Imaging and quantification of preferential solute transport in soil macropores John Koestel and Mats Larsbo

Department of Soil and Environment, Swedish University of Agricultural Sciences (SLU), PO Box 7014,

750 07 Uppsala, Sweden

Correspondence to: John Koestel (john.koestel@slu.se)

Abstract

Despite significant advances during the last decades, there are still many processes related to non-

equilibrium flow and transport in macroporous soil that are far from completely understood. The use

of X-ray for imaging time-lapse 3-D solute transport has a large potential to help advance the

knowledge in this field. We visualized the transport of potassium iodide (20 g iodide l-1 H2O) front

through a small undisturbed soil column (height 3.8 cm, diameter 6.8 cm) under steady-state

hydraulic conditions using an industrial X-ray scanner. In addition, the electrical conductivity was

measured in the effluent solution during the experiment. We attained a series of seventeen 3-D

difference images which we related to iodide concentrations using a linear calibration relationship.

The solute transport through the soil mainly took place in two cylindrical macropores, by-passing

more than 90% of the bulk soil volume during the entire experiment. From these macropores the

solute diffused into the surrounding soil matrix. We illustrated the properties of the investigated

solute transport by comparing it to a 1-D convective-dispersive transport and by calculating the

temporal evolution of the dilution index. We furthermore showed that the tracer diffusion from one

of the macropores into the surrounding soil matrix could not be exactly fitted with the cylindrical

diffusion equation. We believe that similar studies will help establish links between soil structure and

solute transport processes and lead to improvements in models for solute transport through

undisturbed soil. This article has been accepted for publication and undergone full peer review but has not beenthrough the copyediting, typesetting, pagination and proofreading process which may lead todifferences between this version and the Version of Record. Please cite this article as an‘Accepted Article’, doi: 10.1002/2014WR015351

Introduction

Soil macropores have long been recognized as important pathways for preferential water flow and

solute transport [Beven and Germann, 1982; Vogel et al., 2006; Jarvis, 2007]. Despite significant

advances during the last decades, there are still many processes related to non-equilibrium flow and

transport in macroporous soil that are far from completely understood. For example, the exchange of

solutes between the macropores and the surrounding soil matrix and adsorption and degradation of

reactive solutes on macropore walls are processes that need to be investigated further [Köhne et al.,

2002; Jarvis, 2007, Beven and Germann, 2013]. The use of new techniques such as 3-D imaging of

macropore geometries in combination with real-time measurements of solute transport has the

potential to advance the knowledge of non-equilibrium flow and transport in soil macropores [Jarvis,

2007; Wildenschild and Sheppard, 2013].

In recent years several imaging methods have been tested for measuring the 3-D evolution of water

or solute fronts. Most prominently these were electrical resistivity tomography (ERT) [Binley et al.,

1996; Koestel et al., 2009], positron emission tomography (PET) [; Khalili et al., 1998; Boutchko et al.,

2012], single-photon computed tomography (SPECT) [Perret et al., 2000b; Vandehey et al., 2013],

magnetic resonance imaging (MRI) [Amin et al., 1993; Bechtold et al., 2011], neutron computed

tomography (NCT) [Lopes et al., 1999; Kaestner et al., 2007] and X-ray tomography (XRT) [Heijs et al.,

1996; Luo et al., 2008]. PET and SPECT yield rather coarse resolutions of some millimeters or

centimeters. The spatial resolution of ERT is in the same range if the method is applied to small soil

columns with heights and diameters of centimeters up to a few decimeters. XRT, NCT and, in

principle also MRI are better suited to resolve fine structures as they allow resolutions in the

micrometer range. Olsen et al. [1999] presented an illustrative example demonstrating the different

resolutions of ERT and XRT images of soil columns. The strength of ERT is its applicability to larger

scales [e.g. Revil et al., 2004; Nguyen et al., 2009], whereas PET and SPECT may prove useful for

tracing specific radio-labeled organic compounds, colloids, viruses or microbes. MRI is a powerful

2

tool for non-invasive 3-D visualizations of organic materials. MRI has also been used to image the

time-lapse evolution of tracer plumes in sands [e.g. Bechtold et al., 2011]). Its application to

undisturbed soil has, however, been found problematic due to the abundance of elements with

undesirable paramagnetic properties [Cislerova and Votrubova, 2002].

2-D Neutron radiography has often been used for visualizing time-lapse processes like infiltration of

water into soil [e.g. Badorreck et al., 2013] or root-water uptake [e.g. Carminati et al., 2010]. 3-D

imaging studies using this technique in soil science are, however, still scarce. One example is Schaap

et al. [2008], who measured the 3-D resolved water content in a heterogeneously packed sand box

during a drainage and imbibition experiment. The main reason is probably the limited availability of

adequately equipped neutron sources. A similar limitation exists for XRT if a synchrotron beamline is

used for imaging, as for example in Altman et al. [2005] or Wildenschild et al. [2005]. However,

synchrotron XRT was introduced earlier than NCT into geosciences [e.g. Coles et al., 1998], and soil

science applications are more common. The main advantage of synchrotron XRT compared to

industrial or medical XRT is that it provides monochromatic X-ray beams whose wavelengths are

adjustable [Wildenschild and Sheppard, 2013]. This leads to fewer image artifacts and offers the

possibility of visualizing tracers by capitalizing on their X-ray fluorescence properties [Wildenschild

and Sheppard, 2013].

In contrast to NCT, compact XRT scanners are commercially available in the form of medical,

industrial and lately even desktop X-ray scanners. These systems operate with a polychromatic X-ray

beam and, compared to a synchrotron beamline, with less power. Since the early 1980s, numerous

hospitals acquired medical 3-D XRT scanners which were sometimes made available to image soil

samples [Wildenschild and Sheppard, 2013]. The first publications using this technique in soil science

date to the 1980s. In these early studies, XRT was used to map the 3-D distribution of soil bulk

density and water content [Petrovic et al., 1982; Hainsworth and Aylmore, 1983], image the soil

macropore system (i.e., all pores larger than two or three times the XRT resolution) and the

3

distribution of air and water therein [e.g. Hanson et al., 1991; Heijs et al., 1996]. With XRT it is

possible to detect the location of a tracer plume or front if the tracer exhibits a sufficiently large

density contrast to the soil water (Steude et al. [1990]; Anderson et al. [1992]). Comprehensive

reviews on XRT studies within soil science and hydrology have been published by Helliwell et al.

[2013], Taina et al. [2008] and Wildenschild et al. [2002].

Early studies on solute transport that involved XRT were restricted to conventional breakthrough

curve (BTC) experiments where the effluent BTC was compared to the 3-D structure of the

macropore network [Gupte et al., 1996; Olsen et al., 1999]. Similar later studies involved solute

transport models that were parameterized using XRT image-data [Kasteel et al., 2000] or compared

the soil macropore structure with dye staining patterns [Cislerova and Votrubova, 2002;

Vanderborght et al., 2002]. Another notable example is the study by Luo et al. [2010] who used

regression to investigate relationships between structural characteristics of the macropore network

and corresponding BTC features. Finally, significant progress has recently been achieved by Köhne et

al. [2011] who successfully predicted inert tracer BTCs under unsaturated flow conditions from a

pore network model constructed from the statistics of topological features of the X-ray-derived pore-

space. However, none of the above discussed studies contain images of the evolution of a solute

plume or front.

