Tài liệu Nonequilibrium transport and sorption of organic chemicals during aquifer remediation doc

Some important influences are: - equilibrium amount of sorption; - kinetics of sorption; - variation in flow velocities of the soil liquid caused by heterogeneities in the soil; and - ki

Nonequilibrium transport and sorption of organic chemicals during aquifer remediation

CORS VAN DEN BRINK

IWACO, Consultants for Water & Environment, PO Box 8064, 9702 KB Groningen,

The Netherlands

WILLEM J ZAADNOORDIJK

[WACO, Consultants for Water & Environment, PO Box 8520, 3009 AM Rotterdam,

The Netherlands

Abstract Aquifer remediation operations are often behind schedule Usually, a rather

sharp concentration decrease shortly after the start of an operation is followed by a situation in which hardly any concentration decrease is observed Furthermore, the concentration increases after stopping the groundwater recovery These phenomena are caused by so-called tailing An important cause of tailing is the phenomenon that equilibrium is not reached for some of the transport and sorption processes involved

To predict these effects of tailing, IWACO has developed a program SORWACO, which describes the behaviour of solutes along a path line Processes for which equilibrium is reached quickly as well as processes for which equilibrium is reached only slowly are taken into account The program has been verified against break-through curves observed in column experiments reported in the literature The program parameters were calibrated using the data of several experiments The resulting set of parameter values accurately described the transport for different flow velocities The fact that quite good results can be obtained without a lot of data from a specific site makes the program a valuable tool for the design of remediation operations The program is especially useful when extensive input data are not available so that detailed three-dimensional or stochastic models cannot be applied The use of the program is illustrated by means of a case study The progress was monitored and the data show good correspondence with the predictions of the program

Transport et désorption différences de produits chimiques organiques pendant la restauration d'un aquifère

Résumé Les opérations de restauration d'aquifères interviennent souvent tardivement

En général, la concentration élevée en éléments chimiques indésirables décroît rapidement dès le début de l'opération, puis intervient une période pendant laquelle la diminution de concentration est à peine observable Parfois même, la concentration augmente à nouveau après l'arrêt du traitement des eaux souterraines Ce phénomène est causé par un transport et une désorption retardés (tailing) Ce retard est lié au fait que l'arrêt de l'opération ne signifie pas que l'équilibre est atteint pour le transport et la désorption des éléments Afin de prédire les effets de ce retard, IWACO a développé

le programme informatique de modélisation, SORWACO, qui décrit le comportement des substances en solution le long d'un filet d'écoulement Aussi bien les processus pour lesquels l'équilibre est atteint rapidement que ceux pour lesquels il est atteint lentement ont été pris en compte Le programme a été vérifié par rapport aux courbes

de dégradation observées sur colonnes expérimentales et décrites dans la littérature Les paramètres du programme ont été calés en utilisant les données de plusieurs expérimentations Les valeurs des paramètres obtenues décrivent précisément le transport pour différentes vitesses d'écoulement Le fait que de bons résultats puissent être obtenus sur un site spécifique même en l'absence d'un grand nombre de données

le concernant, fait que le programme est un outil fiable pour la conception des opérations de restauration Le programme est en particulier utile lorsque des modèles tridimensionnels ou stochastiques détaillés ne peuvent être utilisés par manque de données de base en quantité suffisante Dans cet article, l'utilisation du programme est

Open for discussion until I October 1997

illustrée par une étude de cas L'avancement de l'opération a fait l'objet d'un suivi et les résultats des mesures présentent une bonne correspondance avec les prédictions faites initialement avec le programme

INTRODUCTION

The design of an aquifer remediation operation is merely a case of practical experience today The contaminant is flushed out of the soil by means of a system of injection and recovery wells The time needed and the amount of water that has to be flushed through the soil to reach a certain required concentration are both important The amount of water is expressed in terms of the so-called flush factor, which is equal to the ratio of the volume of this water and the volume of the pores in the soil

to be flushed

The time needed and the amount of water (flush factor) are estimated based on experience with similar types of pollutants and soils In this way, processes and para-meters which determine the course of the remediation are taken into account only indirectly Moreover, it is not possible to gain insight in a particular situation by determining the influence of various parameters Some important influences are:

