Journal of Hydrology 452–453 (2012) 83–89

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Journal of Hydrology

journal homepage: www.elsevier .com/ locate / jhydrol

Investigation of water seepage through porous media using X-rayimaging technique

Sung Yong Jung a, Seungmin Lim a, Sang Joon Lee b,⇑a Center for Biofluid and Biomimic Research, Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), San 31, Hyojadong, Pohang790-784, South Koreab Center for Biofluid and Biomimic Research, Department of Mechanical Engineering, Division of Integrative Biosciences and Biotechnology, Pohang University of Scienceand Technology (POSTECH), San 31, Hyojadong, Pohang 790-784, South Korea

a r t i c l e i n f o s u m m a r y

Article history:Received 5 April 2011Received in revised form 8 March 2012Accepted 14 May 2012Available online 25 May 2012This manuscript was handled by PhilippeBaveye, Editor-in-Chief

Keywords:X-ray imagingPorous mediaWater seepage

0022-1694/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.jhydrol.2012.05.034

⇑ Corresponding author. Tel.: +82 54 279 2169; faxE-mail addresses: tjddyd94@postech.ac.kr (S.Y. Jun

Lim), sjlee@postech.ac.kr (S.J. Lee).

Dynamic movement of wetting front and variation of water contents through three different porousmedia were investigated using X-ray radiography. Water and natural sand particles were used as liquidand porous media in this study. To minimize the effects of minor X-ray attenuation and uneven illumi-nation, the flat field correction (FFC) was applied before determining the position of wetting front. Inaddition, the thickness-averaged (in the direction of the X-ray penetration) water content was obtainedby employing the Beer–Lambert law. The initial inertia of water droplet influences more strongly on thevertical migration, compared to the horizontal migration. The effect of initial inertia on the horizontalmigration is enhanced as sand size decreases. The pattern of water transport is observed to be signifi-cantly affected by the initial water contents. As the initial water contents increases, the bulb-type trans-port pattern is shifted to a trapezoidal shape. With increasing surface temperature, water droplets areeasily broken on the sand surface. This consequently decreases the length of the initial inertia region. Dif-ferent from the wetting front migration, the water contents at the initial stage clearly exhibit a preferen-tial flow along the vertical direction. The water transport becomes nearly uniform in all directions beyondthe saturation state.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Unsaturated flow in porous media have been investigated forquite a few decades (Sahimi, 1994) because it has many practicalapplications, including flows of water through ground, flows ofchemicals through filtration, catalysis, transport in lungs, and soon (Adler, 1992; Andrade et al., 1997).

Understanding water transport through porous media is impor-tant in predicting the propagation of the wetting front in both deepand subsurface water penetration. Such water transport has beenstudied by theoretical (Diment et al., 1982; Hill and Parlange,1972; Küntz and Lavallée, 2001; Raats, 1973) and experimentalanalyses (Bernadiner, 1998; Lu et al., 1994; Diment and Watson,1985; Hill and Parlange, 1972) by examining the movement ofthe wetting front with varying governing factors such as infiltra-tion velocity, heterogeneity of porous media and initial watercontents.

ll rights reserved.

: +82 54 279 3199.g), lovelim@postech.ac.kr (S.

Previous experimental studies using optical imaging methodare limited to two-dimensional infiltration systems due to theopaqueness of porous media. Recently, non-invasive imaging tech-niques (gamma radiation, magnetic resonance imaging (MRI), X-ray radiography, and neutron radiography) have been employedto visualize flow phenomena in porous media and to identifyembedded physical processes (Brusseau et al., 2007; Oostromand Lenhard, 2003; Yoon et al., 2008). Gamma ray imaging is oneof the most frequently used methods in characterizing the liquidpenetration in porous media (Oostrom and Lenhard, 2003). Itsmeasurement range is relatively broad covering from a few centi-meter to several meters. However, due to long acquisition time (inthe order of a minute), this imaging technique is not suitable tovisualize the transient flows with a temporal resolution of a fewseconds.

MRI also can be used to visualize 2D and 3D water transportoccurring in porous media (Yoon et al., 2008). 3D volumetric MRIimages can be obtained with a high spatial resolution. Usingfast-imaging pulse sequences (e.g., 2D slice-by-slice imaging), itis possible to observe transient flow phenomena with the timescale of several hundreds of milliseconds. However, the MRI signalis attenuated largely by the presence of ferromagnetic and

84 S.Y. Jung et al. / Journal of Hydrology 452–453 (2012) 83–89

paramagnetic materials. In addition, the magnetic resonance scan-ner is expensive and not easy to handle without the help of a spe-cial operator.

