A capillarity-advective model for gas break-through in clays

A capillarity-advective model for gas break-through in clays

James Graham a,*, Krista Gelmich Halayko b, Harold Hume c, Timothy Kirkham b,Malcolm Gray d, Dennis Oscarson a

aUniversity of Manitoba, Winnipeg, Manitoba Canada R3T 2N2bManitoba Hydro, Winnipeg, Manitoba Canada R3C 2P4

cAtomic Energy of Canada Limited, Chalk River, Ontario, Canada K0J 1J0dAtomic Energy of Canada Limited, Mississauga, Ontario, Canada L5K 1B2

Received 10 March 2000; accepted 13 July 2001

Abstract

Laboratory testing has investigated how gases can break through compacted specimens of illite, bentonite, and sand–illite or

sand–bentonite mixtures. Specimens were formed with a wide range of initial clay densities, water contents and degrees of

saturation. Tests were done using two different test procedures. In one, equal increments of gas pressure were applied at

constant time intervals until break-through was observed. In the second, the pressure was held constant, and the time required

for break-through recorded. Results show that the pressure at break-through increases with clay density and decreases with

degree of saturation. When the degree of saturation is below about 85% in illite and clay–illite, and 93% in bentonite and sand–

bentonite, there is only a small resistance to gas migration. Above these degrees of saturation, break-through pressures rise

sharply. In an approach that differs from some others that have been reported, it is postulated that gas migration is only possible

when its pressure is higher than a Gas Entry Value (GEV) that is related to capillarity effects in the largest pores of the material.

Thereafter, the rate of advance of the gas–water interface depends on advective flow, that is, on the pressure (hydraulic)

gradient across the specimen. Analysis shows that times to break-through should decrease inversely with pressure increase and

this was observed in the experiments. Tests were also done on specimens made with non-polar paraffin instead of water. This

inhibited the development of bound water in diffuse double layers (DDLs) and led to break-through at much lower pressures.

D 2002 Elsevier Science B.V. All rights reserved.

Keywords: Clay; Clay–sand mixtures; Compaction; Unsaturated; Gas; Capillarity; Advection; Break-through

1. Introduction

Clays and clay–sand mixtures are increasingly

favoured as barriers for isolating wastes from the

biosphere. Until recently, most attention has been paid

to determining their ability to impede water flow and

to sorb potentially damaging contaminants. More

recently, concern has been expressed about their

ability to contain gases generated by the waste. This

paper examines the question of the pressures at which

gas will begin to ‘break through’ clay-based barriers.

Clays used for lagoon liners or landfill covers

must be carefully selected if desiccation shrinkage

and its accompanying fracturing are to be success-

fully controlled. This usually involves the choice of

0013-7952/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.

PII: S0013 -7952 (01 )00106 -5

* Corresponding author. Tel.: +1-204-474-9682; fax: +1-204-

474-7513.

E-mail address: [email protected] (J. Graham).

www.elsevier.com/locate/enggeo

Engineering Geology 64 (2002) 273–286

low- to intermediate-plastic clay (Boynton and Dan-

iel, 1985) or an engineered clay–sand mixture. In

such mixtures, clay provides adequately low intrinsic

permeability while sand provides resistance against

shrinkage and cracking.

The research described in following sections arises

from (but is not limited to) Canadian proposals for

deep disposal of heat-generating nuclear fuel waste in

the granitic rocks of the Canadian Shield (Atomic

Energy of Canada Limited, AECL, 1994). The concept

uses a 50–50 mixture of quartz sand and sodium

bentonite as one of the barriers in a multi-barrier

system. Other components of the system include the

wasteform itself, a manufactured container, and the

surrounding rock mass. In one form of the concept,

sand–bentonite (known as ‘buffer’) is compacted into

boreholes in the floor of excavated vaults. In the

confined space round containers, its purpose is to

provide support, assist in heat transfer, minimize

advective flow of ground water towards containers,

and sorb some of the radionuclides that will be

released after a container is breached. At its ‘reference’

dry density of 1.67 mg/m3 at water content 18.5% and

degree of saturation 85%, the Canadian buffer is clay-

dominated. Its hydraulic conductivity is about 10� 11

to 10� 13 m/s and effective friction angle about 17.5j(Lingnau et al., 1995; Dixon et al., 1999). The sand

component reduces shrinkage (and therefore cracking)

caused by water content changes that accompany

thermal and other gradients. In contrast with this

clay-dominated material, urban and industrial landfills

use sand–clay mixtures with clay contents in the range

4–10%. Such mixtures are sand-dominated, with the

clay acting simply as an impervious filler and the sand

providing shear resistance.

Several researchers (for example, Jeffries et al.,

1991; Wickramaratna et al., 1993; Horseman, 1994;

Kirkham, 1995; Agg et al., 1996) have predicted that

gases may be produced in nuclear disposal vaults

through biological degradation of organic materials,

anaerobic corrosion of metals placed in the repository

during construction, or by radiolysis. Because of the

duration of potential hazards and the necessity of

providing maintenance-free enclosure, methods for

collecting and treating gaseous products can not be

seriously considered for long-term use. Concern has

therefore been raised that high gas pressures might

develop (Volckaert et al., 1997). These pressures

could increase the loading on the canisters and poten-

tially damage the fabric of clay buffers. As a result,

the rate of gas migration to the biosphere would be

increased. Others have suggested that an ability to

retain high gas pressures close to canisters of waste

fuel might delay ground water reaching the canisters,

delay contamination and breaching, and therefore

delay possible migration of radionuclides through

the ground water system to the biosphere. With this

approach, high breakthrough pressures can be seen as

beneficial. Results reported by, for example Gray et al.

(1996), Halayko (1998), Hume (1999) and Horseman

et al. (1997, 1999) may differ by almost two orders of

magnitude in broadly similar materials. The differ-

ences are believed to be associated with the failure

mechanisms that have been assumed and the details of

the testing procedures. Because of the lack of con-

sensus on the mechanisms involved, it is important

to consider how gases will be contained within, or

released from, compacted clay barriers.