Studies that include time-lapse XRT image data of the progression of a solute plume in two or three

dimensions are still scarce. Already in the early 1990s, Steude et al. [1990] presented vertical cross-

sections of a tracer plume progression, and Anderson et al. [1992] presented tracer velocity

distributions in horizontal cross-sections of repacked soil columns. To our knowledge, the first 3-D

XRT-derived solute transport data was published by Clausnitzer and Hopmans [2000]. They

investigated solute breakthrough in a sub-centimeter-scale sample with packed glass beads using an

industrial XRT scanner. The temporal resolution was, with approximately 30 minutes per image,

relatively poor but the spatial resolution of the equipment was, however, comparably good and

4

provided voxel sizes with edge lengths below 100 µm. While the article of Clausnitzer and Hopmans

[2000] focused on technical aspects of the time-lapse imaging process, Perret et al. [2000a] published

a dataset including thirteen horizontal time-lapse 2-D sections of an inert tracer front progression in

an 85 cm long and 7.7 cm wide saturated, undisturbed soil column. The experiment of Perret et al.

[2000a] was conducted with a medical X-ray scanner which provided a spatial resolution of 195 µm in

the horizontal plane for each 2-mm thick slice. According to the authors, the acquisition time for one

2-D-slice was as short as 2 seconds. The publication of Perret et al. [2000a] features, among other

things, a quantitative comparison of the BTCs in the matrix and macropore domain. They also

observed diffusion of the tracer from the macropores into the matrix and that a large fraction of the

matrix as well as dead-end or isolated macropores were by-passed. Luo et al. [2008] also conducted

experiments with an inert tracer on a saturated undisturbed soil column. The tracer concentration

evolution with time was imaged in two horizontal 2-D breakthrough planes. As a complement to this

analysis, two radiographs of the tracer front progression in the whole column were obtained from

orthogonal positions. The column was 10 cm in diameter and 30 cm in height and the spatial

resolution in the breakthrough plane was 105.5 µm. The acquisition time for one pair of radiographs

and the two horizontal cross-sections was approximately 27 minutes. The water-flow was stopped

during scanning. The findings of Luo et al. [2008] are very similar to the ones of Perret et al. [2000a]

except that Luo et al. [2008] observed that 10 to 19% of their soil column contained entrapped air.

They, therefore, stressed the importance of entrapped air for understanding solute transport under

assumed saturated conditions.

Thus, the potential of time-lapse XRT-imaging of solute transport through soil has so far only

marginally been exploited. A full 3-D XRT-derived visualization of a tracer plume or front with equally

good resolution in all space direction has, as far as we know, not yet been published in peer-

reviewed literature. Time-lapse 3-D datasets of solute transport through soil offers new possibilities

for quantifying solute transport properties. The objectives of our study were, therefore, i) to

demonstrate that present industrial XRT scanners are able to provide high-quality and high-

5

resolution 4-D data on solute transport through undisturbed macroporous soil, and ii) to make use

of this 4-D data to quantify properties of the transport process which cannot be inferred from

traditional breakthrough experiments. To illustrate the potential benefits of such a data set we

calculated the evolution of the dilution index [Kitanidis, 1994], a measure of the strength of

preferential transport. The dilution index has previously been calculated from 2-D experiments on

repacked sands [Ursino et al., 2001] or investigated in numerical experiments [e.g. Kapoor and

Kitanidis, 1996; Rolle et al., 2013]. As an additional illustration of the value of such data, we

quantified the diffusion of solutes from a cylindrical macropore into the surrounding soil matrix and

compared the measurements to a numerical solution of the cylindrical diffusion equation.

Methods and materials

X-ray tomography

In this study, we used the GE Phoenix v|tome|x m XRT scanner installed at the Department of Soil

and Environment at the Swedish University of Agricultural Sciences (Uppsala), which has a 240 kV X-

ray tube, a tungsten target (beryllium window) and a GE 16´´ flat panel detector. We imaged the

transport of a KI-solution (potassium iodide) through a soil column, collecting 1372 radiographs per

3-D image frame with a discretization of 2024 × 2024 pixels, corresponding to a resolution of 48.93

µm. The acquisition time for all 1372 radiographs was three minutes. The X-ray scans were carried

out at a voltage of 170 kV with an electron flow corresponding to 350 µA. The exposure time for each

radiograph was 131 µs. The radiographs were subsequently inverted to a 3-D image using the GE

image reconstruction software datos|x and exported as TIFF-stacks (tagged image file format) with

16-bit greyscale resolution. The resulting spatial resolution of the reconstructed 3-D images was 48.9

µm in all directions.

6

Experimental setup

The experiments were carried out on a cylinder sample (approximately 38 mm high, 68.2 mm

diameter) with undisturbed soil from Ultuna (59°49´N; 17°39´E), three km south of Uppsala, Sweden.

The sample was taken on 20 November 2012 at 10-cm depth from a field under long-term reduced

tillage. Shallow cultivation had been carried out on 18 September. At the time of sampling, the soil

was bare. The soil is a silty clay (44% clay, 42% silt, 14% sand) developed from post-glacial lake

sediments and has a large potential for preferential transport [Larsbo et al., 2009]. The organic

carbon content (2.6%) and the porosity (55%) have previously been measured for this soil [Larsbo et

al., 2009].

A polyamide cloth (mesh size 50 μm) was attached to the bottom of the sample in order to minimize

internal erosion. The sample was then placed on a perforated plastic lid. An approximately 3-mm

thick layer of fine sand was placed on the sample surface to ensure good contact between the

sample and a mini-disk tension infiltrometer (Decagon Devices Inc., Pullman, WA, USA), which was

used to supply iodide solutions in subsequent transport experiments. The sample was first slowly

saturated from the bottom with tap water. To further reduce entrapped air in the sample, about ten

pore volumes of tap water were slowly forced to flow through the column from the bottom upwards.

Finally, the saturated sample was placed in a sealed container under near-vacuum for one night. The

whole process took approximately 20 days and was carried out at approximately 20 °C.

The tracer experiment was conducted inside the X-ray scanner to minimize disturbance which would

occur during the moving and installation of the sample and to enable multiple scans at a high time

resolution [Wildenschild and Sheppard, 2013]. The simple experimental setup is described

schematically in Fig. 1. The sample was attached firmly to the rotating scanning stage. The drainage

from the column was collected in a funnel which directed the drainage into a stationary circular

collector. The drainage water was then led through a 3-mm diameter tube to a flow-through vessel

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(D201, WTW GmbH, Weilheim, Germany) where the electrical conductivity was measured every

minute using an electrical conductivity meter (Cond 3310, WTW GmbH, Weilheim, Germany).

A mini-disk tension infiltrometer filled with 80 ml of tap water was gently placed on the sand surface.

