predicting the gas diffusion coefficient in undisturbed soil from soil water characteristics

7
Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics P. Moldrup,* T. Olesen, P. Schj0nning, T. Yamaguchi, and D. E. Rolston ABSTRACT The gas diffusion coefficient in soil (£>p), and its dependency on soil physical characteristics, governs the diffusive transport of oxygen, greenhouse gases, fumigants, and volatile organic pollutants in agricul- tural, forest, and urban soils. Accurate models for predicting />,, as a function of air-filled porosity (E) in natural, undisturbed soil are needed for realistic gas transport and fate simulations. Using data from 126 undisturbed soil layers, we obtained a high correlation (r 2 = 0.97) for a simple, nonlinear expression describing D t at -100 cm H 2 O of soil water potential (D P>lm ) as a function of the corresponding air-filled porosity (s m ), equal to the volume of soil pores with an equivalent pore diameter >30 urn. A new D e (s) model was developed by combining the D,, M (F. m ) expression with the Burdine relative hy- draulic conductivity model, the latter modified to predict relative gas diffusivity in unsaturated soil. The D tM and Burdine terms in the £>P(£) model are both related to the soil water characteristic (SVV'C) curve and, thus, the actual pore-size distribution within the water content range considered. The D e (s) model requires knowledge of the soil's air-filled and total porosities and a minimum of two points on the SWC curve, including a measurement at -100 cm H 2 O. When tested against independent gas diffusivity data for 21 differently tex- tured and undisturbed soils, the SWC-dependent D f (e) model accu- rately predicted measured data and gave a reduction in root mean square error of prediction between 58 and 83% compared to the classical, soil type-independent Penman and Millington-Quirk models. To further test the new D r (e) model, gas diffusivity and SWC measure- ments on undisturbed soil cores from three 0.4-m soil horizons (sandy clay loam, sandy loam, and loamy sand) within the 4 to 7 m depth below an industrially polluted soil site were carried out. For these deep subsurface soils the SWC-dependent model best predicted the measured gas diffusivities. T HE GAS DIFFUSION COEFFICIENT IN SOIL (Dp) and itS variations with soil type and soil air-filled porosity (s) typically control soil aeration (Buckingham, 1904; Taylor, 1949), fumigant emissions (Brown and Rolston, 1980), volatilization of volatile organic chemicals from industrially polluted soils (Petersen et al., 1996), and soil uptake or emission of greenhouse gases such as methane (Kruse et al., 1996). Accurate, predictive D P (e) models representative of natural, undisturbed soils are essential to better simulate and understand these gas transport and fate processes. Early £> P (e) models depended only on the soil air- P. Moldrup and T. Olesen, Environ. Engineering Lab., Dep. of Civil Engineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aal- borg, Denmark; P. Schj0nning, Dep. of Crop Physiology and Soil Sci., Danish Inst. of Agric. Sci., Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark; T. Yamaguchi, Dep. of Civil and Environ. Engineering, Faculty of Engineering, Hiroshima Univ., 1-4-1 Kagami- yama, Higashi-Hiroshima, 739, Japan; and D.E. Rolston, Soils and Biogeochemistry, Dep. of Land, Air, and Water Resour., Univ. of California, Davis, CA 95616. Received 17 Feb. 1999. *Corresponding author ([email protected]). Published in Soil Sci. Soc. Am. J. 64:94-100 (2000). filled porosity (Buckingham, 1904; Penman, 1940; Call, 1957). The most widely used of these one-parameter models is the Penman (1940) model £>n = 0.66e [1] where D f is the gas diffusion coefficient in soil (cm 3 soil air cm" 1 soil sec" 1 ), D 0 is the gas diffusion coefficient in free air (cm 2 air sec" 1 ), and e is the soil air-filled porosity (cm 3 soil air cm" 3 soil). The next generation of D? models also included soil- type effects in the form of the soil total porosity, <& (m 3 m" 3 ) (Millington and Quirk, 1960,1961; Lai et al., 1976). The most widely used two-parameter model is that of Millington and Quirk (1961): D 0 [2] Comparing gas diffusivity models with measured data for a number of differently textured sieved and repacked soils, Jin and Jury (1996) concluded that the hitherto overlooked Millington and Quirk (1960) model DP [3] best described the measured data as compared to the classical models. Moldrup et al. (1997) combined the Penman and Millington-Quirk model approaches into the general PMQ model D ? r,^ e 3 —- = 0.66e D 0 \d>/ [4] and showed that m = 3 for gas diffusivity in undisturbed soils, and m = 6 for gas diffusivity in sieved, repacked soils, gave improved descriptions compared to earlier two-parameter D P models. This study also implied a significant difference between gas diffusivity in undis- turbed and repacked soils and a larger soil-type depen- dency for gas diffusivity in undisturbed compared to repacked soils. Troeh et al. (1982) presented a three-parameter model for more accurately curve-fitting measured D f (e.) data, including a threshold value of air-filled porosity where the gas diffusivity approached zero due to inter- connected water films. Although this model can fit mea- sured data very well (Petersen et al., 1994), it should be used with great care when simulating gas diffusion and reaction in wet soils. The D P /D 0 values at low air- filled porosities may appear equal to zero in a nonloga- rithmic scale plot but can actually be in the range (D P / Abbreviations: MQ, Millington and Quirk; PMQ, Penman-Millington- Quirk; RMSE, root mean square error; SWC, soil water characteristic. 94

