- Email: [email protected]
Investigations on gas permeability in porous media
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Investigations on gas permeability in porous media a
b
Jeevan Joseph , Ganaraj Kuntikana , D.N. Singh a b
b,∗
T
Department of Civil Engineering, National Institute of Technology Trichy, Tamil Nadu, 620015, India Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
ARTICLE INFO
ABSTRACT
Keywords: Porous media Gas permeability Pore-characteristics Mineralogy Knudsen flow Gas-porous media system
Permeability of gases in porous media is a vital parameter for the design of landfill liners and buffers for nuclear waste repositories, gas extraction from petroleum reservoirs and hydrate bearing sediments, vapor extraction to decontaminate soils, carbon dioxide sequestration, etc. It is well understood that the gas-phase permeability in porous media is predominantly governed by the porosity, pore-characteristics (viz., diameter and distribution), properties of the gas (viz., density, molecular size and weight, sorption capacity, and viscosity) and their state of saturation (Sr). However, the nature of the flow of gas (viz., molecular, viscous and Knudsen), is influenced by the mean free-path, its compressibility and mean diameter of the pores. All these factors and complexities pose a challenge in determining the intrinsic permeability, K, which otherwise is assumed to be a (i) constant and (ii) fingerprint of porous media. In this context, and to facilitate easier determination of the gas-phase permeability, Kg, of porous media, a test setup: Gas Conductivity Measuring device, GasCoM, has been developed. Efforts have also been made to understand the influence of the characteristics of the gas (viz., active, inert, non-polar, monoatomic, diatomic and mixture of several gases) on Kg of different porous media (viz., soils of entirely different physico-chemical-mineralogical characteristics compacted at different densities and saturation, and commercially available alumina discs, referred to as standard porous media, SPM). A critical synthesis of the experimental data reveals that the flow of gas in porous media gets significantly influenced by (a) the hygroscopic moisture content, which also highlights the importance of its mineralogy and (b) its tortuosity. Furthermore, a correlation that can be employed for estimation of the Kg, for various gas-porous media systems, GPMSs, has been proposed and validated by using experimentally obtained results.
1. Introduction Gas permeability, Kg, of porous media has significant role in geoenvironmental engineering such as: (a) soil vapour extraction (Hohener, and Ponsin, 2014; Huang, and Goltz, 2017; Hutzler et al., 1991; Magalhães et al., 2009; Simpanen et al., 2017), (b) the extraction of natural gas from unconventional resources (Dangayach et al., 2015; Johnson et al., 2011; Joseph et al., 2016; Khlebnikov et al., 2017), (c) design of liners for the containment of volatile nuclear waste (Cui et al., 2009; Hassine et al., 2017; Wieczorek et al., 2017), (d) landfill liners (Bouazza, and Vangpaisal, 2003; Moon et al., 2008; Vangpaisal, and Bouazza, 2004) and (e) soil amendment for agricultural activities (Wong et al., 2016), as depicted in Fig. 1. The situations depicted in Fig. 1 necessitate determination of Kg of the ‘gas-porous media systems’, GPMSs, compacted to different density states (i.e., the dry-density and degree of saturation). The thermo-mechanical energy fields prevailing in these situations, might also result in pore-desaturation (i.e., Sr < 1) and in the process altering the pore-
∗
characteristics of porous media (Thakur, and Singh, 2005; Gumaste, and Singh, 2013; Iyer et al., 2017). Hence, a better understanding of GPMSs is necessary for predicting the (i) extent of soil pollution, (ii) natural gas extraction potential and (iii) suitability of decontamination techniques. The suitability of compacted clay as ‘gas barrier’ for landfills has been attempted by Moon et al. (2008), simulating the field conditions on a laboratory scale. However, the experimental methodology was simplified by employing nitrogen gas as the flowing fluid, rather than gasses of landfill origin. The study reported Kg values of clay ranging from 2.03 × 10−10 to 4.96 × 10−9 cm2, and therefore its suitability as landfill liner was objected. Further, Kg of the biochar amended clays, to verify their suitability as an alternative landfill liner material, was investigated by Wong et al. (2016). A flexi-wall permeameter was employed, with compressed air as the flowing fluid, and the gas flow was measured with a flow meter, connected at the outlet of a triaxial cell. Interestingly, the study reported decrease in Kg with increase in biochar content and degree of compaction.
Corresponding author. E-mail addresses: [email protected] (J. Joseph), [email protected] (G. Kuntikana), [email protected] (D.N. Singh).
https://doi.org/10.1016/j.jngse.2019.01.017 Received 20 November 2018; Received in revised form 23 January 2019; Accepted 28 January 2019 Available online 31 January 2019 1875-5100/ © 2019 Elsevier B.V. All rights reserved.
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Nomenclature η ψ ηa γd γw A CH CL D Dl Dm dm e ef emax emin G GasCoM GPMSs He Ip K Kg Kg (Comp.) Kn Kw lf LOTM Me
MIP N2 NA NVR P0 Pg PM Pp Q R Re SPM Sr T USCS v V Va Vv Vw wh wl wp XRD γd, MIP ΔP/l θ λ μ ρ
Porosity Total suction Percentage air void Dry-unit weight Unit weight of water Area of cross-section Clay with high plasticity Clay with low plasticity Pore-diameter Characteristic length Molecular diameter Mean pore-diameter Voids ratio Final voids ratio Maximum voids ratio Minimum voids ratio Specific gravity Gas conductivity measuring device Gas-porous media systems Helium Plasticity index Intrinsic permeability Gas permeability Gas permeability (computed) Knudsen number Intrinsic hydraulic conductivity Final length Laser obscuration time measurement Methane
Gas permeability studies on partially saturated geosynthetic clay liners have affirmed a decrease in Kg with increase in water saturation (Vangpaisal, and Bouazza, 2004). Similar studies were conducted by Rouf et al. (2014) on needle punched geosynthetic clay liners, at differential nitrogen gas injection pressures (ranging from 1 kPa to 10 kPa). These authors have highlighted the impact of normal stress, confining stress and the saturation states on Kg. In another study, Chuvilin et al. (2016) have carried out gas permeability experiments on sandy soils, of different moisture contents, corresponding to their frozen state. Reduction in permeability of several orders of magnitude has been reported for Sr ≈ 50%. Incidentally, very interesting and challenging experiments have been performed by Johnson et al. (2011) on the sediments bearing methane gas hydrates, from Mount Elbert site, on the Alaska North Slope (ANS). In this study, nitrogen gas was employed as the flowing fluid, instead of methane, to avoid the chances of hydrate formation. An inverse relation between Kg with hydrate saturation has been inferred from the study, which also highlights the impact of thermodynamic conditions viz., temperature and pressure, on the flow characteristics of gasses in porous media. Klinkenberg (1941) has reported the variations in flow characteristics (viz., continuum, viscous and Knudsen) in porous media on account of the gas characteristics and injection pressure, mean diameter of the pores, and the prevailing temperature conditions. It has been reported that the nature/type of the gasses viz., active, inert, non-polar, monoatomic, diatomic and mixture of several gasses, and porous media viz., soils of entirely different physico-chemical-mineralogical characteristics, compacted at different densities and saturation, and the pore-characteristics such as diameter and distribution, would also significantly influence K, which otherwise is assumed to be a (i) constant and (ii) fingerprint of the porous media (Dullien, 1991; Webb, 2006). Unfortunately, most of these studies have ignored the influence of the inherent properties of the GPMSs while determining Kg.
Mercury intrusion porosimeter Nitrogen Avagadro's number Normalized voids ratio Outlet gas pressure Gas injection pressure Porous media Packing pressure Discharge Universal gas constant Reynolds number Standard porous media Degree of saturation Temperature Unified soil classification system Molecular mass Bulk volume Volume of air Volume of voids Volume of water Hygroscopic moisture Liquid limit Plastic limit X-ray diffraction Dry-density obtained from mercury intrusion porosimetry Pressure gradient Volumetric moisture content Mean free path Viscosity Density
Under these circumstances, an attempt has been made to develop a correlation that can be employed for the estimation of Kg for various GPMSs corresponding to Sr < 1. In this regard, an easy to operate laboratory setup, GasCoM, which facilitates determination of Kg for different GPMSs, has been developed and its efficiency for achieving the said objective has been demonstrated. The experimental studies were carried out by employing different gases viz., inert, non-polar, monoatomic, diatomic and mixture of gasses, and partially saturated porous media of distinct characteristics viz., mineralogy, texture and state of compaction. Furthermore, the validity of this correlation has been demonstrated by comparing the results vis-à-vis those obtained from GasCoM. 2. Experimental investigation 2.1. Porous media characteristics The characteristics of porous media, PM, and the gasses employed for the flow study, keeping in view of their prevalence, as depicted in Fig. 1, are listed in Table 1 and Table 2, respectively. The PM included samples from, (i) onshore soils (S-1, S-2, and S-3), (ii) offshore sediment (S-4), and (iii) synthetic materials consisting of bentonite and fly ash (BT and FA), based on their recurrence in specific field application. The specific gravity, G, (employing an Ultra-Pycnometer, Quantachrome, USA) and the consistency limits (liquid limit, wl, plastic limit, wp, plasticity index, Ip) of these PM, were determined as per the guidelines specified by (ASTM-D2487, 2011; ASTM-D4318, 2010; ASTM-D5550, 2014), respectively. The hygroscopic moisture content, wh, of these PM were also determined, as per the procedure described in the literature (Shah, and Singh, 2005) and the results are listed in Table 1. In addition, sintered alumina discs (read-standard porous media, SPM, procured from Cobra Technologies, The Netherlands), which hold rigid and non-compressible pore structure were also employed, to 82
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 1. Different gas-porous media systems: (a) Air purging for vapor extraction, (b) the free gas zone beneath the hydrate bearing sediments, the compacted clay liners for (c) disposal of nuclear waste in the repositories and (d) top covers of landfills. Table 1 Basic characteristics of porous media selected for the study. Sl. No.