- equilibrium amount of sorption;

- kinetics of sorption;

- variation in flow velocities of the soil liquid caused by heterogeneities in the soil; and

- kinetics of exchange between portions of the soil liquid phase with different flow velocities

IWACO has developed the program SORWACO to increase insight into the influence of the individual processes and parameters on the course of the remediation with the possibility of intermittent recovery The program calculates the changes of the pollutant concentration along its path through the soil and as a function of time This pathline has to be split up into a number of cells, which have fixed positions that do not change with time The parameters may have different values for each cell (e.g bulk density, porosity, and organic carbon content of the soil)

The equilibrium of the pollutant between the groundwater and the solid phase of the soil is described by a Freundlich isotherm This nonlinear sorption isotherm does not vary in time

Sorption takes place at the so-called "sorption sites" of the soil Two classes of sorption sites are distinguished (Boesten, 1986; Brasseau, 1992b) The sorption sites

of class 1 are continuously in equilibrium The class 2 sorption sites are not continuously in equilibrium with the soil solution The rate of (de)sorption at class 2 sites is driven by the shortage (or excess) of the sorbed amount relative to the concentration in the soil liquid phase, which in turn depends on the properties of the solute/soil combination and the velocity of the groundwater When such a sorption shortage or excess exists one talks about "sorption related nonequilibrium"

The soil liquid phase is divided into a fast and a slow moving portion to account for the variations in velocity that occur in a porous medium The exchange of pollutant between these portions is driven by the concentration difference and is

further determined by the extent of the slow and fast moving portions of the liquid phase, the respective velocities, and the diffusivity A "transport related nonequilibrium" exists if the concentrations are not equal and there is exchange between the portions of the liquid phase

The program SORWACO takes both the transport and sorption related nonequilibrium into account It calculates the concentration of the pollutant in each cell at every time step The concentration in the water flowing out of the last cell is the concentration of the water that enters the purification or discharge system

It is possible to calculate the impact of intermittent groundwater recovery on both the decrease of the concentration during the recovery and the increase when the recovery is stopped The groundwater flow is assumed to be steady Changes in the flow pattern are not accounted for When intermittent recovery is considered, it is assumed that the flow directions remain the same so that the groundwater flow pattern does not change Only the size of the flow velocity is different The calculations describe the behaviour of one substance Interaction with other chemicals, like cation exchange reactions or precipitation reactions, is neglected The time needed to reduce the concentrations to the required values and the flush-factor can be derived directly from the output of SORWACO In this way the program can be used during the design of an aquifer remediation operation Usually the prediction is evaluated and adjusted during the operation resulting in an improved prediction for the following periods of the operation

THEORY

Recent literature shows that much has been learned about the effects of diffusion, dispersion, advection and adsorption on chemical transport in soils (van Genuchten & Wierenga, 1976; Goltz & Roberts, 1988; Ptacek & Gillham, 1992) Numerous models have been developed in attempts to describe the one-dimensional transport of chemicals These models are important because they continuously increase insight into the basic transport mechanisms involved and, consequently, improve the capability to predict the fate in the soils of such diverse chemicals as pesticides, chlorinated hydrocarbons and heavy metals

In SORWACO, the solute transport is assumed to be one-dimensionally advective and dispersive The conservation equation states that the change of the total mass concentration C in the system must match the gradient of the advective and

dispersive flux /plus the decay R, (e.g Bolt, 1982):

where t indicates time and x the ordinate along the pathline of the groundwater flow [L] The total amount C, the flux J, and the decay R, are given by:

J = QVC<D %} ( 3 )

R,= k,c (4)

in which c denotes the concentration in the soil liquid phase, 9 the volumetric

soilwater content [L3 L"3], p the bulk density of the soil [M L/3], S the adsorbed

concentration [M M"1], v the average pore water velocity [L t"1], D the dispersion

coefficient and k, the decay rate

Equations (1) to (4) do not suffice for the description of contaminant transport

which includes tailing Two phenomena will be added to arrive at a set of equations

that is capable of simulating properly transport with tailing: transport related

non-equilibrium and sorption related nonnon-equilibrium

Transport related nonequilibrium

Equations (1) to (4) imply that single values of the velocity and of the dispersion

coefficient describe the advective and dispersive transport of the entire soil liquid

phase This results in the calculation of effluent curves which are characteristically

sigmoidal or symmetrical in shape However, experimental curves often show a

much earlier breakthrough and a much longer tailing This extreme tailing does not

occur only in unsaturated soils (van Genuchten & Wieringa, 1976; Boesten, 1986)

but also in saturated soils (Goltz & Roberts, 1988; Ptacek & Gillham, 1992)

