Estimation and Mapping of the Transmissivity of the Nubian Sandstone Aquifer in the Kharga Oasis, Egypt

Article Estimation and Mapping of the Transmissivity of the Nubian Sandstone Aquifer in the Kharga Oasis, Egypt

Mustafa El-Rawy 1,2,* and Florimond De Smedt 3

1 Department of Civil Engineering, Faculty of Engineering, Minia University, Minia 61111, Egypt 2 Civil Engineering Department, College of Engineering, Shaqra University, Dawadmi 11911, Ar Riyadh, Saudi Arabia 3 Department of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium; [email protected] * Correspondence: [email protected] or [email protected]

Received: 14 December 2019; Accepted: 20 February 2020; Published: 23 February 2020

Abstract: The Nubian sandstone aquifer is the only water source for domestic use and irrigation in the Kharga oasis, Egypt. In this study, 46 pumping tests are analyzed to estimate the transmissivity of the aquifer and to derive a spatial distribution map by geostatistical analysis and kriging interpolation. The resulting transmissivity values are log-normally distributed and spatially correlated over a distance of about 20 km. Representative values for the transmissivity are a geometric average of about 400 m2/d and a 95% confidence interval of 100–1475 m2/d. There is no regional trend in the spatial distribution of the transmissivity, but there are local clusters with higher or lower transmissivity values. The error map indicates that the highest prediction accuracy is obtained along the central north-south traffic route along which most agricultural areas and major well sites are located. This study can contribute to a better understanding of the hydraulic properties of the Nubian sandstone aquifer in the Kharga oasis for an effective management strategy.

Keywords: Nubian sandstone aquifer; transmissivity; Kharga oasis; well ﬂow; pumping test; double porosity

1. Introduction The Nubian sandstone aquifer located under the eastern part of the Sahara Desert is considered to be the largest fossil groundwater reservoir in the world. It has an area of more than 2 106 km2 × shared by Egypt, Libya, Sudan and Chad. Groundwater is a vital factor for economic growth and sustainable development in Egypt, especially in the desert areas [1]. The Nubian sandstone aquifer covers a large area of the order of 830,000 km2 in Egypt, mainly in the Western Desert and partly in the Eastern Desert and Sinai [2]. The aquifer is composed of Paleozoic-Mesozoic sandstone embedded with shale and clay beds and overlaying impermeable crystalline basement rocks. The thickness of the aquifer varies up to 3500 m [3,4]. In the Western Desert, the aquifer is unconﬁned south of latitude 25◦ N where the sandstone outcrops and conﬁned to the north where the sandstone is overlain by impermeable marine shale and clay [1]. The age of the groundwater is estimated between 20,000 and 49,000 years [3,5]. Estimates of water storage in the Nubian sandstone aquifer in Egypt are around 40,000 109 m3, but this is non-renewable because groundwater recharge in the Western Desert is × negligible [1,6]. The large-scale development of the Nubian sandstone aquifer in Egypt started in 1960 in the major oases of the Western Desert and the total extraction of groundwater is expected to be in the order of 2.8 109 m3/y for the year 2020 [2]. The Nubian sandstone in Kharga oasis is strongly dissected, laminated and cross-bedded [7]. The thickness ranges from 300 to 1000 m, but the exact geometry is complicated and not well known

Water 2020, 12, 604; doi:10.3390/w12020604 www.mdpi.com/journal/water Water 2020, 12, 604 2 of 14 because of the many fractures zones that indicate differential movements [7–10]. The Nubian sandstone in Kharga oasis consists of several water-bearing layers separated by clay and shale beds, which can restrict the vertical movement of groundwater locally, but because they are discontinuous, the Nubian sandstone forms a single aquifer complex on a regional scale [3,8,10–12]. Overlying layers consisting of shale and clay are partly eroded in the Kharga plain, but are still sufficiently thick and impermeable to confine the aquifer system [8,10]. Information about the hydraulic properties of the Nubian sandstone aquifer in the Western Desert is limited and fragmented. Shata [3] assumed an average hydraulic conductivity of 5 m/d, which however seems too high for sandstone as reported in the literature, e.g., [13]. Ebraheem et al. [9] developed a regional groundwater flow model of the Nubian sandstone aquifer in the Western Desert and concluded that the transmissivity is 1100 m2/d for the Kharga oasis. Mahmod et al. [12,14] assumed transmissivity values in the range 50–500 m2/d for their groundwater model of the Nubian sandstone aquifer in the Kharga oasis. Elewa et al. [15] reported transmissivity values ranging from 11 m2/d to 1490 m2/d as a result of 90 pumping tests conducted in the Nubian sandstone aquifer in a large area in the Western Desert south of the Kharga oasis. Hamdam et al. [16] reported transmissivity values between 236 m2/d and 3045 m2/d as a result of 12 pumping tests conducted in the Nubian sandstone aquifer in the El-Bahariya oasis, about 300 km northwest of the Kharga oasis. Masoud and Osta [17] analyzed 26 pumping tests in the Nubian sandstone aquifer of the El-Bahariya oasis and reported transmissivity values between 191 m2/d and 970 m2/d; the discrepancy with the previous study was not explained. Groundwater is the only water source for domestic use and irrigation in the Kharga oasis. Originally, groundwater was captured from springs and free-flowing shallow wells, until the installation of deep wells for large-scale irrigation starting in 1960. Since then, groundwater exploitation has steadily increased and groundwater levels have fallen, causing springs and free-flowing wells to run dry and more deep wells were needed. Groundwater is currently being abstracted in the Kharga oasis with around 1400 wells with a total flow rate of 0.2 109 m3/y. Two areas of decline were created in the ± aquifer as a result of overexploitation, one in the north in El-Kharga with a drawdown in groundwater levels of 60–80 m and one in the southern Bulaq-Ghormachine region with a drawdown of 40–60 m. Because groundwater reserves in the Kharga oasis have severely decreased, adequate management of groundwater extraction is strongly recommended [14]. However, hydrogeological data required for simulation of groundwater flow and prediction of the effects of groundwater abstraction are largely missing, creating a problem for sustainable management of the groundwater resources [9,12,14]. Therefore, this study aims to contribute to a better understanding of the hydraulic properties of the Nubian sandstone aquifer in the Kharga oasis by (1) estimating the transmissivity of the aquifer through interpretation and analysis of a series of pumping test conducted in deep wells, (2) geostatistical analysis of the spatial variation of the obtained transmissivity values, and (3) mapping of the transmissivity by kriging interpolation.