PM
Designation
G
(%)
USCS
Size fraction
1
Onshore soils
2 3
Offshore sediment Synthetic soils (Bentonite and fly ash)
4
Standard porous media (SPM)
S-1 S-2 S-3 S-4 BT FA SPM-1 SPM-2 SPM-3 SPM-4 SPM-5
2.76 2.63 2.61 2.56 2.52 2.79 3.97
Consistency Limits
wh
Clay
Silt
wl
wp
Ip
16 18 2 49 44 68 NA
84 82 98 51 56 32
40 39 53 92 263 Non-plastic
18 11 19 34 42
22 28 34 58 221
3.1 5.0 5.2 8.1 9.1 2.4 <1
CL CL CH CH CH NA
NA: Not applicable.
simulate the pore characteristics of natural deposits like shale, chalk, mudstone and sandstone etc. (refer Table 1). The grain size-distribution characteristics of these PM, except for SPM, obtained from Laser Obscuration Time Measurement, LOTM (Ambivalue, Netherlands), is depicted in Fig. 2. The mineralogical composition of the PM selected for this study was obtained by employing an X-ray diffraction (XRD) spectrometer (X'Pert PRO, PANalytical, The Netherlands). The presence of active(Montmorillonite) and passive- (Quartz, Calcite, etc.) minerals in PM (refer Table 3), and the characteristics of gasses (viz., inert, non-polar, monoatomic, diatomic and mixture of gasses etc.), reveal the
Table 2 Basic properties of the gasses employed in the present study. Gas
Dma (Å)
mb (g/mol)
ρ (kg/m3)
μ ( × 10−5 Pa s)
Helium (He) Methane (Me) Nitrogen (N2) Compressed dry air (Air)
3.64 3.98 1.40 1.50
4.0 16.0 28.0 28.9
0.16 0.65 1.13 1.20
1.96 1.12 1.78 1.82
ρ: Density (at Normal temperature and pressure), μ: Viscosity (at 25 °C). a Dm: Molecular Diameter. b Molecular mass. 83
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 2. Grain-size distribution characteristics of the soils used in this study. Table 3 Mineralogical composition of different porous media. PM
Minerals Present
S-1 S-2 S-3 S-4 BT FA SPM
Quartz, Orthoclase, Moganite Quartz low, Moscovite, Albite Quartz low, Moscovite Quartz low, Magnetite, Zeolite Quartz low, Anothite, Montmorillonite Quartz low, Magnetite, Calcite, Anorthite Corundum
experimental determination of Kg. The constant gas source at the required pressure, for performing the flow study was ensured with the help of gas regulator attached to the corresponding gas cylinders. The gas injection pressure, Pg, is monitored continuously with the help of a pressure transducer (Humboldt, USA) and the volume of gas coming out of the specimen is measured by employing a volume measuring device (GCTS, USA). The gas permeability of the PM specimen was conducted in the test set up, GasCoM (Fig. 4), that has been developed for (i) preparing specimens of different density and (ii) to perform gas flow studies at that state. The specimen preparation has been carried out by filling a known amount of the powdered material (as per the target dry density, γd, of the specimen on which gas permeability study has to be performed) in the specimen holder, unit C (specimen size of 5 cm diameter and 2.5 cm thickness can be prepared), from the top of jacket. The plunger, with porous disk (PD-1), fitted in it, is lowered down in
extensiveness of the investigation carried out in this study. 2.2. Determination of Kg Fig. 3 depicts the major components which are essential for the
Fig. 3. Experimental layout for conducting gas permeability studies on PM. 84
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
states has been obtained from Eq. (4). d, MIP
d
=
= G
w
d, MIP .
1 + ef
(2)
lf
(3)
l
where G is the specific gravity of porous media, γd, MIP, lf and ef refer to the dry-density, height, and voids ratio of the specimen, after its removal from the unit C.
e = (G
w
d
)
1
(4)
Where as, γd and e refer to the dry-density and voids ratio of the specimen (of height, l), corresponding to any stage between emax and emin. Furthermore, in order to benchmark the specimen, i.e., to define its compaction state, represented by the intermediate voids ratio, e, and to eliminate the effect of errors associated with the determination of the voids ratio, the parameter; normalized voids ratio, NVR, has been introduced (refer Eq. (5)), except for the SPM. The NVR being a measure of the ability of the specimen to undergo densification beyond its natural state, its lower limit (=0) corresponds to the loosest state and the upper limit (=1) corresponds to the densest state.
NVR = (
Fig. 4. Details of the test setup for gas permeability studies.
through the sleeve of the jacket and the whole assembly is mounted on a loading frame. Subsequently, the static pressure, Pp (in kPa), is applied in increments, through the loading pad to compact the material inside unit C, to achieve a specimen of the target density, γd. This procedure offers higher flexibility to create specimens with different compaction states (mainly density and pore-structure). Subsequently, the vacuum pump, the gas cylinder and the volume measuring device is connected to the ports If, Ig and Og, respectively, of the GasCoM. The entrapped air in the specimen is removed by applying vacuum pressure (−50 kPa) in the specimen through If (confirming that other ports remain closed). The gas injection pressure, Pg, has been adjusted to generate a pressure gradient, ΔP/l, of 10 kPa/cm across the specimen through the port Ig, with the help of a gas regulator (attached to the gas source). However, the investigations related to the gas flow through the SPM were carried out by employing a flexi-wall permeameter cell owing to their rigidity and standard size, instead of GasCoM (other steps remaining the same as described earlier). It's worth realizing that the smaller size of the sample provided the flexibility to perform permeability studies for a wide range of pressure gradient (viz., 5–100 kPa/ cm). The gas permeability, Kg, was determined by employing Darcy's equation, for viscous and compressible gases, as given in Eq. (1) (Wu et al., 1998).
Kg =
2 µ l P0 Q A (Pg2 P02)
emax e ) emax emin
(5)
3. Results and discussion The packing pressure, Pp, employed to compact the specimens of the porous media, to different dry density, was determined and the results in the form of voids ratio, e, versus Pp are presented in Fig. 5. It can be observed that e remains practically constant for Pp > 3.0 MPa and hence the maximum Pp was limited to 3.75 MPa, for the specimens considered in the present study. The differential and cumulative voids ratio of different PM, as a function of the pore-diameter, d, are depicted in Fig. 6(a) and (b), respectively. From Fig. 6(a), it can be realized that all the PM exhibit a mono-modal distribution of the pores. The mean diameter of the pores, dm, has been obtained from the analysis (Iyer et al., 2017) of Fig. 6(a) and the results are presented in Table 4. It can be noted that dm covers a wide spectrum of the pore-size (viz., 58–2609 nm). However, it was noticed that removal of the specimen from the unit C causes a bit of swelling gain in e, due to stress release (refer Fig. 7). Hence, ef (i.e., the final voids ratio obtained from the MIP) has been employed to back compute emax, e and emin, by following Equations (2)–(4). The voids ratio of the specimens obtained through this exercise, is presented in Table 4. Inorder to ensure that the gas pressure, Pg, is not high enough to destroy the pore-structure of the specimen, the total suction, ψ, was measured by employing a dewpoint potentiometer, WP4, by following the methodology presented by Iyer et al. (2013) and the results are presented in Table 5. Considering the fact that Pg adopted for various specimens (in kPa, range) is several orders of magnitude lower than their suction (in MPa range), the possibility of damage of pores has been ignored. Further, to ensure laminar gas flow conditions through the pores of the soil specimen, Reynolds number, Re, was computed.
(1) −5
Where μ is the viscosity of the gas in ( × 10 Pa s), l is the length of the specimen (in cm), Q is the discharge (in cm3/s), A is the area of crosssection (in cm2), and Pg and P0 are the injection and outlet gas pressures (in Pa) respectively. It should be noted that P0 in the present study has been maintained as atmospheric. Further, in order to understand the significance of pore characteristics (viz., pore diameter and distribution) of the specimen, on Kg, the mercury intrusion porosimetry, MIP, (employing Pore Master, Quantachrome, USA) has been performed on the specimen extracted from the unit C (after freeze drying). The voids ratio obtained at this stage, referred as final void ratio, ef, has been utilized to back compute the density, γd, (at various stages of compaction) by employing Eq. (2) and Eq. (3). Further, the voids ratio corresponding to other density
Re =
. v. D l µ
(6) 3
where, ρ is the density of the gas (kg/m ) flowing with velocity v (m/s), Dl is the characteristic length of the specimen, assumed to be equal to dm . It can be noticed from Fig. 8 that the laminar flow condition for gasses in the porous media are satisfied in the present study (i.e., Re < 1 and Re < 6, as proposed by Bear (1972), and Wu et al. (1998), 85
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 5. The state of compaction of different specimens of the porous media tested for gas permeability.
Fig. 6. The mercury intrusion porosimetry results for different porous media exhibiting (a) differential voids ratio, (b) cumulative voids ratio.
respectively) and hence, Darcian flow could be acertained. The variation in Kg, of porous media, corresponding to the NVR is depicted in Fig. 9. It can be noticed from the figure that as expected, Kg decreases with an increase in NVR, irrespective of the specimen type and the gases employed in this study. Incidentally, the loosest state of all the PM (corresponding to NVR = 0) yield almost similar Kg values, irrespective of the gas employed for conducting the tests. However, a wide scatter in Kg values has been noticed for the densest state of the PM (corresponding to NVR = 1). Interestingly, it has been observed that data presented in Table 4 indicate that dm and ef for PM S-2 are higher (1.5 and 1.2 times, respectively) than those for PM S-1. As such, Kg versus NVR trends for the
PM S-1 and PM S-2 should not have matched. However, a closer look at the Kg versus NVR trends for PM S-1 and PM S-2, both classified as CL as per the USCS, indicate linear fits (Trends A, B, C and D) with R2 very close to unity (refer Fig. 10). A reasonable justification for this observation could be the difference in the hygroscopic moisture contents, which is 3.1% and 5.0%, for PM S-1 and S-2, respectively (refer to Table 1). The hydrophilic nature of PM S-2, as it contains Muscovite (refer Table 3) mineral (Cantrell, and Ewing, 2001) adds up to its water affinity as compared to its counterpart PM S-1. Incidentally, when trends A, B, C and D are superimposed on each other (refer to Fig. 11), it can be realized that the Kg follows the sequence He > N2≈Air > Me. It should be noted that these gasses 86
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
pertain to various applications depicted in Fig. 1. Based on the above discussion, it can be opined that Kg is influenced by the presence of hygroscopic moisture, wh, which would result in reduction of its pore diameter and eventually a reduced Kg. With this in view, the percentage air voids, ηa, for different specimens was computed, by employing Eqs. (7a) and (7b) and listed in Table 5.
