Advances in Water Resources 77 (2015) 82–89

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Advances in Water Resources

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Rapid imbibition of water in fractures within unsaturated sedimentaryrock

http://dx.doi.org/10.1016/j.advwatres.2015.01.0100309-1708/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding authors at: Department of Physics and Geology, University ofTexas-Pan American, Edinburg, TX 78539, USA; Department of MechanicalEngineering, University of Texas-Pan American, Edinburg, TX 78539, USA (C.-L.Cheng), Department of Earth and Planetary Sciences, University of Tennessee –Knoxville, Knoxville, TN 37996, USA (E. Perfect). Tel.: +1 956 665 2464 (C.-L. Cheng),tel.: +1 865 974 6017 (E. Perfect).

E-mail addresses: chengc@utpa.edu (C.-L. Cheng), eperfect@utk.edu (E. Perfect).

C.-L. Cheng a,b,⇑, E. Perfect c,⇑, B. Donnelly c, H.Z. Bilheux d, A.S. Tremsin e, L.D. McKay c, V.H. DiStefano f,g,J.C. Cai h, L.J. Santodonato i

a Department of Physics and Geology, University of Texas-Pan American, Edinburg, TX 78539, USAb Department of Mechanical Engineering, University of Texas-Pan American, Edinburg, TX 78539, USAc Department of Earth and Planetary Sciences, University of Tennessee – Knoxville, Knoxville, TN 37996, USAd Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USAe Experimental Astrophysics Group, Space Sciences Laboratory, University of California, Berkeley, CA 94720, USAf Bredesen Center for Interdisciplinary Research and Graduate Education, University of Tennessee – Knoxville, TN 37996, USAg Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USAh Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, PR Chinai Instrument and Source Design Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

a r t i c l e i n f o

Article history:Received 16 September 2014Received in revised form 18 January 2015Accepted 19 January 2015Available online 28 January 2015

Keywords:Neutron radiographyFractured porous mediaUnsaturated flowCapillarityFluid spreadingRough surfaces

a b s t r a c t

The spontaneous imbibition of water and other liquids into gas-filled fractures in variably-saturated por-ous media is important in a variety of engineering and geological contexts. However, surprisingly fewstudies have investigated this phenomenon. We present a theoretical framework for predicting the1-dimensional movement of water into air-filled fractures within a porous medium based on early-timecapillary dynamics and spreading over the rough surfaces of fracture faces. The theory permits estimationof sorptivity values for the matrix and fracture zone, as well as a dispersion parameter which quantifiesthe extent of spreading of the wetting front. Quantitative data on spontaneous imbibition of water inunsaturated Berea sandstone cores were acquired to evaluate the proposed model. The cores with differ-ent permeability classes ranging from 50 to 500 mD and were fractured using the Brazilian method.Spontaneous imbibition in the fractured cores was measured by dynamic neutron radiography at theNeutron Imaging Prototype Facility (beam line CG-1D, HFIR), Oak Ridge National Laboratory. Wateruptake into both the matrix and the fracture zone exhibited square-root-of-time behavior. The matrixsorptivities ranged from 2.9 to 4.6 mm s�0.5, and increased linearly as the permeability class increased.The sorptivities of the fracture zones ranged from 17.9 to 27.1 mm s�0.5, and increased linearly withincreasing fracture aperture width. The dispersion coefficients ranged from 23.7 to 66.7 mm2 s�1 andincreased linearly with increasing fracture aperture width and damage zone width. Both theory andobservations indicate that fractures can significantly increase spontaneous imbibition in unsaturated sed-imentary rock by capillary action and surface spreading on rough fracture faces. Fractures also increasethe dispersion of the wetting front. Further research is needed to investigate this phenomenon in othernatural and engineered porous media.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction including the storage of hazardous wastes within the deep vadose

The movement of water and other liquids in fractures withinunsaturated earth materials is important in a variety of contexts,

zone, enhanced oil recovery, shale gas extraction, and water dam-age to the foundations of buildings and other structures. Advancesin neutron, nuclear magnetic resonance, and X-ray imaging tech-nologies have significantly improved our experimental capabilitiesto visualize fracture flow in variably-saturated porous media. As aresult, researchers are now able to routinely quantify the distribu-tion and movement of water within a wide range of natural andengineered materials at the spatial and temporal resolutions rele-vant to fracture flow.

