Amine Hafsi MS Thesis

8/11/2019 Amine Hafsi MS Thesis

1/93


2/93

Design Methodology for Permeable Reactive Barriers Combined with

Monitored Natural Attenuation

Amine Hafsi

The Charles E. Via Department of Civil Engineering

(ABSTRACT)

Permeable reactive barrier (PRB) technology is increasingly considered for in situ treatment of

contaminated groundwater; however, current design formulas for PRBs are limited and do not

properly account for all major physical and attenuation processes driving remediation. This study

focused on developing a simple methodology to design PRBs that is easy to implement while

improving accuracy and being more conservative than the available design methodologies. An

empirical design equation and a simple analytical design equation were obtained to calculate the

thickness of a PRB capable of degrading a contaminant from a source contaminant concentration

sC to a maximum contaminant level MCLC at a Point of compliance POC . Both equations integrate

the fundamental components that drive the natural attenuation process of the aquifer and the

reactive capacity of the PRB. The empirical design equation was derived from a dataset of random

hypothetical cases that used the solutions of the PRB conceptual model (Solution I). The analytical

design equation was derived from particular solutions of the model (Solution II) which the study

showed fit the complex solutions of the model well. Using the hypothetical cases, the analytical

equation has shown that it gives an estimated thickness of the PRB just 15 % lower or higher than

the real thickness of the PRB 95 percent of the time. To calculate the design thickness of a PRB,

Natural attenuation capacity of the aquifer can be estimated from the observed contaminant

concentration changes along aquifer flowpaths prior to the installation of a PRB. Benchscale or

pilot testing can provide good estimates of the required residence times (Gavaskar et al. 2000),

which will provide the reactive capacity of the PRB needed for the calculation. The results of this

study suggest also that the installation location downgradient from the source of contaminant is

flexible. If a PRB is installed in two different locations, it will achieve the same remediation goals.

This important finding gives engineers and scientists the choice to adjust the location of their PRBs

so that the overall project can be the most feasible and cost effective.


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iv

AB C

................................................................................................................................................................ 1

INTRODUCTION................................................................................................................................................................

1.1 B ..........................................................................................................................................................

1.2 A ......................................................................................................................................

1.3 .............................................................................................................................................

1.4 B ....................................................................................................................

1.5 B ............................................................................................

REFERENCES....................................................................................................................................................................

............................................................................................................................................................. 15

MATHEMATICALMODEL ANDSOLUTIONS........................................................................................................................1

2.1 .............................................................................................................................................................

2.2 .......................................................................................................................................

2.3 B C ......................................................................................................................................

2.4 .............................................................................................................................................................

2.4.1 ................................................................................................................................................

2.4.2 .............................................................................................................................................

2.5 ..................................................................................................................................

2.5.1 C ..................................................................

2.5.2 B( ) A L ..........26

2.5.3 B( ) B L ..................................................................................29

2.5.4 AC B .....................................................................................................


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v

.............................................................................................................................................................. 33

DESIGNMETHODOLOGY...................................................................................................................................................

3.1 .....................................................................................................................................

3.1.1 .............................................................................................

3.1.1.1 A ( A) ............................................

3.1.1.2 .................................................................................................................

3.1.2 ....................................................................................................................................

3.1.3 ...............................................................................

3.1.4 ....................................................................................................

3.2 ....................................................................................................................................

3.3 ............................................................................................................................................

............................................................................................................................................................. 47

CASESTUDY....................................................................................................................................................................

4 1. B ........................................................................................................................................

4 2. ...................................................................................................................................

4 2 1 A NAC .................................49

4 2 2 B .......................................52

4 2 3 B B NAC ................................................52

4 2 4 B ...............................................................................................................

REFERENCES......................................................................................................................................................................

............................................................................................................................................................. 54

ENGINEERINGSIGNIFICANCE...........................................................................................................................................