Upload: de

Post on 21-Dec-2016

213 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics

Predicting the Gas Diffusion Coefficient in Undisturbed Soilfrom Soil Water Characteristics

P. Moldrup,* T. Olesen, P. Schj0nning, T. Yamaguchi, and D. E. Rolston

ABSTRACTThe gas diffusion coefficient in soil (£>p), and its dependency on

soil physical characteristics, governs the diffusive transport of oxygen,greenhouse gases, fumigants, and volatile organic pollutants in agricul-tural, forest, and urban soils. Accurate models for predicting />,, as afunction of air-filled porosity (E) in natural, undisturbed soil areneeded for realistic gas transport and fate simulations. Using datafrom 126 undisturbed soil layers, we obtained a high correlation (r2 =0.97) for a simple, nonlinear expression describing Dt at -100 cmH2O of soil water potential (DP>lm) as a function of the correspondingair-filled porosity (sm), equal to the volume of soil pores with anequivalent pore diameter >30 urn. A new De(s) model was developedby combining the D,,M(F.m) expression with the Burdine relative hy-draulic conductivity model, the latter modified to predict relative gasdiffusivity in unsaturated soil. The DtM and Burdine terms in the£>P(£) model are both related to the soil water characteristic (SVV'C)curve and, thus, the actual pore-size distribution within the watercontent range considered. The De(s) model requires knowledge ofthe soil's air-filled and total porosities and a minimum of two pointson the SWC curve, including a measurement at -100 cm H2O. Whentested against independent gas diffusivity data for 21 differently tex-tured and undisturbed soils, the SWC-dependent Df(e) model accu-rately predicted measured data and gave a reduction in root meansquare error of prediction between 58 and 83% compared to theclassical, soil type-independent Penman and Millington-Quirk models.To further test the new Dr(e) model, gas diffusivity and SWC measure-ments on undisturbed soil cores from three 0.4-m soil horizons (sandyclay loam, sandy loam, and loamy sand) within the 4 to 7 m depthbelow an industrially polluted soil site were carried out. For thesedeep subsurface soils the SWC-dependent model best predicted themeasured gas diffusivities.

THE GAS DIFFUSION COEFFICIENT IN SOIL (Dp) and itSvariations with soil type and soil air-filled porosity

(s) typically control soil aeration (Buckingham, 1904;Taylor, 1949), fumigant emissions (Brown and Rolston,1980), volatilization of volatile organic chemicals fromindustrially polluted soils (Petersen et al., 1996), andsoil uptake or emission of greenhouse gases such asmethane (Kruse et al., 1996). Accurate, predictive DP(e)models representative of natural, undisturbed soils areessential to better simulate and understand these gastransport and fate processes.

Early £>P(e) models depended only on the soil air-

P. Moldrup and T. Olesen, Environ. Engineering Lab., Dep. of CivilEngineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aal-borg, Denmark; P. Schj0nning, Dep. of Crop Physiology and Soil Sci.,Danish Inst. of Agric. Sci., Research Centre Foulum, P.O. Box 50,DK-8830 Tjele, Denmark; T. Yamaguchi, Dep. of Civil and Environ.Engineering, Faculty of Engineering, Hiroshima Univ., 1-4-1 Kagami-yama, Higashi-Hiroshima, 739, Japan; and D.E. Rolston, Soils andBiogeochemistry, Dep. of Land, Air, and Water Resour., Univ. ofCalifornia, Davis, CA 95616. Received 17 Feb. 1999. *Correspondingauthor ([email protected]).

Published in Soil Sci. Soc. Am. J. 64:94-100 (2000).

filled porosity (Buckingham, 1904; Penman, 1940; Call,1957). The most widely used of these one-parametermodels is the Penman (1940) model

£>n= 0.66e [1]

where Df is the gas diffusion coefficient in soil (cm3 soilair cm"1 soil sec"1), D0 is the gas diffusion coefficientin free air (cm2 air sec"1), and e is the soil air-filledporosity (cm3 soil air cm"3 soil).