= Vv V or a
= Vw V + Va V
(7a) (7b)
=
Where Vv, Vw, Va and V denote the volumes of voids, water, air and the bulk specimen, respectively, whereas θ is the volumetric moisture content. Additionally, to understand the influence of ‘nature’ of flow of gases through porous media, their mean free path, λ (in m), corresponding to the Pg, has been computed by employing Eq. (8).
=
2
RT Dm2 NA Pg
(8)
Fig. 7. Depiction of emax, emin and ef of the specimen during packing and removal from the unit C.
Where R is the universal gas constant (=8.314 J/mol. K), T is the temperature in Kelvin, Dm is the molecular size of the gas molecule (A°) and NA is the Avagadro's number (=6.02 × 1023/mol). Knudsen (1909) has reported that a linear variation of gas discharge with pressure gradient (Darcian flow, which is primarily valid for noncompressible and viscous fluids in their laminar region) is valid for the continuum flow, when λ < < dm. Furthermore, based on the studies reported by earlier researchers (Alzaydi, 1975; Livesey, 1998; Scanlon et al., 2002), the nature of flow viz., molecular, transitional and Knudsen flow, through PM has been categorized based on the Knudsen number, Kn (=λ/dm), as depicted in Fig. 12. Another possibility that has been depicted in this figure is, an increase in Q with increase in Kn (> 10). Such a situation would occur at extremely lower pressure gradients, and/or when porous media contains very fine pores, the flow of gases remains ‘non-zero/slip flow’ at the solid interface. This condition results in non-Darcian flow as
Table 5 The mean diameter, porosity, air porosity, and suction of different specimens of the porous media (PM) after extraction from the unit C.
Table 4 The datasheet employed for determination of the voids ratio of the specimens of different porous media (PM). PM
ef
emin
emax
dm (nm)
Specimen
ea
Sr (%)
S-1
0.79
0.75
1.61
1280
S-2
0.97
0.93
1.95
1878
S-3
0.63
0.58
1.35
2382
S-4
0.98
0.94
2.33
1109
BT
0.81
0.73
1.92
1485
FA
2.43
2.35
3.64
2609
S1-A S1-B S1-C S1-D S2-A S2-B S2-C S2-D S3-A S3-B S3-C S3-D S3-E S3-F S3-G S3-H S3-I S3-J S3-K BT-A BT-B BT-C BT-D BT-E FA-A FA-B
1.35 1.16 0.99 0.85 1.67 1.43 1.24 1.07 1.26 1.16 1.07 0.91 0.78 0.66 1.92 1.79 1.37 1.16 0.99 1.67 1.40 1.19 1.00 0.85 3.07 2.65
6.40 7.49 8.74 10.21 7.96 9.25 10.70 12.36 10.66 11.56 12.53 14.71 17.30 20.41 10.81 11.61 15.22 17.92 21.06 13.70 16.31 19.31 22.82 26.95 2.21 2.56
a
PM
η
ηa
dm (nm)
ψ (MPa)
S-1 S-2 S-3 S-4 BT FA SPM-1 SPM-2 SPM-3 SPM-4 SPM-5
0.44 0.39 0.49 0.49 0.45 0.71 0.14 0.25 0.26 0.29 0.36
0.36 0.25 0.36 0.29 0.22 0.64
1280 1878 2382 1109 1485 2609 63 69 58 100 144
147 114 132 128 87 115 48 51 55 51 63
described by Voudrias, and Li (1992) and Webb (2006). Such a situation would also result in greater collision of the gas molecules with the pore-walls as compared to the collision between the molecules of the gas, which might result in an increased Q (Dullien, 1991). It should be realized that in the loosest state of porous media, the dm would be higher and hence Kn→0. Hence, the flow of gasses in porous media, corresponding to this stage, would be highest and ‘pure molecular’ in nature. Fig. 13 depicts the variation in volumetric discharge of the flowing fluid, Q, through the PM (excluding SPM), with respect to their Kn values. It can be observed that these PM exhibit transitional flow. Incidentally, for the flow to fall in the Knudsen region, either Pg should be extremely low and/or porous media should be of low dm (Alzaydi, 1975). It appears that these conditions could not be satisfied by several GPMSs (refer Fig. 13) considered in the present study, except for the SPM. In this context, the flow study through SPM, under different Pg (values ranging between 5 kPa and 100 kPa) has been carried out and the results are depicted in Fig. 14. Interestingly, it has been noticed that the Q for all the gases becomes asymptotic corresponding to lower Pg. Similar observations were reported by Izadi, and Stephenson (1992), in fine grained porous media at lower water contents. However, the focus of their study was to understand the variation in slip flow with saturation of pores. In order to provide a justification for this anomaly, a conceptual
Obtained from Eq. (4).
87
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 8. Reynolds number for the specimens of different porous media.
viscosity ( × 10−5 Pa s) and density (kg/m3) of the gas at 25 °C, ηa is the percentage air void, λ is the mean free path (cm), A is the area of crosssection and l is the length (read thickness in cm) of the porous media. It should be noted that ξ is a constant and it incorporates the physical properties of the gas flowing in the porous media. It should be noted that the validity of Eq. (9) is dependent on the following assumptions and conditions:
schematic, depicting the flow through a cylindrical and tortuous pore, has been considered (Fig. 15). From this figure, it can be realized that the probability of the gas molecules colliding with the pore-walls would be higher for the tortuous pores, due to random distribution of porecharacteristics viz., size and shape, as compared to the cylindrical pores. Moreover, the effective length, Le, considered for gas molecule to traverse through a tortuous pore would be different from that of a cylindrical pore (of length, L). Hence, this follows that Kn through the tortuous pores would be (much) higher than the cylindrical pores. Therefore, the present study reveals that the Knudsen regime could only be defined at a higher range (Kn > > 10), for a tortuous pore, than what has been specified in the existing literature. The results obtained from these studies have been further utilized for developing an empirical relationship that can be employed for computing the gas permeability, Kg (Comp.). In this regard, the linear regression analysis, incorporating the pore characteristics, and the physical properties of the gas, corresponding to different thermodynamic states (viz., temperature and pressure) of different GPMSs has been considered. The best-fit empirical relationship, obtained through this exercise is presented in Eq. (9).
K g (Comp.) = . where, =
dm
a
l2
A
1 m0.5 µ2.5
0.9
1. This relationship is valid only for laminar flow of gasses through unsaturated (Sr < 1) porous media. 2. Porous media follows the mono-modal distribution of pore characteristics (i.e., the dm is unique). 3. The variations in gas properties, with temperature, are to be incorporated in ξ. 4. The gas injection pressure, Pg, does not cause phase change of the gas. 5. The l/D ratio of specimens considered in the study ranges from 0.25 to 0.75. Fig. 16 depicts a comparison of the computed and experimentally determined (from the GasCoM) gas permeability values, denoted as Kg(Comp.) and Kg (GasCoM), respectively. It can be observed from the figure that the computed and experimentally obtained Kg values match extremely well (i.e., all the data falls within 95% prediction band and close to 45° line) for the porous media
(9) and m, μ and ρ are the molecular weight (g/mol), 88
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 9. The gas permeability of different gas-porous media systems.
considered in this study. As depicted in Fig. 16, though data obtained in this study belongs to a wide range of GPMSs (i.e., 58≤dm ≤ 2609), further studies should be conducted on the specimens with dm belonging to either sides of this range to check the robustness of the Eq. (9).
been demonstrated that even for the Kundsen number, Kn, > 10, the gas discharge remains almost constant and it does not pick up. This calls for improvising the test setups used in this study, particularly sophisticated instrumentation that could control the gas injection pressures, Pg, (< 1 kPa). Furthermore, an empirical relationship that can be employed for computing Kg of different GPMSs has been proposed and its validity with respect to the experimental results has been established. Though the results obtained in this study correspond to porous media for which 58≤dm ≤ 2609 nm, it is authors' belief that this relationship would be very useful for determining the Kg of porous media with a wide spectrum of the mean pore sizes. Hence, further studies are warranted on GPMSs consisting of other gasses and porous media with the mean pore-size lying outside 58≤dm ≤ 2609 nm range. It should also be appreciated that this empirical relationship would evade the tedious task of conducting gas permeability tests and just by substituting the attributes of the gas and porous media (i.e., only the mean pore-size, which can easily be obtained by conducting the mercury intrusion porosimetry) characteristics to estimate Kg.
4. Concluding remarks The present study highlights the significance of determination of gas permeability, Kg, through partially saturated porous media of entirely different physico-chemical-mineralogical characteristics, compacted at different densities and saturation. In order to achieve this objective, a laboratory setup, GasCoM, has been developed and gas permeability experiments were carried out by employing different gasses (viz., Helium, Nitrogen, Methane and compressed dry Air). The study highlights the significance of the hygroscopic moisture, which indirectly reflects the mineralogy of porous media, on the gas permeability of different Gas-Porous Media System, GPMSs. Furthermore, the effect of presence of ‘tortuous pores’ in porous media has been studied and it has 89
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 10. The variation in gas permeability with normalized voids ratio for the porous media S-1 and S-2.
