Proceedings of Hydrology Days 2002, Pages 56 – 63, April 1 – 4, 2002

Hydrology Days 2002

Real-time measurement of water profiles in a sand using neutron radiography

Mark Deinert Nuclear Science and Engineering, Cornell University, Ithaca, NY 14853 J.-Yves Parlange1, Tammo S. Steenhuis Department of Biological and Environmental Engineering, Cornell University, Ithaca, NY 14853 Kenan Ünlü Ward Center for Nuclear Sciences, Cornell University, Ithaca, NY 14853 John Selker Department of Bioresource Engineering, Oregon State University, Corvallis, OR 97331 K. Bingham Cady Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853 Abstract. Digital images of water profiles in an air-water-sand system were obtained using real-time neutron radiography. This imaging technique provided measurements of moisture content at video frame rates with a spatial resolution of 0.2 mm2 and an image area > 400 cm2. The experiments were conducted using aluminum chambers filled with SiO2 sand packed to a total porosity of 0.33. The velocity and water content within a flow field were obtained by measuring the intensity change of a neutron beam as it passed through the experiment chamber. The variation in matric potential within the flow field was obtained and the results were compared to the measurements of matric potential made by Selker (1992). 1. Introduction The need for better methods with which to image transient flows in porous media has been discussed by a number of authors (e.g. Darnault et al., 2001; DiCarlo et al., 1997). Neutron radiography can be used for quantitative imaging of hydrologic phenomena at video frame rates, with great sensitivity to variations in moisture content, sub-millimeter resolution and image fields greater than a few hundred square centimeters. 1 Department of Biological and Environmental Engineering Riley-Robb Hall Cornell University Ithaca, NY 14853 Tel: 607-255-2476 e-mail: jp58@cornell.edu

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We used real-time neutron radiography to image both fluid infiltration into dry sand and steady state flow fields. The results were used to measure wetting front velocities, the hydraulic conductivity of the media, the average moisture content in a flow field as a function of distance from a wetting front, and to deduce the variation in matric potential within the flow field. 2. Theory For a wetting front moving at constant velocity Selker, et al. (1992) derived an expression relating the one-dimensional flux in a flow field to the hydraulic conductivity and diffusivity of the media:

)( + )( v θξθθθ K

ddD= (1)

where θ is the horizontal average of the soil moisture content {cm3•cm-3}, K(θ) is the hydraulic conductivity {cm•sec-1}, D(θ) is the diffusivity {cm2• sec-1} v is the wetting front velocity {cm•sec-1} and ξ = vt - z where t is time {sec} and z {cm} is the distance from the point of infiltration (positive down). When dθ /dξ = 0.0:

v θ = K(θ). (1a) Using the relation K dh = D dθ, Selker et al. (1992) rewrote Eq. (1) as:

∫ −−=

)(/v1

θθξ

Khd (2)

where h is the matric potential {cm}. Equation (2) can be rewritten to provide a means for measuring h(vt - z) to within an additive constant:

)(

v- 1 - )( 'ξθθξ

ξd

Khh 1 ∫

∞

= (3)

where ξ' is a dummy variable, h1 is the asymptotic value of h when ξ → 4, effectively ξ > 7 cm for this work. 3. Experiments We measured the hydraulic conductivity of a porous media using an experiment in which the flow rate was stepped up from 2.5 - 20.0 ml•min-1. The experiment was performed on air-dried 20 - 30 sieve sand. The only preparation of the media was a thorough rinse with distilled water followed by drying. At each flow rate the system was allowed to come to steady state after which the average moisture content in the flow field, as well as the area through which the flow moved, were measured using neutron radiography (see Figs. 1 and 2).

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Water was withdrawn from the bottom of the experiment chamber through underflow drains attached to a vacuum pump (see Fig. 1a). The underflow drains were covered with a mesh screen to prevent media from leaving the chamber and the vacuum was adjusted so that water would pass through them. Figure 3 shows a calibration curve for the radiographs that relates the fractional change in image intensity, I(x,z)/Io(x,z), to the thickness of water through which the neutrons passed. The average moisture content vs vertical position in these steady state flow fields were also measured and found to be effectively constant in all cases. Equation (1a) was used to obtain K(θ). Figure 1. Schematic of experimental setup.

25 cm

20.5 cm

1.35 cm

Water Supply

Underflow drains

Imaging system

Experiment chamber

Incident neutron beam

Attenuated beam

Computer and digitizer

Figure 1a

Figure 1b

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Figure 2. Images of a 20.0 ml/min steady state flow field (Fig. 2a) and of a flow infiltrating a dry experiment chamber (Fig. 2b). These images give I(x,z). The regions where fluid is present appear lighter and have I(x,z) < Io(x,z). The image circle is 23 cm in diameter. The images were captured using a Precise Optics Thompson Tube neutron image intensifier connected to a Videcon camera. The images were digitized using NIH image 1.62 running on a G3 Macintosh with a Scion LG-3 interface. A pixel had an area of 0.2 mm2.

− z

x

Figure 2a.

- z

x

Figure 2b.

