The study area is located in the northeastern desert of Algeria (lower Sahara) near the city of Ouargla (Fig. ), 31∘54′ to 32∘1′ N and 5∘15′ to 5∘27′ E, with a mean elevation of 134 (m a.s.l.). It is located in the quaternary valley of Oued Mya basin. The present climate belongs to the arid Mediterranean type , as it is characterized by a mean annual temperature of 22.5 ∘C, a yearly rainfall of 43.6 mm yr-1 and a very high evaporation rate of 2138 mm yr-1.

Ouargla's region and the entire lower Sahara has experienced during its long geological history alternating marine and continental sedimentation phases. During Secondary era, vertical movements affected the Precambrian basement, causing, in particular, collapse of its central part, along an axis passing approximately through the Oued Righ Valley and the upper portion of the Oued Mya Valley. According to Furon (1960), a epicontinental sea spread to the Lower Eocene of northern Sahara. After the Oligocene, the sea gradually withdrew. It is estimated at present that this sea did not reach Ouargla and transgression stopped at the edge of the bowl . The basin is carved into Mio-Pliocene (MP) deposits, which alternate with red sands, clays and sometimes marls; gypsum is not abundant and dated from the Pontian era (during the MP) . The continental Pliocene consists of a local limestone crust with puddingstone or lacustrine limestone (Fig. ), shaped by eolian erosion into flat areas (regs). The Quaternary formations are lithologically composed of alternating layers of permeable sand and relatively impermeable marl .

The exploitation of Mio-Pliocene aquifer is ancient and at the origin of the creation of the oasis . The piezometric level was higher (145 m a.s.l.) but overexploitation at the end of the 19th century led to a catastrophic decrease of the resource, with presently more than 900 boreholes .

The exploitation of the Senonian aquifer dates back to 1953 at a depth between 140 and 200 m, with a small initial rate of approximately 9 L s-1; two boreholes have been exploited since 1965 and 1969, with a total flow rate of approximately 42 L s-1, for drinking water and irrigation.

The exploitation of the Albian aquifer dates back to 1956; presently, two boreholes are exploited:

El Hedeb I, 1335 m deep, with a flow rate of 141 L s-1;

The sampling programme consisted of collecting samples along transects corresponding to directions of flow for both the Phr and CT aquifers, while it was possible to collect only eight samples from the CI. A total of 107 samples were collected during a field campaign in 2013 along the main flow path of Oued Mya. Of these, 67 were from piezometers tapping the phreatic aquifer, 32 from CT wells and the last 8 from boreholes tapping the CI aquifer (Fig. ). Analyses of Na+, K+, Ca2+, Mg2+, Cl-, SO42- and HCO3- were performed by ion chromatography at Algiers Nuclear Research Center (CRNA). Previous and yet unpublished data sampled in 1992 are used here too: 59 samples for the Phr aquifer, 15 samples for the CT aquifer and 3 samples for the CI aquifer for chemical analyses and data of 18O and 3H .

PHREEQC was used to check minerals–solutions equilibria using the specific interaction theory (SIT), i.e., the extension of Debye–Hückel law by Scatchard and Guggenheim incorporated recently in PHREEQC 3.0 . Inverse modeling was used to calculate the number of minerals and gases' moles that must, respectively, dissolve or precipitate/degas to account for the difference in composition between initial and final water end members . This mass balance technique has been used to quantify reactions controlling water chemistry along flow paths . It is also used to quantify the mixing proportions of end-member components in a flow system .

Inverse modeling involves designing a list of scenarios (modeling setups) that take into account the most plausible combinations of geochemical processes that are likely to occur in our system. For example, the way to identify whether calcite dissolution/precipitation is relevant or not consists of solving the inverse problem under two alternate scenarios: (1) considering a geochemical system in which calcite is present and (2) considering a geochemical system without calcite. After simulating the two scenarios, it is usually possible to select the setup that gives the best results as the solution to the inverse modeling according to the fit between the modeled and observed values. Then one can conclude whether calcite dissolution/precipitation is relevant or not. This stepwise strategy allows us to identify the relevance of a given chemical process by inversely solving the problem through alternate scenarios in which the process is either participating or not .

In the geochemical modeling inverse, soundness of results is dependent upon valid conceptualization of the system, validity of basic concepts and principles, accuracy of input data and level of understanding of the geochemical processes. We use the information from the lithology, general hydrochemical evolution patterns, saturation indices and mineral stability diagrams to constrain the inverse models.

Piper diagrams drawn for the studied groundwaters (Fig. ) broadly show a scatter plot dominated by a sodium chloride facies. However, when going into small details, the widespread chemical facies of the Phr aquifer are closer to the NaCl cluster than those of the CI and CT aquifers. Respectively, CaSO4, Na2SO4, MgSO4 and NaCl are the most dominant chemical species (minerals) that are present in the phreatic waters. This sequential order of solutes is comparable to that of other groundwater occurring in north Africa and especially in the neighboring area of the chotts (depressions where salts concentrate by evaporation) Merouane and Melrhir .

