Biodegradation of petroleum hydrocarbons: modeling and ...lib.ugent.be/fulltxt/RUG01/001/789/944/RUG01-001789944_2012_0001_AC.pdfconsists of injection of a gas mixture of reactants

Faculteit Bio-ingenieurswetenschappen

Academiejaar 2010 – 2011

Biodegradation of petroleum hydrocarbons: modeling and

performance check of a respiration field test

Michiel Van Gestel

Promotor: Prof. dr. ir. Piet Seuntjens

Tutor: ir. Jo Bonroy

Masterproef voorgedragen tot het behalen van de graad van

Master na Master in de Milieusanering en het Milieubeheer

Faculteit Bio-ingenieurswetenschappen

Academiejaar 2010 – 2011

Biodegradation of petroleum hydrocarbons: modeling and

performance check of a respiration field test

Michiel Van Gestel

Promotor: Prof. dr. ir. Piet Seuntjens

Tutor: ir. Jo Bonroy

Masterproef voorgedragen tot het behalen van de graad van

Master na Master in de Milieusanering en het Milieubeheer

i

DANKWOORD

Graag wens ik iedereen te bedanken die heeft bijgedragen tot het afwerken van deze thesis.

Ik bedank Prof. Dr. ir. Piet Seuntjens voor het vertrouwen in mij om dit onderwerp uit te

werken. Mijn tutor ir. Jo Bonroy wil ik bedanken voor zijn steun en advies zowel bij het

onderzoek als het schrijven van de scriptie. Zijn opvolging en feedback was voor mij van

grote waarde.

Maarten Volckaert wil ik bedanken voor de praktische hulp bij het uitvoeren van staalnames

en veldproeven.

Tenslotte wens ik mijn vriendin en toeverlaat Liesbeth te bedanken voor haar eindeloos

geduld en om me nogmaals te steunen bij het schrijven van een scriptie. Ik dank ook zowel

mijn als haar ouders voor de goede zorgen en raad, niet enkel het voorbije jaar maar tijdens

mijn gehele studietraject.

ii

TABLE OF CONTENTS

DANKWOORD .......................................................................................................................... i

TABLE OF CONTENTS ........................................................................................................... ii

FIGURES .................................................................................................................................. iii

TABLES .................................................................................................................................... iv

SYMBOLS ................................................................................................................................. v

Greek ...................................................................................................................................... v

ABSTRACT .............................................................................................................................. vi

SAMENVATTING .................................................................................................................. vii

1. Introduction ......................................................................................................................... 1

1.1. Vadose zone respiration tests ...................................................................................... 1

1.2. Passive oxygen transport in soils ................................................................................. 2

2. Materials and methods ........................................................................................................ 6

2.1. Site description ............................................................................................................ 6

2.2. Respiration check ........................................................................................................ 7

2.3. Symmetry and homogeneity check .............................................................................. 8

2.4. Respiration field test .................................................................................................... 8

2.5. Modeling ...................................................................................................................... 9

3. Results and discussion ...................................................................................................... 11

3.1. Respiration check ...................................................................................................... 11

3.2. Soil physical parameters ............................................................................................ 12

3.3. Symmetry and homogeneity check ............................................................................ 14

3.4. Respiration field test .................................................................................................. 16

3.5. Model performance .................................................................................................... 20

4. Conclusion and scope for further investigation ................................................................ 23

5. Appendix ........................................................................................................................... 24

6. References ......................................................................................................................... 28

iii

FIGURES

Figure 1 Setup outline ................................................................................................................ 6

Figure 2 Schematic overview of the numerical finite element model with boundaries ........... 10

Figure 3 Moisture retention curve to determine values for b according to Campbell (1974) .. 10

Figure 4 Measured oxygen levels for an ex-situ respiration check .......................................... 11

Figure 5 Moisture content in function of depth ........................................................................ 12

Figure 6 Air filled porosity in function of depth ...................................................................... 12

Figure 7 Measured diffusibility in function of depth ............................................................... 13

Figure 8 Measured diffusibility in function of moisture content ............................................. 13

Figure 9 Measured diffusibility in function of air filled porosity ............................................ 14

Figure 10 Symmetry and homogeneity check (advective transport).. ...................................... 15

Figure 11 Symmetry and homogeneity check (diffusive transport only) ................................. 16

Figure 12 Respiration field test measurement data .................................................................. 17

Figure 13 Steady state respiration rates .................................................................................... 18

Figure 14 Soil oxygen profiles 10 days after carbon source injection ..................................... 19

Figure 15 Contour plot for the steady state respiration, constructed using measured

diffusibility data ....................................................................................................................... 20

Figure 16 Effective diffusion coefficient in function of gravimetrical moisture content,

measurements and model estimations ...................................................................................... 22

Figure A-1 Soil moisture characteristic curve (effective water head in m3.m

-3) ...................... 24

Figure A-2 Contour plot for the steady state respiration, constructed using the Penman (1940)

model for diffusibility data ....................................................................................................... 24

Figure A-3 Contour plot for the steady state respiration, constructed using the Millington and

Quirk (1959) model for diffusibility data ................................................................................. 25

Figure A-4 Contour plot for the steady state respiration, constructed using the model

suggested by Jin and Jury (1996) for diffusibility data ............................................................ 25

Figure A-5 Contour plot for the steady state respiration, constructed using the Marshall (1959)

model for diffusibility data ....................................................................................................... 26

Figure A-6 Contour plot for the steady state respiration, constructed using the Moldrup et al.

(2000a) model for diffusibility data ......................................................................................... 26

Figure A-7 Contour plot for the steady state respiration, constructed using the Troeh et al.

(1982) model for diffusibility data ........................................................................................... 27

iv

TABLES Table 1 Soil physical parameters ............................................................................................. 14

Table 2 Diffusibility model performance ................................................................................. 20

v

SYMBOLS

b Campbell (1974) PSD index

Ca air phase oxygen concentration (mg .m-3

)

Cw liquid phase oxygen concentration (mg .m-3

)

D0 diffusion coefficient in free air (m2.s

-1)

De diffusion coefficient in soil air (m2.s

-1)

fOC organic carbon content (%)

H Henry’s constant (-)

J mass flux (mg .m-2

.s-1

)

Kb biodegradation rate (mg .kg-1

.h-1

)

Kd liquid-solid partitioning constant (m3.kg

-1)

KO2 O2 usage (% .h-1

)

r respiration rate (mg O2 .kg-1

h-1

)

Sa air saturation (m3 air . m

-3 pore space)

u parameter to represent blocked pores (m3.m

-3)

v parameter to control curvature (-)

Greek

α constant in the Penman (1941) diffusivity model taken to be (0.66)

ε air filled porosity (m3 air .m

-3 soil)

ε100 air filled porosity at -100 cm water head (m3 air .m

-3 soil)

θa volumetric air content (m3.m

-3)

θw volumetric water content (m3.m

-3)

