Abstract

This study employs the surface geoelectrical resistivity method to investigate the aquifer repositories by estimating the geohydrodynamic parameters; aquifer quality index (AQI), flow zone indicator (FZI), permeability, hydraulic conductivity, fractional porosity, formation factor, normalized porosity index, and tortuosity. The data were obtained from vertical electrical sounding (VES) employing Schlumberger electrode configuration across 17 locations within the study area. The interpretation of the field data was done using the computer software package known as the WINRESIST and the results gave the values of resistivity, depth and thickness of each geoelectric layer at each VES point. The values of aquifer resistivity and thickness were used to estimate the geohydrodynamic parameters, and their variation trends are shown in the contour maps. It was delineated that high permeability zone have high porosity, AQI, FZI, and hydraulic conductivity but low formation factor and tortuosity. This is a reflection of high pore connectivity and groundwater transmissibility in the aquifer repositories. The various plots illustrate the interrelationship between the parameters and gave unique information which could be employed in groundwater contamination modeling, management and abstraction.

Highlights

  • Groundwater repository was characterized using the geohydrodynamic parameters.

  • Geohydrodynamic parameters were estimated using aquifer resistivity and thickness values.

  • High permeability zone has high ϕ, AQI, FZI, and K but low F and τ.

  • Results revealed variations and interrelations of the estimated geohydrodynamic parameters.

  • High pore connectivity and groundwater transmissibility in aquifer repositories were reflected.

INTRODUCTION

The occurrence of groundwater in any region depends on the dynamic behavior of the earth subsurface, which is characterized by numerous pore spaces (voids and interstices). The number, connectivity, size and shape of these pore spaces affects the characteristics of the subsurface. The physical and hydrogeologic properties that constitute an aquifer affect the aquifer yield, and also affect the flow of groundwater in the aquiferous zone. The earth subsurface is made up of different rock types with different porosity and permeability characteristics; as such, the movement of groundwater varies across the subsurface. Effective porosity and permeability of a formation are two parameters that have great influence on groundwater exploitation (Abed 2014; George et al. 2017a; Ibuot et al. 2019). According to Abuseda et al. (2015), permeability that allows groundwater transmission is reliant on factors such as the pore geometry, grain shape and size, cementation factor, etc. Permeability is a tensor quantity: not only does it vary from place to place, but it also varies with respect to direction; the variations can be described as heterogeneity or anisotropy depending on location and direction. The depth of rocks below the land surface affects their porosity and permeability: as their depths increase below the subsurface, porosity and permeability decreases. At great depth, the pore spaces and cracks in rocks are more compact in size due to the weight of overlying rocks. The geometric patterns of grains and the resulting porosity affect the cementation factor of the formation extensively. Transmission of pore fluid in aquifer repositories can be affected by the occurrence of dead-end pores or trapped impermeable geomaterials (Obianwu et al. 2011; George et al. 2018). A productive aquifer must contain interconnected pores that are both numerous and large enough to aid the flow of groundwater. These parameters are the basis for the aquifer quality index (AQI) and the flow zone indicator (FZI) and characterized the quality and flow characteristics of aquifer units.

According to Amaefule et al. (1993), Abed (2014) and George et al. (2017b), AQI and FZI relate the petrophysical properties at small and large scale, and also help in estimating the dynamic properties by employing the pore geometry factor and tortuosity. These parameters (AQI and FZI) are generic tools used in assessing contamination and heterogeneity of aquifer units (George et al. 2017b). AQI is an indicator that characterizes rock quality based on the relation of porosity and permeability of a medium and depends on the grain size and typologies of rocks. The FZI quantifies the flow character of the hydrogeologic unit and is related to the formation's void ratios/normalized porosity indices (Amaefule et al. 1993; George et al. 2017b). Estimation of permeability is important in groundwater circulation owing to the composite geometry of the connected pore spaces and the complex nature of the porous media (Carman 1937; Saar & Manga 1999). Kozeny (1927) and Carman (1937) expressed permeability as a function of the physical properties of the interconnected pore system, which include porosity and tortuosity. The arrangement of the pores and grains geometry of a formation affects the hydraulic conductivity and permeability of the rocks in that formation, and can also be employed in determining properties like the volume ratio, permeability, hydraulic conductivity, and so on. The flow of groundwater contaminants is controlled by the hydraulic conductivity of the hydrogeologic units (George et al. 2018; Ibuot et al. 2019). Tortuosity is a permeability dependent parameter that influences the flow of groundwater through an aquifer unit.

