Relating hydraulic and geoelectric parameters of the Jayant aquifer, India

Journal of

Hydrology ELSEVIER

Journal of Hydrology 167 (1995) 23-38

[21

Relating hydraulic and geoelectric parameters of the Jayant aquifer, India G.S. Yadav Department of Geophysics, Banaras Hindu University, Varanasi-221 005, lndia

Received 11 June 1993; revision accepted 24 September 1994

Abstract

Geoelectrical soundings with Schlumberger arrays were carried out close to nine pumpingtest sites in the Jayant project, a part of the Singrauli Coalfields, Madhya Pradesh, India, to relate geoelectric parameters to hydraulic parameters, such as hydraulic conductivity and transmissivity. The interpretation of the sounding data was carried out using partial curve matching and the final model parameters were obtained using the computer program AIMRESI. Water samples collected from different pumping-test sites were analyzed to obtain water resistivity. The relationship between transmissivity and normalized aquifer resistivity is discussed in this paper. Normalized aquifer resistivity is a very good predictor for transmissivity in this aquifer.

1. Introduction G r o u n d w a t e r reservoirs form an important source of uncontaminated water. A knowledge of hydraulic parameters is important in determining the natural flow of water through an aquifer and its response to water extraction. The pumping test has traditionally been the standard method used to evaluate the hydraulic parameters of subsurface material for characterizing aquifers. However, geoelectrical soundings, which are extensively used for the location of aquifers, can also be simultaneously used for determining hydraulic parameters o f aquifers. Some investigators have studied the relationship between electrical and hydrological parameters of aquifers. Jones and Buford (1951) measured the formation factor and intrinsic permeability o f some graded sand samples and found that as the grain size increases, the respective formation factors and the intrinsic permeabilities also increase. Croft (1971) developed a relation between the aquifer intrinsic permeability and formation factor for given porosity ranges. 0022-1694/95/$09.50 © 1995 - Elsevier Science B.V. All rights reserved SSD1 0022-1694(94)02637-8

24

G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

Various investigators have attempted to establish the empirical and semi-empirical relationships between various aquifer parameters and geoelectric parameters (Ungemech et al., 1969; Duprat et al., 1970; Kelly, 1977; Heigold et al., 1979; Mazac and Landa, 1979; Urish, 1981; Kosinski and Kelly, 1981; Niwas and Singhal, 1981, 1985; Frohlich and Kelly, 1985; Onuoha and Mbazi, 1988; Mbonu et al., 1991; Yadav et al., 1993). Kelly (1977) established an empirical relationship between aquifer resistivity and aquifer hydraulic conductivity and a semi-empirical relationship between the aquifer formation factor and hydraulic conductivity for glacial outwash materials of the Upper Pawcatuck River Basin in southern Rhode Island, USA. Kosinski and Kelly (1981) have attempted to establish a direct equivalence between 'normalized transverse resistance' and aquifer transmissivity. A few studies, though, have shown an inverse relationship (Mazac and Landa, 1979; Heigold et al., 1979). Urish (1981) used an assumed inverse correlation between porosity and hydraulic conductivity to explain direct correlations between apparent formation factor and hydraulic conductivity. Niwas and Singhal (1985) established an analytical relationship between modified transverse unit resistance and aquifer transmissivity. Mbonu et al. (1991) attempted to define the aquifer geometry of the study area and correlate some aquifer properties determined from pumping test analysis with those calculated from the results of surface geoelectric soundings. In the present study, an attempt is made to correlate hydraulic conductivity and transmissivity with the apparent formation factor. An attempt is also made to develop a relationship between hydraulic transmissivity and normalized aquifer resistivity.