Fig. 1. Wetting front elevation versus time predicted using Eqs. (2) and (3) for atwo-region porous medium with hki = 50 lm and s = 1.8 in the unfractured matrixand hki = 150 lm and s = 1.2 in the fracture zone. All of the other parameters in Eqs.(2) and (3) were the same for the two regions, i.e. r = 0.0728 N/m, l = 0.001 Ns/m2,cos(h) = 1, q = 1000 kg/m3, and g = 9.81 m/s2.

C.-L. Cheng et al. / Advances in Water Resources 77 (2015) 82–89 83

While a large body of literature exists documenting water entryinto gas-filled fractures under positive water pressures (e.g.,[2,10,12,22,23]), surprisingly few studies have investigated wateruptake into fractures when the gauge pressure of the water is zeroor less. These studies have involved either fractured cementitiousmaterials (concrete, engineered cementitious composites, andmortar) or rocks (granodiorite and sandstone).

The rapid penetration of water into individual air-filled frac-tures in steel-reinforced concrete was visualized using neutronimaging by Zhang et al. [40]. S�ahmaran and Li [27] found throughsorptivity testing that micro-cracks induced by mechanical loadingincreased the rate of water uptake in engineered cementitiouscomposites. Zhang et al. [41,42] confirmed this finding using neu-tron radiography, while Snoeck et al. [29] and Van Tittelboom et al.[35] employed the same method to investigate the crack sealingefficiency of various water repellant chemicals on capillary uptakein fractured mortar mixtures.

An early neutron imaging study of water imbibition into agranodiorite rock core containing a fault-gouge filled fracturewas conducted by Lunati et al. [17]. Due to the thickness of thecore, however, a relatively long exposure time (�40 s per image)was needed to obtain a reasonable spatial resolution. Hall [6] usedneutron radiography to quantify differential water uptake into aninitially air-dry sandstone core that had been subjected to triaxialcompression until just after macroscopic failure. Local fluid flowvelocities, extracted from image analysis of the neutron radio-graphs, indicated that water movement was fastest within com-pacted (low porosity) shear bands. This behavior was attributedto higher capillary forces within the shear bands, possibly due toincreased micro-crack density associated with localized damage.

Some of the above observations have been qualitatively inter-preted in terms of the dynamics of capillary uptake [38]. To date,however, no theoretical framework has been proposed that allowsfor a quantitative explanation of this phenomenon. The majorobjectives of this research were to: (i) present a theoretical modelfor predicting the 1-dimensional movement of water into a singleair-filled fracture within a porous medium, and (ii) acquire quanti-tative data on spontaneous imbibition of water in unsaturatedfractured Berea sandstone cores using dynamic neutron radiogra-phy with which to evaluate the proposed model.

2. Theoretical framework

The dynamics of water displacing air within a single straightcapillary tube are well established [37]. Washburn’s model wasderived by combining the Young–Laplace equation for the pressuredrop across the interface between two static fluids, with theHagen–Poiseuille equation for the pressure drop in a fluid flowingthrough a cylindrical tube. Cai et al. [1] modified this basic modelto predict the dynamics of capillary rise in a single tortuous capil-lary tube.

Here we represent a porous medium as a bundle of non-inter-acting tortuous capillary tubes, replacing the single tube diameter,k, in [1] with an effective diameter, hki, representing the centraltendency of the tube diameters within the capillary bundle, i.e.

dLdt¼ kh ir cos h

8ls2

1L� qg kh i2

32ls2 ð1Þ

where L is the height of the wetting front at time t, r is the air–water surface tension, h is the water–solid contact angle, l is theviscosity of water, q is the density of water, s is the tortuosity,and g is the gravitational acceleration. Integrating Eq. (1) fromL = 0 at t = 0 to L at time t yields:

t ¼ � A

B2 ln 1� BA

L� �

� LB

ð2Þ

where A ¼ kh ir cos h= 8ls2� �

and B ¼ qg kh i2= 32ls2� �

. At earlytimes, the effects of gravity are insignificant so that the last termon the right-hand side of Eq. (1) can be neglected. Integrating theresulting expression produces a linear relationship between thewetting front elevation and the square root of time, i.e.

