Estimation of hdraulic conductivity using geoelectrical data for assessing of scale effect in a karst aquifer

<jats:p>The Salman Farsi Dam was constructed on the Ghareh-Aghaj river in the catchment of the Asmari limestone aquifer, Changal Anticline, Zagros region, Iran. In order to estimate the hydraulic conductivity of the aquifer, combination of geoelectrical (i.e., bulk resistivity of the aquifer) and hydrophysical (i.e., electrical conductivity of groundwater) data are used as an alternative approach. Porosity of the aquifer is estimated based on the modified form of Archie’s empirical law assuming well-cemented carbonate rocks. Formation resistivity factor and critical pore size of the Asmari limestone aquifer are used for estimating the hydraulic conductivity on the small scale based on the Thompson Equation. The results suggest an average porosity and hydraulic conductivity of 14.4 % and 0.016 m/day, respectively. The estimated value for hydraulic conductivity is smaller than values previously determined for the aquifer, based on tracer, pumping and Lugeon tests. Comparison of the hydraulic conductivity obtained by different methods revealed scale effect of hydraulic conductivity measurements in the Asmari limestone aquifer. As a result, application of the geoelectrical and hydrophysical data can provide a cost-effective and efficient alternative to estimate hydraulic conductivity in karst aquifers on the small scale.Keywords: hydraulic conductivity, Karst, Scale effect, Vertical electrical sounding, Iran.Uporaba geoelektričnih podatkov za oceno hidravlične prevodnosti in učinka merila v kraškem vodonosnikaJez Salman Farsi je postavljen na reku Ghareh-Aghaj v območju kraškega vodonosnika Asmari, ki pripada antiklinali Changal v gorovju Zagros, Iran. Hidravlično prevodnost vodonosnika smo ocenili z kombinacijo meritev celokupne električne upornosti vodonosnika in električne prevodnosti podzemne vode. Ocena poroznosti je temeljila na prilagojeni obliki Archiejevega empiričnega zakona, pri čemer smo predpostavili dobro cementirane karbonate. Iz upornosti formacije in kritične velikosti por smo s Thompsonovo enačbo izračunali hidravlično prevodnost v majhnem merilu. Dobljena povprečna poroznost tako znaša 14,4 %, povprečna prevodnost pa 0.016 m/dan. Vrednosti hidravlične prevodnosti so precej manjše of prej dobljenih vrednosti iz sledilnih, črpalnih in Lugeonovih poskusov, kar kaže na pomemben učinek merila v obravnavanem vodonosniku. Raziskava med drugim kaže na primernost geoelektričnih in hidrofizikalnih podatkov za stroškovno ugodno oceno hidravlične prevodnosti v majhnem merilu.Ključne besede: Hidravlična prevodnost, kras, učinek merila, vertikalno električno sondiranje, Iran.</jats:p>

section_content: ALIREZA NASSIMI & ZARGHAM MOHAMMADI Hydraulic conductivity (K) is an important parameter to describe the main characteristics of aquifers especially in heterogeneous karst terrain. Several methods are known for determining of hydraulic conductivity in karst aquifers. Accuracy and applicability of these methods are related to match the real field conditions with the theoretical assumptions of each method. Therefore comparison of the results of different methods is difficult. In order to assess a reliable result it is necessary to know and introduce hydrogeological conditions of the study area. 

The scale effect for karst terrains was first reported by Király (1975). Karstification is related to the enlargement of fractures and bedding planes and resulting in high variation of estimated hydraulic conductivity which is typically between 10 -10 to 10 -1 m/s (Király 1975; Sauter 1991; quinlan et al. 1992; Rovey 1994; Kovács 2003; Geyer 2008 ). This causes difficulties in karst aquifers (white 2007). with increasing scale (i. e., distance or volume) of hydraulic conductivity measurements, role of macrofractures and dissolution openings are increased in karst terrain, so it is expected that the estimated hydraulic conductivity increases. Some work pointed larger possible ranges in hydraulic conductivity than other media for karst aquifers (white 1988; Ford & williams 1989; Smart et al. 1991). 

