Measuring gas diffusion in landfill cover material

Proceeding Sardinia 2007, Eleventh International Waste Management and Landfill Symposium S. Margherita di Pula, Cagliari, Italy; 1-5 October 2007 © 2007 by CISA, Environmental Sanitary Engineering Centre, Italy

MEASURING GAS DIFFUSION IN LANDFILL COVER MATERIAL S.E. ALLAIRE*, J. LAFOND*, AND A. CABRAL**

*Centre de Recherche en Horticulture, Université Laval, Québec, Qc, Canada, G1K 7P4 ** Civil Engineering Department, University of Sherbrooke, Sherbrooke, Qc, Canada, J1K 2R1

SUMMARY: Large quantities of gases emitted by landfills move through their cover material mainly by convection and diffusion. Diffusion is important for lateral flow of gas and is primordial for O2 movement to support CH4 oxidation. Five laboratory methods used for measuring the relative gas diffusion coefficient (Ds/Do) were compared. All methods gave similar Ds/Do. Long soil columns in closed system result in slightly higher Ds/Do, probably due to boundary effect. Methods with transient boundary conditions are simpler. Larger cores allow the study of heterogeneity in gas movement, important in landfill cover materials, but initial and boundary conditions are more difficult to control. When macropores are involved, the Millington-Quirk model (1960) better predicted the Ds/Do measured with the different methods. However, the Moldrup et al. (2000) model best predicted all Ds/Do when macropores were not considered. There were no obvious trends of model performance relative to specific measuring methods.

1. INTRODUCTION

Landfills emit large quantities of methane (CH4). Most systems can capture no more than 60% of gases emitted by decomposing wastes (USEPA, 2002). The other 40% pass through the cover material and is released to the atmosphere. Methanotrophic bacteria living in cover materials (soils) can oxidize CH4 in aerobic conditions (Sheutz and Kjeldsen, 2004). Aerobic conditions occur when oxygen move by diffusion from the soil surface in counter direction to the upward convective flux of CH4 created by pressure gradients in the waste mass. Diffusion is also important in landfill covers, affecting lateral flow of gases where lateral pressure gradients are relatively low. This process decreases the efficiency of gas collection systems. As a consequence, proper estimation of gas diffusion in landfill covers is an important issue.

Different field methods have been developed to measure gas diffusion in soils. Initial and boundary conditions, soil core dimensions and hypotheses vary between these methods. To the Authors’ knowledge, only the study by Werner et al. (2004) compared different methods to obtain the ratio between the coefficient of gas diffusion in soils and in the air, Ds/Do, both in the field and in the laboratory. However, the study by Werner et al (2004) only used data available in the literature. They could not establish a direct comparison between data measured in a single location with different methods. From the available data, there were no obvious differences in Ds/Do values determined with different field methods. Werner et al. (2004) found only three studies (Jellick and Shnabel, 1986; Rolston et al., 1991; Ball et al., 1994) that compared Ds/Do

Sardinia 2007, Eleventh International Waste Management and Landfill Symposium

measured with field methods with those from laboratory methods. They concluded that a) field and laboratory measurements are equivalent approaches for determining Ds/Do; b) studies comparing various methods for a same site are lacking; and c) that the evaluation of various methods for heterogeneous and structured media is highly needed. The goal of this study was thus to compare five laboratory methods for measuring Ds/Do and to test the ability of models to predict Ds/Do measured with different methods.

2. FUNDAMENTALS OF GAS DIFFUSION

2.1. Gas diffusion process

Gas diffusion is described using the 1st and 2nd Fick’s laws, respectively for steady state and transient conditions. Fick’s laws can be written in the following manner for gas flux in soils:

1st Fick’s law qds = -Ds dCg/dz (1)

2e Fick’s law 2

2

z

CD

t

C gs

ga

(2)

where qds is the diffusive flux density in soil (g.m-2.s-1), dCg is the concentration difference between two points (g.m-3), dz is the distance between two points (m), a (= P-v) is the air-filled porosity (m3.m-3), t is the time (s), v is the soil water content (m3.m-3), P (=1-a/s) is the porosity (m3.m-3), a is the bulk density (Mg m-3), and s is the solid density (≈ 2.65 Mg.m-3). Ds (m-2.s-1), which is lower than Do due to the presence of solid particles and liquid in the pores, is usually normalized using Do at the same pressure and temperature. Ds/Do is assumed constant for all gases in a given soil at a given a and a (Currie, 1960).

