Introduction

Recently, groundwater has played an essential role as one of the primary sources of water supply in Sudan (Mohammed et al. 2022b). The Nile River is the main geomorphological feature in central Sudan; however, the use of Nile water for drinking is limited due to its high turbidity (Farah et al. 2000). Moreover, delivering Nile water to the distribution stations and water purification is highly costly. Consequently, groundwater demand has increased due to population growth, developments in agriculture, and civilization (Mohammed et al. 2022a). The main obstacle to groundwater development is the lack of understanding of the geological and hydrogeological conditions necessary for effective groundwater management. Inadequate knowledge leads to groundwater pollution, inappropriate groundwater control, and borehole drilling failure (Agyemang 2022). Investigating the factors that affect the occurrence and flow of groundwater and the estimation of aquifer parameters will assist in advancing our understanding of groundwater aquifer characteristics (Urom et al. 2022). Knowledge about geological and hydrogeological conditions requires an integrated approach to provide detailed information about aquifer characteristics, thus fulfilling groundwater supply sustainability.

Groundwater aquifer yield is greatly influenced by geological factors such as aquifer lithology and geometry (Anomohanran et al. 2021). The most accurate method for determining the potentiality of groundwater aquifers is borehole drilling (Szabó 2015). However, drilling techniques are time-consuming and expensive. Hydrogeological parameters, including hydraulic conductivity, storativity, and transmissivity, are crucial in evaluating aquifer productivity (Eyankware et al. 2022). The ideal method for estimating these parameters is performing pumping tests to provide information about aquifers’ yield and drawdown (Fetter 2018; Vijayaprabhu et al. 2022). However, these experiments are costly and time-consuming (Opara et al. 2021). Alternatively, the geoelectrical resistivity method is efficient and reliable in detecting aquifer geometry or estimating hydrogeological parameters (Iserhien-Emekeme et al. 2021; Falowo 2022; Mohammed et al. 2023a). In this study, the electrical resistivity method using vertical electrical sounding technique is integrated with the step drawdown pumping test to characterize the groundwater aquifer in the Omdurman area.

Vertical electrical sounding (VES) is the most frequently used method in groundwater investigation to delineate potential groundwater zones and determine aquifer characteristics (Genedi and Youssef 2023; Mohammed et al. 2023b). The VES approach was chosen for this study because it uses basic equipment, has simpler field logistics, and requires less time and resources to analyze data (Asfahani and Al-Fares 2021; de Almeida et al. 2021). Several works have been documented in the literature on the effective use of the VES technique to delineate potential groundwater zones and model groundwater aquifer characteristics (Soomro et al. 2019; Arunbose et al. 2021; Omeje et al. 2021; Oudeika et al. 2021; Alarifi et al. 2022; El Makrini et al. 2022; George et al. 2022; Gyeltshen et al. 2022). In this study, the geophysical and hydrogeological parameters are interconnected since these parameters depend on the petrophysical characteristics of the aquifers. Several tests were conducted to establish these connections (Heigold et al. 1979; Niwas and Singhal 1981; Yusuf et al. 2021). For instance, Dar Zarrouk parameters, a combination of layer resistivity and thickness, are used to detect aquifer characteristics such as longitudinal conductance and transverse resistance. These parameters are directly connected to aquifer parameters based on the analogy between groundwater and electrical current flow. Dar Zarrouk parameters are widely used in the hydrogeological investigation (Ait Bahammou et al. 2021; Asfahani and Al-Fares 2021; Gaikwad et al. 2021; Oli et al. 2021; George et al. 2022; Tepoule et al. 2022). For instance, Rao et al. (2022) combined remote sensing and Dar Zarrouk parameters to estimate the aquifer characteristics in basement terrains where fractures and weathering profiles are the only water-bearing formations. Nugraha et al. (2022) calculated Dar Zarrouk parameters to delineate the potential zones of groundwater based on the vertical electrical sounding data. Sankar et al. (2022) and Alabi et al. (2021) applied Dar Zarrouk parameters to predict the vulnerability of groundwater aquifers to surface and subsurface pollution. Naidu et al. (2021) used longitudinal conductance and transverse resistance to delineate the interface between the fresh and saline water in coastal aquifers. However, the Dar Zarrouk modeling, like all geophysical approaches, is subjected to solution ambiguity. As a result, pumping test data is used to calibrate the geophysical modeling in this investigation.