2. Methods

2.1. Study Area and Data The Kharga oasis is a topographic depression in the southern part of the Western Desert about 200 km west of the Nile valley (Figure1). The depression is located on an anticline with a main axis that extends from north to south, which also coincides with the major faults [11]. The altitude varies from zero to 120 m. The oasis is characterized by a tropical arid climate with high humidity and little rainfall. The Kharga oasis is one of the driest areas of the Eastern Sahara and probably one of driest places on earth [18]. It is very hot in summer with a maximum daily temperature of more than 40 ◦C, but mild in winter because the temperature can drop below zero at night. Rainfall is extremely low, on average less than 1 mm/y, although occasionally torrential storms can occur [7,8]. The Kharga oasis is an agricultural community; the cultivated land is approximately 11,400 ha and date palm is the main WaterWater2020 20, 1220,,604 12, x FOR PEER REVIEW 3 of3 of14 14

oasis is an agricultural community; the cultivated land is approximately 11,400 ha and date palm is cashthe crop main alongside cash crop olive alongside and other olive fruit trees and [other19]. Groundwater fruit trees [19 is]. abstracted Groundwater by approximately is abstracted 1100 by 6 3 shallowapproximately wells from 1100 farmers shallow with wells a total from abstraction farmers with rate a total of 8.3 abstraction 10 m /y andrate aboutof 8.3 10 3006 m government3/y and about or 6 3 industrial300 government deep wells or withindustrial a total deep abstraction wells with rate a oftotal 198.1 abstraction 10 m /y rate (Ministry of 198.1 of 10 Water6 m3/y Resources (Ministry andof Irrigation,Water Resources Egypt, personal and Irrigation, communication, Egypt, personal October communication, 2019). October 2019).

FigureFigure 1. 1.Location Location of of the the study study area area andand pumpingpumping test wells.

PumpingPumping tests tests are are regularly regularly performedperformed by by the the General General Administration Administration of Groundwater of Groundwater in El- in El-Kharga.Kharga. TheseThese areare single-wellsingle-well tests involv involvinging pumping pumping with with a a constant constant rate rate in in the the range range 80 80–300–300 m m3/h3/ h for halffor half a day a day and and manual manual recording recording of of the the water water level level inside inside thethe well, initially at at one one-minute-minute intervals intervals and gradually increased in time to 30 minutes or more. The observations during the pumping tests are Water 2020, 12, x FOR PEER REVIEW 4 of 14

Water 2020, 12, 604 4 of 14 and gradually increased in time to 30 minutes or more. The observations during the pumping tests are often complicated by the narrowness of the well tubes and the great depth of the wells, and oftenespecially complicated by the initially by the narrowness steep and rapid of the drop well in tubes the andwater the level great in depth the well. of the We wells, acquired and especiallypumping bytest the data initially from steep46 wells and that rapid have drop been in the executed water level by the in the General well. WeAdministra acquiredtion pumping of Groundwater test data from in 46the wells last decade. that have The been position executed of the by wells theGeneral is shown Administration in Figure 1, in which of Groundwater we have numbered in the last the decade. wells Thefrom position north to of south. the wells The is locations shown in of Figure the wells1, in whichvary over we havethe study numbered area but the are wells mostly from clustered north to south.around The major locations sites, mainly of the wells El-Kharga, vary over Ghormachine the study area and but Paris. are mostlyWe have clustered technical around logs for major some sites, of mainlythe wells; El-Kharga, Figure 2a Ghormachine shows, for andexample, Paris. the We havetechnical technical log of logs well for 11 some in Al of theKharga. wells; A Figure general2a shows,description for example, of the wells the technicalwith a schematic log of well geological 11 in Al cross-section Kharga. A general is given description in Figure of2b. the The wells depth with of athe schematic wells varies geological from 225 cross-section m to 784 ism given(Table in 1). Figure The 2wellsb. The are depth drilled of theto a wells depth varies where from sufficient 225 m tosandstone 784 m (Table layers1). are The penetrated wells are drilledto install to a a screen, depth whereso that sutheﬃ exactcient lower sandstone limit layersof the Nubian are penetrated aquifer tosystem install remains a screen, unknown so that theat the exact well lower locations. limit ofRe thecorded Nubian total aquifer screen systemlengths remainsvary between unknown 101 atm theand well 202 m locations. with diameters Recorded of approximately total screen lengths 0.68 m vary (13 between3/8”) for 101the upper m and casing 202 m and with 0.34 diameters m (6 5/8”) of approximatelyfor the screen (Figure 0.68 m (132b).3 /8”) for the upper casing and 0.34 m (6 5/8”) for the screen (Figure2b).

Soil surface

Cement Shale Casing: φ∼68 cm

∼200 m 10 m overlap Filter

Sandstone Screen: φ∼34 cm

∼400 m

(a) (b)

FigureFigure 2.2. Technical loglog ofof well well 11 11 ( a(a);); schematic schematic geological geological and and technical technical log log of of the the wells, wells, with with orders orders of magnitudeof magnitude of theof the depth depth and and diameter diameter of theof the wells wells (b). (b).