The study of groundwater repositories is important, since the movement of contaminants in the hydrogeological units is controlled by the hydrodynamic characteristics of the subsurface formation and also the geological settings. The knowledge of the flow dynamics is necessary as it can help in reducing the risk of contamination flow and also provides information that will aid in a proper groundwater management and development strategy (Abd-Elhamid & Javidi 2011; George et al. 2015; Obiora et al. 2016a; Aleke et al. 2018). Different geophysical processing tools are available as a result of advancement in technology, and this has aided the estimation of the subsurface hydrodynamic properties, delineation of pore space geometry and heterogeneity of the aquiferous layers through the use of electrical resistivity data (Soupios et al. 2007; Niwas et al. 2011; Obianwu et al. 2011; Ibanga & George 2016; Obiora et al. 2016b; Ekanem 2020; Ezema et al. 2020). The disadvantages of using the pumping test to determine the geohydrodynamic parameters have been overcome by the use of an indirect geophysical method (electrical resistivity technique) to estimate the parameters, and these parameters are known to correlate well with the parameters from pumping tests in boreholes (George et al. 2017a; Ibuot et al. 2019). Electrical resistivity method has been proven useful in characterizing the subsurface aquifer pore properties and the mechanism of electrical conduction through the subsurface (Soupios et al. 2007; Khalil & Monterio Santos 2009; Ibuot et al. 2013; George et al. 2015; Obiora et al. 2018). The electrical resistivity data aids in generating information that are useful in delineating the aquifer repositories and its distribution (Mbonu et al. 1991; Riddell et al. 2010; Ibuot et al. 2013; Andrade 2014; Alhassan et al. 2015). This study aimed at estimating the aquifer geohydrodynamic properties from electrical resistivity data necessary for groundwater flow management, contaminant flow studies and monitoring.

LOCATION AND GEOLOGIC SETTING

The study area (University of Nigeria, Nsukka) is located within longitudes 7°23/0//E to 7°26/0//E and latitude 6°51/24//N (Figure 1(a)) and lies within the Ajali and Nsukka geological formations (Figure 1(b)) which are parts of the Anambra sedimentary basin. The Ajali Formation is underlain by shaley impermeable units of Mamu Formation that trapped the Ajali aquifers. According to Agagu et al. (1985), the Ajali Sandstone (upper Maastritchian) is about 451 m thick. Lithologically, the Ajali formation has poorly consolidated sandstone characteristically cross bedded with minor clay layers (Reyment 1965). The lithology of Nsukka is mainly sandstones intercalating with clay, interbedded shales, siltstones, sands and thin coal seams (Simpson 1954; Reyment 1965), but they have become lateritized in many places where they characteristically form resistant capping on mesas and buttes. The Nsukka Formation is physiographically dooted by numerous cone shaped hills which are separated by low lands and broad valleys and are laterite capped (Ogbukagu 1976). The Nsukka Formation with Imo Shale marks the onset of another transgression in the Anambra Basin during the Paleocene (Obaje 2009). The most important topographical features observed in the study area are the North-South trending cuesta over Ajali sandstone.

Figure 1

(a) Location map of the study area. (b) Geologic map of the area showing the location of the study area within the University of Nigeria, Nsukka and the geological cross section along the line trending SW-NE.

Figure 1

(a) Location map of the study area. (b) Geologic map of the area showing the location of the study area within the University of Nigeria, Nsukka and the geological cross section along the line trending SW-NE.

THEORY, METHODS AND DATA ACQUISITION

The subsurface characteristics/properties affect groundwater abstraction and flow and depend on the formation pore connectivity, pore angularity, compaction, pore-grain volume ratio, resistivity and heterogeneity of formations (George et al. 2017a). Estimating petrophysical properties such as permeability and porosity helps in predicting other parameters and their relationships with each other. In assessing the flow characteristics of an aquifer there is need to estimate some parameters, which include formation factor (F), tortuosity (τ), FZI, AQI, and normalized porosity index (NPI).