A step drawdown test assesses the effectiveness and characteristics of the groundwater well and the aquifer (Dufresne 2011; Kurtulus et al. 2021). The test is typically carried out by continuously pumping water out of the well for a specific time while periodically checking the water level (Clark 1977). The outcomes of a step drawdown test can reveal important details regarding the aquifer yield and efficiency as well as the aquifer characteristics, including permeability, hydraulic conductivity, and transmissivity (Tizro et al. 2014). The step drawdown data can potentially analyze the ideal pumping rate and the aquifer’s long-term sustainability (Nabawy et al. 2019). Step drawdown tests are often conducted with other tests, such as pumping and slug tests, to provide a complete understanding of the well and aquifer system. These tests can be helpful for water resource management, irrigation, and other applications that rely on groundwater (Avci et al. 2010). In this study, the step drawdown test is conducted to validate the results of the geophysical measurements.

The primary goal of the current study is to delineate potential groundwater zones and model the aquifer characteristics in the Omdurman area using an integrated approach, including geoelectrical and pumping test methods. In analyzing groundwater aquifers, this integrated approach gives an appropriate solution for sustainable water supply in the Omdurman area, Sudan. It benefits the local government in designing a development plan and safeguarding groundwater resources for future generations.

Study area

The research area is in Omdurman city, considered the second-largest city in Sudan. Omdurman city has been called the historical capital as it was the first capital in the new Sudan’s history. The study area is situated in Omdurman city, west of the Nile River and White Nile. It is bounded by longitudes 32°–32° 40 and latitudes from 15° to 16° 20 (Fig. 1). The study area is situated in the Savanna belt with a semiarid climate and average annual precipitation range from 100 to 200 mm/year. The Savanna belt is associated with a hot climate, with temperatures reaching more than 40° in summer. The studied area covers about 9880 km2. Topographically, the study area is almost flat, with some sandy ridges appearing in scattered localities throughout the region. These plains rise gradually from around 300 in the eastern part to more than 500 m above sea level towards the west.

Fig. 1
figure 1

Geographic map showing the location of the Omdurman area in Sudan and the location of the study area in Omdurman

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The geology of the study area consists of four geological units from older to younger: Precambrian basement rocks, Cretaceous Omdurman formation, and Quaternary deposits. Geological formations older than the Cretaceous Omdurman formation are assigned to basement rocks (Vail 1983). Basement rocks comprise all crystalline rocks, including metamorphic rocks and intrusive and extrusive igneous rocks (Kheiralla 1966). The gneisses, granites, and acidic dykes make up the lithology of the basement rocks in the study area (Elzien et al. 2014). The term Omdurman formation is first introduced by (Awad 1994) to refer to Cretaceous sedimentary rocks in the west Nile River area. Omdurman formation comprises cross-bedded sandstone intercalated by fine sediments (Wycisk et al. 1990). The term Omdurman formation was also used by (Bireir 1993) to refer to the silicified sandstone units in the western Nile River. According to (Kheiralla 1966), conglomerates, quartzite sandstone, and mudstone are the primary units forming the Omdurman formation. The Quaternary formation comprises gravel, unconsolidated sand, silt, and clay. Figure 2 illustrates the geological units in the study area. Omdurman formation and quaternary deposits are the main aquifer units in the study area (Elkrail and Adlan 2019).