X-ray and neutron tomography methods have been employedto visualize physical phenomena in porous media (Brusseauet al., 2007; Sukop et al., 2008; Turner et al., 2004; Zhou et al.,2010). Although the acquisition time for one image is usually short(several ms), a large number of 2D projection images are used (typ-ically 360 or 720 2D images) to reconstruct one 3D image. There-fore, the 3D tomography method has been used to quantitativelycharacterize the pore-network and fluid distribution in porousmedia.

On the other hand, the temporal variation of liquid flows seep-ing through porous media has been investigated using time-re-solved 2D X-ray and/or neutron radiography (Mahadevan et al.,2007; Milczarek et al., 2005; Ridgway et al., 2006; Tullis andWright, 2007). In this study, 2D X-ray radiography was employedto investigate the dynamic movement of wetting front and varia-tion of water contents in porous media as a function of time fromthe initial impingement up to the quasi-steady (saturation) condi-tion. This imaging method provides 2D images of water thicknessaveraged (in the direction of the X-ray propagation) for a shorttime interval with high spatial resolution. Water and natural sandwere used as liquid and porous media in this study. The differencebetween the vertical and horizontal movements of wetting frontwas investigated. In addition, variation of the migration character-istics was observed with varying the temperature and initial watercontent of the porous media.

2. Experimental setup and data analysis

2.1. Experimental apparatus and method

Fig. 1a shows the schematic diagram of the experimental setupused in this study. A syringe pump was employed to supply water

Fig. 1. (a) Schematic diagram of experimental setup. (b) A typical X-ray i

into an opaque cylinder-type container of 4.5 cm in diameter. TheX-ray imaging system consists of an X-ray tube (Varian A272) andan X-ray CCD camera (Hamamatsu, C9300). The X-ray tube andcamera were synchronized using a photocoupler chip and a tran-sistor transistor logic (TTL) signal from a delay generator. In eachexperiment, X-ray images were captured consecutively at intervalsof 6.4 s. Image recording time was expressed as ti when ith imagewas captured.

The test samples and water were kept in an experimental roomair-conditioned at a controlled temperature for a day. The sandsurface was maintained at temperatures of 25 and 40 �C, depend-ing on experimental condition. Water was dropped from the tipof a needle of 0.495 mm in diameter as a point source. The tip ofthe needle was positioned at 20 mm above the surface of the por-ous medium. The dynamic viscosity of water is 8.90 � 10�4 and6.531 � 10�4 Pa s at the temperatures of 25 and 40 �C, respectively.Water was supplied from a syringe pump at a flow rate of 1000 lL/min. Sand was sieved with a meshed sieve shaker, and three sandsamples having different mean diameter were collected separatelyto be used as porous media. Thereafter, the sand samples were nat-urally packed into a container. The diameter range of the sandsample Cases 1, 2 and 3, is 75–100, 100–125 and 150–200 lm,respectively. The corresponding porosity is 0.58, 0.55 and 0.53,respectively. The permeability of the sand samples Cases 1, 2 and3 was evaluated to be 2.011, 2.145 and 2.279 (�10�9 m2). The bulkdensity of the sand samples Cases 1, 2 and 3 was 1.26, 1.34 and1.35 g/cm3, respectively. The initial water content of the sand sam-ple was controlled to be 0%, 2.5%, 5%, 10%, 15%, 20%, and 25%. Eachexperiment was repeated two times.

2.2. Determination of wetting front

X-ray illumination is usually uneven due to the anode heel ef-fect (Seibert, 2004) when a medical X-ray tube is used as a lightsource. Therefore, the flat field correction (FFC) is commonly

mage (left) and the light intensity profile along the line A–A0 (right).

S.Y. Jung et al. / Journal of Hydrology 452–453 (2012) 83–89 85

adopted to improve the quality of captured X-ray images. The FFCcan be expressed as

FFC image ¼ object image� offset imagegain image� offset image

� scale factor ð1Þ

where the gain image is the image captured without test samplesunder the same experimental condition, and the offset image isthe image taken without X-ray illumination. To improve the visibil-ity of water distribution further, the background image taken beforesupplying water was used as the gain image in this study.

Fig. 1b shows a typical X-ray image and the intensity profile ex-tracted along the line A–A0. IL and IH represent the average intensi-ties of X-ray image with and without water supply, respectively.Point A is the center location at which the liquid drop impingeson the sand surface. The vertical depth of water penetration Z(t)in an X-ray image is defined as the distance from point A to pointC where the light intensity is (IH + IL)/2. In a similar manner alongthe horizontal direction, the horizontal boundary was determinedby averaging the boundaries R1(t) and R2(t).