ξ relative soil gas diffusivity (-)

ρb bulk density (kg .m-3

)

ρO2 O2 density (1.330 kg .m-3

at 25°C)

ρs particle density (kg .m-3

)

φ total pore space (m3 void .m

-3 soil)

vi

ABSTRACT

Substantial aerobic biodegradation reduces soil remediation costs of petroleum hydrocarbon

spills considerably. Optimizing this aerobic biodegradation requires adequate understanding

and control of the oxygen transport in the soil. Advection-dispersion models used to develop

remediation designs, commonly describe diffusion by means of the free-air soil diffusion

coefficient corrected for tortuosity according to Millington and Quirk (1961). Effective

diffusion coefficient estimates using this model as well as other classical models which

estimate soil gas diffusivity from the air filled pore volume were compared to ex-situ

measurements of the soil diffusion coefficient by means of a two-chamber method. The

resulting advection-dispersion models can be used to estimate the biodegradation during an

in-situ respiration test. Additionally, in-situ oxygen concentration profiles were measured in a

test field with galvanic fuel cell-oxygen sensors (R-17MED Oxygen Sensor, Teledyne

Analytical Instruments, City of Industry, CA) for the determination of the respiration rate.

The accuracy of the estimated biodegradation based on the diffusion coefficient model and

oxygen concentrations was evaluated for a sandy soil in comparison to the ex-situ diffusion

coefficient measurements.

A three-dimensional finite element equilibrium model with radial symmetry was used to

reconstruct the diffusive oxygen transport during the field test and to estimate the respiration.

The fitted respiration rate based on the tortuosity model (Millington and Quirk, 1961)

deviated considerably from the results using measured diffusion coefficients. Best results

were obtained using the model of Moldrup et al. (2000a). The observed deviations indicate

that soil diffusion measurements are required to improve the rough biodegradation estimate

provided by models using the diffusion coefficient approximated by tortuosity models.

vii

SAMENVATTING

Aerobe biodegradatie kan de bodemsaneringskosten voor een vervuiling met

petroleumkoolwaterstoffen substantieel verlagen. Het optimalizeren van de aerobe

biodegradatie vergt een adequate kennis van en controle op het transport van zuurstof in de

ondergrond. De advectie-dispersie vergelijking die vaak gebruikt wordt voor het ontwerp van

saneringsinstallaties beschrijft diffusie meestal met een voor tortuositeit gecorrigeerde

(Millington en Quirk, 1961) diffusieconstante in de vrije atmosfeer. De effectieve

diffusieconstante, geschat met dit model, alsook met andere klassieke tortuositeitsmodellen

die gebruik maken van het luchtgevulde poriengehalte om de diffusibiliteit te schatten werden

vergeleken met ex-situ metingen voor de diffusiecoefficient uitgevoerd met behulp van een

twee-kamer-methode. De resulterende advectie-dispersie modellen werden gebruikt om

biodegradatiesnelheden te schatten gedurende een in-situ respiratietest. Verder werden met

galvanische zuurstofsensoren (R-17MED Oxygen Sensor, Teledyne Analytical Instruments,

City of Industry, CA) eveneens in-situ zuurstofprofielen gemeten in een test veld om de

respiratiesnelheid te bepalen. De correctheid van de geschatte biodegradatie, gebruik makend

van de modellen voor de diffusiecoefficient en de zuurstofprofielen werd voor een

zandbodem vergeleken met die op basis van ex-situ gemeten diffusiecoefficienten.

De respiratie en het diffusieve zuurstoftransport gedurende de veldtest werd geschat met

behulp van een drie-dimensonaal, eindige elementen, evenwichtsmodel met radiale

symmetrie. De respiratiesnelheden bepaald met de tortuositeitsmodellen (Millington en Quirk,

1961) weken aanzienlijk af van de resultaten verkregen met ex-situ gemeten data. De beste

resultaten werden verkregen met het model van Moldrup et al. (2000a). De geobserveerde

afwijkingen tonen echter aan dat de diffusieconstanten in de bodem gemeten moeten worden

om de schattingen voor biodegradatiesnelheden met de tortuositeitsmodellen voor de

schatting van diffusieconstanten te corrigeren.

CHAPTER 1 : INTRODUCTION

1

1. Introduction

Biological treatment can reduce soil cleanup costs considerably (Brown et al. 1999). In-situ

soil remediation techniques further economize due to the absence of earth moving (De Kreuk,

2005). Aerobic treatment of biodegradable contaminants also provides economically

interesting options for in-situ soil remediation because aerobic treatment is generally a faster

process in comparison with anaerobic alternatives.

Aerobic biodegradation techniques require biodegrading micro-organisms as well as oxygen

provided to them. Soil cleanup methods such as bioventing (USACE, 2002), biosparging

(USEPA, 1995b; Brown et al., 1999), bioslurping (Khan et al., 2004), and natural attenuation

(USEPA, 1996) depend on these conditions to perform properly.

Soil respiration tests provide valuable information on the presence of both oxygen and

biodegrading bacteria (USACE, 2002). Quantifying the microbial oxygen consumption allows

for optimizing aerobic biodegradation. A minimum concentration of 5% oxygen should

generally be guaranteed for aerobic biodegradation to be optimal (USEPA, 1995a; USACE,

2002).

In this paper a modeling approach for the quantification of microbial oxygen consumption in

the vadose zone is presented. As during the considered field scale respiration test only passive

oxygen transport occurs the diffusion coefficient will determine the oxygen flux. Different

models for scaling the free air diffusion coefficient to soil conditions are compared to

measured data.

1.1. Vadose zone respiration tests Respiration tests can be performed both in-situ and ex-situ. In-situ respiration testing involves

measuring the oxygen consumption in a respirometer. Different methods are available for

oxygen concentration measurements in respirometers, the Flemish Waste Agency (2005)

advises measurements in a continues air flow over a microcosm for soil sanitation feasibility

studies.

More reliable results are obtained by an in-situ soil respiration test as small scale variations in

biodegradation rates occur due to soil heterogeneity (Davis et al., 2003). The U.S. Air Force

has developed a protocol for such an in-situ respiration test. The “start stop” test consists of

injecting air for a short period of time to ensure aerobic conditions. Subsequently air samples

are extracted and analyzed for oxygen and carbon dioxide. Respiration rates are determined

from the oxygen concentration drop over time. Natural background respiration is accounted

for using data from a background well installed in a similar but uncontaminated area. Oxygen

diffusion is included using an inert tracer gas added to the injected air (Hinchee et al., 1992;

USACE, 2002; OVAM, 2005).

Urmann et al. (2005) developed a similar respiration field test. The authors “push pull” test

consists of injection of a gas mixture of reactants (e.g. methane and oxygen) together with a

non-reactive tracer gas. Injection is directly followed by extraction of the gas mixture together

with soil air. Accounting for gas dilution and transport using the tracer gas rate constants can


2

be determined for the microbial conversion of the reactive gas mixture quantifying microbial

activity.