6/93

vi

........................................................................................................................................................... 56

........................................................................................................................................................... 77


7/93

vii

F 2 1: C

.......................................................................................................................................................

F 2 2 : C S I S II

E ( ) ..........................................................................................................................................

F 2 2 : C S I S II

E ( ) ..........................................................................................................................................

F 2 3: S PRB

........................................................................................................................................................

F 2 4 : C 3 A L

E ( ) ..........................................................................................................................................

F 2 4 : C 3 A L

E ( ) ..........................................................................................................................................

F 2 5 : E ( ) C C ,

PRB M I M II,

. ........................................................................................................................................

F 2 5 : E ( ) C C , PRB M I M II,

. .......................................................................................................................................


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viii

F 2 6: E ( ) C C ,

PRB M I, nd B NAC ...........31

F 3 1 : PRB D C sstd

Awall C C vs Dk A ,. ...................................................................................37

F 3 2 : D C F A ................................................................................................38

F 3 3 : D C F A ................................................................................................38

F 3 4: P VA A .............................................................................................................................................

F 3 5: P PO B ...........................................................................................................................................

F 3 6: E D E ................................................................................

F 3 7: A D E ............................................................................

F 4 1: M S F (B ., 1998).........................................................

F 4 2 : M F (B ., 1998) ....................................................................

F 4 3 : TCE (IT C ., 1991).....................................................................

F 4 4: L M B M W PR

2005) ...............................................................................................................................................................


9/93

ix

AB

T 1 1: S (U.S. EPA R

T F S , EPA/600/F 97/008) .......................................................................................

T 3 1: ( )( )1

1

001.0,,400001.0,,

===

d V m LC

d V LC

A APOC A

A APOC A

..................................................................................................39

T 3 2: ( ) ( )( )

===

==

1

11

001.0,,400001.0,,ln001.0, / 1.0,ln

d V m LC d V LC

C d d mV LC

A APOC A

A APOC Astd

A

A APOC A

......40

T 3 3:( )

std A

A APOC A

C

d V m LC 1001.0,,400 == . AV ........................................................................................42

T 4 1: B T R D (B ., 1998) .................


10/93

1

Chapter 1

1.1 B

G . I U

56% (V L

H

. C

(K

2001). F , A

(D , 1999).

T U.S E P A (EPA)

217,000 U.S $ 190

(EPA, 1996).C


11/93

2

. H ,

, ,

(M , 2003). C ,

. C

(PCE), (TCE), (TCA), N

( ; )

.

G

,

(T .1990; G .1992; N R C , 1994). T

. H ,

P R B (PRB )

(P . 199

P ,

, TCE

(S . 2000), . C , PRB

,

, (P

T

. S ,


12/93

3

(P . 1998).

T PRB . I

. H ,

. F PRB

;

. I ,

,

T , PRB

(MNA) .

1.2 A

W , ,

, , (U.S. EPA, 199

N O H S P

(NCP)

EPA, 1990 ). U , (U.S.

H , , ,

. T EPA MNA


13/93

4

MNA

,

, ,

(U.S. EPA, 1997, .1).

T , , MNA

(L . 1997). S

( . ., )

MNA . C

U.S. A

P G 6 . O

B C MNA

( , , , ,

) F . (2001). T .

1.3

I ,

. I ,

. A G

,

F V G N P 1912 (P


14/93

5

1998). F , 1980 , S

1982 G

C (VI) H


15/93

6

, ,

(I S R T S , EPA, 1995).

T 15

(U.S. EPA, 2002). T EPA

(U.S. EPA, 1997). T EPA 20%

. T 1

. 1997).

R US

. PRB

. T , F O,

PCE TCE,

R ,

(B . 1996). T

,

. O

, .