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 10.0

0.05

0.1

0.15

0.2

0.2

I(x,z)/Io(x,z)

cm water

Figure 3. Imaging system calibration. A polystyrene step standardwas used to correlate the fractional change in image intensity,I(x,z)/Io(x,z), to the amount of water through which the neutronswould have to pass in order to produce that change. Here I(x,z) isthe image intensity (in pixel values) of a location (x,z) on the stepstandard and Io(x,z) is the image intensity at the same location whenthe standard is not attenuating the neutron beam.

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Once K(θ) was known, the chamber was dried with air pulled through the underflow drains by the vacuum pump. The dryness of the chamber was checked by comparing its original dry weight to its weight after drying. A series of infiltration experiments were conducted using a flow rate of 1.3 ml•min-1 (see Fig. 2b). Neutron radiography was used to measure the wetting front velocity v (see Fig. 4), the average moisture content in the flow field as a function of location relative to the wetting front, θ(ξ), and the area through which the flow moved. Values for h(ξ) were generated by numerical integration of Eq. (3) using data on v, θ and K. 4. Results and Discussion The sand filled chamber remained virtually unchanged over the course of the experiments and always dried to within 0.1 gm of its original weight. All experiments formed nearly identical flow paths and measurements from neutron images were able to account for water entering the chamber to within better than 1%. A constant flux, 20 ml•min-1 experiment was conducted where the flow field was allowed to evolve for 2 hours. The results showed no measurable change in the width of the flow field, a strong indication that fluid only moved vertically and that the one-dimensional assumption in Eqs. (1) – (3) was reasonable, at least for experiments of only a few minutes duration. A plot of K vs θ /θsat is shown in Fig. 5. In total, K was measured in three different experiments all giving results consistent to within ~ 5 %. The error bars on the graph were calculated using the error propagation formula (Knoll, 1989). A curve fit to the data shows a power law relation like that of Brooks and Corey

distance = 0.192 * t R2 = 0.994

0 1 2 3 4 5 6

0.0 5.0 10.0 15.0 20.0 25.0 30.0 t {sec}

distance {cm}

Figure 4. Distance traveled by the wetting front vs time. The location ofthe wetting front was determined by tracking the location (x,z) at whichI(x,z)/Io(x,z) ≤ 0.98. In all experiments the flows showed little variation inhorizontal position (x).

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(1964). Figure 5. Hydraulic conductivity {cm•min-1} vs θ •θ -

sat where θsat is the saturated water content = 0.31. Two infiltration experiments were done, the results of one are shown in Fig. 6. A plot of h(ξ) is shown in Fig. 7. The results are similar to those given in Selker et al. (1992), except that the absolute value of h1 was not measured in the present work. The h(ξ) measurements were done every 0.45 mm (the linear dimension of a pixel in this study). 5. Conclusions 1) Real-time neutron radiography was used for quantitative imaging of transient and steady state flows in porous media. The spatial and temporal resolution of real-time neutron radiography, coupled with its sensitivity to variations in moisture content and its ability to image non-translucent media make it an ideal tool for laboratory studies. 2) The technique was used to measure the hydraulic conductivity in an unconsolidated sand rapidly and directly and the results showed a power law relation like that of Brooks and Corey (1964). The technique was also used to determine the variation in h within the flow field with measurements done every 0.45 mm (the linear dimension of a pixel for this study). 3) The assumption of constant velocity infiltration made by Selker et al. (1992) was confirmed in the single step experiments used in this work.

R2 k = 115.42 θ /θ sat)

3.346

= 0.990

0.0

5.0

10.0

15.0

20.0

25.0

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 θ •θ-1

sat

K {cm•min-1}

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Figure 7. Matric potential vs. ξ.

-8

-6

-4

-2

0

2

4

6

0 1 2 3 4 5 6 7 8 9

ξ {cm}

h - h1 {cm}

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

0 2 4 6 8 10 12 14 ξ {cm}

θ

Figure 6. Average flow field moisture content vs distance. Thelocation of the wetting front can be seen at 0.54 cm. The data weregenerated by tracking the wetting front on 300 image frames andaveraging the θ(ξ) measurements, where θ(ξ) is the average flowfield moisture content at the location ξ. The data shown were takenduring a 20 second period at 15 image frames per second.

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References Brooks, H.R., A.T. Corey, 1964: Hydraulic Properties of Porous Media.

Hydrology Papers, 3. Colorado State Univ., Fort Collins, CO. Darnault, C.J.G., D.A. DiCarlo, T.W.J. Bauters, A.R. Jacobson, J.A. Throop,

C.D. Montemagno, J.-Y. Parlange, and T.S. Steenhuis, 2001: Measurement of fluid contents by light transmission in transient three-phase oil-water-air systems in sand. Water Resour. Res., 37, 1859-1868.

DiCarlo, D.A., T.W.J Bauters, T.S. Steenhuis, J.-Y. Parlange, and B.R Bierck, 1997: High-speed measurements of three-phase flow using synchrotron x-rays. Water Resour. Res., 33, 569-576.

Knoll, G.F., 1989: Radiation Detection and Measurement. 2nd Ed. John Wiley and Sons, Inc.

Selker, J.S., J-Y. Parlange, and T.S. Steenhuis, 1992: Fingered flow in two dimensions. Part 2: Predicting finger moisture profile and measurement of conductivity. Water Resour. Res., 28, 2523-2528.