2.3. Quantification of water contents

Water thickness x at an arbitrary position can be estimated byemploying the Beer–Lambert law (Cullity, 1978);

I ¼ I0expð�lxÞ ð2Þ

Fig. 2. X-ray spectrum of the X-ray tube at 750 mm distance from the focal spot.

Fig. 3. Temporal variation of wetting front position along the (a) vertical and (b) horizon

where l is the linear absorption coefficient of water. I0 and I are theincident and transmitted intensities of X-ray beam, respectively.These intensity values were extracted from the same pixel positionof the background and object images to calculate water thickness xat the location.

Fig. 2 shows the energy spectrum of the X-ray tube obtained at750 mm distance from the focal spot. The X-ray tube has energyspectrum in the range from 15 to 140 keV. We performed a preli-minary test to find the optimum voltage and current conditionsof the X-ray tube to capture X-ray images with good contrast.The optimal conditions were found to be 80 kVp in voltage and100 mA in current. Under this condition, the energy spectrumranges from 15 to 80 keV and the average energy level is about45.8 keV. The mass absorption coefficient of water is about0.244 cm2/g for this energy band of X-ray (Hubbell and Seltzer,2004). Therefore, the linear absorption coefficient (l) of watercan be evaluated by multiplying the water density to the massabsorption coefficient of water.

3. Results and discussion

3.1. Migration of wetting front

The transport of water through a porous medium follows theNavier–Stokes equation. The dynamic movement is caused bygravity and pressure difference acting on the fluid. If the flow is as-sumed to be stationary and incompressible, and the viscous drag isproportional to the flow velocity, the Navier–Stokes equation forcreeping flow can be simplified to the following Darcy’s law;

q ¼ �KrU ð3Þ

where q is the volume flow rate through a unit cross section; K is ahydraulic conductivity that depends not only on the number andconfiguration of pores of the porous medium, but also on the viscos-ity of the fluid seeping through it; and U = (w + a) represents the to-tal pressure. a and w denote the external forces and pressures,respectively. For most capillary problems, gravity is the only exter-nal force to be considered. Forces acting on the boundary surfaces ofwetted water are directly related with the capillary phenomena bywhich the pressure gradient is determined.

In case of 0% initial water contents, temporal variations of thewetting front position are shown in Fig. 3. The symbols of circle,triangle and square represent the sand sample Cases 1, 2 and 3,respectively. In Fig. 3a, the position of the wetting front in the ver-tical direction rapidly increases in the initial stage and then grad-

tal directions at the sand temperature of 25 �C with the initial water contents of 0%.

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ually increases. The water droplet dropped from a needle has initialinertia in the region of the impingement point. The slope of thegraph represents the seepage velocity, and the region influencedby the initial inertial is classified into two regions by consideringthe slope change. In the inertia influence region (IIR), in whichthe slope is decreased, the inertia force is dominant compared toother forces such as gravity and capillary. Therefore, the seepagevelocity decreases as inertia decreases. In the inertia non-influenceregion (INR), in which the slope is constant, Eq. (3) can be applied.In general, the hydraulic conductivity decreases with increasingvertical distance from the sand surface due to compaction by grav-ity. Decreasing hydraulic conductivity leads to velocity reduction,as vertical distance is increased in INR. The variation of hydraulicconductivity according to vertical depth is insignificant, becausethe length of the test volume is relatively short in this experiment.Therefore, the vertical seepage velocity of the wetting front is al-most constant in INR.

In the region of IIR, compared with Cases 2 and 3, the propaga-tion velocity of the wetting front in the vertical direction is smallerfor the Case 1, sand particles of smaller diameter. On the otherhand, the seepage velocity of the wetting front along the horizontaldirection exhibits the opposite tendency. More initial inertia istransferred toward the horizontal direction with decreasing sanddiameter. This seems to be the result of more breakage of the waterdroplet, although water penetration also depends on the configura-tion of sand package, structure of sand aggregation, and so on.

In INR, however, the seepage velocity of the wetting front hassimilar values irrespective of sand size. In general, the hydraulicconductivity K is decreased with decreasing sand porosity. There-fore, the seepage velocity is decreased under the same externalforce. In INR, gravity force seems to be negligible at all positions,because the amount of water above the wetting front is small.The most common formula for capillary force is given by (Pakari-nen et al., 2005);

FC ¼ 4prr cos h ð4Þ

where r is the surface tension, r is the particle radius, and h is thecontact angle. Assuming the same contact angle, capillary force isproportional to particle size and surface tension. At the same tem-perature, capillary force increases with increasing particle size. Dueto the opposite effects of hydraulic conductivity and capillary force,the vertical velocity of the wetting front has a similar value, regard-less of sand size.