The tension at the bottom of the infiltrometer stainless-steel pressure plate was set to 0.5 cm. To

minimize artifacts due to X-ray scattering from the stainless steel pressure plate, the sand surface

and, hence, the bottom of the pressure plate was positioned in the same horizontal plane as the X-

ray source. When the infiltration rate and the electrical conductivity of the effluent water had

reached steady-state, the column was scanned for the first time. The minidisk tension infiltrometer

was then replaced (at time t=0) by an identical infiltrometer with the same tension setting filled with

80 ml of KI solution (20 g iodide per liter H2O), corresponding to an electrical conductivity of 207 mS

mm-1. The exchange of the infiltrometers took about 10 seconds. The column was subsequently

scanned every 5 minutes during the first hour, every 10 minutes during the second hour and at half-

hourly and hourly time intervals for the remainder of the experiment, which was stopped after 6

hours. Because the solution storage volume of the minidisk tension infiltrometer is limited to 80 ml

the infiltrometer was replaced a second time with an identical infiltrometer with the same tension

settings filled with the same KI-solution 250 minutes after the first KI-solution filled infiltrometer had

been installed.

After the end of the breakthrough experiment, we scanned an empty PVC column in which one

plastic vessel filled with tap-water and one filled with KI-solution were placed. The composition of

tap water and KI-solution was identical to the ones used during the tracer experiment. High-quality

X-ray radiographs were collected (2000 radiographs in 21 minutes). The corresponding 3-D image

was later used to relate the time-lapse image gray values to iodide concentrations. The two vessels

were placed at the same radial distance from the center of rotation to minimize beam hardening

artifacts.

8

The effluent breakthrough curve recorded in the flow-through vessel was affected by a time-lag

relative to the bottom of the soil column because of the travel time required for the effluent to reach

the flow-through vessel (Fig. 1). Furthermore, mixing of solutes took place in the circular collector, in

the connecting tubes and in the flow-through vessel. We, therefore, measured the breakthrough

curve corresponding to the ‘dead-volume’ of the outflow system by applying a pulse of tracer

solution directly to the funnel below the soil sample (see Fig. 1) and slowly flushing it through the

flow-through vessel. The dead-volume breakthrough curve was used to estimate the breakthrough

curve at the bottom of the soil column by de-convolution.

Image processing

In total, 25 frames (3-D images) were obtained during the transport experiment. The four frames

between t = 2 and t = 26 minutes could not be evaluated because of a malfunction during the X-ray

image acquisition which had been triggered by an operating error. We lost an additional three frames

(at t = 46, 81 and 181 minutes) due to failed data transfers to external hard disks. As a result, 18

frames were evaluated according to the procedure described below.

Image registration

Image processing was carried out using the FIJI distribution [Schindelin et al., 2012] of ImageJ

[Abramoff et al., 2004] and MATLAB. First, the image resolution of each frame was reduced by a

factor of two in all dimensions to limit the computation time during the following image processing

steps. As a result, each image-voxel had an edge-length of 97.85 µm. In the next step, the 3-D images

were registered (i.e. spatially aligned) using the ‘descriptor-based series registration (2d/3d + t)’

ImageJ-plugin which is based on the registration approach published in Preibisch et al. [2010]. After

this, we removed the horizontal voxel-layers on the top and bottom from the 3-D images. The voxel-

layers removed at the top corresponded to the sand layer that had been added to ensure good

hydraulic contact between the infiltrometer and soil. The discarded voxel-layers at the bottom

9

contained parts of the plastic cap at the outlet. The number of horizontal voxel layers retained in

each frame was 381, corresponding to a column height of 37.3 mm.

Illumination correction

A quantitative interpretation of the brightness of X-ray images requires a homogeneous illumination,

so that objects of the same density are depicted with identical gray values over the entire 3-D image.

This is, however, only approximately the case for images acquired with beams from X-ray tubes

where electrons are shot onto a metal anode to generate the X-rays. The electron beam causes

abrasions on the anode material, which lead to shifting brightness distributions with time in the

beam cone emitted from the X-ray tube. This in turn causes artificial illumination fluctuations in the

X-ray images, which need to be corrected for. Beam-hardening artifacts which are inevitable in

images acquired with polychromatic X-rays are expected to cancel out with the subtraction of two

images. Since we are only investigating difference images beam hardening artifacts, are probably of

minor importance.

In our case, illumination heterogeneities will result in incorrect estimates of solute concentration. We

assumed that the air bubbles and the PVC column wall had a spatially and temporally constant

density from which it follows that also the corresponding gray values, g (-), in the X-ray images were

spatially and temporally constant. The density of individual stones also remained constant during the

experiment. We sampled 291 voxels from the PVC column wall in each of the 381 horizontal layers

resulting in a total of 110871 voxels for one 3-D image (Fig. 2a). In addition, we sampled voxels from

randomly selected air bubbles in 14 individual horizontal layers (in total 1110 voxels per image),

water-filled macropores in 35 horizontal layers (in total 3499 voxels per image), and stones in 18

horizontal layers (in total 11107 voxels per image). The gray values for PVC column wall, air bubbles,

water-filled macropores and stones are denoted gp, ga, gw and gs, respectively. Air bubbles, water-

filled macropores and stones were identified by visual inspection. Examples for voxels sampled from

the different categories are illustrated in Fig. 2a. The gray values of PVC wall, air bubbles, water-filled

10

macropores and stones were samples from each of the 18 evaluated frames. Vertical profiles of the

corresponding gray values are shown for frame 1 and frame 18 in Fig. 3.

As a first correction step, we normalized the gray values for each 3-D image to a vertically constant

median gray value (12000) for the PVC column wall. This was done for each horizontal layer, i,

according to:

𝐆𝑖,𝑛𝑜𝑟𝑚 = 𝐆𝑖,𝑜𝑟𝑖𝑔 + 12,000− median�𝐠𝑝,𝑖�,

(1)

where Gi,orig and Gi,norm are the gray values of all voxels in the horizontal layer i before and after the

normalization and gp,i are the 291 gray values sampled from the PVC column wall in layer i.

In a second step, we scaled the 3-D images to a unique gray-scale gradient between the median gray

values corresponding to air and stones. We derived the respective correction functions from the

matrices Ma and Ms consisting of the median sampled gray values of air and stones, respectively:

𝐌𝒂 =

⎣⎢⎢⎢⎢⎡ 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,1

(1)� 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,2(1)� ⋯ 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,18

(1) �

𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,1(2)� 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,2

(2)� ⋯ 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,18(2) �

⋮ ⋮ ⋱ ⋮𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,1

(14)� 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,2(18)� ⋯ 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑎,18

(1418)�⎦⎥⎥⎥⎥⎤

(2)

and

𝐌𝒔 =

⎣⎢⎢⎢⎢⎡ 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,1

(1)� 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,2(1)� ⋯ 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,18

(1) �

𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,1(2)� 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,2

(2)� ⋯ 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,18(2) �

⋮ ⋮ ⋱ ⋮𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,1

(18)� 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,2(14)� ⋯ 𝑚𝑒𝑑𝑖𝑎𝑛 �𝑔𝑠,18

(18)�⎦⎥⎥⎥⎥⎤

(3)

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where the superscripts and subscripts h and f in 𝑔𝑎,𝑓(ℎ) and 𝑔𝑠,𝑓

(ℎ) correspond to the hth sampled air

bubble or stone in the fth frame. From the two matrices we calculated the arithmetic mean of the

column vectors ma and ms as well as the arithmetic mean of the row vectors na and ns. Then, matrices

of the illumination precision, Ea and Es, were calculated from the following element-wise

subtractions:

𝐄𝑎 = [𝐦𝑎 𝐦𝑎 … 𝐦𝑎]−𝐌𝑎

(4)

and

𝐄𝑠 = [𝐦𝑠 𝐦𝑠 … 𝐦𝑠] −𝐌𝑠

(5)

where entries of zero denote accurate illumination, while entries smaller and larger than zero denote

overly dark and overly bright illuminations, respectively. Boxplots for the values in the 18 columns in

Ea and Es are shown in Fig. 4a and b, where each boxplot corresponds to the illumination accuracies

of one of the 18 evaluated 3-D frames.