AQI is an empirical relationship that relates porosity and permeability using Equation (1):
formula
(1)
where is the permeability in mD and is the porosity in %, while the units of AQI and FZI are in meters (m).
The FZI, which quantifies the flow character of an aquifer, was estimated from Equation (2):
formula
(2)
where NPI is the normalized porosity index, which can be deduced using Equation (3):
formula
(3)
Permeability, which is the ability of a porous medium to allow the transmission of groundwater, can be determined using the relationship as in Equation (4). This property is independent of the fluid properties but depends on the pore distribution and connectivity.
formula
(4)
where K is the hydraulic conductivity, is the dynamic water viscosity, which is given as 0.0014 according to Fetter (1994), is the density of water taken as 1,000 and g is the acceleration due to gravity taken as 10 .
The formation factor (F), which is the ratio of bulk resistivity to water resistivity, was estimated using Archie's law as given in Equation (5). It represents the microscopic property of the subsurface formation. According to Archie, the formation factor depends only on porosity and suggested that electrical conduction was entirely due to ionic transport.
formula
(5)
where a is the pore geometry factor, m is the cementation factor, is the fractional porosity, where and . These constants affect geometry spread of the formation factor and porosity. The depositional processes of sediments influence natural soil-water conductivity as it affects the formation factor (F), thus rendering Archie's law invalid. Archie's law is not applicable in a freshwater environment where the pore fluids are low in salinity and the low electrical conductivity of pore-water can shunt surface conduction along grains (Purvance & Andricevic 2000; George et al. 2015). Atkins & Smith (1961) describe a cementation factor to reflect the distinctive differences in formation geometry and pore magnitudes. It also gives information on the non-connectivity between pore spaces or rise in pore communications (Aleke et al. 2018; George et al. 2018). The geometry factor, a, reflects the influence of the mineral grains on current.
The hydraulic conductivity (K) was estimated from Equation (6) according to Heigold et al. (1979), this is a key factor in groundwater transportation in the subsurface.
formula
(6)
where is the aquifer resistivity. The values of K characterize the dynamic behavior of hydrogeologic units to allow flow of groundwater and can influence the productivity of boreholes/wells and the velocity of pollutant spread.
Fractional porosity (ϕ) is a volumetric parameter calculated according to Marotz (1968) in Equation (7). Fractional porosity, according to Aleke et al. (2018), is affected by the particle composition of rocks, their mode of formation and the pressures to which they are exposed. Increase in porosity reduces the electrical resistivity of a formation and has a significant effect on the cementation factor of the propagating medium.
formula
(7)
where K is hydraulic conductivity in and is the fractional porosity.
The shape of the interconnected pore space is described by tortuosity. It is a geometric parameter associated with hydraulic, electrical or diffusive properties (Clennell 1997; Matyka et al. 2008) and influences the transfer of particles in the hydrogeologic units. Equation (8) therefore gives an expression that relates formation factor (F), porosity ( and tortuosity (τ).
formula
(8)

These parameters were estimated for each VES point and used to classify the hydrogeologic units within the study area.

The vertical electrical sounding (VES) technique, using Schlumberger electrode configuration, was employed in this geophysical survey and the soundings were conducted at seventeen (17) locations within the maximum current electrodes separation (AB) ranging from 800 m to 900 m. The electrical resistivity method involves injecting current into the ground by means of a pair of current electrodes and the potential difference was measured using the IGIS resistivity meter across the potential electrodes (Telford et al. 1990; Lowrie 1997). The integration of VES with Schlumberger electrode array enhanced delineating the subsurface resistivity with depth. The measured field data was converted to apparent resistivity () using Equation (9).
formula
(9)
where AB = current electrode spacing, MN = potential electrode spacing, and the geometric factor G is given as;
formula
(10)

The values of the calculated apparent resistivity were plotted on bi-log graph sheets against half current electrode spread, and the curves obtained were smoothened. The smoothening was performed by averaging the two readings at the crossover points, or deleting any outlier at the crossover points that did not conform to the dominant trend of the curve. Also deleted were data that stood out as outliers in the prevalent curve trend, which could have caused serious increase in root-mean square error (RMSE) during the modeling phase of the work. The apparent resistivity data were input into the WINRESIST computer software program and the interpreted data gives a set of VES curves (Figure 2(a) and 2(b)) with values of resistivity, depth and thickness of each VES point.

Figure 2

(a) Modeled VES curve at VES 1. (b) Modeled VES curve at VES 3.

Figure 2

(a) Modeled VES curve at VES 1. (b) Modeled VES curve at VES 3.

