Investigation of petrophysical and hydrogeological parameters of the transboundary Nubian Aquifer system using geophysical methods

The recent research aims to investigate the petrophysical and hydrogeological parameters of the Nubian aquifer system (NAS) in Northern Khartoum State, Sudan, using integrated geophysical methods, including surface electrical resistivity and geophysical well-logging. The Nubian aquifer is a transboundary regional aquifer that covers vast areas in Sudan, Egypt, Libya and Chad. The well-logs, including self-potential (SP), natural gamma ray (GR), and long normal resistivity (RS), are integrated with Vertical Electrical Sounding (VES) measurements to delineate the hydrostratigraphical units. As a result, two aquifers are detected. An upper aquifer comprises coarse sand with an average thickness of 50 m and a lower aquifer of sandstone with more than 200 m thickness. For a thorough evaluation of the aquifers, in the ﬁ rst stage, the petrophysical and hydrogeological parameters, including formation factor, total and effective porosity, shale volume, hydraulic conductivity, and transmissivity, are measured solely from geophysical well-logs. In the second step, the results of geophysical well

Investigation of petrophysical and hydrogeological parameters of the transboundary Nubian Aquifer system using geophysical methods

Introduction
The escalation of water investigation research is attributed to its growing significance in shaping developmental strategies across various domains, including industry and agriculture (Aliou et al., 2022;Zhou et al., 2022;Liu et al., 2023).The rapid population growth has led to the evolution of groundwater exploration methodologies for the characterization of local and regional aquifer systems (Adagunodo et al., 2018;Rabeh et al., 2019).Characterizing transboundary regional aquifers is a complex task in hydrogeological research to comprehend and effectively manage shared groundwater resources (Puri and Aureli, 2005;Sindico et al., 2018;Yin H. et al., 2023;Yuan et al., 2023).This distinctive problem requires extensive cross-border investigations to identify subsurface structures, lithological variations (Tie et al., 2023), and hydrogeological features (Nijsten et al., 2018).The Nubian Aquifer System (NAS) is a significant transboundary aquifer that serves as a crucial groundwater reservoir.It covers the dry areas of Egypt, Libya, Chad, and Sudan, making it one of the largest in the world (Sultan Araffa et al., 2009;Mohamed et al., 2017;Mohamed, 2019;Mohammed et al., 2023c).The aquifers in question are of great importance in maintaining water resources and supporting the lifestyles of people in the nations mentioned (Voss and Soliman, 2014).The significance of the NAS resides in its transboundary nature, highlighting the necessity for accurate evaluation of its attributes to ensure the sustainable exploitation of groundwater.
Petrophysical and hydraulic parameters of groundwater aquifers are crucial elements that must be considered for managing groundwater extraction (Yusuf and Abiye, 2019;Ugbaja et al., 2021;Abbas et al., 2022;Römhild et al., 2022;Yin L. et al., 2023).The evaluation of these parameters is essential for enhancing the accuracy of hydraulic stress prediction (Szűcs et al., 2013;Amiri et al., 2022;Zhu et al., 2022).Furthermore, it gives dependable data inputs for simulating groundwater flow and contaminant transport (Mathon et al., 2008;Khadri and Pande, 2016;Amiri et al., 2022).The ideal manner for estimating the hydraulic and petrophysical parameters is by taking core samples from groundwater aquifers during well drilling (Szabó et al., 2015;Khalil et al., 2022;Li et al., 2023;Sang et al., 2023;Yuan et al., 2023).Another approach is pumping tests, which depend on a series of assumptions that occasionally may not be valid (De Clercq et al., 2020;Römhild et al., 2022).It assumes that the aquifer is homogenous, isotropic, and has an infinite extent and neglects groundwater storage during the test (Misstear, 2001).Moreover, in heterogeneous aquifer systems, the estimation of these parameters is restricted to the measurement point; therefore, error is inevitable during the generalization of the results (Avci et al., 2010;Mohammed et al., 2023c;Flores et al., 2023;Yang et al., 2023).To address these drawbacks, geophysical methods are widely applied for groundwater exploration and aquifer characterization since they provide a continuous estimate of hydrogeological and petrophysical parameters (Szabó et al., 2015;Fejes et al., 2021;Mohammed et al., 2023e).The primary purpose of open-hole wireline logging is to identify variations in petrophysical and hydrogeological parameters along groundwater wells and correlate them with the surrounding wellbores (Szabó, 2018;Gouasmia et al., 2022;Mohammed et al., 2023a).Non-focused resistivity tools are often suited for hydrogeological problems (Szabó, 2015).(Ebong et al., 2014;Madun et al., 2018;Oudeika et al., 2021;Alao et al., 2022;Mohamed et al., 2022;Mohamed et al., 2023a;Taha et al., 2021).These methods are typically implemented in exploratory studies to install groundwater wells (Hezzi et al., 2021).VES is the most popular resistivity technique for defining potential groundwater zones and calculating hydraulic parameters such as transmissivity and hydraulic conductivity (Arétouyap et al., 2019;Mohammed et al., 2023e;Omeiza et al., 2023).This technique was efficiently used to quickly and affordably determine the depth of the water table, aquifer thickness, and vertical and horizontal geological variation (Szűcs et al., 2021).
Due to urbanization and population growth in Khartoum State, a severe freshwater supply shortage has been faced.As a result, the Water resources agencies are currently focusing on improving groundwater reserves to cover the water supply deficit (Li et al., 2023;Wu et al., 2023;Yin et al., 2023).Several works have been conducted to evaluate the hydraulic parameters of the Nubian aquifer (Elkrail et al., 2004;Abdalla, 2009;Algafar et al., 2011;Mohamed et al., 2023a); nevertheless, these studies rely solely on pumping test analysis.The main objective of the present study is to investigate the potentiality of the transboundary Nubian Aquifer System (NAS) and ascertain its petrophysical and hydrogeological characteristics through the integration of surface and subsurface geophysical techniques.The NAS can be used as a framework for comprehending the hydrogeological dynamics of aquifers that span across multiple borders.The recent study aims to examine the characteristics of the NAS and establish general guidelines that may be utilized to evaluate shared aquifer systems globally.The implemented approach will function as a valuable tool for assessing analogous aquifers with similar hydrogeological conditions.