Fig. 12. The conceptual diagram depicting the variation of gas flow in the porous media. Fig. 11. A comparison of the permeability of different gases in porous media S1 & S-2. 90
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 15. The schematic of Knudsen flow through (a) cylindrical- and (b) tortuous-pores.
Fig. 13. Nature of the gas flow through the specimens of different porous media (except the standard porous media).
Fig. 14. The variation in gas discharge (at different gas injection pressure) and the corresponding Knudsen number for different standard porous media. 91
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
27 (No. 18), 1–7. https://doi.org/10.1016/j.copbio.2013.08.018. Huang, J., Goltz, M.N., 2017. Analytical solutions for a soil vapor extraction model that incorporates gas phase dispersion and molecular diffusion. J. Hydrol. 549, 452–460. https://doi.org/10.1016/j.jhydrol.2017.04.013. Hutzler, N.J., Murphy, B.E., Gierke, J.S., 1991. State of technology review : soil vapor extraction systems. J. Hazard Mater. 26 (No. 2), 225–229. https://doi.org/10.1016/ 0304-3894(91)80008-C. Iyer, K., Jayanth, S., Gurnani, S., Singh, D.N., 2013. Influence of initial water content and specimen thickness on the swcc of fine-grained soils. Int. J. GeoMech. 13 (No. 6), 894–899. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000265. Iyer, K., Joseph, J., Lopes, B.C.F., Singh, D.N., Tarantino, A., 2017. Water retention characteristics of swelling clays in different compaction states. Geomechanics Geoengin. 13 (No. 2), 88–103. https://doi.org/10.1080/17486025.2017.1396363. Izadi, M.T., Stephenson, R.W., 1992. Measurement of gas permeability through clay soils. In: David, M.N.S., Nielsen, M. (Eds.), Current Practices in Ground Water and Vadose Zone Investigations. American Society for Testing and Materials, Philadelphia. Johnson, A., Patil, S., Dandekar, A., 2011. Experimental investigation of gas-water relative permeability for gas-hydrate-bearing sediments from the Mount Elbert gas hydrate stratigraphic test well, Alaska North Slope. Mar. Petrol. Geol. 28 (No. 2), 419–426. https://doi.org/10.1016/j.marpetgeo.2009.10.013. Joseph, J., Singh, D.N., Kumar, P., Dewri, S.K., Tandi, C., Singh, J., 2016. State-of-the-Art of gas hydrates and relative permeability of hydrate bearing sediments. Mar. Georesour. Geotechnol. 34 (No. 5), 450–464. https://doi.org/10.1080/1064119X. 2015.1025929. Khlebnikov, V.N., Antonov, S.V., Mishin, A.S., Bakulin, D.A., Khamidullina, I.V., Liang, M., Gushchin, P.A., 2017. A new method for the replacement of ch 4 with Co 2 in natural gas hydrate production. Nat. Gas. Ind. B 3 (No. 5), 1–7. https://doi.org/10. 1016/j.ngib.2017.02.005. Klinkenberg, L. J., "The permeability of porous media to liquids and gases", Presented at the Drilling And Production Practice, January 1, 1941, American Petroleum Institute, New York. Knudsen, M., 1909. The law of the molecular flow and viscosity of gases moving through tubes. Ann. Phys. 28 (No. 1), 75–130. Livesey, R.G., 1998. In: Lafferty, J.M. (Ed.), Flow of Gases through Tubes and Orifices", Foundations of Vacuum Science and Technology. John Wiley and Sons, United States, pp. 81–140. Magalhães, S.M.C., Ferreira, J.R.M., Castro, P.M.L., 2009. Investigations into the application of a combination of bioventing and biotrickling filter Technologies for soil decontamination processes-a transition regime between bioventing and soil vapour extraction. J. Hazard Mater. 170 (No. 2–3), 711–715. https://doi.org/10.1016/j. jhazmat.2009.05.008. Moon, S., Nam, K., Kim, J.Y., Hwan, S.K., Chung, M., 2008. Effectiveness of compacted soil liner as a gas barrier layer in the landfill final cover system. Waste Manag. 28 (No. 10), 1909–1914. https://doi.org/10.1016/j.wasman.2007.08.021. Rouf, M.A., Singh, R.M., Bouazza, A., Rowe, R.K., Gates, W.P., 2014. Gas permeability of partially hydrated geosynthetic clay liner under two stress conditions. Environmental Geotechnics 3, 325–333. https://doi.org/10.1680/envgeo.14.00009. Scanlon, B.R., Nicot, J.P., Massmann, J.W., 2002. In: Warrick, A.W. (Ed.), Soil Gas Movement in Unsaturated Systems", Soil Physics Companion. CRC Press, pp. 297–341. Shah, P.H., Singh, D.N., 2005. Generalized archie's law for estimation of soil electrical conductivity. J. ASTM Int. (JAI) 2 (No. 5), 1–20. Simpanen, S., Yu, D., Mäkelä, R., Talvenmäki, H., Sinkkonen, A., Silvennoinen, H., Romantschuk, M., 2017. Soil vapor extraction of wet gasoline-contaminated soil made possible by electroosmotic dewatering–lab simulations applied at a field site. J. Soils Sediments 1–7. https://doi.org/10.1007/s11368-017-1717-1. Thakur, V.K.S., Singh, D.N., 2005. Rapid determination of swelling pressure of clay minerals. J. Test. Eval. 33 (No. 4), 239–245. https://doi.org/10.1520/JTE11866. Vangpaisal, T., Bouazza, A., 2004. Gas permeability of partially hydrated geosynthetic clay liners. J. Geotech. Geoenviron. Eng. 130 (No. 1), 93–102. https://doi.org/10. 1061/(ASCE)1090-0241(2004)130:1(93). Voudrias, E.A., Li, C.Y., 1992. Importance of knudsen diffusion on benzene vapor transport in unsaturated soil. Chemosphere 25 (No. 5), 651–663. https://doi.org/10. 1016/0045-6535(92)90428-T. Webb, S.W., 2006. "Gas Transport Mechanisms", Gas Transport in Porous Media. Springer, The Netherlands, pp. 5–26. Wieczorek, K., Gaus, I., Mayor, J.C., Schuster, K., García-Siñeriz, J.-L., Sakaki, T., 2017. In-situ experiments on bentonite-based buffer and sealing materials at the mont terri rock laboratory (Switzerland). Swiss J. Geosci. 110 (No. 1), 253–268. https://doi. org/10.1007/s00015-016-0247-y. Wong, J.T.F., Chen, Z., Ng, C.W.W., Wong, M.H., 2016. Gas permeability of biocharamended clay: potential alternative landfill final cover material. Environ. Sci. Pollut. Control Ser. 23 (No. 8), 7126–7131. https://doi.org/10.1007/s11356-015-4871-2. Wu, Y.-S., Pruess, K., Persoff, P., 1998. Gas flow in porous media with klinkenberg effects. Transport Porous Media 32 (No. 1), 117–137. https://doi.org/10.1023/ A:1006535211684.
Fig. 16. A comparison of the gas permeability obtained from empirical relationship (Eq. (9)) with the experimental results (using GasCoM).
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jngse.2019.01.017. References Alzaydi, A.A., 1975. Flow of Gases through Porous Media (Ph.D). The Ohio State University, Ohio, USA (76-3367). ASTM-D2487, 2011. Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System). West Conshohocken, PA, USA. www.astm.org. ASTM-D4318, 2010. Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils. ASTM International, West Conshohocken, PA. www.astm.org. ASTM-D5550, 2014. Standard Test Method for Specific Gravity of Soil Solids by Gas Pycnometer. ASTM International, West Conshohocken, PA. www.astm.org. Bear, J., 1972. Dynamics of Fluids in Porous Media. Dover Publications, New York, pp. 800. Bouazza, A., Vangpaisal, T., 2003. An apparatus to measure gas permeability of geosynthetic clay liners. Geotext. Geomembranes 21 (No. 2), 85–101. https://doi.org/ 10.1016/S0266-1144(02)00058-4. Cantrell, W., Ewing, G.E., 2001. Thin film water on muscovite mica. J. Phys. Chem. B 105 (No. 23), 5434–5439. https://doi.org/10.1021/jp004305b. Chuvilin, E.M., Grebenkin, S.I., Sacleux, M., 2016. Influence of moisture content on permeability of frozen and unfrozen soils. Kriosfera Zemli XX, 66–72. Cui, X., Bustin, A.M.M., Bustin, R.M., 2009. Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications. Geofluids 9 (No. 3), 208–223. https://doi.org/10.1111/j.1468-8123.2009.00244.x. Dangayach, S., Singh, D.N., Kumar, P., Dewri, S.K., Roy, B., Tandi, C., Singh, J., 2015. Thermal instability of gas hydrate bearing sediments: some issues. Mar. Petrol. Geol. 67, 653–662. https://doi.org/10.1016/j.marpetgeo.2015.05.034. Dullien, F.A., 1991. In: Brenner, H. (Ed.), Porous Media: Fluid Transport and Pore Structure. Academic press, San Diego, California, pp. 574. Gumaste, S.D., Singh, D.N., 2013. Laboratory studies to investigate the influence of thermal energy on soil-fabric. Geomechanics Geoengin. Int. J. 8 (No. 3), 209–214. https://doi.org/10.1080/17486025.2012.727038. Hassine, S.B.H., Dymitrowska, M., Pot, V., Genty, A., 2017. Gas migration in highly water-saturated opalinus clay microfractures using a two-phase trt lbm. Transport in Porous Media, vol. 116, 975–1003. No. 3. https://doi.org/10.1007/s11242-0160809-5. Hohener, P., Ponsin, V., 2014. In situ vadose zone bioremediation. Curr. Opin. Biotechnol.
