A MODEL WITH MASS TRANSPORT LIMITATIONS FOR PUMP AND

TREAT REMEDIATION OF SOILS POLLUTED WITH NAP[,

CESAR GOMEZ-LAHOZ, RAFAEL A. GARCIA-DELGADO and DAVID J. WILSON*

Departamento de Ingenieria Quimica, Facultad de Ciencias, Campus Universitario de Teatinos, Universidad de Malaga, 29071-Malaga, Spain

Abstract. A model is presented for the description of the pump and treat (or flushing) remediation of the saturated zone with non-aqueous phase liquid (NAPL) present as droplets. Sensitivity analysis shows that the most important variables are the NAPL droplet size and the distance through which the dissolved organic compound must diffuse to reach the advecting aqueous phase. The time needed to achieve complete remediation for different initial contaminant concentrations in soil depends more on the NAPL droplet radius and the size of the stagnant boundary layer than on the initial contaminant mass itself. Location of wells and flux rates are of little significance over the time needed for completion as long as all the water that flows through the contaminated region is captured in the recovery well.

1. Introduction

Pump and treat has been traditionally the in situ technology most used for the remediation of sites where contamination is present in the saturated zone. Pump and treat remediation has been initiated at hundreds of sites but very few closures have been achieved. Success is usually limited by several factors that have been discussed extensively elsewhere (see for instance Mackay and Cherry, 1989). This technique may be used to remove different kinds of contaminants, such as metallic ions or various types of organic pollutants, but probably the most difficult situations arise with some liquid halogenated compounds of very low aqueous solubility, high toxicity, and densities greater than water - the dense non-aqueous phase liquids (DNAPLs).

The fate of DNAPLs in the soil and aquifer environment (Schwille, 1988; Huling and Weaver, 1991; Feenstra and Cherry, 1987) depends on the properties of the soil (porosity, permeability, presence of clay lenses, rock fractures, preferential paths, etc.), the characteristics of the DNAPL (amount released, viscosity, density, solubility, etc.), and on the way in which the DNAPL was released (as a small continuous leak for a long period of time or as an instantaneous large discharge (Poulsen and Kueper, 1992). In any case, establishing the precise location of the DNAPL without excavation is difficult, and, even if most of it could be removed from pools by miraculously successful placement of the recovery wells, some will remain as residual DNAPL droplets, ganglia or fingers.

* Permanent address: Department of Chemistry, Box 1822, Sta. B, Vanderbilt Universty, Nashville, TN 37235, U.S.A.

Environmental Monitoring and Assessment 32:161-186, 1994. (~) 1994 Kluwer Academic Publishers. Printed in the Netherlands.

162 CESAR GOMEZ-LAHOZ ET AL.

When water flows through DNAPL-containing soils, even in the case of homo- geneous porous aquifers, the aqueous contaminant concentrations registered at monitoring wells located downstream are usually well below saturation. The slow rate of the mass transfer has been ascribed (Powers et al., 1991, 1992) to: (1) rate limited mass transport between the nonaqueous and aqueous phases; (2) the bypassing of advective aqueous phase around contaminated regions of low aqueous permeability; and (3) non-uniform flow due to aquifer heterogeneities. These mass transfer limitations become more evident when the advective flow increases, i.e. when one is performing pump and treat remediations, and they lead to extremely long lifetimes of the DNAPL droplets that act as reservoirs to supply contaminant to the ground water slowly.

Several physical phenomena contribute to the tendency of the water flow paths to avoid the more heavily contaminated domains. One of the most important is the effects of DNAPL ganglia on the water conductivity of soil. This is a function of the degree of water saturation of the medium, so the mere presence of the non- aqueous liquid phase leads to a local area of very low hydraulic conductivity. The Millington and Quirk (1961) model predicts, for homogeneous media, a decrease in the relative aqueous conductivity (K) following the equation:

K = K0(~) 1°/3

where K0 is the water conductivity for water-saturated soil and (b (0 < • < 1) is the degree of saturation (~ = volume of water/void volume). Some authors (Schwille, 1988; Williams and Wilder, 1971) consider that the relative permeability reaches zero values for degrees of saturation substantially higher than zero.

Thus, a stagnant water film exists around the DNAPLs, and the contaminants must diffuse through this layer to reach the advecting water. Molecular diffusion constants of most compounds in the water phase are extremely small, so diffusion transport is very slow. A number of papers has studied the complexity of processes with linked diffusion-advection; these include work by Naymik (1987), Huyakorn et al. (1983), Bibby (181), Grisak and Pickens (1980a, 1980b, 1981), Rasmuson and Neretnieks (1980, 1981), Neretnieks (1980), Noorishad and Mehran (1982), Tang et al. (1981), Sudicky and Frind (1982).

In this paper we present a model describing the pump-and-treat remediation of a DNAPL-contaminated aquifer. The model utilizes the basic picture of DNAPL solution employed by Kayano and Wilson (1993) but special attention is given to the system of injection and extraction wells, and the model gives a more realistic treatment of the removal of the organic compound (OC). The aquifer is assumed to be of constant thickness, and a two-dimensional treatment is given to a rectangular domain within the aquifer which includes the injection and recovery wells. (Here we report on runs with one injection and one recovery well, but any number is allowed.) This domain is divided by a rectangular grid into a number of compartments to allow the numerical integration. Figure 1 is a representation of the domain and some of the notation used.