Van De Steene et al. (2007) used a quasi-steady-state model according to Baehr and Baker

(1995) to calculate oxygen consumption rates in biopiles. The authors compared the results to

those calculated using the transient model of Hinchee et al. (1992) in which the oxygen

consumption rate is calculated from the slope of the linear regression curve fitted to the

oxygen depletion as a function of time (according to the U.S. Air Force protocol). Van De

Steene et al. (2007) found the quasi-steady-state model to predict lower oxygen consumption

rates compared to those predicted by the transient method. Errors in oxygen diffusion

modeling were suggested to be responsible for these discrepancies.

1.2. Passive oxygen transport in soils

Similar to solute transport in porous media three distinct processes are distinguished for gas

phase transport in soils. Advective flow, mechanical dispersion and molecular diffusion

determine the oxygen concentration at any place and time during air injection

(Brusseau, 1991).

Bulk movement of oxygen in the soil air phase occurs as a result of pressure gradients in total

air pressure. In case of passive transport these pressure gradients only occur as a result of

specific processes such as atmospheric pressure changes at the soil surface, soil temperature

changes, infiltration and wind blowing over the soil. Due to the time scale and specific test

setup of the respiration test advective transport can be neglected. As a result mechanical

dispersion is omitted in further discussion of soil oxygen transport as well.

Oxygen transport in the soil system will be completely dependent on molecular diffusion

during respiration testing. Mathematically molecular diffusion can be expressed by Fick’s

first law (equation 1).

1

J mass flux (mg .m-2

.s-1

)

De diffusion coefficient in soil air or effective diffusion coefficient (m2.s

-1)

∇Ca air phase oxygen concentration gradient (mg .m-3

.m-1

)

Phase partitioning may have a great influence on soil gas concentrations. In a three phase soil

system oxygen partitions between air and water. Chesnaux (2009) described that in case solid

phase adsorption is absent the advection dispersion equation for solute transport in water can

also be applied for gas phase transport of oxygen. Hence the three dimensional advection-

dispersion equation for oxygen transport in homogeneous soils is described by equation 2.

2

θa volumetric air content (m3.m

-3)

θw volumetric water content (m3.m

-3)

Cw liquid phase oxygen concentration (kg .m-3

)


3

The phase distribution of gas molecules in a three phase soil system is expressed by

Brusseau (1991) as a retardation factor (equation 3).

3

H Henry’s constant (-)

ρb bulk density (kg .m-3

)

Kd liquid-solid partitioning constant (m3.kg

-1)

Considering oxygen does not adsorb on soil particles (Chesnaux, 2009) equation 3 can be

simplified to equation 4.

4

Further simplification of equation 4 is possible when soil oxygen phase transition from gas to

liquid phase is considered to be slow. In this case R can be omitted since the multiplier

becomes 1 (Hamamoto et al., 2009). It must be stated that R as a retardation factor is only of

significance in transient models. At steady state R can be omitted.

Both in transient as steady state models the effective diffusion coefficient can be expected to

have a significant influence on concentrations over time and equilibrium concentrations

respectively. Because of the presence of water and soil particles only part of the cross section

is available for transport i.e. the air filled pore space. Furthermore diffusing particles cover a

longer path length between two points in a soil system compared to free air diffusion. Hence

the effective diffusion coefficient in the soil will be lower.

In order to account for these effects Currie (1960) introduced the relative effective diffusivity

(equation 5).

5

ξ relative effective diffusivity (-)

De diffusion coefficient in soil air (m2.s

-1)

D0 diffusion coefficient in fee air (m2.s

-1)

Soil gas diffusivity is assumed to be independent of the diffusing gas (Currie 1984,

Shimamura, 1992). Proposed relations between diffusivity and volumetric soil air content for

any gas therefore can be applied to oxygen transport.


4

Penman (1940) proposed a simple linear equation to describe the diffusion of carbon disulfide

through packed soil cores (equation 6). The author recommended a constant of 0.66 based on

his tests on samples with air filled pore spaces between 0.195 and 0.676.

6

α constant (0.66)

ε air filled porosity (m3

air .m-3

soil)

Millington and Quirk (1959) proposed a different approach to estimate the diffusivity based

on total soil porosity and the pore saturation of the considered soil air phase (equation 7).

7

φ total soil porosity (m3 void .m

-3 soil)

Sa air saturation (m3 air .m

-3 pore space)

Millington and Quirk (1961) also found a relation between soil gas diffusivity and air filled

porosity which is probably the most used (equation 8).

8

Jin and Jury (1996) compared measured soil gas diffusion coefficient data with model

predictions for a variety of different textured, repacked soils. They found a revised version of

the Millington and Quirk (1961) model to give the best results (equation 9).

9

Troeh et al. (1982) combined the linear equation of Penman (1940) with the approach of

Millington and Quirk (1961). The result is an empirical equation that includes a parameter to

account for blocked (equation 10).

10

with 0 ≤ u < 1

u ≤ ε ≤ 1

1 ≤ v ≤ 2

u parameter to represent blocked pores (m3.m

-3)

v parameter to control the functions curvature (-)


5

Moldrup et al. (2000a) also incorporate the presence of blocked pores. They started from the

Marshal (1959) model (equation 11) to build their water induced linear reduction (WLR)

model. As they found the Marshal (1959) model to give the best results for dry, sieved and

repacked soils, they expanded it with a linear reduction term (ε.φ-1

) to account for water

induced blocking of the air space in pores.

11

12

Gas diffusion in undisturbed soil was found to be influenced by soil type and content of large

pores by Moldrup et al. (2000b). This led to the incorporation of soil water retention data. The

diffusivity was described well for different soil textures at a soil water content corresponding

to -100 cm water head by equation 13.

13

ε100 air filled porosity at -100 cm water head (m3 air .m

-3 soil)

Moldrup et al. (2000b) expanded the model to water contents different to those corresponding

to -100 cm water head by adding a term related to the soil water retention curve. The

Campbell (1974) PSD index (b, the slope of the soil water retention curve in a log-log

coordinate system) is added to equation 13 giving equation 14.

14

b Campbell (1974) PSD index

The goal of this study is to assess the impact of different available soil gas diffusivity models

on the estimation of biodegradation rates. For this purpose a field scale respiration test was

performed and subsequently modeled.

CHAPTER 2 : MATERIALS AND METHODS

6

2. Materials and methods

2.1. Site description

The test field consists of an enclosed, artificially applied soil (95% sand, 2% loam, 3% clay).

The rectangular plot of sandy soil is confined by four impermeable walls which reach to the

bottom of the homogeneous sand layer. The test plot measures 2 m by 3 m while the depth

amounts to 1.60 m. Free drainage is possible through the natural sandy soil located beneath

the controlled soil layer. Infiltration of rain is avoided by a plastic shelter.

