Evaluation of diffusive gas flux through covers with a GCL

Geotextiles and Geomembranes 18 (2000) 215}233

Evaluation of di!usive gas #ux through covers with a GCL Michel Aubertin!,*, Mostafa Aachib", Karine Authier# !Department of Civil, Geological and Mining Engineering, E! cole Polytechnique, C.P. 6079, Succ. Centre-ville, Montre& al, Que& bec, Canada H3C 3A7 "Ecole Hassania des Travaux Publics, De& partement de l'hydraulique, km 7, Route d'El Jadida, B.P. 8108 Casablanca, Oasis, Morocco #Golder Associates, 63 place Frontenac, Pointe-Claire, Que& bec, Canada H9R 4Z7 Received 2 February 1999; received in revised form 17 August 1999; accepted 14 September 1999

Abstract The main purpose of geosynthetic clay liners (GCLs) used in cover systems is to limit the in"ltration of water to the wastes disposed underneath. In many situations however, the cover system should also be able to limit gas #ux, so that undesirable products emitted from the wastes, like radon or methane, will not escape to the atmosphere. In other situations, covers may have to prevent oxygen from the atmosphere to come into contact with reactive materials, such as sulphidic tailings that could otherwise generate acid. It is thus important for cover design to evaluate gas #ux through the GCL used in the system. This gas #ux is usually controlled by di!usion through the porous media, because such highly saturated "ne grained materials have a very low gas permeability. In this paper, the authors brie#y review the basic theory used to calculate di!usive gas #ux F , and introduce an experimental procedure to ' evaluate, in the laboratory, the e!ective di!usion coe$cient D which controls this #ux. % Experimental results obtained on a nonwoven needlepunched GCL are shown and compared to values ensuing from a predictive model that relates D to porosity and degree of saturation. % Sample calculations on gas #ux in cover systems are "nally presented and discussed. ( 2000 Elsevier Science Ltd. All rights reserved. Keywords: GCL; Gas; Di!usion; Cover; Oxygen; Laboratory tests

* Corresponding author. Tel.: 001-514-340-4711 Ext. 4046; fax: 001-514-340-4777. E-mail address: [email protected] (M. Aubertin) 0266-1144/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 6 - 1 1 4 4 ( 9 9 ) 0 0 0 2 8 - X

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1. Introduction For a majority of waste disposal facilities created over the years, the closure scheme to control the transport of solids and #uids in and out of the site involves the installation of a cover system. This is the case for instance for many municipal and hazardous waste land"lls, contaminated soils and industrial refuse sites, and mineral wastes surface impoundments. Covers, like other types of hydrogeological barrier systems, aim at protecting human health and the environment against exposure to the contaminants enclosed within the site. This is achieved by reducing the transport of unwanted substances to or from the disposal facilities. Covers (sometimes called caps) installed on wastes are usually made from a number of materials placed in di!erent layers, each playing one (or more) speci"c role(s) in the overall system behavior. Various con"gurations have been devised to ensure e$ciency, long term stability, and durability of engineered covers, making use of materials such as "ne grained soils, geomembranes, cement products, bitumen, and even other types of waste (e.g. Daniel and Koerner, 1993; Senes, 1994; Aubertin et al., 1995). As one of the key function of a properly designed cover system is to limit the in"ltration of water into the wastes, it is customary to include at least one layer of a low hydraulic conductivity material. Geosynthetic clay liners (GCLs), which have been utilized frequently in base liners, may also become the preferred clay barrier material for covers. GCLs constitute a relatively new, but rapidly expending component of the geosynthetic market. They are made from a combination of a thin layer of granular or powdered bentonite (i.e. about 3 to 5 kg/m2 of sodium montmorillonite minerals) sandwiched between two woven and/or nonwoven geotextiles, or sometimes glued onto a geomembrane; this latter type of GCLs will not be considered in this paper however. In this geocomposite, the bentonite, because of its a$nity for water, provides the desired hydraulic properties while the geotextiles insure the mechanical stability of the thin layer. GCLs have numerous advantages, including #exibility and relatively high strain at failure, self-healing properties, resistance to freeze-thaw e!ects, lower thickness than compacted clay (for an equal water #ux), high manufacturing quality, rapidity and relative ease of installation, and competitive costs. Of course, these geocomposites also have some disadvantages, such as a relatively small leachate attenuation capacity, short containment time, limited internal and interface shear strengths, and a risk of uneven bentonite thickness under applied normal stress (e.g. Stark, 1998). Nevertheless, GCLs are regarded very positively as a candidate material for cover systems (e.g. Daniel and Richardson, 1995; Koerner and Daniel, 1997). Fairly exhaustive presentations on GCLs characteristics can be found in a number of recent publications (e.g. Koerner et al., 1995; Koerner, 1996; Well, 1997). The literature on GCLs readily shows that these are being intensively investigated, mostly in regards to hydraulic conductivity and related solute transport phenomena (e.g. Daniel, 1996; Bouazza et al., 1996; Takahashi et al., 1996; Ruhl and Daniel, 1997; Petrov and Rowe, 1997; Lake et al., 1997). Many studies have also been conducted on mechanical properties a!ecting engineering works stability and "eld performance (Frobel, 1996; Gilbert et al., 1996; Richardson, 1997a,b; Daniel et al., 1998; Fox, 1998),

