研究ノート., March 2012, Vol. 120, 55 ‒ 60

55NotesA simple and low cost method for measuring gas diﬀusivity andair permeability over a single soil cylinder
Purwoko Hari KUNCORO1 and Kiyoshi KOGA2

rie, 1960 ; Osozawa, 1987 ; Rolston and Moldrup,
Abstract : A low cost uniﬁed system for relative gas

2002 ; Resurreccion et al., 2008）．However, such mech-）and air permeability（k ）measure-anism takes a budgeting allocation for the construction

ments has been developed. Instead of the conventionaland might require certain sealing‒effort prior to thesliding‒mechanism, plastic ﬁlms shutter has been pro-measurement.

diffusivity（00 measurement. While for the kOn the other hand, modern tools like air pump, massmeasurement, a method has been introduced by utiliz-

ﬂow meter, and pressure sensor/gauge have been com-

ing the principle of Mariotte s bottle and manometers

monly used to measure the air permeability k [µm2]instead of much costing air pump, mass flow meter,（Chief et al., 2006 ; Hamamoto et al., 2009a）．Certainly,

posed for theandsuch tools must be convenient in handling and eligible

k of Toyoura sand were in a good agreement withfor precise data measurement. However, they might

those obtained in the literature, and the proposed

be remained much costing among us who had severe

method enabled to lower the apparatus cost up to 40 %limitation on the research‒budgeting circumstance.

of the common method cost.
Key Words : g a s d i f f u s i v i t y , a i r p e r m e a b i l i t y ，measurement

cost method for measuring

and pressure sensor/gauge. The measured0

Accordingly, this study is aimed to propose a low
0

and k over a single

soil cylinder.

1. Introduction

2. Development of the measurement method

Diffusion that is driven by concentration gradientand convection that is driven by pressure gradient are

2. 1 Soil specimen preparation
Toyoura sand with 0. 42 ‒ 0. 02 mm in particle size

the two main process of gaseous‒transport in the soil

fractions（Table 1）is repacked into a 471 cm3 cylinder（Hillel, 1998）．Information on those properties is ofwith 10 cm i.d. and 6 cm length and is used forimportance for describing soil aeration（Taylor,and k measurements undergoing air‒dry and vari-1949 ; Glinski and Stepniewski, 1985）and for assessing

ably‒saturated conditions. For the measurement at

the greenhouse gases emission（Ball et al., 1997 ; Smithair‒dry condition, the Toyoura sand is simply air‒dried

et al., 2003）as well as volatile gas movement in theprior to the repacking. While for the measurement atsoil（Jury et al., 1990 ; Petersen et al., 1996）．In addi-

variably‒saturated conditions, repacked air‒dried Toy-tion, such information is also valuable to be used as aproxy for soil hydraulic conductivity properties

oura sand is ﬁrst, water saturated, and then be drainedat ‒ 50, ‒ 75, and ‒ 125 cm soil water matric potentials（Poulsen et al., 2001 ; Chief et al., 2006）．

using hanging water column method. The Toyoura0

The parameter for gas diffusion is gas diffusivity,

sand is not repacked undergoing wet condition since

which is commonly expressed as a relative diﬀusivity

such handling may cause a change in its structure asis the gas diﬀusivity in soil [m2 s‒1]

the Toyoura sand mainly consists of the elongated soil0andin which2‒1

0

is the gas diﬀusivity in free air [m s ]. For this0

measurement, a sliding‒mechanism has been

particles（Hamamoto et al., 2009b）．

widely employed for insulating the initial concentrationof the tracer gas used in the diﬀusion chamber（Cur1

Graduate School of Agriculture, Iwate University, 3 ‒ 18 ‒ 8 Ueda,
Morioka 020 ‒ 8550, Japan. Corresponding author : Purwoko Hari
Kuncoro2
Faculty of Agriculture, Iwate University, 3 ‒ 18 ‒ 8 Ueda, Morioka
020 ‒ 8550, Japan.
2011 年 11 月 9 日受稿，2011 年 12 月 28 日受理
土壌の物理性 120 号，55 ‒ 60（2012）

Table 1 Physical properties of the used Toyoura sand atair‒dry condition.
‒

Bulk density（g cm 3）‒
Particle density（g cm 3）
Gravimetric water content（%）‒
Total porosity（m3 m 3）

1. 58
2. 64
almost zero
0. 40

土壌の物理性 第 120 号（2012）56

2. 2 Gas diﬀusivity measurement

stainless steel mesh plate（Fig. 3a）using the same（and also for the later k ）measurement isgrease prior to the measurement. Such a vacuum

conducted at 20 ℃ with three of replication for each ofgrease usage is preferable since it can provide a suﬃ-

expected soil air content ε[m3 m‒3]. As suggested bycient sealing‒function prior to the measurement but

El‒Farhan et al.（1996），the size of diﬀusion chamber

yet enables the plastic ﬁlms to be easily peeled oﬀ foris designed to be almost similar to that of the soil cyl-the measurement.