PUMP AND TREAT 163

(0, YT)

l y Injection well 0

I

(1, 1) I (2, 1)

(0, 0)

Fig. 1.

(1)

(2)

(i-l, j) " ~

(Xw, YT) (nx, ny:

Contaminated region

Recovery well @

tn. x (XT, 0)

Geometry and notation of a system with an injection and a recovery well.

The basic assumptions of the model are as follows:

The soil is homogeneous and isotropic, and advection may be described by means of a potential function with one term for each well (injection or extrac- tion).

Part of the aqueous phase is mobile and the other portion is immobile, trapped in porous structures of low permeability. These structures may be lenses or discontinuous layers of clay, silt or till.

(3) NAPL is present as droplets surrounded by the immobile aqueous phase.

Thus, clean up of the aquifer requires

(a) solution of the droplets by diffusion through a boundary layer;

(b) diffusion of the dissolved OC through the immobile aqueous phase;

(c) the recovery of the contaminant in the mobile aqueous phase.

We describe first the advection terms, then diffusion through the immobile phase, followed by solution of the droplets. Then the model is presented, after

164 CESAR GOMEZ-LAHOZ ET AL.

which a sensitivity study of the parameters is made. The nomenclature used in the paper is given in the appendix.

2. Advection Terms

The advection of water in the presence of n~ wells and a uniform natural flow in the x-direction are described by the following potential function, each term of which satisfies Laplace 's equation:

n w

W = v°x + ~ A~ loge[(x - x~) 2 + (y - y,~)2] . (1) A=I

The A;~ can be related to the volumetric flux from the wells (A~ is positive for injection wells) by means of the following procedure: In the vicinity of the Ath well, W is given by:

W = A;~ log e r 2 -q- terms regular at r = 0 (2)

where r 2 = (x - x),) 2 --~ (y - y.~)2

A W vr - A r -- 2A~/r + terms regular at r = 0 (3)

27r 27r

= h / vr r dz9 = h / 2A~, dO = h 47r AA . Q~ (4) , / , /

0 0

Thus:

W = v°x + ~ loge[(X - x;02 + (y - y;02] (5) A=I

naz o Q~ (x - x~)

v~=v~+~ 2¢~h (x-x.x) 2+(y-y~)2 (6) A=!

~w Q;~ (y - Y;0 (7) Vy = ~ 27r h (x - x - ~ 2 -+'-~ - y~)2

A=I

and the advective terms for mobile OC are described by the following mass bal- ance:

= hAyv [S@j)C?_,,j + S(- pCS] t / A V ~ - - -d~ ) adv"

+ h A y v .R. C m C m z,3[--S(--V 5 ) i-t-I,j--s(vRj)i,j] + h +

-~- hAxviF,,j [--S(--VFj)ci,r~+I- S(viFj)CS] (8)

PUMP AND TREAT 165

/ /

DNAPL I droplet

Advee t ive w a t e r

oooo oOOOoOO 1 o 00%00 0 2 0 0 ` 0 0 0 0 0 O 0

0 O 0 O 0 0 O 0 O 0 0 0 0 O 0 O 0 O 0 0 C o o° %o000 °o g o % ~..oOOOo o o o o°°°°o°°oo 2 O o o o o

i 0 o o o o o O O o o 0 0 0 0 0 O 0

I O O O O O O O O O O O O O O O 0 O 0 O 0 0 O 0 0 0 0 0 0 0 0 0 0 O 0 0 0 ,, o o o o °o °ggo o o o o o 20%%0 o o o o o

/

/

Fig. 2. Model for diffusion transport of dissolved OC from the aqueous phase in a low permeability domain. The slabs used to mathematically represent the domain are shown.

where C ~ is the aqueous contaminant concentration in the mobile phase of the (i, j ) th compartment, AV is the volume of the compartment (AV = h Ax Ay), u is the porosity associated with mobile water, and v~j is the average value of the superficial velocity normal to the left (vLj), right (vR), back (vB4), or front

v~ ~J S (vFj) faces of the ( i , j ) th compartment. S(v~j) = 1 for v~j > 0 and S(v~,j) = 0 for v .s. < 0. Each velocity is the average of a finite number (p + 1) of values

7,~3 - -

obtained from equations (6) or (7) for coordinates located equidistantly along the border of the compartment, with a p value large enough to make the mass transport conservative (volumetric flux into the compartment = volumetric flux out of the compartment). This is expressed as follows:

P

vL'~,3 = ~ v:c[(i-- 1 ) A x , ( j - e / p ) A y ] / ( p + l) ~ = 0

P

v .R . w = ~ v ~ [ i A x , ( j - ~ / p ) A y ] / ( p + l) ~ - 0

P

v B. = ~ Vy[( i - -c /p) A x , ( j - 1) A y ] / ( p + l) ~ 0

P v .F . w = ~ vy[(i - e/p) Ax , j Ay] / (p + 1).