Fig. 2
figure 2

Geological map of Omdurman area showing the main geological units and geological structures modified after (Elzien et al. 2014)

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Groundwater occurs in the weakly cemented sandstone beds of the Omdurman formation under confined to semiconfined conditions. This is due to the presence of thick to thin aquitards and aquicludes composed of silts and clays. Nile River is the main source of groundwater recharge at a radius of 12 km. However, in the regions outside the Nile influence, groundwater aquifers are recharged from wadies and ephemeral streams (Farah et al. 2000). Groundwater levels in the study area vary between 23 m in the surroundings of the Nile River to more than 70 m in the western part of the study area. Therefore, groundwater flows mainly from the eastern to the western parts of the study area (Fig. 3).

Fig. 3
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A map showing the groundwater level and main direction of groundwater flow

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Materials and methods

Geoelectrical investigation

In this research, 12 VES measurements were conducted using Schlumberger configuration with maximum electrode spacing (AB) of 900 m. In the Schlumberger configuration, the depth of penetration increases as the electrode spacing increases. The apparent resistivity is acquired by multiplying Schlumberger geometric factor and the electrical resistance. The obtained apparent resistivity is processed using IPI2WIN software. This software applies one-dimensional geophysical inversion using the damped least square method to compare the observed data to a synthetic model. The acceptability of the resulting model is based on the fitness criteria between the observed and calculated apparent resistivity curves (Bobachev 2002). The estimated model was then analyzed and interpreted qualitatively by dividing the model area into high and low electrical anomalies and quantitatively by detecting the thicknesses and true resistivity of different geological sequences. In a model-based inversion, the problem of ambiguity arises in which the same model can be referred to various geological and hydrogeological phenomena. A priori information needs to be added to the resulting model to deal with this drawback. This study integrated geological maps and reports from previous surveys with the geophysical data for reliable interpretation of the vertical electrical sounding curves. Based on this combined interpretation, four hydrogeological profiles extending southeast were established with true thicknesses and resistivities.

Dar Zarrouk and hydrogeological parameters

The principle of the electrical resistivity method is founded on detecting the potential variation as electrical current travels through the earth’s layers (Reynolds 2011). Groundwater flow is influenced by the same petrophysical factors that influence current flow, including porosity and water saturation. (Niwas and Singhal 1981). Dar Zarrouk parameters such as longitudinal conductance (S, Ω-1) and transverse resistance (R, Ωm2) are calculated to estimate the aquifer characteristics. These parameters depend on the relation between the flow of electrical current and groundwater. Dar Zarrouk parameters are estimated based on the layer thicknesses (h) and true resistivity (ρ) obtained from 1D inversion of the vertical electrical sounding data. The use of Dar Zarrouk parameters simplifies the evaluation of electrical models by reducing the uncertainty of the VES data interpretation. The longitudinal conductance (S) and transverse resistance are measured using Eqs. 1 and 2. Furthermore, the protective capacity of the groundwater aquifer is determined using the total longitudinal conductance values following the classification provided by Oladapo and Akintorinwa (2007) (Table 1). The protective capacity of the hydrogeological columns detects its capability to prevent the aquifer from the surface and subsurface contamination.

Table 1 The classification of aquifer protective capacity suggested by Oladapo and Akintorinwa (2007)
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$$S=\frac{h}{\rho }= \sum_{i=1}^{n}\frac{{h}_{i}}{{\rho }_{i}}$$
(1)
$$R=h* \rho = \sum_{i=1}^{n}{h}_{i}*{\rho }_{i}$$
(2)

The hydraulic conductivity reflects the movement of groundwater through a unit width of the aquifer. This investigation measured it with an experimental formula suggested by Heigold et al. (1979). This formula is founded on the connection between the hydraulic conductivity (K), and the resistivity of the aquifer layer composed of granular materials (ρaq) (Eq. 3). The transmissivity (T), which refers to the rate of groundwater flow in the full width of the aquifer, is calculated using Eq. 4. The transmissivity is further validated using Niwas and Singhal (1981) formula, which is a theoretical relationship between the aquifer transmissivity (T) and Dar Zarrouk parameters including longitudinal conductance (S) and transverse resistance (R) (Eqs. 5 and 6). These theoretical equations are based on the analogy between Darcy’s law of groundwater flow and Ohm’s law of electricity flow.