L ¼ Cffiffitp

ð3Þ

where C ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffikh ir cos h

4ls2

qis a constant commonly referred to as the sorp-

tivity [5,21,24].The brittle failure of a loaded porous material can be expected

to result in an increase in the effective diameter, hki, of the fracturezone as compared to the unfractured matrix. The tortuosity, s, ofthe fracture zone is also likely to be decreased relative to that inthe unfractured matrix. The impact of such changes on rates ofcapillary rise within these two regions can be predicted fromEqs. (2) and (3) as illustrated in Fig. 1. Although increasing hkireduces the late-time equilibrium height of capillary rise in thefracture zone relative to that in the unfractured matrix, waterimbibition is markedly increased at early times. This effect is mag-nified when there is a corresponding reduction in tortuosity of thefracture zone (Fig. 1). Thus, capillary dynamics can explain themore rapid uptake of water in a fracture than in the surroundingmatrix during spontaneous imbibition.

In addition to capillary uptake within a fracture aperture, rapidwetting can also occur due to surface spreading of water on theside walls of the fracture. This phenomenon was first demon-strated by [30], and several recent experimental studies (e.g.,[9,16,36]) have documented the spreading of various liquids oversurfaces with different roughness attributes. Dragila [7] and Hayet al. [8] have proposed a theoretical model to explain the physicsof fluid spreading on rough surfaces.

We now derive an equation for the rapid early time uptake ofwater within an air-filled fracture that incorporates both capillarityand surface spreading. Assume L is the height of the wetting frontat time t in a smooth-walled fracture. Then the total height of thewetting front, x, at time t due to the combination of capillarydynamics and surface spreading effects in a rough-walled fractureis given by [8]:

x ¼ Dffiffitpþ L ð4Þ

where D is a constant of proportionality that is strongly dependenton the roughness geometry [8]. Substituting Eq. (3) into Eq. (4) andsimplifying the result gives:

84 C.-L. Cheng et al. / Advances in Water Resources 77 (2015) 82–89

x ¼ Dffiffitpþ C

ffiffitp¼ E

ffiffitp

ð5Þ

where E ¼ C þ Dð Þ is a lumped sorptivity parameter that combinesthe effects of both aperture capillarity and the wetting of rough sidewalls.

Lenormand [14] studied the pore-scale interfacial geometriesresulting from immiscible displacement of one fluid by anotherin a porous medium. Based on the relative dominance of viscousversus capillary effects the displacement can be categorized as ofone of the following types: viscous fingering, capillary fingering,or stable displacement. The displacement of air by water in ahomogenous porous medium during spontaneous imbibitionresults in a uniform wetting front at the macroscopic scale, so thatflow can be approximated as a 1-dimensional problem [11]. Thepresence of one or more fractures, however, introduces a secondflow domain, with water moving more rapidly in the fractures thanin the surrounding matrix. Over time the wetting front develops aspatially non-uniform profile with many peaks and depressions[41]. For this reason, macroscopic models for predicting spontane-ous imbibition in heterogeneous porous media often include a dis-persion parameter to account for capillary dispersion (e.g.,[4,13,39]).

Here we derive a first approximation of the spatial dispersion ofthe wetting front in a fractured porous medium in terms of the var-iance of the distances traveled within the matrix and fracturezones, respectively. We consider spontaneous imbibition only atearly times (i.e., neglecting the effect of gravity). It is assumed thatflow in both the matrix and fracture zones is 1-dimensional, withno interactions between the two flow domains. From Eq. (3), thedistance traveled by the wetting front at time, t, in the matrix,Lm, can be written as:

Lm ¼ Cm

ffiffitp

ð6Þ

where Cm is the matrix sorptivity. Likewise, from Eq. (5) the dis-tance traveled by the wetting front at time, t, in the fracture zone,xf, is given by:

xf ¼ Ef

ffiffitp

ð7Þ

where Ef is the fracture sorptivity. The dispersion coefficient, D, rep-resenting the spatial spreading of the wetting front in a heteroge-neous porous medium, can be calculated from the variance, r2, ofthe travel distances using the following expression [3,19]:

D � r2

2tð8Þ

For a dual domain porous medium comprised of an unfracturedmatrix and a fracture zone, the variance of the travel distances isgiven by:

r2 ¼ xf � Lm

2

� �2

ð9Þ

Substituting Eqs. (6), (7) and (9) into Eq. (8) and simplifying theresult produces the following expression for the dispersion of the