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on the e!ect of exposure conditions for long term behavior (James et al., 1997; Hewitt and Daniel, 1997), and on issues related to design and installation (Mackey, 1997). But despite this abundance of activities, it appears that, so far, little attention has been paid to the capabilities of GCLs to control gas #ux. It is however a key issue for many types of wastes which can produce or interact with gases in a manner that can be damaging to the environment. This is the case for instance with land"lls that generate methane, carbon dioxide, and vapours from petroleum or chlorinated compounds (e.g. Barlaz and Ham, 1993), which are gases that should not escape freely from the disposal site. The same could be said also about sites used for phosphate fertilisers or for uranium ore tailings and waste rocks, which can release radon (Rn-222), a gas that should not be allowed to move to the atmosphere without control (e.g. Heinsohn and Kobel, 1999). Also, sulphidic minerals (such as pyrite and pyrrothite) often found in milling wastes and mined rocks, should not come into contact with atmospheric oxygen in order to prevent acidi"cation of the leachate. For such cases, the cover system must e$ciently reduce gas #ux into these disposal sites (e.g. Harries and Ritchie, 1985; Nicholson et al., 1989; Collin and Rasmuson, 1990; Aubertin and Chapuis, 1991; Aubertin et al., 1993, 1995, 1996; Achib et al., 1998). This last issue has provided the impetus behind this investigation. Although geosynthetic clay liners have already been used in various mining applications, such as heap leach pad and sedimentation bassins (e.g. CETCO, 1996 GCLs project lists), the question of oxygen #ux recently became an issue when a GCL was used in an actual cover system for closure of an acid generating tailings site in QueH bec, Canada (Bienvenu, 1998; Dufour, 1999). There are unfortunately few relevant studies available (to the authors' knowledge) that deal with gas transport in GCLs. Naue-Fasertechnik (1992) have issued a report on gas permeability in GCLs, which should be very low if the degree of saturation is high, while Koerner and Allen (1997) have discussed the di$culties related to measurement and interpretation of water vapour transmission through geosynthetics. This general absence of information on gas #ux creates problems for designers who want to use GLCs, because of a lack of meaningful data. And above this paucity of information, there appears to be an absence of research dealing with gas di!usion, which is known to be a dominant transport mechanism in low porosity media. In this paper, the theory on gas di!usion is brie#y reviewed. It is shown how porosity and degree of saturation can a!ect gas #ux. A laboratory test procedure to measure the di!usion properties required for gas #ux calculations is then described, and experimental results are presented. These results compare well to those obtained with a predictive model that relates the e!ective di!usion coe$cient D to basic % material properties. As a typical application, the authors "nally present some sample calculation results on gas #ux through cover systems.

2. Di4usive gas transport A number of phenomena involve gas transport in partly saturated porous media such as soils, waste rocks, and tailings. In natural systems, one can mention gas