Geography and geology
The study area is part of the Khartoum sub-basin, which is located in the Northern periphery of the Nile rift basin and covers more than 288 km 2 (Figure 1B).The region has a semi-arid to arid climate, with temperatures exceeding 40 °C from May to September (Mohammed et al., 2023b).The rainy season, however, is limited to the remaining few weeks of summer.Khartoum state is a component of the Pan-African series that supervised the genesis of various rock units and geological structures.The Pan-African Basement Complex limits the Khartoum sub-basin to the Northeast and Southwest and confines its bottom boundary at a depth of more than 500 m (Köhnke et al., 2017).Figure 1C shows the geological map of the study area.The Northern Khartoum state is in a transition zone between the basement igneous complex to the North and the sedimentary basin to the South (Zeinelabdein and Elsheikh, 2014).The main geological units in the study area are the Precambrian basement rocks, Cretaceous Nubian Formation, and recent deposits.The basement complex consists of gneisses, schists, and granites, and the depth varies between zero, mainly to the North and Eastern sides of the area, and reaches up to 500 m in the Southern parts (Hussein and Awad, 2006).The Cretaceous Nubian formation consists of conglomerates, sandstone, and mudstone intruded by basaltic volcanic rocks that overlie the Precambrian basement rocks (Schrank and Awad, 1990).The recent deposits in the study area include windblown and alluvium wadi deposits, and the lithology comprises sand, gravel, and silt of depths ranging from 3 up to 15 m (Haggaz and Kheirallah, 1988).

Hydrogeology
The Nubian aquifer is a transboundary system that covers 2.2*10 6 km 2 distributed in Sudan, Libya, Tchad, and Egypt (Mohamed et al., 2023).The Nubian aquifer is the primary groundwater supply source in the Khartoum basin that covers more than 30% of the landmass of Sudan.Groundwater occurs in the unconsolidated sand and weakly cemented sandstone beds of the Nubian formation under leaky confined to non-leaky confined conditions (Mohammed et al., 2023f).This condition is due to thin to relatively thick aquitards and aquicludes composed of silts and clays (Abdelsalam et al., 2016).The thickness of the Nubian aquifer varied between 10 m to more than 450 m (Algafar et al., 2011).The groundwater levels in the Nubian aquifer vary between 19 and 32 m.The water table is close to the surface in the Western part near the Nile River, and the depth of the water level reaches its maximum in the Eastern regions.Consequently, the general direction of groundwater flow is from the Eastern to the Western part of the study area (Figure 1C).Nilotic and meteoric waters are the two primary types of recharged water that can be distinguished in the study region (Farah et al., 2000).Nilotic groundwater leaked from the Nile River to the groundwater aquifer (Mohamed et al., 2023), and meteoric groundwater in areas outside the influence of the Nile River due to the water infiltration from wadies and ephemeral streams (Farah et al., 2000;Mohammed et al., 2023d).