~----0

(9)

166 CESAR GOMEZ-LAHOZ ET AL.

3. Diffusion Through the Stagnant Water

The analysis that follows is similar to that performed for fractured rock aquifers (Narasimhan, 1982), in which the discrete fractures are partitioned into volume elements, and the mass balance equations for these volume elements are developed and solved. It is also similar to the one developed previously for soil vapor extrac- tion (Rodrlguez-Maroto et al., 1994) and sparging (Gomez-Lahoz et aI., 1994). Assume that the stagnant water is held in a rectangular region (as the one repre- sented in Figure 2) of thickness 2L, let the total cross-sectional area of the stagnant region in one compartment be A, and the porosity of the material containing the non-mobile liquids be Ustg. Then:

w A V = UstgA 2L (10)

where co is the porosity of AV associated with the immobile water. Then the total area (2A, since advective water is present at both sides of the stagnant region so diffusion occurs in both directions) for diffusive transport is:

co/ \V 2A = (10')

PstgL

We divide the length L into nu slabs, each slab containing an average immobile water concentration, C~,j, k, of OC and a total NAPL mass, mi,j,k, so the mass balance for the kth slab gives:

co A V dC~,j, k (k = 2, 3, ..., n~, - 1)

nu dt

w A V

PstgL

rearranged to:

dC~,j,k

dt

For k = nu

dC .~- Z~J~u dt

and for k = 1

dC~,j,1 _

dt

D CW ~kit ( i,j ,k+l -- 2C~,j,k q- C~,Z~,k-l) dmi,J,kdt

D C ~° C w ( i,j,k+ - 2C j,k + i,j,k-1) /]stg (z~U) 2

(11)

nu dmi,j,k wA V dt

(11')

where the coefficients for C~,j, 1 and C/,~ take into account the distance for diffusion between the center of the first slab and the mobile phase is Au/2 .

D Ttu -- 3C~,j, 1 -{- 2C/,~) dmi,j ,1 (13) Pstg(A2t) 2 w AV dt

D CW CW nu dmi,j,n~ (12) Ustg(Au) 2 ( - i,j,n~ + i,j,n~--l) w A V dt

PUMP AND TREAT 167

4. N A P L S o l u t i o n

First, we assume that NAPL is present as spherical droplets which initially have a radius a0, surrounded by a boundary layer of immobile aqueous phase of radius b. The number of droplets in each compartment of volume AV is given by n, where

n

and

n - -

47r a 3 POC

3

3zxvc0 N

- - A V C N (14)

ab C ( r ) - b - a

and

dC ab

dr b - a r 2

a

d I 1 r 2 dr r 2 - ~ r = 0 ; (r 2 a ) (15)

which integrates to:

C(r) = C1/r + C2 (16)

with C(a) = C ~ and C(b) = C ~ as boundary conditions. This leads to:

C ~ _ C w n u C 2 (17)

r

dmi,j,k

dt

C 8 - - C W

(18)

Therefore the rate of solution of NAPL in the kth slab of the (i, j ) th compartment is obtained from Fick's first law, the previous equation, and the number of droplets in each slab as:

- - - [droplets in each slab] [rate of solution of each droplet]

- [ 3 A v c N ] [ 47cr2Dab C s - C w ] (19) L?Z u47ra03pOC j k l) ---a r-2 J I

The mass and the radius of each droplet are related to the initial mass and radius by:

a/ao = ( m i , j , k / m O ) 1/3 . (20)

A reasonable estimate for b is half the distance between droplets. This is obtained from the amount of water per droplet, V~:

(14 / ) 47r %3 Poc

Assuming steady state diffusion, we have for a single spherical droplet of radius

168 CESAR GOMEZ-LAHOZ ET AL.

V 11/3 AVco 1/3 {TrcdPoc]l/3 b - -~ - 1 / 2 ( - - - - ~ ) = a0\ 6CoN )

Substitution of equations (20) and (21) into equation (19) gives:

dmi,j,~ 3AV Co N D(C ~ - CW)(mi,j,k/mo) 1/3

at n~a~poc[1 - (ao/b)(mi,j,k/mo)U 3]

(21)

(22)

5. The Model

The model requires solving the advection terms in equation (8) together with the terms of the contaminant flux coming from the immobile aqueous phase by diffusion. This last is given by:

/ d C ~ , w AV D /Y A V \ - - ~ / d i f f . [ ° ' J / -- PstgL A u / 2 (Cwi'j'l -- C~,j)m (23)

c w c D 02

T ] d i f f . -- U//stgL A u / 2 ( i,j,l -- %3)" (23t)

Then, on combining equation (23 I) with equation (8), we have:

dC~ 1 dt - u A x vLj[S(vLj) cim-i'J "-~ S(--vLj) C~]

1 + -'~--~zVR'[--S(--ViRj)cir~I,j- S(v/B,j) C~j]

1 B + Vi-- v +

--~ ~ , v F j [ - - S ( - - v F j ) C~,j+l -- S(vFj) C~]

w D -1- - - (C~,Wj,1 - C~,'~) (24)

tJ UstgL Au/2

which is integrated forward in time together with equations (11'), (12), (13) and (22) by means of a predictor-corrector algorithm.

6. Results

Initialization consists of specifying the model parameters, the dimensions of the contaminated zone and of the domain of interest, and the initial OC concentration, which is assumed to be initially homogeneous within the contaminated region,

PUMP AND TREAT 1 6 9

having the same value for water concentration in the mobile and immobile aqueous phases. NAPL will be present if the amount of contaminant is more than that needed to reach saturation in the aqueous phases. The model permits one to track the mass of OC in the aquifer, the amount extracted from the wells, and the amount that escapes across the subsurface outer boundaries of the domain. Most runs were made using two wells aligned with the natural flow (i.e. flow in the absence of wells, v%, and the system was symmetric about a line drawn between the two wells. In

X /

this case only half of the domain was integrated, with the corresponding changes in the boundary conditions; this causes no differences in the results obtained.