2. Area under study This study was conducted in the north-eastern part of the Singrauli Coalfields, Sidhi district of Madhya Pradesh, India, covering an area of about 9.7km 2 as shown in Fig. 1. The area is drained by two main streambeds, namely Matwani and Balia, which originate in the northern hills, flow south and meet in Govind Ballabha Pant Sagar located about 6 km to the south-east. The Barakar sandstones with a thin soil cover form a plateau with an escarpment facing south (Fig. 2). The Recent to Quaternary alluvium carried by a number of streambeds flowing from the northern hills has been deposited all along the streambed courses in the area. The thickness of alluvial cover varies between 3 and 10 m. In the north-eastern part of the coalfield, the Barakar formation stands out as a high plateau over the Talcher plains in both the south and east. The Barakar sandstone is medium to coarse grained, highly to moderately weathered and poorly consolidated up to a depth of 65 m and at some places extends even up to 100 m. Groundwater occurs in the intergranular pore spaces of alluvial sands and poorly consolidated sandstones, under phreatic and semi-confined conditions. It also occurs in the secondary porosity in the sandstones formed by weathering, joints and fractures. The main sources of recharge to the groundwater are precipitation, seepages from two major streambeds and the Matwani reservoir. The water levels in the area measured from wells during pre-monsoon and post-monsoon periods

G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

25

INDIA

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Fig. 1. Location map of the study area.

indicate that the depth to water ranges from 3.5 to 11.30m and from 1.0 to 9.0m below ground level on the downstream and upstream sides, respectively.

3. Theory Archie (1942) experimentally established that the resistivity of a clean, waterbearing formation (i.e. one containing no appreciable amount of clay and no hydrocarbons) is proportional to the resistivity of the brine with which it is fully saturated. The constant of proportionality is called the formation factor. This is true when the formation is dean. If the aquifer formation is made of shaly sandstones then the use

G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

26

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G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

27

of an apparent formation factor, F~ is more appropriate and is defined as F,~ = R / R w

(1)

where R is the resistivity of a formation rock and Rw is the resistivity of the saturating water. The Dar Zarrouk parameters (i.e. transverse resistance, Z, and longitudinal conductance, C) are defined as Z = hR

and C = h/R

(2)

where h is the thickness of the aquifer. Transmissivity, T, is related to hydraulic conductivity, K, as T = Kh

(3)

Niwas and Singhal (1981) determined analytically the relationship between tranSmissivity and transverse resistance of the aquifers on the one hand and the transmissivity and longitudinal conductance on the other. In 1985, they modified these relationships by using a 'modified aquifer resistivity', R ' = R R w / R w (where Rw is an average water resistivity), instead of 'aquifer resistivity' which is known as 'normalized aquifer resistivity' (Kosinski and Kelly, 1981). Accordingly, transmissivity is related to normalized transverse resistance, Z I (Niwas and Singhal, 1981), as T = aZ'

(4)

where a = K / R ' , Z ' = hR' and R' is the normalized aquifer resistivity. Now considering the normalized longitudinal conductance, C ' ( = h/R'), it can also be written as 7" = ( K K ) c '

(5)

Rearranging Eq. (5) gives T = (KC')R'

(6)

There is a need to test the validity of the above equation. The equation is valid if the hydraulic conductivity of these aquifer materials increases as their longitudinal conductance decreases in the same order. Hence, a symbol, b, is defined as b = KC'

(7)

G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

28

From the field data analysis, it can be shown that transmissivity is related to the normalized aquifer resistivity for a groundwater basin where b remains constant.

4. Field data and its interpretation

Geoelectrical soundings using a Schlumberger array with a maximum spread length of 600 m were carried out in the close vicinity of nine pumping-test sites. Nine water samples, collected from the respective borewells, were used for the measurements of water resistivity. The hydraulic transmissivity and conductivity were computed from the pumping test carried out by the Central Mine Planning and Design Institute (Savanur et al., 1987). To perform the quantitative interpretation of geoelectrical soundings, a two-step procedure was adopted. In the first step, a preliminary interpretation was carried out using the partial curve matching technique of Ebert (1943) and Koefoed (1979). In the second step, the sampled field curve was interpreted in terms of the final layer parameters using a computer program (Yadav, 1982), viz. Automatic Iterative Method of Resistivity Sounding Interpretation (AIMRESI). The layer parameters thus obtained were compared with the litholog of the borehole.

5. Results and discussion

Sounding results reflect, geoelectrically, four layer curves of the KH-, QH-, KQand HK-types. The final geoelectric layer parameters (resistivities and thicknesses) are given in Table 1. The comparison between the lithologs of the borewells (P-2, P-4 and P-5) and the corresponding results of the geoelectrical soundings (GS-2, GS-4 and GS-5) are presented in Figs. 3, 4 and 5, respectively. For convenience, lithological Table 1 Geoelectrical layer parameters (resistivity and thickness) obtained from the interpretation of geoelectrical soundings GS No.

