Potential use of time domain reflectometry for measuring water content in rock

Journal o f Hydrology, 138 (1992) 8 9 - 9 6

89

Elsevier Science P u b l i s h e r s B.V., A m s t e r d a m

[3]

Potential use of time domain reflectometry for measuring water content in rock S.L. Hokett, J.B. Chapman and C.E. Russell Desert Research Institute, 755 E Flamingo, Las Vegas, NV 89119, USA (Received 30 March 1991; revision accepted 7 February 1992)

ABSTRACT Hockett. S.L., C h a p m a n , J.B. and Russell, C.E., 1992. Potential use of time domain reflectometry for measuring water content in rock. J. Hydrol., 138: 89-96. Quantifying water movement through bedrock materials requires a technique which can accurately measure water content at precise locations within the medium. Time Domain Reflectometry (TDR) is widely used to measure the water content of soil and has a measurement sensitivity which is tightly confined to the area immediately surrounding the probes. This study applies T D R to the measurement of water content in rocks. The technique was evaluated using sandstone and welded tuff in a series of laboratory experiments. A block of each rock type was instrumented with a series of evenly spaced T D R probes. Each block was first saturated with water and then allowed to air dry. The water content was determined gravimetrically using the T D R over a period of several weeks. The results indicate that the T D R technique can be used to determine the water content of rock with an accuracy comparable with that reported for the technique used in soils.

INTRODUCTION

In arid to semi-arid regions, the rate at which groundwater recharge is occurring is important, as it relates to water supply issues as well as to environmental assessment of areas for such purposes as hazardous waste disposal. In many of these areas, fracture flow through unsaturated bedrock represents the most likely hydrological process capable of delivering recharge. Quantifying matrix diffusion during fracture flow is important in estimating recharge. This interaction can be simulated using various unsaturated flow models but very little model validation has been done to date, in large part because of the lack of a good technique to measure water content in rock on a scale small enough to be suitable for laboratory studies. In recent years, time domain reflectrometry (TDR) has been widely accepted as a highly accurate, Correspondence to: S.L. Hokett, Desert Research Institute, 755 E Flamingo, Las Vegas, NV 89119, USA.

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© 1992 - - E l s e v i e r Science P u b l i s h e r s B.V. All r i g h t s r e s e r v e d

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simple and dependable method of determining volumetric soil water content (Topp et al., 1980). A laboratory study is presented to show that TDR can also be used for determining water content in rock. PREVIOUS WORK

Water content measurements are made with a pair of parallel metal rods (waveguides) driven into the soil. Electrical connection from the TDR unit to the wave guides allows a high-frequency electromagnetic wave (EMW) to be transmitted through the soil along the length of the wave guides. EMW reflections occur at the point where the wave enters the wave guides and from the end of the wave guides. These reflections are viewed on the TDR oscilloscope, and the distance between the two reflections is measured with the TDR unit. This distance relates to the travel time of the EMW through the soil along the length of the wave guides. It has been demonstrated that EMW travel time through soil is a function of the soil's dielectric constant (k,), which is controlled primarily by soil water content. An empirical equation relating the EMW travel time to soil water content was developed by Topp et al. (1980). Their research showed that calibration for individual soil type was not necessary and that factors such as soil texture, bulk density, salt content and temperature did not affect TDR measurements of soil water content. Although other methods are available for measuring the water content of rock based on the dielectric method (Shen et al., 1985), these are designed for borehole logging or for the measurement of core water content using coaxial cell chambers. TDR offers a more flexible methodology which can easily accommodate a variety of experimental configurations. MATERIALS AND METHODS The effectiveness of TDR for measuring water content in sandstone and welded tuff was tested using a Tektronix model 1502 cable tester (Tektronix, Beaverton, OR). The transmission line consisted of a 50f~ coaxial cable connected to a 180 f~ balanced antenna wire with an Anzac tp 103 impedance matching transformer (Adams-Russell Co., Burlington, MA). The antenna wire was connected to the wave guides with alligator clips. TDR traces were read manually using the TDR oscilloscope. Raw data were converted to volumetric water content using the Topp et al. (1980) equation.

Bare soil experiments This experiment was done to determine the accuracy of the TDR unit in a

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Days Fig. I. TDR-determined water content compared with gravimetric water content, measured over a 75 day period in bare soil subjected to evaporation.

proven medium for comparison with results in each rock type. A closedbottom cylindrical weighing lysimeter with a diameter of 25 cm and height of 32 cm was partially filled with air-dried fine- to medium-grained homogeneous sand. The lysimeter was instrumented with 12 evenly spaced stainless steel wave guides of 23cm x 0.64cm diameter. A volume of water sufficient to saturate the soil (3810 ml), was then added to the lysimeter and the volumetric water content was determined gravimetrically using known volume and weight relationships. T D R measurements were made for all wave guide pairs and averaged to reduce potential spatial variability. This value was statistically compared with the water content value determined gravimetrically as the lysimeter air dried during a 75 day period.

Sandstone experiments A sandstone block with a top surface area of 23 cm x 21 cm, and a height of 18 cm was instrumented with 16 evenly spaced 15 cm x 0.64 cm T D R wave guides. T D R wave guides were installed in the rock by drilling slightly undersized holes with an electric drill fitted with a masonry bit and then hammering the rods into the rock. Undersized drill holes ensured good contact between the probes and the rock, and minimized air gaps, which can

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S,L. HOKETT ET AL.