This paper examines how elevated gas pressures

cause gas migration through compacted specimens of

illite-rich and bentonite-rich laboratory specimens.

While gas diffusion through the pore fluid may also

play an important role (Hume, 1999), attention focu-

ses here on advective transfer of gas through the

pores of the specimens. Before this is possible, con-

tinuous air passages must exist, or be developed, in

the pore voids.

2. Mechanisms of gas break-through

Four principal mechanisms have been identified for

gases breaking through clay barriers. These include

(a) two-phase advective flow, which pushes water

aheadof thegasphaseunder the control of a com-

bination of capillarity and hydraulic gradient;

(b) diffusion of gas through intervening fluid to

neighbouring voids with lower gas concen-

tration;

(c) deformation of the soil fabric creating larger

pores to accommodate gas flow; and

(d) fissuring and hydraulic fracturing produced

when the minor principal effective stress be-

comes lower than the tensile strength of the

material.

J. Graham et al. / Engineering Geology 64 (2002) 273–286274

The experiments in this program concentrated on

the advective flow condition outlined in item (a).

Delahaye and Alonso (1998) used a probabilistic

approach to model the likelihood of preferential path-

ways developing in the material. Development of flow

channels in a heterogeneous sample was then simu-

lated using a coupled hydromechanical model. This

paper can be seen as an experimental complement to

their modelling. The diffusion in mechanism (b) was

studied and reported by Hume (1999). With respect to

the related mechanisms (c) and (d), it is noted that

suctions in unsaturated soils produce elevated tensile

strengths (Tang and Graham, 2000). The mechanisms

for gas break-through appear to depend strongly on the

conditions of the tests. In rigidly confined tests,

fracturing does not seem to occur in saturated speci-

mens (Gray et al., 1996), though channeling appears

possible (Delahaye and Alonso, 1998). Under these

conditions, channeling may involve local non-homo-

geneities that allow some compression while other

parts are expanding (Delahaye and Alonso, 1998).

The situation will be different in tests done in flexible

wall (triaxial) cells (Horseman et al., 1999) where

fracture is possible, even in saturated specimens. Most

disposal vaults will place bentonitic barriers in con-

fined spaces between containers and the surrounding

rock. While thermal gradients can be expected to

produce moisture and density changes, and therefore

some volume changes, it seemed appropriate to initiate

break-through research using rigidly confined cells.

A combination of capillarity and advective flow

(mechanism a) appears the most likely process in

confined specimens. The capillarity may not extend

over the whole specimen, but may appear as channel-

ing only in regions with larger pore sizes. This

becomes important in clays that have been compacted

rather than reconstituted from a slurry.

Fig. 1 shows simplified representations of macro-

pore structures in illite and bentonite. As in some of

the simpler models such as the Poiseuille model for

water flow through clays, potential flow paths in Fig.

1a and b are represented by cylinders. In reality of

course, the channels are irregular in cross-section and

form tortuous vugs connected by narrower throats

(Fig. 1c). They can be modelled better using more

complex models such as the Kozeny–Carman model.

Fig. 1 will be described in more detail in a later

section following more general discussion.

It was mentioned earlier that experiments were done

on specimens of compacted illite and bentonite. Most

nuclear waste disposal programs are proposing com-

pacted bentonite or sand–bentonite mixtures for

advective and dispersive barriers. Early tests in this

program using incremented gas pressures suggested

that bentonite could withstand very high gas pressures

without break-through (Gray et al., 1996). This, plus an

awareness that bentonite has high surface activity and

complex swelling behaviour, led to a decision to test

illite and sand–illite specimens. The simpler behaviour

of the illite made it possible to use simpler equipment,

lower pressures, and a wider range of density and

saturation, at least in the early stages of the program

(Kirkham, 1995). Later, higher capacity equipment

was designed and commissioned (Hume, 1999).

Mercury Intrusion Porosimetry (MIP) showed that

the illitic specimens had some tendency towards

closely spaced twin peak frequencies of pore sizes at

about 1 and 0.1 Am though the grain size distributions

were largely unimodal (Wan et al., 1995). The bento-

Fig. 1. Simplified representation of pore structures: (a) illite, (b)

bentonite, (c) open and occluded channels.

J. Graham et al. / Engineering Geology 64 (2002) 273–286 275

nitic specimens were clearly bimodal, with peak fre-

quencies in the ranges 10–100 and 0.025–0.1 Am. In

each case, the larger pores (macropores) in the distri-

bution are considered to be inter-ped pores and the

smaller pores (micropores) are intra-ped pores.

In illite, most of the positive charge deficit brought

about by isomorphous substitution is satisfied by

‘fixed’ potassium ions (Mithchell, 1976). As a result,

illite does not form large diffuse double layers (DDLs)

and the ‘bound water’ layer is small. Thus in Fig. 1a,

most of the pore passages in the schematic representa-

tion of illite have been shown as available for flow

when water is expelled by an advancing gas–water

front. In contrast, bentonite is a highly active clay that

uses hydrated cations to satisfy some of its positive

charge deficit. In the compacted sand–bentonite in this

study (Fig. 1b), low water contents and small intra-ped

pores (micropores) limit the full development of

DDLs. Intra-ped pores contain a significant proportion

of water that is electrically bonded to the mineral

surfaces. This water has higher viscosity than normal

water and is not readily available for flow. Due to the

high activity and swelling characteristics of bentonite,

it is likely that the inter-ped voids (macropores) con-

tain not only water but also more viscous soft clay gels

(Pusch, 1993). These gels have to be disrupted and

displaced by gas before break-through occurs. Only in

the largest passage in Fig. 1b (corresponding to con-

tinuous inter-ped voids in Fig. 1c) is there a proportion

of water that can be readily removed.