Table 1Mean values and associated standard errors (in parentheses) of measured hydraulic param

Permeabilityclass (mD)

Matrix porosity(m3 m�3)

Matrix sorptivitya

(mm s�0.5)Fracture aperturewidth (lm)

50 0.19 (0.01) 2.90 (0.21) 140 (20)200 0.25 (0.01) 4.05 (0.19) 780 (120)500 (replicate 1) 0.24 (<0.01) 3.77 (0.24) 350 (50)500 (replicate 2) 0.24 (<0.01) 4.55 (0.25) 120 (10)

a Average of the two replicate measurements reported in Fig. 4.

wetting front during early-time spontaneous imbibition in a frac-tured porous medium:

D � 18

Ef � Cm� �2 ð10Þ

Eq. (10) indicates that the dispersion coefficient is directly propor-tional to the difference in the sorptivities for the fractured andunfractured zones.

3. Materials and methods

3.1. Rock cores

Commercially available Berea sandstone cores with differenthydraulic properties were investigated. They were purchased fromCleveland Quarries (Vermillion, OH). According to Cleveland Quar-ries the mineralogical composition is of the Berea sandstone is asfollows: 93.13% Silica (SiO2), 3.86% Alumina (Al2O3), 0.11% FerricOxide (Fe2O3), 0.54% Ferrous Oxide (FeO), 0.25% Magnesium Oxide(MgO), and 0.10% Calcium Oxide (CaO). The individual cores were2.54 cm dia. � 5.08 cm long. They were supplied in three differentpermeability classes: �50, �200, and �500 mD. The porosities ofthe cores, determined from the solid volume measured with atemperature-controlled helium gas pycnometer (HumiPyc Model1, InstruQuest Inc., Coconut Creek, FL) and the bulk volume mea-sured with a NextEngine Desktop 3D Scanner (NextEngine Inc.,Santa Monica, Ca, USA) using the method of [25,26], were 0.19,0.25, and 0.24 for the 50, 200, and 500 mD permeability classes,respectively (Table 1).

3.2. Core preparation and fracture induction

The cores were wrapped in Kapton� tape (DuPont, Wilmington,DE) to provide a no flow barrier along the sides. The wrapped coreswere then fractured longitudinally by compression between paral-lel flat metal plates following the Brazilian method for determiningindirect tensile strength [15]. An example of a typical fracture zoneproduced by the Brazilian method is shown in Fig. 2.

3.3. Water imbibition setup

Prior to analysis the fractured cores were oven dried at 105 �Cfor 24 h. After cooling down they were suspended above a freewater table in a high purity aluminum cell that was open to theatmosphere. The aluminum cell was placed in the CG-1D neutronbeam line of the Neutron Imaging Prototype Facility at the HighFlux Isotope Reactor (HFIR), Oak Ridge National Laboratory (ORNL).The cell was positioned immediately in front of the detector (seebelow), and was connected to a Mariotte bottle [18] located out-side of the beam line using Tygon� tubing (Saint-Gobain S.A., LaDéfense, Courbevoie, France). The water table in the aluminum cellwas controlled externally using the Mariotte bottle. The waterlevel was carefully raised over time until it just touched the baseof each core. The time of contact was taken as the baseline time,

eters for the fractured Berea sandstone cores.

Fracture damage zonewidth (lm)

Fracture zone sorptivity(mm s�0.5)

Dispersion coefficient(mm2 s�1)

620 (80) 17.87 (0.78) 28.01 (3.71)1,610 (100) 27.12 (0.96) 66.53 (6.63)1,310 (80) 19.86 (0.85) 32.36 (4.38)1,170 (130) 18.32 (0.54) 23.70 (2.72)

Fig. 2. Example of a longitudinal air-filled fracture zone (dark gray) in an oven dry50 mD permeability class Berea sandstone core (light gray) imaged using neutronradiography at the HFIR’s CG-1D beam line, ORNL (see [11] for technical details). Forscale, the core is 2.54 cm dia. � 5.08 cm long. The aluminum container and basalreservoir can also be seen in outline. The core was wrapped in Kapton tape toprovide a no flow barrier along the sides. The top of the core was wrapped morethickly than the bottom resulting in the contrasting lighter and darker sections. The28 � 28 mm2 FOV for the fracture imbibition images in Fig. 3 is shown as a whitebox.