RESULTS AND DISCUSSION

The VES results give the values of resistivity, thickness and depth of each layer within the maximum current electrode separation (Table 1). The geohydrodynamic parameters were computed from the values of aquifer resistivity and thickness (Table 2) and the result showed that the aquifer layer is characterized by relatively high resistivity values ranging from 198.2 to 23,398.0 Ωm with its thickness ranging from 37.7 to 160.3 m. The high resistivity values in this layer may be attributed to the compact nature of the subsurface, moisture content, current magnitude and the presence of highly resistive materials. The hydraulic conductivity (K) was estimated from Equation (6), with values ranging from 0.033 to 2.7818 m/day. The contour map (Figure 3) shows the spread of hydraulic conductivity and areas with high K values are observed in northern parts of the study area and decreases southwards. Since hydraulic conductivity is controlled by the intergranular porosity and fracturing, the low values of K in the southern parts may be attributed to poor communication channels in the pore spaces and the variation in grain size. According to literatures, the movement of groundwater contaminants is controlled by hydraulic conductivity (Chandra 2008; Obianwu et al. 2011; Ibanga & George 2016; Ibuot et al. 2017; Obiora et al. 2018).

Table 1

Summary of measured electrical resistivity data in the study area

VESLongitude (OE)Latitude (ON)Layer resistivity
Thickness (m)
Depth (m)
ρ1ρ2ρ3ρ4ρ5ρ6h1h2h3h4h5d1d2d3d4Elevation (m)
7.4065 6.8585 398.9 874.7 2,855.5 4,554.0 6,809.9 – 1.3 6.4 53.1 83.1 – 1.3 7.7 60.8 143.9 442 
7.4127 6.8693 422.3 2,553.3 2,455.6 5,713.9 7,118.9 – 1.5 9.0 35.7 104.6 – 1.5 10.5 46.2 150.8 418 
7.4231 6.8613 1,714.9 866.1 4,284.2 4,089.3 7,661.0 – 1.4 2.9 35.0 108.4 – 1.4 4.3 39.3 147.7 458 
7.4267 6.8613 3,108.3 756.2 2,714.2 7,211.7 33,327.2 – 0.9 3.2 46.1 109.8 – 0.9 4.0 50.2 160.0 468 
7.4079 6.8691 626.1 185.7 14,163.8 6,799.0 2,086.4 – 1.4 2.9 28.3 114.9 – 1.4 4.4 32.7 147.6 416 
7.4222 6.8525 331.6 103.5 2,212.0 23,398.0 4,332.0 – 2.8 4.6 7.1 137.3 – 2.8 7.4 14.5 151.8 475 
7.4098 6.8596 196.6 760.9 320.2 11,463.1 3,617.1 – 0.7 7.1 14.2 98.2 – 0.7 7.8 22.1 120.3 454 
7.4089 6.8698 547.4 570.6 1,125.9 6,261.6 1,322.4 – 3.2 7.4 15.8 117.2 – 2.2 10.6 26.4 143.6 414 
7.4056 6.8681 4,884.9 7,208.6 3,993.5 15,235.9 1,094.3 – 5.0 8.3 25.8 86.9 – 5.0 13.3 39.1 126.0 419 
10 7.4123 6.8716 346.2 2,403.9 232.0 11.3 – – 2.0 97.5 37.7 – – 2.0 99.5 137.2 – 419 