The model was implemented in Turbobasic and run on a microcomputer using a 80486 DX microprocessor and having a clock speed of 50 MHz. Typical run times were between 5 and 15 min, and the longest run required around 1 h of computer time.

Default parameters are given in Table I. Variations from this set of values are indicated in the text and figure captions as they occur. The streamlines for these parameters are shown in Figure 3. It can be seen that all the streamlines running through the contaminated area reach the recovery well, so that no OC should escape from the domain of interest through the subsurface boundaries under these circumstances.

A first set of runs was performed to study the variations in the cleanup time and contaminant concentrations that result when variations are made in the thickness 2L of the domains from which the contaminant must diffuse. Figures 4(a) and 4(b) show the contaminant reduced mass (M / = [initial mass - mass pumped out] / [initial mass]) and reduced concentration of the solution pumped out (C' = [Cwe~l/CS]) (for domains of thickness (2L) 1, 1.5, 2 (default), 3 and 4 cm. Recall that the diffusion takes place from both sides of the domains so that the location furthest from the mobile water will be at one half of this distance.

As can be seen, since the recovery well is out of the region initially contaminated, a very short period is observed where the contaminant concentration of the effluent increases; this lasts for only few minutes. The mobile water coming from the contaminated region to the wells is initially saturated with contaminant. As the clean up proceeds, clean water enters the contaminated region and the contaminant in the domain diffuses to the mobile at a rate that is not enough to maintain saturation. Therefore, the very short first period is followed by a period of several hours during which there is a sharp decrease in the effluent contaminant concentration as the OC-saturated water is pumped out. This decrease becomes more pronounced as the thickness of the low permeability domains increases. Afterwards, the effluent OC concentration becomes quite steady as the amount of contaminant diffusing to the mobile phase from stagnant zones is essentially equal to that being pumped out. As can be seen in Figure 4, after several weeks (or months for the higher values of 2L), the cleanup approaches completion and the contaminant concentration plot shows another sharp drop.

170 CESAR GOMEZ-LAHOZ ET AL.

TABLE I

Default parameters for pump and treat runs.

Height of the contaminated zone and domain of interest, (h) 5 m Length of the domain of interest; water flow direction

without wells (XT) 30 m Width of the domain of interest (YT) 30 m Contaminated zone:

Minimum value on the X axis 8 m Maximum value on the X axis 22 m Minimum value on the Y axis 8 m Maximum value on the Y axis 22 m

Natural water superficial velocity (v °) 10 .5 m/s Number of divisions along the X direction (n,) 15 Number of divisions along the Y direction (ny) 15 Porosity associated with mobile water (u) 0.2 Porosity associated with stagnant water (co) 0.2 Thickness of the low permeability domains (2L) 2 cm Number of slabs in L 5 Porosity of low permeability domains (ustg) 0.4 Soil density, dry basis: psoii 1.7 g/cm 3 Initial contaminant concentration 2000 mg OC/kg dry soil Contaminant diffusion coefficient in stagnant water (D) Contaminant solubility in water (C s) NAPL density (poc) NAPL droplets initial radius (a0) Time step (At) Well descriptions:

Injection well volumetric flux (Q 1) X coordinate of the injection well (Xl) Y coordinate of the injection well (Yl) Extraction well volumetric flux (-Q2) X coordinate of the extraction well (x2) Y coordinate of the extraction well (y2)

2 .10 -1° m2/s

1100 mg/1 1.46 g/cm 3

0.1 cm 1000 s

0.003 m3/s 5m

15m 0.005 m3/s

25 m 15 m

F r o m the point o f v iew o f a field operator who can only measure the O C

concent ra t ion in the r ecove ry well effluent and m a y not k n o w the amoun t o f

con t aminan t remain ing in the soil, the tailing effect descr ibed above m a y be very

d iscouraging , s ince apparent ly on ly little progress is being made dur ing the plateau o f the concent ra t ion curves and there is no indicat ion that one is app roach ing

comple t ion o f the remedia t ion task at a reasonable rate. Thus, when N A P L is present

and the remedia t ion is rate-l imited by mass- t ransfer p h e n o m e n a one should expec t a substantial per iod o f t ime dur ing which the effluent concent ra t ion will r emain at

PUMP AND TREAT 171

Fig. 3. Streamlines obtained for the default values (corresponding to parameter values given in Table I).

relatively low values without much further decrease, and with no indication as to how far in the future the end of the cleanup process is. However, the contaminant reduced mass curves in Figure 4 show that, as long as the value of the effluent OC concentration is not extremely low, the remediation is not failing to progress.

Figures 5(a) and 5(b) show the results obtained with different droplet radii; the rest of the parameters are as in Table I. In this series the initial droplet radii (a0) were 0.01, 0.05, 0.1 (default), 0.2 and 0.3 cm. Again the same stages of cleanup as seen above appear clearly in the effluent reduced concentration curves:

(1) an initial transient increase followed immediately by a sharp decrease during the first few hours, which is larger in size for those systems that will take longer to clean up (i.e. for the larger drop sizes);

(2) a diffusion kinetics-limited plateau that lasts several days;

(3) a terminal phase in which the effluent concentration decreases rapidly to zero.