$$K=386.4 {\uprho }_{aq}^{-0.93283}$$
(3)
$$T=K*b$$
(4)
$$T=K\sigma R$$
(5)
$$T=\frac{K S}{\sigma }$$
(6)

Step drawdown test

The step-drawdown test is performed in the eastern Omdurman area for six groundwater wells to explore the aquifer’s hydrogeological parameters and the wells’ performance. Jacob (1947) first conceptualized and examined the step-drawdown test, and Rorabaugh (1953) subsequently modified it. The boundary conditions of this test assume that the aquifer is confined to an infinite extent, homogenous, and the well fully penetrates the groundwater aquifer. Following the groundwater well installation, step-drawdown tests were carried out to evaluate the aquifer loss (B) and well loss (C) coefficients needed to calculate well performance measures and aquifer transmissivity.

The Jacob (1947) formula (Eq. 7) provides a description of the elements of total drawdown (S) (m) in a discharge well and its relation to the pumping rate (Q) (m3/day) as

$$\mathrm{S}=\mathrm{BQ}+{\mathrm{CQ}}^{2}$$
(7)

where B (day/m2) and C (day2/m5) are aquifers and well loss coefficients, respectively, while BQ (m) and CQ (m) are the components of the drawdown due to aquifer and well loss.

Specific drawdown (S/Q) is the step decline of the water level due to specific discharge from the well due to aquifer loss and the components of the well loss, and it is calculated by transforming Eq. 8 to linear form as

$$\frac{S}{Q}=B+CQ$$
(8)

The linear regression plot between specific drawdown (S/Q) and well discharge (Q) is performed to measure the aquifer coefficient result from laminar flow and well loss coefficients from the turbulent flow. In this plot, the intercept of the linear trend is the aquifer loss, and the slope of the line is the well loss.

The specific capacity (\({S}_{c}\)) (m3/day/m) denotes the aquifer discharge per unit total drawdown and is defined as the amount of the discharged water per unit decline of the water level. In the steady-state conditions, the specific capacity is identified by a consistent discharge rate, and it is calculated (Eq. 9) as

$${S}_{c}= \frac{Q}{S}= \frac{1}{B+CQ}$$
(9)

The measured value of specific capacity can be used to assess the aquifer’s transmissivity (T) (m2/day). The experimental equation suggested by Razack and Huntley (1991) (Eq. 10) offers a straightforward method for obtaining an approximate estimate of transmissivity for porous aquifers as

$$T=33.6{\left(\frac{Q}{S}\right)}^{0.67}$$
(10)

The proportion of aquifer loss to total head loss is then used to assess the pumped well’s performance. It illustrates the link between the measured internal and predicted drawdown outside the well (Kruseman and De Ridder 1994). The well efficiency can be calculated (Rorabaugh 1953) (Eq. 11) as

$${E}_{w}\left(\%\right)= \frac{BQ}{BQ+C{Q}^{2}}*100$$
(11)

Results and discussions

Qualitative interpretation of VES data

The measured apparent resistivity is matched with master curves (Fig. 4) to obtain thicknesses and true resistivities of the subsurface layers. Firstly, the curves were qualitatively interpreted to gain general knowledge about electrical resistivity distribution with depth. The shape of the VES curves gives insight into the thickness and number of layers. The type of curve is characterized by the relationship between the values of resistivities (ρ1, ρ2, and ρ3) if the ground is made up of three layers. As a result, there are four distinct types (Orellana and Mooney 1966): H-type: in which ρ1 > ρ2 < ρ3, A-type: in this case ρ1 < ρ2 < ρ3, K-type: where ρ1 < ρ2 > ρ3, and Q-type: ρ1 > ρ2 > ρ3. Figure 5 shows the type-curve map of the study area, which shows homogeneous curve types dominated by HK and HA. When the curve ends with A-type, it denotes a base layer of high resistivity. Curves end with K type denoting a low resistivity layer in the bottom, which might be due to the presence of conductive layers. In this study, the northern and southern parts of the study area are occupied by HK type, while HA type dominates the central parts.