One approach by means of which this extreme tailing can be accounted for is the

introduction of regions within the soil liquid phase that have different flow velocities

Coats & Smith (1964) used a mobile and an immobile region Leistra (1977) used a

region with a low velocity instead of an immobile region Stagnitti et al (1993) used

a larger number of regions each having a different velocity Advective solute

transport is more important in the regions with higher velocity, while the solute flux

in the slower regions is mainly controlled by diffusion through those regions The

physical structure of the soil is responsible for the differences in groundwater

velocity Slow moving portions will occur, for instance, within loamy layers in a

sandy aquifer

Dividing the liquid phase into a fast and slow moving portion, the conservation

equation (1) can be written as:

"àT = - - & • - * ' • ' - • ' / - ( 5 a )

where the subscripts / and s refer to fast moving and slow moving liquid regions

respectively, and J Hs is the exchange between the fast moving and slow moving

liquid phase:

Jf^„=k s j(c f -C s ) (6) The mass transfer coefficient, k sf , in equation (6) determines the rate of exchange

between the two liquid regions This rate is proportional to the difference in

concentration between the fast and slow moving portions of the soil liquid phase

In the derivation of equations (5) and (6) no restrictions have been made on the

adsorption in both regions Thus, the adsorption around the larger pores (fast moving

portion) can be different from that of the micropores (slow moving region) in

SORWACO, as is the case in reality

Sorption related nonequilibrium

The equations presented so far do not describe the relationship between the adsorbed

concentration S and the solute concentration c In the literature both equilibrium

(Bolt, 1982) and nonequilibrium equations (Boesten, 1986; Brusseau, 1992a,b) are

available for this purpose Nonlinear equilibrium isotherms do not provide a

satisfactory explanation of the asymmetrical and nonsigmoidal curves of

concentra-tion vs time that are observed during groundwater remediaconcentra-tions of organic chemicals

Further improvement can be realized by a two-site adsorption mechanism (Boesten,

1986; van den Brink, 1987) Such a mechanism accounts for the fact that the various

constituents of the solid phase (e.g soil minerals, organic matter, aluminium and

iron oxides) are likely to react differently with a dissolved chemical

In the two-site sorption model, the sorption sites are divided into two fractions

Adsorption on one fraction (class 1 sites) is assumed to be instantaneous, while

adsorption on the other fraction (class 2 sites) is thought to be rate limited, so that

equilibrium is not reached This is called sorption related nonequilibrium The total

adsorption, S, is equal to the sum of the amount sorbed by the class 1 sites S x and the

amount sorbed by the class 2 sites S 2 :

At equilibrium, the amount sorbed by both types of sites is described by the

Freundlich isotherm:

Si,equilibrium = F\KpC " = S] ( 8 )

^equilibrium = Fl Kf C ( 9 )

where F l and F 2 refer to the ratio between the class 1 and class 2 sorption sites For

field application there is usually no information on the values of F, and F2 A value

of 0.7 is then used for F, This value is based on measurements on adsorption

kinetics carried out by Boesten (1986) The parameter K F denotes the Freundlich

sorption coefficient [L3/n M"1/n] and n the Freundlich exponent It is assumed that KF

is the same for both the class 1 and class 2 sites because sufficient information on the

sorption is not available for field sites (Brusseau, 1992b) It may be concluded from

the experimental work of Boesten (1986) that the total amount of sorption sites

exceeds the amount measured in short term sorption experiments The practical

consequence of these results is that the sum of the parameters F x and F 2 may

exceed 1 This phenomenon is of great importance for remediation operations in

which time-dependent desorption is one of the factors that cause tailing

The sorbed concentration at the class 1 sites, S,, can be calculated from

equation (7) The amount at the class 2 sites is not directly related to the

concentration in the soil liquid phase, but the rate of change is (Boesten, 1986; van

den Brink, 1987):

ot

where k d2 is a first-order rate coefficient and F 2 K F c v " the equilibrium amount sorbed

at the class 2 sites corresponding to the current soil liquid concentration c

(equation (8))