Geoelectrical methods are the well-known geophysical methods for determining geological structures and overburden thickness (Drew & Goldscheider 2007). Geoelectrical methods employ artificial electrical fields. Results are usually provided as resistivity (Bechtel et al. 2007 ). These methods are suitable for locating major conduits, macrofractures and other preferential flow paths based on electrical resistivity. In these methods, information on the structure and properties of the underground are achieved without drilling, i. e. at relatively low cost (Drew & Goldscheider 2007). Results of geoelectrical methods may be difficult to interpret without ambiguity (non-uniqueness). Resolution is generally reduced with depth of investigation (i. e., the greater the depth, the lower the resolution) (Drew & Goldscheider 2007). 

Vertical Electrical Sounding (VES) is the most used method for geoelectric surveying, although nowadays 2D or even 3D geoelectric measurements are state-ofthe art, but using VES in this case is appropriate. VES measures the resistivity of a formation. This method has been used successfully in various environments such as limestone or alluvium (Sahu & Sahoo 2006; Dawoud & Raouf 2009; Sikandar et al. 2010). 

Hydrochemical methods gain hydrochemical characterization (such as electrical conductivity) of groundwater bodies and information on water quality and contamination problems. Hydrochemical methods also may be used as natural tracers for the origin and movement of the water (Drew & Goldscheider 2007). 

Combination of geoelectrical and hydrochemical surveys represents indirect methods of studying the porosity and hydraulic conductivity in a limestone aquifer. Geoelectrical (i. e., bulk resistivity of aquifer) and hydro-al (i. e., bulk resistivity of aquifer) and hydrochemical (i. e., electrical conductivity of groundwater) data have been used to obtain porosity in limestone or alluvial aquifers (Keller 1988; Pengra & wong 1999; Slater 2007; Asfahani 2012; Sikandar & Christen 2012; Khalil & Monteiro Santos 2013) based on Archie's empirical law (Archie 1942). According to Archie's law, electrical resistivity increases with decreasing porosity. In the following, porosity has been used to identify hydraulic conductivity in alluvial aquifers (Slater 2007; Asfahani 2012; Sikandar & Christen 2012; Khalil & Monteiro Santos 2013) based on the Kozeny-Carman equation (Kozeny 1927; Carman 1937; Bear 1972; Domenico & Schwartz 1990). Preliminary applications of the Kozeny-Carman equation have been limited to the alluvial aquifers due to assumptions of this equation. Garing et al. (2014) proposed that the Kozeny-Carman equation is replaced by the Thompson equation (Thompson et al. 1987 ) for limestone aquifers. 

The objectives of this research are: (1) estimation of the porosity and hydraulic conductivity in the Asmari limestone aquifer via combination of geoelectrical and hydrochemical data; (2) comparison of the estimated hydraulic conductivity with results of previously applied methods such as Lugeon, pumping and tracer tests.

section_name: INTRODUCTION GEOLOGy AND METHODS

section_content: The Salman Farsi Dam Site (SFDS) is located at the entrance of the Karzin Gorge on the Ghareh-Aghaj River (Fig. 1 ). The gorge is nearly V-shaped and symmetrical at the dam site. Slope dip of the right bank is about 25° in the lower sections, increasing to 55° from elevation 850 m above mean sea level (a. m. s. l. ). Dip slope of the left bank is low on the alluvial plain, then increasing to 25° to 50° upwards from elevation 880 m a. m. s. l. . The river bed is about 833 m a. m. s. l. and 20 m wide. The river channel is filled by alluvial deposits on the left bank, whereas bedrock outcrops on the right side (Fars Regional water Authority 1994). A simplified stratigraphic sequence of the study area is shown in Tab. 1. 