Materials and methods
In this research, an innovative approach that integrates surface geophysics, well logging, and hydrogeological data is followed to The workflow of the study that involves the integration of geophysical and hydrogeological data.Borehole logs of LOG 1 location and its correspondent lithology.SP is the spontaneous potential, GR is the natural gamma ray, and RS is the deep resistivity log.
explore the geometry, petrophysical, and hydrogeological parameters of the Nubian aquifer system.The workflow of the study is illustrated in Figure 2, and the description of the applied methods is indicated in the following subsections.

Surface geophysical method
Electrical resistivity method employing vertical electrical sounding (VES) using Schlumberger array.The measurements were taken using SAS 100 resistivity meter.The electrical (ΔV) is measured using potential electrodes (MN) because of current (I) injection into the subsurface using current electrodes (AB).This potential difference measurement provides information about the apparent electrical resistivity with depth.In the Schlumberger configuration, the current and potential electrode are placed close together with the measurement point at the center of the array.These electrodes are symmetrically arranged along a profile, with outward increasing distances of electrode spacing from the central point (Omeiza et al., 2023).This arrangement allows for a wide range of electrode spacings.In this study, the maximum current electrode spacing reached 750 m and 200 m for the potential electrodes.Schlumberger protocol offers flexibility in electrode spacing, making it suitable for a wide range of subsurface investigations as it allows for better coverage and depth penetration compared to the other configurations, such as Wenner and dipole-dipole.
The apparent resistivity (ρ a ) is acquired by multiplying the resistance of geological formation (R) by the Schlumberger configuration factor (K). Eqs 1, 2 are frequently used to measure ρ a as IPI2WIN software is used to analyze the apparent resistivity to determine the layer properties, including resistivity and thickness (Bobachev, 2002).The actual curve of the recorded apparent resistivities is matched to the synthesized curves, and the model performance criteria determined the resulting model's validity.Like other potential field methods, the electrical method is deterred by the problem of ambiguity.To address this issue and ensure a realistic evaluation of the geophysical model, priori information about the studied area must be gathered.This study uses parametric wells to validate the resulting geoelectrical models.Eight lithological logs obtained from boreholes drilled for groundwater exploitation at a depth range from 100 to 270 m are employed.The geological samples were taken in these logs at a depth interval of 1 m.

Geophysical well-logging
The geophysical well-logging data employed in this investigation has been sourced from the Khartoum State Water Corporation (KSWC) and was initially acquired in physical, hard-copy format.Borehole logs of LOG 2 location and its correspondent lithology.SP is the spontaneous potential, GR is the natural gamma ray, and RS is the deep resistivity log.
Subsequently, the data was digitized to conform to the requisite standard format using Didger software (Geosoft).The data was collected in October 2018 as part of the Zero Thirsty project.The Sudanese government supervised this project to sustain the water supply in Sudan.In this research, spontaneous potential (SP), natural gamma ray (GR), and long normal resistivity (RS) logs were used.
The petrophysical and hydrogeological parameters are estimated based on the geophysical logging data, namely, GR and RS logs.The estimated parameters are the formation factor, total and effective porosity, shale volume, and hydraulic conductivity.The concept of formation factor (F) has been demonstrated through empirical tests (Archie, 1942).It is defined as the ratio between the resistivity of the clean and saturated aquifer (R 0 ) and the resistivity of the pore water (R w ) (Eq. 3).In this study, R w is obtained from hydrochemical analysis of the groundwater samples.
The higher the porosity (φ) of a formation, the smaller its resistivity and formation factor for a particular aquifer saturated with brine.As a result, porosity and the formation factor are mutually contradictory.Additionally, it depends on the distribution of pore sizes and pore structure.Archie (1942) suggested a formula between porosity and formation factor (Eq. 4).The main disadvantage of this formula is that it is highly sensitive to the presence of shale; as a result, it gives an overestimated value of porosity.However, it is useful in sandy formations with low shale content.
Formation porosity is the percentage of the pores volume to the total volume of rocks.Geological formations may exhibit a wide range of porosities.Porosity can range from almost zero in hard rocks to 60% or more in shales and clays.For accurate estimation of porosity, zone parameters, including cementation exponent (m) and tortuosity factor (a), are evaluated.Total porosity (φ t ) includes all the pores, while effective porosity (φ e ) is the proportion of the interconnected pores to the total volume of rock, excluding the shale volume (V sh ).In this study, the effective porosity is calculated using (Eq.5) proposed by Schlumberger (1991).
Estimation of shale volume is necessary as it affects most of the petrophysical parameters, such as total and effective porosity.In this research, V sh is estimated following a non-linear relationship Borehole logs of LOG 3 location and its correspondent lithology.GR is the natural gamma ray, and RS is the deep resistivity log.
Frontiers in Earth Science frontiersin.org06 proposed by Larionov (1969) (Eq.6).It is an empirical formula suggested to reduce the over-estimation of V sh based on gamma-ray index (I γ ) of the geological formation.
V sh 0.33 2 2pIγ − 1 (6) The I γ is calculated following a linear formulation (Eq.7) proposed by Schlumberger (1984) between the natural gammaray reading of the point of measurement (GR log ), gamma-ray reading for clean sand (GR min ), and shaly layers (GR max ).
The hydraulic conductivity is estimated to evaluate groundwater aquifer productivity.In this study, hydraulic conductivity (K) is measured based on an empirical relationship using the resistivity of the water-bearing formation (R aq ) (Eq. 8) suggested by Heigold et al. (1979).

