Modeling transport processes and differential accumulation of persistent toxic organic substances in groundwater systems

Ecological Modelling, 22

( 1 9 8 3 / 1 9 8 4 ) 135--143 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

135

.XlODELING TRANSPORT PROCESSES AND DIFFERENTIAL ACCUblULATION OF PERSISTENT TOXIC ORGANIC SUBSTANCES IN GROUNI)WATER SYSTE.~IS CHRISTOPHER G. IJCHRIN l~epartment o f E n v i r m n n e n t a l S c i e n c e , R u t g e r s U n i v e r s i t y ,

New Brunswick, NJ (IJ.S.A.)

ABSTRACT

[Ichrin, C.G., 1984. Modeling transport processes and differential accumulation of persistent toxic organic substm~ces in groundwater systems. Ecol. Modelling, 22: 135-143. Groundwater potential

represents

volume

the major freshwater

for the United States.

organic compounds

has recently been identified

ally in urbanized

areas.

of groundwater paramount

pollution

interest

blodeling

resulting

for ensuring

groundwater

conventional

The ability

movement

pollutants

in general,

hydrophobic

Their potential comprising

the soil matrix

and desorption

modeling

difficulties

from past and existing

the potability

The paper presents sorption models. tioning

assumption

time variable soil matrix

segments

Since the processes

of ad-

and not completely

Incorporating

is demonstrated.

equations equations.

development

submodel

A numerical

sys-

techniques. of several

to the classical

is presented.

dynamic

equi]ibrium

algoritm

parti-

for so]ving

The resultant

the control

first-order,

differential

phase mass balances.

in a

is f:ormu-

as well as unsaturated

for solute/liquid

ordinary

The algorithm

of segmenting

are coupled through the reaction

0304-3800/84/$03.00

sorption

in rather complex equation

for both saturated consists

can be formulated

tial equations

a complex

reversible,

liquid phase and solid phase concentrations

in three dimensions

for the solute/solid

pollutants.

is quite high.

the conceptual

Another N simultaneous

are, however, matter

for which N simultaneous,

equations

of

with the particulate

Their relationship

The technique

is of resource

and accumulation

substances

only by advanced numerical

lated so as to be useful ditions.

sources

systems have been successfully

Trace organic

are dynamic

pollutant

spread

association

arise.

solvable

by

especi-

of this important

and the transport

into large scale system models results tems, usually

the potential

and do not behave as conventiona]

for selective

sorption

in many states,

to predict

in groundwater

modeled by many investigators.

supply" in terms of

l,arge scale contamination

ordinary

volume

coninto N

differential

phase mass balances. equations

can be developed

The liquid phase/solid

phase

term in the liquid phase

is a set of 2N simultaneous

which can be solved by classical

© 1984 Elsevier Science Publishers B.V.

ordinary

numerical

differen-

techniques.

136

]

] NTRODUCTION

Groundwater in

the

the

United

States

freshwater

used

on it the of

as

the

long

standing

are

past

not

several

veral

years

that

by so

called

New J e r s e y , has

and

has

arisen

the

Federal existing

problem

nicknamed

"Superfund."

As o f

the

industrialized

national The

tants

in

saturated

who t r e a t e d (1975), The as

and

time

of

ground-

organic

hazardous the

a mechanism

for

this

cleanup,

paper,

has

New Y o r k ,

to

of

sub-

compounds

Pennsylvania,

eventual

waste

groundwater identifying commonly

New J e r s e y ,

65 s i t e s

se-

large

of

identified

differential

chloride (1980),

behavior

chromium

who m o d e l e d

of

for

accumulation groundwater

toxic

as

a

representing

28% o f

selective

in

has

substances

substance,

with

(1975), Pinder

and Moosburner

decaying

groundwater

hydrophobic.

association

successfully

Pinder

substance,

a first-order in

pollu-

been and

a conservative as

genera],

"traditional"

Bredehoeft

a conservative

nitrate

organic are,

as

of

systems

including

concentration

substances

potential

had

investigators

who m o d e l e d

these

the

past

substances

create and

bacteria

particular,

organic

the

the

Recognition

these

to

as

sup-

within

as

within

such

been

contamination

such

been

by synthetic 1980).