We now return to the processes of capillarity and

advection that we see as complementary mechanisms

controlling the migration of gas through confined

clay-rich soils. When the material has high degrees

of saturation (and discontinuous air voids), surface

tension effects at curved gas–water interfaces in the

macropores of compacted clays control the ability of

gas to enter the void spaces and displace pore water in

an accelerating advective process (Halayko, 1998). It

seems likely that this process will take place at

pressures below those needed for fracturing, though

longer durations will be required. Others (for exam-

ple, Harrington and Horseman, 1999) have suggested

that the break-through pressure is related to swelling

pressure. It is not clear how this relates to the capil-

larity-advective model being suggested here.

Capillary pressures (and therefore Gas Entry Values

(GEVs)) increase with decreasing pore diameter (Mith-

chell, 1976). Returning to Fig. 1a, a gas pressure p1 is

insufficient to offset the capillary pressures in any of

the voids. At pressure p2 and time t2, the pressure is

higher than the GEV for the largest pore channel, and

the channel begins to accept gas. Water is removed at a

rate controlled by the intrinsic permeability of the

channel, the viscosity of the pore liquid, and the gas

pressure gradient across the specimen. At t3,p3, the

largest channel has emptied of pore fluid and is trans-

mitting gas at a rate controlled by the permeability of

the channel and the viscosity of the gas. If a steady flow

of gas is supplied, this higher pressure p3 permits gas to

enter intermediate pore channels. At t4,p4 intermediate

pores have emptied of water and gas is entering the

smallest pore channels. Finally, at t5,p5 all pores are

transmitting gas.

Here we are thinking of pore channels that link the

larger pore sizes, that is, the macropores in compacted

bimodal clays. This simplified model is similar to the

Air Entry Value (AEV) concept that is used to describe

the performance of porous filter discs made of stone,

ceramic, or sintered metal. Since the practical applica-

tion in nuclear waste disposal vaults will involve other

gases besides air, the term ‘Gas Entry Value’ (GEV)

will be used. Below the GEV of the largest pores, gas

will not flow through illite (except by diffusion).

Higher compactive effort will produce higher density,

smaller macropores, and hence a higher GEV, pc. Once

pc has been exceeded, gas flow will increase progres-

sively with further pressure increases. The time

required for gas to move across the specimen will

depend on the rate at which pore fluid can be removed

by advective flow, that is, on the hydraulic conductiv-

ity and hydraulic gradient.

In the simplified representation of bentonitic speci-

mens in Fig. 1b, bound water restricts the effective size

of the pore channels. In the figure, gas cannot overcome

capillarity effects until the pressure is p4. Water in the

intermediate and smallest pore sizes has higher viscos-

ity and remains ‘bound’. By pressure p5, the largest

channel has emptied and ‘break-through’ has occurred.

The smaller channels are still not accepting gas. In this

case we could expect gas break-through to be abrupt.

Again, the break-through pressure will depend on

density, and the time to break-through will depend on

hydraulic conductivity and hydraulic gradient.

Several researchers (for example, Wheeler, 1988;

Jeffries et al., 1991; Fredlund and Rahardjo, 1993)


state that the gas phase will become continuous if the

degree of saturation is at or below a critical value. This

figure is often quoted to be about 85%, though the

number can be expected to vary with soil type. Only

when the gas phase in larger inter-ped pores becomes

continuous will gas flow readily through a soil. At this

stage, intra-ped pores (micropores) and smaller inter-

ped pores (macropores) will still tend to be water-filled

(Gens and Alonso, 1992; Silverstein and Fort, 1997).

Fredlund and Rahardjo (1993) reinforce this point by

stating that a small change in the degree of saturation

of a soil can significantly alter its hydraulic conduc-

tivity. These changes can have considerable impact,

for example in modelling seepage quantities and

hydraulic potentials in earth dams. The corollary of

this observation is that below a certain degree of

saturation (which will depend on mineralogy, particle

size distribution, and compactive effort), macropores

will be continuous and the soil will provide essentially

no resistance to gas flow. This concept is currently

being examined in our laboratories.

3. Analysis

Assuming gas will not enter a specimen until the

gas pressure can overcome surface tension effects in

capillaries at the gas–water interface, the GEV pc can

be calculated approximately from

pc ¼ 2Ts=r ð1Þ

Here, Ts is surface tension which depends on fluid

viscosity and on gas–water interactions; and r is some

measure of the average effective pore size, probably

tending towards the larger end of the distribution of

macropore sizes. It is a considerable approximation to

use the average pore size observed in MIP tests to

represent the variable pore sizes in compacted speci-

mens. This is especially true in bentonites and sand–

bentonites with their bimodal pore size distribution,

bound DDLs and gel structures. The approach used in

this section ignores the effects of statistically variable

pore size distributions and the probability that the

gas–water interface will progress by ‘fingering’ (Con-

ciani et al., 1995; Delahaye and Alonso, 1998).

Once the GEV expressed by Eq. (1) has been

exceeded, advance of the gas–water interface depends

on the rate at which the pressure gradient across the

specimen forces water from the pores. In Fig. 2, a gas

pressure pg is applied at the bottom AAVof an initially

saturated specimen of length L. A smaller pressure

(atmospheric or some other controlled value) po is

applied at the top CCV. At the stage shown in the

figure, intrusion of gas has intruded to BBV and has

forced water from the first (L� z) of the specimen.

(As noted earlier, ‘fingering’ is ignored.) The pore

water pressure is therefore pg at BBVand po at CCV.These pressures produce a hydraulic gradient

ihðzÞ ¼ ðpg � poÞ=z ð2Þ

which increases with time as the saturated region

BBV–CCVdecreases in length. Under a hydraulic gra-

dient ih = p/cwz, the Poiseuille model predicts the

average velocity of fluid flow

v ¼ dz=dt ¼ ðr2pÞ=ð8zgÞ ð3Þ

where cw is unit weight of water, r is average pore

radius, p=( pg� po) is pressure difference across the

length z of specimen that has not yet been penetrated

by gas, and g is fluid viscosity. The actual, or intrinsic,

flow velocity will be larger than this by a ratio (1 + e)/

e, where e = voids ratio, about 0.6 in the testing

program described later. Because of uncertainties

associated with the MIP data and how to handle the

effects of pore size distributions, this effect has been

ignored in following paragraphs.