2.2. Pumping Test Analysis 2.2. Pumping Test Analysis The pumping tests conducted in the Kharga oasis display a number of features that complicate The pumping tests conducted in the Kharga oasis display a number of features that complicate their interpretation. Initially, there is a large head loss in all wells due to turbulent flow in the gravel their interpretation. Initially, there is a large head loss in all wells due to turbulent flow in the gravel pack (filter) and well screen and in the aquifer adjacent to the well where the flow is also turbulent. pack (filter) and well screen and in the aquifer adjacent to the well where the flow is also turbulent. TheThe initialinitial drawdowndrawdown (change(change inin head)head) isis alsoalso influencedinfluenced byby well-borewell-bore storage,storage, soso thatthat thethe drawdown isis lowerlower thanthan theoreticallytheoretically expected,expected, butbut thisthis eeffectffect isis limitedlimited inin time.time. AfterAfter thethe initialinitial phase,phase, thethe drawdowndrawdown inin the the well well appears appears to increaseto increase as if theas if aquifer the aquifer is confined, is confined, which is which revealed is inrevealed a diagnostic in a semi-logdiagnostic plot semi-log of the time-drawdown plot of the time-drawdown relationship as relationship initially non-linear as initially but graduallynon-linear becoming but gradually linear overbecoming time. However,linear over thereafter time. However, the drawdown thereafter slows the downdrawdown and reaches slows adown pseudo and steady reaches state, a pseudo which occurssteady forstate, almost which all theoccurs wells for around almost a all pumping the wells time around of 200–1000 a pumping min. The time reason of 200 for–1000 this apparentmin. The stabilizationreason for this of theapparent drawdown stabilization in the wells of the is drawdo not clear,wn because in the wells the pumping is not clear, tests because only last the about pumping half a day,tests whichonly last istoo about short half to a reveal day, which the long-term is too short hydraulic to reveal behavior the long-term of the Nubian hydraulic sandstone behavior aquifer of the system.Nubian Ideally,sandstone the aquifer pumping system. tests Ideally, should bethe conducted pumping fortests several should days be conducted to see if a truefor several stable statedays hasto see been if a achieved,true stable which state has seems been unlikely achieved, because which thereseems is unlikely no natural because aquifer there recharge, is no natural or that aquifer other phenomenarecharge, or arethat occurringother phenomena that demonstrate are occurring the truethat demonstrate nature of the the aquifer, true nature such asof the double aquifer, porosity such behavior,as double delayedporosity yield behavior, or leaky delayed aquifer yield conditions. or leaky aquifer The most conditions. likely explanation The most islikely double explanation porosity behavior,is double which porosity is very behavior, common which for fractured is very sandstone common aquifers.for fractured Field explorationsandstone andaquifers. conceptual Field

Water 2020, 12, 604 5 of 14 models [20,21] show that when a pumping test is performed in such media, the ﬂow to the well initially consist of water released from the fractures, while gradually water is also released from the matrix so that the drawdown slows down and reaches a pseudo steady-state, after which the drawdown increases again as more and more groundwater is released from the matrix. Another possible explanation is a leaky aquifer system, whereby groundwater is gradually released from overlying, or more likely underlying, less permeable aquifers, which stabilizes the drawdown [20,21]. In this regard, we point out that none of the wells was reported to have reached the lower limit of the Nubian sandstone. Finally, it also possible that during a pumping test ground water levels fall below the top of the aquifer, causing unconﬁned conditions and dewatering of the aquifer [20–22]. Because of these complications, we only analyze the drawdown in the initial phase before the transition to the pseudo steady-state using the Theis [23] equation as proposed in the literature [20–22] including a well loss term 2 ! Q Srw 2 sw(t) = s + W t > 25r /T, (1) 0 4πT 4Tt c

3 1 where sw (L) is the drawdown in the well, s0 (L) is the well loss due to turbulence, Q (L T− ) is 2 1 the pumping rate, T (L T− ) is the local aquifer transmissivity around the well, W is the Theis well function [23], S (-) is the local storage coefficient around the well during the initial phase of the pumping test, rw (L) is the effective radius of the well, t (T) is the time since pumping started and rc (L) is the radius of the well casing. The time condition in Equation (1) is needed to exclude well-bore storage effects [20], resulting in pumping times of 4–42 min for a well casing radius of 0.34 m (Figure2) and a possible range of transmissivity values of 100–1000 m2/d. Because the well loss is unknown, it is not possible to estimate the aquifer properties by traditional curve matching of the Theis equation and the observed drawdown in the well versus time. However, the effective radius of the well and the aquifer storage coefficient can be expected to be very small, so that the argument in the Theis function is small and the function can be simplified using the Jacob approach for sufficiently large times [20–22]   2.3Q 2.25Tt s (t) s + log  t > 25Sr2 /T. (2) w 0  2  w ≈ 4πT S f rw

Because the well loss is constant as it only depends on the pumping rate and the physical properties of the well, the slope of the drawdown plotted against the logarithm of time is constant and the transmissivity of the aquifer can be estimated as

2.3Q ds T / w . (3) ≈ 4π d log t

Therefore, the transmissivity can be estimated provided that a linear segment is present in the observed s versus logt graph before the transition to the pseudo-steady state. Note that it is not possible to estimate the storage coeﬃcient of the aquifer, because the well loss and the eﬀective radius of the well are unknown.