A screened filter is placed in the middle of the plot at a depth from 1.40 m to 1.60 m. The

filter served as an injection point and consists of a 0.05 m diameter PVC pipe. The tube was

filled with glass wool and fitted with a filter sock to prevent clogging.

R-17MED Oxygen Sensors (Teledyne Analytical Instruments, City of Industry, CA) were

installed radially at distances of 0.4 m, 0.8 m and 1.2 m around the injection point. A total of

9 sensors connected to a CR10X datalogger (Campbell Scientific, Logan, UT) were installed.

Soil air oxygen content was measured in concentric circles around the injection point. At each

distance the soil air was monitored at 1.60 m, 1.00 m and 0.50 m below the surface. The setup

outline can be seen in figure 1.

Figure 1 Setup outline

Sensor

Depth

(m)

1 1.6

2 1.6

3 1.6

4 1

5 1

6 1

7 0.5

8 0.5

9 0.5

Injection 1.6


7

The controlled sandy soil layer has a particle density (ρs) of 2.64 x 10³ kg .m-³ and organic

carbon content (fOC) of 0.04 %. Soil bulk densities were calculated on three undisturbed soil

samples. Soil moisture content was measured gravimetrically in six different depth intervals

of 0.25 m.

Data on soil moisture content at different pressures (sandbox measurements) for the sandy

layer was available from prior measurements. The soil moisture characteristic curve was

estimated using this data and the van Genuchten (1980; m = 1- 1/n) equation incorporated in

the RETC code for quantifying the hydraulic functions of unsaturated soils (van Genuchten et

al., 1991).

Diffusivities were measured in the laboratory according to the method of Bonroy et al.

(2011). Measurements were performed on undisturbed soil samples set at the previously

measured soil moisture contents.

Soil gas diffusion coefficients were calculated at six depth intervals using measured

diffusivities and the diffusion coefficient in free air. The free air diffusion coefficient was

calculated using the method of Fuller et al. (1966) for calculating diffusion coefficients in

binary pairs of gasses as a function of temperature and pressure. The O2 in N2 diffusion

coefficient was calculated at atmospheric pressure (101325 Pa) and 16°C taken to be the

average soil temperature over 1.60 m of depth.

2.2. Respiration check

The biodegradation capacity in the test plot was tested by an ex-situ respiration test to check

the presence of microbial activity. The underlying natural soil of the plot was selected over

the artificially applied sand layer since low organic carbon contents and high soil oxygen

concentrations in the sandy layer indicated low microbial activity.

A soil sample (1.817 kg) spiked with 0.01724 kg.kg-1

sugar (C12H22O11) was allowed to

mineralize inside an airtight chamber (7.76 x 10-4

m3). Glass beads were added to the sample

to diminish the free air space around the soil sample. Soil water content was determined

gravimetrically. Porosity and air content were calculated based on sample mass, volume and

water content.

The chamber was fitted with a R-17MED Oxygen Sensor (Teledyne Analytical Instruments,

City of Industry, CA) to record head space air oxygen levels. The O2 concentration’s decline

was converted into respiration rates in mg O2 per kg dry soil using equation 15.

15

r respiration rate (mg .kg-1

h-1

)

KO2 O2 usage (% .h-1

)

ρO2 O2 density (1.330 kg .m-3

at 25°C)


8

Respiration rates can be directly converted into biodegradation rates (Kb, mg .kg-1

.h-1

) by

division with the relative amount of oxygen necessary to mineralize the substrate. The

stoichiometric equation for mineralization of sugar yields a correction factor of 1.12 g .g-1

.

Soil sanitation studies often make use of an equivalent hexane (C6H14) biodegradation rate. In

this case a correction factor of 3.53 g .g-1

is be used.

2.3. Symmetry and homogeneity check

The test plot’s artificially applied sandy soil layers homogeneity was checked to ensure the

assumption of symmetry was valid. Nitrogen gas (N2, 99.98% pure) was injected at an

averaged pressure of 2.22 mbar and an averaged throughput of 2.73 x 10-2

m3.s

-1. Injection

pressures were measured by a differential pressure transducer (Honeywell 26PC, Honeywell

Sensing and Control, Freeport, IL). Injected gas mass throughput was measured by a mass

flow sensor calibrated for N2 (Brooks Instruments 58605 Series, Brooks Instruments, B.V.,

Netherlands). Purging lasted until O2 sensor outputs stabilized for sensors located at 0.4 m

and 0.8 m from the screened filter. Steady state O2 concentrations within at least 0.8 m of the

screened filter were assumed at this time. Oxygen levels did not stabilize for sensors located

at 1.20 m of the filter due to time limits.

After this point in time N2 gas injection was stopped and atmospheric O2 was allowed to enter

the soil system from the surface boundary. The test comprises a study of the soil-atmosphere

equilibrium re-establishment. Soil O2 measurements were recorded until complete stable O2

concentration readings were achieved for all sensors. Equilibrium conditions were considered

to be fulfilled when O2 levels ceased rising.

2.4. Respiration field test The low organic carbon level in the sandy soil layer and the consequent low O2 respiration

hinder respiration measurements. To establish a recordable soil O2 profile respiration was

enhanced at the top of the underlying soil. A carbon source (syrup, 5.88% C12H22O11) was

injected in the screened filter and allowed to spread over the natural soil layer at the bottom of

the artificial sandy soil pack. A total carbon source addition of 1 kg in 16 l of water was

injected.

Oxygen, necessary for aerobic biodegradation entered only from the atmosphere-soil system

boundary. Since pressure gradients are not applied in this test all O2 transport is diffusive. A

concentration gradient will thus develop over the sandy soil layer. Soil oxygen levels are

monitored during the test in order to calculate concentration gradients. Concentration

gradients are calculated for the steady state situation when biodegradation, O2 consumption

and supply are constant.


9

2.5. Modeling

The respiration field test is simulated using a mathematical model programmed in Excel.

Incorporation of different gas diffusivity calculations in the mathematical models allows

assessing the diffusion coefficient’s impact on predicting soil O2 fluxes and microbial O2

consumption estimation. Since only Fick’s first law is applied to calculate the O2 flux the

diffusion coefficient is expected to be of importance.

Model selection was based on the need to simulate multiphase (gas and water phase) transport

in a three dimensional grid. Assuming radial symmetry two dimensional models can also be

applicable.

A mesh of 240 nodes was build to model the sand layer. A total of 15 columns and 16 rows of

cells correspond to 0.1 m by 0.1 m cells in most of the model and 0.15 m by 0.15 m cells in

the first row and column of the grid. The grid is build up as a radial slice of the test plot with

the respiration located in the lower left cells (figure 2). Since radial symmetry is assumed

concentrations calculated at a certain place in this slice are equal in a circle around the

injection point with a radius equal to the distance of the injection point and an equal distance

from the soil surface.