Remembering that the advancing gas–water inter-

face shortens the length of the saturated zone and

Fig. 2. Gas and water pressures in a partly evacuated specimen.


increases the hydraulic gradient, the expression for

average velocity at time t and evacuated length (L� z)

can be integrated to give the time required for break-

through in a test where p is held constant.

tb ¼ 4gL2=ðr2pÞ ð4Þ

In a test where the pressure is increased at a

constant rate p, integration produces the following

expression for the time required for gas to break

through the specimen.

tb ¼

ffiffiffiffiffiffiffiffiffiffi8L2gpr2

sð5Þ

Once tb has been found, the break-through pressure

pb in incremental pressure tests can be calculated from

pb = ptb. Related expressions can be derived from the

Kozeny–Carman equation for seepage velocity. These

equations can be used for predicting break-through

times and pressures that can be compared with exper-

imental results.

It is also instructive to consider the stress states at

BBVand CCVin Fig. 2. At BBV, the gas pressure acts onboth the solid particles and the water menisci. There-

fore, the total stress rz = pg. The pore gas and pore

water pressures at BBVwill be equal. That is rzV=rz� u = 0. Fracturing is imminent but will be inhibited

by the cohesion and tensile strength produced during

compaction. By continuity, the total stress rz must be

constant across the whole height of the specimen up to

CCVwhere the pore gas pressure is po. The effective

stress rzV= rz� u at CCVis therefore pg� po. Thus,

there is a pore water pressure gradient across the spe-

cimen that causes water to flow from BBVtowards CCV.There is also an effective stress gradient from CCVtowards BBV that leads to compression and decreased

water content at CCV, and the possibility of expansion

and increased water content at BBVespecially in ben-

tonitic specimens.

4. Experimental program

The experimental program investigated (a) the

possibility of a ’threshold’ degree of saturation below

which there would be little resistance to gas flow, (b)

the inter-relationship between gas pressure gradient

and time-to-breakthrough, and (c) water content

changes in the specimens. Tests were performed on

compacted specimens of illitic and bentonitic clays;

and on sand–illite and sand–bentonite mixtures. The

materials used in the program are defined as follows.

Illite is a commercially marketed product used in

Canada as a mortar plasticizer. It is obtained by

grinding and processing a Dundas shale member from

the Georgian Bay Formation (Ordovician). It is a soft,

gray, illite-bearing shale with moderate chlorite and

no detectable expanding minerals. (See Table 1.)

Bentonite is a greenish-gray sodium bentonite from

the Bearpaw Formation (Upper Cretaceous). It is a

highly plastic expansive clay with a large specific

surface area. (See Table 1.)

Sand is a crushed, sieved and fractionated quartz

sand with 20% passing US Standard Sieve No. 16 and

retained on No. 30; 29% sizes 20–40; 22% sizes 40–

70 and 29% sizes 70–140.

Water is deaired, distilled water.

Gas is argon supplied from a commercial high

pressure gas cylinder. It was chosen because it is inert,

has low solubility in water, and will not alter the pH of

the water. It was decided not to use the gases that are

likely to be produced in a repository environment

(among them methane and hydrogen) because of the

risk of fire or explosion.

Paraffin oil is general laboratory reagent grade. It

was used in a small number of tests to investigate the

effect of a non-polar fluid (in contrast with water,

which is a polar fluid) on break-through pressure.

Table 1

Comparison of the properties of illite and bentonite used in the

program

Property Illite Bentonite

Primary clay mineral hydrous mica montmorillonite

Plasticity index, Ip 11 208

Liquid limit, wL 31 257

Plastic limit, wP 20 49

Unified Soil Classification CL CH

Specific weight 2.76 2.75

Specific surface area (m2/g) 43–81 519–631

Free swell volume (ml/g) < 1 > 9

Optimum moisture

content % from

Modified Proctor Test

12 10a

a Modified Proctor Tests on bentonite do not show a define

‘peak’. Almost the same dry density can be achieved with water

contents ranging from 10% to 40% (after Dixon, 1995).


Specimens were made at controlled values of dry

density, water content and saturation. The ranges of

the parameters that have been studied are shown in

Table 2. Mechanical properties of the clay–sand

mixtures have been described in a series of publica-

tions, for example Lingnau et al. (1995), Tanaka et al.

(1997).

Specimens were compacted directly into the test

cells using static compaction to achieve the required

combination of density and water (or paraffin) content.

In some cases, specimens were tested at their ‘as

compacted’ degree of saturation Sr. In others, efforts

were made to produce fully saturated specimens by

applying a back pressure of 0.2–1.0 MPa (and rarely, 5

MPa) on water-filled burettes attached to the top and

bottom of the specimens. These ‘saturated’ specimens

regularly achieved degrees of saturation exceeding

98%.

Two sets of specially designed test cells and con-

trol equipment were used in a total of almost 350 tests.

The work was done by graduate students Kirkham

(1995), Halayko (1998), and Hume (1999). Tests were

initially run on illite and sand–illite specimens using

increments of 0.2 MPa gas pressure added at 5-min

intervals. The equipment had a maximum pressure

capacity of 10 MPa. Results of the initial tests were

reported by Gray et al. (1996).