2.2. Relative gas diffusion coefficient models (Ds/Do)

Since measuring methods are time consuming and expensive, models have been developed for predicting Ds/Do. The simple methods listed in Table 1 are usually chosen so that diffusion can be calculated from easily measured parameters such as v and a. The models vary in their approach, the type of materials they can account for, and the range of v used for their development. Since Ds for a gas in the liquid phase is about 10 000 times lower than in the gas phase, models are usually a function of a and P of the porous media. They vary in the importance accorded to a and P and in the manner they calculate the restricting factor, which usually accounts for pore tortuosity, constrictivity, and connectivity (Weerts et al., 2001). These models (Table 1) are widely used in numerical simulations, but their use has some drawbacks and they are sensitive at different levels to errors in the input parameters. It seems from the literature that there is no obvious best model a priori for a soil. The choice of a model is thus usually supported by measured Ds/Do in the material of interest. This is an important reason for using precise measuring methods.

3. EXPERIMENTAL STUDY

Five laboratory methods for measuring Ds/Do were compared (Table 2, Figure 1): (1) small repacked columns in a closed system (Small-Closed), (2) long repacked columns in a closed system (Long-Closed), (3) small repacked or intact columns in an open system (Small-Open), (4) large 2-D columns with macropores in a closed system (2D-Closed), and (5) large intact


monoliths in a closed system (Monolith-Closed). A sandy loam (77% sand, 17% silt, and 6% clay) was selected for all tests. The samples were taken a few meters apart. There were no obvious cracks in this soil. The soil was sieved through a 2-mm mesh, dried at 105ºC for 24 hours and was hand packed in fine layers to 1.3-1.4 Mg.m-3, except for the monoliths. Gas sampling was performed with a 100 L gas tight syringe and the samples were inserted into 0.01 L gas tight vials. Gas concentrations were obtained using a gas chromatograph. The carrier gas was He. For all methods employed in the present study, the temperature (20ºC) and atmospheric pressure were maintained constant during the experiments. The systems were gas tight, except for the upper part of the Small-Open method. Prior to injecting the tracer gas, the systems were flushed with He under a fume hood. Either argon or neon was injected. The values of Do of Ar and Ne are 2.0 x 10-5 and 6.5 x 10-5 m2 s-1, respectively.

Table 1. Selected existing simple gas diffusivity models Author Model Comments Tested material

Penman (1940) a

o

s

D

D66.0 Jin & Jury (1996) : Overestimates

Ds/Do Sand, glass bits

Currie (1960) a

o

s

D

D γ varies from 0.8 to 1.0

γ and μ vary with material Many types of wet and dry granular materials

Millington & Quirk (1960) 3

2

2

PD

D a

o

s Jin & Jury (1996) concluded: best

model for intact and repacked soils Tested by Jin & Jury

(1996) sur loamy sand

Millington & Quirk (1961) 2

310

PD

D a

o

s

Jin & Jury (1996) concluded: underestimates Ds/Do, not appropriate

for wet soils Soils

Troeh et al. (1982)

1

a

o

s

D

D μ and υ are empirical Material not important

Xu et al. (1992) 2

51,2

PD

D a

o

s Ds/Do =0 for P0.10

Loamy clay soil aggregates

Moldrup et al. (1997)

3

12

66,0

m

aa

o

s

PD

D

m = 3 for intact and m = 6 for repacked soils

Intact and repacked soils

Moldrup et al. (1999) b

ba

o

s

PD

D3

32

b = Campbell (1974) soil water

retention parameter Intact soils

Moldrup et al. (2000) PD

D a

o

s5,2

Based on Marshall (1959)

Repacked, all textures but organic

γ and μ refer to pore shape, diameter, continuity and tortuosity.

The Small-Closed method is also referred as the two-chamber method (Rolston and Moldrup, 2002). The columns were made of 0.51 m diameter ABS tube. The soil was re-moistened until the desired v was reached. One sample was prepared for each a. The columns were weighted after gas flux measurements to obtain the exact v, a, and a. The injection and flux chambers had a volume of 1.6 x 10-4 m3. The Ne concentration was monitored in both injection and flux chambers.