been

toward

In

Connecticut,

large-scale

by several

a n d Wood

metals.

sites

only

contamination

heavy

of

has water

total.

transport

modeled

state,

the

and

Government

and

only

substances

source

potential highly

over

Consequently,

surface

pollutants

has

toxic

(EPA,

a major

has

and

groundwater

California as

it

it

relying

198]).

where

directed

been

25% of

supplies

perspective,

Itowever,

"traditional"

in Nassachusetts,

sites

caused

in

areas

supply

population

(CEQ,

has

Moreover,

pesticides

identified

disposal

with

the

a supply

in

freshwater

presently

water

from

concern

hazardous

including

drinking

aw~-lable.

concern

contamination

been

of

the

50% o f

especially

that

wel]s

It

1980).

resource,

compounds.

water scale

source this

readily

95% o f

approximately

concern,

water

nitrogen

stances

(.Josephson,

decades

drinking

and

of

approximately

with

primary

development

plies

of

comprises

is

substance

quite

complex

As a r e s u l t ,

particulate

matter

their

is

quite

high. Soil

can

settling

of

be viewed small

as

a filtration

particles,

hydrodynamics,

electrostatic

reactions,

sorption

pension mow~l

and (Uchrin,

can

becomes

be

even

more

molecular all

affect

Much l i k e whereupon

complex

as

some

the

fate

a filter, these

gravitational

interception,

chemica] of

a soil's

contamination of

in which

diffusion,

interactions,

can

1985).

exhausted,

medium

can

removal

micro-

interactions a solute

capacity spread. processes

and

or

a susfor

re-

The problem are

rover-

137

sJble

and hysteretic

contaminated

water

(e.g.,

adsorption

is passed

through

and desorption).

a contaminated

Thus

soil,

if an un-

leaching

can

occur. The p r o c e s s e s

involved

of toxic

organics

a simple

first-order

research

effort

Brunswick, tion both

kinetic

currently

New J e r s e y ,

numerical

tions

adsorbing

A + S

~

for

and d i f f e r e n t i a l

too complex to

performed the

modeling

at

accumulation

be c h a r a c t e r i z e d

This

paper

Rutgers and s o l i d

phase soil

a

New

of a finite

and u n s a t u r a t e d

by

describes

University,

development

liquid

saturated

sec-

concentra-

systems

in

modes.

SUBMODEL

of a solute,

as an elementary

sorption

being

in both

DYMAMICS

The sorption pressed

are

decay expression.

and d e s o r b i n g

SORPTION

transport

USA, i n v o l v i n g

algorithm

of pollutants

2

in the

in groundwater

A, onto an adsorbing

reversible

reaction

medium,

accounting

S, can be ex-

for both ad-

and desorption: kA

(3)

A'S

w h e r e k A and kD a r e spectively,

forward

An e q u a t i o n

and r e v e r s e

describing

the

reaction

rate

net

of adsorption

rate

coefficients,

re-

c a n be

formulated:

dq _ dt kAC C s where

kdq

(2)

C is the concentration

tration

of vacant

adsorption

is the so]id phase Rearranging Q

Equation

(Mass solute/Mass

C s is the concenadsorber),

of A (Mass solute/Mass

2 and defining adsorber),

(M/LI),

the total

At e q u i l i b r i u m

concentration

as the sum of the vacant

of sites,

sites

(kD/kA)q] (dq/dt

= 0),

Equation

3 reduces

to

the

familiar

Langmuir

Equation:

the subscript,

Q, is commonly describes

and

(3)

Ce Q (kA/kD) qe = 1'% Ce(kA/kD) where

and q

adsorber).

sites yields:

dq d--~ = k A [ C ( Q - q )

Isotherm

sites

concentration

(Mass solute/Mass

occupied

of A in solution

e, denotes

referred

the energy

can be obtained

(4) equilibrium

conditions.

to as the adsorption

or intensity

from batch

reactor

capacity

of adsorption studies

The parameter, while

(Weber,

carried

(kA/kD)

1972).