16/93

7

1 1: S (U.S. EPA RT F S , EPA/600/F 97/008)

,

C

,B ,

,C ,

C ,

C , C

,,

C

S . 1995 D . 1995 J . 1996 J 1995 O . 1996

C & . D

2 /L DCE 300 /LTCE

400 /LTCE

10 /L TCE10 /L

C (VI)

700 /L TCE & DCE15 /L VC

E & RV

F &G

CT

F &M G

N A S W SB

S

NA

S JS P

N A 100 + 100 490 +490

NA

1040

. N A 1 R 1 NA

4

F F F F F

5 16 11 A . 23 10 15

44 NA 20 150 40 (4 40 = 160)

4.5 16 3 2 G , = 2 = 6

90 15 70 450 NI

D

15 20 18 40 17 28 3 26 10 15 20 25

44 A . 200 1000 150 1200

& .

HDPE F

H2O F

W H2O

,

T .. C

F

L . G

.

C N I $375 K $400 K $500 K NI


17/93

8

M 26 PRB US

.(U.S. EPA , RTDF, 2001). A

,

. H ,

.

I J 1996, , 46

, 7.3 0.6 U.S. C G S C

(USCG) E C , N C

(TCE) (B . 1999).

I S 1997, F C U ,

10 ,

( VI) ,

(AFO) , . A 1 ( VI)

(AFO)

99.9% (U.S. G S , 1997).

I 1999, C C A F S F ,

(0.01%) 20,000 DNAPL, TCE

3 /L TCE

1,2 (DCE). A 12.2 , 12.2

1.2 E 12.2 1.2

.% VI, 79 .% 5 .%


18/93

9

TCE

M 1999 MCL

. 2000).

I A 1999, P A F B N H PRB

VOC 1,000 /L

TCE . A 487 359

+50 U.S. ) 473 3 . I

, 20

6 PVC . T

(C . 2000).

I 1998, PRB C T S S

J 915 TCE

6,000 8,000 /L 50 /L . T

TCE P R

1950 1984

TCE. T 3,000

7.6 , 46 27.4 250

. T

, 50% TCE ,

7,000 /L 3,500 /L. T

PRB


19/93

10

H

.

B

, PRM

.

1.5 D B

T PRB

. T E A UK (N G & C

L C , 2002)

:

F Bres B S V t L **= . (1 1)

( )k

C C t T res

0ln= . (1 2)

T C = ( / ); 0C = ( / ); rest =

( ); BV = ( / );k = (1); F S =

.

T

. T


20/93

11

N , PRB ,

(R .2005). T

. A ,

.

R . I

PRB N 2005 . A

, ,

PRB. A ,

PRB


21/93

12

A , W.L.; S , E.L. I . E . C .1977, 16(2), 158 162

B , R.C. ;R.D. N ; R.E. H ; R. B ; P.L. M C ; L. S ; J.T. W ; C ; M. R ; E.J. B ; R.C. B ; T.M. V ; J.M. T ; C.H. W . NB H C G W . B , LP , B R , FL. 1994.

B D.W.; C.J. P ; J.L. J . I C (VI) : L .. . . 1997. 31(12), 3348 3357.

B D. W. . A . V 2, P M , . . A

A/600/ 99/095 ( . . A, , , 1999).

B , B. T., C , S. W. S , D. J. A. & M , D. M. A BTEX .

.1996

C , J. I P R W P A F B U BT : P RTDF P B A T M. 16 17, 2000,

.

C , F.H., P.M. B , C.C. C . 2005. B F . 25, . 2:

131 141

D , F. P; J. N. J . M N A C S .A.1999

F ,M.G.; M.A.W ; J.C.L .B C M N A . .. 2001.

F. L , F. L. T , D. K. T , T W E (L , C , MI, 1990).

G , R. W.; S. F. O H . E D H A V I . . . 32, . 6, 958 967.1994

G , R.W; D.R.B . R . , C ,

24, , . 1992

H , G. V H F E PRB . B A , A 15 16, 1998, B , .


22/93

13

I , H.; T. K ; J.J. L . T R C C UP . A C . 1997.