2.3. Geostatistical Analysis Exploratory data analysis involves the derivation of the cumulative frequency distribution of the transmissivity estimates and ﬁtting by a log-normal probability distribution

1 z m f (z) = exp − , (4) √2πσ2 − 2σ2 where z = ln T is the log-transformed transmissivity, m is the mean and σ2 is the variance. The ﬁtting is veriﬁed by a Kolmogorov–Smirnov test. Water 2020, 12, 604 6 of 14

Geostatistical data analysis of the log-transformed transmissivity estimates involves the derivation of the empirical variogram, ﬁtting by a model variogram, cross-validation of the model variogram and interpolation by kriging to obtain a map of the predicted log-transformed transmissivity values [24]. The empirical variogram is calculated in a standard way as

1 X h i2 γ(h) = z(xi) z xj , (5) ( ) (i,j) N(h) 2N h ∈ − where γ is the variogram or semi-variance, h (L) is the lag distance, N is the number of data pairs within the lag distance interval and x (L) is the location vector. The empirical variogram is fitted by an exponential model γ(h) = n + (s n)[1 exp( 3h/r)], (6) − − − where n is the nugget, s is the sill and r (L) is the practical range. The model parameters n, s and r are estimated by restricted maximum likelihood using the likfit function of the geoR package for geostatistical data analysis [25]. The variogram model is verified by cross-validation using the xvalid function of geoR, whereby data points are removed one by one and predicted by kriging using the remaining data. The standardized differences between observed and predicted z values should be unbiased and follow a standard normal distribution. For prediction of the log-transformed transmissivity, ordinary kriging is used, which is a least-squares linear regression estimator, so

XN(x) z(x) = λiz(xi), (7) i=1 where N is now the number of data points selected within the neighborhood of x and λi are the kriging weights determined so that the estimation is unbiased and minimizes the error variance. A map of the predicted log-transformed transmissivity is derived with the ordinary kriging routine of ArcMap using six neighboring data points and a smoothing factor of 0.2. The resulting minimum error variance can be determined as XN(x) 2 σ (x) = λiγ( x xi ) µ, (8) E i=1 k − k − 2 where σE is the error (or kriging) variance and µ is a Langrage multiplier.

3. Results

3.1. Pumping Test Analyses All pumping tests show an almost instantaneous large drawdown in the well due to turbulent flow, followed by a drawdown due to the release of groundwater water from the aquifer, possibly influenced by the effects of well-bore storage, and a transition to a pseudo steady state at larger times. In all pumping tests, a straight-line segment is present in the semi-log graph of drawdown versus time before the transition to the pseudo steady state, making it possible to estimate the local transmissivity of the aquifer in the vicinity of the wells with Equation (3). The results of the pumping test analyses are presented in Table1. In the table, we show the well depth, the depth to the static water level in the well before the pumping test, the pumping test rate, the drawdown after 1 min as an indicator of the well loss, the maximum drawdown at the end of the pumping test and the estimated transmissivity. The depth to the static water level in the well is usually large, while the initial drawdown after one minute of pumping varies from a few meters to more than 30 m and the maximum drawdown from a few meters to more than 50 m. The estimated transmissivity values vary over a wide range from 73 m2/d to 1201 m2/d. We like to point out that these estimates represent local transmissivity values around wells, which are likely influenced by local conditions. As an example, we show the analysis of the pumping tests that were performed in well 42 in Paris and well 19 in Bulak. Figure3 shows the observed drawdown in the wells against time on a log-scale Water 2020, 12, 604 7 of 14

(Figure3a,c) and the slope of the observed drawdown against time on a log-scale (Figure3b,d). In case of well 42, the aquifer transmissivity is high, so that the response of water released from the aquifer is fast and the straight-line segment very prominent. Moreover, the transition to the pseudo steady-state is very abrupt. There is also a large head loss of about 16 m in the first minutes of the pumping test due to turbulent flow in and around the well, while effects of well-bore storage last only for about 3 min. The slope of the drawdown versus time is very erratic, but nevertheless shows an 8–200 min time interval with a more or less constant slope. The slope of the fitted straight line segment is 0.766 m for a pumping rate of 210 m3/h, which makes it possible to estimate the transmissivity with Equation (3) as 1201 m2/d. In case of well 19, the transmissivity is much smaller. In the first minute of the pumping test there is a very large head loss of about 21 m due to turbulent flow, and the influence of well-bore storage is noticeable to about 15 min. The drawdown increases gradually and the presence of a straight-line segment is less evident, yet a time interval with a constant slope can be noted in the middle part of the graph just before the transition to the pseudo steady-state. This is also reflected in the graph showing the slope versus time, in which it can be seen that the slope gradually increases to reach a plateau around 30–200 min, where the slope becomes maximum, after which the slope abruptly drops to zero. The slope of the fitted straight line is 3.61 m for a pumping rate of 200 m3/h, resulting in an estimated transmissivity with Equation (3) of 260 m2/d. The analyses of the pumping tests conducted in the other wells is similar. It is generally noted that the time intervals with a constant slope are larger and more prominent in case of large transmissivity and vice-versa, so it can be concluded that estimates of small transmissivities are less accurate than estimates of large transmissivities.

Table 1. List of the pumping test wells with location, coordinates, well depth, depth to the static water level (h), pumping test rate (Q), drawdown after 1 min (s1), maximum drawdown (sm) at the end of the pumping test and estimated transmissivity (T).