This approach, in which the sorption and transport related nonequilibrium are

described explicitly, is using almost the same theoretical framework as the

two-domain approach of Brusseau (1992b) A difference is the capability of SORWACO

to describe the sorption by a nonlinear sorption isotherm In addition, the soil liquid

is divided into two regions with different flow velocities, instead of a mobile and an

immobile region However, the main difference consists of concepts which facilitate

practical use:

- SORWACO describes the transport along a pathline in three-dimensional

groundwater flow (and not uniform flow);

- SORWACO uses the concentrations in the soil liquid phase as input, and

calculates the total mass which is usually not measured; and

- parameter values from the literature work well with SORWACO (except for

organic carbon content for which some measurements are usually available)

In practical cases, the first goal of a field investigation is to determine the extent

of the contamination In an early stage of the investigation, not much effort is given

to the collection of data that are needed to predict the duration of the aquifer

remediation In a later stage, when it has been decided to carry out a remediation,

additional data can be collected to establish better input data for SORWACO

Moreover, as results of the remediation become available, they can be used to further

improve the SORWACO model

IMPLEMENTATION IN THE PROGRAM SORWACO

Equations have been given in the previous sections for the fast and slow moving

region and the class 1 and class 2 sites separately The way they are implemented in

the program SORWACO is illustrated in Fig 1 The two soil liquid regions are

indicated by boxes as well as the solid phase The sorptions by the class 1 and class 2

sites have been indicated by the "equilibrium sorption" and the "nonequilibrium

sorption" arrows respectively

The volumetric flux, q, is related to the velocity and can be written as:

f

flux out

fast moving portion groundwater

physical exchange

flux

in

equilibrium sorption

slow moving portion groundwater

t

Fig 1 Setup of SORWACO

non-equilibrium sorption

equilibrium sorption

where the subscripts/and s refer to the fast and slow moving regions respectively

The total amount C can be split into parts associated with the slow and fast

moving portions of the soil liquid phase:

The amount in the slow moving soil liquid phase is equal to (equations (2) and (7)):

where S s is the adsorbed concentration related to the slow moving region of the soil

(expressed per unit mass of soil assigned to this region) and / is the mass fraction of

the solid phase assigned to the fast moving region

Since only class 1 sites are associated with the fast moving soil liquid phase, the

total amount in this phase is given by:

where S f is the adsorbed concentrations related to the fast moving region of the soil

(expressed per unit mass of soil assigned to this region)

Initially, the solid phase is in equilibrium with the liquid phase:

^.(-.initial

C/initial - 9 / C/initial + P K F F y /(C/initial) ( 1 6 )

The equations (2), (3), (4), (5a), (5b), (6), (11), (13) and (14) describe the system

operation together with the initial conditions of equations (15) and (16) and boundary

conditions The concentration in the water flowing into the model on one side is

equal to a specified value of the background concentration On the other side, the

water leaves the model with the concentration calculated for the final cell

The equations are converted into an iterative finite difference algorithm The

iterations are necessary since the amount sorbed by the class 1 sites depends

nonlinearly on the soil liquid concentration (equation (8)) Therefore this amount is

calculated by applying equations (8) and either (13) or (14) alternatively at the

beginning of each time step At the end of each time step the values of the total

amounts, C s and C f , are calculated by means of equations (5a) and (5b)

COMPARISON WITH COLUMN EXPERIMENTS

Use of the program SORWACO was evaluated by comparing the laboratory results

of column experiments from the literature with the breakthrough curves calculated by

means of SORWACO The impact of variations in pore water velocity on the

nonequilibrium sorption and transport of organic chemicals was investigated by

Brasseau et al (1991) and Brusseau (1992a) In those studies, miscible displacement

experiments were carried out with different organic chemicals and aquifer media

having low organic carbon contents (0.02-0.39%) Four column experiments were

evaluated The experiments analysed, with respect to the type of sorbent, chemical,

and (nonequilibrium) parameters, are listed in Table 1 The values of the parameters