K , P.; T. L ; P. K . R TCE C P RB V I . 2001.1

L , K.; P. F . P S N A CO G W .A.1997.

M ,D.K.;P.C.J ;C.B . B MTBE P RT . C .

N R C . A . A ,, .C., 315 . 1994

P , R. W. S P R D , NRMRL, ORD, U.S. EPA

P , R. W.; R. M. P ; D. W. B ; J. L. V ; D. S ; T. S ; P. D. P ; R. LP R B T F C R .. . A .1998

P ,R.M. P & A S S , L V , NV

R , A.J.; R. S ; J. R. C . A M D I BR B . 2005.

R , D.R.; M.B. C ; C.A. C ; J. Q . NASA PRB I DM :P RTDF P B A T M . 16 17,

2000, , . S F.; T. M . R

C & , . 8, 2, 103 1(2000)

S , J. N G &C L C , E A

S , K. H.; J. R. F . R D H P .1972. . . .3,640,821.

T , C.C., D , C.B. 1990. C S

E S T . 24:1464 1466.

U.S. E P A . F A I S R TP R B . 2002

U.S. E P A . R T D F. . / / /PRBSUMMS. A 2001


23/93

14

U.S. E P A . U M N A S , . A 1999

U.S. E P A . O S W E R 9200. U M N A S , RCRA C AU S T .1997.

U.S.E P A . C U N W S : M TT . A 542 96 005A.1997.

U.S. E P A . N O H S PC P : F (NCP).. .55(46):8733 8734. 1990

U.S. G S ,U.S. B L M ,U.S. D E D O P R B T R D U F GF C , U . . 1 2.1997

W , T.H.; M.A., S ; D.E.; M ; E.K G ; J.T W ; B.H W ; D.H KJ.E. H ; P. H ; F.H. C .. AC . 1 5. A C A B , A , . 1997

W , P.; W H.; K A.; H S.; S K. G (B /W , G 2002

V , J. P B R P C T S . B A , A 15 16, 1998, B , . 1998


24/93

15

Chapter 2

2.1

T PRB

.

F :

1- S 1)

PRB ,

, 2

, ,

,

PRB .


25/93

16

2- C 7,500

PRB

sC MCLC P

POC

3- I

PRB

PRB

PRB 1

PRB ,

4-

PRB .

2.2

T , ,

N

. I PRB,

. D PRB,

.


26/93

17

T 1 D (

,S C , ) ,

: (F

B , , Bv ,

B B A A nV nV = . (2 1)

An = L3/ L 3 ; Bn = L3/ L 3 ;

AV = .

CA , A CB , B CA , A

CS

2 1: C .

LALB

LPOC

V A

Source

A A B


27/93

18

C ,

,

022

=

B B B

B B

B C xC

V xC

D . (2 2)

BC M/L3

B A A L L x L + ; B D L2/T ; B

T1

. S

, , ,

022

=

A A A

A A

A C xC

V xC

D . (2 3)

AC M/L3

A L x 0


28/93

19

( ) 0= xC A .(2 4 )

:

B A C C = A L x = .(2 5)

B A C C = B A L L x += .(2 6)

A A A A

A A B B B B

B B C nV xC

n DC nV xC

n D +

=+

A L x = .(2 7)

A A A A

A A B B B B

B B C nV x

C n DC nV

x

C n D +

=+

B A L L x += .(2 8)

A L

B L

.

E 2 7

E 2 8

2.4

2.4.1

T

AU L

x X = .(2 9 )

B

A B L

L x X = ..(2 9 )

B APOC

B A D L L L

L L x X

= .(2 9 )


29/93

20

U )10( U ;

B )10( B ; D

< D0 ; POC L

POC. T POC L

.

T E 2 2, 2 3 (A A)

:

1. F 10 = AU L

x X

)exp()1()exp()( 22 U nd

AU nd

AU R A X NAC C X NAC C X C += .(2 10)

2. F 10

= B

A B L

L x X

)exp(*)exp()exp(*)exp()( 13 Bnd

B R B

nd B B

nd B

R B

nd B B

R B X NAC L NAC C X NAC L NAC C X C += ...