For each frame, a correction function, cf(g), was calculated from the matrices N and H with

𝐍 = �𝐧𝒂𝐓 𝐧𝒑𝐓 𝐧𝒔𝐓�

(6)

where np is a row vector with eighteen entries which correspond to the median gray values of the

column wall which were set to 12000 in the first illumination correction step described above. The

vectors ea and es are row vectors of the column averages of Ea and Es, respectively, and were used to

define

𝐇 = �𝐞𝑎T 𝐞𝑝T 𝐞𝑠T�

12

(7)

where 𝐞𝑝𝑇 is a row vector containing 18 zeros, corresponding to the perfect illumination of the

column wall attained in the first correction step.

The dimensionless correction function cf(gj,norm) for the fth frame was attained by fitting a second

order polynomial to the fth row of matrices N and H. The illumination corrected 3-D frame f was then

obtained by applying

𝑔𝑗,𝑐𝑜𝑟𝑟 = 𝑔𝑗,𝑛𝑜𝑟𝑚−𝑐𝑓�𝑔𝑗,𝑛𝑜𝑟𝑚�

(8)

to all voxels j in frame f, where gj,norm is the gray value of the jth voxel in frame f after the first

illumination correction step and gj,corr is the illumination corrected gray value of the same voxel after

the second illumination correction step. The gray values after the second correction step are shown

in Fig. 5.

Creating the time-lapse image series

We created 17 time-lapse difference images by subtracting the gray values of frame 1 from all other

frames. Assuming no image artifacts, the gray value of a difference image is proportional to the

increase in iodide mass with respect to frame 1. Negative gray values in a difference image may be

due to noise in the image data or caused by e.g. swelling of the soil matrix or displacement of air

bubbles during the experiment. We reduced the amount of image noise by applying a 3-D median

filter to the 17 difference images. We chose the footprint-radius of the 3-D median filter such that

negative and positive voxels in the stone located at the center of the soil column (see Fig. 2a) largely

disappeared. This was the case for a radius of four voxel lengths (391.4 µm). Finally, we once again

reduced the image resolution by half to shorten the time required to compute and evaluate the 3-D

difference images. It follows that each voxel in the time-lapse difference image had an edge length of

195.7 µm. Hereafter, the gray value of voxel j of the time-lapse difference image d is denoted as γj,d.

13

Evaluating the image data

Segmenting the soil column into air, macropore and stone domains

We used the maximal gray values sampled for the air-filled voxels (9201) and water-filled macropore

voxels (11120) of frame 1 as a threshold to determine the location of air-bubbles and water-filled

macropores at the start of the experiment (see Fig. 5a). Likewise, we used the minimum gray value

sampled from frame 1 for stones (13988) to determine the location of stones in the soil column.

Establishing a relationship between gray value and iodide mass

We selected one representative horizontal layer from the 3-D image of the PVC column with the tap

water and KI-solution samples (Fig. 2b) to establish a linear relationship between gray values in the

time-lapse difference images and the iodide mass. We sampled 291 gray values from the PVC wall,

61110 gray values corresponding to tap water and 61857 gray values corresponding to the tracer

solution (Fig. 2b). We scaled the tap water and KI-solution image linearly, such that the voxels

located in the water-filled vessel and in the PVC wall had identical median gray values as the ones of

the water-filled macropores and the PVC wall in frame #1 of the illumination-corrected time-lapse

images. In a final step, we subtracted the illumination corrected median values corresponding to

tracer solution and tap water, which yielded the gray value, γsat = 791, corresponding to the

maximum possible increase of tracer concentration, Cmax (i.e. 20 g iodide l-1 H2O). The tracer mass mj,d

(g) in voxel j in the time-lapse difference image d could then be calculated from the corresponding

gray value, γj,d, according to:

𝑚𝑗,𝑑 =𝑉𝑣𝑜𝑥 𝐶𝑚𝑎𝑥𝛾𝑠𝑎𝑡

𝛾𝑗,𝑑

(9)

where Vvox is the volume of one voxel (= 7.495 · 10-6 cm3). It is noted that the gray values g of the

time-lapse difference images are not only influenced by the iodide mass but also by the abundance

of potassium. The latter is known to adsorb to cation-exchange sites in the soil, replacing initially

14

adsorbed ions. Since these will differ in mass, it follows that Eq. 9 is not an exact calculation of the

iodide mass but rather an approximation.

We expressed the noise-level inherent in the time-lapse images, εillu, as the standard deviation of the

sampled gray values of air, stone and wall after the second correction step in relation to the maximal

possible tracer contrast, γsat. We assumed that the air bubbles remained stationary during the

experiments and that no tracer was able to enter stones or the PVC wall gray values such that the

variance of the gray values of these regions should be stationary. The noise-level ratio for the

sampled air bubbles was hence defined as

ε𝑎,𝑖𝑙𝑙𝑢 =𝑠𝑡𝑑�γ𝑎,𝑐𝑜𝑟𝑟�

γ𝑠𝑎𝑡.

(10)

The noise levels for stones, εs,illu, and the PCV wall, εp,illu, were calculated in the same way.

Mass-balance calculations

Using Eq.9 the total X-ray-derived iodide mass in the column, Md,Xray (g), was calculated for each time-

lapse difference image d by summing overall mj,d in each difference image,

𝑀𝑑,𝑋𝑟𝑎𝑦 = � 𝑚𝑗,𝑑

𝑗𝑚𝑎𝑥

𝑗=1

(11)

where jmax (= 18,279,900) is the number of voxels located within the soil column. The value of Md,Xray

at the time when frame d was scanned, td (min), should equal M d,I/O, defined as the difference

between cumulative iodide mass inflow and outflow from time t=0 to td.

𝑀d,I/O = 𝑞� 𝐶𝑚𝑎𝑥 − 𝐶𝑜𝑢𝑡(𝑡) 𝑑𝑡𝑡𝑑

𝑡=0

15

(12)

where q is the constant water flow rate (l h-1) and Cout(t) (g l-1) the iodide concentration in the effluent

at time t.

The iodide concentration in the effluent at the bottom of the soil column, Cout(t), was obtained from

the breakthrough curve measured during the experiment, Uex(t’) (mS mm-1), and the dead volume

breakthrough curve, Udv(t’) (mS mm-1) by de-convolution, where t’ (minutes) denotes time discretized

into one-minute steps (i.e. the resolution of the electrical conductivity data). Uex(t’) and Udv(t’)

designate the electrical conductivity breakthrough curves after the background electrical

conductivity of tap water (U0 = 5.2 mS mm-1) was subtracted.