Diffusion system

0.45 m

0.45 m

Injection chamber

Flux chamber

Small-Closed Long-Closed

Small-Open 2-D-Closed Monolith-closed

0.1 m

Injection chamber

Flux chamber

Soilcolumn

Valve Diffusion system

0.051 m

Samplingports

C(0,0)=CoC(L,0)=0

C(0,t)= Cc(t)C(L,t)=Cf(t)

Injection chamber

Flux chamber

Soilcolumn

0.45 mValve

C(0,0)=CoC(L,0)=0

C(0,t)= CoC(L,t)=Cf(t)

Injection chamber

Air

Soilcolumn

Valve

0.1 m

C(0,0)=CoC(L,0)=0C(0,t)= Cc(t)C(L,t)=0

C(0,0)=CoC(L,0)=0C(0,t)= CoC(L,t)=Cf(t)

Macropores

0.6 m

0.6 m

0.025 m

Injection chamber

Flux chamber

Soilcolumn

81 Sampling

ports


Diffusion system

0.45 m

0.45 m

Injection chamber

Flux chamber

Injection chamber

Flux chamber

Small-Closed Long-Closed

Small-Open 2-D-Closed Monolith-closed

0.1 m

Injection chamber

Flux chamber

Soilcolumn


0.051 m

Samplingports

C(0,0)=CoC(L,0)=0


0.1 m

Injection chamber

Flux chamber

Soilcolumn


0.051 m

Samplingports

C(0,0)=CoC(L,0)=0


Injection chamber

Flux chamber

Soilcolumn

0.45 mValve

C(0,0)=CoC(L,0)=0


Injection chamber

Flux chamber

Soilcolumn

0.45 mValve

C(0,0)=CoC(L,0)=0


Injection chamber

Air

Soilcolumn

Valve

0.1 m

C(0,0)=CoC(L,0)=0C(0,t)= Cc(t)C(L,t)=0

Injection chamber

Air

Soilcolumn

Valve

0.1 m

C(0,0)=CoC(L,0)=0C(0,t)= Cc(t)C(L,t)=0


Macropores

0.6 m

0.6 m

0.025 m

Injection chamber

Flux chamber

Soilcolumn

81 Sampling

ports


0.6 m

0.6 m

0.025 m

Injection chamber

Flux chamber

Soilcolumn

81 Sampling

ports


Figure 1. Scheme of laboratory methods for measuring relative gas diffusivity (Ds/Do).

For the Long-Closed method, the same tube, injection and flux chambers were used, but the soil columns were 0.475 m long (Figure 1; Table 2). One sample was prepared for each v. Argon was injected at a constant flow rate, after flushing the column with He. Gas samples were withdrawn from points 0.05 m apart. The sampling frequency varied with soil v.

In the case of the Small-Open method, also known as the Currie method (Rolston and Moldrup, 2002), the column casing was made of 0.10-m diameter, 0.077-m long, PVC tube. The soil was initially dry and packed. Soil v was controlled by imposing soil suction with pressure plates after saturation. The system was installed under a fume hood and low flow was applied to avoid convection, so that concentration in the air remained undetectable. Argon was injected in the chamber for 30 sec. After opening the valve, the selected gas was allowed to diffuse.

In the case of the 2D-Closed method, the columns were packed with dry soil in thin layers. Macropores with a diameter of 0.005 m and a length of 0.32 m were created during packing using an aluminium mosquito screen. After packing, a head 0.05 m of water was applied at the soil surface for 5 min. Five days were allowed before installing the injection and flux chambers. Neon or argon concentration was maintained constant in the injection chamber. Eighty one regularly distributed sampling ports covered the entire soil profile. The experiment was repeated with various macropore positions.

For the Monolith-Closed method, the casing was made of ABS (0.45 m in diameter and 0.40 m high). The initial v of the monoliths was not controlled. The columns remained in standing position. Neon gas concentration was maintained constant in the injection chamber. During injection, neon concentration was measured from ports 0.07 m apart (vertical direction), at three horizontal distances from the casing, and five equally spaced in radial positions. After completion of gas flux measurements, soil samples were collected in order to obtain a, v, P and a at the same positions.

Table 2. Comparison of laboratory methods that are used in this paper for measuring Ds

Method Solution Boundary conditions

Required measures

Advantages Disadvantages

Small-Closed VLAtDLC

tLCs

c

c /),

,ln(

for long testing period (Taylor, 1949)

C(0,0)=Co C(L,0)=0 C(0,t)= Cc(t) C(L,t)=Cf(t)

Cc(t), L, V

Small samples, fast, only a few measurements required, any gas can be used, no soil drying, wide range of a

Can not detect heterogeneity unless large number of samples

Long-Closed )),(),(()(

),(),(

2123

13

13

1232

tzCtzC

zz

S

V

tt

tzCtzCD s

s

C(0,0)=Co C(L,0)=0 C(0,t)= Co C(L,t)=Cf(t)

C(z,t), V, S

For intact or repacked samples; allows the study of layered media

More sensitive to wall effect, more or less difficult to pack,

Small-Open hhL

VtDh

LC

tLC s

c

c

)(

)/exp(2

,

,22

1

21

(Carslaw and Jeager, 1959)