The model consists of a set of equations (Fick’s first law) between these cells which state

equilibrium between the O2 concentrations of every cell. Concentration gradients are

calculated between every cell’s middle. A cell’s concentration changes as a result of incoming

and outgoing mass fluxes in vertical and horizontal direction. The mass flux is a function of

the concentration gradient but also of the cell’s location since the fluxes boundary surface

increases with the distance from the injection filter. Diffusive fluxes are calculated using

diffusion coefficients corresponding to the soil gas diffusivity model under investigation.

Both the sides and bottom of the artificial soil layer are considered impermeable layers for O2

diffusion. Fluxes over these boundaries are set to zero by defining a Neumann boundary

condition for O2 transport for each cell side lying on a boundary. Dirichlet boundary

conditions at the atmosphere-soil boundary keep O2 at constant atmospheric levels. Finally

measured O2 concentrations at the points stated in figure 1 are incorporated in the model as

Dirichlet boundary conditions.

The equations are solved iteratively between the boundary conditions until steady state

diffusive fluxes are detected. The convergence criteria is set to 0.0001 g between the

incoming O2 over the soil surface and the lower left cell (where O2 is consumed) is met. A

schematic outline of the model is presented in figure 2.


10

Figure 2 Schematic overview of the numerical finite element model with boundaries

Diffusivity models (equations 1 to 12) are incorporated in the respiration model as calculation

methods for the effective diffusion coefficient based on air filled porosity. Parameters u and v

in the Troeh et al. (1982) model are first estimated using the least squares fit method and

measurement data. The Campbell (1974) PSD index could not be estimated due to the

characteristics of the soil moisture curve. Data points plotted on a log-log scale should

produce a straight line with slope –b. However the data points in the moisture retention curve

(figure 3) show no straight line, hence correct estimation of b and usage of equation 14 is not

possible.

Figure 3 Moisture retention curve to determine values for b according to Campbell (1974)

1.6m

1.5m

i

1.0m

0.5m

0.4m 1.2m0.8m

1 2 3

4 5 6

7 8 9

Dirichlet boundary condition: 21 % O2

Neu

man

n b

ou

nd

ary

con

dit

ion

: N

o F

low

Neu

man

n b

ou

nd

ary

con

dit

ion

: N

o F

low

Neumann boundary condition: No Flow

0,001

0,01

0,1

1

10

100

0,01 0,1 1

Wa

ter p

ote

nti

al

(-b

ars

)

Water content (cm3.cm-3)

CHAPTER 3 : RESULTS AND DISCUSSION

11

3. Results and discussion

3.1. Respiration check Oxygen levels during the ex-situ respiration test are presented in figure 4. The respiration test

was stopped after 30 h and 16 min when no further significant O2 changes were observed.

The O2 consumption is fairly linear up to 15 h and 55 min when O2 levels drop below 0.05

mol .mol-1

. Lower O2 levels result in an exponential decrease of biodegradation due to limited

O2 supply (USEPA, 1995a; USACE, 2002).

A linear regression curve can be fitted to the measurements up to 15 h 55 min. The resulting

curve has a slope of -0.00905 mol O2 .mol-1

.h-1

and an offset of 0.18517 mol .mol-1

O2 (R2 =

0.9931). The offset’s value lower than 0.21 mol .mol-1

is due to the time lag between closing

the airtight chamber and the first measurement.

Application of equation 15 on the linear part of the measurements results in a respiration rate

of 4.72 mg .kg-1

.h-1

. The corresponding sugar biodegradation rate is 4.21 mg .kg-1

.h-1

. The

equivalent hexane biodegradation rate is 1.34 mg .kg-1

.h-1

.

Based on the ex-situ respiration test an in-situ respiration test was considered to be possible

provided a carbon source was added. Respiration occurs in the natural soil underlying the

sandy soil layer.

Figure 4 Measured oxygen levels for an ex-situ respiration check

0

0,03

0,06

0,09

0,12

0,15

0,18

0,21

0 5 10 15 20 25 30 35

Oxy

gen

co

nce

ntr

ati

on

(m

ol.

mo

l-1)

Time (h)


12

3.2. Soil physical parameters Results for the soil physical parameters are given first (summarized in table 1) in order to

interpret results for the soil’s symmetry and homogeneity check. Soil moisture contents rise

linearly (slope = 27.472 kg .kg-1

.m-1

; offset = 1.0487 kg .kg-1

; R2 = 0.9849) in function to

sampling depth with a maximum gravimetrical soil water content of 8.642 % at 1.6 m of

depth and 4.077 % at the surface (figure 5).

Figure 5 Moisture content in function of depth

Air filled porosity is directly related to the soil water content. Soil bulk density is assumed to

be constant over depth. Total porosity is calculated based on the soil bulk density and particle

density. Air filled porosity in turn is calculated as total porosity minus volumetric water

content. Hence results for air filled porosity in function of depth are directly related to those

of the soil water content. A linear regression proved useful for the experiment (slope =

-18.348 m3.m

-3.m

-1; offset = 6.9323 m

3.m

-3; figure 6).

Figure 6 Air filled porosity in function of depth

Assuming a constant total porosity the soil gas diffusivity can only be influenced by moisture

content. Increasing moisture contents with depth correspond to dropping diffusivities due to

the diminishing air space in soil pores (figure 7).

0

0,25

0,5

0,75

1

1,25

1,5

0,04 0,05 0,06 0,07 0,08 0,09

Dep

th (

m)

θg (kg.kg-1)

0

0,25

0,5

0,75

1

1,25

1,5

0,300 0,320 0,340 0,360 0,380

Dep

th (

m)

ε (m3.m-3)


13

Figure 7 Measured diffusivity in function of depth

At approximately 0.75 m of depth a lag is observed in the diffusivity measurements. A large

increase in blocked air filled soil pores due to soil water contents rising from 0.064 kg.kg-1

to

0.068 kg.kg-1

is responsible for this effect (figure 8). The soil moisture characteristic curve

(appendix figure A-1) shows these water contents (0.096 m3.m

-3 to 0.102 m

3.m-

3) to

correspond approximately to field capacity. Capillary water can thus be assumed to be

responsible for the blocking of air filled soil pores.

Measured soil gas diffusion coefficients do not change gradually with the air filled pore space

(figure 9). At an increase of 0.333 m3.m

-3 to 0.339 m

3.m

-3 air filled pore space the soil gas

diffusivity increases dramatically. Based on the moisture content and soil water retention

curve (figure A-1) at these values for air filled porosities a large number of blocked pores are

expected to cause this effect.