We constrained the de-convolution problem by first fitting a log-normal transfer function to Udv(t’) by

minimizing the sum of squared differences according to:

𝑢𝑑𝑣(tʹ) = arg min𝜇,𝜎

� �𝑈𝑑𝑣(𝑡′)∑𝑈𝑑𝑣(𝑡′)

− 𝑢𝑑𝑣(𝑡ʹ;𝜇,𝜎)�2𝑡𝑒𝑛𝑑

0

(13)

where tend (min) is the last time for which electrical conductivity was measured and µ (minutes) and

σ (-) are the parameters of the log-normal transfer function

𝑢(𝑡) = 1√2𝜋𝜎𝑡

𝑒𝑥𝑝 �− [𝑙𝑛(𝑡)−𝜇]2

2𝜎2�.

(14)

Next we fitted a double log-normal transfer function to Uex(t)

𝑢𝑒𝑥(𝑡′) = 𝑎𝑟𝑔𝑚𝑖𝑛𝜇1,𝜎1,𝜇2,𝜎2,𝛽𝑒𝑥

� �𝑈𝑒𝑥(𝑡′)𝑈𝑚𝑎𝑥

− 𝛼(𝑡′) ∗ 𝑢𝑒𝑥(𝑡′; 𝜇1,𝜎1,𝜇2,𝜎2,𝛽𝑒𝑥)�2𝑡𝑒𝑛𝑑

0

(15)

16

where the asterisk denotes a convolution, α(t’) is the Heaviside step function which is one for all t’ ≥

0 and zero otherwise, Umax (= 201.8 mS mm-1) is the electrical conductivity of the tracer solution

minus the electrical conductivity of the background (tap water), and

𝑢𝑒𝑥(𝑡′; 𝜇1,𝜎1,𝜇2,𝜎2,𝛽𝑒𝑥) = 𝛽𝑒𝑥 𝑢1(𝑡′;𝜇1,𝜎1) + (1 − 𝛽𝑒𝑥) 𝑢2(𝑡′;𝜇2,𝜎2),

(16)

where µ1 and σ1 as well as µ2 and σ2 are the dimensionless parameters of the first and second log-

normal transfer functions u1 and u2 and βex (-) is a weighting factor.

The transfer function corresponding to the breakthrough curve at the bottom of the soil column,

uso(t’), was obtained by fitting another double log-normal function such that

𝑢𝑠𝑜(tʹ) = arg min𝜇3,𝜎3,𝜇4,𝜎4,β𝑠𝑜

��𝑢ex(𝑡′) − 𝑢𝑏𝑙(tʹ) ∗ 𝑢𝑠𝑜(tʹ; 𝜇3,𝜎3,𝜇4,𝜎4,β𝑠𝑜)�2𝑡𝑒𝑛𝑑

0

(17)

where µ3 (min), σ3 (-), µ4 (min), σ4 (-), and βso (-) are the parameters defining the shape of uso(t’).

Finally, Cout(t) was obtained by assuming a linear relationship between electrical conductivity and

iodide concentration according to:

𝐶𝑜𝑢𝑡(𝑡) = 𝐶𝑚𝑎𝑥[α(t) ∗ 𝑢𝑠𝑜(𝑡)].

(18)

Characterizing the solute transport process

The degree of physical non-equilibrium is an important property of a solute transport process

through porous media, which reflects the extent to which solute transport is channeled within so-

called preferential transport paths, thereby by-passing large fractions of the soil matrix [Jarvis et al.,

17

1991; Flühler et al. 1996; Hendrickx and Flury, 2001]. The dilution index, E (mm3), which characterizes

the degree of dilution of a solute plume [Kitanidis, 1994] is an explicit measure of the degree of

preferential transport. It can also be interpreted as a measure of the entropy inherent in a solute

transport process. The dilution index Ed (mm3) of the solute distribution calculated for the whole

column in image d is defined by

𝐸𝑚𝑒𝑎𝑠,𝑑 = 𝑉𝑣𝑜𝑥 𝑒𝑥𝑝 ��𝑚𝑗,𝑑

𝑀𝑑 𝑙𝑛 �

𝑚𝑗,𝑑

𝑀𝑑�

𝑗𝑚𝑎𝑥

𝑗=1

�.

(19)

At least a two-dimensional tracer mass distribution is required to calculate the dilution index. To our

knowledge, calculations of the dilution index for three-dimensional tracer transport through

undisturbed soil have not yet been published.

Comparison with equivalent one-dimensional convective-dispersive transport

One-dimensional solute transport models are often used to predict solute transport for engineering

and environmental management purposes. The most widely used model is the convection-dispersion

equation (CDE), which is implemented in popular off-the-shelf software such as CXTFit [Toride et al.,

1999] and HYDRUS [Simunek et al., 2008]. The CDE describes solute transport assuming perfect

(maximal) dilution or mixing given a specific transport velocity, vCDE (mm min-1), and dispersivity,

λ (mm). The CDE, therefore, corresponds to a solute transport process which is macroscopically

devoid of preferential transport characteristics. In our study, the scale of discretization corresponds

to the resolution of the X-ray time-lapse difference images. It is illustrative to compare Ed to the

dilution index of an equivalent one-dimensional convective-dispersive solute transport process. This

provides an opportunity to quantify the difference between the measured transport process and

transport assuming absence of preferential transport characteristics.

We fitted the one-dimensional CDE to the breakthrough curve at the bottom of the soil column:

18

𝜁𝑓,𝐶𝐷𝐸(tʹ) = arg min𝑇,𝑃

��𝐶out(𝑡′) − 𝐶𝑚𝑎𝑥�α(tʹ) ∗ 𝜁𝑓,𝐶𝐷𝐸�tʹ;𝑇,𝑃���2𝑡𝑒𝑛𝑑

0

(20)

where ζf,CDE(t’) (-) is the solution of the CDE for a first-type boundary condition and a Dirac-input

tracer application [Toride et al., 1999] with the retardation coefficient and the dimensionless

transport distance set to one and

𝜁𝑓,𝐶𝐷𝐸�𝑡 ʹ;𝑇,𝑃� = � 𝑃4𝜋𝑇3

𝑒𝑥𝑝 �−𝑃

4𝑇[1 − 𝑇]2�

(21)

where T is the dimensionless time defined as:

𝑇 =𝑡′ 𝑣𝐶𝐷𝐸𝐿

(22)

and P (-) is the macroscopic Péclet number:

𝑃 =𝐿𝜆

.