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exchanges due to the metabolic activity of micro-organisms around roots, soil denitri"cation, methane formation, and oxidation of organic matter (e.g. Campbell, 1985; Grundmann et al., 1998). Gas transport in soils is also of interest for projects dealing with mobility of volatile organic chemicals (e.g. Hutzler et al., 1989; Gimmi et al., 1993; Jin et al., 1994; Popovicova and Brusseau, 1995), and for venting and treating processes applicable to contaminated soils (Imamura et al., 1994; Stylianou and DeVantier, 1995). Gas distribution and motion has also been investigated for its in#uence on the mechanical properties of unsaturated soils (e.g. Pietruszczak and Pande, 1991,1992). Physical processes associated with gas transport include convection and advection due to total pressure gradients, dissolution in the aqueous phase, chemical and adsorptive reactions, and molecular di!usion. Permeability K (¸2/¹), which controls ' gas #ux by convection/advection, is a well known property that is easily obtained as it does not directly depend (in "rst analysis) on the #uid characteristics (Hillel, 1980; Grant and Cronevelt, 1993; Fleureau and Taibi, 1994; Rodeck et al., 1994), and only varies with pore size and distribution. Because K is expected to be very low in highly ' saturated GCLs, it is not the main property of interest for gas transport in such media. It has been shown that gas #ux in highly saturated "ne grained soils is mostly controlled by di!usion (Collin, 1987; Collin and Rasmuson, 1988). Di!usion is a generic transport process, encountered in #uids (liquids and gases), by which molecules that can move randomly are redistributed until an equilibrium is reached when concentration becomes uniform. The di!using element moves from the higher concentration region to the lower concentration region. As somewhat similar random molecular motions are also associated with conductive heat transfer, the same mathematical equations have been used for heat #ux and di!usive #ux in isotropic substances. Solute di!usion has been an extensively studied transport process in soils, especially those used in hydrogeological barriers such as liners and covers (e.g. Gillham et al., 1984; Rowe, 1987; Daniel and Schackelford, 1988; Rowe et al., 1995); it has also been studied recently for GCLs (Lake et al., 1997). Gas di!usion in soils and in other porous media has equally been the subject of many investigations over the years (e.g. Currie, 1960a,b, 1961; Lai et al., 1976; Pritchard and Currie, 1982; Reible and Shair, 1982; Troeh et al., 1981; Jellick and Schnabel, 1986; Rolston, 1986; Collin and Rasmuson, 1988; Aachib et al., 1993; Yanful, 1993; Reardon and Moddle, 1995; Aubertin et al., 1995, 1996, 1999; Aachib, 1997; Mackay et al., 1997). Accordingly, there is a wealth of information available on the topic, and only a brief presentation is given here. The main di!usion equation, known as Fick's "rst law, can be written as follows for the gas #ux: LC F "!D , ' % LZ

(1)

where F is given as a mass transfer rate per unit area (M/¸2¹); C is the concentration ' of the di!using substance (M/¸3); Z is the spatial coordinate (¸) measured perpendicularly to the unit cross sectional area; D is the e!ective di!usion coe$cient of the %

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substance (¸2/¹); the negative sign in Eq. (1) indicates that #ux occurs in the opposite direction to the concentration increase. This equation implies that there is a linear relationship (for a given D ) between the mass #ux F and the concentration gradient % ' between two points. When Eq. (1) is rewritten in terms of partial pressure gradients (e.g. Hillel, 1980; Fredlund and Rahardjo, 1993), one can establish a parallel between Fick's "rst law and the well known Darcy's law used for advection transport, with D in the former % playing a somewhat similar role as the hydraulic conductivity k in the latter. As is the case with k, the value of D also varies with #uid and porous media characteristics, % such as molecular weight, porosity, and degree of saturation. Fick's "rst law given by Eq. (1) can be generalised for three-dimensional conditions (in the same way that Darcy's law has been extended), but only uniaxial #ow is considered here. Under transient conditions, concentration can vary in time and in space. Continuity conditions imply that a concentration variation in time is balanced by a #ux variation over the corresponding position. For one-dimensional #ux in an isotropic non reactive medium, one can then write (Crank, 1975): LC L2C "D % LZ2 Lt

(2)

which is the usual form of Fick's second law. More general expressions can also be developed for anisotropic or heterogeneous media and for reactive materials that consume or generate a di!usive element (Crank, 1975; Hillel, 1980). However, only Eqs. (1) and (2) will be needed in the following for the determination of the e!ective di!usion coe$cient D and for sample calculations % of gas #ux through GCLs and cover systems. To obtain #ux and concentration pro"les, Fick's laws can be solved analytically for relatively simple boundary conditions (e.g. Crank, 1975), while more general applications often require numerical calculations (e.g. Rowe and Booker, 1985,1987; Rowe et al., 1994; Aachib and Aubertin, 1999). In all situations however, the starting point is the determination of the e!ective di!usion coe$cient value.

3. The e4ective di4usion coe7cient 3.1. Basic relationships With Fick's laws, gas #ux and concentration variation are seen to be proportional to the e!ective di!usion coe$cient D . This parameter represents a material property % that is state dependent, as it varies with basic characteristics such as porosity and water content. In a porous medium, gas di!usion is much faster in the air "lled pore space, characterized by the volumetric air content h (h "n(1!S ), where n is the total ! ! 3 porosity and S is the degree of saturation), than in the water "lled pore space, 3 characterized by the volumetric water content h (h "n!h "nS ). It is useful 8 8 ! 3

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to recall that the volumetric water content represents the ratio between volume of water and total volume (i.e. when S "1, h "n and h "0); h can be related to 3 8 ! 8 the usual gravimetric water content w through this simple expression: h " 8 w(1!n)D , where D is the solid relative density. 3 3 When the air phase in the partly saturated medium is continuous, a condition that occurs when the degree of saturation is below about 85 to 90% (e.g. Corey, 1957; Matyas, 1967), gas di!usion mostly occurs within the air "lled pores. D can then be % expressed solely as a function of h , because there is very little di!usion in the water ! phase. At higher saturation however, as can be expected in a GCL, the air phase becomes discontinuous and gas will di!use in both air (if any) and water, the latter implying a solubilization process. When di!usion occurs simultaneously in air and water "lled pores, the resulting e!ective di!usion coe$cient can be expressed as a summation of both contributions, so that one can write: D "D #HD % ! 8