C.-L. Cheng et al. / Advances in Water Resources 77 (2015) 82–89 85

t = 0, for the imbibition measurements. The height of the watertable was then held constant for the duration of each experiment.

3.4. Dynamic neutron radiography

Neutrons are ideally suited to the task of visualizing the distri-bution and movement of water within variably-saturated porousmedia [20]. This is because they are strongly attenuated by thehydrogen atoms in water molecules, but are relative insensitiveto the gas phase in pores and minerals (such as silica and iron)which constitute the solid matrix. Digital images of the spatial pat-tern of neutron attenuation within a sample can be acquired inboth 2- and 3-dimensions (2-d and 3-d, respectively). Neutronradiography is the preferred mode of data collection for dynamicprocesses such as the rapid uptake of water within fractures since2-d radiographs can be acquired much more rapidly than 3-dtomograms.

Dynamic neutron radiography of the spontaneous imbibition ofwater displacing air in fractured Berea sandstone cores was per-formed at CG-1D Neutron Imaging Prototype Facility (HFIR, ORNL).CG-1D is a cold neutron beam line with a curved guide, whicheliminates gamma’s and epithermal neutrons from the spectrum.The neutron wavelengths vary between 0.8 and 6 Å, with peakintensity at 2.6 Å. Apertures with different diameters (d) are usedat the entrance of the helium-filled flight path (pinhole geometry)to allow for ‘/d variation from 400 to 800, where ‘ is the distancebetween the aperture and the detector. With these ‘/d ratios, thebeam has a very small angular divergence (a fraction of a degree)and an intensity of 107 neutrons/cm2/s.

The detector consisted of stacked neutron sensitive microchan-nel plates (MCP’s) placed above a quad Timepix readout with a28 � 28 mm2 field of view (FOV) [32]. The cold neutron detectionefficiency is 70% [31]. The native spatial resolution of the detectoris 55 lm determined by the pixel size of the Timepix readout, butsub-15 lm spatial resolutions can be achieved through event cen-troiding [33]. The detector configuration with fast parallel elec-tronics allows readout times of �290 ls [32,34] enabling >1 kHzframe rates. In our experiments, the dry rock cores were imagedat 25 lm spatial resolution with the MCP detector in centroidingmode. For the dynamic spontaneous imbibition experiments neu-tron radiographs were acquired at frequencies of 10–20 framesper second (50–100 ms, microsecond) (in order to acquire suffi-cient number of neutrons per image) with the detector in nativespatial resolution mode.

3.5. Image analysis and parameter estimation

The raw neutron radiographs were imported into ImageJ [28].The high spatial resolution images were normalized with respectto the open beam and despeckled to visualize the rock core andfracture damage zone (Fig. 2). The width of the fracture damagezone was measured at 15 equally-spaced locations along the entirelength of the core, and mean values and standard errors were cal-culated from these measurements. Additionally, images of the topand bottom faces of the fractured cores were acquired with a dig-ital camera, and these images were analyzed in ImageJ. The widthof the fracture aperture on each core face was measured at 10equally-spaced locations. The measurements from both fracturefaces were then averaged to provide estimates of the mean fractureaperture width and its standard error.

The wetting images were normalized with respect to the initialimage of the time sequence (when the core was completely dry) sothat only the imbibing water was resolved (Fig. 3). The resultingnormalized images were despeckled and thresholded so that thevertical distance between the water table and the tips of the wet-ting fronts in the matrix and fracture zone could be quantified overtime (Fig. 3).

Matrix and fracture zone sorptivities, Cm and Ef, were estimatedfrom the progression of the wetting front versus square root oftime data using linear regression with no intercept. A total of 6Berea sandstone cores were analyzed: 4 fractured cores (one fromeach permeability class plus a second core from the 500 mD per-meability class to assess between core variability) and 2 unfrac-tured cores (from the 200 and 500 mD permeability classes).Estimates of Cm (matrix sorptivity) for the 50 mD and second500 mD permeability class cores were obtained by analyzing theunfractured matrix on either side of the water-filled fracture zone,well away from the lateral spread of the wetting plume. To assesswithin core variability, two measurements of Cm were made withinthe unfractured matrix of each core. Dispersion coefficients for thefractured cores were calculated from the resulting estimates of Cm

and Ef using Eq. (10).