Attention then moved to bentonite specimens. Pre-

liminary tests showed that the same procedures led to

higher pressures (and therefore gradients) in bentonite

than in illite. The required pressures exceeded the 10

MPa capacity of the original equipment. The higher

capacity cell and control equipment shown in Figs. 3b

and 4, respectively, have a capacity exceeding 50 MPa

at 150jC. Fig. 3a shows a line diagram of the 10 MPa

cell and Fig. 3b shows a photograph of the similar but

heavier 50 MPa cell. The upper left in Fig. 3b shows

the cell base with tie-down bolts passing through a

Table 2

Range of parameters in the experimental program

Soil type Dry density

(mg/m3)

Water content

(%)

Degree of

saturation

(%)

Illitic clay 1.85–2.10 10–16 67–100

Bentonitic clay 0.6–1.45 30.0–63.5 60–100

Sand– illite 1.97–2.30 5.4–13.0 45–100

Sand–bentonite 1.67 11.4–20.4 50–89Fig. 3. (a) Line drawing of 10 MPa test cell. (b) Photograph of 50

MPa test cell.


thick-walled cell. At lower right is the top plate, which

is bolted tightly to the base and cell. Because of the

high pressures and use of gas, the equipment was

designed according to ASME Section VIII, Division

I, Boiler and Pressure Vessel Code (1995), and fab-

ricated according to CSA B51-M1995 (Boiler, Pres-

sure Vessel and Pressure Piping Code). The cell is

sealed by ethylene propylene O-rings with 90 durom-

eter hardness. When assembled, the specimen cavity is

23.1 (depth)� 50.5 mm (diameter). A 50-mm diame-

ter disc of Whatman #40 filter paper is placed between

the specimen and a 3.2-mm thick stainless steel porous

discs (porosity type H) above and below the specimen.

5. Results

Typical results of incremental pressure tests are

shown in Figs. 5 and 6. The results are from an

unsaturated bentonite specimen (Fig. 5) and an unsa-

turated sand–illite specimen (Fig. 6). In both figures,

the test was run by increasing the gas inflow pressure

in a series of small increments of constant duration. (In

Fig. 5, pressures were increased to about 50 MPa, the

safe capacity of the test equipment, and then held

constant until break-through occurred). An initial back

pressure po of 0.2 MPa was used in the gas collection

vessel. Gas ‘break-through’ was inferred when pres-

sures in the collection vessel began to increase. In the

bentonite, this was frequently, but not always, abrupt

and unambiguous (Fig. 5), perhaps indicating a chan-

nelling of gas or fracturing of the specimen in the way

suggested by Pusch (1993) and Horseman et al. (1997)

who also used incremental procedures. The rapid

increases in gas collection pressure in the bentonite

specimens may also support the suggestion in Fig. 1b

that much of the water in bentonite is bound to the

mineral particles, with only larger inter-ped pores

(macropores) having water that can be evacuated by

gas pressure. Similar proposals have been made by

Dixon et al. (1999) in discussions on hydraulic con-

ductivity.

In illitic specimens, the gas break-through pressure

was often lower and less clearly defined. In Fig. 6 for

example, no increases in gas collection pressure were

seen until the inflow pressure pg was 2.4 MPa. With

further pressure increases, the gas collection pressure

increased progressively. This indicates a successive

replacement of water by gas in the way suggested in

Fig. 1a. These interpretations of the mechanisms of

gas break-through pressure will be used in the follow-

ing section where the effects of density and saturation

on gas transmission are reviewed.

Results from incrementally loaded illite and sand–

illite specimens are summarized in Fig. 7. Note that the

Fig. 4. Control panel for 50 MPa test equipment.

Fig. 5. Typical results from an incremental pressure test on unsatu-

rated bentonite.


density scale in Fig. 7 has been expressed as effective

clay dry density qc defined as the dry density of the

clay–water–air phases in unsaturated sand–clay mix-

tures, neglecting the effect of the sand that acts simply

to assist heat transfer and reduce shrinkage. This

allows comparison of results from tests on both illite

and illite–sand specimens. Earlier work by Dixon et

al. (1996) showed that qc also controls the swelling

pressure and hydraulic conductivity of sand–clay

mixtures. Fig. 7 shows that break-through pressures

in incremental pressure tests on specimens with high

degrees of saturation increase sharply with dry density.

This can be expected from Fig. 1a and c since higher

compaction effort will decrease the size and frequency

of potential flow channels. Fig. 7 shows close agree-

ment between results from illite specimens with

Sr >80% (solid line) and sand–illite specimens with

Sr = 95–100% (dashed line). On the other hand, when

the saturation was below 80% (dash–dot line), the

break-through pressure was much lower, probably

reflecting a higher frequency of continuous flow

channels.

The relationship is more complex than can be

shown in the simple 2D drawing in Fig. 7. Increased

resistance to break-through can come from either an

increase in degree of saturation or an increase in clay

density. The key consideration is the degree of open-

ness of potential flow channels (Fig. 1c). The 3D nature

of the relationship is suggested in Fig. 8. The results in

the figure come from illite specimens but can be

expected to refer also to sand–illite if the dry density

scale is replaced by effective clay dry density qc.

Broadly similar behaviour was observed in benton-

ite and sand–bentonite specimens. Fig. 9 shows results

from bentonite specimens that had been back-pres-

sured to increase the saturation but still exhibited some

differences in degrees of saturation. In these tests, only

a small proportion of the specimens reached break-

through before 10 MPa (the capacity of the first test

equipment) using the incremental loading procedure

described earlier. It was these results that led to

development of the 50-MPa equipment shown in Figs.

3 and 4. In Fig. 9, only unsaturated specimens reached

break-through. When break-through happened, the

pressures were quite low, usually less than 2 MPa.

When reviewing data like those shown in Figs. 5–

9, there was a concern that the results might be

strongly influenced by the procedures used to achieve

saturation, particularly at the faces of the specimens

that were directly connected to the water supply. It was

Fig. 6. Typical results from an incremental pressure test on unsatu-

rated sand– illite.

Fig. 7. Break-through pressures from incremental pressure tests on

illite and sand– illite specimens in terms of effective clay dry

density.

Fig. 8. Break-through pressures from incremented pressure tests on

illite in terms of water content, dry density and degree of saturation.


also realised that compacted materials in disposal

vaults will be unsaturated, at least in the period before

full wetting up from returning ground water pressures.

A second series of tests was therefore done on benton-

ite specimens without back pressuring. Fig. 10 shows

results from these ‘as compacted’ specimens with

different degrees of saturation. The results show that

irrespective of water content and (clay) dry density,

application of relatively low pressures permitted

break-through when the degree of saturation was

below around 90%. Once again, very high pressures

were observed with saturations above 90%.