.(2 11)

3. F 10

=

B APOC

B A D L L L

L L x X

( ) )exp(*)1(exp)( 4 D RPOC nd A R Bnd A D R A X L NAC L NAC C X C += .(2 12)

= R AC s A C C = = R BC

s B C C = . E 2 10, 2 11, 2 12

=nd A NAC [ ] Ae A Ae Ae P Dk PP 4)(21 2 + = NAC .(2 13)


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21

=nd A NAC [ ] Ae A Ae Ae P Dk PP 4)(2

1 2 ++ = NAC .(2 14)

A

A A A

e D

v LP = = P ;

A

A A

A V

L Dk

= = D ,

I

=nd B NAC [ ] Be B Be Be P Dk PP 4)(21 2 + = NAC PRB ..(2 15)

=nd B NAC [ ] Be B Be Be P Dk PP 4)(2

1 2 ++ = NAC PRB (2 16)

B

B B Be D

v LP = = P ;

B

B Bwall V L

Dk = = D

, I

A

B R B L

L L = .(2 17)

A

B APOC RPOC L

L L L L

= .(2 18)

+= A

e

A A P

Dk 411

21

++= A

e

A A P

Dk 411

21 .(2 19)

+= B

e

B B P

Dk 411

21

++= B

e

B B P

Dk 411

21 .(2 20)

:

++

= Be B Be R B

B A

B A P Dk P L 4) / 11(exp*C 21 .(2 21)

sC C C '''

'CC 2122 += .(2 22 )


31/93

22

W1''

1'C

22

=C

.(2 22 )

+

+

+

++=

Ae A

Ae

Be B

Be

A B

A B

A B

A B

Be B

Be

P Dk PP Dk P

P Dk PC

4exp*4exp*

4exp1''

22

2

2

.(2 22 )

( )

( )

+

+

++

++

=

Ae A

Ae

B

A B

B

A B R B

Be B

Be

Ae A

Ae

B

A

B

A

R B

Be B A

e A

R B

Be B

Be

P Dk P L

P Dk PC

P Dk P

L

PP

L

P Dk PC

C

4)(exp*4

exp

4)(exp11

*exp

4exp1

'''

21

2

1

2

2

2

..

.(2 22 )

( ) ( )

+++

+

+++

+=

R B

B

e B

B

e

B

e R B

B

e B

B

e

B

e

Ae A

Ae

Ae

Ae A

Ae

Ae

L

P Dk PPC

L

P Dk PP

P Dk PPC P Dk PPC C

2

4)(exp

2

4)(exp

4)(21

exp)1(4)(21

exp

2

1

2

22

22

3 .(2 23)

( ) ( )

( )

++

++++

++

=)1(*4)(

21

exp

11*4)(

21

exp1

1*4)(21

exp

2

21

23

4 R B

Ae A

Ae

Ae

R B

Be B

Be

Be R

B

Be B

Be

Be

LP Dk PP

LP Dk PPC

LP Dk PPC

C

....(2 24)


32/93


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24

2.5 D

2.5.1 C

I S I S II,

( ) ( ) . B

MCLC lg / 5

POCs S I . U lg / 5 MCLC , S

II

, , PRB. F 2 2 F 2 2

.

2 2 : C S I S

E ( )


34/93

25

2 2 : C S I S

E ( )

T S I S II

D ,

. T

0.2

8.2 ( ). T

. T S II

S I.


35/93

26

2.5.2 B( ) A L

2 3: S PRB S 1 PRB )1( A L .

S 2 PRB )2( A L .