(3)

with D "h D0 ¹ , (4) ! ! ! ! (5) D "h D0 ¹ . 8 8 8 8 In these equations, D and D are the di!usion coe$cient components corresponding ! 8 to the air and water phases respectively, while H is the modi"ed Henry's law constant for equilibrium concentration (H"0.03 for oxygen in an air}water system at room temperature). D0 and D0 are the di!usion coe$cients in an opened medium (without 8 ! obstacles), with D0 (in air) being about 4 orders of magnitude higher than D0 (in 8 ! water); for example, at room temperature (RT+203C), D0 +1.8]10~5 m2/s and ! D0 +2.5]10~9 m2/s for oxygen, and D0 "2.2]10~5 m2/s and D0 "1.8]10~9 m2/s 8 ! 8 for methane (e.g. Fredlund and Rahardjo, 1993; Scharer et al., 1993; Heinsohn and Kobel, 1999). Finally, ¹ and ¹ in Eqs. (4) and (5) are tortuosity coe$cients that ! 8 re#ect the non linear #ow path of gas in the air and water phases respectively. Collin (1987) and Collin and Rasmuson (1988) have modi"ed a statistical model previously proposed by Millington and Shearer (1971) to predict the value of the e!ective di!usion coe$cient from basic material properties. The ensuing equations for D can be used to relate the tortuosity terms in Eqs. (4) and (5) to basic material % characteristics. According to this model, one can write:

and

h2x`1 ¹ " ! ! n2

(6)

h2y`1 ¹ " 8 , 8 n2

(7)

where the values of x and y are obtained by solving the two following limiting conditions: h2x#(1!h )x"1, ! ! h2y#(1!h )y"1. 8 8

(8) (9)

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For soils, typical values of x and y are within the range 0.6 to 0.75, with x+y (e.g. Aachib and Aubertin, 1999). The Collin (1987) model, in which all the terms are explicitly de"ned (no calibration required), has been used successfully by the authors to relate measured and calculated D values for a number of particulate media such as % soils and tailings (Aachib et al., 1993; Aubertin et al., 1995, 1996, 1999; Aachib and Aubertin, 1999); some of the results are shown below (see Fig. 4). Alternatively, one could estimate the value of the tortuosity coe$cients from simple empirical expressions. Using the relationship between D and S proposed by Eberling % 3 et al. (1994), one can develop the following: hx1 ¹ "q ! , ! nx2

(10)

hy1 ¹ "q 8 , 8 ny2

(11)

where q, x , x , y , y are parameters deduced from curve "tting adjustments to 1 2 1 2 experimental data. Typically, one "nds that q"0.27$0.08, x "2.26$0.4, and 1 x "x #1, while y "0 and y "1 are used for consistency (e.g. Scharer et al., 2 1 1 2 1993; Eberling et al., 1994). These two equations have also been applied by the authors to test results on soils and tailings (Aubertin et al., 1995). With such models, it is required that the value of ¹ when the medium is dry ! (S "0) be equal to the value of ¹ for a fully saturated medium (S "1), which is the 3 8 3 case for the two models shown here. When solving Fick's laws using analytical or numerical solutions, the value of F and D are sometimes decomposed into the porosity component and the apparent ' % di!usive #ux (FH) or coe$cient (DH) (e.g. Rowe et al., 1994; Aachib and Aubertin, 1999). This type of representation can be written as: F "h FH ' %2

(12)

D "h DH, % %2

(13)

and

where h is an equivalent porosity of the media. If the system is completely dry or %2 fully saturated, then it can be considered that h equals n. However, in a three phase %2 system (solid}water}air), the equivalent porosity h must take into account the two %2 #ow paths. From Eqs. (3)}(5), one can deduce that: h "h #Hh . %2 ! 8

(14)

As mentioned above, the second term on the right side of Eq. (14) only becomes signi"cant for the di!usion #ux when the degree of saturation S is above about 3 85 to 90%. As GCLs are usually highly saturated, Eq. (14) is used for the calculations below.