Pumping test analysis
Pumping tests are regulated field investigations intended to gather data on groundwater yield and hydraulic parameters.Pumping test data for five groundwater wells is evaluated to determine the hydraulic parameters of the aquifers, including transmissivity (T), storativity (S), and hydraulic conductivity (K).In this study, the measured hydraulic parameters obtained from geophysical Well logging are validated with those of the pumping test to ensure the uniqueness of the geophysics-based method.The test duration varied between 100 and 300 min, and T, S, and K are estimated using Cooper Jr and Jacob (1946), and it is designed for leaky confined aquifers under transient flow conditions.This method operates by fitting a straight line in a time plot since the pumping started against its corresponding drawdown in a semilogarithmic paper.The slope of the line in one logarithmic cycle is measured to give the average drawdown (Δs) and transmissivity (Eq.9).
Since hydraulic conductivity describes the rate of flow in the unit width of the aquifer and transmissivity defines the rate of flow in the full width (b) of the aquifer, Eq. 10 is used for the determination of K.

T Kpb
(10) The estimated T, the well radius (r), and the intercept of the Cooper-Jacob straight line (t 0 ) are then used to measure the storativity (S) of the aquifer.It is defined as a volume of water that can be released for storage per unit surface area of the aquifer per unit change in hydraulic gradient (Pongmanda and Suprapti, 2020).The S is dimensionless, and by using Cooper Jr and Jacob (1946) assumptions, it can be calculated using Eq.11  4 Results