(23)

The CDE-equivalent flux concentration breakthrough curve, Cf,CDE(t) (g l-1) is then directly obtained

from the results of Eq. 20 by:

𝐶𝑓,𝐶𝐷𝐸(𝑡) = 𝐶𝑚𝑎𝑥�α(t) ∗ 𝜁𝑓,𝐶𝐷𝐸(𝑡)�

(24)

19

We also calculated resident concentration profiles for an equivalent one-dimensional CDE transport

according to:

𝐶𝑟,𝐶𝐷𝐸�𝑧, 𝑡 ʹ� = 𝐶𝑚𝑎𝑥�α(t) ∗ 𝜁𝑟,𝐶𝐷𝐸�𝑧, 𝑡 ʹ;𝑇,𝑃��

(25)

where

𝜁𝑟,𝐶𝐷𝐸�𝑧, 𝑡 ʹ;𝑇,𝑃� = � 𝑃𝜋𝑇

𝑒𝑥𝑝 �−𝑃

4𝑇[𝑍 − 𝑇]2� −

𝑃2𝑒𝑥𝑝(𝑃𝑍) 𝑒𝑟𝑓𝑐

⎝

⎛𝑍 + 𝑇

�4𝑇𝑃 ⎠

⎞

(26)

is the analytical solution of the CDE for a third-type boundary condition [Toride et al., 1999]. The

subscript r denotes resident concentration and Z is the dimensionless transport distance given by:

𝑍 =𝑧𝐿

(27)

where z (mm) is the transport depth. The values of the CDE parameters vCDE and λ were obtained

from Eq. 20.

The resident concentrations, CDEr (z, t), were used to derive resident mass profiles at times

corresponding to the time-lapse difference images d, scaling the zeroth spatial moment of CDEr to

Md,Xray. The resident concentration profiles were also used to calculate equivalent dilution indices

ECDE,d (mm3) for time-lapse difference images d,

𝐸𝐶𝐷𝐸,𝑑 =1

𝑖𝑚𝑎𝑥 𝑒𝑥𝑝 ��

𝐶𝑟,𝐶𝐷𝐸(𝑧𝑖, 𝑡𝑑)𝑀0,𝐶𝐷𝐸(𝑡𝑑)

𝑙𝑛 �𝐶𝑟,𝐶𝐷𝐸(𝑧𝑖, 𝑡𝑑)𝑀0,𝐶𝐷𝐸(𝑡𝑑)

�𝑖𝑚𝑎𝑥

𝑖=1

�

(28)

20

where imax (= 190) is the number of horizontal voxel layers i. M0,CDE is the zeroth spatial moment of

CDEr at time td.

Investigating radial diffusion of iodide from a cylindrical macropore

As another example of the usefulness of high quality X-ray tomography data for analysis of small-

scale (i.e. macropore scale) solute transport processes, we calculated the radial diffusion from a

macropore into the surrounding soil matrix. Solute transport in cylindrical macropores has been

studied both theoretically and experimentally [van Genuchten et al., 1984; Rahman et al., 2004].

Cihan and Tyner [2011] recently showed that an analytical solution for advective flow in a cylindrical

macropore coupled to diffusion into the surrounding soil matrix could accurately reproduce

measured data on solute breakthrough. The use of detailed data on solute concentrations in the

macropore and in the matrix surrounding the macropore allows for a direct evaluation of the solute

diffusion from the macropore to the matrix. We identified one approximately cylindrical macropore

with a radius of 1 mm (Fig. 6a) located at 15-mm depth from the soil surface. Average masses per

volume of bulk soil in the radial direction were calculated for three times (26, 71 and 301 min) for 0.2

mm radial increments from the macropore wall to a radius of 6 mm (Fig. 6 d-f).

Measurements were compared to a numerical solution of the cylindrical diffusion equation:

𝜕𝐶𝑚𝑎𝑡𝑟𝑖𝑥

𝜕𝑡=𝐷𝑚𝑎𝑡𝑟𝑖𝑥

𝑟𝜕𝜕𝑟�𝑟𝜕𝐶𝑚𝑎𝑡𝑟𝑖𝑥

𝜕𝑟�

(29)

where Cmatrix (µg ml-1) is the concentration in the soil matrix, Dmatrix (mm2 s-1) is the effective matrix

diffusion coefficient and r (mm) is the radius. The inner boundary condition (r=1 mm) was given by

linear interpolation of measured average concentrations in the macropore at 15-mm depth. Zero

diffusion was assumed at the outer boundary of the simulation domain (r=50 mm). Eq. 29 was solved

numerically using the Euler method in the Powersim software (Powersim v. 2.54). The volumetric

water content of the soil matrix which is needed to convert concentrations in solution to masses per

21

volume of bulk soil was set to 55% based on previous measurements of volumetric water content at

a pressure potential of -10 cm made on the same soil [Larsbo et al., 2009]. The value of the diffusion

coefficient, assumed to be spatially uniform, was calibrated by minimizing the root mean square

error between measured and simulated data assuming equal weights for all data points.

Results and discussion

Suitability of experimental setup

The elaborate and time-consuming illumination correction approach clearly facilitated quantification

of the image data (compare Figs. 3 and 5). However, there was still considerable bias and noise in the

illumination corrected images (Fig. 5). The presence of a bias is clear from the gray values of the air

bubbles for which no trend with soil depth should be visible if only noise was present. Yet the air

bubbles closer to the soil surface were imaged somewhat darker than the ones closer to the bottom.

Only moderate correlations between gray values of the 18 randomly selected air bubbles and

distance from the column walls were found (average Spearman correlation coefficients of 0.45 with

an average p-value of 0.07). This suggests that the ring-shaped beam hardening artefacts were

present. For future studies, an improved illumination correction may be achieved by using column

walls that are made of two materials of contrasting density and also include air pockets at regular

intervals, which could be used to harmonize the brightness of time-lapse X-ray images. Beam

hardening artifacts were more pronounced in the lower 4 mm of the soil column (Figs. 3 and 5). The

reason causing the pronounced beam hardening artifacts at the bottom was the fact that we had

positioned the top of the soil column into the same horizontal plane as the X-ray source, which led to

a larger variability in length of X-ray trajectory through the bottom of the soil column. Here the

underestimation of gray values corresponding to the PVC column was successfully corrected,

whereas the ones for the water-filled macropores were not (Fig. 3a and 5a). At these depths, circular

dark regions symmetrical to the rotation axis of the column were visible in the horizontal cross-

sections (not shown). Since we applied a global thresholding segmentation approach, it follows that

22

the extent of air bubbles and water filled macropores (Figs. 7a and b) was slightly overestimated in

the central parts of the column close to the base. Correspondingly, the extent of stones (Fig.7c) was

probably underestimated in this region.

For the time-lapse difference images, the beam hardening problems were less important because

similar artifacts were present in each of the 18 recorded images. Figure 8 demonstrated that

respective ring-shaped patterns were not prominent in horizontal cross-sections of the iodide

concentrations in the soil. As already stated, the bottom of the soil column was an exception. Here,

the subtraction of two images did not completely cancel out beam hardening artifacts in the time-

lapse images as the gray values for macropores obviously saturated with tracer solution were

systematically smaller close to the rotational axis at the base of the column. This led to an

underestimation of the tracer mass in the bottommost voxels of the time-lapse images. More

problematic than beam hardening were fluctuations in the image illumination asymmetric to the soil

column’s outline, which occurred between individual time-lapse images. We believe that these

fluctuations were caused by temporal intensity variations in brightness of the X-ray beam cone due

to abrasion of the anode material (tungsten) in the X-ray tube. In future experiments, such

fluctuations may be reduced by re-calibrating the flat-panel detector to the X-ray beam in between

consecutive image frames.