Fig. 4. Variation of (a) vertical and (b) horizonta

3.2. Temperature effect on the movement of wetting front

Local seepage velocity of the wetting front at time ti was calcu-lated using the equation;

Vlocal ¼ZðtiÞ � Zðti�1Þ

DTð5Þ

where DT is the time interval between two consecutive X-rayimages. Fig. 4 shows variations of the local vertical and horizontalvelocities of the wetting front. All the velocities approach graduallyto a constant value after initial fluctuation. The boundary betweenIIR and INR is determined by the change of local velocity mode fromfluctuating to invariant. Although the velocity at 40 �C is faster thanthat at 25 �C along the horizontal direction (Fig. 4b), the length ofIIR is shorter along both directions. When a water drop impactsthe porous sand surface, the droplet is broken into pieces in some-times (Hapgood et al., 2002). Water droplets are more easily brokenwhen the Weber number (We = u2qfd/c) is higher. Here, u is the fall-ing velocity of a droplet before the impact, qf is the fluid density,and d is the diameter of the droplet. The diameter of the droplet in-jected from a circular nozzle can be estimated by 2[cD/2g(qf � qg)]1/

3, where D is the nozzle diameter and qg is the air density. The We-ber numbers are 33.844u2 and 34.499u2 at 25 and 40 �C, respec-tively. The droplet velocity for both temperatures can be assumedto have the same value, because the distance from the nozzle tothe sand surface is fixed. Therefore, as the sand temperature in-creases, water droplets are more easily broken and the water ismore evenly spread in all directions.

The capillary pressure (Pc) is related somewhat with the degreeof saturation (S). The dynamic capillary pressure can be expressedas (Mirzaei and Das, 2007);

ðPC;dyn � PC;equÞS ¼ �sð@S=@tÞS ð6Þ

where PC,dyn is the dynamic capillary pressure, PC,equ is the capillarypressure at equilibrium condition, and s is the capillary dampingcoefficient. The damping coefficient s depends on properties of por-ous medium and fluid, degree of saturation, heterogeneity, etc.Therefore, the short IIR caused by increased sand temperatureseems to attribute to the stable supply of water in all directions.

In INR, the seepage velocity of the wetting front is similar forboth sand temperatures. The hydraulic conductivity of soil was re-ported to increase with the increase of soil temperature due to de-creased fluid viscosity (Haridasan and Jensen, 1972; Moore, 1941).Hopmans and Dane (1985) correlated the soil hydraulic conductiv-ity (KT) with temperature (T) using;

l local velocity of the wetting front (Case 2).

Fig. 5. (a) The projected water distribution at t = 25.6 s for various initial water contents. Temporal evolution of water distribution in the direction of X-ray propagation whenthe initial water contents are (b) 0 and (c) 10%.

S.Y. Jung et al. / Journal of Hydrology 452–453 (2012) 83–89 87

KT ¼lref

lTKref ð7Þ

where Kref is the hydraulic conductivity measured at a referencetemperature, and lref and lT denote the water viscosity at the

Fig. 6. Temporal evolution of vertical (upper) and horizontal (lower) water co

reference temperature and the soil temperature. The viscosity ofwater decreases with increasing the temperature, and the hydraulicconductivity is increased according to Eq. (6). If particle size is thesame, capillary force is directly related to surface tension and

ntents in the unit area (115 lm2) at sand temperatures of 25 �C (Case 2).

Fig. 7. Temporal evolution of vertical (upper) and horizontal (lower) water at sand temperatures of 40 �C (Case 2).

88 S.Y. Jung et al. / Journal of Hydrology 452–453 (2012) 83–89

contact angle. Surface tension decreases with increasing tempera-ture. Capillary force decreases for the same contact angle, as tem-perature increases. Therefore, the hydraulic conductivity andcapillary force are mutually contradictory with respect to sand tem-perature. Due to the cancellation effect of these two aspects, theseepage velocity of the wetting front looks similar, regardless ofsand temperature.