92
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Investigations on gas permeability in porous media a
b
Jeevan Joseph , Ganaraj Kuntikana , D.N. Singh a b
b,∗
T
Department of Civil Engineering, National Institute of Technology Trichy, Tamil Nadu, 620015, India Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
ARTICLE INFO
ABSTRACT
Keywords: Porous media Gas permeability Pore-characteristics Mineralogy Knudsen flow Gas-porous media system
Permeability of gases in porous media is a vital parameter for the design of landfill liners and buffers for nuclear waste repositories, gas extraction from petroleum reservoirs and hydrate bearing sediments, vapor extraction to decontaminate soils, carbon dioxide sequestration, etc. It is well understood that the gas-phase permeability in porous media is predominantly governed by the porosity, pore-characteristics (viz., diameter and distribution), properties of the gas (viz., density, molecular size and weight, sorption capacity, and viscosity) and their state of saturation (Sr). However, the nature of the flow of gas (viz., molecular, viscous and Knudsen), is influenced by the mean free-path, its compressibility and mean diameter of the pores. All these factors and complexities pose a challenge in determining the intrinsic permeability, K, which otherwise is assumed to be a (i) constant and (ii) fingerprint of porous media. In this context, and to facilitate easier determination of the gas-phase permeability, Kg, of porous media, a test setup: Gas Conductivity Measuring device, GasCoM, has been developed. Efforts have also been made to understand the influence of the characteristics of the gas (viz., active, inert, non-polar, monoatomic, diatomic and mixture of several gases) on Kg of different porous media (viz., soils of entirely different physico-chemical-mineralogical characteristics compacted at different densities and saturation, and commercially available alumina discs, referred to as standard porous media, SPM). A critical synthesis of the experimental data reveals that the flow of gas in porous media gets significantly influenced by (a) the hygroscopic moisture content, which also highlights the importance of its mineralogy and (b) its tortuosity. Furthermore, a correlation that can be employed for estimation of the Kg, for various gas-porous media systems, GPMSs, has been proposed and validated by using experimentally obtained results.
1. Introduction Gas permeability, Kg, of porous media has significant role in geoenvironmental engineering such as: (a) soil vapour extraction (Hohener, and Ponsin, 2014; Huang, and Goltz, 2017; Hutzler et al., 1991; Magalhães et al., 2009; Simpanen et al., 2017), (b) the extraction of natural gas from unconventional resources (Dangayach et al., 2015; Johnson et al., 2011; Joseph et al., 2016; Khlebnikov et al., 2017), (c) design of liners for the containment of volatile nuclear waste (Cui et al., 2009; Hassine et al., 2017; Wieczorek et al., 2017), (d) landfill liners (Bouazza, and Vangpaisal, 2003; Moon et al., 2008; Vangpaisal, and Bouazza, 2004) and (e) soil amendment for agricultural activities (Wong et al., 2016), as depicted in Fig. 1. The situations depicted in Fig. 1 necessitate determination of Kg of the ‘gas-porous media systems’, GPMSs, compacted to different density states (i.e., the dry-density and degree of saturation). The thermo-mechanical energy fields prevailing in these situations, might also result in pore-desaturation (i.e., Sr < 1) and in the process altering the pore-
∗
characteristics of porous media (Thakur, and Singh, 2005; Gumaste, and Singh, 2013; Iyer et al., 2017). Hence, a better understanding of GPMSs is necessary for predicting the (i) extent of soil pollution, (ii) natural gas extraction potential and (iii) suitability of decontamination techniques. The suitability of compacted clay as ‘gas barrier’ for landfills has been attempted by Moon et al. (2008), simulating the field conditions on a laboratory scale. However, the experimental methodology was simplified by employing nitrogen gas as the flowing fluid, rather than gasses of landfill origin. The study reported Kg values of clay ranging from 2.03 × 10−10 to 4.96 × 10−9 cm2, and therefore its suitability as landfill liner was objected. Further, Kg of the biochar amended clays, to verify their suitability as an alternative landfill liner material, was investigated by Wong et al. (2016). A flexi-wall permeameter was employed, with compressed air as the flowing fluid, and the gas flow was measured with a flow meter, connected at the outlet of a triaxial cell. Interestingly, the study reported decrease in Kg with increase in biochar content and degree of compaction.
Corresponding author. E-mail addresses: [email protected] (J. Joseph), [email protected] (G. Kuntikana), [email protected] (D.N. Singh).
https://doi.org/10.1016/j.jngse.2019.01.017 Received 20 November 2018; Received in revised form 23 January 2019; Accepted 28 January 2019 Available online 31 January 2019 1875-5100/ © 2019 Elsevier B.V. All rights reserved.
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Nomenclature η ψ ηa γd γw A CH CL D Dl Dm dm e ef emax emin G GasCoM GPMSs He Ip K Kg Kg (Comp.) Kn Kw lf LOTM Me
MIP N2 NA NVR P0 Pg PM Pp Q R Re SPM Sr T USCS v V Va Vv Vw wh wl wp XRD γd, MIP ΔP/l θ λ μ ρ
Porosity Total suction Percentage air void Dry-unit weight Unit weight of water Area of cross-section Clay with high plasticity Clay with low plasticity Pore-diameter Characteristic length Molecular diameter Mean pore-diameter Voids ratio Final voids ratio Maximum voids ratio Minimum voids ratio Specific gravity Gas conductivity measuring device Gas-porous media systems Helium Plasticity index Intrinsic permeability Gas permeability Gas permeability (computed) Knudsen number Intrinsic hydraulic conductivity Final length Laser obscuration time measurement Methane
Gas permeability studies on partially saturated geosynthetic clay liners have affirmed a decrease in Kg with increase in water saturation (Vangpaisal, and Bouazza, 2004). Similar studies were conducted by Rouf et al. (2014) on needle punched geosynthetic clay liners, at differential nitrogen gas injection pressures (ranging from 1 kPa to 10 kPa). These authors have highlighted the impact of normal stress, confining stress and the saturation states on Kg. In another study, Chuvilin et al. (2016) have carried out gas permeability experiments on sandy soils, of different moisture contents, corresponding to their frozen state. Reduction in permeability of several orders of magnitude has been reported for Sr ≈ 50%. Incidentally, very interesting and challenging experiments have been performed by Johnson et al. (2011) on the sediments bearing methane gas hydrates, from Mount Elbert site, on the Alaska North Slope (ANS). In this study, nitrogen gas was employed as the flowing fluid, instead of methane, to avoid the chances of hydrate formation. An inverse relation between Kg with hydrate saturation has been inferred from the study, which also highlights the impact of thermodynamic conditions viz., temperature and pressure, on the flow characteristics of gasses in porous media. Klinkenberg (1941) has reported the variations in flow characteristics (viz., continuum, viscous and Knudsen) in porous media on account of the gas characteristics and injection pressure, mean diameter of the pores, and the prevailing temperature conditions. It has been reported that the nature/type of the gasses viz., active, inert, non-polar, monoatomic, diatomic and mixture of several gasses, and porous media viz., soils of entirely different physico-chemical-mineralogical characteristics, compacted at different densities and saturation, and the pore-characteristics such as diameter and distribution, would also significantly influence K, which otherwise is assumed to be a (i) constant and (ii) fingerprint of the porous media (Dullien, 1991; Webb, 2006). Unfortunately, most of these studies have ignored the influence of the inherent properties of the GPMSs while determining Kg.
Mercury intrusion porosimeter Nitrogen Avagadro's number Normalized voids ratio Outlet gas pressure Gas injection pressure Porous media Packing pressure Discharge Universal gas constant Reynolds number Standard porous media Degree of saturation Temperature Unified soil classification system Molecular mass Bulk volume Volume of air Volume of voids Volume of water Hygroscopic moisture Liquid limit Plastic limit X-ray diffraction Dry-density obtained from mercury intrusion porosimetry Pressure gradient Volumetric moisture content Mean free path Viscosity Density
Under these circumstances, an attempt has been made to develop a correlation that can be employed for the estimation of Kg for various GPMSs corresponding to Sr < 1. In this regard, an easy to operate laboratory setup, GasCoM, which facilitates determination of Kg for different GPMSs, has been developed and its efficiency for achieving the said objective has been demonstrated. The experimental studies were carried out by employing different gases viz., inert, non-polar, monoatomic, diatomic and mixture of gasses, and partially saturated porous media of distinct characteristics viz., mineralogy, texture and state of compaction. Furthermore, the validity of this correlation has been demonstrated by comparing the results vis-à-vis those obtained from GasCoM. 2. Experimental investigation 2.1. Porous media characteristics The characteristics of porous media, PM, and the gasses employed for the flow study, keeping in view of their prevalence, as depicted in Fig. 1, are listed in Table 1 and Table 2, respectively. The PM included samples from, (i) onshore soils (S-1, S-2, and S-3), (ii) offshore sediment (S-4), and (iii) synthetic materials consisting of bentonite and fly ash (BT and FA), based on their recurrence in specific field application. The specific gravity, G, (employing an Ultra-Pycnometer, Quantachrome, USA) and the consistency limits (liquid limit, wl, plastic limit, wp, plasticity index, Ip) of these PM, were determined as per the guidelines specified by (ASTM-D2487, 2011; ASTM-D4318, 2010; ASTM-D5550, 2014), respectively. The hygroscopic moisture content, wh, of these PM were also determined, as per the procedure described in the literature (Shah, and Singh, 2005) and the results are listed in Table 1. In addition, sintered alumina discs (read-standard porous media, SPM, procured from Cobra Technologies, The Netherlands), which hold rigid and non-compressible pore structure were also employed, to 82
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 1. Different gas-porous media systems: (a) Air purging for vapor extraction, (b) the free gas zone beneath the hydrate bearing sediments, the compacted clay liners for (c) disposal of nuclear waste in the repositories and (d) top covers of landfills. Table 1 Basic characteristics of porous media selected for the study. Sl. No.