Depth h Q s s T Well Location Latitude Longitude 1 m (m) (m) (m3/h) (m) (m) (m2/d) 1 El-Sherka 25.597 30.647 405 54.40 120 30.80 53.60 180 2 El-Sherka 25.569 30.641 712 78.24 200 16.58 24.80 171 3 El-Sherka 25.518 30.642 349 63.50 80 22.30 36.45 109 4 El-Kharga 25.451 30.549 312 45.38 180 6.46 11.58 222 5 El-Kharga 25.449 30.611 784 66.00 200 9.70 20.52 294 6 El-Kharga 25.435 30.552 307 40.03 200 15.22 21.95 163 7 El-Kharga 25.435 30.577 412 89.35 200 9.56 13.44 422 8 El-Kharga 25.425 30.547 315 62.80 200 7.33 18.88 207 9 El-Kharga 25.409 30.555 304 29.16 200 7.02 12.91 932 10 El-Kharga 25.392 30.549 313 25.00 200 3.50 11.60 553 11 El-Kharga 25.383 30.545 351 24.20 200 5.61 8.74 537 12 El-Kharga 25.379 30.521 640 72.00 202 1.95 10.80 473 13 El-Kharga 25.378 30.545 737 22.50 220 8.04 11.54 477 14 El-Kharga 25.373 30.596 358 11.78 200 18.72 23.02 826 15 Genah 25.349 30.548 327 26.65 200 10.47 13.95 687 16 Port Said 25.333 30.548 357 30.33 200 9.12 11.97 668 17 Genah 25.276 30.574 750 39.00 230 15.40 22.34 317 18 Bulaq 25.254 30.567 485 23.70 220 23.30 39.10 181 19 Bulaq 25.236 30.624 421 26.78 200 21.30 26.37 260 20 Bulaq 25.211 30.531 430 - 220 11.70 15.73 542 21 Ghormachine 25.114 30.544 470 25.34 300 36.76 49.21 417 22 Ghormachine 25.084 30.555 495 43.00 207 8.35 22.50 221 23 Ghormachine 24.994 30.562 574 39.36 220 18.89 25.07 407 24 Ghormachine 24.901 30.582 588 36.50 200 18.30 21.40 898 25 Ghormachine 24.867 30.567 732 36.00 220 13.20 20.91 497 26 Ghormachine 24.837 30.563 673 28.40 200 17.60 23.80 354 27 Paris 24.771 30.569 434 30.38 220 18.71 22.91 749 28 Paris 24.752 30.590 447 28.00 225 20.50 23.90 821 29 Paris 24.742 30.637 444 - 150 19.10 21.48 147 30 Paris, Ain Ramah 24.713 30.586 534 37.20 230 7.40 19.79 270 31 Paris 24.710 30.616 435 38.15 180 12.90 15.17 975 32 Paris, Ain Alhajjar 24.705 30.624 469 47.00 225 9.22 28.92 173 Water 2020, 12, x FOR PEER REVIEW 8 of 14

Water 2020, 12, 604 Paris, Ain 8 of 14 32 24.705 30.624 469 47.00 225 9.22 28.92 173 Alhajjar 33 Paris 24.697 30.587 434 35.73 220 18.75 21.80 827 Table 1. Cont. 34 Paris 24.689 30.584 385 39.00 200 23.33 33.18 212 35 Paris, El-Balad 24.669 30.602 Depth475 45.00h Q200 20.90s 26.23s 432T Well Location Latitude Longitude 1 m 36 Paris 24.657 30.601 (m)384 37.50(m) (m2103/h) (m)16.02 (m)24.08 (m5212/d) 3337 ParisDosh 24.570 24.697 30.703 30.587 434298 35.7338.60 220220 18.7523.49 21.8034.50 827166 3438 Paris 24.569 24.689 30.586 30.584 385403 39.00- 200260 23.3319.95 33.1825.36 212883 35 Paris, El-Balad 24.669 30.602 475 45.00 200 20.90 26.23 432 3639 Paris 24.530 24.657 30.646 30.601 384420 37.5034.12 210150 16.0217.20 24.0820.01 521841 3740 DoshParis 24.521 24.570 30.630 30.703 298424 38.6030.10 220210 23.4914.57 34.5016.70 166957 3841 Paris 24.516 24.569 30.615 30.586 403427 33.60 - 260210 19.9511.60 25.3617.55 883625 39 Paris 24.530 30.646 420 34.12 150 17.20 20.01 841 4042 Paris 24.516 24.521 30.643 30.630 424348 30.1033.54 210220 14.5720.27 16.7024.13 1201 957 4143 Paris, Paris El-Kasr 24.507 24.516 30.615 427325 33.6039.50 210215 11.6014.87 17.5519.56 625494 4244 Darb ParisEl-Arbaien 24.437 24.516 30.641 30.643 348280 33.5441.96 220150 20.2715.14 24.1321.20 1201200 4345 Darb Paris, El El-Kasr-Arbaien 24.413 24.507 30.637 30.615 325235 39.5055.25 215150 14.8718.75 19.5627.88 494212 44 Darb El-Arbaien 24.437 30.641 280 41.96 150 15.14 21.20 200 Paris, Zaynab 4546 Darb El-Arbaien24.405 24.413 30.6 30.63725 235225 55.2553.00 150170 18.7511.50 27.8825.82 21273 46 Paris, ZaynabEl-Deeb El-Deeb 24.405 30.625 225 53.00 170 11.50 25.82 73

18 1.5

(a) Well 42 (b) Well 42 )

17 ) 1.0

(

a r

D 16 0.5 Observations Observations Model fit Model fit 15 0.0 1 10 100 1000 1 10 100 1000 Time (min) Time (min)

27 6 (c) Well 19 (d) Well 19 26 5 Observations

Model fit )

25 )

m 4

(

w p

o 24 3

a r

D 23 2 Observations 22 Model fit 1

21 0 1 10 100 1000 1 10 100 1000 Time (min) Time (min) FigureFigure 3. Plots 3. Plots showing showing drawdown drawdown against against log-time log-time for wellfor well 42 ( a42), slope(a), slope of drawdown of drawdown against against log-time log- for welltime 42 for (b ),well drawdown 42 (b), drawdown against log-time against forlog- welltime 19for (wellc) and 19 slope(c) and of slope drawdown of drawdown against against log-time log for- well 19time (d); for the well solid 19 ( lined); the shows solid the line straight-line shows the straight ﬁt to estimate-line fit to the estimate transmissivity. the transmissivity.

