ary o 8*D Exertion

. >" long a" oxygen i" !re"ent, the de+line in

8*D re%aining ?6 i" ex!onential

. @ the "y"te% i" +lo"ed, "$+h a" in a 8*D ottle,

the D* "$!!ly i" ixed, and no re!leni"h%ent

ro% the at%o"!here +an tae !la+e

– Thi" i" the +a"e or laoratory 8*D %ea"$re%ent"

– >llo" +on"tr$+tion o a #$antitatie D* $dget eteen

"tart and the ini"h o the te"t

. 9hatL" dierent ao$t hat ha!!en" in <the orld:= – Sy"te% i" o!en

– 8*D i" exerted, $t D* de!letion i" o!!o"ed y

+ontin$o$" re!leni"h%ent ro% the at%o"!here



*xygen Re!leni"h%ent y >t%o"!heri+ Reaeration

. Reaeration rate i" 1"t order ith oxygen dei+it

. Rate +oei+ient i" related to "trea% +hara+teri"ti+" – elo+ity, T$r$len+e, De!th

( )

r "

r

"-1

r

"

dCI rate o reaeration I M C -C6

dt

here,C I "at$ration oxygen +on+entration, %g ? I ir"t - order reaeration rate +oei+ient, t

Can al"o ex!re"" in ter%" o the "at$ration dei+it, D I C -C

(ii r

dDng I - D

dt



9hat Doe" Reaeration ?oo ?ie:



Reaeration *LConnor and Doin" For%$la

. 8a"ed on "$ra+e reneal theory

– /odel i" that <!ar+el"= o ater are ro$ght to air-aterintera+e or "o%e inite ti%e !eriod

– (a" ex+hange tae" !la+e only hile a ater <!ar+el= i" atthe "$ra+e

– >ter %oing aay ro% the "$ra+e, ater <!ar+el= %ixe"ith the li#$id $l

0'5 0'5

r r 1'5 1'5

-1 -1

r r

S@ Engli"h C$"to%ary

; ;

I 3'3 I12'

d 6, ; %!"6, %6 d 6, ; !"6, 6



Reaeration Ch$r+hill et al. 126 For%$la

. 8a"ed on e%!iri+al "t$die" o reaeration o $nder-

"at$rated ater" don"trea% o da%" on the Tenne""eeRier

. Correlated %ea"$red reaeration rate" ith elo+ity ;6and de!th o lo 6

r r 1'7 1'7

-1 -1

r r


; ; I 5'02 I11'

d 6, ; %!"6, %6 d 6, ; !"6, 6



Reaeration *en" and (i" 146 For%$la

. Cond$+ted "t$die" o 8riti"h "trea%" here oxygen a"

artii+ially de!leted y "$lite additione

. Co%ined 8riti"h and Tenne""ee Rier data

– Correlated %ea"$red reaeration rate" ith elo+ity ;6 and

de!th o lo 6

0'7 0'7

r r 1'5 1'5

-1 -1

r r


; ; I 5'32 I 21'

d 6, ; %!"6, %6 d 6, ; !"6, 6



CEE 5134 - 20 -

>t%o"!heri+ Reaeration

D e ! t h , 4 % 6

D e ! t h ,

4 0 t 6

. /ethod o Coar 176

. ;"e" or%$lae o

– *LConnor J Doin"

– Ch$r+hill

– *en"-(i". @n!$t "trea% elo+ity

and de!th o lo

. Sele+t r d-16 at

inter"e+tion o lo and de!th

+oordinate"



CEE 5134 - 22 -

Reaeration Coei+ient E"ti%ation ro% Strea% De"+ri!tion"

9ater 8ody De"+ri!tion r

day"-1 K 20 oC6

S%all !ond" and a+ater" 0'10-0'23

Sl$ggi"h "trea%" and large lae" 0'23-0'35?arge "trea%" o lo elo+ity 0'35-0'4

?arge "trea%" o nor%al elo+ity 0'4-0'

Sit "trea%" 0'-1'15

Ra!id" and aterall" N 1'15

So$r+e eay, Roe and T+hoanoglo$", 15



CEE 5134 - 23 -

Te%!erat$re Corre+tion" or Rate Coei+ient"

. ule o% $humb i" that io+he%i+al rea+tion rate"

do$le ith a 10 oC te%!erat$re in+rea"eanLt o R$le6

. >rrheni$" E#$ation %ay e $"ed to %orerigoro$"ly +orre+t rate +oei+ient" or dieren+e" in te%!erat$re

a2 a1

a2 a1

a2 a1

ET -T 6

RT TTa2

Ta2

o

a2 a1

E

RT T T2-T16

T2 T1

I

*3er the range o nat$ral te%!erat$re"

0 - 40 C6, the !rod$+t o T T i" O +on"tant,and allo" $" to deine 7

I e ''' and 1"t e#$ation e+o%e"7 Iθ θ

g

e

>rrheni$"

anLt o

S o $ r + e 7

1 1 1 ' 1

i 2 i ! e d i a ' + o %



CEE 5134 - 24 -

Deter%ine 8*D;?T in Strea% ater /ixing ith Di"+harge

. Con"tr$+t %a"" alan+e on rier lo and a"te

di"+harge to get 8*D;?T o %ixt$re

9a"te G,

@n!$t ?

