Pore-scale dynamics of salt transport and distribution in drying porous mediaNima Shokri

Citation: Physics of Fluids (1994-present) 26, 012106 (2014); doi: 10.1063/1.4861755 View online: http://dx.doi.org/10.1063/1.4861755 View Table of Contents: http://scitation.aip.org/content/aip/journal/pof2/26/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetic resonance imaging study on near miscible supercritical CO2 flooding in porous media Phys. Fluids 25, 053301 (2013); 10.1063/1.4803663 Lattice Boltzmann method for modeling heat and mass transfers during drying of deformable porous medium AIP Conf. Proc. 1453, 211 (2012); 10.1063/1.4711177 Drying of salt solutions in porous materials: Intermediate-time dynamics and efflorescence Phys. Fluids 20, 077101 (2008); 10.1063/1.2954037 Linear stability analysis of immiscible two-phase flow in porous media with capillary dispersion and densityvariation Phys. Fluids 16, 4727 (2004); 10.1063/1.1812511 How ions distribute in a drying porous medium: A simple model Phys. Fluids 14, 1389 (2002); 10.1063/1.1451081

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PHYSICS OF FLUIDS 26, 012106 (2014)

Pore-scale dynamics of salt transport and distributionin drying porous media

Nima Shokria)

School of Chemical Engineering and Analytical Science, University of Manchester,Manchester M13 9PL, United Kingdom

(Received 19 July 2013; accepted 27 December 2013; published online 16 January 2014)

Understanding the physics of water evaporation from saline porous media is importantin many natural and engineering applications such as durability of building materialsand preservation of monuments, water quality, and mineral-fluid interactions. Weapplied synchrotron x-ray micro-tomography to investigate the pore-scale dynamicsof dissolved salt distribution in a three dimensional drying saline porous mediausing a cylindrical plastic column (15 mm in height and 8 mm in diameter) packedwith sand particles saturated with CaI2 solution (5% concentration by mass) with aspatial and temporal resolution of 12 μm and 30 min, respectively. Every time thedrying sand column was set to be imaged, two different images were recorded usingdistinct synchrotron x-rays energies immediately above and below the K-edge valueof Iodine. Taking the difference between pixel gray values enabled us to delineatethe spatial and temporal distribution of CaI2 concentration at pore scale. Resultsindicate that during early stages of evaporation, air preferentially invades large poresat the surface while finer pores remain saturated and connected to the wet zone atbottom via capillary-induced liquid flow acting as evaporating spots. Consequently,the salt concentration increases preferentially in finer pores where evaporation occurs.Higher salt concentration was observed close to the evaporating surface indicatinga convection-driven process. The obtained salt profiles were used to evaluate thenumerical solution of the convection-diffusion equation (CDE). Results show thatthe macro-scale CDE could capture the overall trend of the measured salt profilesbut fail to produce the exact slope of the profiles. Our results shed new insighton the physics of salt transport and its complex dynamics in drying porous mediaand establish synchrotron x-ray tomography as an effective tool to investigate thedynamics of salt transport in porous media at high spatial and temporal resolution.C© 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4861755]

I. INTRODUCTION

Understanding the physics of water evaporation from porous media saturated with salt solutionis important in many natural and engineering processes such as durability of building materials andpreservation of pavements, paintings, and historical monuments, CO2 sequestration, permeabilityalternation, and intrusion of groundwater aquifers by saline water.1–7 Many chemical reactions andbiological activities in soil are modified due to the presence of salt in the environment affecting theecosystem functioning, plant growth and human health. Thus it is important to develop accuratemodeling and experimental tools to describe and predict the dynamics of salt distribution in dryingporous media under a given boundary condition.

Initially, the evaporation rate from saturated porous media is relatively high and rather constant(the so-called stage-1 evaporation) limited by the atmospheric conditions, followed by a lower value

a)Author to whom correspondence should be addressed. Electronic mail: nima.shokri@manchester.ac.uk. Telephone:+44 161 3063980.