3.2. Statistical Analysis of Transmissivity

Figure4 shows the cumulative frequency distribution of the transmissivity estimates and the ﬁtted log-normal probability distribution, with parameters listed in Table2. The maximum deviation between the observed and modelled frequency is 0.10 while the Kolmogorov–Smirnov goodness of WaterWater 20 202020, 1, 21,2 x, xFOR FOR PEER PEER REVIEW REVIEW 9 9of of 14 14

3.3.22. .Statistical Statistical A Analysisnalysis of of T Transmissivityransmissivity Water 2020, 12, 604 9 of 14 FigureFigure 4 4 shows shows the the cumulative cumulative frequency frequency distribution distribution of of the the transmissivity transmissivity estimates estimates and and the the fittedfitted log log-normal-normal probability probability distribut distribution,ion, with with parameters parameters listed listed in in Table Table 2. 2. The The maximum maximum deviation deviation betweenfitbetween test gives the the observed aobserved deviation and and of modelled 0.20modelled for a frequency significancefrequency is is 0.10 level0.10 while while of 0.01, the the soKolmogorov Kolmogorov the fitted log-normal––SmirnovSmirnov goodness goodness probability of of fitdistributionfit test test gives gives isa a acceptable.deviation deviation of of 0.20 0.20 for for a a significance significance level level of of 0.01, 0.01, so so the the fitted fitted log log-normal-normal probabi probabilitylity distributiondistribution is is acceptable. acceptable. 11

00.9.9 OObbseservrveedd y y 00.8.8

c Log-normal fit

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u q

q 00.6.6

00.5.5

i t

t 00.4.4

l u

u 00.3.3

m u

u 00.2.2

C C 00.1.1 00 1100 11000 110000 1100000 TTrarannsmsmisisisvivitiyty ( m(m2/2/dd))

FigureFigure 4. 4. Cumulative CumulativeCumulative frequency frequency frequency distribution distribution distribution of of the the estimated ofestimated the estimated transmissivity transmissivity transmissivity and and fitted fitted log andlog-normal-normal ﬁtted distribution.log-normaldistribution. distribution.

Table 2. List of the estimated geostatistical parameters of the transmissivity of the Nubian sandstone TableTable 2. 2. List List of of the the estimated estimated geostatistical geostatistical parameters parameters of of the the transmissivity transmissivity of of the the Nubian Nubian sandstone sandstone aquifer in the Kharga oasis (the parameters refer to lnT, where T is given in m2/d). aquifeaquifer rin in the the Kharga Kharga oasis oasis (the (the parameters parameters refer refer to to ln lnTT, ,where where T T is is given given in in m m2/d)2/d). . Parameter Symbol Units Value ParameterParameter SymbolSymbol UnitsUnits ValueValue Mean MeanMean m 푚푚 -- - 5.955.95 5.95 Variance σ2 - 0.472 VarianceVariance 휎휎22 - - 0.4720.472 Nugget n - 0.199 Sill NuggetNugget s 푛푛 -- - 0.1990.199 0.517 Range SillSill r 푠푠 km- - 0.5170.517 22.58 RangeRange 푟푟 kmkm 22.5822.58 Figure5 shows the transmissivity values plotted against latitude and longitude. The geometric meanFigureFigure transmissivity 5 5 shows shows the the value transmissivity transmissivity of 385 m2/ dvalues values is also plotted plotted indicated a againstgainst in thelatitude latitude figure. and and Although longitude. longitude. it The isThe possible geometric geometric to 2 meanidentifymean transmissivity transmissivity regions with value largervalue of of or 385 385 smaller m m/d2/d is transmissivity is also also indicated indicated values in in the the nofigure. figure. significant Although Although correlation it it is is possible possible can be to to detectedidentify identify regionsbetweenregions with the withtransmissivity larger larger or or smaller smaller and the transmissivity transmissivity location of the values values wells; no no so significant there significant appears correlation correlation to be no regional can can be be detected trend detected in betweentransmissivity.between the the transmissivity transmissivity Furthermore, and and no significantthe the location location correlation of of the the wells; wells; can so beso there detectedthere appears appears between to to be be the no no transmissivity regional regional trend trend and in in transmissivity.thetransmissivity. depth of the Furthermore wells.Furthermore, ,no no significant significant correlation correlation can can be be detected detected between between the the transmissivity transmissivity andand the the depth depth of of the the wells. wells. 10000 10000 ) 10000

) 10000

)

/ / / (a) (b(b))

(a) 2

(

1000 1000 y 1000

y 1000

i i

m 100

T T 1100 1100 224.44.4 224.46.6 224.48.8 225.50.0 225.52.2 225.54.4 225.56.6 330.05.5 330.06.6 330.07.7 Latitude (km) Longitude (km) Latitude (km) Longitude (km) FigureFigure 5. 55. Transmissivity. TransmissivityTransmissivity plotted plotted plotted against againstagainst latitude latitude latitude (a) and (a (a) against ) and and against againstlongitude longitude longitude (b); the dashed (b (b);); the the line d dashed representsashed lineline 2 representstherepresents geometric the the meangeometric geometric transmissivity mean mean transmissivity transmissivity value of 385 value value m /d. of of 385 385 m m2/d.2/d.