This is shown more clearly in Fig. 11. Here the

break through pressure pb is plotted against Sr for

specimens with a wide range of (clay) dry densities

between 0.95 and 1.45 mg/m3. Figs. 9 and 10 show no

trend for pb to vary systematically with either increased

density or with water content taken separately. It is the

combination of density and water content as expressed

for example in Fig. 11 by degree of saturation Sr that

seems to be the best measure of break-through pres-

sure. Fig. 11 suggests that open channels will exist in

the inter-ped voids (macropores) of bentonites and

sand–bentonites when the saturation is less than about

93%. Above that, the resistance to gas migration

increases sharply.

Also of interest in these tests was an observation

that on removal from the cells, the gas inlet end of the

specimen had higher water content than the outlet end,

despite the entry of gas at the inlet end (Hume, 1999;

Halayko, 1998). This observation led to the under-

standing of the effective stresses in the specimens that

was expressed in the earlier discussion of Fig. 2. This

concluded that the inlet end of the specimen would be

working at low (in principle, zero) effective stress

(Fig. 2). Bentonite is strongly swelling in nature, and

the low effective stresses allow the inlet end to expand

while the outlet end compresses. Water must therefore

be moving, towards the outlet end of the specimen

where the gas–water front is advancing, and else-

where towards the inlet end as the clay expands under

low effective stress.


‘saturated’ bentonite in terms of water content and dry density.


unsaturated in terms of water content and dry density.


bentonite as a function of degree of saturation.


After this was realized, further tests were performed

to examine the applicability of the pressure– time

relationships expressed by Eqs. (4) and (5). The first

tests examined whether break-through pressures varied

with the rate at which inlet pressures were incremented

(Eq. (5)). Two tests were done on illite specimens with

pressure increments of 0.2 MPa added every hour

instead of every 5 min as in the standard tests. Break-

through occurred at 2.2 and 1.8 MPa, respectively. The

average break-through pressure from the slower tests

was 56% of the ‘standard’ faster value at this density

and water content. Four further tests were then con-

ducted with a range of constant pressures and the time

to break-through tb measured. The clay densities were

2.04 mg/m3 and the degrees of saturation closely

similar. The results shown in Table 3 suggest that for

a given degree of saturation, break-through times vary

inversely with gas pressure in the way suggested by

Eq. (4).

A more complete series of constant-pressure tests

was done on back-pressured bentonite specimens. (It

will be remembered that break-through pressures in

standard (5 min) incremented tests on bentonite speci-

mens were usually very high, frequently greater than

the 50-MPa capacity of the test equipment.) In con-

trast, in the constant-pressure tests, break-through was

observed at relatively lower pressures in all speci-

mens, with test durations that were always longer than

those reached in corresponding incremental pressure

tests. For example, a constant-pressure test at

qc = 1.00 MPa and pb = 0.3 MPa produced break-

through after tb = 120.5 h. No break-through was

observed at the same qc when pressures were incre-

mented at the standard rate (5 min/increment) up to 50

MPa, the maximum capacity of the equipment.

Constant-pressure tests were done at two different

inlet gas pressures (4.8 and 9.8 MPa) on bentonite

specimens with density qc ranging from 0.8 to 1.4 mg/

m3. Results are shown in Fig. 12. The times to break-

through tb increased with clay density and decreased

with pressure. Since the specimen length was constant,

increases in pressure represent increases in gradient,

and therefore an ability to remove water more quickly

from the pore channels. Fig. 13 shows results from a

more complete set of constant-pressure tests at

qc = 1.00 mg/m3. They indicate that times to break-

through in constant-pressure tests vary inversely with

pressure in the way suggested by Eq. (4).

It is noted in Fig. 13 that pressures above pb = 2.8

MPa (1/pb = 0.36) produce no further decrease in tb.

This is not fully understood at present. The models of

gas break-through outlined earlier assume a constant

pore structure. However, it was shown earlier, partic-

ularly in high-pressure tests, that the inlet end of some

of the bentonite specimens expanded while the outlet

end compressed. The compression produces reduced

hydraulic conductivity towards the outlet end (Dixon

et al., 1999) and this can cause the break-through to be

Table 3

Break-through times from constant pressure tests on illite

Number Degree of

saturation

Pressure pb(MPa)

Break-through

time tb (h)

1 97.2 0.8 >336

2 96.9 1.8 22.7

3 96.9 2.8 0.3

4 97.2 2.8 0.2

Fig. 12. Times to break-through in constant pressure tests ( pg = 4.8

and 9.8 MPa) on saturated bentonite specimens with different

effective clay dry densities.

Fig. 13. Times to break-through in constant pressure tests on sa-

turated bentonite specimens (qc = 1.00 MPa) as a function of inverse

gas pressure ( pg� 1).


delayed. Further understanding of this effect requires

modeling like that undertaken by Delahaye and

Alonso (1998).

6. Discussion

Fig. 1 implied that the presence of diffuse double

layers would bind water to mineral particles and make

it more difficult for gas to displace water. The presence

of bound water would therefore induce higher break-

through pressures in incremental pressure tests and

longer times to break-through in constant pressure

tests. This effect was examined in a series of tests on

both illite and bentonite specimens that were prepared

using non-polar paraffin instead of polar water as the

pore fluid. The paraffin inhibits the development of

DDLs and the proportion of water bound to the mineral

particles. If differences were to be observed, they

would be smaller in illite than in bentonite because

DDLs are less developed in illites.

To make the non-polar specimens, illite was mixed

with paraffin oil to an equivalent water content (paraf-

fin content) of 12% and compacted to qc = 2.05 mg/m3

and Sr = 95.6%. These parameters had been used in

many standard tests with water as the pore fluid, and

repeatable results had been obtained. Results are shown

in Table 4. The values of w in the table are for water or

for paraffin oil, depending on which pore fluid was

used. Use of paraffin oil in illite reduced the average

break-through pressure by 41% from 3.75 to 2.2 MPa.