03

inder, which is 463 cm in net volume with 11 cm i.d.
and 5 cm length, in order to minimize errors which
may be incurred by non‒mixing of the gas in thechamber. On the other hand, O‒ring is used to seal thechamber and no‒leakage condition is conﬁrmed by immersing the apparatus into water.

duringmeasurement(a)beforemeasurement

N2 inlet/ gas outlet

Soil
SliderFig. 2 Photo of the diﬀusionmeter apparatus.

MeshO2
sensorSince O2 will be used as a tracer gas, N2 is prelimi-

Diffusionchambernary injected into the diﬀusion chamber until the O2
concentration reaches almost zero. The measurement

(b)

Soil

Mesh plate

begins when the circle‒shaped plastic film, which issubsequently followed by ring‒shaped plastic film, is

5.8 cmMainskeletonO2
sensorGas
outlet
Plastic
films

pulled down.

O ringStainless steel
ring

Mesh

11.4 cm I

9.8 cm I(a)

N2 inlet
7.6 cmHook

RubberpackingMainskeleton
DiffusionchamberFig. 1 Conventional sliding‒mechanism（after Osozawa,
1987）（a）and the proposed diﬀusionmeter apparatus（b）.

Ring-shaped
plastic film

Circle-shaped
plastic film(b)Instead of the conventional sliding‒mechanism（Fig.

8.7 cm I1a），a set of plastic ﬁlms that is equipped with a hook
is used as a shutter（Fig. 1b）．These 0. 2 mm thickplastic ﬁlms of polypropylene shape into a circle and a

10.8 cm I
Fig. 3

7.6 cm I

Mesh plate（a）and Plastic ﬁlms shutter（b）．

ring as shown in Fig. 3b. The end part of outer surfaceof this circle‒shaped plastic ﬁlm is ﬁrst, attached to theinner‒surface of the ring‒shaped plastic film using

For the sake of its simplicity, the shutter may be de-vacuum grease. And then, the outer‒surface of thissigned into a single circle‒shaped plastic film only,ring‒shaped plastic ﬁlm is attached to a 0. 3 cm thickwhich is about 10. 8 cm in diameter. However, such

研究ノート：A simple and low cost method for measuring gas diﬀusivity and air permeability
large diameter may cause a certain part of this plastic

2. 3 Air permeability measurement

ﬁlm to be sometimes remained attached to the mesh

After the057

measurement, the same chamber

plate as the maximal hook displacement inside theand soil cylinder are used for k measurement using

chamber is only about 4 cm so that the pulling‒force

Mariotte s bottle and manometers. Manometer A is at-may be insuﬃciently transferred to this furthest point.

tached to the N2 inlet port of the chamber and manom-Hence, the process of air mixing in the chamber may

eter B is connected to the air in the Mariotte s bottle,

be constrained, particularly over area beneath this di-whereas the gas outlet port is connected to the pipe ofagonally remained plastic ﬁlm.

the Mariotte s bottle（Fig. 5）．Meanwhile, the plastic

Thus, the shutter that consists of a ring and a smaller circle of plastic films is preferable in this study.

film shutters are remained peeled off from the meshplate.

This smaller diameter of 8. 7 cm makes the circle‒
shaped plastic ﬁlm can be easily peeled oﬀ previously.
Therefore, air mixing in the chamber can be surely
started even if the ring‒shaped plastic ﬁlm remained

Mariotte's bottle

Manometer A
Air convection

diagonally across the chamber.

HA

HB

1
2

Soil

Chamber

Manometer B

Fig. 5 Air permeameter apparatus.

Fig. 4

Photo of the mesh plate and plastic ﬁlms

shutter.

Along the measurement, concentration of O2 in thechamber is measured by a galvanic O2 sensor（KE ‒12,
Yuasa Co.）and the output is recorded by a data logcan be calculated from theger. Then, the value ofslope（linear regressed）of the plot of relative O2 convs. time

centration

as described by Currie（1960）

and Rolston and Moldrup（2002）．The relative O2 conFig. 6 Photo of tools set‒up for k measurement.

is deﬁned as

centration

−

＝

（1）

0

−

As the water is open‒released from the outlet of the0is the initial O2 concentration in the cham-ic air is pulled into the system through the soil speci-

ber（%），

is O2 concentration in the chamber at timemen, and the occurred pressure gradient across the（%），andis O2 concentration in free air（%）．

soil specimen becomes constant because the level of

Mariotte s bottle（26 liter in capacity），the atmospherin which

Finally, by taking‒50rie, 1960），the value of‒1

as 2. 0 x 10 m s at 20 ℃
（Cur-

the water outlet has been fixed along the measure-can be determined.

ment. The expected pressure gradient for a certain

02

measurement, however, can be set to some extent bysimply adjusting the level of this water outlet.