Figure 6a shows directional and omnidirectional empirical variograms of the log-transformed transmissivity calculated with a lag of 6 km; for the omnidirectional variogram we also show the empirical variogram near the origin with a lag of 2 km to indicate the convergence to the nugget. It can be concluded from the figure that there is no significant anisotropy in the spatial correlation. Thus, an isotropic exponential model can be fitted to the data using restricted maximum likelihood resulting in model parameters as listed in Table 2. The optimal value of the nugget and range are strongly determined by the spatial variation near the origin and at short distances, while the sill is determined by the spatial variation at large distances. We also applied other variogram models, such Wateras spherical2020, 12, 604and Gaussian, but obtained no improvement. 10 of 14 The range indicates that the transmissivity is spatially correlated over a distance of approximately 22 km. The nugget represents about 40% of the sill and can be attributed to bemeasurement concluded fromerrors the, differences figure that in there well is construction no significant or anisotropy to spatial variation in the spatial on a correlation. scale that is Thus, smaller an isotropicthan the distances exponential between model the can wells be fitted considered to the datain this using study. restricted The validity maximum of the likelihoodvariogram resultingmodel is inverified model by parameters cross-validation. as listed Figure in Table 6b shows2. The a optimalgraph of value the quantiles of the nugget of the standardized and range are errors strongly and determinedthe corresponding by the spatial quantiles variation of a standard near the origin normal and distribution. at short distances, The average while theof thesill is standardized determined byerrors the is spatial 0.009, variation the variance at large is 0.999 distances. and the We data also points applied in the other quantile variogram plot closely models, follow such asthe spherical 1:1 line, andall of Gaussian, which indicate but obtained the validity no improvement. of the variogram model.

0.7 (a) 2.5

0.6 N-S (b)

r o

0.5 NW-SE r

a r

0.4 W-E d

i i

r 0 d

a 0.3

SW-NE r

V d

0.2 n

Omnidirectional a t 0.1 S Model 0 -2.5 0 10 20 30 40 -2.5 0 2.5 Distance (km) Normal value Figure 6.6. Empirical variogram in didifferentfferent directions and fittedfitted omnidirectionalomnidirectional exponentialexponential model variogram with with parameters parameters given given in Table in Table2( a); 2 verification (a); verification of the variogram of the variogram model by model cross-validation, by cross- showingvalidation, the showing quantiles the of quantiles the standardized of the standardized errors and errors the corresponding and the corresponding quantiles fromquantiles a standard from a normalstandard distribution normal distributio (b). n (b).

TheFigure range 7a shows indicates the thatmap the with transmissivity the spatial distribution is spatially correlatedof the transmissivity over a distance obtained of approximately by ordinary 22kriging km. interpolation The nugget represents (Equation about7) and 40% the associated of the sill anderror can map be showing attributed the to spatial measurement distribution errors, of 2 2 ditheff erenceskrigingin variance well construction 휎퐸 (Equation or to 8) spatial divided variation by the on sample a scale variance that is smaller 휎 (Table than the 2). distances between the wells considered in this study. The validity of the variogram model is verified by cross-validation. Figure4. Discussion6b shows a graph of the quantiles of the standardized errors and the corresponding quantiles of a standard normal distribution. The average of the standardized errors is 0.009, the variance is 0.999 Representative values for the transmissivity of the Nubian sandstone aquifer in the Kharga oasis and the data points in the quantile plot closely follow the 1:1 line, all of which indicate the validity of can be derived from Figure 4 and Table 2, more specifically a geometric mean of 384 m2/d and a 95% the variogram model. confidence interval of 100–1475 m2/d. Ebraheem [9] calibrated a regional groundwater flow model Figure7a shows the map with the spatial distribution of the transmissivity obtained by ordinary for the Nubian sandstone aquifer in the Western Desert using observed groundwater levels, and kriging interpolation (Equation (7)) and the associated error map showing the spatial distribution of obtained an overall value of 1100 m2/d for the transmissivity in the Kharga oasis, which fits within the kriging variance σ2 (Equation (8)) divided by the sample variance σ2 (Table2). our confidence intervalE but is substantially larger than our geometric mean. Mahmod et al. [12,14] 2 4.used Discussion transmissivity values within the range 50–500 m /d for their groundwater model of the Nubian sandstone aquifer in the Kharga oasis, which is rather on the low side compared to our results. However,Representative the proposal values by Shata for the [3] transmissivity to estimate the of transmissivity the Nubian sandstone on the basis aquifer of an in average the Kharga hydraulic oasis 2 canconductivity be derived of from5 m/d Figure leads4 to and values Table for2, morethe transmissivity specifically a between geometric 1500 mean m2/d of and 384 m5000/d m and2/d for a 95% an 2 confidenceaquifer thickness interval in of the 100–1475 range m of / 300d. Ebraheem–1000 m, [which9] calibrated is much a regional larger than groundwater obtained flow in this model study. for theDomenico Nubian and sandstone Schwartz aquifer [13] in give the Westerna maximum Desert value using of observed approximately groundwater 0.5 m/d levels, for the and hydraulic obtained an overall value of 1100 m2/d for the transmissivity in the Kharga oasis, which fits within our confidence interval but is substantially larger than our geometric mean. Mahmod et al. [12,14] used transmissivity values within the range 50–500 m2/d for their groundwater model of the Nubian sandstone aquifer in the Kharga oasis, which is rather on the low side compared to our results. However, the proposal by Shata [3] to estimate the transmissivity on the basis of an average hydraulic conductivity of 5 m/d leads to values for the transmissivity between 1500 m2/d and 5000 m2/d for an aquifer thickness in the range of 300–1000 m, which is much larger than obtained in this study. Domenico and Schwartz [13] give a maximum value of approximately 0.5 m/d for the hydraulic conductivity of sandstone. Such a value is WaterWater 20202020, 12, ,x12 FOR, 604 PEER REVIEW 11 of 1114 of 14 conductivity of sandstone. Such a value is more realistic for the highly fractured Nubian sandstone, in whichmore realistic case the for transmissivity the highly fractured would beNubian 150–500 sandstone, m2/d, which in which corresponds case the transmissivity much better to would our be results,150–500 although m2/d, somewhat which corresponds on the low much side. better to our results, although somewhat on the low side.