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In a layered system where D varies with the position along the gas #ux trajectory, % a representative equivalent value for the system can be obtained from the harmonic mean, which can be estimated by using the following equation (Scharer et al., 1993): h DM " . (15) % m h * + D i/1 %* This equation provides the harmonic mean of D (L2/T) to be used in Eqs. (1) and % (2) to evaluate the #ux through the layered system (assuming that the #ux is perpendicular to the layers); D is the coe$cient for layer i; h is the thickness of layer %* i i (corresponding to a uniform D ); h represents the total thickness of the system %* (h"Rh ); and m is the number of layers used to evaluate DM . This equation is similar i % to the expression developed for the equivalent hydraulic conductivity perpendicular to a layered system (e.g. Bowles, 1994). 3.2. Experimental evaluation Although the value of D can be obtained from in situ "eld measurements (e.g. % Rolston et al., 1991), it can be easier and more practical, especially with GCLs, to evaluate it under well controlled conditions in the laboratory. For that purpose, the authors have developed an experimental procedure inspired by techniques used for similar measurements made on soils and other porous media (Aachib et al., 1993; Aubertin et al., 1995; Tremblay, 1995; Aachib, 1997). Some of the existing techniques have been described by Rolston (1986), Glauz and Rolston (1989), Schackelford (1991), Aachib et al. (1993), and Tremblay (1995). The method employed here makes use of a di!usion cell with a decreasing source concentration. The experimental set-up, which is a modi"cation of the one used by Yanful (1993), is shown in Fig. 1. The laboratory evaluation of D values was performed for oxygen, but the proced% ure could easily be adapted for other gas constituents. The tests were done in three di!usion cells, each consisting of a source reservoir, the porous medium through which #ux takes place, and a collector reservoir. The procedure involves transient conditions in a closed system with source concentration decreasing over time while that of the receptor increases proportionally to the di!usive #ux. The concentration in the source reservoir (and of the receptor reservoir if required) is measured periodically during the test. The di!usion coe$cient D through the porous medium is obtained by % "tting the experimental data (concentration versus time) to a theoretical solution using a MATLAB program (Math Works 1995) described by Aachib and Aubertin (1999). The same results have also been obtained by an appropriate use of POLLUTE, a "nite layer contaminant transport program (Rowe et al., 1994). The imposed boundary conditions are presented below. The basic technique used to solve the problem have been given by Rowe and Booker (1985) and will not be repeated here. The experimental set-up consists of a transparent PVC cylinder with an internal diameter of 8.5 cm and a length between 20 to 30 cm (according to the size of the sample). The cylinder is closed by two capping plates. A Teledyne (320P or 340 PBS)

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Fig. 1. Schematic representation of the di!usion cell used to measure oxygen #ux; these measurements allow a calculation of the e!ective di!usion coe$cient D of the material. %

oxygen concentration measurement device is used, with the sensor "xed at the top of the source reservoir. To check the mass balance during testing, another sensor can also be "xed in the bottom reservoir, but this is not required for non reactive materials. The four valves in the PVC tube serve to purge the system with nitrogen before the test starts, and these remain closed during di!usion so the cell is air-tight. Previous measurements with manometers during preliminary tests performed on soils have shown that the pressure gradient between the bottom and top of reservoirs is negligible, so it does not create signi"cant advective gas transport (Tremblay, 1995). All the tests were run on Bento"x (BF) samples (from the same sheet) having a nominal mass/area of about 4.3 kg/m2 and a bentonite mass/area of 3.3 kg/m2. It is a needlepunched GCL made of a nonwoven geotextile on one side and a composite geotextile on the other side. It is well known that GCL behavior depends on its water content, porosity, and con"ning pressure, so special care was taken to control these factors during testing. For the di!usion tests, the GCL sample is "rst cut to the size of a cell ring. The PVC tube interior is coated with grease to ensure contact between the wall and the GCL. Some bentonite is also added close to the wall to improve contact. The GCL is placed on a 5 cm-thick sand layer and covered by another 5 cm of sand. Concrete sand with about 85% of the grains smaller than 1 mm (and a small air entry value) was used; note that it is useful (but not essential) to establish the D }S relationship of the sand % 3 before testing the GCL. The amount of water added is calculated according to the manufacturer's speci"cation's to fully (or partly in one case shown here) saturate the