Both

out to equilibrium

138 by plotting exist

(I/qe) versus

including

(i/Ce).

the Freundlich

Other equilibrium

isotherm models

(1926):

qe = KCe 1 / n where

(5)

K and n are empirical

describing

the kinetics

clude the linear

(approximating

n of unity),

the BET

meter model

(Brunauer,

developed

column

has shown

the sorption of organic hibits hysteresis. thus required.

~-tdq = Kr(Kcl/n_

where

3

5 with an a four p a r a

the kinetics

the results

1978).

In addition.

such as Equation

having

isotherm analyses.

ex3, is

from

first established It should be noted (dq/dt > 0) or net

for hysteresis.

5 and setting

Isotherm can be developed

this expression

equal

to

conditions:

q)

(6)

K r is a reaction eta].

of

frequently

kA, can be calibrated

experiments

Other

rate coefficient investigators

(I/T), calibratable

have suggested models

from the

including

(1971).

LIQUID PHASE MODEL

The three-dimensional

EQUATION mass balance

servative),

adsorbing

V (s V C)

V (UoC ] - p 6~ + ~__C_C @ S at at

where

and Cleary,

for the Freundlich

qe from Eqn.

in-

(1980). for describing

onto soil particles

parameter,

for non equilibrium

batch studies. Lindstrom,

Ce, or Eqn.

may differ for net adsorption

kinetic model

(l/Kr)(dq/dt)

isotherm models

and recently,

The use of a dynamic model,

(dq/dt < 0) to account

by subtracting

1938),

et al.

(van Genuchten

and Q from equilibrium

A dynamic

4 for small

et al.,

substances

The additional

that these parameters desorption

from batch experiments

Other

as their use in predicting

the batch adsorption/desorption (kA/kD)

derived

isotherm models

is problematic

studies

Eqn.

by van Vliet,

The use of equilibrium of sorption

constants

of net adsorption.

solute

~ is the diffusion

U o is pore velocity

equation

(con-

coefficient

(7) in the x, y, z directions

in the x, y, z directions

sity of the soil matrix

for a non-reacting

in a saturated porous medium can be written

(M/L3);

@ is moisture

and q is the solid phase concentration

(L2/T);

(L/T);

p is the bulk den-

content

(dimensionless);

(mass solute/mass

soil).

139 Equation simulating

7 can be applied transport

experiments. Davidson,

of a solute

Several

et al.

isotherm models

to a one-dimensional in labratory

investigators

(1968),

Kay and Elrick

and Rao and Davidson submode],

case for

column and field column

including

for the adsorption

(spatial)

(1967),

(1979)

have used linear

coupling

it to Equation

7,

yielding:

pK)

62C 6C D T ~ - Uo ~x

where D is an apparent obtainable

column.

tracer

Since the equation

adsorption

and desorption.

can only be accounted

so-called partition or net desorption

in a non-linear

solution

equation

linear,

systems

performed niques 4

into solving

partial

by Crittenden

1.

segments

The use of an isotherm model differential

equation

usually must be employed. by coupling

Equations

along with alternates.

equations.

and Weber

other

for

Numerical

solutions

carbon columnar

(1978) using

non-

to similar

systems have been

finite difference

(1980) using orthogona]

3 and

The problem

tech-

collocation.

SECTION ALGORITHM

A one-dimensional Figure

for the

net adsorption

sorption must be addressed

applied to activated

both

discussed

values

for both C and q in two simultaneous,

differential

and Weber and Liu FINITE

on whether

for a solid phase mass balance.