(a) (b)

FigureFigure 7. Map 7. Map with with the spatial the spatial distribution distribution of the of transmissivity the transmissivity of the of Nubian the Nubian sandstone sandstone aquifer aquifer in in the Khargathe Kharga oasis oasis obtained obtained by kriging by kriging interpolation interpolation (a) and (a) andthe corresponding the corresponding error error map map showing showing the the spatialspatial distribution distribution of the of estimated the estimated kriging kriging variance variance divided divided by sample by sample variance variance (b). (b).

SimilarSimilar values values have have been been obtained obtained from from pum pumpingping tests tests in the in theNubian Nubian sandstone sandstone aquifer aquifer in other in other regions. Elewa et al. [15] reported transmissivity values in the range 11–1490 m2/d for the Nubian regions. Elewa et al. [15] reported transmissivity values in the range 11–1490 m2/d for the Nubian sandstonesandstone aquifer aquifer in the in Western the Western Desert Desert south south of the of Kharga the Kharga oasis, oasis, which which closely closely matches matches our ourresults. results. HamdHamdanan and andSawires Sawires [16] [reported16] reported transmissivity transmissivity values values for the for Nubian the Nubian sandstone sandstone aquifer aquifer in the El in- the 2 BahariyaEl-Bahariya oasis, oasis,about about300 km 300 northwest km northwest of the of Kharga the Kharga oasis, oasis, in the in range the range of 236 of– 236–30453045 m2/d, m which/d, which is is largerlarger than than our ourresults, results, but butMasoud Masoud and and Osta Osta [17] [ reported17] reported for t forhe thesame same area area transmissivity transmissivity values values in in 2 the therange range 191– 191–970970 m2/d, m which/d, which is much is much better better in line inline with with our ourresults. results. No references have been found in the literature that discuss the spatial variability of the transmissivity in the Kharga oasis. The current results (Figure 7a) indicate that there no regional trend

Water 2020, 12, 604 12 of 14

No references have been found in the literature that discuss the spatial variability of the transmissivity in the Kharga oasis. The current results (Figure7a) indicate that there no regional trend in the spatial variation, but there clearly noticeable local clusters with higher or lower transmissivity values. Particular locations with high transmissivity are El-Kharga and Paris, and locations with low transmissivity are El-Sherka, Bulak and Darb El-Arbaien. Note that the size of these clusters is determined by the spatial correlation of the transmissivity values, which according to the geostatistical analysis is in the order of maximum 22 km, as represented by the variogram (Figure6a). This distance is probably related to the structural settings of the Nubian sandstone, in particular the distance between major fault systems. It is also striking that the lowest values for the aquifer transmissivity are found at the extremities of the oasis, more specifically in El-Sherka in the north and in Darb El-Arbaien in the south. The only other transmissivity values resulting from pumping tests in Kharga oasis reported in the literature are from Elewa et al. [15] on the southern border of the oasis in Paris and Darb El-Arbaien. The reported transmissivity values are in the range 200 m2/d and 600 m2/d. Our results in this area show a large spatial variation with transmissivity values above 700 m2/d in South Paris that fall sharply to less than 200 m2/d in Darb El-Arbaien, which again indicates to large structural differences in the Nubian sandstone complex. The uncertainty of the transmissivity map is reflected in the error map (Figure7b). To get an idea of the errors involved, the kriging variance is divided by the sample variance of the observed log-transmissivity frequency distribution. So, the error can be interpreted as the uncertainty of the spatial correlated transmissivity with respect to the uncertainty of the transmissivity in case we assume there is no spatial correlation. Errors larger than one imply more uncertainty and vice versa. The areas in the center have an error smaller than one and thus the transmissivity estimates have a higher accuracy, while at the edges of the study area the error is greater than one, which means that the transmissivity estimates are the least accurate. It is well known that kriging errors are mainly determined by the locations of the data points [24], which results in a higher accuracy around data clusters and lower accuracy at locations with fewer or no data points. This also applies to the current results, as the error map clearly indicates that the highest accuracy is obtained along the middle north-south axis, which more or less corresponds to the main traffic route along which most agricultural areas and major well sites are located.

5. Conclusions Groundwater reserves in the Kharga oasis have fallen sharply and good management of the groundwater extraction is urgently needed, but hydrogeological data necessary for simulating groundwater flow and for predicting the effects of pumping wells are lacking. Therefore, 46 pumping tests have been analyzed to estimate the transmissivity of the Nubian sandstone aquifer and to derive a map of the spatial distribution of the transmissivity by kriging interpolation. The resulting transmissivity values are log-normally distributed with a geometric average of 384 m2/d and a 95% confidence interval of 100–1475 m2/d. The spatial correlation can be modeled by an exponential variogram with a practical range of 22 km, which is confirmed by cross-validation. The spatial distribution of the transmissivity shows no specific regional trend, but local clusters are noted with higher transmissivity values in El-Kharga and Paris and noticeable lower transmissivity values in El-Sherka, Bulak and Darb El-Arbaien, which is probably a result of the structural differences in the Nubian sandstone complex. The error map indicates that the prediction accuracy is greatest along the middle north-south axis with major agricultural areas and well sites and lowest at the at locations with fewer or no wells. The resulting transmissivity map can be used as a starting point for modeling and the error map for planning additional field work.

Author Contributions: Conceptualization, M.E.-R.; methodology, M.E.-R. and F.D.S.; software, M.E.-R. and F.D.S.; validation, M.E.-R. and F.D.S.; writing—original draft preparation, M.E; writing—review and editing, M.E.-R. and F.D.S. All~authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Water 2020, 12, 604 13 of 14

Acknowledgments: The authors like to express their sincere appreciation to the General Administration of Groundwater in El-Kharga, Ministry of Water Resources and Irrigation, Egypt for providing the pumping test data. We also thank Dr. Patrick Lachassagne and two other anonymous reviewers for their valuable comments and suggestions. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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