Small differences in the plots are obtained between runs with very small drop sizes because solution of the drops is no longer rate controlling, so only diffusion from

172 CESAR GOMEZ-LAHOZ ET AL.

0.8-

0.6-

0.4-

0.2-

3'o

3 4

60 90 t (days)

120

0.1:.

0.01:

0.0011 0

1 j

1 .5-- - -_

I [

3'0 60 90 19.0

t (days)

Fig. 4. (a) and (b). Plots of reduced mass and effluent concentration for different sizes of the clay domains 2L = 1, 1.5, 2, 3 and 4 cm. Other parameters as in Table I.

PUMP AND TREAT ] 73

the stagnant zones determines the concentration in the mobile water and therefore the cleanup time. On the other hand, as the drop size increases the system becomes very sensitive to the droplet size, as the droplet solution becomes the limiting factor.

As discussed for Figure 4, plots of the reduced mass evolution with time, shown in Figures 5 through to 10, indicate that the time needed for completion of the cleanup corresponds to the terminal phase of the concentration curves (Figures 5b to 10b).

A third series of simulations is shown in Figures 6(a) and 6(b), in which the initial concentration of contaminant in the contaminated area has been varied between 250 and 2500 mg of OC/kg of soil. The three regions seen previously are observed here, too, for all the curves except for the one corresponding to the smallest initial contaminant concentration. In this case the initial aqueous concentration (250. 1.7/0.4 = 1062.5 rag/1 aqueous phase) is below saturation (1100 mg/l). Thus there is no NAPL present to act as a reservoir to supply large amounts of OC to the mobile phase, so no plateau region in the effluent concentration curve is observed for this run.

As the amount of OC increases the amount of NAPL also increases and the plateau in effluent OC concentration therefore lasts for longer periods of time. The times needed to reach completion of the cleanup are less than proportional to the initial mass, however, because this series of runs assumes that the NAPL droplets (if NAPL is present) have the same initial diameter in all runs. Therefore, as the initial amount of contaminant increases both the number of droplets and the water- NAPL interfacial area increase proportionally, and the distance between droplets (2b), used as twice the boundary layer thickness for the dissolution, decreases. Therefore the rate of solution is faster at the higher initial OC concentrations, and the effluent OC concentration in the plateau region increases towards the value that would result from equilibrium with respect to the kinetics of droplet dissolution. In this situation the mass transport to the mobile aqueous phase is controlled only by diffusion through the stagnant aqueous phase to the mobile water. If the increase in the initial mass is associated with larger droplets size (maintaining the number of droplets constant) the cleanup time of the system increases more rapidly with increasing initial total contaminant mass.

The next series of runs shows the influence of the well positions with respect to the initially contaminated region: the wells are in all cases aligned so that the recovery well is in line with the injection well in the flow field. The default values given in Table I place the injection and extraction wells 3 m outside the left and right borders of the initially contaminated region respectively. The plots of reduced contaminant mass and concentration in Figures 7(a) and 7(b) correspond to runs performed for well positions 3 m and 1 m inside the contaminated zone (presented in the figures as - 3 and - 1 ) and both wells 1 m outside, together with the default positions (3 m outside). Figure 7(b) includes a schematic representation of the positions of the wells.

174 CESAR GOMEZ-LAHOZ ET AL.

0.4-

1- •

0.8-

0.6-

0.2-

0 0

.2 .3

50 100 150 200 250 300 t (days)

Q

0.1

0.01:

0,001 0

\

/ .01

! r

50 i ,

100 150 260 250 300 t (days)

Fig. 5. (a) and (b). Plots of reduced mass and effluent concentration for different initial droplet radii ao = 0.01, 0.05, 0.1, 0.2 and 0.3 cm. Other parameters as in Table I.

PUMP AND TREAT 175

O

1-

0.8-

0.6-

0.4-

0.2-

0 0

2500

r

20 40 60 t (days)

80

1.

Ct~

" ~ _ _ . ~ /1000

0.1: / 2 0 0 0

0.01:

0.001 ? 5 0 . / I

0 20 40 60

t (days)

2500

80

Fig. 6. (a) and (b). Plots of reduced mass and effluent concentration for different initial contaminant concentration 250, 500, 1000, 1500, 2000 and 2500 mg OC/kg soil. Other parameters as in Table I.

176 CESAR GOMEZ-LAHOZ ET AL.

o

0.8-

0.6-

0.4-

0.2-

1'5 3'0 4'5 60 t (days )

0

0.1

0.01

-3

-1

0.001(~ 1'0 2'0 3'0 4'0 5'0 60 70

t (days)

Fig. 7. (a) and (b). Plots of reduced mass and effluent concentration for different well locations. Other parameters as in Table I.

PUMP AND TREAT 177

As can be seen, the system is quite insensitive to the location of the wells as long as the water flowing through the contaminated region is recovered in the extraction well and the solution and diffusion mass transport kinetics of OC to the mobile water are controlling. Of course, for those runs with the wells located inside the contaminated zone the very short initial period that was observed in the previous runs, during which the concentration values increase, does not appear.

Another series was performed in which the Y coordinates of the wells were varied while the X coordinates were kept at the default values. Plots of reduced contaminant mass and concentration are presented in Figures 8(a) and 8(b). Figure 8(b) includes a diagram showing the positions of the wells. No significant differ- ences were obtained with respect to the results obtained for the default parameters up to the maximum misalignment value checked of 8 m [injection well coordinates = (5, 23), recovery well coordinates (25, 7)].