土壌の物理性 第 120 号（2012）

58

Soon after the manometer A became stable, the k

＝

−ρ g

（2）

measurement can be conducted by recording thechange of air volume in the Mariotte s bottle and thewhile, absolute air pressure in the Mariotte s bottle

reading of manometer A and manometer B for a cer-[Pa] will betain time interval（e.g. 2 minutes）within a set of replication（e.g. 6 times）．Average of the calculated k from

＝

−ρ g

（3）

those measurements is then taken as the ﬁnal k value.
By carrying ideal gas equation, mole number of thepermeated air through soil＝（in which
[m3],

2

2

−

1

[mole] can be written as

）/

（4）

1

is the volume of air in the Mariotte s bottle

is gas constant [J K‒1 mol‒1], andis absolutetemperature [K].
As absolute pressure of the permeated air at the[Pa] iscenter of the specimen
＝（

＋

）/2

（5）

according to the Boyle s law, the volume of the permeated air at the center of the specimen Δ[m3] during

the measurement can be calculated as

（

Δ ＝

＝2

Hence, volume ﬂux of air

2

2

−

1

＋

1

）

（6）

[m s‒1] during measuring

time Δ [s] will be＝in which
Fig. 7

Photo of the used Mariotte s bottle.

Δ

（7）

Δ

is the cross‒sectional area of the specimen[m2].
Finally, k [µm2] can be calculated as

Principally, k will be calculated from the volume ﬂux
of the permeated air, and the volume of the permeated

k ＝

η

（8）

ρ g

air itself is determined from the water level in the
Mariotte s bottle. Hence, a certain calibration is prelim-in whichinary required to convert the measured water level

the air dynamic viscosity [Pa s].

into air volume in the Mariotte s bottle.
Since air volume changes with absolute air pressure,the value of k can be determined through the follow-

is the length of the specimen [m] and η is

3. Results and discussion
Although measured0

and k , particularly at

ing procedure. Suppose suﬃx 1 and 2 denote the start

wet conditions, tended to be slightly lower than thoseand the end of the measurement, respectively, whileobtained in the literature（Hamamoto et al., 2009b），

is absolute atmospheric pressure [Pa], ρ is water

there was a fairly good agreement between them（Fig.

density [kg m‒3], g is gravitational acceleration [m s‒2],8）．Those slightly lower values, particularly in k ,andwere possibly attributed to the lower ratio of fringes

is the difference in water level in manometer[m]. Hence, absolute air pressure in the chamber

between sand particle and wall of the soil cylinder to[Pa] can be expressed as

the soil cross‒sectional area, namely the inner diameter of the soil cylinder in this study was 10 cm, where-

研究ノート：A simple and low cost method for measuring gas diﬀusivity and air permeability
as it was 5 cm in the literature. Accordingly, the developed method was considered to be acceptable for059Table 2 Cost estimation over the measurement apparatus（in thousand Japanese yen）．

and k measurements.

0Developed
MethodCommon
Method‒164. 8+:Slider compartment
Main skeleton

+

‒

+

25. 0

Chamber

14. 5

14. 5+

Mesh plate

4. 5+

‒

O2 sensor

25. 0*

25. 0*

Others（valve, pipe, etc.）

9. 0¶

7. 0¶

Mass ﬂow meter‒

100. 0*Pressure sensor‒

50. 0*Air pump‒

50. 0*k :Large glass bottle‒

80. 0*

Others（valve, pipe, etc.）

¶

10. 0

10. 0¶

Total amount :168. 0421. 3+

estimation made by local ironworks* market price（mostly appeared as middle prices）¶

estimation made by the authors

fied

0

and k measurements. As the developed

method enables to lower the apparatus cost significantly, further study on
Fig. 8 Measured
ous air content ε．

（a）and measured k （b）at vari-00

and k （e.g. eﬀects of

the added organic matter and compaction on them）
becomes possible even within limited research‒budgeting circumstance.

The developed method enabled to lower the cost up

Acknowledgement

to 40 % of the common method cost as it omitted the

The authors would like to thank Mr. Syun Arai andmost cost of slider compartment, mass flow meter,

Ms. Yuko Hori for their kind support and assistancespressure sensor, and air pump（Table 2）．The slider

during the experimental part of this study.

compartment much costs due to the required perfect-

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旨

単一の土壌円筒についてガス拡散係数と通気係数を連続的に測定するための単純で安価な方式を開発した．拡散係数の測定は従来のスライド方式に代えて，試料（内径 10 cm，高さ 6 cm）と拡散室（内径11 cm，高さ 5 cm）の間に設けた網板にプラスティック・フィルム製のシャッターをグリースで貼りつけ，これを引き落とす方法によった．円環形と円形のシャッターを組み合わせることにより，開放を確実にすることができた．通気係数の測定はマリオット瓶で発生させた負圧を利用して行った．通気量はマリオット瓶中の空気の体積と圧力の測定結果から計算した．豊浦砂について測定したガス拡散係数と通気係数の値は既往の研究と近似し，新方式は有用であると判断された．新方式により装置の製作費は40 ％に低減すると見積もられた．
キーワード：ガス拡散係数，通気係数，測定