11 7.4038 6.8719 314..7 1,532.9 5,083.7 198.2 9.0 – 1.3 21.9 40.9 41.3 – 1.3 23.2 64.1 105.5 402 
12 7.4105 6.8651 408.3 1,266.1 61.1 6,191.5 2,598.5 – 1.0 2.0 11.1 184.3 – 1.0 3.0 14.1 198.5 425 
13 7.4016 6.8589 798.9 258.8 3,847.1 20,428.3 3,901.3 – 1.8 9.2 12.8 138.7 – 1.8 11.0 23.5 162.2 432 
14 7.4091 6.8625 393.4 42.3 16,724.1 1,246.8 821.5 – 1.8 2.3 39.5 116.1 – 1.8 4.1 43.6 159.8 436 
15 7.4132 6.8639 1,758.8 1,196.7 1,445.2 1,270.8 781.7 – 5.4 13.1 79.2 71.9 – 5.4 18.6 97.7 169.6 430 
16 7.3980 6.8617 2,151.0 4,350.2 2,446.5 9,774.9 2,455.5 – 5.6 10.3 29.6 114.0 – 5.6 15.9 45.4 159.4 409 
17 7.4067 6.8696 213.7 493.1 15,855.9 2,517.0 3,785.6 – 0.5 4.9 28.4 160.3 – 0.6 5.5 34.0 194.3 412 
VESLongitude (OE)Latitude (ON)Layer resistivity
Thickness (m)
Depth (m)
ρ1ρ2ρ3ρ4ρ5ρ6h1h2h3h4h5d1d2d3d4Elevation (m)
7.4065 6.8585 398.9 874.7 2,855.5 4,554.0 6,809.9 – 1.3 6.4 53.1 83.1 – 1.3 7.7 60.8 143.9 442 
7.4127 6.8693 422.3 2,553.3 2,455.6 5,713.9 7,118.9 – 1.5 9.0 35.7 104.6 – 1.5 10.5 46.2 150.8 418 
7.4231 6.8613 1,714.9 866.1 4,284.2 4,089.3 7,661.0 – 1.4 2.9 35.0 108.4 – 1.4 4.3 39.3 147.7 458 
7.4267 6.8613 3,108.3 756.2 2,714.2 7,211.7 33,327.2 – 0.9 3.2 46.1 109.8 – 0.9 4.0 50.2 160.0 468 
7.4079 6.8691 626.1 185.7 14,163.8 6,799.0 2,086.4 – 1.4 2.9 28.3 114.9 – 1.4 4.4 32.7 147.6 416 
7.4222 6.8525 331.6 103.5 2,212.0 23,398.0 4,332.0 – 2.8 4.6 7.1 137.3 – 2.8 7.4 14.5 151.8 475 
7.4098 6.8596 196.6 760.9 320.2 11,463.1 3,617.1 – 0.7 7.1 14.2 98.2 – 0.7 7.8 22.1 120.3 454 
7.4089 6.8698 547.4 570.6 1,125.9 6,261.6 1,322.4 – 3.2 7.4 15.8 117.2 – 2.2 10.6 26.4 143.6 414 
7.4056 6.8681 4,884.9 7,208.6 3,993.5 15,235.9 1,094.3 – 5.0 8.3 25.8 86.9 – 5.0 13.3 39.1 126.0 419 
10 7.4123 6.8716 346.2 2,403.9 232.0 11.3 – – 2.0 97.5 37.7 – – 2.0 99.5 137.2 – 419 
11 7.4038 6.8719 314..7 1,532.9 5,083.7 198.2 9.0 – 1.3 21.9 40.9 41.3 – 1.3 23.2 64.1 105.5 402 
12 7.4105 6.8651 408.3 1,266.1 61.1 6,191.5 2,598.5 – 1.0 2.0 11.1 184.3 – 1.0 3.0 14.1 198.5 425 
13 7.4016 6.8589 798.9 258.8 3,847.1 20,428.3 3,901.3 – 1.8 9.2 12.8 138.7 – 1.8 11.0 23.5 162.2 432 
14 7.4091 6.8625 393.4 42.3 16,724.1 1,246.8 821.5 – 1.8 2.3 39.5 116.1 – 1.8 4.1 43.6 159.8 436 
15 7.4132 6.8639 1,758.8 1,196.7 1,445.2 1,270.8 781.7 – 5.4 13.1 79.2 71.9 – 5.4 18.6 97.7 169.6 430 
16 7.3980 6.8617 2,151.0 4,350.2 2,446.5 9,774.9 2,455.5 – 5.6 10.3 29.6 114.0 – 5.6 15.9 45.4 159.4 409 
17 7.4067 6.8696 213.7 493.1 15,855.9 2,517.0 3,785.6 – 0.5 4.9 28.4 160.3 – 0.6 5.5 34.0 194.3 412 
Table 2