Table 4 also shows results from similar tests done

on a limited number of bentonite specimens com-

pacted to an average qc = 1.15 mg/m3, w = 50.4% and

Sr = 99.1%. As expected, the reduction in pb was much

larger in this case, a 95% reduction from an average of

4.0 to 0.2 MPa. It is emphasized that in both the illite

and bentonite tests, the specimens were made to the

same dry density (and particle separation) with both

water and paraffin.

Work was also done on modelling expected gas

break-through pressures using Eqs. (4) and (5) in

conjunction with Poiseuille and Kozeny–Carmen

equations for hydraulic conductivity. It is rare to be

able to predict hydraulic conductivities in clay to better

than one order of magnitude (Dixon et al., 1999). This

means that break-through pressures and times of

break-through cannot be predicted with better accu-

racy. Modelling also needs to consider the question of

average and intrinsic flow velocities outlined in an

earlier section. The modelling has been reported by

Halayko (1998) and Hume (1999) but will not be

considered further in this paper. Thus the word ‘model’

in the title of the paper refers to a conceptual model

and the equations developed in Eqs. (4) and (5).

Figs. 11 and 12 show that there are degrees of

saturation below which potential flow channels may

offer only limited resistance to gas migration. Sim-

ilarly, Fig. 13 suggests an inverse relationship between

break-through pressure and test duration. The question

then arises if there is any pressure below which no

flow will take place. Will even very low pressures

eventually permit gas transfer if sufficient time is

permitted? As explained earlier, we believe that

advective flow cannot take place below the Gas Entry

Value. This value corresponds to the capillary pressure

that arises from surface tension relationships between

the mineral particles, pore fluid phase, and gas phase.

In dense bentonites like the Canadian Reference

Buffer Material, it is possible there may be no con-

tinuous channels in unbound water. Experiments to

investigate these possibilities are now almost com-

plete. Hume (1999) examined the possibility that

diffusive flow may be possible at pressures below

the Gas Entry Value.

Others, particularly Horseman and his co-workers,

have used different test procedures and obtained

different results. Further study is clearly required to

establish the relationship between test techniques and

Table 4

Comparison of results using polar and non-polar pore fluids

Specimen Pore fluid qc(mg/m3)

w (%) Sr (%) Pressure,

pb (MPa)

Clay: illite

T40 water 2.05 12.3 96.9 3.8

T50 water 2.04 12.0 94.1 4.0

ITU-2 water 2.04 12.6 98.3 3.6

ITU-2B water 2.04 12.6 98.3 3.6

INPFU-1A paraffin 2.05 12.0 95.6 2.0

INPFU-1B paraffin 2.05 12.0 95.6 2.4

Clay: bentonite

BNPFU-3A water 1.15 50.6 99.3 3.6

BNPFU-3B water 1.15 50.6 99.3 5.4

BNPFU-2 paraffin 1.15 50.0 98.8 0.2


the fundamentals of gas break-through in clays and

sand–clay mixtures.

7. Conclusions

Two different test procedures, (1) incremental load-

ing with fixed times and (2) constant loading with

different durations, have produced quite different

understanding of the nature of gas break-through.

Incremental tests in this program and elsewhere are

done relatively quickly in tests that last typically

several hours. The test reported in this paper produced

gas break-through pressures of the order of 10 MPa in

illite and 50 MPa or more in bentonite. Alternatively,

tests run more slowly with constant pressures produce

break-throughs at pressures as low as 0.3 MPa after 5

days. These results differ markedly from the fracture

approach adopted in some other programs.

In illite, break-through flow appears to develop

sequentially through many flow channels. The pore

size distribution obtained from MIP tests shows that

illite contains a wide variety of pore sizes. It is also

known that there is little bound water. In incremen-

tally loaded tests, as pressure increases, more pores

become available for flow as their GEV is exceeded.

Gas break-through will occur when the largest pore

channel (which first commenced de-saturation) has

fully drained from the gas inlet to the gas outlet side

of the specimen. In bentonite, the pore size distribu-

tion is strongly bimodal, with few pores of intermedi-

ate size. Diffuse double layers form as bound or

‘structured’ water between the clay particle surfaces.

This process can completely block small pores, create

gel structures in large pores, and inhibit movement of

water under gas pressure gradients.

In saturated specimens, gas break-through pressures

increase with effective clay dry density qc. Use of qc inthis way allows results from pure clays and various

sand–clay mixtures to be compared. In sand–clay

mixtures, the sand particles are inactive in the flow

of gas and water, and clay dry density can be used to

describe the expected behaviour. Inter-ped pores (mac-

ropores) decrease in size and frequency as dry density

increases and in this way influence flow rates. Resist-

ance to gas break-through is low below a threshold

value of degree of saturation. This appears to be

approximately 85% in illite and 93% in bentonite.

The differences relate to the frequency and geometry

of larger inter-ped pore spaces and to the presence of

diffuse double layers. Pore sizes are smaller and diffuse

double layers more frequent in bentonite than in illite.

Break-through is at least partly time-dependent.

Long durations permit break-through at low pressures.

Short time durations require high pressures. These

results are consistent with models that assume gas

break-through occurs after gas enters the macropores

and extrudes water by an advective process. It is not

yet clear if there is a lower pressure limit imposed by

capillarity, below which no flow will take place.

Acknowledgements

Support was provided by Atomic Energy of Canada

Limited (AECL), the Natural Sciences and Engineering

Research Council of Canada (NSERC), and the

CANDU Owners Group (COG). The authors acknowl-

edge valuable input and technical assistance frommany

colleagues at the University of Manitoba and White-

shell Laboratories. The reviewers presented comments

that led to clarification of the presentation of this

research.

References

AECL, 1994. Environmental Impact Statement on the concept for

disposal of Canada’s nuclear fuel waste. Atomic Energy of

Canada Limited, Report AECL 10711, COG-93-1, Sept. 1994.

Agg, P.J., Cummings, R.W., Rees, J.H., Rodwell, W.R., Wikramar-

atna, R., Gas generation and migration research, Nirex Science

Report No. 96-002.