4. Results and discussion

The matrix porosity and fracture characteristics of the Bereasandstone cores are given in Table 1. The matrix porosity of the50 mD permeability core was substantially lower than the matrixporosities of the cores in the other permeability classes (Table 1).

The Brazilian method created fractures with aperture widths(measured on the top and bottom of the cores) ranging from120 to 780 lm (Table 1). There was no obvious relationshipbetween the width of the fractures and the matrix porosity orpermeability class of the cores. Instead, aperture width and

0 sec 0.1 sec 0.2 sec 0.3 sec

0.5 sec 1.0 sec 1.2 sec 1.4 sec

Lm

xf

LmRep 1 Rep 2

Fig. 3. Time sequence of neutron radiographs running from left to right and top to bottom showing the rapid uptake of water into a longitudinal, air-filled fracture zone inBerea sandstone (�50 mD). The images have been normalized with respect to the initial dry image, so that only water (black) is visible. The rock core, similar to the one inFig. 2, was positioned above a water table which contacted its base immediately after the first image. The height of the water table was then held constant. The annotations onthe 1.4 s image indicate where the distances traveled by the wetting front in the matrix, Lm, (2 replicate locations) and fracture zone, xf, were measured. For scale the width ofeach image is 26 mm.

86 C.-L. Cheng et al. / Advances in Water Resources 77 (2015) 82–89

fracture morphology appeared to vary randomly, highlighting theprobabilistic nature of the tensile failure process. The 50 mD andsecond 500 mD permeability class cores produced simple planarfractures that were uniformly narrow (Table 1), whereas the200 mD and first 500 mD permeability class cores produced com-plex planar fractures with bifurcations that were much wider andmore variable (Table 1).

The width of the fracture damage zone (estimated from theneutron radiographs) varied between 2 and 10 times the widthof the fracture aperture (Table 1). This zone included damage,deformation, and micro-cracking in addition to the fracture open-ing. The width of the fracture damage zone generally increased inproportion to the width of the fracture aperture (Table 1). Noapparent relationship was found between the width of damagezone and the matrix porosity, or the core permeability class.

Water uptake into all of the fractures was extremely rapid.Fig. 3 is a time sequence of neutron radiographs showing watermoving into the air-filled fracture damage zone of the 50 mD per-meability core. The pore water pressure was never positive as evi-denced by the menisci visible where the sides of the core contactthe water table (Fig. 3). At the end of this sequence of images thewetting front in the fracture zone had traveled approximately anorder of magnitude further than the wetting front in the matrix(i.e., the dark gray zone at the base of the core).

The Bond number (Bo) is a dimensionless quantity that can beused to demonstrate that gravity was negligible under the condi-tions of our experiments. The equation for the Bond number canbe written as:

Bo ¼ ðqw � qnÞgkrwn

ð11Þ

where qw and qn are the densities of the wetting and non-wettingfluids, respectively, k is the intrinsic permeability, rwn is the surfacetension of the interface between the wetting and non-wettingphases. If Bo� 1 then gravity can be ignored. For water and air asthe wetting and non-wetting fluids, respectively (qw = 1000 kg/m3,

qn = 0 kg/m3, and rwn = 0.0728 N/m) and g = 9.81 m/s2, the perme-ability values investigated in this study (k = 4.9 � 10�15 to4.9 � 10�14 m2) result in calculated Bo numbers of between6.6 � 10�9 and 6.6 � 10�8 which is much less than unity; so wecan safely assume the effect of gravity was negligible under the con-ditions of our experiments.

Quantitative results from the image analyses of the neutronradiographs are summarized in Fig. 4 and Table 1. The spontaneousimbibition of water into both the sandstone matrix and the frac-ture damage zone exhibited square-root-of-time behavior. This isevidenced by the excellent coefficient of determination (R2) values(i.e. >0.9) for Eqs. (6) and (7) fitted to the experimental observa-tions regardless of the location of the uptake (Fig. 4). It can be seenthat the first point of some of the data sets (e.g., the fracture zonein Fig. 4a and the matrix in Fig. 4c) tends to fall below the best fitline. These outliers indicate deviations from square-root-of-timebehavior at very early times. Possible causes of these deviationsare: (1) the base of the core may not have be perfectly aligned withthe water surface resulting in partial contact at very early times,and (2) the first image was integrated over a relatively long periodof time (5–10 ms) relative to the rate of wetting at very early times.