The next generation of D? models also included soil-type effects in the form of the soil total porosity, <& (m3

m"3) (Millington and Quirk, 1960,1961; Lai et al., 1976).The most widely used two-parameter model is that ofMillington and Quirk (1961):

D0[2]

Comparing gas diffusivity models with measured datafor a number of differently textured sieved and repackedsoils, Jin and Jury (1996) concluded that the hithertooverlooked Millington and Quirk (1960) model

DP[3]

best described the measured data as compared to theclassical models. Moldrup et al. (1997) combined thePenman and Millington-Quirk model approaches intothe general PMQ model

D? r,^ e 3—- = 0.66e —D0 \d>/ [4]

and showed that m = 3 for gas diffusivity in undisturbedsoils, and m = 6 for gas diffusivity in sieved, repackedsoils, gave improved descriptions compared to earliertwo-parameter DP models. This study also implied asignificant difference between gas diffusivity in undis-turbed and repacked soils and a larger soil-type depen-dency for gas diffusivity in undisturbed compared torepacked soils.

Troeh et al. (1982) presented a three-parametermodel for more accurately curve-fitting measured Df(e.)data, including a threshold value of air-filled porositywhere the gas diffusivity approached zero due to inter-connected water films. Although this model can fit mea-sured data very well (Petersen et al., 1994), it shouldbe used with great care when simulating gas diffusionand reaction in wet soils. The DP/D0 values at low air-filled porosities may appear equal to zero in a nonloga-rithmic scale plot but can actually be in the range (DP/

Abbreviations: MQ, Millington and Quirk; PMQ, Penman-Millington-Quirk; RMSE, root mean square error; SWC, soil water characteristic.

94

Page 2: Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics

MOLDRUP ET AL.: PREDICTING GAS DIFFUSION FROM SOIL WATER CHARACTERISTICS 95

D0 > 10~4) where gas diffusion still dominates comparedto solute diffusion.

More conceptually advanced £>P(e) models includemacroscopic pore distribution models (Nielson et al.,1984; Freijer, 1994; Steele and Nieber, 1994). Thesemodels take into account soil physical characteristicssuch as pore-size distribution and include several empir-ical and likely soil type-dependent constants. The mod-els are valuable for understanding diffusion dependencyof soil texture and structure based on calibration tomeasured data but are not immediately applicable forpredicting A>(e) for a given soil without first carryingout gas diffusivity measurements (Freijer, 1994).

Recent work has focused on simpler and more directlyapplicable soil type-dependent Z3P(e) models, using the-Campbell (1974) soil water retention parameter to de-scribe pore-size distribution. Moldrup et al. (1996) sug-gested using the tortuosity term from the Burdine(1953)-Campbell (1974) unsaturated hydraulic conduc-tivity model. This in combination with a measured refer-ence-point value of gas diffusivity (equal to the mea-sured Df value at the highest air-filled porosityconsidered in each study) gave accurate predictions ofDp(e) for 16 undisturbed soils. Moldrup et al. (1999)showed that measurements of gas diffusivity or gas per-meability at a single soil water potential (between -100and -500 cm H2O), in combination with the Ball (1981a)tortuous tube gas flow model and the introduction of asoil type-dependent equivalent tube radius, significantlyimproved the £>P(e) descriptions for six undisturbed soilsrepresenting a broad soil texture interval.

Although the need for only a single porosity (Moldrupet al., 1996) or single potential (Moldrup et al., 1999)reference-point measurement of £>P much reduces thetime and difficulty associated with measuring the entire£>p(e) relation, any actual measurement of Df for a givensoil is in practice outside the scope of most chemical-transport and fate-modeling studies, because it is experi-mentally involved and requires special measurementequipment.

In this study, we therefore (i) establish a predictiverelation between DP and e at a given soil water potential(reference point), (ii) insert this reference point expres-sion in the Burdine (1953)-Campbell (1974)-Moldrupet al. (1996) relative gas diffusivity model to develop asimple Z)p(e) model that is fully based on the soil watercharacteristic (SWC) curve, and (iii) validate the newSWC-based gas diffusivity model against independentdata for undisturbed surface and subsurface soils.