6 have been used by investigators thus results

thus examining

the previously

partial

technique

into an initially

the case of a pollutant

solutions,

K, depending

(L2/T),

8 has an analyti-

for by using different

of non-equilibrium

a second model

is linear,

is being exhibited.

a numerical

The problem

Equation

fed constantly

Unfortunately,

coefficient,

than linear results

for the column

studies.

by superimposing

hysteresis

equation

coefficient

for the case of a pollutant

"slug" can be examined

which

(8)

dispersion

from nonadsorbing

cal solution "clean"

~C T~ = o

(1 + ~ s

column can be segmented

An individual jl, and j2.

can take place accross

segment,

Advective

into N segments

as shown in

k, can be isolated with contiguous

and dispersive

any interface,

(k,j).

transport

of a solute

The advective

mass

flux

into and out of segment k can be formulated:

•

C(j

,k)

Q(k,j2) C(k,j )

where Q/A is the apparent interface

(M/L2-T)

volumetric

and C(j,k)

(9) flux rate across

is the concentration

the indicated

at that

interface

140 o,e i

1

o,c~ Fig.

].

Finite

(M/L3),

shown

section

in Figure

some c o m b i n a t i o n mathematically

C(jl)

C(k,j2)

= ~(k,j2)

C(k)

~(k,j)

+ ~(jl,k)

+ B(k,j2)

~'are w e i g h t i n g

+ B(k,j)

The c o n c e n t r a t i o n

at any

interface

in the two a d j a c e n t

will

segments,

beee

stated

as:

= ~(jl,k)

~ and

2.

of c o n c e n t r a t i o n s

C(jl,k)

where

schematic.

= 1 and

and,

C(j2)

(I0)

factors:

(a,~)

Substitution of E q u a t i o n

C(k);

> 0

(Ii)

I0 into E q u a t i o n

9 can be e x p r e s s e d

as a sum:

J

{-

A(k,j)

(a(k,j)

C(k)

g(k,j)

(lZ?

C(j))}

j=j~ where a p o s i t i v e the

total

Q/A r e p r e s e n t s

a flux

number of segments contiguous

leaving

s e g m e n t k and J c o n n o t e s

to k (dimensionless).

141

Jl

I r

k

Advective Transport - DisDersive Transport

Fig.

2.

Isolated

Dispersive

mass

E(j ,k) 0 (j ,k) L(j,k)

where

E(j,k)

related 0(j,k)

dispersion

is the moisture

j and k (L),

@(j)

+ B(j,k)

coefficient

content

commonly

content

in adjacent

across

interface

at the interface

length,

The moisture content

(dimension-

the average

at the interface

cells using

length

can be

~ and B:

@(k)

the total mass balance

medium

can be formulated:

(IS)

is a characteristic

to the moisture

Finally,

any interface

- C(k))

@(j,k)

= ~(j,k)

porous

flux across

(C(j)

and L(j,k)

of segments

schematic.

is the apparent

(j,k)(L2/T); less);

segment

(14)

equation

for a solute

in an unsaturated

can be expressed: J

V(k) ~cg(O(k) d

+ LE ( j~, k t)

where

C(k))

t~ ( j , k )

W' (k)

is

= ~ A(k,j){4 . J=]l

@(j)

+ g(j,k)

an e x t e r n a l

Q(k'J)c~(k A ---~" ' j) C(k)

0(k))(C(j)-C(k))]

source

to

segment

+ B(k,j)

dq + W' (k) P]]T

k (M/T).

Thomann

C(j))

(15)

(1972)

142 has shown how this term can be used to establish a Dirichlet boundary condition.

The Neumann boundary condition can be established using the

flux parameters.

For saturated conditions,

@ is constant and equals

@s and the model equation reduces to:

J V(k) ~ ( C ( k ) )

= >

A(k,j){-Uo(k,j)(c~(k,j ) C(k) + B(k,j)

C(j))

j=jl

+ E(j,k)tc L--Cj-?~ ( j ) - C ( k ) ) }

p dq e s dE + W(k)

A system of 2N simultaneous,

(16)

first-order,

ordinary differential

equa-

tions results for systems where both liquid and solid phase mass balance equations must be solved for C and q. employed to solve such a system as presented here,

A Runge-Kutta

(Carnahan,

is also usefull

technique can be

et al., 1969).

for multi-dimensional

The algorithm cases,

as the

segments do not have to be oriented in series. .5

SUMMARY

A numerical pollutant

algorithm has been presented to solve for time varying

liquid phase and solid phase concentrations

in one, two, or three dimensions.

in a porous medium

The algorithm is formulated

so as to

be useful for both unsaturated as well as saturated conditions. solution technique consists of segmenting the control volume segments for which N simultaneous,

first-order,

The

into N

ordinary differential

equations can be formulated for solute/liquid phase mass balances. Another N simultaneous

ordinary differential

for the solute/solid phase mass balances.

equations

can be developed

The liquid phase/solid phase

equations are coupled through the reaction term in the liquid phase equations.