Delineation of aquifers geometry
The results of well-logging are shown in Figures 3-5.LOG 1 (Figure 3) of a total depth of 133 m combined with the lithology description of the borehole shows that the top of the study area is made up of superficial deposits of a thickness of 10 m.The second layer is indicated by GR and RS logs since it shows low resistivity and high gamma radiation.This layer of 25 m thickness is described as a clay layer.The clay layer is followed by a saturated sand layer of 35 m thickness.The sand layer is likely to be the upper aquifer of the study area.A mudstone layer is observed from a 70-95 m depth.This layer is followed by a relatively high resistivity saturated sandstone layer of thickness range from 95 to 133 m.This layer is probably the primary aquifer in the study area.
LOG 2 is located in the southern part of the study area and is connected to a total depth of 220 m (Figure 4).According to this log, the topsoil of 10 m thickness is followed by a low resistivity layer with thickness of 25 m.This layer is described as a clay layer.The third layer is made up of sand and extends from 30 to 55 m.This layer is separated from the sandstone aquifer with a mudstone layer of 20 m thickness.The primary sandstone aquifer lies over a highly resistive layer of silicified sandstone.
LOG 3, with a total depth of 270 m, is situated in the southeastern part of the study area and is illustrated in Figure 5.It revealed that the superficial deposits composed of sand and silt of thickness of 7 m are the region's top layer, followed by a clay layer of 35 m thickness.The sand layer, with a thickness of 40 m, lies below the clay layer.As suggested by GR and RS logs, the sand layer is likely to be a secondary aquifer in the study area.This layer is followed by a mudstone layer of 10 m thickness.In LOG 3, an exchange between mudstone and sandstone is observed from a depth of 60-170 m.All these layers rest over a relatively high resistivity layer of thickness of more than 100 m.This layer is interpreted as saturated sandstone and described as the primary groundwater aquifer in the study area.
The vertical electrical sounding (VES) technique is employed to extrapolate the result obtained from geophysical well-logging.The resulting electrical curves obtained from the 1D least damped square inversion of the VES measurement are illustrated in Figure 6.Most VES stations revealed that the area mainly comprises 4 to 5 geoelectrical layers.The top layer of average resistivity (ρ) and thickness of 160 Ωm and 6 m, respectively, are correlated to the superficial deposits indicated by well-logging methods.The second layer is associated with resistivity ranging between 8.5 and 28 Ωm and thickness range between 14.7 and 48.3 m.This layer is interpreted as clay.The third layer of average resistivity of 120 Ωm is indicated as saturated sand of average thickness of 60 m.The fourth layer, which correlated to mudstone of an average thickness of 30 m, disappeared in some VES stations, such as S11 and S12.The bottom layer of resistivity ranges from 120 to 292 Ωm is interpreted as saturated sandstone.From the high resistivity values of this aquifer, it can be deduced that the pore water is of low salinity.
For the delineation of groundwater aquifers, two hydrogeological profiles are constructed based on the data obtained from geophysical well logs, VES measurements, and lithological logs.The integrated approach results revealed that the study area consists of two aquifers (Figure 7 a, b, and c).An upper aquifer comprises sand with a thickness range from 20 to 50 m, and a lower aquifer with a thickness of more than 200 m is composed of sandstone.The lower aquifer is non-leaky confined due to the presence of a relatively thick mudstone layer with an average thickness of 25 m.Vertical flow components hydraulically connect the upper and lower aquifers.Furthermore, combining the wells logging and VES measurement aided in detecting the spatial variation in the depth to the upper and lower aquifers.The

Petrophysical and hydrogeological parameters
The results of the estimated petrophysical and hydrogeological parameters are summarized in Table 1.For LOG 1, the average formation resistivity of the upper and lower aquifer is 83 and 120 Ωm, and pore water resistivity is 20 and 25 Ωm.Thus, for the upper aquifer, the average formation factor is 4.3, while for the lower aquifer The spatial variation of the electrical resistivity for the (A) upper and (B) lower aquifers.
is 4.8.Since the formation factor is inversely proportional to porosity, the upper aquifer is associated with higher porosity (33%) than the lower aquifer (27%).This is likely due to the high pore-water resistivity.The average shale volume of shallow and deep aquifers is 22% and 19%.As a result, the effective porosities are 24% and 22%.
The average hydraulic conductivity of the deep aquifer is 4.9 m/day, while for the shallow aquifer, the hydraulic conductivity is 5.8 m/day.However, the transmissivity of the deep aquifer (490 m 2 /day) is much higher than that of the shallow aquifer (120 m 2 /day).This is due to the high thickness of the deep aquifer compared to the shallow.The average formation resistivity of the upper and lower aquifers for LOG 2 is 94 and 180 Ωm, while the pore water resistivity is 40 Ωm.Due to this, the average formation factor for the upper aquifer is 2.3 and 4.5 for the lower aquifer.The upper aquifer is associated with 42% porosity, while the porosity of the lower aquifer is 32%.In shallow and deep aquifers, there are 6% and 10% of shale volume.It follows that the effective porosities are 39% and 29%.The hydraulic conductivity and transmissivity for the shallow and deep aquifers are 5.5 and 3.5 m/day and 192 and 683 m 2 /day.
For LOG 3, the pore water resistivity is 27 Ωm, while the average formation resistivity of the above and lower aquifers is 72 and 107 Ωm.As a result, the lower aquifer's average formation factor is 3.9, and the upper aquifer's average formation factor is 2.6.The lower aquifer has a porosity of 34%, whereas the higher aquifer has a porosity of 47%.Shale volume is present in shallow and deep aquifers at 6% and 10%.The effective porosities are therefore 31% and 20%.The shallow and deep aquifers' respective hydraulic conductivity is 7.8 and 5.7 m/day, while the transmissivity values are 199 and 733 m 2 /day.