Computed values of aquifer geoelectric and geohydrodynamic parameters

VESLongitude (OE)Latitude (ON)(Ωm)ha (m)K (m/day)Kp ()NPIFAQI (m)FZI(m)
7.4065 6.8585 4,554.0 83.1 0.149 2.09E-08 0.170 0.204 7.455 1.124 0.030 0.470 
7.4127 6.8693 5,713.9 104.6 0.121 1.69E-08 0.160 0.190 8.131 1.140 0.027 0.409 
7.4231 6.8613 4,089.3 108.4 0.165 2.31E-08 0.174 0.211 7.166 1.117 0.031 0.502 
7.4267 6.8613 7,211.7 109.8 0.097 1.36E-08 0.150 0.177 8.937 1.158 0.025 0.354 
7.4079 6.8691 6,799.0 114.9 0.103 1.44E-08 0.153 0.180 8.721 1.154 0.026 0.368 
7.4222 6.8525 23,398.0 137.3 0.033 4.54E-09 0.101 0.112 16.261 1.280 0.018 0.162 
7.4098 6.8596 11,463.1 98.2 0.063 8.84E-09 0.131 0.150 11.005 1.199 0.022 0.264 
7.4089 6.8698 6,261.6 117.2 0.111 1.55E-08 0.156 0.185 8.433 1.147 0.027 0.387 
7.4056 6.8681 15,235.9 86.9 0.048 6.78E-09 0.119 0.135 12.706 1.228 0.020 0.218 
10 7.4123 6.8716 232.0 37.7 2.401 3.36E-07 0.294 0.417 3.255 0.979 0.090 2.551 
11 7.4038 6.8719 198.2 41.3 2.7818 3.89E-07 0.301 0.431 3.148 0.974 0.095 2.778 
12 7.4105 6.8651 6,191.5 184.3 0.112 1.57E-08 0.157 0.186 8.394 1.146 0.027 0.390 
13 7.4016 6.8589 20,428.3 138.7 0.035 5.16E-09 0.107 0.119 14.97 1.263 0.019 0.178 
14 7.4091 6.8625 1,246.8 116.1 0.500 7.00E-08 0.224 0.288 4.911 1.048 0.047 1.004 
15 7.4132 6.8639 1,270.8 71.9 0.491 6.88E-08 0.223 0.287 4.937 1.049 0.047 0.993 
16 7.398 6.8617 9,774.9 114 0.073 1.03E-08 0.137 0.159 10.211 0.375 0.023 0.292 
17 7.4067 6.8696 2,517.0 160.3 0.260 3.64E-08 0.194 0.241 6.070 0.344 0.036 0.669 
VESLongitude (OE)Latitude (ON)(Ωm)ha (m)K (m/day)Kp ()NPIFAQI (m)FZI(m)
7.4065 6.8585 4,554.0 83.1 0.149 2.09E-08 0.170 0.204 7.455 1.124 0.030 0.470 
7.4127 6.8693 5,713.9 104.6 0.121 1.69E-08 0.160 0.190 8.131 1.140 0.027 0.409 
7.4231 6.8613 4,089.3 108.4 0.165 2.31E-08 0.174 0.211 7.166 1.117 0.031 0.502 
7.4267 6.8613 7,211.7 109.8 0.097 1.36E-08 0.150 0.177 8.937 1.158 0.025 0.354 
7.4079 6.8691 6,799.0 114.9 0.103 1.44E-08 0.153 0.180 8.721 1.154 0.026 0.368 
7.4222 6.8525 23,398.0 137.3 0.033 4.54E-09 0.101 0.112 16.261 1.280 0.018 0.162 
7.4098 6.8596 11,463.1 98.2 0.063 8.84E-09 0.131 0.150 11.005 1.199 0.022 0.264 
7.4089 6.8698 6,261.6 117.2 0.111 1.55E-08 0.156 0.185 8.433 1.147 0.027 0.387 
7.4056 6.8681 15,235.9 86.9 0.048 6.78E-09 0.119 0.135 12.706 1.228 0.020 0.218 
10 7.4123 6.8716 232.0 37.7 2.401 3.36E-07 0.294 0.417 3.255 0.979 0.090 2.551 
11 7.4038 6.8719 198.2 41.3 2.7818 3.89E-07 0.301 0.431 3.148 0.974 0.095 2.778 
12 7.4105 6.8651 6,191.5 184.3 0.112 1.57E-08 0.157 0.186 8.394 1.146 0.027 0.390 
13 7.4016 6.8589 20,428.3 138.7 0.035 5.16E-09 0.107 0.119 14.97 1.263 0.019 0.178 
14 7.4091 6.8625 1,246.8 116.1 0.500 7.00E-08 0.224 0.288 4.911 1.048 0.047 1.004 
15 7.4132 6.8639 1,270.8 71.9 0.491 6.88E-08 0.223 0.287 4.937 1.049 0.047 0.993 
16 7.398 6.8617 9,774.9 114 0.073 1.03E-08 0.137 0.159 10.211 0.375 0.023 0.292 
17 7.4067 6.8696 2,517.0 160.3 0.260 3.64E-08 0.194 0.241 6.070 0.344 0.036 0.669 
Figure 3

Contour map showing the distribution of hydraulic conductivity.