MATERIALS AND METHODSSoil cores were collected at a former manufactured-gas

plant site in the city center of Hj0rring, 50 km north of Aalborgin Northern Jutland, Denmark. In situ remediation for coaltar compounds has been carried out at the site since 1993.At the specific soil sampling location the soil is unpollutedthroughout the vadose zone profile (depth of the vadose zoneis around 10 m). The soil type is mainly loamy sand, but morefinely textured horizons were identified in the 4 to 7 m soilzone during establishment of nearby groundwater monitoringwells. When a new groundwater monitoring well was installed

in 1998, two large intact soil cylinders (1-m length, 0.1-m i.d.)were collected from the 4 to 5 and 6 to 7 m soil depths. Anonuniform clay pocket was observed in the upper 15 cm ofthe 4 to 5 m soil cylinder. The upper part of the 6 to 7 mcylinder appeared more finely textured than the lower part.We therefore focused on three 0.4-m soil horizons: the 4.2 to4.6, 6.0 to 6.4, and 6.4 to 6.8 m horizons.

From the large soil cylinders, six smaller intact soil cores(0.034-m length, 0.061-m i.d., 100 cm3 sample volume) werecollected at equal distance throughout each 0.4-m horizon.No sublayering was observed. At the sampling depths equalamounts of soil were then collected and mixed together toobtain a depth-weighted soil sample for soil texture analysis.The bulk soil was air-dried, crushed, and sieved through a 2-mm aperature sieve. The bulk soil and the 18 intact 100 cm3

soil cores (six from each 40-cm horizon) were stored in thedark at 2°C until the measurements were made.

Particle density was measured on the bulk soil by themethod of Blake and Hartge (1986) and soil texture by themethod of Gee and Bauder (1986). Soil water retention wasmeasured by the method of Klute (1986). The intact soil coreswere saturated in sand boxes and subsequently drained tothree water potentials (1P), using either a hanging water col-umn (^ = -50 and -100 cm H2O) or a pressure plate appara-tus OP = -500 cm H2O). The Campbell (1974) soil waterretention parameter, b, was determined as the slope of thesoil water characteristic curve in a log-log coordinate plot.

Gas diffusivity (Z)P) was measured on the intact cores afterdrainage to each of the three water potentials. The experimen-tal setup was first suggested by Taylor (1949) and furtherdeveloped by Schj0nning (1985a). Soil gas diffusion was mea-sured with oxygen as the experimental gas at 20°C. Calculationwith a simple oxygen consumption model using typical con-sumption rates from Danish subsoils showed that oxygen con-sumption could be considered negligible during the short peri-ods needed to measure DP at each soil water potential. Table1 shows the basic soil physical characteristics and Table 2 themeasured soil water retention data (given as the air-filledporosity at each of the three soil water potentials), the fittedCampbell (1974) soil water retention parameter b, and themeasured gas diffusivities for the three Hj0rring soil layers.

To compare gas diffusivity models, the root mean squareerror (RMSE) of prediction was used for best overall fit com-pared to the measured data

[5]

where d, is the difference between the predicted and the mea-sured value of Dp/Do at a given air-filled porosity, and n isthe number of measurements.

Predicting Reference-Potential Gas DiffusivitySchj0nning et al. (unpublished data) measured gas diffusiv-

ity at -100 cm H2O of soil water potential for 113 differentDanish soils and soil layers. Together with data from Ball(1981b), Heidman (1989), and Schj0nning (1989), gas diffusiv-ity measurements at -100 cm H2O were available for a totalof 126 undisturbed soils and soil layers. The clay content ofthe 126 soils ranged between 1.6 and 23.2%, organic mattercontent between 0.1 and 4.1%, sampling depth between 0 and1.8 m, and soil core volume between 100 and 227 cm3. Foreach soil, gas diffusivity measurements at ty = —100 cm H2Owere carried out on three to six (in most cases five), closelysampled (typically within 0.25 m2), undisturbed soil cores, giv-ing a total of 752 DP measurements. Based on the similar soil

Page 3: Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics

96 SOIL SCI. SOC. AM. J., VOL. 64, JANUARY-FEBRUARY 2000

Table 1. Soil physical characteristics of the Hj erring soil.

Soil depthm4.2-4.66.0-6.46.4-6.8

Soil type Particle density Bulk density Clay Silt

Sandy clay loamSandy loamLoamy sand

2.69 1.512.68 1.662.67 1.62

24.815.711.2

9.210.85.0

Sand

66.073.583.8

Organicmatter

0.22.11.6

core sizes and sampling and experimental procedures, it wasassumed the data from the different studies could be com-pared. Figure 1 shows the relation between the measured gasdiffusivities at -100 cm H2O of soil water potential (Z)p,ioo)and the corresponding soil air-filled porosities at -100 cmH2O (GIOO). Considering the data were collected from manydifferent soils and soil depths and represent different cultiva-tion practices (conventional, reduced tillage, no tillage), it issurprising a very high correlation between Dp^ and SIOD wasobserved (coefficient of regression r2 = 0.97), yielding

= 2e?0 0.04£ loo [6]

Including terms with Em in the second and fourth power didnot increase the coefficient of regression. Using mean valuesof three to six closely spaced £>P|10o measurements for the 126soil layers (instead of the 752 individual De<m measurements)did not change the best-fit £>p,ioo(eioo) relationship (Eq. [6])but did slightly increase the coefficient of regression (to r2 =0.98). Equation [6] seems to accurately describe the measureddata both at high and low air-filled porosities (Fig. 1). It should,however, be noted that the relative deviations of measuredDp values from Eq. [6] are larger at low em values (<0.1 m3

m~3), probably because DP measurements are relatively moreuncertain in near-saturated soils.