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Fig. 2. TDR-determined water content values compared with those determined gravimetrically in the first sandstone experiment. (Note that T D R readings are consistently higher than gravimetric results.)

cause serious underestimation of water content (Annan, 1977). The block volume (9721 cm 3) was measured by water displacement. The sandstone block was oven dried at 105°C until there was no significant weight loss over a 24 h period, and this weight was assumed to represent the weight at 0 m 3 m 3 water content. The block was then soaked in a water bath for several days until no additional weight gain was observed over a 2 4 h period. Initial volumetric water content was calculated gravimetrically using the following formula: volumetric water content

=

(wet weight - dry weight)/volume of block

The T D R water content (0t) was determined by averaging the readings from all the T D R wave guides. As the block air dried, water content measurements were performed gravimetrically (0g) as described above and with T D R until no further water loss occurred. The experiment was then repeated.

Volcanic tuff experiment A block of volcanic tuff o f similar size to the sandstone block was instrumented as described above and the same experimental procedure was followed, comparing (0t) with (0g).

93

TIME DOMAIN REFLECTOMETRY FOR ROCK WATER CONTENT

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Fig. 3. Results from the second sandstone experiment, showing similar results to the first rock experiment. Once again, TDR values are consistently higher than gravimetric results. RESULTS AND DISCUSSION

The relationship between 0t and 0g is shown for the bare soil experiment and each of the rock experiments in Figs. 1, 2, 3 and 4, respectively. The results for TDR-measured water content for these experiments are statistically compared with gravimetrically determined water content in Table 1. In both sandstone experiments, 0t was consistently higher than 0g. This difference was evident for measurements taken through the entire range from saturated to very dry conditions, which indicates that the probe to rock contact was sufficient to avoid a detectable air gap effect. If air gaps were affecting the readings, measurements would be more influenced when the medium was near saturation than when dry, as the dielectric difference between the gap and the medium would be greater in wetter conditions (Hokett et al., 1992). The observation that 0t is consistently higher than 0g is not surprising, as average dry rock dielectric constants range from approximately 5 for quartzite to 11 for basalt (Griffin and Marovelli, 1967) as compared with about 2.5 for average dry soils (Topp and Davis, 1985). The higher dielectric constant for dry rock as compared with soil is a result of lower effective porosity in rock and differences in mineralogical composition. It should be noted that the difference between soil and rock dielectric

94

S.L. HOKETT ET AL.

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constants is relatively small compared with the difference between them and the dielectric constant of water (80). The over-prediction in water content caused by using the standard soil calibration curve can be corrected easily given the linear relationship between 0t and 0g. To illustrate this, the second sandstone data set was corrected using the linear regression data calculated from the first sandstone experiment, with the corrected T D R value as the dependent variable and the uncorrected TDR value as the independent variable; the constants were calculated from the TABLE

1

The results of water content measurements for the four experiments on bare soil, sandstone I, sandstone II and volcanic tuff, presented in terms of the differences between water c o n t e n t , as determined by the T D R and by gravimetric methods Material

Soil

Sandstone ! Sandstone II Tuff

Mean difference

SD ( m 3 m -3)

r2

t-test at 5 % c o n f i d e n c e

( m 3 m -3) 0.007 0.017 0.022 0.007

0.006 0.008 0.006 0.010

0.99 0.98 0.99 0.98

t t t t

= = = =

1.27 vs. 2.0 2.1 vs. 2.1 3.5 vs. 2.2 0.69 vs. 2.1

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Fig. 5. Corrected values of TDR for the second sandstone experiment compared with gravimetric water content determinations. These results compare well with the results from the bare soil evaporation experiment (Fig. l).

results of the first sandstone experiment. After applying this correction, the mean difference (8 t - 8g) was reduced from 0.02 to 0.003 m 3m 3 water content (Fig. 5). The results from the welded tuff experiment were within the reported accuracy for the T D R system for soil (___0.02 m 3m 3), and correction was not applied to the data. The welded tuff lithology may be responding more like a soil system than the sandstone, as a result of its higher effective porosity (15 vs. 10%). CONCLUSIONS

This work indicates that T D R can be applied successfully to the measurement of water content in rocks, with an accuracy comparable with that reported for the technique in soils ( 1 0 . 0 2 m 3 m -3 water content; Topp and Davis, 1985). Calibration for specific rock type m a y be necessary in lithologies which have dielectric constants that differ significantly from that of soil. This technique may be useful for validation of unsaturated flow models used to study complex hydrological relationships such as matrix diffusion during fracture flow. In addition, T D R could be used for in situ monitoring of infiltration through fractured rock. The technique has several characteristics

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S.L, HOKETT ET AL.

that make it well suited for such studies: (1) it gives an immediate response to changes in water content, (2) the sensitivity of measurements is confined primarily to the area immediately around and between the wave guides, (3) the technique can be computer automated, allowing continuous measurements during experiments, and (4) it is suitable for use in small laboratory-size samples. REFERENCES Annan, A.P., 1977. Time-domain reflectometry: air gap problem for parallel wire transmission lines. In: Report of Activities, Part B. Geol. Surv. Can. Pap., 77-1B: 59-62. Griffin, R.E. and Marovelli, R.L., 1967. Dielectric constants and dissipation factors for six rock types between 20-100MHz. US Dep. Interior, Bur. Mines Rep. 6913: 1-21. Hokett, S.L., Chapman, J.B. and Russell, C.E., 1992. TDR response to lateral soil water content heterogeneity. Soil Sci. Soc. Am. J., 56: 313-316. Shen, L.C., Savre, W.C., Price, J.M. and Athavale, K., 1985. Dielectric properties of reservoir rocks at ultra-high frequencies. Geophysics, 50: 692-704. Topp, G.C. and Davis, J.L., 1985. Time-domain reflectometry (TDR) and its application to irrigation scheduling. In: D. Hillel (Editor), Advances in Irrigation, Vol. 3. Academic Press, Orlando, FL, pp. 107-127. Topp, G.C., Davis, J.L. and Annan, A.P., 1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour. Res., 16: 574-582.