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GCL (Authier, 1997). The top sand layer is covered by a perforated plate (about 50 holes, 0.5 cm in diameter) that supports a dead load equivalent to the expected vertical pressure in situ (typically between 10 and 30 kPa). An open space of about 0.5 cm is kept between the weight and the plate, so oxygen can #ow freely to the sand layer. It usually takes 7 to 10 days to fully hydrate the nonwoven needlepunched GCLs, as determined from swelling of the sample (Authier, 1997). Once hydration is completed, the cell is purged with nitrogen that was previously circulated through water to prevent humidity loss in the GCL. The top reservoir is then very brie#y opened to attain atmospheric conditions with an oxygen concentration of about 20.9% (C "9.3 mol/m3"0.3 kg/m3). This constitutes the initial condition of the di!usion 0 test, which is then allowed to run until a steady state is approached. This may take a few hours to a few days, depending on the D value (see Fig. 2). The concentration % pro"le over time serves to back calculate D from a similar curve obtained from the % numerical solution which is adjusted to "t the experimental results (Fig. 2). In these calculations, C "C at t "0 and is left to decrease after the test starts, while 4063#% 0 0 C "0 at t "0 and increases thereafter. The thickness h of the sample 3%#%1503 0 (h"h #h ) is also introduced in the model for the calculations with h for GCL 4!/$ %2 each layer, so DH can be obtained (see Eq. (13)) from the curve "tting process. Before and sometimes during testing, various veri"cations are performed to check the air-tightness of the cells, the accuracy of the oxygen sensor, their stability over time, and their proneness to consume oxygen. A simple mean to make these checks is to simply observe readings stability for a closed reservoir full of air or of nitrogen. Results from the di!usion tests (such as those presented in Fig. 2) show that di!usion occurs in two stages, because of the two materials used. The "rst stage, relatively short (a few minutes), is due to di!usion in the top sand layer that has a relatively low degree of saturation (usually S )50%, because of the capillary e!ects 3 created by the GCL); accordingly, the sand has a D value that is fairly close to D0 (see ! % Eqs. (3)}(11)). The second and much longer stage is that of oxygen di!usion through the highly saturated GCL. For the sample calculations with the MATLAB program shown in Fig. 2, the value of D was "rst established for the top sand layer, and then used to evaluate that of the % GCL. The detailed results shown in Table 1 were obtained on the BF samples described above. Fig. 3 shows a comparison between the measured values of D for the GCL and the % relationship between D and S as described by the Collin (1987) model (Eqs. (3)}(9)) % 3 with the above given values for D0 and D0 at RT (RT+200C). As can be seen, the 8 ! experimental results appear to correlate well to the calculated values. The accordance

c Fig. 2. Comparison between experimental measurements of oxygen concentration variation during di!usion tests, and the corresponding values deduced from model calculations: (a) (D ) "4.6]10~8 m2/s; (D ) "9.5]10~8 m2/s (Test 1 in Table 1); % 4!/$ % GCL (b) (D ) "7.1]10~7 m2/s; (D ) "8.57]10~11 m2/s (Test 2 in Table 1); % 4!/$ % GCL (c) (D ) "2.0]10~7 m2/s; (D ) "1.42]10~11 m2/s (Test 3 in Table 1). % 4!/$ % GCL

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Table 1 Experimental data obtained during di!usion testing of GCLs

Test identi"cation 1 2 3 4 5 6 7

S (%) 3

w! (%)

n

Hydrated thickness (10~3 m)

71 100 100 100 100 100 100

59.0 105.9 145.3 110.6 93.5 106.3 109.1

0.638 0.609 0.757 0.623 0.573 0.575 0.571

7.4 8.6 7.6 7.8 8.5 8.3 8.3

Estimated D (10~11 m2/s) % 9500 8.57 1.42 1.11 0.81 2.69 0.80

!w"h /100[(1!n)D ], where D "2.13 (relative density of solids). 8 3 3

Fig. 3. Comparison between the experimental results and the values of D as a function of S , given by Eqs. % 3 (3)}(9).

is particularly good if one considers the uncertainty that exists on the actual porosity and thickness of the hydrated GCL and sand layers, the homogeneity of water and bentonite distribution, the relative precision of the oxygen sensor, and the adjustment of the predicted and measured concentration versus time curve. The same equation has also been compared to various results obtained on di!erent types of soils and tailings using a similar experimental procedure (Aachib and Aubertin, 1999; Aubertin et al., 1999). Fig. 4 shows some of these results, including the values obtained on GCLs. The curve shown here, for an average porosity of 0.4, is very similar to the one that has been calculated with the Eberling et al. (1994) model (see Eqs. (10) and (11));

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Fig. 4. Di!usion coe$cients values measured for di!erent soils, tailings and GCLs; predicted values using Eqs. (3)}(9) are also shown.

the latter is not shown in the "gure but detailed results were given in a report published in Canada by MEND (Project 2.22.2a, Aubertin et al., 1995). The results shown here nevertheless con"rm that the models described above represent fairly well the experimental observations.

4. Discussion The results presented above illustrate how D values have been obtained experi% mentally for GCLs, and how such values can be a!ected by water content and porosity. In this investigation, most measurements have been done on fully hydrated (S +1 or 100%) GCLs because this corresponds to anticipated servicing conditions in 3 the "eld. As shown by the result at S "71% (test no. 1), and by numerous results on 3 other porous media (Fig. 4; see also Aubertin et al., 1995, 1996, 1999; Aachib and Aubertin, 1999), it appears essential that the degree of saturation be maintained close to 100% at all time if gas di!usion control is one of the key role of the cover system.