It is possible to group the units of the Asmari Formation in three principal sub-units and to correlate them with the stratigraphy. The upper unit of the Asmari Formation is made out of a very heterogeneous sequence of thinly bedded limestone with marls and siltstones. The central unit is more homogeneous and thickly bedded. Tab. 1: Summarized stratigraphy of the study area (Fars Regional Water Authority 1994). Lithologically, this unit is characterized by the vuggy, porous limestone, and the nummulitic limestone, so called "calcarenite". Finally the lower unit of the Asmari Formation is characterized by a very regularly bedded, finely grained brown limestone at the top, very thickly bedded cherty limestone in the center and an extremely regularly sequence of thinly bedded limestone with thin marly beds at the base (Fars Regional water Authority 1994). 

There are a few joint sets in the dam site area. The major joints are predominant and play a basic role in underground karst features. However minor joints (much shorter in length) have also been important in some parts of the investigated area. According to the statistical orientation, two main systems of joints (small-scale faults) are presented: J1 (135/80°) and J2 (275/80°) (Vucković & Milanović 2001). 

The main discontinuities (J1 and J2) were developed by the stress field of the folding phase. Both systems are very steeply dipping, subvertical to vertical (Vucković & Milanović 2001). 

System J1 was frequently slickensided and striated due to shearing. In the geological past, movements have occurred either in the form of transcurrent or normal reverse faults. Rock wall contacts vary between rough and undulating. Some of them have aperture 0. 5-2 m, filled with mylonitic material (clay and sandy clay with crushed limestone blocks) (Vucković & Milanović 2001). 

System J2 is quite uniformly orientated and mostly found on the left dam bank. Displacements range between a few decimeters and up to several meters (Vucković & Milanović 2001). 

A few flat lying discontinuities (18/32, 161/22 and 133/25) were measured on the right abutment (Vucković & Milanović 2001). At this area, high karstification is generally located around the intersection of faults or discontinuities (Fazeli 2007).
section_name: STUDy AREA

section_content: Porosity was calculated via the modified form of Archie's empirical law for well-cemented sedimentary rocks (Keller 1988) :

where ρ e is the bulk resistivity of aquifer, σ w is the electrical conductivity of groundwater, and Ø is the porosity. Then S, the water saturation, is in this case S=1, and from two measurements (ρ e and σ w ) could be determined the porosity, if both α (the tortuosity factor) and m (the cementation exponent) are known. The parameters α and m are used to force the function to fit the data from a given rock. Parameters α and m for well-cemented sedimentary rocks are in the order 0. 62 and 1. 95, respectively (Keller 1988). Garing et al. (2014) who showed the results of Thompson equation fit remarkably well with heterogeneous carbonate rocks situation. Hydraulic conductivity (m/s) was computed by using the Thompson equation (Thompson et al. 1987 ): where d c is the critical pore size (pore size below which mineral precipitation no longer occurs, 10 µm in the Asmari limestone aquifer), F is the formation resistivity factor F= ρ e • σ w ), ρ is density of the fluid (996. 636 kg/m 3 at 25°C), μ is the dynamic viscosity of the fluid (0. 00089 kg/(m*s) at 25°C), and g is the gravity (9. 81 m/s 2 ). 

The geoelectrical method, VES, was performed in the SFDS by the Tehran University Geophysics Insti-tute. The electrical resistivity (ρ e ) was measured on two profiles, which were located around the Ghareh-Aghaj River (Fig. 2 ). VES's were conducted in the 12 points of the Asmari limestone aquifer at the SFDS by employing a Schlumberger electrode configuration. The electrode spacing (AB/2) used for all the soundings was maximum up to 1000 m (Riahi et al. 1997). Electrical conductivity of groundwater (σ w ) was extracted from Fars Regional water Authority (1997).
section_name: METHOD OF STUDy

section_content: The results of the estimated porosity and hydraulic conductivity are presented in Tab. 2. The average porosity was estimated 14. 4 %, based on combination of the geoelectrical and hydrochemical data (Tab. 2). Addition-and hydrochemical data (Tab. 2). Additionally, the average porosity was estimated 12. 2 % from 46 rock samples of the study area in the laboratory (Fars Regional water Authority 1995). The difference is due to the difference in location of the sampling points. 