The salinity of the phreatic aquifer varies considerably depending on the location (namely, the distance from wells or drains) and time (due to the influence of irrigation) (Fig. a).

Its salinity is low around irrigated and fairly well-drained areas, such as the palm groves of Hassi Miloud, just north of Ouargla (Fig. ), that benefit from freshwater and are drained to the sabkha Oum El Raneb. However, the three lowest salinity values are observed in the wells of the Ouargla palm grove itself, where the Phr aquifer water table is deeper than 2 m.

Conversely, the highest salinity waters are found in wells drilled in the chotts and sabkhas (a sabkha is the central part of a chott where salinity is the largest) (Safioune and Oum er Raneb) where the aquifer is often shallower than 50 cm.

The salinity of the CT (Mio-Pliocene) aquifer (Fig. b) is much lower than that of the Phr aquifer and ranges from 1 to 2 g L-1; however, its hardness is larger and it contains more sulfate, chloride and sodium than the waters of the Senonian formations and those of the CI aquifer. The salinity of the Senonian aquifer ranges from 1.1 to 1.7 g L-1, while the average salinity of the CI aquifer is 0.7 g L-1 (Fig. c).

A likely contamination of the Mio-Pliocene aquifer by phreatic groundwaters through casing leakage in an area where water is heavily loaded with salt, and therefore particularly aggressive, cannot be excluded.

The calculated saturation indices (SIs) reveal that waters from CI at 50 ∘C are close to equilibrium with respect to calcite, except for three samples that are slightly oversaturated. They are, however, all undersaturated with respect to gypsum (Fig. ).

Moreover, they are oversaturated with respect to dolomite and undersaturated with respect to anhydrite and halite (Fig. ).

Waters from the CT and phreatic aquifers show the same pattern, but some of them are more largely oversaturated with respect to calcite, at 25 ∘C.

However, several phreatic waters (P031, P566, PLX4, PL18, P002, P023, P116, P066, P162 and P036) that are located in the sabkhas of Safioune, Oum er Raneb, Bamendil and Aïn el Beïda's chott are saturated with gypsum and anhydrite. This is in accordance with highly evaporative environments found elsewhere .

No significant trend of SI from south to north upstream and downstream of Oued Mya (Fig. ) is observed. This suggests that the acquisition of mineralization is due to geochemical processes that have already reached equilibrium or steady state in the upstream areas of Ouargla.

The facies shifts progressively from the carbonated cluster (CI and CT aquifers) to the evaporites' cluster (Phr aquifer) with an increase in sulfates and chlorides at the expense of carbonates (SI of gypsum, anhydrite and halite). This is illustrated by a decrease of the [HCO3-] / ([Cl-] + 2[SO42-]) ratio (Fig. ) from 0.2 to 0 and of the [SO42-] / [Cl-] ratio from 0.8 to values smaller than 0.3 (Fig. ) while salinity increases. Carbonate concentrations tend towards very small values, while it is not the case for sulfates. This is due to both gypsum dissolution and calcite precipitation. Chlorides in groundwater may come from three different sources: (i) ancient sea water entrapped in sediments, (ii) dissolution of halite and related minerals that are present in evaporite deposits and (iii) dissolution of dry fallout from the atmosphere, particularly in these arid regions .

The [Na+] / [Cl-] ratio ranges from 0.85 to 1.26 for the CI aquifer, from 0.40 to 1.02 for the CT aquifer and from 0.13 to 2.15 for the Phr aquifer. The measured points from the three considered aquifers are linearly scattered with good approximation around the unity slope straight line that stands for halite dissolution (Fig. ). The latter appears as the most dominant reaction occurring in the medium. However, at very high salinity, Na+ seems to swerve from the straight line towards smaller values.

A further scrutiny of Fig.  shows that CI waters are very close to the 1 : 1 line. CT waters are enriched in both Na+ and Cl- but slightly lower than the 1 : 1 line while phreatic waters are largely enriched and much more scattered. CT waters are closer to the seawater mole ratio (0.858), but some lower values imply a contribution from a source of chloride other than halite or from entrapped seawater. Conversely, a [Na+] / [Cl-] ratio larger than 1 is observed for phreatic waters, which implies the contribution of another source of sodium, most likely sodium sulfate, that is present as mirabilite or thenardite in the chotts and the sabkha areas.

The [Br-] / [Cl-] ratio ranges from 2 × 10-3 to 3 × 10-3. The value of this molar ratio for halite is around 2.5 × 10-3, which matches the aforementioned range and confirms that halite dissolution is the most dominant reaction taking place in the studied medium.