1070-6631/2014/26(1)/012106/9/$30.00 C©2014 AIP Publishing LLC26, 012106-1

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012106-2 Nima Shokri Phys. Fluids 26, 012106 (2014)

which is limited by transport properties of porous media, the so-called stage-2 evaporation.8–13

During stage-1, the evaporative flux is supplied by the capillary-induced liquid flow from largerpores at a receding drying front (defined as the interface between saturated and partially wet zone)to the water-filled fine pores at the evaporating surface. This mechanism is the key to maintain arelatively constant evaporation rate despite of the decreasing water content of the medium duringstage-1.8 At a certain depth of the drying front, the downward gravity and viscous forces overcomethe upward capillary driving force, disrupting the hydraulic continuity with the surface.8, 9 Thedisruption of capillary liquid pathways marks the end of stage-1 evaporation; consequently liquidmeniscus recedes from the surface to a level below the surface and forms a new vaporizationplane.8, 14 This transition marks the onset of stage-2 evaporation; a period with a lower evaporationrate limited by the diffusion through the porous media.14 The subsequent evaporation is governedby the capillary liquid flow from the wet zone at bottom to the newly formed vaporization plane(located inside the porous medium), liquid vaporization at that level, and vapor diffusion throughthe overlying dry layer close to the surface as described theoretically and experimentally in otherstudies.8, 14

During evaporation from porous media saturated with saline solution, salt is transported towardthe evaporation surface by convection due to the upward capillary-induced liquid flow, whereasdiffusion tends to spread the salt uniformly and homogenize the salt concentration in space.15–17 Theresulting interplay between convection and diffusion influences the dynamics of salt transport inporous media. When the salt concentration at the surface exceeds the salt solubility limit, precipitationoccurs which is called efflorescence referring specifically to evaporatively driven soluble salt fromthe interior of the porous media to the surface where evaporation practically takes place.17 Asstated in Veran-Tissoires et al.,18 “the understanding of the efflorescence formation and growth atthe surface of a porous material is surprisingly not very advanced.” Although evaporation fromporous media saturated with pure water is a relatively well understood process,8–14, 19–25 our physicalunderstanding and ability to model the fate and transport of salt in drying saline porous media is stilllimited, leaving many fundamental questions open such as the dynamics of salt transport within thecomplex pore network or its relation with the heterogeneities of porous media.

Recently effects of several parameters such as surface heterogeneity,18 salt concentration,16

structure of porous media,26, 27 and wettability of the grains28 on solute transport and precipitationpatterns in drying porous media have been investigated at macro-scale. The majority of the previousstudies on the drying of saline porous media were performed at the continuum scale where processesoccurring at the pore level which in many cases controls the macroscopic behavior are not captured.With a few exceptions,29 dynamics of salt transport at pore scale in drying porous media have beenrarely studied experimentally largely due to the complexity of the problem and limitations imposedby available techniques. Thanking to recent advances in three-dimensional (3D) imaging techniques,the drying dynamics of saline porous media could be investigated in 3D. Shokri et al.29 was one of thefirst who used synchrotron x-ray tomography to study drying of saline porous media at pore-scale.As a first-order approximation, they assumed a linear relationship between salt mass fraction andgray value of the liquid in the recorded images to determine salt concentration. Such an assumptionmay introduce certain errors in estimation of total salt concentration as discussed in Shokri et al.29

The obtained pore-scale data were used to evaluate the performance of the analytical solution of theconvection-diffusion equation (CDE) introduced in Guglielmini et al.17

Accurate pore-scale information is needed to understand the physics of salt transport anddistribution in drying porous media required to develop reliable predictive models. This paperhas been motivated by the important application of salt transport and dynamics in drying porousmedia which is relevant to the environment, sustainability, and many engineering applications.Within this context, the key objectives of the present paper are (a) to offer a novel method toaccurately determine the dynamics of dissolved salt transport and distribution in a 3D drying porousmedium at pore-scale using the synchrotron x-ray micro-tomography technique with a high temporaland spatial resolution, (b) to enhance the physical understanding of the mechanism governingsolute transport in drying porous media, and (c) to evaluate numerically the performance of themacro-scale convection-diffusion equation in describing the measured salt profiles in drying porousmedia.