In general, the high values of £>Piloo/£>0 and em in Fig. 1represent the easily drainable sandy soils with high air-filledporosities at —100 cm H2O, while the low values are for clayeysoils. Equation [6] includes a direct effect of the soil type (soilwater characteristic curve) on DPiWo- At "9 - -100 cm H2O, theair-filled pores have an equivalent pore diameter of >30 jjim. Itseems that the total volume of these large pores (= EIOO) largelycontrols the Dftloo/D0 values because the DP100 (sm) relationis universal for different soils and soil depths (Fig. 1).

Equation [6] seems robust for predicting DP at -100 cmH2O. It may also be useful for predicting Df at a soil watercontent equal to natural field capacity for a wide range ofsoils, because field capacity will likely occur close to -100 cmH2O except for very sandy or very clayey soils (Beukes, 1987).At present, however, sufficient data to test Eq. [6] against insitu Df measurements at natural field capacity soil water con-tent are not available. Equation [6] will instead be used as areference-point expression in a more conceptual, SWC-basedDP(e) model.

Soil Water Characteristic-BasedGas Diffusivity Model

Inserting Eq. [6] in the Burdine (1953)-Campbell (1974)relative, unsaturated hydraulic conductivity model, modified

to gas diffusivity in unsaturated soil according to Moldrup etal. (1996) yields

I P \2+3/b—= (24,0 + 0.04e1(W)eml [7]

where b is the Campbell (1974) soil water retention parameter.Equation [7] does not require a reference-point measurementof DP, but two parameters (b and zm) related to the SWCneed to be known. This means the SWC must be measuredat a minimum of two, but preferably more, different soil waterpotentials (to estimate b), including at Mf = —100 cm H2O(to obtain e10o). The chosen soil water potentials should bebelow the air-entry potential for the soil considered, in orderfor the Campbell (1974) SWC model to be valid. Soil waterpotentials of -100 and -500 cm H2O are appropriate for mostsoil types (Moldrup et al., 1999).

In this study, Pick's law is assumed valid. The contributionof Knudsen diffusion is neglected because it is quantitativelyimportant only for very fine-grained materials (Thorstensonand Pollock, 1989). Thus, a direct influence of smaller poresizes on gas diffusion is not considered. Pore-size distributionrather than pore size is thought to influence gas diffusivity,because the pore-size distribution largely governs the connec-tivity and tortuosity of the air-filled pore system. In Eq. [7], thisdependency of gas phase tortuosity on pore-size distribution isdescribed by the Burdine tortuosity-connectivity term usingthe Campbell pore-size distribution (soil water retention) pa-rameter, b.

Figure 2 shows the new D?(e) model principle for a clayloam soil (data from Schj0nning et al., 1999). The b value isdetermined as the slope of the SWC curve in a log-log coordi-nate plot (Fig. 2a). Measurements of the SWC were availableat four different soil water potentials (-30, -100, —500, and—1500 cm H2O) for six closely sampled intact soil cores. Usingmean values of DP measurements on five or more closelysampled, intact soil cores largely reduced the effects of mea-surement uncertainty and local-scale spatial variability on gasdiffusivity in undisturbed soils (Moldrup et al., 1999). Thepredictions by the new SWC-dependent De model (Eq. [7])are shown in a log(DP/D0)-log(e) coordinate plot (Fig. 2a),which yields a straight line with a slope equal to 2 + 3/'b, andin a normal DPID0-e coordinate plot (Fig. 2b).

The new Df(e) model predicts the measured gas diffusivitiesfor the clay loam soil well (within the SD of measured Df).

RESULTS AND DISCUSSIONThe new SWC-dependent DP model was tested

against independent (not included in Fig. 1) gas diffusiv-

Table 2. Soil water characteristics and gas diffusivities at three soil water potentials (—50, —100, and —500 cm H2O) for the Hjerringsoil. The Campbell (1974) soil water retention parameter, b, is given. Numbers in parentheses are standard deviations.