1 2 3 4 5 6 7 8 9

Layer 1

Layer 2

Layer 3

Layer 4

R1 (~m)

hi (m)

R2 (~m)

h2 (m)

R3 (~m)

h3 (m)

R4 (gm)

h4 (m)

8.2 57.1 47.9 11.0 10.0 46.4 21.8 30.4 25.2

1.9 2.8 2.7 3.1 2.8 2.0 2.6 1.5 3.2

24,8 26,6 22.6 28.0 20.4 14.8 30.8 20.1 35.5

5.9 5.9 9.1 21.4 11.4 6.2 4.8 6.0 4.6

7.5 11.8 12.8 10.4 16.5 25.8 4.5 58.5 2.5

41.2 62.7 77.7 53.8 44.3 48.0 42.8 30.0 41.3

13.5 16.6 16.3 18.4 11.9 12.8 10.5 14.6 17.6

cc cc oc ec oo c¢ oo oo oo

G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

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Fig. 3. Illustration of the interpreted results obtained from the AIMRESI program for GS-2 and correlation of geoelectric layer parameters with the actual borewell P-2. The abbreviations are CI: Clay, S: Sand, K: Kankar (type of hard irregular shaped granules formed in alluvium), St: Sandstone, Sh: Shale, F: Fine grained, M: Medium grained, C: Coarse grained, Md: Moderately, Pr: Poorly, Wd: Weathered sandstone.

units encountered in the borewells are abbreviated as CI: Clay, S: Sands, K: Kankar (type of hard irregular shaped granules formed in alluvium), St: Sandstones, Sh: Shales, F: Fine grained, M: Medium grained, C: Coarse grained, Md: Moderately, Pr: Poorly, Wd: Weathered sandstones. The drilling time log is presented in the lower portion of the figures to show the compactness of the different lithological units encountered in the borehole. The correlation of the geoelectric layers of GS-2 with the corresponding litholog for tubewell P-2 drilled down to a depth of 100 m is shown in Fig. 3. The first and second layers having resistivities 57.1 and 26.6 f~m correspond to fine grained sands (F-S) and coarse grained weathered sandstones (C-Wd), respectively. The first boundary

G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

30

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of these layers is not fully correlated owing to a change in moisture content. The formation changes that occur between depths of 9.8 and 75.4m contribute varying amounts of groundwater from various lithological units. The various types of lithological units presented sequentially in this depth range are coarse grained weathered sandstones (C-Wd), carbonaceous shale (Carb-Sh) coarse grained moderately weathered sandstones (C-Md-Wd), fine grained poorly weathered sandstones ( F - P r - W d ) and medium grained poorly weathered sandstones (M-Pr-Wd). The composite effect of all these layers is shown in a third geoelectric layer with resistivity 11.8 f~m. These layer changes are not reflected in the sounding curve owing to their relatively small thicknesses and gradual changes in their compactness and grain sizes. The last layer mapped by the geoelectrical sounding is caused by the presence of coarse grained sandstones (C-St), fine grained poorly weathered sandstones ( F Pr-Wd) and alternate beds of sandstones/shales (St/Sh) which show a combined

G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

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resistivity of 16.6 f~m. Similarly, the lithologs of the tubewells P-4 and P-5 are also compared with the results of corresponding geoelectrical soundings in Figs. 4 and 5, respectively. A combined geoelectrical-geological cross-section oriented approximately in a N W - S E direction incorporating the results of six geoelectrical soundings (GS-2, GS-1, GS-6, GS-5, GS-7 and GS-9) along with corresponding lithologs is presented in Fig. 6. Sounding results reveal the presence of three distinct geoelectrical layers overlying alternate thin beds of shale and sandstone. The first layer is made up of clay, sandy clay mixed with kankar. The second layer comprises various grades of loose sands. A combined geoelectric layer with varying grades of loose sands and highly to poorly weathered sandstones is present in the third layer which forms the main source of groundwater.

32

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G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

33

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(Fa).