Between core variability of the matrix and fracture zone wateruptake measurements can be assessed by comparing the results forthe two 500 mD permeability class cores in Fig. 4c and d. In gen-eral, both sets of measurements were reasonably comparable;coefficients of variation (CV) calculated from the slopes of theregression equations for the two cores were 6% and 12% for thematrix and fracture zone data, respectively. In some respects, onemight have expected greater variability between the fracture imbi-bition measurements for these two cores due to the different aper-ture and damage zone widths (Table 1).

The replicate measurements of spontaneous imbibition of waterinto the unfractured matrix of each core permit an assessment ofthe within core variability for this measurement. The results inFig. 4 indicate generally good reproducibility; the 50 mD permeabil-ity class core (Fig. 4a) exhibited the greatest variability with a CV of

(b)(a)

(d)(c)

Fig. 4. Height of the wetting front versus the square root (Sqrt) of time in the matrix (2 replicate measurements per core) and fracture zones of Berea sandstone measuredusing dynamic neutron radiography. Each graph corresponds to a different permeability class: (a) 50 mD, (b) 200 mD, (c) 500 mD (core #1), and (d) 500 mD (core #2). Thereplicate matrix measurements in (a) and (c) were measured on the sides of the fractured cores, while those in (b) and (d) were measured on separate unfractured cores. Theslopes of the fitted linear regression models represent the sorptivity estimates.

C.-L. Cheng et al. / Advances in Water Resources 77 (2015) 82–89 87

17%, while the CV’s for the other three cores were all <2.5%. Sincethere was only one fracture damage zone per core it was not possibleto assess within-core variability for this parameter.

The matrix sorptivities ranged from 2.90 to 4.55 mm s�0.5

(Table 1), and increased linearly as the permeability class increased(Fig. 5a). The matrix sorptivity coefficient changed by a factor of �2as the permeability changed by a factor of �4 which is consistentwith the traditional assumed square dependence of the permeabil-ity on the mean pore size (Table 1).

The average value for the 50 mD permeability class core was�2.5 times higher than the average matrix sorptivity for Bereasandstone determined by [11] using the same method. The coresanalyzed by [11] were supplied by a different company and hada slightly lower average permeability of �42 mD. Moreover, dueto differences in the detector systems employed by the two stud-ies, water uptake data were collected over two completely differ-ent time frames. In the present study, measurements were madeover the range 0.1–2.0 s, whereas the [11] data were obtained overthe range 5–50 s with a charge-coupled device (CCD) detector atthe same beam line. Thus, the lower matrix sorptivities reportedin [11], as compared to those in Table 1 can be attributed to a com-bination of lower core permeability and the increased effect ofgravity at later times as described by Eq. (2).

The fracture damage zone sorptivities were between 4 and 7times greater than the corresponding matrix sorptivities (Table 1).The sorptivities of the fracture damage zones ranged from 17.87 to27.12 mm s�0.5 (Table 1), and increased linearly with increasing

fracture aperture width (Fig. 5b). The fracture sorptivity coeffi-cients for the 50 and 500 md (replicate #2) permeability coressamples were similar, which is consistent with the similar fractureaperture widths in these two samples (Table 1).

The sorptivity results indicate that fractures can significantlyincrease spontaneous imbibition in unsaturated sedimentary rockby capillary action and surface spreading on rough fracture faces.Our results are consistent with the studies by S�ahmaran and Li[27] and Zhang et al. [40,41], which showed enhanced sorptionin fractured cementitious materials. The rates of water uptakeobserved in the present study were surprisingly rapid. The fracturesorptivities in Table 1 indicate that wetting fronts can travelbetween 2 and 3 cm in 1 s in unsaturated damage zones.

We ran a simple qualitative experiment to isolate the phenom-enon of water spreading over a rough fracture surface, Eq. (4) fromthe dynamics of capillary rise within a narrow fracture aperture,Eq. (3). An oven-dry 500 mD permeability class Berea sandstonecore was fractured as described previously. The two halves of thefractured rock core were carefully separated and one half wasrotated 180� relative to the other half. The two halves were thenplaced side-by-side, at the same time, in a shallow pan of waterso that water uptake could be monitored simultaneously on theinterior (fracture face) and exterior surfaces of the core.