Figure 8 Measured diffusivity in function of moisture content

0

0,25

0,5

0,75

1

1,25

1,5

0,1 0,12 0,14 0,16 0,18 0,2

Dep

th (

m)

ξ (-)

0,1

0,12

0,14

0,16

0,18

0,2

0,04 0,05 0,06 0,07 0,08 0,09

ξ (-

)

θg (kg.kg-1)


14

Figure 9 Measured diffusivity in function of air filled porosity

Table 1 Soil physical parameters

ρb (kg.m-3

) ρs (kg.m-3

) φ (m3.m

-3) fOC (%)

1.497x103

2.64x103

0.435 0.04

z (m) θg (kg.kg-1

) ε (m3.m

-3) ξ (-)

*

0.00-0.25 0.04077 0.374 0.2384

0.25-0.50 0.05309 0.355 0.1872

0.50-0.75 0.06403 0.339 0.1775

0.75-1.00 0.06841 0.333 0.1188

1.00-1.25 0.08011 0.315 0.1076

1.25-1.50 0.08642 0.306 0.1016 *Based on measurements (Bonroy et al., 2011)

3.3. Symmetry and homogeneity check

Sensor readings for the first phase of the test fields symmetry and homogeneity check are

presented in figure 10. Nitrogen gas injection lasted for 3h 31min. During the test O2 levels

start to drop first close to the injection point. At 1.2 m distance changes in sensor output

readings occured last. A faster change for oxygen levels on 1 m depth compared to 1.6 m of

depth at 0.4 m distance from the injection point indicated an importance upward advective

and diffusive flux of N2 gas.

The minimum O2 level was primarily determined by distance from the injection filter.

Secondly O2 levels dropped first at 1.6 m depth and last at 0.5 m depth. This sequence of O2

level changes is the result of the simultaneous radial advective and diffusive flux from the

injection well and the diffusive O2 flux towards the soil-atmosphere boundary.

The obtained results for the first phase were in correspondence with those expected for a soil

which is homogeneously constructed in a radial symmetry around the injection point.

0,1

0,12

0,14

0,16

0,18

0,2

0,300 0,320 0,340 0,360 0,380

ξ (-

)

ε (m3.m-3)


15

Figure 10 Symmetry and homogeneity check (advective transport). The sensor at 0.8 m distance and 1 m depth is not

included since unrealistic values were observed due to sensor malfunction.

Soil oxygen sensor outputs for the second phase (no N2 injection; only diffusive O2 transport)

of the symmetry and homogeneity check are presented in figure 11. Measurements were

stopped after 100 h when no further significant changes in O2 levels were observed and O2

levels had nearly risen to atmospheric levels.

For the time lapse to soil-atmosphere equilibrium due to O2 diffusion from the field surface

only the sensor depth was a determining factor. Sensors located closest to the surface first

reached atmospheric O2 levels. Equal depths at different distances from the injection point

reached equilibrium equally fast provided initial O2 levels were similar.

Diffusive O2 fluxes from the atmosphere towards the sandy soil system corresponded to the

expectations for a homogeneous soil, constructed symmetrically around the center point

(injection filter). The assumption of a constant effective diffusion constant over horizontal

distance held.

Based on the symmetry and homogeneity check the assumption of a homogeneous test plot

was valid. The effective diffusion constant is considered to vary only in depth due to the

linearly changing moisture content over depth.

0

0,03

0,06

0,09

0,12

0,15

0,18

0,21

0 0,4 0,8 1,2 1,6 2 2,4 2,8 3,2 3,6

Oxy

gen

co

nce

ntr

ati

on

(m

ol.

mo

l-1)

Time (h)

0.4m Distance

0.5m deep

1.0m deep

1.6m deep

0.8m Distance

0.5m deep

1.0m deep

1.6m deep

1.2m Distance

0.5m deep

1.0m deep

1.6m deep


16

Figure 11 Symmetry and homogeneity check (diffusive transport only)

3.4. Respiration field test Results for O2 levels during the in-situ respiration test are presented in figure 12. Although a

minimal O2 level was found after 9 days measurements lasted 23 days. The O2 level’s time

path due to respiration of the applied carbon source is clearly visible closest to the injection

point (i.e. at 1.6 m deep at 0.4 m distance of the injection point). Soil O2 levels at the other

measurement points change in approximately the same relative order as observed in the

symmetry and homogeneity check. As a result respiration is considered to occur only close to

the injection point. The injected carbon source is assumed to have spread poorly over the

sandy layer’s underlying natural soil. Considerable amounts of solute might have left the

system under study due to drainage.

Microbial soil O2 consumption occurs as can be seen in the sensor readings 1.6 m deep, at 0.4

m distance of the considered point of respiration. Given the low organic carbon levels the soil

system behaves as an oligotrophic environment containing only small numbers of micro-

organisms. The number of bacteria to immediately start metabolizing the carbon source was

considered low. The oligotrophic environment in combination with an initial substrate

concentration of 62.5 mg.l-1

resulted in logarithmic biodegradation kinetics (Simkins and

Alexander, 1984), hence O2 consumption will also followed a logarithmic path.

Oxygen levels only started to fall after approximately 2 days indicating very low respiration

rates before this time, due to the low initial number of metabolizing bacteria. After 2 days the

lag phase was over and bacteria were both adapted to the carbon source and increasing in

numbers. Biodegradation rates picked up and O2 levels dropped. Due to the developing

0

0,03

0,06

0,09

0,12

0,15

0,18

0,21

0 20 40 60 80 100

Oxy

gen

co

nce

ntr

ati

on

(m

ol/

mo

l-1)

Time (h)

0.4m Distance

0.5m deep

1.0m deep

1.6m deep

0.8m Distance

0.5m deep

1.6m deep

1.2m Distance

0.5m deep

1.0m deep

1.6m deep


17

concentration gradient a diffusive O2 flux towards the injection point established itself. After

approximately 9 days equilibrium between O2 consumption and supply has installed. At this

time the respiration rate was equal to the rate of diffusion from the soil-atmosphere boundary.

After approximately 12 days O2 levels started to rise again. Due to declining amounts of

available carbon source the O2 consumption rate diminished. Soil O2 concentration gradients

were established in correspondence to the diffusive atmospheric O2 flux required to provide

sufficient O2 for respiration.

Figure 12 Respiration field test measurement data. Measurement data for the oxygen sensor at 1 m depth, at 0.8 m

distance from the injection well is not provided due to sensor malfunction.

The transient method of Hinchee et al.(1992) can be used to estimate the respiration rate.

Oxygen concentrations can be considered to be linear over time between day 6 and 7. At this

time O2 usage amounts to 9.72 x 10-4

mol O2 .mol-1

air.h-1

. Assuming all O2 to come from half

a sphere with radius 0.4 m around the injection point the respiration rate corresponds to

53.72 mg O2 .h-1

. If all O2 is assumed to be used for respiration of the added carbon source

and the respiration rate is considered to be constant, after 10 days 0.01151 kg or only 1 % of

the carbon source is consumed. This would either mean a great part of the solute (99 %)

drained out of the system under study or the respiration rate is underestimated. It is concluded

that the found respiration rate is a considerable underestimation since O2 supply by diffusion

is not accounted for and measurements were not conducted in the zone where respiration

occurred.