Fig. 4
figure 4

Example of the inverted VES curves using IP2WIN software for a S1, b S2, c S3, and d S4

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Fig. 5
figure 5

The results of the qualitative interpretation of the VES curves along the constructed profiles

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Quantitative interpretation of VES curves

Earth materials have a wide range of resistivity, ranging from extremely low to very high. This broad range of variation is due to several variables, such as mineral composition, petrophysical parameters, and fluid contents (Maillet 1947). The quantitative interpretation of VES curves is based on the geophysical inversion of the measured apparent resistivity, and the result of 1D inversion was used to build geoelectrical sections. Subsequently, these resistivity cross-sections are then interpreted and converted to hydrogeological sections.

The resistivity cross-section of profile 1 is shown in Fig. 6a. This profile includes S1, S2, and S3, with a 17 km distance long. The resulting hydrogeological section (Fig. 7a) revealed five layers. The first layer of resistivity ranging from 112 to 145 Ωm is interpreted as superficial deposits. The thickness of this layer varies between 0.8 and 1 m. The second layer is associated with resistivity values between 32.1 and 42.7 Ωm and an average thickness of 3 m. This layer of low resistivity values is referred to as the presence of clay. These homogeneous thicknesses of the upper layers indicate continuous deposition with no influence on geological structures. The third layer has resistivity values of 165–397 Ωm with a thickness range between 18 and 26.4 m. It is interpreted as fine dry sand. The fourth layer is of high resistivities ranging from 1000 to 1881 Ωm with thicknesses ranging from 147 to 160 m, and this layer is attributed to silicified or ferruginous sandstone. The fifth layer of an average resistivity of 193 Ωm is considered to be the main aquifer in the study area. The thickness of this aquifer is between 150 and 500 m (Köhnke et al. 2017).

Fig. 6
figure 6

The resistivity cross sections for a profile 1 b profile 2 c profile 3 and d profile 4. The depth of sounding is in the vertical axes while the distance between the stations is in the horizontal

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Fig. 7
figure 7

Geological cross section obtained from the interpretation of the reistivity cross section of a profile 1, b profile 2, c profile 3, and d profile 4

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Profile 2, as shown in Fig. 6b, and Fig. 7b, includes S4, S5, and S6 with a length of 39 km. The first layer is interpreted as superficial deposits with resistivity ranging from 120 to 131 Ωm and an average thickness of 1 m. The second layer is described as clay and was associated with resistivity values between 50 and 63.1 Ωm with an average thickness of 7 m. The third layer has resistivity values of 293–364 with a thickness range between 15 and 20 m. It is interpreted as fine dry sand. This layer is affected by two normal faults; as a result, it disappeared in S5. The fourth layer is silicified sandstone with resistivities ranging from 1677 to 1886 Ωm and an average thickness of 125 m. The bottom layer is attributed as saturated sandstone with average resistivity of 200 Ωm.

Figures 6c and 7c illustrate the resistivity cross-section and the resulting hydrogeological section of profile 3, respectively. Profile 3 consists of S7, S8, and S9. The first layer, as usual, is interpreted as superficial deposits followed by a clay layer of low resistivity and an average thickness of 20 m. In this profile, the fine sand layer is intermitted by normal fault, so it appeared only in the western part of the profile. The central part of the study area is highly affected by normal and reverse faults (Hussein and Awad 2006). As a result, the saturated sandstone layer appeared above the highly resistive silicified sandstone. In this profile, the average thickness of the aquifer is up to 300 m, with resistivity varying between 234 and 400 Ωm.