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The laboratory measurements allow practical calculations of gas #ux through a GCL. To illustrate how one can perform such calculations, a simpli"ed steady state solution of Fick's laws is used. This solution can be written as (Nicholson et al., 1989): D (C !C ) 1 , F " % 0 ' h

(16)

where C is the concentration above the GCL, C the concentration below the GCL, 0 1 and h is the thickness of the GCL. For a GCL sandwiched between two relatively dry sand layers placed on reactive tailings that would quickly consume oxygen, the #ux can be estimated using the following parameter values: C "0.3 kg/m3 (constant atmospheric concentration), 0 C "0 (oxygen consumed), D "5.5]10~11 m2/s and h"0.008 m (from our 1 % measurements). This gives a #ux F of about 65 g per square meter per year. This ' value would be somewhat higher than the targeted #ux obtained with e!ective covers to control acid mine drainage, which is about 20 to 50 g/m2/yr (Aubertin et al., 1999). This would nevertheless represent a decrease of the oxygen #ux by a factor of about 250 when compared to the uncovered situation. The e$ciency of a cover system incorporating a GCL could be improved by adding a layer of relatively "ne grained soil with a high capacity to retain water by capillarity. For instance, 30 cm of silt with a degree of saturation of 80% (with D +2]10~8 m2/s) above the GCL would give % a #ux of about 58 g/m2/yr; this value is obtained with DM of the system given by Eq. % (15). If the silt is able to maintain a minimum degree of saturation of 90% (with D + % 2.5]10~9 m2/s), as expected from our calculations using unsaturated #ow modelling techniques (e.g. Aubertin et al., 1995,1997), then the #ux F would be reduced to less ' than 36 g/m2/yr, which is within the targeted range. For the transient period that precedes steady-state, one could evaluate the #ux evolution using a relatively simple analytical solution expressed as (Crank, 1975; Aachib et al., 1993; Aubertin et al., 1999):

A B

A

B

DH 1@2 a !(2m#1)2h2 F "h FH"2C h + exp , (17) '(5) %2 0 %2 pt 4DHt m/1 where h and DH are de"ned by Eqs. (13) and (14), using DM given by Eq. (15); t is the %2 % time (¹), h is the total cover thickness (¸); m is an integer. In this equation, C remains 0 constant as previously de"ned; the initial oxygen content of the cover is considered to be nil. As an example, if h"0.3 m and an equivalent DM value of 6]10~10 m2/s are % used with Eq. (17), a steady state #ux of 18 g/m2/yr is obtained; the transient #ux given by this equation is shown in Fig. 5. Also shown on this "gure is the value obtained from POLLUTE (Rowe et al., 1994) at the top and bottom of the cover placed on the reactive tailings. The correlation between the analytical and numerical results is very good in this case. These results also illustrate how #ux evolves above and below a cover system. Of course, in practical applications, one must "rst evaluate the water balance and humidity distribution for the cover, and use actual data to establish the D value % for #ux calculations. The simple results presented above nevertheless illustrate the

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Fig. 5. Evaluation of the oxygen #ux calculated from Eq. (17) and using POLLUTE (see text for details).

positive e!ect of a properly designed cover system with a GCL on the amount of gas that can #ow through the cap. 5. Conclusion Controlling the gas #ux may be one of the goals of a cover system placed on reactive wastes such as municipal refuse, uranium tailings, and sulphidic waste rocks. To evaluate the amount of gas #owing through a cap that includes a GCL, one must "rst establish the value of the e!ective di!usion coe$cient D required to apply Fick's % di!usion laws. In this paper, the authors have presented an experimental procedure to make such measurements. The results obtained on Bento"x samples are shown to correlate well with values measured on other porous media and to those obtained from a predictive model developed for soils. The importance of the degree of saturation on gas #ux is particularly well illustrated by these results. Using the values measured in the lab, it is shown, with analytical and numerical solutions, that a properly designed cover system with a GCL can constitute an e!ective barrier to limit gas #ux. Acknowledgements The authors would like to thank Antonio Gatien, Monica Monzon and AnneMarie Joanes who contributed to the experimental program. Lucette de GagneH and Annik Marchand have helped prepare the manuscript. References Aachib, M., 1997. ED tude en laboratoire de la performance des barrie`res de recouvrement constitueH es de rejets miniers pour limiter le DMA. Ph.D. Thesis, Mineral Engineering Dept. ED cole Polytechnique de MontreH al.