Using a numerical finite element model with Fick’s first law for diffusive O2 transport trough

the soil system the respiration rate was also estimated. Assuming steady state conditions at

any time and using the measured soil O2 concentrations as Dirichlet boundary conditions

0,09

0,12

0,15

0,18

0,21

0 5 10 15 20 25

Oxy

gen

co

nce

ntr

ati

on

(m

ol.

mo

l-1)

Time (days)

0.4m Distance

0.5m deep

1.0m deep

1.6m deep

0.8m Distance

0.5m deep

1.6m deep

1.2m Distance

0.5m deep

1.0m deep

1.6m deep


18

respiration rates are calculated every half hour (figure 13). However at the start of the

experiment O2 within the soil pores was first consumed, only when concentrations dropped a

gradient, and thus O2 fluxes established. Oxygen consumption around the injection point and

diffusive O2 supply from the soil-atmosphere boundary can thus only assumed to be in

equilibrium later on in the experiment. After 12 days the O2 concentration 1.6 m deep at 0.4 m

distance from the injection point started to rise again. The O2 concentration and consumption

therefore is considered to describe steady state conditions best 12 days after the carbon source

is injected.

At this time the O2 consumption rate was estimated to be 4117 mg O2 .h-1

. If O2 consumption

is considered to be only used for respiration of the added carbon source and respiration rates

are considered constant over time, after 10 days 0.88221 or nearly 90 % of the carbon source

is consumed. A minimum of 10 % of the solute can be considered to have drained out of the

sandy soil layer.

Figure 13 Steady state respiration rates

A soil O2 profile was drawn at the steady state situation taken 12 days after carbon source

injection (figure 14). At 1.2 m distance of the injection point no significant change of O2 level

over depth was noticeable. Oxygen consumption has not reached levels high enough to distort

O2 levels at 1.2 m distance of the carbon source. The assumption of radial symmetry therefore

was proven to be valid. The rectangular geometry of the test plot will have no influence since

O2 concentrations are constant at 1.2 m from the injection point.

At 0.4 m distance of the injection point a significant O2 concentration drop over depth was

noticeable. Oxygen levels did not drop linearly from 0 m to 1.6 m depth. This was due to both

the geometrical outline of the experiment and the diminishing soil gas diffusivity over depth.

If imaginary spheres were constructed around a single point where respiration occurs, mass

transfer should be constant over each boundary of those spheres. However fluxes do not, since

for smaller radii larger fluxes are necessary to transport an equal total amount of mass. Hence

given a constant diffusion coefficient O2 concentration gradients will become steeper with

increasing depth. In addition to this effect the lower diffusivity with increasing depth required

a steeper concentration gradient since the effective diffusion coefficient otherwise resulted in

a lower mass flux.

2500

2700

2900

3100

3300

3500

3700

3900

4100

4300

4500

0 5 10 15 20

Oxy

gen

co

nsu

mp

tio

n

(mg

O2.h

-1)

Time (days)


19

Figure 14 Soil oxygen profiles 10 days after carbon source injection

The effects of the test outline and changing soil gas diffusivity over depth can be seen clearly

in a contour plot constructed with data from the numerical finite element diffusion model

using measurement data for diffusivities (figure 15). Iso-concentration lines become gradually

closer to each other as the distance from the surface increases. This effect is also visible as the

distance from the injection point (bottom left) increases in the x direction. In this case not the

changing diffusivity but only the radial symmetry is responsible for the effect since the

effective diffusion coefficient is constant at a given depth. White marks indicate the

coordinates of O2 concentration measurements used as Dirichlet boundary conditions.

Measurements at 0.8 m distance and 1 m deep as well as at 1.2 m distance and 1.6 m deep are

missing due to sensor failure. Bending of the concentration contour around the measurement

data for the sensor at 0.8 m distance, 0.5 deep was considered an artifact due to variations in

sensor readings (concentration difference < 0.01 mol .mol-1

).

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

0,09 0,12 0,15 0,18 0,21D

epth

(m

)

Oxygen concentration (mol .mol-1)

0.4m

Distance0.8m

Distance


20

Figure 15 Contour plot for the steady state respiration, constructed using measured diffusivity data

3.5. Model performance Model performance for each different studied soil gas diffusivity estimation model is assessed

both on correspondence of measured effective diffusion coefficients to predicted ones in

function of soil moisture content as on calculation of the modeled respiration. Results are

given in table 2. Graphical data is presented in figure 16, data for the Millington and Quirk

(1959) model is not shown because the model greatly overestimates diffusion coefficients.

Table 2 Diffusivity model performance

Model Penman

(1940) Marshall

(1959)

Millington

& Quirk

(1959)

Millington

& Quirk

(1961)

Jin &

Jury

(1996)

Troeh et

al. (1982) Moldrup et al.

(2000a)

Correlation for ξ 0.956 0.958 0.960 0.962 0.959 0.956 0.960

SSE on De (x10-4

) 12.91 5.86 158.59 1.24 5.61 1.22 1.48

Steady state respiration

(mg.h-1

) 5557 5056 11071 3716 5288 3997 3997

Relative difference to

respiration modeled

with measurement

data for ξ (%)

34.98 22.81 168.91 -9.74 28.44 -2.91 -2.91


21

All models give a rather high correlation between measured and predicted soil gas diffusivity

data indicating they all manage to capture the change in effective diffusion coefficient as soil

moisture contents rise. However the Penman (1940) as well as the Millington and Quirk

(1959) and revised Millington and Quirk (1961) (referred to as Jin and Jury (1996) model as

they suggest to use this) model registered a high sum of squared errors compared to the other

models. It was graphically verified (figure 16) that the models overestimated the diffusion

coefficient in the sandy soil. Sallam et al. (1984), Jin and Jury (1996) and Aachib et al. (2004)

also reported the Penman (1940) model to overestimate diffusivities. However Jin and Jury

(1996) found the revised Millington and Quirk (1961) model to describe diffusivities best.

As a result the application of any of these models to calculate the steady state respiration rate

overestimates the diffusive flux and thus respiration (table 2). Figures A-2, A-3 and A-4 in

appendix show the contour plots for calculated soil O2 levels using the Penman (1940),

Millington and Quirk (1959) and revised Millington and Quirk (1961), referred to as Jin and

Jury (1996) model respectively. Soil O2 concentrations did not change significantly as they

were mainly controlled by the Dirichlet boundary conditions. As a result the total mass

transfer was increased to maintain these measured concentration gradients.

The Marshall (1959) model gave rather good estimates for the effective diffusion coefficient

at low soil moisture conditions (figure 16). This was in correspondence with the results of

Moldrup et al. (2000b) who found this model to describe soil gas diffusion coefficients best in

dry, sieved and repacked soil. At higher soil moisture contents, however, the Marshall model

also overestimated diffusion coefficients. As an effect the sum of squared errors and estimated

respiration rate were very similar to those estimated using the Jin and Jury (1996) model

(table 2). The contour plot for calculated soil oxygen levels (appendix, figure A-5) is very

similar to that constructed using the previous models to estimate the soil gas diffusivity.