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012106-3 Nima Shokri Phys. Fluids 26, 012106 (2014)

II. EXPERIMENTAL CONSIDERATIONS

The evaporating system consisted of a cylindrical plastic column with an inner diameter of8 mm and a height of 15 mm. The column was packed with sand grains saturated with a water-CaI2

solution of 5% concentration by mass. The sand particle size distribution is presented in the insetof Fig. 1 measured using a CAMSIZER Digital Image Processing Particle Size (from Horiba).The resulting average packing porosity was 0.38. The porosity variation through the sand pack isillustrated in Fig. 1 computed from the recorded pore-scale images.

All boundaries were closed except the top boundary which was open to air for evaporation. Theevaporation experiment was conducted using synchrotron x-ray microtomography at the GeoSoilEn-viroCARS (GSECARS) BM-13BMD beamline at the Advanced Photon Source, Argonne NationalLaboratory, IL.30 Image reconstruction was performed using programs developed by GSECARS toconvert x-ray attenuation to 3D volumetric data. The resolution of the images was 12.012 μm. Theheight of the imaged zone in each scan was 6.25 mm. To visualize phases distribution over the entirecolumn height, the column was shifted after each scan resulting in three blocks of images illustratingthe cross sectional area of the sand column. In the following analysis, the top 13.25 mm of the sandcolumn is used which includes 1103 reconstructed images of the horizontal cross sections with grayvalues representing density distribution throughout the porous medium.

The synchrotron beam was tuned to specific incident energies to use the x-rays absorptionK-edge value as a mean to determine the element of interest in 3D volume.31, 32 In the present study,the distribution of dissolved salt through the drying sand column was determined by performing twoscans at different x-rays energies in which the x-rays energies were selected to be just below andabove the absorption edge of the Iodide. In other words, every time the drying sand column wasset to be imaged, two different images were recorded (each of which took ∼4 min) using distinctx-ray energies immediately above (33.2690 keV) and below (33.0690 keV) the K-edge value ofIodine (33.1694 keV). Taking the difference between the pixel gray values enabled us to delineatethe spatial and temporal distribution of salt concentration at pore scale in the drying sand column.The experiment was continued for 12 h. The scanning time of the entire column (which includesthree blocks of cross sectional images recorded with two different x-rays energies) was about 25min in each scan resulting in almost two scans per hour during the course of the experiment. Tocalibrate the gray values, CaI2 solutions with concentration of 2%, 5%, and 25% (by mass) were alsoimaged (in the absence of sand grains) at the same energy levels above (33.2690 keV) and below(33.0690 keV) the Iodine K-edge value. The inset of Fig. 2 shows the calibration curve which wasused to relate the gray value at any given pixel and time to the salt concentration so that the temporaland spatial salt distribution could be delineated at pore-scale.

Also presented in Fig. 2 is the salt concentration profile over the entire sand column calculatedfrom the images scanned at the beginning of the experiment which is in a reasonable agreementwith the 5% initial salt concentration. In contrary to Shokri et al.29 in which the drying sandcolumn was scanned only at one synchrotron x-ray energy level and the reported salt concentrationswere computed assuming a linear relationship between the salt concentration and gray values of

FIG. 1. Spatial variation of porosity through the sand column computed using the pore-scale images recorded by synchrotronx-ray tomography. The inset shows the particle size distribution of sand grains used in the experiment.

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FIG. 2. Computed salt concentration by image analysis at the onset of the experiment (when the sand column was initiallysaturated with salt solution of 5% concentration). The inset shows the calibration curve used to convert the gray valuedifferences to the salt concentration.

liquid phase, the salt concentrations computed in this study represents the absolute values of saltconcentration at any given location in the 3D drying sand column thanking to scanning the columnat two different energy levels immediately below and above the K-edge value of Iodine.

