Pumping test analysis for assessment of hydraulic parameters and aquifer system formation in hilly terrain

Groundwater conditions (GWCs) of an area depends on aquifer hydraulic parameters such as storativity (Sr) or storage coefficient (Sc), transmissivity (Tr) and hydraulic conductivity (k). It plays a key role concerning groundwater flow modeling, well performance, solute and contaminant transport assessment and also for identification of areas for additional hydrologic testing. Specifically, the geologic formation of a region controls the porosity and permeability; however, in hilly terrain prospecting ground water potential is more challenging due to its limited extent and its occurrences that are usually confined to fractures and weathered rocks. The present study aims at estimating the hydraulic parameters through pumping test analysis to assess aquifer system formation on hilly terrain from 16 bore wells. The aforesaid parameters were examined through a case study in some selective regions of Hamirpur district of Himachal Pradesh, India. The study area is controlled under two main geological horizons that is the post-tertiary and tertiary. The papers end with comparative results of hydraulic parameters and the aquifer systems formation on different GWCs, which may be helpful in the outlook of sustainable groundwater resource in the regions.


INTRODUCTION
Groundwater is the vital source of fresh water supply for industrial, agricultural and domestic purposes and hence largely contributes to the economic development of a region. Several inherent advantages of groundwater against the surface source escalate its demand. However, due to rapid population growth, urbanization and overwhelming pollution, there is an urgent need to ensure efficiently its sustainable utilization. Thus, to ensure proper management of vital groundwater resources, a prior knowledge of aquifer parameters is necessary. Groundwater zones designate the water bearing formation in the earth crust that acts as conduits for transmission and as reservoirs for storing water. Prospecting potential groundwater zones is a crucial task for the hydrogeologists especially in hilly terrain regions and those areas exposed to arid and semi-arid climatic conditions (Chandra et al. 2010). The availability of groundwater in hilly terrain is of limited extent because its occurrences that are usually confined to fractures and weathered rocks. The distributions and location of groundwater can be examined based on direct or through indirect analysis of some observable terrain features such as geologic, geomorphic, landforms and their hydrologic characteristics (Ndatuwong & Yadav 2014). For the past few decades characterizing aquifer systems and identifying groundwater resources has become of prime importance in the field of hydrogeology (Lachaal et al. 2011).
Conversely, mismanagement of water resources in an area causes negative effects including depletion of the aquifer storage, declination of groundwater level, seawater intrusion in coastal areas, land subsidence, quality deterioration and thereby creating environmental problems in other water bodies (Voudouris 2006). Such problems could be better understood by evaluating the local geological and hydrogeological characteristics that account for the hydraulic properties of these aquifers (Konkul et al. 2014). Hence, the necessity for groundwater management and the conservation studies at watershed level has gained importance worldwide (Gaur et al. 2011). In addition, proper delineation of potential groundwater resource is of prime importance in the scheme of water resource management (Bhuiyan 2020).
Pumping test is one of the suitable means for computing reliable and representative values of the hydraulic characteristics of aquifers (Kruseman & de Ridder 1994;. Pumping rate, flow pattern of groundwater due to pumping, etc. plays an important role for the management and sustainable development of groundwater resource (Zahid et al. 2017). The test is attempted by pumping a well at an almost constant pace while measuring water level variations at the same pumped well and a nearby well if possible (Mawlood & Ismail 2019).
It is estimated that 10 percent of the world's food supply is based on unsustainable pumping of groundwater (World Bank 1998). Hence, in order to evolve pragmatic and scientific planning for the management of groundwater resources, one needs to quantify the characteristic of hydro-geologic parameters. This requires knowledge of aquifer properties, specifically hydraulic conductivity and transmissivity (Sinha et al. 2008;Sattar et al. 2014).
The present study conducted a pumping test analysis for the estimation of hydraulic parameters and examined aquifer system formations in hilly terrain. The study use 16 bore wells in some selected regions of Hamirpur district, Himachal Pradesh, India.

Study area description
Hamirpur district is one among the 12 districts of Himachal Pradesh (H.P), India covering a total area of 1,118 sq. km (2.01% of total state area). It lies between latitudes 31°24 0 48″ to 31°53 0 35″ and longitudes 76°17 0 50″ to 76°4 3 0 42″ and is separated from Kangra district by Beas river in the north, Bakar and Sir khads from Mandi district in the east while Una district falls in its west and it touches Bilaspur district in the south. The district terrains are mostly undulating and hilly. The surface elevation ranges from 400 m to 600 m above mean sea level (MSL) along the Beas river valley and in lower reaches of Kunah Khad in the northern part of the district. In the eastern part, the district elevation is above 900 m above the MSL. The variation in altitude is typically in between 600-900 m above MSL. The western side hill ranges of Sola Singhi mark the boundary, with elevation reaching about 1,145 m above MSL. However, in the north-eastern region gorges and deep gulleys form part of the district. Figure 1 shows the map of the study area.