Rier

Flo

Gr , ?

r

/ixed

Flo

Gr MG

, ?

0

r r 0

r

3

r

3

3

r

3

G ? MG ?? I

G MG

here,

G I Flo in Rier, ? t

G I Flo o 9a"teater Di"+harge, ? t

? I ;lti%ate 8*D o rier ater, % ?

? I ;lti%ate 8*D o a"teater di"+harge, % ?



CEE 5134 - 25 -

Si%!liied S+he%ati+ Re!re"entation o /odel

. >""$%e F and deine +ontrol ol$%e a" a $nit re+tangle

. Control ol$%e %oe" don"trea% at +on"tant elo+ity

. Deter%ine the initial oxygen +ontent ater %ixing ?06

. Co%!$te D* at any ti%e y "oling dierential e#$ationor 8*D exertion and at%o"!heri+ reaeration



CEE 5134 - 2 -

Dierential E#$ation or redi+ting ?ongit$dinal D* roile

. @dentiy a "ingle l$id ele%ent in the "trea%

– Con"tant ol$%e

– Con"tant elo+ity

. 9rite a %a"" alan+e or oxygen on the ele%ent a"

ae+ted y 8*D exertion and at%o"!heri+ rearation – >++$%$lation I in!$t – o$t!$t P rea+tion

– Sin+e the l$id ele%ent i" <inta+t,= there i" no lo in or o$t,and the %a"" alan+e e+o%e"

g gin in o$t o$t

dC I G C - G C - 48*D exertion6 M4Rearation6

dt

g gin o$t

dC I 0 - 0 - 8*D exertion6 M Rearation6

dt



CEE 5134 - 27 -

deox reaer

d r "

"

d

Re%e%er the %a"" alan+e 7

dC dC dC I M

dt dt dt

S$"tit$te the rate ex!re""ion" 7dC

I - ? M C -C6dt

For %ath +on3enien+e, ex!re"" in ter%" o dei+it, D I C -C 7

dD dCI 0 - I

dt dt

g g

r ? - D

Streeter-hel!" Deelo!%ent, +ontin$ed



CEE 5134 - 2 -


d

d

- t

d 0 r

- t

r d 0

S$"tit$te the 8*D Exertion Ex!re""ion

dDI ? e - D

dt

Rearrange to dD

M D I ? edt

The aoe i" o the "tandard or%

d)M) I G hi+h i" not "e!arale6

dx



CEE 5134 - 2 -


r r

dr r r

r dr

dt t

- t t t t

r d 0

4 - 6t t

d 0

;"e the integrating a+tor

e I e

/$lti!lying ea+h ter% y the integrating a+tor gie"

dDe M D e I ? e e

dt

>nd''''

dDe I ? e

dt

∫



CEE 5134 - 30 -


0

0

r dr

r dr

- 6t t

d 0

- 6t t d 0

r d

0 0d 0 d 00

r d r d

Se!arate ariale" and integrate

d De I ? e dt

(iing

?De I e M C

-

>t o$ndarie" o t I 0 and D ID , e hae

? ?D e I e M C '''' C ID -

- -

∴

∫ ∫



CEE 5134 - 31 -


r dr

d r r

- 6t t d 0 d 00

r d r d

- t - t - td 0 d 00

r d r d

-d 0

r d

>!!lying the integration +on"tant

? ?De I e M D -

- -

Soling or D

? ?D I e M D e - e

- -

8y gro$!ing lie ter%", "i%!liy to

?D I e

-

)d r r t - t - t

0- e M D e



CEE 5134 - 33 -

Co%!$te the Criti+al Dei+it

. The +riti+al dei+it D6 o++$r" here the rate o +hange o

D ith ti%e I 0 dDdt I06

. /ay e +o%!$ted ro% the original DE y "etting the 1"t

deriatie e#$al to )ero

d

d

- t

d 0 r C

- tdC 0

r

dD I 0 I ? e - Ddt

Rearrange to

D I ? e



CEE 5134 - 34 -

Ti%e to Rea+h the Criti+al Dei+it ?oe"t D*6

d r r

d r r

r

- t - t - td 00

r d

- t - t - td 0d r 0 r

r d

- t

dD >" noted, the +riti+al dei+it i" here I 0

dt ?dD d

I 0 I e - e 6M D edt dt -

Taing the deriatie" and "i%!liying

?0 I - e M e 6 - D e

-

Diide y e

0 r dr +

r d d d 0

, tae nat$ral log" on oth "ide" and "ole or t

D - 61t I ln 1-

- ?



> Streeter-hel!" /odel Exa%!le role%

. 9a"teater %ixe" ith a rier re"$lting in

– 8*D I 10' %g? – D* I 7' %g?

– Te%!erat$re I 20 °C

. Deoxygenation +on"tant I 0'2 day-1

. >erage lo I 0'3 %"

. >erage de!th I 3'0 %

. 9hat i" the di"tan+e don"trea% o the %axi%$%oxygen dei+it:

. 9hat i" the %ini%$% al$e o D*:

07z 2007 cee 5134 streeter phelps

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