C(0,0)=Co C(L,0)=0 C(0,t)= Cc(t) C(L,t)=0

Cc(t), L, V

For small intact or repacked samples, the simplest, only few measurements required

Restricted to gas not in ambient air, sensitive to atmospheric pressure change, drying of wet samples

2D-Closed )),(),(()(

),(),(

2123

13

13

1232

tzCtzC

zz

S

V

tt

tzCtzCD s

s


C(x,z,t), V, S, Cf(t)

Best for studying specific heterogeneities and boundary conditions

Requires numerous measurements, wall effect, homogeneous gas application difficult for long period

Monolith-Closed

)),(),(()(

),(),(

2123

13

13

1232

tzCtzC

zz

S

V

tt

tzCtzCD s

s


C(x,z,t), V, S, Cc(t), Cf(t)

For heterogeneities at larger scale (REV), less soil samples

Heavy, difficult to homogeneously apply gas, numerous gas samples

V: volume of the chamber (m3), S: surface of the soil column (m2), L: length of the soil column (m), Cc(t): gas concentration in the injection chamber at a time t (g m-3), Cf(t): gas concentration in the flux chamber t a time t (g m-3), C(z,t): gas concentration (g m-3) in the soil profile at a certain distance z from the injection point at a time t. The indices 1, 2, and 3 associated with z refer to three different distances from the boundary, and the indices 1, 2, and 3 associated with t refer to three different times. Vs refers to soil volume (m3).


4. RESULTS AND DISCUSSION

Since all the methods gave similar Ds/Do (Figure 2), the choice of a method would depend more on its advantages and disadvantages. The first three methods listed in Table 2 can easily cover a wide range of a. In this study, the 2-D-Closed method offered the opportunity to cover a wide range of a because it was initially dry and water did not infiltrate the entire column. Ds/Do could be calculated in low and high a regions, away from the macropores. a could not be controlled in the monoliths, which explains the narrow range of a of the monoliths (Figure 2). Generally, from the point of view of boundary conditions, a variable boundary condition in the injection (decreasing concentration) and flux chambers (e.g. no flow boundary) make easier the manipulations than constant concentration in the injection chamber or zero concentration in the atmosphere (Figure 3).

0

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.5

Air-filled porosity (m3 m

-3)

Ds /

Do (-

)

Short-closed

Long-closed

Short-open

2-D

MonolithsEntire columns, includes macropores

Figure 2. Relative gas diffusion coefficient (Ds/Do) measured with different laboratory methods at different air-filled porosity in a sandy loam soil.

Heterogeneity is a key factor for gas flow since it is often associated with preferential flow in landfill covers. The latter are usually very heterogeneous because they are built with soils from different sites that are mixed and compacted. In addition, revegetation (plant growth), crack for-mation due to wet-dry and freeze-thaw cycles, and erosion, all favor preferential flow. Therefore, deciding on the optimal size of a REV is key to study gas flow through landfill covers. Large intact cores, as in the Monoliths-Closed method, seem more suitable to study the spatial variabi-lity of gas diffusion only if the structure of the sample can be maintained. In this study, intact cores did not result in overall higher Ds/Do (Figure 2), probably because there were no macropo-res. However, heterogeneities in the soil did lead to preferential flow paths; indeed gas flow was highly heterogeneous, as can be observed in Figures 4 and 5. Such large monoliths are however heavy, difficult to handle, destroy the actual cover, and may crack during handling and storage.

The first three methods in Table 2 are easy, fast, cheap, and required only a few gas samples (Figure 3). The main sources of error consist in packing or sampling: higher length:diameter ratios would render packing more difficult. Higher ratios also increase flows along the boundary (cell walls).


Monolith-Closed

0.00

0.25

0.50

0.75

1.00

0 20 40 60

Time (h)

Co

nce

ntr

atio

n (

ug

ml-1

)

Short-Closed

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5

Time (h)

Co

nce

ntr

atio

n (

ug

ml-1

)

2D-Closed

0.00

0.05

0.10

0.15

0.20

0.25

0 10 20 30

Time (h)

Co

nce

ntr

atio

n (

ug

ml-1

)

Long-Closed

0.0

0.5

1.0

1.5

2.0

0 5 10 15Time (h)

Co

nce

ntr

atio

n (

ug

ml-1

)

Injection

Flux

Short-Open

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.0 1.0 2.0 3.0

Time (h)

Ln

(Cc/

Co

))

Figure 3. Example of gas concentration in injection and flux chambers of five methods

Figure 4. Gas concentration distribution at different depths after 8 h and corresponding photos of two monoliths.