Despite these problems, the iodide mass inside the soil column was reasonably well recovered from

the X-ray images during the entire experiment (Fig. 9a). Fig. 9a shows that the X-ray derived iodide

mass, MXray, was slightly smaller than the one derived from the difference between iodide inflow and

outflow, MI/O, during the first half of the experiment. This is partly explained by the underestimation

of tracer mass in the bottom of the column. However, during the second half of the experiment,

MXray was larger than for two out of three time-lapse difference images. The rather small differences

between MXray and MI/O may also be partly explained by the removal of voxels at the top and bottom

of the column as well as the occurrence of cation exchange processes within the column.

23

An increase in the noise level during the tracer breakthrough experiment was noted (Fig. 9b). The

noise levels for the sampled air-bubbles and stones, εa,illu and εs,illu, increased from between 3% to 5%

of the gray value corresponding to a tracer-saturated macropore at the beginning of the experiment

to values between 6% and 8% at the end (Fig. 9b). In contrast, the noise level for the gray values

sampled from the PVC wall was smaller and did not show any clear trend with time (Fig. 9b). This

suggests that illumination errors present in time-lapse 3-D X-ray images depend non-linearly on the

spatial location as well as on the point in time. This limits the precision with which time-lapse 3-D

processes can be quantitatively interpreted. Nevertheless, the root mean squared difference

between MXray and MI/O was 15% of the average Md,I/O, which is small enough to allow for a

quantitative analysis of the solute transport process (also see Fig. 9a).

Shifting locations of air-bubbles, pores and stones during the experiment (e.g. due to swelling or

shrinking of clay minerals in reaction to the potassium and iodide ions applied as a tracer) may offer

one explanation for the increasing imaging error with time. However, if this was the case, it was at

least not visible in the images of tracer concentrations in the soil column. Shifting locations of objects

should cause dark and bright “shadows” around individual features in the time-lapse X-ray images,

which were not observed (Fig. 8). However, this may become more critical when time-lapse images

with higher spatial resolution and lower noise-levels become available. It should also be noted that

we conducted our experiment after we had saturated the soil column for several days with water.

For other initial conditions, e.g. when imaging water infiltration into dry soil, we expect that clay

swelling will make a quantitative analysis of 3-D time-lapse image data even more challenging.

Figure 10 shows the iodide breakthrough curve measured in the flow-through vessel, Uex, as well as

the breakthrough directly at the bottom of the soil column, Cout, which was obtained by de-

convoluting Uex and the dead-volume breakthrough curve, Ubl (the latter is not shown). The large

coefficients of determination (R2 > 0.998; Table 1) achieved for the fits of Uex and Ubl to measured

data demonstrate the validity of the de-convolution approach. Figure 10a also shows that the travel 25

24

time of the tracer in the circular collector, funnel, tubing and flow-through vessel was similar to the

travel time through the soil. Figure 10a also shows that additional dispersion was added to the solute

plume after leaving the soil column. Although the dead volume between the soil and measurement

location could be successfully corrected for, the design of the effluent collector was not completely

optimal (Fig. 1). The circular collector was necessary to collect the outflow water during X-ray image

acquisitions when the column rotated around its vertical axis. Occasionally, droplets of effluent

solution remained immobile for some time on the surface of the circular collector. These droplets

were remobilized during the acquisition of the next X-ray image. This led to the fluctuations in the

electrical conductivity measurements observed at late tracer arrival times (Fig. 10). Each increase in

concentration corresponds to the point of time of one image acquisition. A larger slope of the

circular collector and the use of water-repellent material should eliminate these problems.

Fig. 10 also illustrates that the iodide travel velocity (ca. 5 mm per minute) was large compared to

the time it took to record one 3-D image (in our case 3 minutes). This means that the tracer front

traveled through almost half of the soil column during the time needed for one image acquisition,

which would lead to a considerable smearing of the tracer front in the X-ray images. However, the X-

ray images that were taken between 2 and 26 minutes after the tracer application were lost due to

technical problems. The difference image at 2 minutes only shows gray values below the noise level.

In the difference image at 26 minutes, the tracer had already reached the outflow about 20 minutes

earlier (Fig. 10). During the remaining 270 minutes of the experiment the tracer slowly diffused into

the soil matrix surrounding the main transport paths (Fig. 9). This process was probably slow enough

to render any artificial smearing in the images due to long exposure times negligible.

Characterization of the solute transport

The average infiltration rate during the experiment was approximately 0.018 l h-1 (4.77 mm h-1) with

slight, non-systematic variation (coefficient of variation = 0.14) and no observed trends towards

increased or decreased infiltration rates. Figure 7a illustrates that only a few air bubbles remained in

25

the soil after the 20 day long effort to remove them. In our experiment, air bubbles represented less

than 0.5% of the bulk soil volume which is much less than that reported by Luo et al. [2008]. A

complete removal of entrapped air may, however, only be achieved using a more elaborate

approach, such as the one described in Perret et al. [2000a].

Figure 11 shows the isosurfaces of spreading iodide obtained from the time-lapse difference images

using a threshold of 0.04 µg iodide per voxel. This threshold corresponds to an average tracer

saturation of 50% assuming an average saturated water content of 55% [Larsbo et al., 2009].

Horizontal layers of the same time-lapse difference images showing iodide masses are shown in Fig. 8

for depths of 5, 15, 25 and 35 mm in the soil. Figure 12a shows the percentage of by-passed bulk soil

volume using the same threshold of 0.04 mg iodide per voxel. All these figures illustrate that the

iodide was transported relatively uniformly close to the surface of the soil column. It was then

directed into two large macropores with diameters varying between approximately 0.5 and 3 mm

that extended to the bottom of the soil sample. At approximately 18 to 28 mm depth, much of the

soil matrix was bypassed by the iodide tracer (Fig. 8, 11 and 12a), clearly illustrating preferential

transport in a soil macropore [Beven and Germann, 1982; Jarvis, 2007]. Note that the macropores

into which the iodide is channeled are not continuous at this image resolution (Figure 7b). However,

the hydraulic conductivities of the below resolution bottlenecks are high enough to sustain

preferential transport. A comparison between Figs. 7b and 11 also reveals that most of the

macropore system was non-conducting (i.e., by-passed by the tracer). This is consistent with the fact

that the majority of the macropores were isolated from the tracer-conducting soil volume (Fig. 7b).

During the course of the experiment, iodide slowly diffused from the conducting macropores into the

surrounding soil matrix (Fig. 8 and 11). Nevertheless, more than 90% of the bulk soil volume still had

iodide saturations below 50% between 18 and 28 mm depth 5 hours after the start of the

experiment (Fig. 12a) when the iodide concentration in the effluent had reached 90% of the

maximum concentration. Between approximately 28 mm depth and the bottom of the soil column

the iodide was partly diverted from one of the two macropores (Fig. 11) leading to a spreading of the

26

iodide plume. This delta-like spreading was probably connected to the seepage face at the bottom

boundary, which lead to the activation of larger pores that extended only short distances from the

columns bottom into the soil. Likewise, the solute front in the matrix in the topsoil progressed

downwards with a speed of approximately 1 mm h-1 (Fig. 11 and 12a).