F 2 3 PRB )1( A L

MCLC P POC PRB )2( A L

. T PRB placed away from the

C A

Source

C s

Plume


36/93

27

T S I ( ) ( )

. T :

1. W PRB

A L m2

2. W PRB POC

A L m40

3. W PRB 10 ( ) m50 POC

A L m90

2 4 : C 3 A L

- Example (c)-


37/93

28

2 4 : C 3 A L

E ( )

T F 2 4 F 2 4 PRB


38/93

29

2.5.3 B( ) B L

2 5 :C C ,

PRB M I M II, PRB

E ( )


39/93

30

2 5 : C C ,

PRB M I M II, PRB

E ( )

S I

PRB

( ) ( ). T F 2 5 2 5 ,

PRB N

.

A , PRB

.


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2.5.4 AC B

2 6: C C , PRB M I, nd B NAC

-E ( )

S I

PRB

( ). B

B L Bv B PRB, nd

B NAC 13.8, 10.5

5.6. T F 2 6,

PRB N .


41/93

32

A , PRB nd B NAC ,

. A , F 2 6 PRB

nd

A NAC .


42/93

33

Chapter 3

D

3.1 D

3.1.1

W PRB B L

A L ,

PRB. T

PRB .

T POC

:

),,,,,,,,,,,()( POC s B A B A B A B A B APOC A LC nn L LV V D D f L xC == .(3 1)


43/93


44/93

35

P L ( ). A

, (NAC)

X NAC C C As A = )ln()ln( ), A

A A A A A D

DV V NAC 2

42 ++=

T , P As L NAC C PCL = )ln()ln( PCL ( . .,lg / 2 ).

T

A

sP NAC

C L

)2ln(= .(3 5)

S A L A V D = 2 34 2 35:

A

A

A A A A

s A V

D

DV V

C D

414.2

2

2

4

)2ln(log83.0

++=

.(3 6)

A

A

A A A A

s A A V

D

DV V

C D D f

414.2

2

2

4

)2ln(log83.0)(

++=

.(3 7)

A D E (3 7).

. . .

A 2.5.2, POC

PRB A L E 3 1. A


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36

3.1.1.1 E 3 2 POC PRB

:

),,,,,,()( POC s B B A B APOC A LC LV V f L xC == .(3 7)

AV : F L/T .

BV : T L/T .

A : A T1 .

B : F T1 .

B L : T L .

POC L : D L .

sC : I M/L3 .

3.1.2

U S I 7,500

s

A APOC A

C V L xC ),,( =

POC

. T wall Dk . wall Dk .

s

A APOC A

C

V L xC ),,( =

(>89%) (F 3 1).


46/93

37

3 1 :PRB D C sstd

Awall C C vs Dk A ,.

I , sstd

Awall C C vs Dk A ,. wall Dk .

s

A APOC A

C

V L xC ),,( = POC L m400 AV d m / 1.0

3.1.3

A F 3 1wall Dk :

A A

A

s

std A

wall C C

Dk

=

,

* .(3 8)

A A A . T


47/93

38

:

A

Ae

1088*248.0= .. .(3 9)

113.0*34.46 += A A .(3 10)

3 2 : D C F A

3 3 : D C F A


48/93


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40

3 2:( ) ( )

( )

===

==

1

11

001.0,,400

001.0,,ln

001.0, / 1.0,ln

d V m LC

d V LC

C

d d mV LC

A APOC A

A APOC Astd

A

A APOC A

C ( )

A ( / ) 25 75 200 600 800 1000

0.02 0.230043 0.230042891 0.2300428 0.229392 0.229392 0.229392

0.04 0.432424 0.43242356 0.4324236 0.432424 0.432423 0.432422

0.07 0.721675 0.721675027 0.7216751 0.721675 0.721675 0.721675

0.1 1 1 1 1 1 1

0.2 1.921336 1.921335624 1.9213356 1.921336 1.921336 1.921336

0.6 5.576004 5.576003942 5.5760035 5.576005 5.576004 5.576003

0.8 7.397108 7.397107277 7.3971074 7.397109 7.397108 7.397106

1 9.209606 9.209612596 9.2095838 9.209656 9.209622 9.209636

F T 3, VA A :