PM
Designation
G
(%)
USCS
Size fraction
1
Onshore soils
2 3
Offshore sediment Synthetic soils (Bentonite and fly ash)
4
Standard porous media (SPM)
S-1 S-2 S-3 S-4 BT FA SPM-1 SPM-2 SPM-3 SPM-4 SPM-5
2.76 2.63 2.61 2.56 2.52 2.79 3.97
Consistency Limits
wh
Clay
Silt
wl
wp
Ip
16 18 2 49 44 68 NA
84 82 98 51 56 32
40 39 53 92 263 Non-plastic
18 11 19 34 42
22 28 34 58 221
3.1 5.0 5.2 8.1 9.1 2.4 <1
CL CL CH CH CH NA
NA: Not applicable.
simulate the pore characteristics of natural deposits like shale, chalk, mudstone and sandstone etc. (refer Table 1). The grain size-distribution characteristics of these PM, except for SPM, obtained from Laser Obscuration Time Measurement, LOTM (Ambivalue, Netherlands), is depicted in Fig. 2. The mineralogical composition of the PM selected for this study was obtained by employing an X-ray diffraction (XRD) spectrometer (X'Pert PRO, PANalytical, The Netherlands). The presence of active(Montmorillonite) and passive- (Quartz, Calcite, etc.) minerals in PM (refer Table 3), and the characteristics of gasses (viz., inert, non-polar, monoatomic, diatomic and mixture of gasses etc.), reveal the
Table 2 Basic properties of the gasses employed in the present study. Gas
Dma (Å)
mb (g/mol)
ρ (kg/m3)
μ ( × 10−5 Pa s)
Helium (He) Methane (Me) Nitrogen (N2) Compressed dry air (Air)
3.64 3.98 1.40 1.50
4.0 16.0 28.0 28.9
0.16 0.65 1.13 1.20
1.96 1.12 1.78 1.82
ρ: Density (at Normal temperature and pressure), μ: Viscosity (at 25 °C). a Dm: Molecular Diameter. b Molecular mass. 83
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 2. Grain-size distribution characteristics of the soils used in this study. Table 3 Mineralogical composition of different porous media. PM
Minerals Present
S-1 S-2 S-3 S-4 BT FA SPM
Quartz, Orthoclase, Moganite Quartz low, Moscovite, Albite Quartz low, Moscovite Quartz low, Magnetite, Zeolite Quartz low, Anothite, Montmorillonite Quartz low, Magnetite, Calcite, Anorthite Corundum
experimental determination of Kg. The constant gas source at the required pressure, for performing the flow study was ensured with the help of gas regulator attached to the corresponding gas cylinders. The gas injection pressure, Pg, is monitored continuously with the help of a pressure transducer (Humboldt, USA) and the volume of gas coming out of the specimen is measured by employing a volume measuring device (GCTS, USA). The gas permeability of the PM specimen was conducted in the test set up, GasCoM (Fig. 4), that has been developed for (i) preparing specimens of different density and (ii) to perform gas flow studies at that state. The specimen preparation has been carried out by filling a known amount of the powdered material (as per the target dry density, γd, of the specimen on which gas permeability study has to be performed) in the specimen holder, unit C (specimen size of 5 cm diameter and 2.5 cm thickness can be prepared), from the top of jacket. The plunger, with porous disk (PD-1), fitted in it, is lowered down in
extensiveness of the investigation carried out in this study. 2.2. Determination of Kg Fig. 3 depicts the major components which are essential for the
Fig. 3. Experimental layout for conducting gas permeability studies on PM. 84
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
states has been obtained from Eq. (4). d, MIP
d
=
= G
w
d, MIP .
1 + ef
(2)
lf
(3)
l
where G is the specific gravity of porous media, γd, MIP, lf and ef refer to the dry-density, height, and voids ratio of the specimen, after its removal from the unit C.
e = (G
w
d
)
1
(4)
Where as, γd and e refer to the dry-density and voids ratio of the specimen (of height, l), corresponding to any stage between emax and emin. Furthermore, in order to benchmark the specimen, i.e., to define its compaction state, represented by the intermediate voids ratio, e, and to eliminate the effect of errors associated with the determination of the voids ratio, the parameter; normalized voids ratio, NVR, has been introduced (refer Eq. (5)), except for the SPM. The NVR being a measure of the ability of the specimen to undergo densification beyond its natural state, its lower limit (=0) corresponds to the loosest state and the upper limit (=1) corresponds to the densest state.
NVR = (
Fig. 4. Details of the test setup for gas permeability studies.
through the sleeve of the jacket and the whole assembly is mounted on a loading frame. Subsequently, the static pressure, Pp (in kPa), is applied in increments, through the loading pad to compact the material inside unit C, to achieve a specimen of the target density, γd. This procedure offers higher flexibility to create specimens with different compaction states (mainly density and pore-structure). Subsequently, the vacuum pump, the gas cylinder and the volume measuring device is connected to the ports If, Ig and Og, respectively, of the GasCoM. The entrapped air in the specimen is removed by applying vacuum pressure (−50 kPa) in the specimen through If (confirming that other ports remain closed). The gas injection pressure, Pg, has been adjusted to generate a pressure gradient, ΔP/l, of 10 kPa/cm across the specimen through the port Ig, with the help of a gas regulator (attached to the gas source). However, the investigations related to the gas flow through the SPM were carried out by employing a flexi-wall permeameter cell owing to their rigidity and standard size, instead of GasCoM (other steps remaining the same as described earlier). It's worth realizing that the smaller size of the sample provided the flexibility to perform permeability studies for a wide range of pressure gradient (viz., 5–100 kPa/ cm). The gas permeability, Kg, was determined by employing Darcy's equation, for viscous and compressible gases, as given in Eq. (1) (Wu et al., 1998).
Kg =
2 µ l P0 Q A (Pg2 P02)
emax e ) emax emin
(5)
3. Results and discussion The packing pressure, Pp, employed to compact the specimens of the porous media, to different dry density, was determined and the results in the form of voids ratio, e, versus Pp are presented in Fig. 5. It can be observed that e remains practically constant for Pp > 3.0 MPa and hence the maximum Pp was limited to 3.75 MPa, for the specimens considered in the present study. The differential and cumulative voids ratio of different PM, as a function of the pore-diameter, d, are depicted in Fig. 6(a) and (b), respectively. From Fig. 6(a), it can be realized that all the PM exhibit a mono-modal distribution of the pores. The mean diameter of the pores, dm, has been obtained from the analysis (Iyer et al., 2017) of Fig. 6(a) and the results are presented in Table 4. It can be noted that dm covers a wide spectrum of the pore-size (viz., 58–2609 nm). However, it was noticed that removal of the specimen from the unit C causes a bit of swelling gain in e, due to stress release (refer Fig. 7). Hence, ef (i.e., the final voids ratio obtained from the MIP) has been employed to back compute emax, e and emin, by following Equations (2)–(4). The voids ratio of the specimens obtained through this exercise, is presented in Table 4. Inorder to ensure that the gas pressure, Pg, is not high enough to destroy the pore-structure of the specimen, the total suction, ψ, was measured by employing a dewpoint potentiometer, WP4, by following the methodology presented by Iyer et al. (2013) and the results are presented in Table 5. Considering the fact that Pg adopted for various specimens (in kPa, range) is several orders of magnitude lower than their suction (in MPa range), the possibility of damage of pores has been ignored. Further, to ensure laminar gas flow conditions through the pores of the soil specimen, Reynolds number, Re, was computed.
(1) −5
Where μ is the viscosity of the gas in ( × 10 Pa s), l is the length of the specimen (in cm), Q is the discharge (in cm3/s), A is the area of crosssection (in cm2), and Pg and P0 are the injection and outlet gas pressures (in Pa) respectively. It should be noted that P0 in the present study has been maintained as atmospheric. Further, in order to understand the significance of pore characteristics (viz., pore diameter and distribution) of the specimen, on Kg, the mercury intrusion porosimetry, MIP, (employing Pore Master, Quantachrome, USA) has been performed on the specimen extracted from the unit C (after freeze drying). The voids ratio obtained at this stage, referred as final void ratio, ef, has been utilized to back compute the density, γd, (at various stages of compaction) by employing Eq. (2) and Eq. (3). Further, the voids ratio corresponding to other density
Re =
. v. D l µ
(6) 3
where, ρ is the density of the gas (kg/m ) flowing with velocity v (m/s), Dl is the characteristic length of the specimen, assumed to be equal to dm . It can be noticed from Fig. 8 that the laminar flow condition for gasses in the porous media are satisfied in the present study (i.e., Re < 1 and Re < 6, as proposed by Bear (1972), and Wu et al. (1998), 85
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 5. The state of compaction of different specimens of the porous media tested for gas permeability.
Fig. 6. The mercury intrusion porosimetry results for different porous media exhibiting (a) differential voids ratio, (b) cumulative voids ratio.
respectively) and hence, Darcian flow could be acertained. The variation in Kg, of porous media, corresponding to the NVR is depicted in Fig. 9. It can be noticed from the figure that as expected, Kg decreases with an increase in NVR, irrespective of the specimen type and the gases employed in this study. Incidentally, the loosest state of all the PM (corresponding to NVR = 0) yield almost similar Kg values, irrespective of the gas employed for conducting the tests. However, a wide scatter in Kg values has been noticed for the densest state of the PM (corresponding to NVR = 1). Interestingly, it has been observed that data presented in Table 4 indicate that dm and ef for PM S-2 are higher (1.5 and 1.2 times, respectively) than those for PM S-1. As such, Kg versus NVR trends for the
PM S-1 and PM S-2 should not have matched. However, a closer look at the Kg versus NVR trends for PM S-1 and PM S-2, both classified as CL as per the USCS, indicate linear fits (Trends A, B, C and D) with R2 very close to unity (refer Fig. 10). A reasonable justification for this observation could be the difference in the hygroscopic moisture contents, which is 3.1% and 5.0%, for PM S-1 and S-2, respectively (refer to Table 1). The hydrophilic nature of PM S-2, as it contains Muscovite (refer Table 3) mineral (Cantrell, and Ewing, 2001) adds up to its water affinity as compared to its counterpart PM S-1. Incidentally, when trends A, B, C and D are superimposed on each other (refer to Fig. 11), it can be realized that the Kg follows the sequence He > N2≈Air > Me. It should be noted that these gasses 86
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
pertain to various applications depicted in Fig. 1. Based on the above discussion, it can be opined that Kg is influenced by the presence of hygroscopic moisture, wh, which would result in reduction of its pore diameter and eventually a reduced Kg. With this in view, the percentage air voids, ηa, for different specimens was computed, by employing Eqs. (7a) and (7b) and listed in Table 5.