Fig. 6 shows the results of spontaneous imbibition of water intothe two halves of the fractured core after approximately �1–2 s ofwetting. It can be clearly seen that the wetting front has movedapproximately twice as far on the rough fracture surface as

Fig. 5. Linear regression relationships between the sorptivity and dispersion estimates and core permeability class and fracture parameters: (a) matrix sorptivity versuspermeability class, (b) fracture zone sorptivity versus fracture aperture width, (c) dispersion coefficient versus fracture aperture width, and (d) dispersion coefficient versusfracture zone width. The horizontal and vertical bars around the individual data points represent plus and minus standard errors.

Fig. 6. Spontaneous imbibition of water into a fractured, oven dry 500 mDpermeability class Berea sandstone core showing the differential extent of wettingon the rough interior fracture surface as compared to the smooth exterior surface.

88 C.-L. Cheng et al. / Advances in Water Resources 77 (2015) 82–89

compared to the wetting front on the smooth exterior of the core.This movement occurred in the absence of the second fracture face,indicating that water spread over the rough surface of the exposedfracture face, similar to the observations of [30,36]. The wettingfront on the other half of the core, with its smooth exteriorexposed, can be attributed to capillary rise within the unfracturedmatrix. It is interesting to note that the wetting front on the exte-rior of the core was curvilinear. This was likely due to surfacespreading on the (unseen) fracture face on the other side of this

half of the core which has induced water to move more rapidlyalong the edges. Overall, this simple experiment demonstrates thatsurface spreading contributes significantly to the rapid imbibitionof water in fractured sedimentary rocks.

The dispersion coefficients, calculated from the matrix and frac-ture sorptivities, ranged from 23.7 to 66.7 mm2 s�1 (Table 1).Fig. 5c and d indicate that dispersion increased linearly withincreasing width of both the fracture aperture and its associateddamage zone. The strongest relationship was with the fractureaperture width. The larger the dispersion parameter, the greaterthe spreading of the wetting front within the core.

5. Concluding remarks

Neutron radiography was able to capture the early-timedynamics of spontaneous imbibition of water in fractured, unsatu-rated sedimentary rock cores. Rates of water uptake into the frac-ture damage zones were surprisingly rapid, with wetting frontstraveling between 2 and 3 cm per second. A theoretical modelwas derived to explain these results. The rapid water uptake wasattributed to a combination of early time capillary rise within thefracture aperture and spreading over the rough surfaces of theopposing fracture faces. The theory also permits estimation ofsorptivity values for the matrix and fracture zones, as well as a dis-persion parameter, which quantifies the extent of spreading of thewetting front. The sorptivity of the fracture zone and the disper-sion coefficient both increased linearly with increasing fractureaperture width.

The current theoretical framework represents only a 1-dimen-sional approximation of spontaneous imbibition within a fractured

C.-L. Cheng et al. / Advances in Water Resources 77 (2015) 82–89 89

porous medium. To fully describe this phenomenon the derivationof a 2-dimensional model, that permits interaction between thefracture and matrix, will be needed. The development of such amodel represents an exciting opportunity for future research.

The present results for fractured Berea sandstone are consistentwith observations of rapid water uptake in fractured cementitiousmaterials. Additional research is needed to document this phe-nomenon in other natural and engineered porous media. The phe-nomenon is likely to be particularly important in the case of porousmaterials such as bricks and building stone used in engineeringapplications. Given the current high level of interest in unconven-tional gas from black shale, similar experiments performed on frac-tured shale cores may also be valuable. The spontaneousimbibition of water-based fracking fluids into damage zones cre-ated by hydraulic fracturing operations could potentially result insignificant losses of water (‘‘leakoff’’) with concomitant blockagesof the pathways available for efficient gas extraction.

Acknowledgments

E. Perfect acknowledges support from David E. Jackson of BDYEnvironmental LLC, Nashville, TN through a Faculty AchievementAward. Research conducted at ORNL’s High Flux Isotope Reactorwas sponsored by the Scientific User Facilities Division, Office ofBasic Energy Sciences, U.S. Department of Energy.

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