The resultant

is a set of 2N simultaneous

ordinary differen-

tial equations which can be solved by classical numerical .6

techniques.

ACKNOWLEDGMENTS

The work described herein was supported in part by a grant from the Rutgers University Research Council. sor in the Department University,

of Environmental

New Brunswick,

New Jersey,

The author is an Assistant Science, USA.

Cook College,

Profes-

Rutgers

143

REFERENCES Bredehoeft, J.D., and G.F. Pinder, 1973. Mass transport in flowing groundwater. Water Resources Research, 9:194-210. Brunauer, S., P.II. Emmett, and E. Teller, 1938. Adsorption of gases in multimolecular layers. J. Amer. Chem. Soc., 60:309. Carnahan, B., H.A. Luther, and J.O. Wilkes, 1969. Applied Numerical Methods. Wiley, 604 pp. CEQ, 1981. Contamination of Groundwater by Toxic Organic Chemicals. United States Council on Environmental Quality, 84 pp. Crittenden, J.C., and W.J. Weber, Jr., 1978. Predictive model for design of Fixed-bed adsorbers: Parameter estimation and model development. J. Env. Eng. Div., ASCE, 104:185-197. Davidson, J.M., C.E. Rieck, and P.W. Santelmann, 1968. Inflence of water flux and porous material on the movement of selected herbicides. Soil Sci. Soc. Amer. Proc., 32:629-633. EPA, 1980. Proposed Groundwater Protection Strategy. United States Environmental Protection Agency, Office of Drinking Water. Freundlich, H., 1926. Colloid and Capillary Chemistry. Methuen and Co., Ltd., L o n d o n . Josephson, J., 1980. Safeguards for groundwater. Env. Sci. & Tech., 14:38444. Kay, B.D., and D.E. Elrick, 1967. Adsorption and movement of lindane in soils. Soil Science, 104:314-322. Lindstrom, F.T., L. Boersma, and D. Stockton, 1971. A theory on the mass transport of previously distributed chemicals in a water saturated sorbing porous medium; Isothermal cases. Soil Science, 112:291-300. Moosburner, G.J., and E.F. Wood, 1980. Management model for controlling nitrate contamination in the New Jersey Pine Barrens aquifer. Water Resources Bulletin, 16:971-978. Pinder, G.F., 1973. A Galerkin-finite element simulation of groundwater contamination on Long Island, New York. Water Resources Research, 9:1657-1669. Rao, P.S.C., and J.M. Davidson, 1979. Adsorption and movement of selected pesticides at high concentrations in soils. Water Research, 13:375380. Thomann, R.V., 1972. Systems Analysis and Water Quality Management. Environmental Research and Applications, Inc., 286 pp. Uchrin, C.G., 1983. Removal of Particulate Matter by Filtration. Ch. 6 in Cemistry of Water Treatment (S.D. Faust and O.M. Aly, auth.). Ann Arbor Science, in press. van Genuchten, M.Th., and R.W. Cleary, 1978. Movement of Solutes in Soil: computer simulated and laboratory results. Ch. I0 in Soi] Chemistry (G.M. Bolt and M.G.M. Bruggewert, eds.). Elsevier Publishing Co. van Vliet, B.M., W.J. Weber, Jr., and H. Hozumi, 1980. Modeling and prediction of specific compound adsorption by activated carbon and[ synthetic adsorbents. Water Research, 14:1719-1728. Weber, W.J., Jr., 1972. Physicochemical Processes for Water Quality Control. Wiley, 640 pp. Weber, W.J., Jr., and K.T. Liu, 1980. Determination of mass transport parameters for fixed bed adsorbers. Chem. Eng. Communications, 6:49.