Soil depth (m) 6

4.2-4.66.0-6.46.4-6.8

10.29 (2.37)5.45 (2.70)3.10 (1.15)

£50

0.054 (0.013)0.077 (0.055)0.064 (0.040)

£100_ 3 _ -1

0.070 (0.016)0.105 (0.053)0.093 (0.043)

£500

0.131 (0.024)0.189 (0.055)0.235 (0.079)

/W»o

0.0020 (0.0037)0.0042 (0.0049)0.0023 (0.0017)

Df,tJD,

0.0063 (0.0031)0.0109 (0.0043)0.0076 (0.0028)

OpVA

0.0140 (0.0050)0.0302 (0.0047)0.0441 (0.0203)

Page 4: Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics

MOLDRUP ET AL.: PREDICTING GAS DIFFUSION FROM SOIL WATER CHARACTERISTICS 97

0.16

0 0.1 0.2 0.3 0.4'l

Macro-porosity, e10o (m-i

"Fig. 1. Gas diffusivity as a function of air-filled porosity at -100 cm

H2O of soil water potential. Data for 126 different soils and soillayers (752 measurements).

ity data for 21 soils representing a broad soil textureinterval. The data are from Ball (1981a), Heidman(1989), Freijer (1994), Kruse et al. (1996), Moldrup etal. (1996), and Schj0nning et al. (1999). Soils are bothagricultural and forest soils. The largest data sets arefrom the studies by Freijer (seven soils) and Schj0nninget al. (six soils). In contrast to the case for the 126 soilsin Fig. 1, gas diffusivities for the 21 soils were measuredat four or more soil water potentials (and thus differente values), making it possible to test the new £>P(e) model(Eq. [7]). The number of closely sampled intact soilcores varied between 2 and 18 and averaged about 6.The clay content for the 21 soils was between 1.0 and46.3%, organic matter content between 0.1 and 5.2%,e,oo between 0.1 and 0.37 cm3 cm"3 (except for the mostclayey soil where s100 = 0.05 cm3 cm"3), sampling depthbetween 0 and 1 m, and undisturbed soil core size be-tween 100 and 227 cm3. The three different £>P measure-ment methods used (Ball et al., 1981; Schj0nning, 1985;Freijer, 1994) were assumed comparable because therewas no tendency to place data from one measurementmethod above or below other data.

Figure 3 shows the predictions of the new SWC-dependent DP model compared with the measured datafor six soils from Freijer (1994). The three sandier soils(Fig. 3a-c) as expected have higher sm values comparedto the three more clayey soils (Fig. 3d-f). The new DPmodel (Eq. [7]) accurately predicted the measured DPvalues and, without any kind of model calibration tothe data, gave predictions as good as the calibrated,jointed capillary tube Dr model of Freijer (1994).

Figure 4 shows the prediction of the new D¥ modelagainst data for all 21 soils. The new DP model predictedthe measured gas diffusivities well at both high and lowair-filled porosities (corresponding to high and low D?values in Fig. 4) and for both coarsely textured (0-10%clay) and more finely textured (>10% clay) soils (Fig.4). Dp(e) data for each of the 21 undisturbed soilsshowed a high degree of linearity and did not encounter

oa

OX)o-

-0.8 -0.6 -0.4 -0.2Log (6 or e in m3 m"3)

0.12Lerbjerg3 A

0-1+b=8.7

0.1 0.2e (m3 m'3)

0.3 0.4

D Measured• • - - - Fitted

• Measured Dp/D0(e)—— Predicted Dp/D0(e)

Fig. 2. Illustration of the model parameters in the new gas diffusivitymodel (Eq. [7]). (a) dotted line is fitted soil water characteristiccurve in a log(-ip)-log(6) plot. Straight line is predicted gas diffu-sivity in a log(/V£>o)-log(£) plot, (b) predicted gas diffusivity func-tion in a normal scale plot. The air-filled porosity at -100 cm 1I,O(CIDU) is marked. Standard deviations of both e and /V/>(, (sixclosely spaced measurements) are shown. Data from Schjenninget al. (1999).

significant discontinuites at low air-filled porositieswhen plotted in a log-log scale within a range of DP/D0> 10~4. The good model performance at low air-filledporosities (Fig. 4) supports the concept of a simplepower function model without a threshold soil air-filledporosity but with SWC-dependent parameters that ac-curately predict gas diffusivity in natural, undisturbedsoils.