= Vv V or a
= Vw V + Va V
(7a) (7b)
=
Where Vv, Vw, Va and V denote the volumes of voids, water, air and the bulk specimen, respectively, whereas θ is the volumetric moisture content. Additionally, to understand the influence of ‘nature’ of flow of gases through porous media, their mean free path, λ (in m), corresponding to the Pg, has been computed by employing Eq. (8).
=
2
RT Dm2 NA Pg
(8)
Fig. 7. Depiction of emax, emin and ef of the specimen during packing and removal from the unit C.
Where R is the universal gas constant (=8.314 J/mol. K), T is the temperature in Kelvin, Dm is the molecular size of the gas molecule (A°) and NA is the Avagadro's number (=6.02 × 1023/mol). Knudsen (1909) has reported that a linear variation of gas discharge with pressure gradient (Darcian flow, which is primarily valid for noncompressible and viscous fluids in their laminar region) is valid for the continuum flow, when λ < < dm. Furthermore, based on the studies reported by earlier researchers (Alzaydi, 1975; Livesey, 1998; Scanlon et al., 2002), the nature of flow viz., molecular, transitional and Knudsen flow, through PM has been categorized based on the Knudsen number, Kn (=λ/dm), as depicted in Fig. 12. Another possibility that has been depicted in this figure is, an increase in Q with increase in Kn (> 10). Such a situation would occur at extremely lower pressure gradients, and/or when porous media contains very fine pores, the flow of gases remains ‘non-zero/slip flow’ at the solid interface. This condition results in non-Darcian flow as
Table 5 The mean diameter, porosity, air porosity, and suction of different specimens of the porous media (PM) after extraction from the unit C.
Table 4 The datasheet employed for determination of the voids ratio of the specimens of different porous media (PM). PM
ef
emin
emax
dm (nm)
Specimen
ea
Sr (%)
S-1
0.79
0.75
1.61
1280
S-2
0.97
0.93
1.95
1878
S-3
0.63
0.58
1.35
2382
S-4
0.98
0.94
2.33
1109
BT
0.81
0.73
1.92
1485
FA
2.43
2.35
3.64
2609
S1-A S1-B S1-C S1-D S2-A S2-B S2-C S2-D S3-A S3-B S3-C S3-D S3-E S3-F S3-G S3-H S3-I S3-J S3-K BT-A BT-B BT-C BT-D BT-E FA-A FA-B
1.35 1.16 0.99 0.85 1.67 1.43 1.24 1.07 1.26 1.16 1.07 0.91 0.78 0.66 1.92 1.79 1.37 1.16 0.99 1.67 1.40 1.19 1.00 0.85 3.07 2.65
6.40 7.49 8.74 10.21 7.96 9.25 10.70 12.36 10.66 11.56 12.53 14.71 17.30 20.41 10.81 11.61 15.22 17.92 21.06 13.70 16.31 19.31 22.82 26.95 2.21 2.56
a
PM
η
ηa
dm (nm)
ψ (MPa)
S-1 S-2 S-3 S-4 BT FA SPM-1 SPM-2 SPM-3 SPM-4 SPM-5
0.44 0.39 0.49 0.49 0.45 0.71 0.14 0.25 0.26 0.29 0.36
0.36 0.25 0.36 0.29 0.22 0.64
1280 1878 2382 1109 1485 2609 63 69 58 100 144
147 114 132 128 87 115 48 51 55 51 63
described by Voudrias, and Li (1992) and Webb (2006). Such a situation would also result in greater collision of the gas molecules with the pore-walls as compared to the collision between the molecules of the gas, which might result in an increased Q (Dullien, 1991). It should be realized that in the loosest state of porous media, the dm would be higher and hence Kn→0. Hence, the flow of gasses in porous media, corresponding to this stage, would be highest and ‘pure molecular’ in nature. Fig. 13 depicts the variation in volumetric discharge of the flowing fluid, Q, through the PM (excluding SPM), with respect to their Kn values. It can be observed that these PM exhibit transitional flow. Incidentally, for the flow to fall in the Knudsen region, either Pg should be extremely low and/or porous media should be of low dm (Alzaydi, 1975). It appears that these conditions could not be satisfied by several GPMSs (refer Fig. 13) considered in the present study, except for the SPM. In this context, the flow study through SPM, under different Pg (values ranging between 5 kPa and 100 kPa) has been carried out and the results are depicted in Fig. 14. Interestingly, it has been noticed that the Q for all the gases becomes asymptotic corresponding to lower Pg. Similar observations were reported by Izadi, and Stephenson (1992), in fine grained porous media at lower water contents. However, the focus of their study was to understand the variation in slip flow with saturation of pores. In order to provide a justification for this anomaly, a conceptual
Obtained from Eq. (4).
87
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 8. Reynolds number for the specimens of different porous media.
viscosity ( × 10−5 Pa s) and density (kg/m3) of the gas at 25 °C, ηa is the percentage air void, λ is the mean free path (cm), A is the area of crosssection and l is the length (read thickness in cm) of the porous media. It should be noted that ξ is a constant and it incorporates the physical properties of the gas flowing in the porous media. It should be noted that the validity of Eq. (9) is dependent on the following assumptions and conditions:
schematic, depicting the flow through a cylindrical and tortuous pore, has been considered (Fig. 15). From this figure, it can be realized that the probability of the gas molecules colliding with the pore-walls would be higher for the tortuous pores, due to random distribution of porecharacteristics viz., size and shape, as compared to the cylindrical pores. Moreover, the effective length, Le, considered for gas molecule to traverse through a tortuous pore would be different from that of a cylindrical pore (of length, L). Hence, this follows that Kn through the tortuous pores would be (much) higher than the cylindrical pores. Therefore, the present study reveals that the Knudsen regime could only be defined at a higher range (Kn > > 10), for a tortuous pore, than what has been specified in the existing literature. The results obtained from these studies have been further utilized for developing an empirical relationship that can be employed for computing the gas permeability, Kg (Comp.). In this regard, the linear regression analysis, incorporating the pore characteristics, and the physical properties of the gas, corresponding to different thermodynamic states (viz., temperature and pressure) of different GPMSs has been considered. The best-fit empirical relationship, obtained through this exercise is presented in Eq. (9).
K g (Comp.) = . where, =
dm
a
l2
A
1 m0.5 µ2.5
0.9
1. This relationship is valid only for laminar flow of gasses through unsaturated (Sr < 1) porous media. 2. Porous media follows the mono-modal distribution of pore characteristics (i.e., the dm is unique). 3. The variations in gas properties, with temperature, are to be incorporated in ξ. 4. The gas injection pressure, Pg, does not cause phase change of the gas. 5. The l/D ratio of specimens considered in the study ranges from 0.25 to 0.75. Fig. 16 depicts a comparison of the computed and experimentally determined (from the GasCoM) gas permeability values, denoted as Kg(Comp.) and Kg (GasCoM), respectively. It can be observed from the figure that the computed and experimentally obtained Kg values match extremely well (i.e., all the data falls within 95% prediction band and close to 45° line) for the porous media
(9) and m, μ and ρ are the molecular weight (g/mol), 88
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 9. The gas permeability of different gas-porous media systems.
considered in this study. As depicted in Fig. 16, though data obtained in this study belongs to a wide range of GPMSs (i.e., 58≤dm ≤ 2609), further studies should be conducted on the specimens with dm belonging to either sides of this range to check the robustness of the Eq. (9).
been demonstrated that even for the Kundsen number, Kn, > 10, the gas discharge remains almost constant and it does not pick up. This calls for improvising the test setups used in this study, particularly sophisticated instrumentation that could control the gas injection pressures, Pg, (< 1 kPa). Furthermore, an empirical relationship that can be employed for computing Kg of different GPMSs has been proposed and its validity with respect to the experimental results has been established. Though the results obtained in this study correspond to porous media for which 58≤dm ≤ 2609 nm, it is authors' belief that this relationship would be very useful for determining the Kg of porous media with a wide spectrum of the mean pore sizes. Hence, further studies are warranted on GPMSs consisting of other gasses and porous media with the mean pore-size lying outside 58≤dm ≤ 2609 nm range. It should also be appreciated that this empirical relationship would evade the tedious task of conducting gas permeability tests and just by substituting the attributes of the gas and porous media (i.e., only the mean pore-size, which can easily be obtained by conducting the mercury intrusion porosimetry) characteristics to estimate Kg.
4. Concluding remarks The present study highlights the significance of determination of gas permeability, Kg, through partially saturated porous media of entirely different physico-chemical-mineralogical characteristics, compacted at different densities and saturation. In order to achieve this objective, a laboratory setup, GasCoM, has been developed and gas permeability experiments were carried out by employing different gasses (viz., Helium, Nitrogen, Methane and compressed dry Air). The study highlights the significance of the hygroscopic moisture, which indirectly reflects the mineralogy of porous media, on the gas permeability of different Gas-Porous Media System, GPMSs. Furthermore, the effect of presence of ‘tortuous pores’ in porous media has been studied and it has 89
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 10. The variation in gas permeability with normalized voids ratio for the porous media S-1 and S-2.