Figure 3

Contour map showing the distribution of hydraulic conductivity.

The aquifer permeability was estimated from Equation (4). It has a maximum value of and minimum value of . The permeability distribution (Figure 4) follows the same trend as hydraulic conductivity and decreases towards the south, and the low permeability will affect the movement of groundwater. This implies that regions with low permeability may likely contain relatively impermeable materials such as clay and shale. The low permeability may likely be affected by depth and the weight of the overlying rocks. A plot of permeability against hydraulic conductivity (Figure 5) gives a linear relationship, which indicates that the variations of both parameters are proportional to each other. These parameters greatly controlled the movement of fluids within the aquifer units.

Figure 4

Contour map showing the distribution of permeability.

Figure 4

Contour map showing the distribution of permeability.

Figure 5

A graph of permeability against hydraulic conductivity.

Figure 5

A graph of permeability against hydraulic conductivity.

Using Equation (7) (Marotz 1968), fractional porosity was estimated and the values range from 0.101 to 0.301. Figure 6 shows the variation of this parameter across the study area, with high porosity in the northern part. It can be delineated that as porosity increases, hydraulic conductivity and permeability increase and vice versa. This indicates good pore connectivity and grain size distribution. A graph of permeability against fractional porosity (Figure 7) shows their relationship.

Figure 6

Contour map showing the variation of porosity.

Figure 6

Contour map showing the variation of porosity.

Figure 7

A graph of permeability against fractional porosity.

Figure 7

A graph of permeability against fractional porosity.

Formation resistivity factor (F) ranges from 3.148 to 16.261 and is inversely proportional to porosity, hydraulic conductivity and permeability. The contour map (Figure 8) shows the variation of F as it decreases towards the north, with high values of F in the southern part. The relationship between F and porosity is shown in Figure 9, which gives a high correlation coefficient of 1 (Equation (11)). This agrees with Archie's law and since , it means that the mineral grains are not perfect insulators, and therefore indicates the contribution of mineral grains to electrical conductivity (Archie 1942).
formula
(11)
Figure 8

Contour map showing the variation of formation factor.

Figure 8

Contour map showing the variation of formation factor.

Figure 9

A graph of formation factor against porosity.

Figure 9

A graph of formation factor against porosity.

The calculated fractional porosity was used in accordance with Equation (3) to estimate the normalized porosity index (NPI) with values ranging from 0.112 to 0.431 across the study area. Its variation is displayed in Figure 10.

Figure 10

Contour map showing the distribution of normalized porosity index.

Figure 10

Contour map showing the distribution of normalized porosity index.

Tortuosity (), which is a permeability dependent parameter that also controls the flow of water in an aquifer unit, was calculated from the estimated formation factor and fractional porosity and its value ranges from 0.34 to 1.28. The highest values of tortuosity are observed in the southern parts and increase towards the north (Figure 11). This indicates that high tortuosity corresponds to low permeability and low porosity and this also affects aquifer transmissibility and the pore connectivity.

Figure 11

Contour map showing the variation of tortuosity.

Figure 11

Contour map showing the variation of tortuosity.

Figure 12

Contour map showing the distribution of AQI.

Figure 12

Contour map showing the distribution of AQI.

The AQI was estimated from Equation (1) and the calculated values range from 0.018 to 0.095 μm. AQI changes in the same proportion with porosity, hydraulic conductivity and permeability but inversely related with formation factor. Figure 12 shows the distribution of AQI across the study area with high values observed in the northern zone.

Figure 13

A graph of AQI against fractional porosity.

Figure 13

A graph of AQI against fractional porosity.

Figures 1315 are graphs that show the relationship between porosity, permeability and formation factor. Figures 13 and 14 reveal that an increase in AQI leads to an increase in fractional porosity and permeability (Equations (12) and (13)) with the correlation coefficients of 0.996 each. The effects of these parameters on AQI may be attributed to the pore openings and pore connectivity.
formula
(12)
formula
(13)
Figure 14

A graph of AQI against permeability.

Figure 14

A graph of AQI against permeability.

Figure 15

A graph of AQI against formation factor.