Geological set-up and lithology
The study area comprises two main geological horizons; that is, the post-tertiary and tertiary formations. Major portions of the study area are underlain by tertiary formations, which are characterised by Siwalik-type rocks (Upper, Middle and Lower Siwalik). Figure 2 shows the geological map of the study area. Table 1 summarizes the geological sequences and the lithological details of the study area. Upper Siwaliks consist of conglomerates, coarse-grained sandstones, interbedded with grey and pink clays/silts and sand stone or pebble beds. Middle Siwaliks are comprised of massive sandstone, medium to coarse-grained sandstone with claystone and conglomerate. Conversely, the lower Siwaliks have massive dark grey sandstone and purple shales that are overlain by the micaceous sandstone and grey clay/shales of the middle Siwalik.

Hydrogeology
The nature of the aquifers in the study area is of discontinuous and isolated types. The permeability and porosity settings of the study area are low to moderate and hence the aquifers underlain are not of high yielding types. The eastern part of the study area is widely underlain by boulder beds and conglomerates which are hard and compact, and are usually the reason behind low water bearing horizons. However, in low topographic regions the compact conglomerates formations is overlain by weathered conglomerates, forming potential and shallow aquifers. In the western and central regions feasible groundwater zones are found near major thrusts or faults in sandstone formations having fracture and contact zones.
Due to varied topography and geological structures development of groundwater, the area can be broadly discussed as hilly and valley regions. In the hilly regions, springs are the major source of groundwater development and based on ways of tapping they are called by many names in regional languages such as Bowris, Magars, Chasmas, and so on. Few tappings are done through state agencies like Irrigation & Public Health Department (I&PH) through some schemes to feed the inhabitants. Overall, in the hilly regions, sources of water for domestic and agriculture are obtained through open and/or tube wells, springs and hand pumps. On the other hand, valley areas in comparison to hilly areas are densely populated, thereby inflicting more demand for water for agriculture and domestic purposes. However, in such areas, the state agencies serve various water supply schemes extracted from nearby major rivers, streams (or Nallas) or tributaries with a perennial nature.

MATERIALS AND METHOD
Pumping test data from 16 boreholes were obtained from the study area. Table 2 summarizes the details of the boreholes considered for the hydraulic properties' assessment. The study area is categorized into two main regions (i.e. upper and lower regions) based on ground elevation and well locations. The upper region wells are located in the elevation range ! 800 m while the lower region lies below 800 m. The calculations involve applications of two methods, viz. the Cooper Jacob and Theis methods. Theis (1935) found non-steady flow of groundwater to be analogous to the unsteady flow of heat in a homogeneous solid. The equation is then recognized to be most widely used in transient groundwater hydraulics. The solution in terms of drawdown can be defined as: where, s(r, t) designates the drawdown at a radial distance r from the well at time t after the start of pumping, u ¼ r 2 S=4Tt is the dimensionless quantity that varies with r of the observation well at time t, T represents the transmissivity (m 2 /day) and Q denotes the pumping rate (m 3 =d). S is the aquifer Storativity (dimensionless) and W(u) is the dimensionless exponential integral known as well function which can be approximated as:   (1) and (2). In other words, the Cooper-Jacob method involves truncation of the infinite Taylor series that is used to estimate the well function W(u).
Such truncation leads to avoidance of data that are measured at early stage, and were not counted as valid for the analysis. It is valid for u 0:01 (u values having error of 0.02 i.e. 2% error is acceptable). Thus, u becomes small, for small values of r and at large value of time t, Equation (2) can be written as: After substituting W(u) in Equation (1), the resulting equation becomes: Based on the observations of t and r values the Cooper-Jacob method can be used in three ways: (a) Time-Drawdown Method (when r is constant; that is, the observation well is fixed); (b) Distance-Drawdown Method (when t is constant/fixed; that is, a reading taken from a different observation well), and (c) Time-Distance-Drawdown Method (simultaneous observations are made on drawdown in three or more observation wells). The study adopted the Time-Drawdown Cooper-Jacob method for estimation of the hydraulic parameters. The above equation is plotted as a straight line on semi-logarithmic paper if the limiting condition is met. Thus, straightline plots of s versus t can occur after sufficient time has elapsed. In the case were multiple OWs (observations wells) are considered, more distant wells are deprived to the meet the conditions rather than the adjacent one.
The logarithmic x-axis is taken as time (t) scale while the linear y-axis is plotted for drawdown (s). Both Tr and Sr and be estimated as below:

RESULTS AND ANALYSIS
Both Theis and Cooper-Jacob methods were suitably employed to estimate the aquifer hydraulic parameters in the study area. Tables 3 and 4 show the estimated values of Tr and Sr obtained from the simulated drawdown for all the wells using both methods. Figures 3-7 show the scatter plots of data fitting in Cooper Jacob and Theis curve fitting on drawdown data from the observation wells in both upper and lower regions. It is observed that a good match is obtained between the Theis drawdown and simulated data for the entire pumping period. For the Cooper-Jacob method, Equations (3)-(6) were used for the estimation of aquifer hydraulic parameters. The single well model is utilized in the case where no observation wells are available. This implies considerations of a pumping well to serves as the piezometer; the straight line obtained for the semi-log plot of drawdown against time indicates the radial flow of water into the pumped well. The aquifer was tested for a period between 180 and 240 minutes or was subject to time where equilibrium is reached. In a semi-log graph, data from the pumping phase are plotted against corresponding t values, and then a straight line is plotted through field data points. The values of the drawdown per log cycle of time were determined from the slope of the graph as Ds.
From the estimated hydraulic parameters summarized in Tables 3 and 4, it is observed that the least Tr values were recorded in W13 and W14 whereas the highest Tr is recorded in W15. The Tr potential is classified into five grades as per Gheorghe Standards (1978) ( Table 5) that includes: high potential (.500), moderate potential (50-500), low potential (5-50), very low potential (0.5-5) and Negligible (flat) potentials (below 0 .5) respectively.     Accordingly, it is observed that W12, W15 has high Tr potential while W13 and W14 fall under least or negligible Tr potentials. Similarly, the trends for moderate potential is recorded only for W3, low Tr potential for W1-W4, W16 and very low potential for W5, W6, W7,W 8, W9 and W10 respectively. Low discharge in Table 4 has the observed Tr range of 0:5 m 2 /day. Similarly, the values of K and Sr can be assigned based on Todd (1980), Domenico & Schwartz (1990), Lohman (1972 and Bouwer (1978). The value of K is found to be in the ranges of 0.06 to 270.10. Table 6 shows the observed K values according to Bouwer standards.
Based on Todd (1980), Domenico & Schwartz (1990), Lohman (1972) and Bouwer (1978), and from the ranges of Sr values the aquifer layer types can be categorized as a confined aquifer (0.00005-0.005), Leaky or Semiconfined (0.005-0.05) and unconfined (0.05-0.3). Accordingly, it can be observed that from Tables 3 and 4, the upper regions of the study area are mostly confined aquifers whereas the lower regions falls under unconfined aquifer layers.
To further validate the lithology profile of the bore well, a resistivity survey is also carried out at the site. It is observed that the depth or thicknesses of the lithological layers obtained from VES (vertical electrical sounding) interpretation provides close conformity with the obtained hydraulic parameters. Figure 7 shows the lithological profiles of the wells considering the upper region (W5 and W6) and lower regions wells (W16 and W17) in the study area. These plots were established using the LogPlot Software (Ver. 7.6.138.174). It is observed that in both the regions of the study area, the lithological horizons comprise mostly claystone with traces of conglomerate, and a mixture of clay, gravel, and sandstone. Except for W14, the topmost layers in Figure 7 are generally found to be claystone. The bottom-most layer is usually the gravel content, which is the common water bearing strata in the study area in question.

CONCLUSION
The present study reports on the assessment of hydraulic parameters and the aquifer system formation in hilly terrain, a case study of some selective regions of Hamirpur district, H.P., India. It is observed that the obtained mean Tr values are found to be in the range of 2.47-713.08 while Sr ranges from 9.5E-06-7.56 and the hydraulic conductivity K in the range of 0.06-270.10. Based on the obtained hydraulic parameters, the subsurface formation at the well sites are mainly composed of an assortment of claystone, claystone along with traces of conglomerates, sandstones and gravels which are consistent with the VES data and visual observations in the field. Based on the obtained results, two types of aquifer system were observed; that is, the upper regions aquifer layers is characterised as confined while the lower regions is unconfined (or free layers) type. In future, further study may be carried out on the estimation of infiltration rate and contaminant transport assessment.