Fig. 7 shows the plot of hydraulic conductivity and transmissivity vs. the apparent formation factor. This figure indicates that the transmissivity (T) exhibits better correlation with the apparent formation factor (Fa) than the hydraulic conductivity (K) with Fa. A regression analysis between transmissivity and normalized transverse resistance has been given by Yadav et al. (1993). These two parameters are not well correlated for this area. Niwas and Singhal (1985) reported an analytical relationship between these parameters with various examples. Correlation between transmissivity (T) and normalized aquifer resistivity (R') is presented in Fig. 8. A regression line between R' and T is fitted which yields a slope of 18.14. The fit is very good. The deviations between observed transmissivity and regression line are shown in the inset of the figure. The deviation at point 8 is higher in comparison

G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

34

16

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Fig. 8. Illustration showing the relation between transmissivity (T) and normalized aquifer resistivity (R') with the error between computed and observed transmissivity.

to the other locations. This may be caused by an excessively high transmissivity value observed in the field. For convenience, all the parameters used for the correlations are presented in Table 2. The value o f KC' is given in column 8. The root mean square error estimated between computed transmissivity, Te, and observed transmissivity, To, for seven sites is +26.1 m 3 day -1 m -l . The r.m.s, error is relatively very small which means that this analytical relation holds good for that area. Niwas and Singhal (1985) presented a table showing the various transmissivities derived from the various approaches taking the data from Kosinski and Kelly (1981). Taking the same data, a table (Table 3) has been prepared to show the error analysis of the transmissivity data computed from various approaches (Niwas and Singhal, 1985) by the author. The unit of the transmissivity data has been converted from gallon per day per ft to m 3 day I m-I using a factor of 0.01242m 3 day -1 m -1

G.S. Yadav / Journal o f Hydrology 167 (1995) 23-38

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G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

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G.S. Yadav / Journal of Hydrology 167 (1995) 23-38

37

for 1 gallon per day per ft. An average value of K C I = 3.4 was used for the computation of transmissivity using the present approach and is given in column 7. The r.m.s, error is given at the foot of columns 8-11. The r.m.s, error obtained by the author is slightly higher, but in the same order as that obtained in the other studies mentioned. It is worthwhile mentioning here that the transmissivity is highly correlated with the apparent formation factor as well as the normalized aquifer resistivity, because the normalized aquifer resistivity is defined as the product of the apparent formation factor and the average water resistivity.

6. Conclusions The normalized aquifer resistivity was found to be very well correlated with the transmissivity in the Jayant aquifer. However, the practical applicability of the relation lies in the fact that if the hydraulic transmissivity is known for any reference point in an area, one can get a fairly good idea of the transmissivity of the aquifer at other locations within a basin, from geoelectrical soundings. The conclusions drawn and the techniques used have a reasonable degree of accuracy, although there is scope for further refinement and improvisation.

Acknowledgments Sincere thanks are due to Prof. T. Lal, Department of Geophysics, Banaras Hindu University, for critical assessment of the manuscript. Necessary facilities provided by the D e p a r t m e n t of Geophysics, Banaras Hindu University and information supplied by the Central Mine Planning and Design Institute Limited, Ranchi, are gratefully acknowledged.

References Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Amer. Inst. Min. Met. Eng., Tech. Pub. 1422, Petroleum Technology, 8 pp. Croft, M.G., 1971. A method of calculating permeability from electrical logs. In: Geological Survey Research. U.S. Geological Survey, Professional Paper 750-B, pp. 265-269. Duprat, A., Simler, L. and Ungemach,P., 1970. Contribution de la prospection electriquea la recherchedes caracteristiques hydrodynamiques dun milieu aquifere. Terres Eaux, 23: 23-31. Ebert, A., 1943. Grundlagen zur Auswerkung geoelectrischer Tiefenmessungen. Gerlands Beitr. zur Geophys. BZ, 10: 1-17. Frohlich, R.K. and Kelly, W.E., 1985. The relation between hydraulic transmissivity and transverse resistance in a complicated aquifer of glacial outwash deposits. J. Hydrol., 79: 215-229. Heigold, P.C., Gilkson, R.H., Cartwright, K. and Reed, P,C., 1979. Aquifer transmissivityfrom surficial electrical methods. Ground Water, 17: 338-345. Jones, P.H. and Buford, T.B., 1951. Electric logging applied to groundwater exploration. Geophysics, 16: 115-139.

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