Comparison to an equivalent one-dimensional convective-dispersive transport

Figure 10 illustrates that the CDE cannot properly fit both the early tracer arrival and extreme tailing

observed in our experiment (also see Table 1). The differences between the observed transport

process and the transport modelled by the CDE become even more evident when the resident

concentration profiles are considered. Figure 12b shows that the 1-D resident tracer concentration

profile with depth had maxima both at the top and bottom of the soil column. In contrast, the CDE

predicts a monotonically decreasing tracer concentration from top to bottom. The differences

between observed and modelled CDE transport are also demonstrated by the comparison of dilution

indices (Fig. 13). The dilution index corresponding to the CDE, ECDE, quickly converged to one,

exceeding a value of 0.98 after approximately 56 minutes. A value of one is the upper bound of the

dilution index and indicates a complete absence of concentration gradients. The small concentration

gradients for Cr,CDE compared to the X-ray measured data are illustrated in Fig. 12b. In contrast, the

dilution index calculated from the X-ray measurements, Emeas, was relatively constant at values

smaller than 0.4 during the first hour of the experiment (Fig. 13). Due to diffusion from the tracer-

conducting macropores into the surrounding soil matrix, Emeas slowly increased to a value of

approximately 0.65 towards the end of the experiment (Fig. 13; also compare with Figs. 9 and 11).

Radial diffusion

The cylindrical diffusion equation, as applied here, which assumes a spatially uniform effective

diffusion coefficient and matrix water content could not exactly reproduce the measured data (Fig.

14). There are a number of reasons why a perfect match should not be expected. For example, the

properties of the soil matrix at the macropore wall may be different from the interior soil matrix due

27

to enrichment of clay or organic carbon in aggregate coatings and biopore linings [Worrall et al.,

1997; Mori et al., 1999], which can lead to differences in water content and effective diffusion

(Köhne et al., 2002). Moreover, the exact boundary between the macropore and the soil matrix was

difficult to define. We assumed that this boundary could be approximated by a cylinder both for the

measurements and in the modeling. The maximum possible simulated mass, which would be

approached close to the macropore for large effective diffusion coefficients, is equal to the water

content times the boundary mass per volume bulk soil. Measured values close to the assumed

macropore wall were larger than these values, indicating that the shape, size and position of the

inner boundary were incorrect. A numerical model of radial diffusion could account for spatial

differences in water contents and effective diffusion coefficients. However, such an analysis was

beyond the scope of this study.

Conclusions

We have shown that modern industrial X-ray tomography equipment in combination with an

experimental setup which allows for experiments to be carried out inside the X-ray chamber can

provide high-resolution 3-D data on the time-evolution of non-reactive solute transport in soil.

Limitations in the image precision due to noise and non-linear bias (depending on both the time of

image acquisition and location) made it necessary to apply an elaborate illumination correction

procedure, as well as a significant reduction in the effective image resolution by using a median filter

with a radius of 4 voxels. The resulting time-lapse image series exhibited average noise-levels

between 3% and 8% with respect to the maximum possible contrast in gray values. The value of the

generated data was illustrated by a time-series of images and comparison of these observations with

calculations for a one-dimensional convective-dispersive transport process, the time-evolution of the

dilution index and modelled diffusion rates from a cylindrical macropore. However, the usefulness of

the data is far from limited to these cases. On the contrary, we believe that there is great potential

for this kind of 3-D time evolution data to improve understanding of solute transport processes. For

28

example, the assumptions of the many different solute transport model approaches that have been

developed for predicting transport through soil [see e.g. Köhne et al., 2009] or porous media in

general [e.g. Neumann and Tartakovsky, 2009] could be rigorously tested. Furthermore, time-lapse

3-D solute transport imaging will likely be of great use for quantifying relationships between soil or

porous media structure and solute transport properties such as transport velocity, spreading and

mixing, a topic frequently studied during recent years using numerically generated data [e.g.

Willmann et al., 2008; le Goc et al., 2010].

Acknowledgements

We are grateful to Nicholas Jarvis for helpful discussions and language advice.

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Tables

Table 1: Goodness of fit for log-normal and CDE transfer functions used to model measured data.

property value unit

coefficient of determination (R2) corresponding to udv (eq. 13) 0.9996 -

coefficient of determination (R2) corresponding to uex (eq. 15) 0.9985 -

coefficient of determination (R2) corresponding to ζf,CDE (eq. 20) 0.9516 -

Figures

Figure 1: Experimental setup.

37

Figure 2: (a) Horizontal cross-section through one inverted image at a depth of approximately 17 mm (image resolution of 97.85 µm). The outer diameter of the soil column is 75.2 mm, the inner diameter 68.2 mm with a thickness of the PVC wall of 3.5 mm. Bright and dark pixels indicate large and small bulk densities, respectively. The objects marked are air- filled macropores (green), water-filled macropores (blue) and stones (red). (b) Horizontal cross-section of the 3-D image used to relate gray scale to iodide mass.

Figure 3: Gray values of images 1 and 18 before the illumination correction. It is noted that the gray values corresponding to the soil water are increased for frame #18 due to the presence of potassium iodide.

38

Figure 4: Illumination precision (i.e deviations from the mean illumination) for air bubbles, Ea (left side, see eq. 4), and stones, Es (right side, see eq. 5), before (top) and after (bottom) illumination correction step 2.

Figure 5: Gray values of images #1 and #18 after the second illumination correction step.

39

Figure 6: Diffusion from a cylindrical macropore a) horizontal position of the macropore, b) zoom-in on the macropore, c) illustration of the analyzed area, and d) to f) difference images showing the iodide distribution at three times.

40

Figure 7: Location of (a) air bubbles, (b) macropores and (c) stones.

41

Figure 8: Horizontal cross-sections of the iodide mass at 4 different depths (5, 15, 25 and 35 mm) and four different times after the start of the tracer application (26, 61, 151 and 301 minutes).

Figure 9: (a) Iodide mass inside the soil column. The gray line corresponds to Md,I/O, the black line with circles to the mass derived from the X-ray difference images, Md,Xray. (b) Noise level for the 17 time-lapse difference-images.

42

Figure 8: Original (Uex) and de-convoluted breakthrough curves (Cout). For clarity, only every second data point is plotted. In addition, the equivalent breakthrough curve of a one-dimensional CDE transport is shown (Cf,CDE). The coefficient of determination, R2, for fitting Uex is 0.9985. For further information on the effluent breakthrough curves see Table 1.

43

Figure 9: Iso-surfaces of iodide concentrations exceeding 0.04 µg per voxel at times (a) 26, (b) 61, (c) 151 and (d) 301 minutes.

Figure 10: (a) Fraction of bulk soil volume with less than 0.04 µg iodide per voxel at different times after the start of the tracer application. (b) The resident iodide concentration profiles at the same times. The resident iodide concentration profiles of the equivalent CDE transport are also shown.

Figure 11: The temporal evolution of the dilution index derived from X-ray images and from the equivalent one-dimensional CDE transport.

44

Figure 12: Comparison between measured data using X-ray tomography and modelled diffusion from a cylindrical macropore.

45