III. RESULTS AND DISCUSSIONS

A. Evaporative water losses and hydraulic continuity

To determine the evaporative water losses and calculate the liquid, solid, and air phase distribu-tions at pore-scale, the recorded gray level images were segmented into three phases following theprocedure described in Shokri et al.29 Figure 3 presents typical segmented images that illustrate theair, water, and solid phase distributions at a cross section which was located 2.5 mm below the sandsurface, at three different times from the onset of the experiment. Figure 3 shows the preferentialinvasion of large pores by air while the finer pores (e.g., the ones located at the grain contacts)remained liquid-filled due to the higher capillary pressure required to de-saturate the finer pores.Similar results were reported in other studies.29

The same segmentation algorithm was applied to all recoded cross sections to delineate theevaporative water losses and the dynamics of liquid phase distribution during evaporation. Theresults are presented in Fig. 4 in which the cumulative water losses computed by image analysisduring evaporation together with the evolution of water saturation at the surface versus time arepresented.

The constant slope of the cumulative mass loss curve indicates that the evaporation processwas in the stage-1 evaporation during our experiment. Figure 4 also confirms the presence of waterat the surface during the entire course of the experiment. As explained earlier, during stage-1,liquid is transported toward the surface via capillary induced liquid flow to meet the evaporative

FIG. 3. Two-dimensional horizontal cross sections illustrating the distribution of air (white), liquid (gray), and solid (black)phases at 2.5 mm depth below the sand surface. Numbers at top indicate the elapsed time from the beginning of the experiment.

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012106-5 Nima Shokri Phys. Fluids 26, 012106 (2014)

FIG. 4. Cumulative evaporative water losses from the sand columns. Also illustrated is the evolution of water saturation atthe surface versus time confirming the presence of liquid at the surface during the entire course of the experiment indicativeof the so-called stage-1 evaporation.

demand keeping the surface partially wet and maintaining a constant evaporation rate which is thecharacteristic of the stage-1 evaporation from porous media.9, 11, 13, 14, 20, 26, 29, 33

B. Dynamics of dissolved salt distribution in 3D drying sand column

Figure 5 illustrates the air, solid, and liquid phase distribution at the surface of sand columnafter 8.5 h from the onset of the experiment. Figures 5(a) and 5(b) present typical examples of therecorded images with the x-rays energy levels above and below the K-edge value of the Iodine. Theregions with the higher salt concentrations at the surface are reflected in Fig. 5(a) by bright color.Figure 5(c) illustrates differences in gray values corresponding to images presented in Figs. 5(a) and5(b). The bottom row in Fig. 5 illustrates the same images as the ones presented in the top row butwith a different color-map. In Fig. 5(d), the closer the color is to green (bright color) the higher isthe dissolved salt concentration.

FIG. 5. Images of phase distribution at sand surface after 8.5 h from the onset of the experiment. The image was taken withsynchrotron x-rays energies immediately above and below the K-edge value of Iodine presented in (a) and (b), respectively.(c) Image calculated by subtraction of the pixel gray values in Figs. 5(a) and 5(b). Black, light gray, and dark gray in(a) and (b) correspond to air, liquid and solid phases, respectively. The bright color in (c) indicates the regions withdifferent salt concentrations. The bottom row is basically the same as top except presented with a different color-map toqualitatively illustrate non-uniform salt distribution at surface as influenced by pore sizes. The color spectrum indicates thesalt concentration such that the closer the color is to bright color (green) the higher is the salt concentration in those regions.

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This figure reveals the non-uniform distribution of salt concentration at the surface with higherconcentration in the finer pores.34 As discussed earlier, during stage-1 evaporation, the fine pores atthe surface act as preferential sites for liquid vaporization while the large pores are invaded quicklyby air immediately after the onset of the experiment. This results in preferential deposition of saltin the fine pores which are hydraulically connected to the wet zone via capillary-induced liquidflow. In addition to the preferential salt deposition in the fine pores, Fig. 5 illustrates that the saltconcentration is not uniform even in each individual pore as reflected in the color spectrum in eachpore filled by liquid such that the color (representing the salt concentration) is brighter in regionscloser to the grains’ surface indicating higher salt concentration. This observation infers that thestrongest evaporation takes place near the meniscus contact lines.35