3.3. Water contents along the direction of X-ray beam

Fig. 5 shows the water content distributions in a unit area(115 lm2, considering the magnification factor) in the directionof X-ray propagation. The radiated X-ray beam is broadbandenergy spectrum. Although the experimental condition isunchanged, the X-ray energy arriving at the same pixel of X-rayimages may vary slightly, because the pixel size of the CCD cameraused in this study is very small (9 � 9 lm2). To verify the reliability

Fig. 8. Variation of the water contents for different time (1: 25.6 s, 2: 51.2

of the measured water contents, error analysis was performed onthe measured water content by checking whether water contentsoutside the wetting front is zero or not. From the backgroundand object images captured at time 6.4 s for each experiment,absolute difference in water contents was obtained. The averageerror was found to be 0.18%. For more verifying the accuracy ofour results, the water contents in whole field were integrated,and the flow rate was calculated. The difference between measuredand supplied flow rate is about 5.2%.

The water infiltration process is investigated with changing ini-tial water content of test sand samples. Fig. 5a shows the projectedwater distribution at t = 25.6 s for various initial water contents of0%, 2.5%, 5%, 10%, 15%, 20%, and 25%. The temporal variations ofwater distribution in the direction of X-ray propagation for theinitial water contents of 0% and 10% are shown in Fig. 5b and c,respectively. When the initial water content is small (0–2.5%),the general pattern of water infiltration is in a bulb or hemispher-

s, 3:76.8 s, 4: 102.4 s) at sand temperatures of (a) 25 �C and (b) 40 �C.

S.Y. Jung et al. / Journal of Hydrology 452–453 (2012) 83–89 89

ical shape. This coincides with previous prediction for a pointsurface source (Moncef et al., 2002). As the initial water content in-creases, the pattern of infiltration is changed to a trapezoidalshape. When the initial water content is larger than 5%, water ismostly infiltrated into the horizontal direction in initial stage(�25.6 s). Thereafter, the water is mostly spread along the verticaldirection. Most pores near the water drop impact region are al-ready filled with initial water for the cases of large initial watercontents. The transport of the initially filled water is mainly causedby capillary and gravity forces. The gravity force only affects thevertical movement of water, while the capillary force influenceson all directions. The water initially filled is infiltrated into a dee-per depth. Therefore, along the horizontal direction near the sandsurface, the difference in water content is larger than that alongthe vertical direction. Therefore, the horizontal transport is stron-ger than the vertical transport in initial stage, and the transportpattern is changed into a trapezoidal shape.

Figs. 6 and 7 show the vertical and horizontal water contents inthe direction of X-ray propagation. For better comparison, thewater content is plotted according to distance for different timein Fig. 8. At a sand temperature of 25 �C, the smaller amount ofwater contents along the horizontal direction seems to make thelocal penetration velocity fluctuated (Fig. 4), because the effect ofwater content becomes more significant when water amount issmall (Tullis and Wright, 2007). Although the wetting front propa-gates continuously along both vertical and horizontal directions,the amount of water migrating along the vertical direction is muchlarger than that along the horizontal direction, up to the initial51.2 s at the lower sand temperature of 25 �C (Fig. 6). This impliesthat the water seepage behind the wetting front prefers the verticalmigration over the horizontal migration. This preferential flowpath cannot be detected from the results of wetting front position.However, the preferential flow direction becomes weak in both re-sults of the wetting front and the water contents at a higher sandtemperature of 40 �C. Beyond the saturation point, the preferentialflow disappears and the water transport is nearly uniform to alldirections for both temperature conditions.

4. Conclusions

Water migration through porous media was investigated exper-imentally by using a time-resolved X-ray imaging technique.Movement of wetting front and variation of water contents alongthe vertical and horizontal directions were measured simulta-neously. The positional information of the wetting front was ob-tained by applying FFC to enhance flow field visibility. The watercontent along the direction of X-ray beam propagation was deter-mined by employing the Beer–Lambert attenuation law. The pat-tern of water transport is strongly influenced by the initial watercontents. As the initial water content increases, the infiltration pat-tern is changed from bulb to trapezoidal shape. With increasingsand temperature, the droplet breakage on the sand surface is en-hanced. This decreases the length of the IIR in all directions. Thevariation of water contents along both directions shows that thewater seepage in the region behind the wetting front prefers thevertical migration over the horizontal migration in the initial seep-age stage. Once the water is fully saturated, the preferential flowdisappears and the water transport is nearly uniform to alldirections.

Acknowledgments

This work was supported by the Creative Research Initiatives(Diagnosis of Biofluid Flow Phenomena and Biomimic Research)and the WCU program through the National Research Foundation

of Korea funded by the Ministry of Education, Science and Technol-ogy (R31-2008-000-10105-0).

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