One more series was performed to study different injection rates, Q1, while holding the extracton volumetric flux, -Q2 , constant at the default value. Figures 9(a) and 9(b) present the results for ratios Q1/(-Q2) of 0.0, 0.2, 0.6 (default value), 0.8, and 1.0. As can be seen, only small differences between the reduced effluent concentration curves are obtained, although a slight decrease in the cleanup efficiency is observed as Q1 decreases.

Another series of runs was performed similar to the one shown, but with the wells located inside the contaminated area. In this case, the concentration curves are almost identical to those of Figure 9(b), but an important difference arises between the reduced mass plots for the two sets of runs. The plots of reduced contaminant mass presented in Figure 9 show that only negligible amount of contamination remain in the aquifer after the operation, whereas results obtained with the wells located inside the initially contamination region showed that a significant amount of contaminant was not recovered with the water pumped out when Q1/(-Q2) ratios were 0.8 or 1, but was washed out of the domain of interest. The relative amounts lost were 0.8 and 4.3% respectively. The model used here, in which the domain of interest is divided into a finite number of rectangular compartments, each having a homogeneous concentration and advective mass transport taking place between the compartments, may lead to significant transverse numerical dispersion of the contaminant, much greater than the true transverse dispersion occurring in the aquifers due to water advection. While it is clear that losses of contaminant may occur if very high ratios of injection to extraction rates are used, one must be cautious about the results obtained from this model, because of numerical dispersion.

Figures 10(a) and 10(b) show plots of reduced contaminant mass and concen- tration obtained for different extraction fluxes (--Q2 = 15, 10, 5 (default), 2.5 and 1 Us) while the ratio between the injection and recovery rates was kept constant [Q1/(- -Q2) = 0.6]. Two important conclusions may be drawn here. First, the con- taminant mass flux pumped out of the soil becomes independent of the water flow rate when this reaches sufficiently high values that diffusion transport becomes

178 CESAR GOMEZ-LAHOZ ET AL.

0.8-

0.6-

0.4-

0.2

fo 2'0 3'0 4'0 5'0 60 t (days)

70

0 . 1 ~ " ~

O0

r.)

0.01

0.001 0

o

l'O 2'0 3'0 4'0 5'0 6'0 70 t ( d a y s )

Fig. 8. (a) and (b). Plots of reduced mass and effluent concentration for different well locations. Other parameters as in Table I.

PUMP AND TREAT 179

1

0.8

0.6- 0

0.4-

°" I

o

¢D

0 10 20 30 40 50 60 70 t (days)

0.001

0.1

0.01: 2

3 t 0 1'0 2'0 3'0 40 5'0 6'0 70

t (days)

Fig. 9. (a) and (b). Plots of reduced mass and effluent concentration for different injection/recovery flow rate ratios. Recovery flow rate held constant at - Q 2 = 51]s; other parameters as in Table I.

180 CESAR GOMEZ-LAHOZ ET AL.

the limiting factor. At that point the cleanup time is not reduced with increasing pumping rate, while the costs of energy, the pump, and treatment of the recovered water at the surface are increased. Second, if the recovery well does not pump water out of the soil rapidly enough, the risk of part of the contaminant flowing out of the domain of interest increases. This is illustrated by the curve of 1 1/s in Figure 10. Thus, if diffusion of the contaminant through stagnant regions in the soil is the limiting process, the optimum working flow rate will be the smallest which guarantees recovery of all the contaminant.

When working under limited mass transfer conditions, one may also consider pulsed operation of the wells. A reasonable procedure may be the following. The recovery well is pumped at a rate large enough to assure that no contaminant flows out (downstream) of its area of influence until the OC concentration in the recovered water becomes quite steady, indicating that the mass transfer kinetics from the stagnant to the mobile phase are controlling. Then the pump is stopped to allow the OC concentration in the mobile phase to reach reasonably high values at monitoring wells placed in the contaminated region. At this stage the pump is operated again until the plateau region of the concentration curve is reached. This kind of work cycle may save money by decreasing the amount of water pumped and treated, and is very similar to the pulsed soil vapor extraction (SVE) technique for the remediation of OC contaminants in the unsaturated zone when mass transfer kinetics are limiting.

Nevertheless the situation in the saturated zone of the aquifer is somewhat different from SVE because significant advective transport due to natural water flow may remain after the pump is stopped. The importance of this may be seen in Figure 11, where the OC concentration at a monitoring well located at the center of the contaminated region [(z, y) = (15, 15)] is presented for three runs having different values of the natural superficial velocity (v ° = 10 -5 (default), 10 -6 and 0 m/s); the other parameters have their default values. For these simulations the pumps were stopped after 30 days of operation (Q1 = - Q 2 = 0). As can be seen, a rebound in the concentration is observed, but a maximum is reached for curves (1) and (2), after which the concentration decreases again, indicating that the contaminant is being washed out by the natural flow. Thus, one must be careful if pulsed operation is being considered when choosing the duration of the shut- down period. The contaminant plume may be permitted to reach only those regions which are within the zone of capture of the recovery well when it is operating. Verifying this requires a careful placement of monitoring wells downstream from the recovery well.