( ) ( )

( ) VA

A APOC A

A APOC Astd

A

A APOC A Ad V m LC

d V LC

C

d d mV LC =

==

=

==

1

11

001.0,,400

001.0,,ln

001.0, / 1.0,ln

..(3 11)

A , d mV A / 1.0= ( T 3 1), POC B

:

( ) )exp(001.0, / 1.0, 1 POC std A

A APOC A BC

d d mV LC === .(3 12)


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C , (3 11) (3 12):

( )( )

====

1

1

001.0,,400001.0,,ln*

d V m LC d V LC A B

A APOC A

A APOC AVAPOC

( )( )

=

===

VA

POC

A APOC A

A APOC A

A

B

d V m LC

d V LC exp

001.0,,400001.0,,

1

1

( )

====

VA

POC A APOC A A APOC A A

Bd V m LC d V LC exp*001.0,,400)001.0,,( 11 .. (3 13)

3 4:P VA A

072.0*151.9 += AVA V A .(3 14)


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)*009.0(*0275.01

POC POC e B =

.(3 15)

3 5:P PO B

594.3*009.0 += POC POC L B .(3 15)

1001.0,,400 == d V m LC A APOC A std AC

AV .( T 3 3)

3 3:( )

std A

A APOC A

C

d V m LC 1001.0,,400 == . AV

AV ) / ( d m

( )std

A

A APOC A

C d V m LC 1001.0,,400 ==

0.02 7.85296E 06

0.04 0.009319187

0.06 0.1182682740.08 0.443341395

0.1 1


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AV ) / ( d m

( )std

A

A APOC A

C d V m LC 1001.0,,400 ==

0.2 5.398266307

0.3 9.685354635

0.6 17.64225402

0.8 20.55409107

1 22.54114178

F T ,( )

VAstd

A

A APOC A DC

d V m LC =

== 1001.0,,400 ..(3 16)

:

+=

+=

1V0.1when3.7-V*49.5V*23.7-

1.0V04.0when0.47V*22.69-V*279.82

AA2A

AA2A

VA

VA

D

D

.(3 17)

F , T 2, 3 4

A 10012.0 d , 10015.0 d , 10017.0 d ,

1002.0 d , 10025.0 d :

U E 3 13 3 16:

( ) A

A A A

VA

POC VA

std A A APOC A A

B DC V LC

001.0

,,001.0

exp**),,(

= .. (3 18)


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:

0639.0*5.3439**588.8, ++= APOC APOC L B A .(3 19)

3.1.4 D

F E 3 8 3 18 wall Dk

MCLC . T PRB B L ,

PRB MCL

C POC,

Bwall

B B Dk

V L

*= ..(3 20)

113.034.46001.0

,exp

**

1*)1088exp(*248.0

+

=

A

A

VA

APOC

MCL

S VA

Awall

A B

C

C D Dk

.

.(3 21)

3.2 D

U ( 2.4.2),

PRB MCLC POC L (S A B):


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A B

POC A MCL

s

B NAC NAC

L NAC C

C

L

=*ln

.(3 22)

A NAC = = A

A A A A A D

DV V NAC

2

42 ++= ,

B NAC = PRB = B

B B B B B D

DV V NAC

2

42 ++=

3.3

U ,

PRB 7,500

. F

F 3 7

.

E S

. I , 95 ,

PRB 15 % 45

.


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3 6:E D E

-Model I-

3 7: A D E

M II


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Chapter 4

C

4 1. B

A PRB ( VI) A 199

F M V C (F 4 1)

(CVOC ) ,

1,2 (1,2 DCE), (PCE),

5,000 (F 4 2), N /N E , TCE

5,000 / (F 4 3).


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4 1: M S F (B ., 1998)

4 2 :M F (B ., 1998)


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4 3 : TCE (IT C ., 1991)

4 2.