Profile 4 comprises S10, S11, and S12 (Figs. 6d and 7d). According to (Elkrail and Adlan 2019), this profile depicts the ideal cross-section of the study area with no influence of the geological structure. The first layer of superficial deposits is followed by a clay layer with resistivity values between 39 and 60 Ωm and an average thickness of 3 m. The third layer of fine sand has resistivity values of 234–415 Ωm. The fourth layer of high resistivities is evaluated as silicified or ferruginous sandstone. As in Profiles 1 and 2, the saturated sandstone layer is encountered at depths of 150–200 m.

It can be concluded that the main aquifer in the study area is composed of sandstone with resistivity ranges from 115 to 399 Ωm with an average of of 257 Ωm (Fig. 8a). This study showed high compatibility with the study conducted by (Köhnke et al. 2017), which revealed that the thickness of the sandstone layer in Omdurman ranges from 150 to 500 m. The aquifer isopach map (Fig. 8b) demonstrates the discrepancy in depth to the aquifer, which ranges from 40 m in the central parts to as high as 200 m in the northern and southern parts of the study area.

Fig. 8
figure 8

The spatial variation in the a depth to aquifer and b resistivtiy of the aquifer in the study area

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Dar Zarrouk parameters

Longitudinal conductance and transverse resistance, known as Dar Zarrouk parameters, were calculated to detect the aquifer characteristics (Table 2). The Dar Zarrouk parameters minimize interpreting ambiguities in cases where equivalent lithologies coincide in the analyzed VES data (Mohammed et al. 2023a). The resistivity and thickness of the aquifer are multiplied to obtain the transverse resistance. The transverse resistance in the study area varies between 5587 and 309,853 Ωm2 with an average value of 157,720 Ωm2. Figure 9, a shows the geographic variation in the transverse resistance. The highest value is observed in S2, while the lowest value is in S9. The highest transverse resistance was detected in regions where reasonable thickness and resistivity of the aquifer were observed. Levels of transverse resistance are typically associated with regions that are very transmissive and thus highly permeable to groundwater flow. This suggests that the research area’s prospective aquifer regions expand as transverse resistance rises, which is likely the result of increases in hydraulic conductivities (Naidu et al. 2021). Therefore, based on the values of the transverse resistance, it can be indicated that the northern part of the study area is highly productive compared to the southern parts. The variation in the total thickness of the subsurface layers and, thus, the permeability is indicated using longitudinal conductance (Sankar et al. 2022). The spatial variation in the Longitudinal conductance is shown in Fig. 9b. It varies between 0.14 and 2.5 Ω−1. The highest value is detected in S9, while the lowest is observed in S11. Low longitudinal conductance indicates high aquifer transmissivity (Henriet 1976). Thus, according to the obtained longitudinal conductance values, the aquifer in the southern part of the study area is transmissive compared to the rest of the area. By integrating the results of the transverse resistance and longitudinal conductance it is likely that the central part of the study area has low potential. This can be attributed to high resistivity and low depth to the aquifer in this region.

Table 2 The result of VES inversion and the calculated Dar Zarrouk parameters in the study area
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Fig. 9
figure 9

The geographical distribution of the total a transverse resistance and b longitudinal conductance in the study area

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The protective capacity map for the research area is displayed in Fig. 10. Higher longitudinal conductance values often denote a relatively thick overburden sequence that can reduce the pollutants’ infiltration. The protective strength of the geological column is categorized into poor, weak, moderate, good, very good, and excellent zones (Oladapo and Akintorinwa 2007). In the current research, the protective strength ranged from 1.4 to 2.5 Ω−1. Consequently, the area is divided into moderate and good protective strength classes. The northern and southern parts of the study can be considered as naturally protected from surface and subsurface contamination, whereas the central part is moderately protected. The variation in the protective capacity of the aquifer is mainly due to variations in the depth of water and the presence of impermeable materials. The depth to the aquifer in the central parts of the study area is relatively shallow (Fig. 8b) due to the absence of the silicified sandstone layer. This explains the difference in aquifer vulnerability. However, it can be concluded that the aquifer in the study area is protected, and the groundwater quality is likely to be fresh; nevertheless, a detailed water quality analysis is recommended for accurate evaluation.