The precision of the Long-Closed method, with instantaneous profile calculations (Table 2), is also dependent upon the time interval between sampling spatial points. It took about 1 min for two persons to sample all points, but the time lag between sampling may result in more than 10% error. This instantaneous approach with longer column offers the opportunity of studying soil layering or soil heterogeneity parallel to gas flux.


0 0.05 0.1 0.15 0.2Ds/Do (m2 s-1)

Mono lith 1

Mono lith 2

Mono lith 3

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.8 1 1.2 1.4 1.6Soil density (Mg m

-3)

Dep

th (

m)

0 0.2 0.4 0.6

Water content (m3 m

-3)

Figure 5. Average soil density, water content, and Ds/Do in the soil profile of three monoliths.

The 2D-Closed method offers the opportunity of studying different imposed soil heterogeneities. The use of intact cores with this method is however very difficult. Ds/Do could be calculated from the concentration in the injection and flux chambers, such as in the first methods. Gas distribution in the profile can be used to evaluate the impact of soil heterogeneities. As in the example of Figure 6, low values of a in the wet zone should have resulted in low gas concentration (the right hand side of the column); but it was not the case because a macropore was present, allowing faster gas movement. Error with this method arises from the number of samples required for mapping concentration distribution in the profile. As an example, it took 15 min. for two persons to sample all 81 sampling points. Assuming instantaneous sampling and using two hours apart to calculate Ds/Do, the error would be about 30% for systematic sampling (all ports in the same order for all times) and more than 60% for random sampling assuming linear increase in gas concentration between two sampling times. This method may also have an important boundary effect in the calculation of the overall Ds/Do.

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Gas concentration Air-filled porosity

0

5

10

15

20

25

30

35

40

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Gas concentration Air-filled porosity

0

5

10

15

20

25

30

35

40

Figure 6. Gas concentration (g.ml-1) distribution and air-filled porosity (m3.m-3) after 2 h in a 2D column test.

The Monolith-Closed method (with a representative REV) offers the advantage that gas movement can be studied in similar conditions as in the field, but under controlled temperature and possibly under controlled v. As for the previous methods, Ds/Do could be calculated with gas concentration in the injection and flux chambers (Figure 3), but measuring gas concentration in the profile offers the opportunity to understand where fine spatial variability in gas movement


comes from and by how much. As an example, gas concentration distribution in the column was highly variable (Figures 4 and 5). The concentration increased right below a compacted layer. Gas reached certain sections of the soil five times faster than other sections. Flux and concentration were related to concretion, soil density and a distribution in the profile. This information is important for interpreting data from the field, for developing measuring frequency, sampling size, and interpreting performance in CH4 oxidation, etc. However, the time required for sampling all the samples could be an important source of error. In addition, gap may develop between soil and casing during handling and storing (Allaire et al., 2007). This gap may be filled with different materials. However, water sorption from the soil to this material, material expansion, and remaining small gaps may greatly affect gas flux. The percent of error in Ds/Do related to this measuring method is similar to the 2-D method.

Root mean square error analyses were done in order to evaluate the performance of models to predict Ds/Do measured with the different methods. Of all models listed in Table 1, the Millington-Quirk (1960) model better predicted Ds/Do, irrespective of consideration or the presence of macropores. The Moldrup et al. (2000) model better predicted Ds/Do when macropores were not considered. There were no obvious trends in model performance relative to specific measuring methods, except for the Penman (1940) model, which always performed better with the 2D-Closed method, when macropores were considered. Ds/Do measured with the Short-Open method was better predicted with the Millington-Quirk (1961) model, while values from the Monolith-Closed method were best predicted with the Moldrup et al. (2000) method.

5. CONCLUSION

Gas diffusion measurement is very important in landfill cover material. Ds/Do values measured with five laboratory methods gave similar results. The choice of the method must then depend on available apparatus and cost, as well as case-specific advantages. The Millington-Quirk (1960) and Moldrup et al. (2000) models performed better in predicting Ds/Do. We could not detect a correlation between model performance and measuring method.

ACKNOWLDGMENTS

The authors wish to thank the laboratory work of C. Halde, M. Lafontaine, E. Cormier, and V. Juneau. The authors acknowledge the collaborative work of S.F. Lange for allowing the use of his data and photos, and the Centre SÈVE, and FQRNT for their financial support. Financial support provided by the National Science and Engineering Research Council of Canada, under strategic grant # GHG 322418-05, is also acknowledged.

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Measuring gas diffusion in landfill cover material

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