These rebound curves may also be useful to determine the kinetics of the mass transfer processes taking place in the subsurface, information needed to plan a decrease in the flow rate of the recovery well. It is also absolutely necessary before closure of the site to show that rebound does not occur in order to demonstrate completion of the remediation. Figure 12 shows the rebounds obtained for the same sizes of the low permeability domains as were used in Figure 4 for the

PUMP AND TREAT 181

O

0.8-

0.6-

0.4-

0.2-

0 / 1 - - ~

, 15 go 4'5 6'0 ~5 t (days)

90

1.-

J

0"11

0.01

O.O01F ' ' , ~ ~ , ~ I 0 1'5 3'0 4'5 60 75 90

5 1 10 /

t (days)

Fig. 10. (a) and (b). Plots of reduced mass and effluent concentration for different recovery flow rates:-Q2 = 1, 2.5, 5, 10 and 15 1/s. Injection flow rate QI = 3/5 (-Q2); other parameters as in Table I.

182 CESAR GOMEZ-LAHOZ ET AL.

1.1-

1-

0.9-

0.8-

0.7-

0.6-

0.5-

0.4-

0.3-

0.2i

0.1-

0 0 1'5 7'5 90 165 120 3'0 4'5 6'0

t (days)

Fig. 11. Plots of concentration at a monitoring well located at (15,15), with shutdown of the pumps after 30 days. Natural superficial velocity: (1) v ° = 10 .5 m/s; (2) v ° = 10 - 6 m/s; (3) v ° : 0 m/s. Other parameters as in Table I.

0 10 -6 m/s. It may be somewhat monitoring well located at (15,15) and for v x -- surprising that, even when results shown in Figure 4(b) indicated clearly that the different domain sizes resulted in significant differences between the concentration curves, once the pumps are stopped the rebound curves are quite similar for all o f them. When a similar analysis was performed for SVE significant differences

between the rebound curves were seen (Rodrfguez-Maroto et al., 1994). It was therefore concluded that information about the mass transfer coefficients could be obtained from the SVE rebound curves, so one could plan changes in the operating conditions in order to reduce the costs of the remediation. It seems clear ~ that the natural advection present in the saturated region may interfere with the use of

rebound curves for this purpose in pump and treat operations,

7. Conclusions and Future Work

This model shows clearly the importance of the presence of NAPL in connection with the remediation of the saturated zone by pump and treat or other related technologies (like in situ flushing), and it demonstrates that both the solution of relatively large droplets of NAPL and the diffusion of the OC already in the aqueous phase through a stagnant aqueous boundary layer will limit the efficiency of the cleanup in many field situations. The model also indicates that, under conditions

PUMP AND TREAT 1 8 3

1.1

1"

0.9-

0.8-

0.7-

.~ 0.6-

~ 0.5-

~-~ 0.4-

0.3-

0.2-

0.1-

3

1.5

1'5 3'0 4'5 6'0 7'5 9-0-- 165 120

t (days)

Fig. 12. Plots of concentration at a monitoring well located at (15,15), with shutdown of the pumps after 30 days. Natural superficial velocity = v ° : 10 -6 m/s; 21 = 1, 1.5, 2, 3 and 4 cm. Other parameters as in Table I.

where removal rates are limited by the solution of the NAPL and/or diffusion of the aqueous OC, the location of the wells and the operating flow rates have little influence on the remediation time as long as the recovery wells capture all the water running through the contaminated area, so the minimum flow rates should be chosen which guarantee that no contaminant is flushed out of the region being remediated.

Nevertheless, the model suffers from large transverse numerical dispersion, so it may not be used to make precise decisions about the optimum recovery and injection rates, especially if these values are going to be changed during the course of the operation. Development of models based on a principal direction algorithm will be able to avoid these limitations if one is able to design them to simulate flow paths that change during the process. One expects such a model to permit (a) more precise analysis of the optimum location and operation of the wells as well as (b) improved design of some specific procedures such as pulsed operation of the wells.

Acknowledgements

D.J.W. is greatly indebted to the University of Malaga for its hospitality and the use of its facilities, to Dr. J.J. Rodlffguez-Jimenez for making his visit to Malaga

184 CESAR GOMEZ-LAHOZ ET AL.

possible and for helpful discussions of the project, to Vanderbilt University for financial support during his leave, and to the Spanish Government (DGICYT) for a fellowship in support of this work.

References

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Feenstra, S. and Cherry, J.A.: 1987, 'Dense Organic Solvents in Ground Water', Institute for Ground Water Research, University of Waterloo, Waterloo, Ont., Progress Report No. 0863985.

Gomez-Lahoz, C., Rodrfguez-Maroto, J.M. and Wilson, D.J.: 1994, 'Groundwater Cleanup by In Situ Sparging. VII. VOC Concentration Rebound Caused by Diffusion after Shutdown', Separ. Sci. Technol. 29, 1509.

Grisak, G.E. and Pickens, J.F.: 1980a, 'Solute Transport through Fractured Media. I. The Effects of Matrix Diffusion', Water Resources Research 16, 719.

Grisak, G.E. and Pickens, J.F.: 1980b, 'Solute Transport through Fractured Media. I. Column Study of Fractured Till', Water Resources Research 16, 731.

Grisak, G.E. and Pickens, J.E: 1981, 'An Analytical Solution for Solute Transport through Fractured Media with Matrix Diffusion', J. Hydrol. 52, 47.