Fig. 10
figure 10

Spatial calssification of the study area based on the protective strenght of the aquifer

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Aquifer and wells parameters

The hydrogeological parameters and groundwater well performance are measured by integrating geoelectrical and pumping test data. In this study, hydraulic conductivity is determined empirically using a formula established by (Heigold et al. 1979). The aquifer resistivity serves as the foundation for this method. The hydrogeological characteristics computed from the geoelectrical data are displayed in Table 3. The hydraulic conductivity in the study area varies between 1.4 and 5.2 m/d. The geographic variation of hydraulic conductivity (Fig. 11a) showed that the southeastern and northern parts of the study area are associated with high conductivity while the lowest in the central parts. The highest value is indicated in S10, and the lowest is observed in S4 and S8. The variation in hydraulic conductivity is mainly due to the variation in the petrophysical characteristics of the aquifer, such as porosity, permeability, and shale content (Mohammed et al. 2023a). According to the measured hydraulic conductivities, this aquifer is comparatively heterogeneous. Aquifer transmissivity determines the rate of groundwater movement in the full thickness of the aquifer; therefore, it is calculated by multiplying the hydraulic conductivity by the aquifer thickness. In this research, since the VES measurement’s penetration depth is only 400 m, the average thickness of the aquifer where its bottom is not detected is assumed to be 300 m (Köhnke et al. 2017). Figure 11b shows the areal variation in transmissivity. The obtained transmissivity varied between 435 m2/day in the central part of the study area and 1564 m2/day in the southeastern parts. As suggested by transverse resistance and longitudinal conductance of the aquifer, the central part of the study area can be described as a low potential area for groundwater development compared to the northern and southern parts. However, based on the obtained transmissivities, the groundwater aquifer can be described as productive to highly productive (Krásný 1993) (Table 4) and ideal for groundwater abstraction.

Table 3 The calculated hydrogeological parameters based on the geoelectrical data
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Fig. 11
figure 11

The areal variation of a hydraulic conductivity and b transmissivity calculated from VES data

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Table 4 The classification of groundwater aquifers based on their transmissivity as suggested by (Krásný 1993)
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Step drawdown tests involve pumping a well and measuring the decline in the water level while gradually increasing the well’s pumping rate (Clark 1977). Figure 12 shows an example of the applied number of steps, the duration of the steps, and the change in discharge rate. Analytical techniques and design considerations for step drawdown testing are used to create the best test program. This research follows Jacob’s (1947) straight-line approach to determine aquifer loss, well loss, and hydrogeological parameters (Fig. 13). The measured coefficients and parameters are presented in Table 5.

Fig. 12
figure 12

A plot showing the schedule of the step-drawdown test where the level of drawdown is changed due to a change in discharge rate for a well 1 b well 6 in

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Fig. 13
figure 13

a Straight-line fitting between the discharge rate and specific drawdown for determination of aquifer and well loss coefficients for well 1 and b well 2

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Table 5 The estimated parameters of groundwater aquifer and wells based on the step-drawdown tests
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The calculated average aquifer loss coefficients (B) in groundwater wells, respectively, are 3.9*10–3, 4.9*10–3, 6.2 *10–3, 2.2*10–3, 4.2*10–3, and 7.1*10–3 while the average well loss coefficients (C) are 4.6*10–6, 2.8*10–6, 7.9*10–7, 2.9*10–6, 2*10–6, and 6.9*10–6 (Table 5). The highest value of B is observed in W6 in the southern part of the study area, while the lowest value is indicated in W4 in the central part. However, the change in the aquifer loss is relatively low. The higher aquifer loss in W6 is attributed to the high discharge rate in the well, where the minimum rate used at the first step is 696 m3/day, and the maximum is 1257 m3/day in the last step. This may stimulate the groundwater flow and result in a high B coefficient. The maximum value is detected in W6 and the minimum in W3 for the well loss coefficient. The high value of C is likely to be attributed to gravel pack clogging or mispositioning of the groundwater pump. This is also confirmed by the calculated well efficiency (Ew) in which the W3 of low well loss showed high efficiency (86%) while the W6 of high well loss reported low well efficiency (45.7%) (Table 5). Therefore, it can be indicated that faulty well design and un optimal discharge are both influencing the well and aquifer loss coefficients.