Figure 15

A graph of AQI against formation factor.

A graph of AQI against formation factor (Figure 15) resulted in an inverse relationship with a power expression as given in Equation (14), with a correlation coefficient of 0.961. It can be inferred from the study that as formation factor increases, AQI decreases.
formula
(14)
The FZI, which characterizes the flow in hydrogeologic units, was estimated from Equation (2) and it ranges from 0.162 to 2.778 μm. The distribution of FZI shown in Figure 16 revealed the same trend as AQI. This is an indication that porosity and permeability varies directly with FZI in homogeneous and isotropic aquifer units (George et al. 2017b). A graph of FZI against permeability (Figure 17) illustrates the relationship with a power equation given in Equation (15), having a correlation coefficient of 0.998.
formula
(15)
Figure 16

Contour map showing the distribution of FZI.

Figure 16

Contour map showing the distribution of FZI.

Figure 17

A graph of FZI against permeability.

Figure 17

A graph of FZI against permeability.

Figure 18 gives the relationship between AQI and FZI with a straight line equation (Equation (16)), the slope can be deduced as 33.88 and a negative intercept of −0.510 along the FZI axis.
formula
(16)
Figure 18

A graph of FZI against AQI.

Figure 18

A graph of FZI against AQI.

Just like the AQI, FZI is inversely related to formation factor (F), as an increase in formation factor leads to a proportional decrease in FZI. The relationship between FZI and F is given in a well correlated graph (Figure 19), as illustrated by Equation (17)
formula
(17)
Figure 19

A graph of FZI against formation factor.

Figure 19

A graph of FZI against formation factor.

Figure 20 shows the relationship between FZI and NPI. This reflects the fact that there is a proportional increase between both parameters; as FZI increases, NPI also increases (Equation (18)). In a compact formation such as the study area, if the flow zone indicator decreases, the normalized porosity index will also decrease (Obrzud & Truty 2012; George et al. 2017b). It can be inferred from the study that a positive change in flow zone indicator will lead to a negative change in normalized porosity index.
formula
(18)
Figure 20

A graph of FZI against NPI.

Figure 20

A graph of FZI against NPI.

The hydrodynamic parameters (AQI and FZI), which determine the flow dynamics in a saturated medium (aquifer), are greatly controlled by the pore throat radius and the geometry of the porous medium. This is an indication that the lower the grain sizes and the pore throats, the lower the permeability, flow zone indicator and aquifer quality index. The aquifer repositories in zones with low permeability and low flow zone indicator may likely be polluted since the aquifer units are likely to be intercalated with argillites (Gurunadha et al. 2011; George et al. 2015; Ibuot et al. 2019).

Aquifer quality index and flow zone indicator are veritable tools that can be used to characterize groundwater repository. This is because they are based on pore throat radius and geometry of porous medium, which are related to the hydrodynamic properties of a geologic formation. In all the plots, the observed anomalies are attributed to the influence of the geoelectrohydraulic anisotropies, as well as variations in lithology, mineralogy, size of grains, size and shape of pores and pore channels of arenaceous materials, since hydraulic quality of a geologic formation is controlled by these core geologic properties.

CONCLUSION

Groundwater repository was characterized using the geohydrodynamic parameters, which aid in determining the flow characteristics of the aquifer units. The results of this study reveal the variations and interrelations of the estimated geohydrodynamic parameters. The estimation of these parameters (permeability, formation factor, porosity, tortuosity, normalized porosity index, aquifer quality index and flow zone indicator) was possible through the use of already established petrophysical equations. The estimated parameters were observed to be proportionally related according to the similarity in the trend of parameters, except the formation factor and tortuosity, which exhibit different trends and will relate with AQI and FZI negatively. It can be deduced from the study that the aquifer units are affected by the lithologic characters such as grain size distribution, permeability, porosity and the geometry of the pore space. The contour maps are relevant in showing how these parameters are distributed in the subsurface. The information from these hydrodynamic parameters can be effective tools in understanding groundwater storage and flow, also in hydrogeological modeling, well locations, monitoring and management of groundwater systems.

ACKNOWLEDGEMENTS

The authors are grateful to Tetfund (TETFUND/DESS/UNI/NSUKKA/2017/RP/VOL.I) for sponsoring the research work. We thank Prof. B. M. Anene and Mr C. Egbu of the University of Nigeria, Nsukka, for their encouragement.

DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

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