A comparison of accuracy between the new SWC-dependent Dp model and other frequently used, soiltype-independent DP models is shown in Table 3. Wenote that the data from Freijer (1994) were reduced tomeasurements at six different E values by taking meanvalues at six different soil water potentials (analogousto the data in Fig. 2). Thereby, each of the 21 soils isrepresented by four to six DP measurements to ensureapproximately the same weight for each soil in the statis-tical analysis. A significant increase in accuracy (lowerRMSE) is obtained by introducing the reference-poten-

Page 5: Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics

98 SOIL SCI. SOC. AM. J., VOL. 64, JANUARY-FEBRUARY 2000

0.4

0.3

0.2

0.1

0

0.3

(a) Kootwijk B

3.2% clay

(d) Eijsden Cb=8.6

0.2 - -14% clay

0.1 - - eloft=0.19

(b) Kootwijk Ab=2.8

(c) Oss Cb=3.21.4% clay

0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.50.3

(e) Belvedere Cb=9.2

0.2 - - 16% clay

0.1 --e1(x,=0.13

0.3

0.2 - -

(f) Harderbos Ab=ll . l31% clay

0.1 --£,00=0.17

0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

E (m3 m'3)0.2 0.4 0.6

o Measured Dp/Do — SWC dependent modelFig. 3. Test of the new soil water characteristic-dependent Df/D(l model (Eq. [71) against independent gas diffusivity data for six undisturbed

soils. Data from Freijer (1994).

tial expression Df_m(£m), together with the Burdine-Campbell type expression for relative increase or de-crease in -Dp(s). The new model (Eq. [7]) accuratelypredicted the observed soil-type effects on D? and gavea reduction in RSME of prediction of 83, 77, and 58%compared to the soil type-independent Penman (1940),Millington-Quirk (1960), and Millington-Quirk (1961)models, respectively (Table 3). For the four most sandysoils, the Millington and Quirk (1961) model gave pre-dictions as good as the SWC-dependent model (Eq. [7]),

0.1 --

0.01 --

0.001 --

0.00010.0001 0.001 0.01 0.1 1

Measured Dp/D0

00-10% clay A>10%clayFig. 4. Scatterplot comparison of predicted (Eq. [7]) and measured

gas diffusivities for 21 undisturbed soils. Note logarithmic scale.

Q"O

but for the remaining 17 soils Eq. [7] was superior. TheSWC-dependent model also performed better (39% re-duction in RMSE) than the soil type-independent PMQmodel by Moldrup et al. (1997). This is promising be-cause the PMQ model was calibrated to a data set thatincluded 15 out of the 21 soils considered here, in orderto obtain the optimal value of the PMQ model constantfor undisturbed soil (m = 3 in Eq. [4]).

A basic difference between Eq. [7] and the classical,DP(e) models is that a reference-point gas diffusivity ispredicted at ̂ = -100 cm H2O in Eq. [7]; it is predictedfor dry soil conditions (at the air-filled porosity equalto the soil total porosity, <5 = O) in the classical models.At e = O, the Penman (1940) model becomes Df/D0 =0.66 O while both Millington and Quirk (1960, 1961)models become DPAD0 = €>4'3 equal to the Millington(1959) model. To understand the difference in modelperformance, it is therefore interesting to compare themodels at very high air-filled porosities close to the soiltotal porosity. Figure 5 shows the predictions by thePenman (1940) and the Millington and Quirk (1961)models compared to the new SWC-dependent DP

Table 3. Test of the Penman (1940), Millington and Quirk (1960,1961) (MQ), Modrup et al. (1997) (PMQ), and new soil watercharacteristic-dependent gas diffusivity (SWC-£)p) modelsbased on root mean square error (RMSE) of prediction for 21undisturbed soils.

EquationPenman

[1]MQ (1960)

[3]MQ (1961)

[2]PMQ[4]

SWC-/JP[7]

RMSE 0.110 0.076 0.045 0.031§ 0.019

§ Calibrated to data set including 15 of the 21 soils.

Page 6: Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics

MOLDRUP ET AL.: PREDICTING GAS DIFFUSION FROM SOIL WATER CHARACTERISTICS 99

0.1 0.2 0.3 0.4Measured Dp/D0

0.5

• SWC dependent model n Penman A MQFig. 5. Scatterplot comparison of predicted soil water characteristic-

dependent (SWC-dependent), Penman (1940) and Millington andQuirk (1961; MQ), and measured gas diffusivities at high air-filledporosities (el<& > 0.9).

model, considering DP data for which e/<I> > 0.9. It isobvious that both classical models largely overpredictdiffusivities at high air-filled porosities while the newSWC model satisfactorily predicts the measured data(r2 = 0.75). The SWC-dependent model (Eq. [7]) alsoperformed better at high air-filled porosities when com-pared to the other one- and two-parameter Df models(Buckingham, 1904; Call, 1957; Lai et al., 1971). Theeffects of using the Z)p,ioo(£ioo) expression in combinationwith the Burdine-Campbell tortuosity description, Eq.[7], gives accurate predictions even when extrapolatedto nearly dry soil conditions (e/<D > 0.9), while the classi-cal soil type-independent gas diffusivity models failedto adequately describe gas diffusivity in near-dry soil(Fig. 5).