Using the calibration curve obtained in Fig. 2 and the gray value differences presented inFig. 5(c), one can delineate the pore-scale distribution of dissolved salt concentration at any givenlocation in Fig. 5(c). The same analysis was performed to all cross sections imaged during 23scans performed in this experiment to resolve the temporal and spatial distribution of dissolved saltconcentration through the evaporating sand column. The typical results are presented in Fig. 6(a)showing the salt concentration throughout the evaporating sand column at different times from theonset of the experiment. The slight fluctuations observed in the computed salt profiles in Fig. 6(a)could be related to the accuracy of the method and also the presence of possible heterogeneity as aresult of sand packing in the column. The results obtained show higher salt concentration in regionsclose to the surface. Similar results were reported in other papers too.36

The overall trend of dissolved salt profiles through the evaporating porous media can be describedby evaluating the Peclet number, Pe, quantifying the relative importance of convective to diffusivetransport defined as Pe = eL

Dsε, where e is the evaporation rate, L is the length of the column, Ds

is the effective diffusion coefficient of solute in porous media, and ε is the porosity. A greater saltconcentration close to the surface is expected when Peclet number is more than one indicating aconvection-driven process. This is the case in our experiment in which the Peclet number is estimatedto be about 2. Therefore, the upward convective transport tending to transport the salt toward thesurface dominates the diffusive transport tending to homogenize the concentration in space. As aresult of this competition, the salt concentration is higher closer to the surface.

C. Numerical analysis

The Convection-diffusion equation (CDE) was solved numerically and the obtained results wereevaluated using the pore-scale experimental data measured in this study. Under the assumption ofnegligible ion adsorption on the pore wall and assuming a 1D vertical solute transport, the CDE isgiven by:12, 15, 17, 37

∂(ρεSC)

∂t= ∂

∂z

(ρεSDs

∂C

∂z− ρεSCU

)(1)

FIG. 6. (a) Spatial and temporal distributions of salt concentration at different times throughout the evaporating sand columndeduced from the images recorded by synchrotron x-rays. The numbers in the legend indicate the elapsed time from the onsetof the experiment. (b) Salt profiles obtained by the numerical solution of CDE solved with constant and variable diffusioncoefficient (D0 = 2.045 × 10−9m2/s). The numbers indicate the elapsed time from the onset of the experiment. Se refers tothe saturation-dependent part of Eq. (2); i.e., Se = (S−Sc)/(1−Sc).

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012106-7 Nima Shokri Phys. Fluids 26, 012106 (2014)

with C(z, t) the mass fraction of dissolved salt, ε the porosity, Ds the effective diffusion coefficient ofsolute in porous media, ρ the density of the solution, z the depth below surface, U the average liquidvelocity, t the time, and S the liquid saturation. In the numerical simulation, two definitions were usedfor the effective diffusion coefficient. In the first method, it was assumed that Ds is constant and equalto Ds = ε0.4D0 with D0 the Iodine diffusion coefficient in water, D0 = 2.045 × 10−9m2/s accordingto Flury and Gimmi.38 However, since the liquid structure changes as evaporation proceeds, Ds

should change accordingly. As stated in Sghaier et al.12 surprisingly this effect is generally ignoredin literature and many authors simply assume a constant value for the effective diffusion coefficient.Therefore, in the second method, following Sghaier et al.12 we assume that the diffusion coefficientvaries roughly linearly with the liquid saturation as:

Ds ≈ S − Sc

1 − Scε0.4 D0, (2)

where Sc is the residual liquid saturation (in this study a constant value of Sc = 0.1 is assumed).Equation (1) was solved numerically to evaluate the performance of the CDE on describing thedynamics of dissolved salt distribution in drying porous media. The boundary conditions are thatthe diffusive and convective fluxes are equal at z = 0 and z = L since the ions cannot escapethe liquid phase. We assume that the liquid saturation is spatially uniform and varies with timeas S = 1 − e/(ρεL)t with e the evaporation rate.17 Using a similar mass balance argument as theone used in Huinink et al.,15 the liquid velocity U and the evaporation rate e can be related toeach other using U = e