Boynton, S.S., Daniel, D.E., 1985. Hydraulic conductivity tests on

compacted clay. J. Geotech. Eng., ASCE 111, 465–478.

Conciani, W., Soares, M.M., Crestana, S., 1995. Geotechnical use of

mini tomography. In: Alonso, E.E., Delage, P. (Eds.), UNSAT

’95. Proc. 1st Int. Conf. on Unsaturated Soils. Unsaturated Soils

2. Balkema, Rotterdam, pp. 447–452.

Delahaye, C., Alonso, E.E., 1998. Soil heterogeneity and preferen-

tial paths for gas migration. 5th International Workshop on Key

Issues in waste isolation research. Organized by Escuela Tecnica

Superior de Ingenieros de Caminos Canales y Puertos de Bar-

celona, Universidad Politecnica de Cataluna, Barcelona, Spain,

December 1998.

Dixon, D.A., Gray, M.N., Graham, J., 1996. Swelling and hydraulic

properties of bentonites from Japan, Canada and the U.S.A. In:

Kamon, M. (Ed.), 2nd International Congress on Environmental

Geotechnics, Osaka, Japan, November 1996. Balkema, Rotter-

dam, pp. 317–322.


Dixon, D.A., Graham, J., Gray, M.N., 1999. Hydraulic conductivity

of clays in confined tests under low hydraulic gradients. Can.

Geotech. J. 36, 815–825.

Fredlund, D.G., Rahardjo, H., 1993. Soil Mechanics for Unsaturated

Soils. Wiley-Interscience, New York.

Gens, A., Alonso, E.E., 1992. A framework for the behaviour of

unsaturated expansive clays. Can. Geotech. J. 29, 1013–1032.

Gray, M.N., Kirkham, T., Wan, A.W.L., Graham, J., 1996. On the

gas-break-through resistance of engineered clay barrier materi-

als proposed for use in nuclear fuel waste disposal. International

Conference on Deep Disposal of Radioactive Waste. Winnipeg

MB, Sept. 1996.

Halayko, K.S.G., 1998. Gas flow in compacted clays. MSc thesis,

University of Manitoba, Winnipeg MB, September 1998, 128

pp., plus figures and tables.

Harrington, J.F., Horseman, S.T., 1999. Gas transport properties of

clays and mudrocks. In: Aplin, A.C., Fleet, A.J., Macquaker,

J.H.S. (Eds.), Muds and Mudstone; Physical and Fluid-Flow

Properties. Geol. Soc. Spec. Publ., vol. 158, pp. 107–124.

Horseman, S.T., 1994. The disposal of high level radioactive waste

in argillaceous host rocks. Publ. Tec. ENRESA 1994 (4), 135.

Horseman, S.T., Harrington, J.F., Sellin, P., 1997. Gas migration in

MX80 buffer bentonite. Mater. Res. Soc. Proc. 465, 1003–1010.

Horseman, S.T., Harrington, J.F., Sellin, P., 1999. Gas migration in

clay barriers. In: Pusch, R., Yong, R.N., Grinrod, P. (Eds.),

Symposium on Microstructural Modelling of Natural and Arti-

ficially Prepared Clay Soils with Special Emphasis on the use of

Clays for Waste Isolation, Lund, Sweden, October, 1998. Eng.

Geol., vol. 54 (1–2), pp. 139–149.

Hume, H.B. 1999. Gas break-through in compacted Avonlea ben-

tonite. MSc thesis, University of Manitoba, Winnipeg MB, No-

vember 1998, 169 pp., including figures and tables.

Jeffries, R.M., Liew, S.K., Thomas, J.B., 1991. Gas migration in

deep radioactive waste repositories: a review of processes, data,

and models. United Kingdom Department of Environment. Re-

port No. DOE/HMIP/RR/91/029.

Kirkham, T., 1995. Development of test equipment and procedures

for determination of the gas-break-through pressure of com-

pacted clay materials with preliminary results. MSc thesis, Uni-

versity of Manitoba, Winnipeg MB, August 1995, 266 pp.,

including figures and tables.

Lingnau, B.E., Graham, J., Tanaka, N., 1995. Isothermal modelling

of sand–bentonite mixtures at elevated temperatures. Can. Geo-

tech. J. 32, 78–88.

Mitchell, J.K., 1976. Fundamentals of Soil Behaviour. Wiley, New

York, NY.

Pusch, R., 1993. Current status and future plans for R and D on gas

penetration and release through buffer materials. Reprinted from

International Workshop on Research and Development of Geo-

logical Disposal, PNC Tokai, Japan.

Silverstein, D.L., Fort, T., 1997. Studies in air –water interfacial

area for wet unsaturated particulate porous media systems.

Langmuir 13, 4756–4761.

Tanaka, N., Graham, J., Crilly, T., 1997. Stress–strain behaviour of

reconstituted illitic clay a different temperatures. Eng. Geol. 47,

339–350.

Tang, G.T., Graham, J., 2000. A method for testing tensile strength

on unsaturated soils. Geotech. Test. J. 23, 377–382.

Volckaert, G., Ortiz, L., De Canniere, P., Put, M., Horseman, S.T.,

Harrington, J.F., Impey,M.D., Einchomb, A.J.B., 1997.MEGAS:

modelling and experiments on gas migration in repository host

rocks. CEC Final Report—Phase 1, Eur 16235-EN.

Wan, A.W.L., Gray, M.N., Graham, J., 1995. On the relations of

suction, moisture content and soil structure in compacted clays.

1st International Conference on Unsaturated Soils, Paris, France,

September 1995, 215–222.

Wickramaratna, R.S., Goodfield, M., Rodwell, W.R., Nash, P.J.,

Agg, P.J., 1993. A preliminary assessment of gas migration from

the copper/steel canister. Swedish Nuclear Fuel and Waste Man-

agement Co. SKB Technical Report 93-31, Stockholm, Sweden.

Wheeler, S.J., 1988. A conceptual model for soils containing large

gas bubbles. Geotechnique 38, 389–397.


Documents

A capillarity-advective model for gas break-through in clays