Interpolation of estimated parameters 4.3.1 Petrophysical parameters
Vertical electrical sounding (VES) employed the geophysical well logging results to reveal the geographic variation of electrical resistivity, formation factor, porosity, hydraulic conductivity, and transmissivity.In this study, the areal distribution of the resistivity of aquifers is detected.The maximum resistivity for the upper aquifer, 195 Ωm, is recorded in S1, and the minimum 72 Ωm is observed in LOG 3 (Figure 8A).For the lower aquifer, the lowest resistivity of 120 Ωm is detected in LOG 1, and the highest of 292 Ωm is recorded in S9 in the central part of the study area (Figure 8B).
Accordingly, the spatial variation of formation factor in the shallow and deep aquifers is illustrated in Figures 9A, B, respectively.The formation factor for the upper aquifer ranges from 2.3 in the southern part of the study area to 8 in the eastern part of the study area.For the lower aquifer, the formation factor varies between 3.9 and 8.9.The highest value is observed in the S1 location in the eastern part of the study, while the lowest is detected in the LOG3 location in the western part.Consequently, the areal variation of total porosity is revealed.The geographic distribution is shown in Figures 9C, D for the shallow and deep aquifers, respectively.The range of porosity for the upper aquifer is between 20% and 47%, while the lower aquifer is between 17% and 34%.The upper aquifer has a higher porosity than the lower aquifer because it is made up of coarse sand, which is less compact than the sandstone that makes up the deep aquifer.

Hydrogeological parameters
The interpolation of hydrogeological parameters of hydraulic conductivity and transmissivity is performed with geophysical and pumping test methods.Figure 10 shows an example of the pumping data analysis using Cooper Jr and Jacob (1946) method.The hydraulic conductivity of the upper aquifer is between 2.8 and 7.8 m/day.The highest conductivity is observed in the LOG3 location and the lowest in S1 location in the eastern part of the study area.Figure 11A shows the variation of the hydraulic conductivity of the shallow aquifer over the study area.Generally, the values increase in the Southeastern part of the study area.For the lower aquifer, the hydraulic conductivity ranges from 1.93 m/day in S9 to 5.7 m/day in LOG3.The geographic distribution in Figure 11B shows an almost similar trend to that of the upper aquifer.
The transmissivity for the upper aquifer ranges from 120 in LOG1 to 220 in S12.The spatial variation shown in Figure 11C revealed the central part of the area is of high transmissivity, and the values decrease toward the North, South, and Eastern parts of the research area.For the lower aquifer, the transmissivity is measured by analyzing pumping test data using Cooper Jr and Jacob (1946) method.Figure 8 shows an example of pumping data analysis for LOG3 locations.The estimated transmissivity for the lower aquifer varies between 370 in the Northern part and 733 in LOG3 in the Southwestern part.The areal distribution is illustrated in Figure 11D.The Southern parts of the area are associated with high transmissivity compared to the.Furthermore, the storativity (S) of the leaky confined aquifer is estimated, and it ranged between 5.8e-5 to 2.09e-6.The lowest value of S is likely due to the low compressibility of the Nubian formation in the study area in response to the pressure change.This is also supported by the slight change in drawdown during groundwater pumping.