The total drawdown is measured by combining the components of drawdown due to aquifer and well loss. The spatial variation in total drawdown is illustrated in Fig. 14a. The variation in drawdown is affected by the geometrical and hydrogeological properties of the aquifer along with other factors such as discharge rate and well efficiency. The maximum total drawdown of 14.9 m is reported in W6, while the minimum is in W1. Generally, the total drawdown in the southern parts of the area is higher than in the central and northern parts. In this study, the total drawdown is proportional to the discharge rate and inversely proportional to transmissivity. Consequently, the specific capacity (Sc) of the aquifer is measured. The average Sc of the groundwater wells ranges from 70 m3/day/m in W6 to 215 m3/day/m in W1. The transmissivity varies between 583 and 1226 m2/day. The spatial variation in transmissivity is illustrated in Fig. 14b. Since the transmissivity is inversely proportional to the total drawdown, the areal variation shows a diverse trend in which the northern parts of the study area are associated with high transmissivities compared to the central and southern parts of the study area. The transmissivities obtained from the step drawdown test are compared to the nearest VES station, where the transmissivity is also detected. For instance, W1 is compared to S1. The transmissivity in W1 is 1226 m2/day, whereas in S1 is 1007. However, both transmissivities show a high discrepancy between step drawdown and the geoelectrical method in some locations. This is likely due to the underestimation of the aquifer thickness using geoelectrical methods. Therefore, increasing the depth of penetration of the geophysical method is recommended for accurate estimation of the transmissivity.

Fig. 14
figure 14

The spatial distribution of a total drawdown and b transmissivity obtained from the step-drawdown tests

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Conclusion

This study aimed to model the potentialities of groundwater aquifers in the Omdurman area by integrating vertical electrical sounding (VES) technique and pumping test data. This approach successfully achieved the objectives of the study, and the conclusions can be summarized in the following:

  • The qualitative interpretation of the VES data indicated three curve types, namely HK, K, and HA. The VES curves were further modeled to obtain the true resistivities and thicknesses of the layers. Based on the quantitative interpretation of the VES curves, the resulting hydrogeological models indicated that the principal aquifer system in the area is under confined conditions and composed mainly of coarse sandstones.

  • Dar Zarrouk parameters, including longitudinal conductance and transverse resistance, were measured using the modeled layer resistivity and thicknesses. Consequently, the hydrogeological parameters, including hydraulic conductivity and transmissivity, were calculated. As a result, the spatial variation maps of the modeled aquifer characteristics indicated that the aquifer is highly productive and ideal for groundwater development.

  • A step drawdown test is performed for six groundwater wells to calculate the aquifer characteristics and, therefore, validate the geoelectrical results, and the performance of the two models showed acceptable agreement. The step drawdown test was further used to assess the performance of wells under different hydrogeological stresses, and it revealed that faulty well construction and design are highly influencing drawdowns and well efficiency.

  • In this study, VES techniques combined with the step drawdown test were successfully applied to delineate and characterize the potential zones of groundwater. However, this study recommended applying a detailed geophysical survey to reduce the uncertainty of the resulting geological and hydrogeological models. For instance, geophysical well-logging methods can guide surface geophysical methods in delineating the water-saturated zones and detecting the petrophysical parameters such as porosity and permeability. Further, magnetic resonance sounding (MRS) is highly recommended for accurately estimating hydraulic conductivity and water saturation.