F l and F 2 have been taken from Brusseau (1992a) initially and verified during the

calibration The dispersion coefficient D has been assumed to be equal to zero

The parameters for the Lula medium were calibrated using the breakthrough

curve for the low pore water velocity (5 cm h1) only Next the breakthrough curve

for the high velocity (45 cm h') was predicted and matched the measured values well

(Fig 2) The calibration was carried out with a least-squares criterion The root

mean square (RMS) of the residuals was equal to 0.021 for the calibrated low

Table 1 Type of sorbent, chemical and (nonequilibrium) parameters used in the column experiments

(Brusseau, 1992a)

Sorbent*

Eustis

Eustis

Lula

Lula

Chemical"

TCE

TCE

NAP

NAP

V

(cm h" 1 ) 0.4

86

4

45

K F ""

(ml g 1 ) 0.27 0.27 0.21 0.21

(h 1 ) 0.003 0.003 0.01 0.01

(h 1 ) 0.70 0.70 0.07 0.07

/

0.5 0.5 0.7 0.7

*",

0.5 0.5 0.7 0.7

F 2

0.5 0.5 0.3 0.3

l.i l.i 1.2 1.2 Lula: OC = 0.02%; sand = 91.0%; silt = 5.6%; clay = 3.4%; p = 1.52 g cm 3 ; 0 = 0.32;

Eustis: OC = 0.39%; sand = 95.5%; silt = 3.2%; clay = 1.3%; p = 1.70 g cm' 3 ; 6 = 0.41

NAP = naphthalene; TCE = trichloroethene;

Freundlich exponent n = 1

o

O

0.8-

0.6-

0.4-

0.2-

0-J*5

È

m

-4

f

r

i H | L j l •t^fB==l ^= = * F «" a»

4 5 f Flux Factor

10

Brusseau [1992]

+ v = 5 cm/hr • v=45

SORWACO

— v = 5 cm/hr v = 4 5

Fig 2 Measured (Brasseau, 1992) and calculated (SORWACO) breakthrough curves for Lula medium

0.6

o

œ 0.4

0.2

-1

• / /

7 / i

it

If

r ^i- »

B8

Brusseau [1992]

+ v=0.4 cm/hr

4 5 6 7 Flush Factor

SORWACO v=0.4 cm/hr —

8 9 10

—- v = 8 6

Fig 3 Measured (Brusseau, 1992) and calculated (SORWACO) breakthrough curves for Eustis medium

velocity breakthrough curve The RMS of the residuals for the predicted values of the

high velocity experiment was 0.043

For the Eustis medium, the parameters could not all be calibrated using only the low velocity experiment However, the combined calibration of both the low and the high velocity experiment showed that they could be described with one single set of

SORWACO parameters The RMS of the residuals was 0.039 for the low and 0.016

for the high velocity experiment respectively The breakthrough curves are given in Fig 3

The calibration resulted in higher values for k dl than for k st This implies that the asymmetry of the breakthrough curves is mostly due to transport related non-equilibrium at low pore water velocities and to sorption related nonnon-equilibrium at high velocities

The leftward shift with higher velocity also indicates nonequilibrium (Brusseau, 1992a) As could be expected from the differences in flow velocity, the leftward shift

is greater for the Eustis medium than for Lula medium since the ratios of the high and low velocities in both experiments are equal to 215 and 9 respectively The analysis of the column experiments shows that the operation of SORWACO is applicable for the description of the effects of nonequilibrium, especially during the later parts of a groundwater remediation operation Referring to the practical use of SORWACO, it is important that the parameter values are independent of the pore water velocities, since the pore water velocity may vary along the pathline, and the recovery may be intermittent

DESCRIPTION OF A CASE STUDY

Introduction

SORWACO was used to predict and evaluate the course of an aquifer remediation operation at the Sappemeer gas production site (Veltkamp & Mathijssen, 1991)

Fig 4 Sappemeer gas production site in the northern part of The Netherlands