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Aachib, M., Aubertin, M., 1999. Gas di!usion through variably saturated porous media with application to oxygen barrier (submitted for publication). Aachib, M., Aubertin, M., Chapuis, R.P., 1993. ED tude en laboratoire de la performance des barrie`res de recouvrement constitueH es de rejets miniers pour limiter le drainage minier acide. Un eH tat de la question. Report EMP/RT } 93/32. ED cole Polytechnique de MontreH al. Aachib, M., Aubertin, M. Chapuis, R.P., 1998. ED tude en laboratoire de la performance d'un syste`me de recouvrement multicouche sur des rejets miniers. Proc. CIM Centennial AGM, CD-ROM, 8 pp. Aubertin, M., Aachib, M., Chapuis, R.P., Bussie`re, B., 1996. Recouvrements multicouches avec e!ets de barrie`re capillaire pour contro( ler le drainage minier acide: eH tudes en laboratoire et in situ. Exemples majeurs et reH cents en geH otechnique de l'environnement, Presse de l'ED cole Nationale des Ponts et ChausseH es, Paris, pp. 181}197. Aubertin, M., Aachib, M., Joanes, A.M., Monzon, M., Authier, K., 1999. ED valuation du #ux d'oxyge`ne a` travers les mateH riaux de recouvrement. Proc. Annual Conference of APGGQ, Rouyn-Noranda (Qc, Canada), 19}30. Aubertin, M., Aachib, M., Monzon, M., Joanes, A.-M., Bussie`re, B., Chapuis, R.P., 1997. ED tude de laboratoire sur l'e$caciteH des barrie`res de recouvrement construites a` partir de reH sidus miniers. Rapport de recherche. Project CDT 1899 (December 97) Submitted to MEND-CANMET, 107 pages. Aubertin, M., Chapuis, R.P., 1991. ConsideH ration hydro-geH otechniques pour l'entreposage des reH sidus miniers dans le nord ouest du QueH bec. Proceedings of the Second International Conference on the Abatement of Acidic Drainage Vol. 3, 1}22. Aubertin, M., Chapuis, R.P., Aachib, M., Bussie`re, B., Ricard, J.F., Tremblay, L., 1995. Evaluation en laboratoire de barrie`res se`ches construites a` partir de reH sidus miniers. ED cole Polytechnique de MontreH al, MEND Projet 2.22.2a, CANMET, Ottawa (March '96), 164 pages. Aubertin, M., Chapuis, R.P., Bussie`re, B. Aachib, M. (1993). ProprieH teH s des reH sidus miniers utiliseH s comme mateH riau de recouvrement pour limiter le DMA. Geocon"ne '93. Arnoud, Barre`s and Comes (eds). Balkema, Vol. I., 299}308. Authier, K. (1997). ED tude du transport de l'oxyge`ne dans un geH ocomposite bentonitique. Unpublished Report (Projet de "n d'eH tude), ED cole Polytechnique de MontreH al, 87 pp. Barlaz, M.A., Ham, R.K., 1993. Leachate and gas generation. In: Daniel, D.E. (Ed.), Geotechnical Practice for Waste Disposal. Chapman and Hall, London, pp. 113}136. Bienvenu, L., 1998. ActiviteH s de recherche du ministe`re des ressources naturelles du QueH bec sur le drainage minier acide, Rapport 1997}1998. Entente auxiliaire Canada-QueH bec sur le deH veloppement mineH ral. MNRQ, 38 pages. Bouazza, A., Van Impe, W.F., Van Den Broek, H., 1996. Hydraulic conductivity of a geosynthetic clay liner under various conditions. In: Karmon, (Ed.), Environmental Geotechnics. Balkema, Rotterdam, pp. 453}457. Bowles, J.E., 1994. Physical and Geotechnical Properties of Soils. McGraw-Hill. Campbell, G.S., 1985. Soil Physics with Basic Transport Models for Soil } Plant System. Elsevier, Amsterdam, 150 pp. Collin, M., 1987. Mathematical modelling of water and oxygen transport in layered soil covers for deposits of pyritic mine tailings. Licenciate Treatise. Royal Institute of Technology. Department of Chemical Engineering. S-100 44 Stockholm, Sweden. Collin, M., Rasmuson, A., 1988. Gas di!usivity models for unsaturated porous media. Soil Science Amer. J. 52, 1559}1565. Collin, M., Rasmuson, A., 1990. Mathematical modelling of water and oxygen transport in layered soil covers for deposits of pyritic mine tailings. GAC-MAC Annual Meeting. Acid Mine Drainage Designing for Closure, Vancouver, 311}333. Corey, A.T., 1957. Measurement of water and air permeability in unsaturated soil. Proceedings of the Soil Science Society of America 21 (1), 7}10. Crank, J., 1975. The Mathematics of Di!usion, 2nd Edition. Clarendon Press, Oxford, UK. Currie, J.A., 1960a. Gaseous di!usion in porous media, Part 1 } A non-steady state method. British Journal of Applied Physics 11, 314}318. Currie, J.A., 1960b. Gaseous di!usion in porous media, Part 2 } Dry granular materials. British Journal of Applied Physics 11, 318}324.

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