Fig. 12. The conceptual diagram depicting the variation of gas flow in the porous media. Fig. 11. A comparison of the permeability of different gases in porous media S1 & S-2. 90
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
Fig. 15. The schematic of Knudsen flow through (a) cylindrical- and (b) tortuous-pores.
Fig. 13. Nature of the gas flow through the specimens of different porous media (except the standard porous media).
Fig. 14. The variation in gas discharge (at different gas injection pressure) and the corresponding Knudsen number for different standard porous media. 91
Journal of Natural Gas Science and Engineering 64 (2019) 81–92
J. Joseph, et al.
27 (No. 18), 1–7. https://doi.org/10.1016/j.copbio.2013.08.018. Huang, J., Goltz, M.N., 2017. Analytical solutions for a soil vapor extraction model that incorporates gas phase dispersion and molecular diffusion. J. Hydrol. 549, 452–460. https://doi.org/10.1016/j.jhydrol.2017.04.013. Hutzler, N.J., Murphy, B.E., Gierke, J.S., 1991. State of technology review : soil vapor extraction systems. J. Hazard Mater. 26 (No. 2), 225–229. https://doi.org/10.1016/ 0304-3894(91)80008-C. Iyer, K., Jayanth, S., Gurnani, S., Singh, D.N., 2013. Influence of initial water content and specimen thickness on the swcc of fine-grained soils. Int. J. GeoMech. 13 (No. 6), 894–899. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000265. Iyer, K., Joseph, J., Lopes, B.C.F., Singh, D.N., Tarantino, A., 2017. Water retention characteristics of swelling clays in different compaction states. Geomechanics Geoengin. 13 (No. 2), 88–103. https://doi.org/10.1080/17486025.2017.1396363. Izadi, M.T., Stephenson, R.W., 1992. Measurement of gas permeability through clay soils. In: David, M.N.S., Nielsen, M. (Eds.), Current Practices in Ground Water and Vadose Zone Investigations. American Society for Testing and Materials, Philadelphia. Johnson, A., Patil, S., Dandekar, A., 2011. Experimental investigation of gas-water relative permeability for gas-hydrate-bearing sediments from the Mount Elbert gas hydrate stratigraphic test well, Alaska North Slope. Mar. Petrol. Geol. 28 (No. 2), 419–426. https://doi.org/10.1016/j.marpetgeo.2009.10.013. Joseph, J., Singh, D.N., Kumar, P., Dewri, S.K., Tandi, C., Singh, J., 2016. State-of-the-Art of gas hydrates and relative permeability of hydrate bearing sediments. Mar. Georesour. Geotechnol. 34 (No. 5), 450–464. https://doi.org/10.1080/1064119X. 2015.1025929. Khlebnikov, V.N., Antonov, S.V., Mishin, A.S., Bakulin, D.A., Khamidullina, I.V., Liang, M., Gushchin, P.A., 2017. A new method for the replacement of ch 4 with Co 2 in natural gas hydrate production. Nat. Gas. Ind. B 3 (No. 5), 1–7. https://doi.org/10. 1016/j.ngib.2017.02.005. Klinkenberg, L. J., "The permeability of porous media to liquids and gases", Presented at the Drilling And Production Practice, January 1, 1941, American Petroleum Institute, New York. Knudsen, M., 1909. The law of the molecular flow and viscosity of gases moving through tubes. Ann. Phys. 28 (No. 1), 75–130. Livesey, R.G., 1998. In: Lafferty, J.M. (Ed.), Flow of Gases through Tubes and Orifices", Foundations of Vacuum Science and Technology. John Wiley and Sons, United States, pp. 81–140. Magalhães, S.M.C., Ferreira, J.R.M., Castro, P.M.L., 2009. Investigations into the application of a combination of bioventing and biotrickling filter Technologies for soil decontamination processes-a transition regime between bioventing and soil vapour extraction. J. Hazard Mater. 170 (No. 2–3), 711–715. https://doi.org/10.1016/j. jhazmat.2009.05.008. Moon, S., Nam, K., Kim, J.Y., Hwan, S.K., Chung, M., 2008. Effectiveness of compacted soil liner as a gas barrier layer in the landfill final cover system. Waste Manag. 28 (No. 10), 1909–1914. https://doi.org/10.1016/j.wasman.2007.08.021. Rouf, M.A., Singh, R.M., Bouazza, A., Rowe, R.K., Gates, W.P., 2014. Gas permeability of partially hydrated geosynthetic clay liner under two stress conditions. Environmental Geotechnics 3, 325–333. https://doi.org/10.1680/envgeo.14.00009. Scanlon, B.R., Nicot, J.P., Massmann, J.W., 2002. In: Warrick, A.W. (Ed.), Soil Gas Movement in Unsaturated Systems", Soil Physics Companion. CRC Press, pp. 297–341. Shah, P.H., Singh, D.N., 2005. Generalized archie's law for estimation of soil electrical conductivity. J. ASTM Int. (JAI) 2 (No. 5), 1–20. Simpanen, S., Yu, D., Mäkelä, R., Talvenmäki, H., Sinkkonen, A., Silvennoinen, H., Romantschuk, M., 2017. Soil vapor extraction of wet gasoline-contaminated soil made possible by electroosmotic dewatering–lab simulations applied at a field site. J. Soils Sediments 1–7. https://doi.org/10.1007/s11368-017-1717-1. Thakur, V.K.S., Singh, D.N., 2005. Rapid determination of swelling pressure of clay minerals. J. Test. Eval. 33 (No. 4), 239–245. https://doi.org/10.1520/JTE11866. Vangpaisal, T., Bouazza, A., 2004. Gas permeability of partially hydrated geosynthetic clay liners. J. Geotech. Geoenviron. Eng. 130 (No. 1), 93–102. https://doi.org/10. 1061/(ASCE)1090-0241(2004)130:1(93). Voudrias, E.A., Li, C.Y., 1992. Importance of knudsen diffusion on benzene vapor transport in unsaturated soil. Chemosphere 25 (No. 5), 651–663. https://doi.org/10. 1016/0045-6535(92)90428-T. Webb, S.W., 2006. "Gas Transport Mechanisms", Gas Transport in Porous Media. Springer, The Netherlands, pp. 5–26. Wieczorek, K., Gaus, I., Mayor, J.C., Schuster, K., García-Siñeriz, J.-L., Sakaki, T., 2017. In-situ experiments on bentonite-based buffer and sealing materials at the mont terri rock laboratory (Switzerland). Swiss J. Geosci. 110 (No. 1), 253–268. https://doi. org/10.1007/s00015-016-0247-y. Wong, J.T.F., Chen, Z., Ng, C.W.W., Wong, M.H., 2016. Gas permeability of biocharamended clay: potential alternative landfill final cover material. Environ. Sci. Pollut. Control Ser. 23 (No. 8), 7126–7131. https://doi.org/10.1007/s11356-015-4871-2. Wu, Y.-S., Pruess, K., Persoff, P., 1998. Gas flow in porous media with klinkenberg effects. Transport Porous Media 32 (No. 1), 117–137. https://doi.org/10.1023/ A:1006535211684.
Fig. 16. A comparison of the gas permeability obtained from empirical relationship (Eq. (9)) with the experimental results (using GasCoM).
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jngse.2019.01.017. References Alzaydi, A.A., 1975. Flow of Gases through Porous Media (Ph.D). The Ohio State University, Ohio, USA (76-3367). ASTM-D2487, 2011. Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System). West Conshohocken, PA, USA. www.astm.org. ASTM-D4318, 2010. Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils. ASTM International, West Conshohocken, PA. www.astm.org. ASTM-D5550, 2014. Standard Test Method for Specific Gravity of Soil Solids by Gas Pycnometer. ASTM International, West Conshohocken, PA. www.astm.org. Bear, J., 1972. Dynamics of Fluids in Porous Media. Dover Publications, New York, pp. 800. Bouazza, A., Vangpaisal, T., 2003. An apparatus to measure gas permeability of geosynthetic clay liners. Geotext. Geomembranes 21 (No. 2), 85–101. https://doi.org/ 10.1016/S0266-1144(02)00058-4. Cantrell, W., Ewing, G.E., 2001. Thin film water on muscovite mica. J. Phys. Chem. B 105 (No. 23), 5434–5439. https://doi.org/10.1021/jp004305b. Chuvilin, E.M., Grebenkin, S.I., Sacleux, M., 2016. Influence of moisture content on permeability of frozen and unfrozen soils. Kriosfera Zemli XX, 66–72. Cui, X., Bustin, A.M.M., Bustin, R.M., 2009. Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications. Geofluids 9 (No. 3), 208–223. https://doi.org/10.1111/j.1468-8123.2009.00244.x. Dangayach, S., Singh, D.N., Kumar, P., Dewri, S.K., Roy, B., Tandi, C., Singh, J., 2015. Thermal instability of gas hydrate bearing sediments: some issues. Mar. Petrol. Geol. 67, 653–662. https://doi.org/10.1016/j.marpetgeo.2015.05.034. Dullien, F.A., 1991. In: Brenner, H. (Ed.), Porous Media: Fluid Transport and Pore Structure. Academic press, San Diego, California, pp. 574. Gumaste, S.D., Singh, D.N., 2013. Laboratory studies to investigate the influence of thermal energy on soil-fabric. Geomechanics Geoengin. Int. J. 8 (No. 3), 209–214. https://doi.org/10.1080/17486025.2012.727038. Hassine, S.B.H., Dymitrowska, M., Pot, V., Genty, A., 2017. Gas migration in highly water-saturated opalinus clay microfractures using a two-phase trt lbm. Transport in Porous Media, vol. 116, 975–1003. No. 3. https://doi.org/10.1007/s11242-0160809-5. Hohener, P., Ponsin, V., 2014. In situ vadose zone bioremediation. Curr. Opin. Biotechnol.
92