Huling, S.G. and Weaver, J.W.: 1991, 'Dense Nonaqueous Phase Liquids', EPA ground water issue, EPA/540/4-91-002, March.

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Mackay, D.M. and Cherry, J.A.: 1989, 'Groundwater Contamination: Pump-and-Treat Remediation', Environ. Sci. Technol. 23(6), 630.

Millington, R.J. and Quirk, J.P.: 1961, 'Permeability of Porous Solids', Trans. Faraday 57, 1200- 1207.

Narasimhan, T.N.: 1982, 'Multidimensional Numerical Simulation of Fluid Flow in Fractured Porous Media', Water Resources Research 18, 1235.

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Neretnieks, I.: 1980, 'Diffusion in the Rock Matrix: An Important Factor in Radionuclide Retarda- tion?', J. Geophysical Research 85, 4379.

Noorishad, J. and Mehran, M.: 1982, 'An Upstream Finite Element Method for Solution of Transient Transport Equation in Fractured Porous Media', Water Resources Research 18, 588.

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Powers, S.E., Loureiro, C.O., Abriola, L.M. and Weber, W.J., Jr.: 1991, 'Theoretical Study of the Sig- nificance of Nonequilibrium Dissolution of Nonaqueous Phase Liquids in Subsurface Systems', Water Resources Research 27, 463.

Powers, S.E., Abriola, U M. and Weber, W.J., Jr.: 1992, ' An Experimental Investigation of Nonaque- ous Phase Liquid Dissolution in Saturated Subsurface System', Water Resources Research 28, 2691.

Rasmuson, A. and Neretuieks, I.: 1980, 'Exact Solution for Diffusion in Particles and Longitudinal Dispersion in Packed Beds', AIChEJ26, 686.

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Rodrfguez-Maroto, J.M., Gomez-Lahoz, C. and Wilson, D.J.: 1994, 'Soil Cleanup by In Situ Aeration. XVIII. "Field Scale Models with Diffusion from Clay Structures"', Separ. Sci. Technol. 29, 1367.

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PUMP AND TREAT 185

Sudicky, E.A. and Frind, E.O.: 1982, 'Contaminant Transport in Fractured Porous Media: Analytical Solutions for a System of Parallel Fractures', Water Resources Research 18, 1634.

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A

AA

ao

a

b

C

C / C m,

~ J

C 8

C~,j,k

D

h

L

M I

mi, j ,k

?~

?~u

n w

Appendix: Nomenclature

cross sectional area of low permeability domains present in one compart- ment of volume AV, containing the immoble water (m2).

coefficient of the potential function for the Ath well (mZ/s).

initial NAPL droplet radius (m).

NAPL droplet radius at time t (m).

half distance between droplets, or thickness of the boundary layer for the solution of NAPL (m).

aqueous concentration of OC in water (kg/m 3 of water).

reduced concentration at the recovery well: Cwell/C s.

average concentration of OC in the mobile water of the (i, j ) th compart-

ment (kg/m 3 of mobile water).

aqueous concentration of OC at saturation (kg/m 3 of water).

average concentration of OC in the immobile water of the kth slab of

the (i, j ) th compartment (kg/m 3 of immobile water, contained in the low permeability domains).

initial NAPL concentration (kg NAPL/m 3 soil).

aqueous diffusivity of OC through the immoble water in the low perme- ability domains (m2/s).

thickness of the domain of interest (m).

maximum distance for diffusion in the low permeability domains (m) (volume of the domains in one compartment = A 2L).

reduced contaminant mass in the domain of interest (mass at time t over mass at time 0).

initial NAPL mass in one slab, = Co N A V / n u (kg).

NAPL mass in the kth slab of the (i, j ) th compartment at time t (kg).

number of droplets in one compartment of volume AV.

number of slabs used to represent half the thickness of a low permeability domain into which L is partitioned.

number of wells.

186

n x

7~y

VT

v .S . z~J

W !

W X

XT. x)~

Y YT

Y~ Au AV Ax Ay Y

Ustg

POC

/9soil

CESAR GOMEZ-LAHOZ ET AL.

number of divisions of the domain of interest in the aquifer in the x direction.

number of divisions of the domain of interest in the aquifer in the y direction.

volumetric flux from the Ath well into the aquifer (m3/s).

1 for v > O; S(v) = 0 for v < 0 [functions used in equations (8) and (24)1.

radial superficial velocity around a well (m3/m 2 s).

superficial velocity of ground water in the absence of wells (m3/m 2 s).

mean value of the superficial velocity normal to the S face of the (i, j ) th compartment. S = L (left), R (right), B (back), F (front) (m3/m 2 s).

volume of immobile water per NAPL droplet (m3).

potential function describing water advection (m2/s).

distance along the X axis; natural flow direction (m).

length of the domain of interest (m).

x coordinate of the Ath well (m).

distance along the Y axis (m).

width of the domain of interest (m).

y coordinate of the Ath well (m).

L/n~. h Ax Ay (m3).

XT/nx (m).

YT /ny (m).

porosity associated with mobile water.

porosity of the stagnant region associated with the low permeability domains (volume of voids in the stagnant region/volume of the stagnant region).

NAPL density (kg/m 3 of NAPL).

bulk soil density (kg/m3).

porosity associated with immobile water (volume of voids in the stagnant region/total aquifer volume).