Moldrup et al. (2000a) added a term to address the overestimation problems due to water

induced changes at higher moisture contents. The authors found the model to accurately

describe soil gas diffusion coefficients in sieved and repacked soils at different water

contents. In the sandy soil considered in this study it significantly improved the fit towards

higher moisture contents (figure 16) but it seems to cause an underestimation of the

diffusivity at low moisture contents. In general the model slightly underestimated the

diffusion coefficient but it described effective diffusion better than the previously described

models (table 2) only leading to a small negative deviation of the estimated respiration rate

(table 2). Figure A-6 (in appendix) shows the contour plot for soil oxygen levels at steady

state calculated using the model according to Moldrup et al. (2000a). At 1.6 m of depth, in the

x direction the concentration gradient was larger as compared to the previous models due to

the lower diffusion constant at this depth.

Next to Moldrup et al. (2000a) also Troeh et al. (1982) tried to incorporate water-induced

changes using two experimental parameters u and v. The parameters in this study were

obtained using a least squares fitting method (u = 0.216 and v = 1). Due to the experimental

nature of the model a good fit is evident. Although parameter u should account for water-

induced blocking of the soil pores this drop at approximately 0.68 kg water.kg-1

dry soil was


22

not modeled. Generally the model slightly underestimated effective diffusion coefficients

(figure 16) giving a lower respiration rate as compared to the measurement data (table 2). For

this sandy soil the model was considered equally accurate as the model proposed by Moldrup

et al. (2000a). Oxygen concentrations as a contour plot are depicted in appendix, figure A-7.

The most used model of Millington and Quirk (1961) underestimated the diffusion constant at

low soil moisture content, but seemed to score best at the higher soil moisture contents.

Overall the model of Millington and Quirk (1961) underestimated diffusion coefficients for

the sandy soil. This is in correspondence with the findings of Sallam et al. (1984).

Underestimation of the diffusion coefficients also resulted in a significant underestimation of

the respiration rate (table 2). The contour plot for O2 concentrations during steady state using

the Millington and Quirk (1961) can be seen in appendix, figure A-8.

In an overview of Xu et al. (1992) exponential relationships such as the model of Troeh et

al. (1982) are expected to give the best fit. Although measurement data in this study were best

described by the exponential relationship suggested by Moldrup et al. (2000a) fitting of the

experimental parameters to the model of Troeh et al. (1982) did not result in an exponential

function (v = 1).

Figure 16 Effective diffusion coefficient in function of gravimetrical moisture content, measurements and model

estimations

0,0150

0,0200

0,0250

0,0300

0,0350

0,0400

0,0450

0,0500

0,0550

0,03 0,04 0,05 0,06 0,07 0,08 0,09

De

(cm

2.s

-1)

θg (kg.kg-1)

Measurements

Penman (1940)

Marshall (1959)

Millington & Quirk (1959)

Millington & Quirk (1961)

Jin & Jury (1996)

Troeh et al. (1982)

Moldrup et al. (2000a)

CHAPTER 4 : CONCLUSION

23

4. Conclusion and scope for further investigation Diffusive soil O2 transport during a respiration test in an artificial sandy soil was modeled by

a numerical finite element algorithm with radial symmetry using Fick’s first law and steady

state soil O2 concentrations, giving acceptable respiration rates when measured data for the O2

diffusion coefficient was used. The models performance was further investigated for field

scale testing in natural soils. Expansion of the finite element grid to improve the model’s

resolution might be advisable in this case. Increased amounts of concentration measurements

used as Dirichlet boundary conditions might proof necessary for larger grids to get a quick

and stable model convergence.

Existing models to estimate soil gas diffusivity data were compared to measured diffusivity

data and found to poorly describe the function for diffusivity over the soil moisture content.

None of the models adequately described a drop in soil gas diffusivity measurements at

moisture contents near field capacity. Water-induced blocking of soil pores should be

modeled using data from soil moisture retention curves. The proposed method by Moldrup et

al. (2000b) to incorporate the soil moisture retention curve parameter of Campbell (b, 1974)

did not apply to the sandy soil under investigation. Further investigation should be conducted

on the relation between the van Genuchten soil moisture retention curve and soil gas

diffusivity.

For the investigated classical models linking soil gas diffusivity to air filled porosity the

model of Moldrup et al. (2000a) gave the best results for an artificial sandy soil. Steady state

respiration was estimated within 5 % of that estimated using measured diffusivity data.

Application of the commonly used Millington and Quirk (1961) model in the respiration

calculation resulted in deviations of nearly 10 % in a sandy soil. In comparison to the other

classical models this might still be acceptable although the use of measured data is advisable

since underestimation of the respiration rate will lead to under-dimensioning of aeration

systems with considerable effects on soil cleanup time as a result.

CHAPTER 5 : APPENDIX

24

5. Appendix

Figure A-1 Soil moisture characteristic curve (effective water head in m3.m-3)

Figure A-2 Contour plot for the steady state respiration, constructed using the Penman (1940) model for diffusivity

data


25

Figure A-3 Contour plot for the steady state respiration, constructed using the Millington and Quirk (1959) model for

diffusivity data

Figure A-4 Contour plot for the steady state respiration, constructed using the model suggested by Jin and Jury

(1996) for diffusivity data


26

Figure A-5 Contour plot for the steady state respiration, constructed using the Marshall (1959) model for diffusivity

data

Figure A-6 Contour plot for the steady state respiration, constructed using the Moldrup et al. (2000a) model for

diffusivity data


27

Figure A-7 Contour plot for the steady state respiration, constructed using the Troeh et al. (1982) model for diffusivity

data

Figure A-8 Contour plot for the steady state respiration, constructed using the Millington and Quirk (1961) model for

diffusivity data

CHAPTER 6 : REFERENCES

28

6. References

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CURRIE, J. (1960) Gaseous diffusion in porous media. Part 2. Dry granular materials, British

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CURRIE, J. (1984) Gas diffusion through soil crumbs: the effects of compaction and wetting,

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Effects of heterogeneity and experimental scale on the biodegradation of diesel,

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DE KREUK, J. (2005) Advantages of in-situ remediation of polluted soil and practical

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FULLER, E., SCHETTLER, P. AND GIDDINGS, J. (1966) A new method for prediction of

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HAMAMOTO, S., MOLDRUP, P., KAWAMOTO, K., KOMATSU, T., AND ROLSTON,

D. (2009) Unified measurement system for the gas dispersion coefficient, air permeability,


29

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Biodegradation of petroleum hydrocarbons: modeling and ...lib.ugent.be/fulltxt/RUG01/001/789/944/RUG01-001789944_2012_0001_AC.pdfconsists of injection of a gas mixture of reactants