Discussion
The integration of the geophysical well logging with VES data has provided a comprehensive understanding of the geological and hydrogeological frameworks within the study area, enabling the delineation of distinct hydrostratigraphical units.Across the study area, the consistent identification of superficial deposits highlights the uniformity of the uppermost layers (Haggaz and Kheirallah, 1988).This uniformity is important for evaluating recharge mechanisms (Farah et al., 2000).On the other hand, aquitards identified at varying depths serve as geological barriers influencing vertical groundwater flow (Zeinelabdein and Elsheikh, 2014).The delineated aquifers are affected by these aquitards, which impact their connectivity and facilitate direct groundwater infiltration due to hydraulic gradient differences (Hussein and Awad, 2006).The result of pumping test analysis for LOG3 groundwater well using Cooper-Jacob method.
Furthermore, the spatial disparities in the distribution of aquifer depth and thickness underscore the subsurface heterogeneity, indicating varying groundwater potential throughout the study area (Abdelsalam et al., 2016).However, limitations in the exploration depth, especially for identifying the thickness of the lower aquifer, highlight the necessity for more extensive investigations using more profound exploration techniques like deep resistivity sounding or gravity surveys (Mohamed, 2020).
The petrophysical and hydrogeological parameters derived from the well logs provide crucial insights into the characteristics and The spatial variation in hydraulic conductivity of (A) upper and (B) lower aquifers and the transmissivity of (C) upper and (D) lower Nubian aquifers (The Nile River is shown in blue polygons).
potential productivity of the identified aquifers within the study area.The variation in formation resistivity and pore water resistivity among the upper and lower aquifers across different logs contributes to the differences in porosity and storativity (Farrag et al., 2019).Accordingly, the differences in the distribution of hydraulic conductivity and transmissivity values between the upper and lower aquifers reflect varying permeabilities and thicknesses, with the deeper aquifers exhibiting higher transmissivity due to their substantial thicknesses (Zeinelabdein and Elsheikh, 2014).In general, the obtained values showed a close agreement with the results of (Elkrail and Adlan, 2019).According to (Krásný, 1993) classification, the upper and lower aquifers are defined as high transmissivity aquifers that can be ideal for groundwater development to fulfill the water supply.However, optimizing the pumping rate to suit the measured parameters is advisable for the sustainable management of groundwater resources.
The investigation of the NAS has uncovered crucial patterns of petrophysical and hydrogeological parameters.This complete assessment provides a dataset that may be used as a basis for creating precise hydrogeological conceptual models to simulate the movement of groundwater and the spread of contaminants within the systems (Geng et al., 2020).The NAS acts as a model for interpreting comparable aquifer systems globally, allowing the extension of current findings to other analogous hydrogeological environments.An example of an aquifer system with comparable hydrogeological characteristics is the Taoudeni Basin Aquifer System (TAS), which extends across Algeria, Mali, and Mauritania (Nijsten et al., 2018).Our study promotes a wider viewpoint in comprehending and handling crucial groundwater resources by acknowledging the similarities between the NAS and other aquifers.

Conclusion
The integrated approach using geophysical well-logging, vertical electrical sounding, and pumping test data is employed to delineate and characterize the Cretaceous Nubian Aquifer System in Khartoum state, Sudan.The research area encompasses two hydraulically connected aquifers.These aquifers comprise shallow and deep aquifers that transition from being leaky confined to non-leaky confined due to intercalated clayey and mudstone layers.These layers restrict the vertical movement of groundwater and establish a high hydrostatic pressure that exceeds atmospheric pressure.The actual thickness of the deep aquifer was not determined in the recent investigation since the depth of the sounding cannot detect the top of the Precambrian basement rocks.
The petrophysical analysis of the aquifer materials revealed distinct differences between the shallow and deep aquifers.The deep aquifer exhibits a greater degree of cementation and consolidation.Conversely, the shallow aquifer is characterized by a higher shale volume, resulting in reduced hydraulic conductivity.The estimation of hydraulic parameters, including hydraulic conductivity and transmissivity, demonstrated the considerable groundwater potential within the study area.Consequently, the aquifers can serve as a reliable source of groundwater supply in Khartoum State.Nonetheless, the study highlights the necessity of optimizing groundwater extraction to align with the hydraulic properties of the aquifers.
The integrated approach successfully delineated and characterized the Nubian Aquifer System in Khartoum State; however, this study recommended applying deep electrical methods to determine the thickness of the deep aquifer for the accurate estimation of petrophysical and hydrogeological parameters.The most recent study of the NAS greatly enhances our comprehension of transboundary aquifer systems.In addition to the specific qualities emphasized in the NAS, the findings of this study have prospective implications that can be extrapolated and implemented in aquifer systems that have a heterogeneous lithological and hydrogeological nature.
FIGURE 1 (A) Geography of the Republic of the Sudan.(B) Map of the Khartoum state showing the location of the study area.(C) The lithological (Hussein and Awad, 2006) and piezometric map of the study area.

FIGURE 7
FIGURE 7Hydrogeological cross sections obtained from the interpretation of (A) profile 1, (B) profile 2, and (C) profile 3.

FIGURE 9
FIGURE 9 Contour maps showing the spatial variation in the formation factor of the (A) upper and (B) lower aquifers and the porosity of (C) upper and (D) lower Nubian aquifers (Contours are shown in blue lines while the Nile River in blue polygons).

TABLE 1
The average estimated petrophysical and hydrogeological parameters for the Nubian aquifers were obtained from geophysical well logs.