SεL (z − L). More details about the numerical simulation of the CDE aregiven elsewhere,15–17, 37 thus it is not repeated here. The numerical results obtained are illustrated inFig. 6(b) showing the spatial distribution of dissolved salt concentration through the evaporatingsand column at different elapsed times from the onset of the experiment. Results show that applyingthe CDE at macro-scale captures the overall trend of the measured salt profiles but fails to producethe exact slope of the curves and values of the salt concentration. This is partly due to the preferentialtransport processes occurring at pore-scale during evaporation from saline porous media which arenot considered in the macro-scale solution of the CDE. In other words, the macro-scale CDE cannotaccount for the pore-scale effect that salt is preferentially deposited in the fine pores according tothe pore sizes and the contribution of each pore in the evaporation. To take into account such effects,one needs to carry out 3D simulation with distributed heterogeneity to account for the preferentialphenomena occurring during solute transport in drying porous media. Another source of the deviationcould be attributed to the relationship between the diffusion coefficient and the liquid saturation.

IV. SUMMARY AND CONCLUSIONS

A novel method was used to measure the dynamics of salt distribution during evaporation from a3D porous medium at pore-scale. The pore-scale images obtained by synchrotron x-ray tomographyreveals that at the early stages of evaporation, air preferentially invade large pores at the surfacewhile finer pores remain saturated (due to higher capillary pressure) and connected to the wet zone atbottom via capillary induced liquid flow. The evaporation was supplied by liquid transport toward thesurface and liquid vaporization at that level. Scanning the evaporating column at two different x-rayenergy levels enabled us to accurately determine the temporal and spatial distribution of dissolvedsalt during evaporation at pore-scale. The pore-scale imagery shows that the finer pores at the surfaceact as preferential evaporating sites. Consequently, the salt concentration increases preferentiallyin fine pores where evaporation takes place. This results in non-uniform salt distribution at theevaporation surface which is influenced by the pore size distribution. Also, the recorded pore-scaleimages show that the salt concentration is not even uniform within any individual pore (filled byliquid) such that the salt concentration is higher at regions closer to the pore walls (grains surface)revealing the occurrence of stronger evaporation at the meniscus contact line.

The measured salt profiles were used to evaluate the numerical solution of the convection-diffusion equation in which the variation of the ion diffusion coefficient with the liquid saturationwas also taken into account. Our analysis shows that applying CDE at macro-scale captures theoverall trend of the measured salt concentration profiles but fails to produce the exact slope of the

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012106-8 Nima Shokri Phys. Fluids 26, 012106 (2014)

curves and the exact values of the measured salt concentration. This study showed the limitationof applying macro-scale CDE to model salt distribution in drying porous media without adequateattention to the processes occurring at pore-scale which has been practiced universally by manyresearchers. Our analysis unambiguously shows that the pore-scale understanding of salt transportin drying porous media is required to describe the macroscopic profiles and that one must carryout full 3D pore network simulations with distributed heterogeneity at larger scales to account forthe preferential phenomena occurring during solute transport in drying porous media. Our resultsprovide new insights into the physics of salt transport and its complex dynamics in drying salineporous media relevant to many engineering, environmental and hydrological processes. Besides, thisstudy illustrated the application of the synchrotron x-ray micro-tomography as an effective meansto investigate the dynamics of salt distribution and transport in porous media at high spatial andtemporal resolution.

ACKNOWLEDGMENTS

Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S.Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported bythe U.S. DOE under Contract No. DE-AC02–06CH11357. The synchrotron x-ray microtomographywas conducted at the GeoSoilEnviroCARS (GSECARS) BM-13BMD beamline. We would like tothank Dr. Mark Rivers for his assistance, great suggestions, and expertise in running the experimentwith the synchrotron x-rays tomography. We are grateful to Mr. Peng Zhou (a visiting student inDr. Shokri’s research laboratory) and Nicholas Grapsas (an undergraduate student working underDr. Shokri’s supervision) for conducting the synchrotron experiment. Acknowledgment is made tothe donors of the American Chemical Society Petroleum Research Fund for partial support of thisresearch (PRF No. 52054-DNI6).

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