In order to calculate of the hydraulic conductivity in the small scale, formation resistivity factor (F) is the main parameter. Fig. 3 shows variation of the hydraulic conductivity versus formation resistivity factor (F) at the SFDS. Increasing the formation resistivity factor (F) is accompanied by decreasing of the hydraulic conductivity (Eq. 2 and Fig. 3 ). 

The average hydraulic conductivity was estimated 0. 016 m/day on the small scale at the SFDS (Tab. 2). Hydraulic conductivity has also been calculated for different scales and methods at the SFDS (Tab. 3) by Nassimi and Mohammadi (2016). Tab. 3 nicely shows that the borehole qR 22 at depth 18 to 23 m hit a larger conduit. Fig. 4 shows the hydraulic conductivity versus distance (i. e., scale) at the SFDS. Figure 5 on the hydraulic conductivity in karstified limestone aquifers. These two figures revealed scale effect at the SFDS. 

The average hydraulic conductivity obtained by the combination of geoelectrical and hydrochemical data (Thompson equation) was much less than the Lugeon, pumping and tracer tests results (Fig. 4 ). Smaller values for the hydraulic conductivity based on the Thompson equation (combination of geoelectrical and hydrochemi-geoelectrical and hydrochemi-and hydrochemical data) are due to the scale effect (Fig. 4, Fig. 5 ); be-cause the distance in the samples studied to obtain the Thompson equation (maximum 0. 02 m) is much less than the geometric mean of the distance in the Lugeon (30 m), pumping (97. 8 m) and tracer tests (249. 3 m). In other words, in the karst terrain, estimated values of K based on larger scale experiments is bigger (Bear 1972; Rovey & Cherkauer 1995; Vacher & Florea 2015) and more reliable (Vandenbohede & Lebbe 2003; Nassimi & Mohammadi 2016) than those based on the smaller scale, due to important role of preferential flow paths in the larger scale. Rovey and Cherkauer (1995) showed hydraulic conductivity increases approximately linearly with distance on log-log plots for a range between 20 and 220 m. Some research also showed scale effect in the karst aquifers (Király 1975; quinlan et al. 1992; Rovey 1994; Sauter 2005 ). Scale effect revealed the relative importance of secondary and primary porosity in value of hydraulic conductivity. 

In pumping test with boreholes scale, hydraulic conductivity is affected by both the matrix and fractures (Moench 1984; Nassimi & Mohammadi 2016), but with increasing the scale of the experiments the role of fractures and dissolution routes are increased, and with decreasing the scale the role of matrix are increased. Therefore it is expected that the hydraulic conductivity increases with increasing the scale, and the hydraulic conductivity decreases with decreasing the scale. 

In the study area with several conduits and joint systems, the data obtained from the Thompson equation represents the small scale (mainly matrix conditions), therefore combination of geoelectrical and hydrochemical data would cause considerable underestimation of hydraulic conductivity due to the scale effect in the karst aquifer (Fig. 4 ).
section_name: RESULTS AND DISCUSSION

section_content: Hydraulic conductivity (K) was estimated about 0. 016 m/day based on the Thompson equation (combination of geoelectrical and hydrochemical data) on the small scale in the study area. This value of K much less than the K derived from Lugeon, pumping and tracer test. In the karst terrain, estimated value of K based on the larger scale is more characteristic for karst structures that those based on the smaller scale, due to dominant role of preferential flow paths in the larger scale. As a result, for areas with preferential flow paths, such as karst aquifers, the hydraulic conductivity obtained from larger scale are greater than the hydraulic conductivity obtained from smaller scale. Pumping test shows a value for hydraulic conductivity at the SFDS that matches with dual-porosity (matrix and fracture) in the scale of borehole, but with increasing the scale the hydraulic conductivity are increased, and with decreasing the scale the hydraulic conductivity are decreased. 

The authors thank the University of Shiraz for their support of this work. Also some of hydrogeology data of the study area was supplied by Fars Regional water Authority in Shiraz. The author thanks to the reviewers, one of which was Prof. Georg Kaufmann, for constructive comments and suggestions, which considerably improved this paper.
section_name: CONCLUSIONS