4 2 1 A NAC

M M F P

(F 4 4). M WCI 1 WCI 3

PRB. A

J 1997, PRB. U

CVOC ( T 4 1) J 1997,


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lg / 3180 WIC 1. A lg / 3160

WIC 3. U 4 4, T feet 28 . A

PRB ,

A NAC 100023.0 m . H A NAC

(F 4 3). U ,

85 1) lg / 6200 , 2250

(W09 10) lg / 1600 A NAC

10006.0 m .


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4 4: L M B M W

(B ., 2005)


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4 2 2 B

A M F

PRB B (T 4 2). T

PRB B E 4 1. F

17.4 PRB B 199.3 d .

21)2ln(

T B = .(4 1)

4 1: B D (B ., 1998)

4 2 3 B B NAC

T 0.2 2

An 0.30 PRB Bn 0.33 (B ., 1998). I

PRB

2 / PRB


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W B B D d m E 20560.8

B NAC 119.7 m .

4 2 4 B

U F 4 3, 200 PRB

. B CVOC W9 35,

PRB ,

lg / 8000 . T

sC .

T E 3.22 PRB

(TCE, PCE, DCE, ) lgC s / 8000 = lgC MCL / 2 =

WIC 3 225 :

feet L design B 7.30006.019.7

225*0006.02

8000ln

=

=

T 95% , 15 %

PRB . T M PRB

feet 3.4 PRB 6 . T

PRB .


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Chapter 5

T

PRB . A

PRB

sC

MCLC P POC . B

PR

T 7,500

PRB (S I). T

(S II) . T

. U 7,500 ,

PRB 15 %


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PRB 95 . A ,

15

95

T PRB, N

PRB. B

( G . 2000) , P

.

A PRB

. T

. I PRB

. T

PRB .

G , A. R., G , N., S , B., F , T., J , R. J., H . J. T. D R P

US AIR FORCE, B , C , O . 2000


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MODEL I

POC L

A L

B L

B A L L +

A A A

A A A

B B B

nV

nV

n

V

Source


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MODEL I

Equations (ODEs, BC, Intermediate conditions)

:0 A L x 011

21

2

=

C xC

V xC

D A A A (1)

: B A A L L x L + 022

22

2

=

C xC

V x

C D B B B (2)

: B A L L x + 033

23

2

=

C xC

V x

C D A A A (3)

sC xC == )0(1 (4)

0)(3 + x xC (5)

)()( 21 A A L xC L xC === (6)

)()( 32 B A B A L L xC L L xC +==+= (7)


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11

22 C nV

xC

n DC nV xC

n D A A A A B B B B +

=+

when 1 L x = (8)

33

22 C nV

x

C n DC nV

xC

n D A A A A B B B B +

=+

when B A L L x += (9)

B

A A B B B A A B A n

nV V nV nV qq === (10)


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SOLUTION I

:0 A L x 011

21

2

=

C xC

V x

C D A A A (1)

The characteristic equation is:

04

02

2

>+=

=

A A A A

A A A

DV

xV x D

1a and 2a are the solutions to the equation above:

02

4

2

02

4

22

2

2

1

>++

=+

=

+=

=

B B B B

B B B

DV

xV x D

1b and 2b are the solutions to the equation above:


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02

4

2

0

2

4

22

2

2

1

>++

=+

=

+=

=

A A A A

A A A

DV

xV x D

1a and 2a are the solutions to the equation above:

02

4

2

02

42

2

2

2

1

>++

=+

=


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Using Boundary conditions

s

C xC == )0(1

(4)

Using xa xa

A Be Ae xC L x 21)(0 1 +=

=+== saa C Be Ae xC 0*0*1

21)0( )( I

C B A s=+

0)(3

+ x xC (5)

Using xa xa

B A HeGe xC L L x21

3 )( +=+ where :

0

2

4

2

02

4

22

2

2

1

>++

=+

=

Amine Hafsi MS Thesis

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