In general for the 21 soils, the new SWC-dependentmodel accurately predicted DP over the whole e interval(Fig. 4 and 5, Table 3). The Penman (1940) model over-predicted Dp in the whole e interval. The Millingtonand Quirk (1961) model overpredicted De at high air-filled porosities (and performed worse than the Penmanmodel, Fig. 5), did well predicting DP at intermediateair-filled porosities and, especially for clayey and loamysoils, underestimated DP at low air-filled porosities (typ-ically below 0.10-0.15 m3 m^3).

The 21 soils in Fig. 4 represent surface or near-surfacesoils, and gas diffusivities in deep subsoils have not, toour knowledge, previously been measured. Therefore,we measured Df in the 4 to 7 m soil depth at the Hj0rringformer manufactured-gas plant site (Tables 1 and 2)and tested the new SWC-dependent Df model againstthe measured gas diffusivities. Figure 6 shows that thenew Df model (Eq. [7]) also predicts the measured datawell for the three subsurface soil horizons, and overallperforms better than the widely used Penman (1940)and the Millington and Quirk (1961) models. The Mil-lington and Quirk model performs well for the twohighest Df values but underestimates D? greatly for the

4)•*rfo

0.1 --

0.01 --

0.001 --

0.00010.0001 0.001 0.01 0.1

Measured Dp/D0

• SWC dependent model D Penman A MQFig. 6. Scatterplot comparison of predicted soil water characteristic-

dependent (SWC-dependent), Penman (1940) and Millington andQuirk (1961; MQ), and measured gas diffusivities for the threeHjerring subsoil horizons. See Table 2 for data. Note logarith-mic scale.

remaining seven values corresponding to air-filled po-rosities below 0.13 m3 m~3. The Penman (1940) modeloverestimates Df for all nine values (Fig. 6). Thus, simi-lar conclusions concerning model performance for the21 surface soils and the 3 subsurface soil horizons werereached. It is promising that the new SWC-dependentmodel accurately predicted the smaller values of gasdiffusivity (ZVA. < 0.02-0.05 [Fig. 2-4 and 6]), wheregas diffusivity likely becomes limiting for soil aeration,plant growth (Grable and Siemer, 1968), and aerobicbiodegradation of organic chemicals in contaminatedsoils.

The presently available gas diffusivity data for undis-turbed soils were measured on relatively small intactsoil cores (between 100 and 227 cm3 sample volume).Although the new SWC-dependent DP model well pre-dicts measured diffusivities in the form of mean DPvalues (preferably based on five or more closely sampled[0.4-0.5 m distance] intact soil cores), both small- andlarge-scale spatial variability may be significant (Rols-ton et al., 1991). Thus, gas diffusivity measurements ondifferent sample sizes and evaluation of spatial variabil-ity and scale dependency is an important scope of futuregas diffusivity research.

CONCLUSIONSA soil water characteristic- and thus pore-size distri-

bution-dependent model for predicting gas diffusivityin undisturbed soil is presented. The model requiresmeasurement of the SWC curve at a minimum of twodifferent soil water potentials, including one at -100cm H2O. It accurately predicted gas diffusivity in 21surface-near-surface soils and 3 deep subsurface soilhorizons representing a broad soil texture interval inagricultural, forest, and urban soils. The new modelperformed better than the widely used, soil type-independent gas diffusivity models. We therefore rec-

Page 7: Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics

100 SOIL SCI. SOC. AM. J., VOL. 64, JANUARY-FEBRUARY 2000

ommend its use in vadose zone contaminant transportand fate models, if gas diffusion and reaction simulationsare to be representative for natural, undisturbed soilconditions.

ACKNOWLEDGMENTSThis work was supported by the Danish Technical Research

Council's research talent project entitled "New Methods forMeasuring and Predicting Liquid and Gaseous Phase Trans-port Properties in Undisturbed Soils," the project entitled"Continuation and Evaluation of In Situ Remediation atHj0rring Former Manufactured Gas Plant Site" (funded bythe Danish EPA in cooperation with NIRAS Consulting Engi-neers A/S), the county government of Northern Jutland, themunicipal government of Hj0rring, grant 5P42ESO4699 fromthe National Institute of Environmental Health Sciences, NIH,and the USEPA (R819658) Center for Ecological Health Re-search at Univ. of California-Davis. The contents of this publi-cation are solely the responsibility of the authors and do notnecessarily represent the official view of the NIEHS, NIH, orEPA. The authors gratefully acknowledge a travel grant fromthe Japanese Ministry of Education, Science, Sports, and Cul-ture (Monbushu International Scientific Research Program,Joint Res. 10044162).