In the CI, CT and Phr aquifers, calcium originates both from carbonate and sulfate (Figs.  and ). Three samples from the CI aquifer are close to the [Ca2+] / [HCO3-] 1 : 2 line, while calcium sulfate dissolution explains the excess of calcium. However, nine samples from the Phr aquifer are depleted in calcium, and plotted under the [Ca2+] / [HCO3-] 1 : 2 line. This cannot be explained by precipitation of calcite, as some are undersaturated with respect to that mineral, while others are oversaturated.

In this case, a cation exchange process seems to occur and lead to a preferential adsorption of divalent cations, with a release of Na+. This is confirmed by the inverse modeling that is developed below and which implies Mg2+ fixation and Na+ and K+ releases.

Larger sulfate values observed in the phreatic aquifer (Fig. ) with [Ca2+] / [SO42-] < 1 can be attributed to a Na-Mg sulfate dissolution from a mineral bearing such elements. This is, for instance, the case of bloedite.

The CT and CI aquifers exhibit depleted and homogeneous 18O contents, ranging from -8.32 to -7.85 ‰. This was already previously reported by many authors . On the other hand, 18O values for the phreatic aquifer are widely dispersed and vary between -8.84 and 3.42 ‰ (Table ). Waters located north of the virtual line connecting, approximately, Hassi Miloud to Sebkhet Safioune, are found more enriched in heavy isotopes and are thus more evaporated. In that area, the water table is close to the surface and mixing of both CI and CT groundwaters with phreatic ones through irrigation is nonexistent. Conversely, waters located south of Hassi Miloud up to Ouargla city show depleted values. This is the clear fingerprint of a contribution to the Phr waters from the underlying CI and CT aquifers .

Phreatic waters result from a mixing of two end members. Evidence for this is given by considering the [Cl-] and 18O relationship (Fig. ). The two clusters are (i) a first cluster of 18O-depleted groundwater (Fig. ), and (ii) another cluster of 18O-enriched groundwater with positive values and a high salinity. The latter is composed of phreatic waters occurring in the northern part of the study region.

Cluster I represents the waters from CI and CT whose isotopic composition is depleted in 18O (average value around -8.2 ‰) (Fig. ). They correspond to an old water recharge (paleo-recharge), whose age, estimated by means of 14C, exceeds 15 000 yr BP . Thus, it is not a water body that is recharged by recent precipitation. It consists of CI and CT groundwaters and partly of phreatic waters and can be ascribed to an upward leakage favored by the extension of faults near Amguid El Biod dorsal.

Cluster II, observed in Sebkhet Safioune, can be ascribed to the direct dissolution of surficial evaporitic deposits conveyed by evaporated rainwater.

Evaporation alone cannot explain the distribution of data that is observed (Fig. ). Evidence for this is given in a semi-logarithmic plot (Fig. ), as classically obtained according to the simple approximation of the Rayleigh equation (cf. Appendix): δ18O≈1000×(1-α)log⁡Cl-+k,≈-ϵlog⁡Cl-+k, where α is the fractionation factor during evaporation, ϵ ≡ -1000 × (1 - α) is the enrichment factor and k is a constant . CI and CT waters are better separated in the semi-logarithmic plot because they are differentiated by their chloride content. According to Eq. (), simple evaporation gives a straight line (solid line in Fig. ). The value of ϵ used is the value at 25 ∘C, which is equal to -73.5.

P115 is the only sample that appears on the straight evaporation line (Fig. ). It should be considered as an outlier since the rest of the samples are all well aligned on the logarithmic fit derived from the mixing line of Fig. .

The phreatic waters that are close to cluster I (Fig. ) correspond to groundwaters occurring in the edges of the basin (Hassi Miloud, piezometer P433) (Fig. ). They are low mineralized and acquire their salinity via two processes, namely dissolution of evaporites along their underground transit up to Sebkhet Safioune and dilution through upward leakage by the less-mineralized waters of the CI and CT aquifers (for example, Hedeb I for CI and D7F4 for CT) (Fig. ) .

The rates of the mixing that are due to upward leakage from CI to CT towards the phreatic aquifer can be calculated by means of a mass balance equation. It only requires knowing the δ values of each fraction that is involved in the mixing process.

The δ value of the mixture is given by δmix=f×δ1+(1-f)×δ2, where f is the fraction of the CI aquifer, 1 - f the fraction of the CT and δ1, δ2 are the respective isotope contents.

Average values of mixing fractions from each aquifer to the phreatic waters computed by means of Eq. () gave the rates of 65 % for the CI aquifer and 35 % for the CT aquifer.

A mixture of a phreatic water component that is close to cluster I (i.e., P433) with another component which is rather close to cluster II (i.e., P039) (Figs.  and ), for an intermediate water with a δ18O signature ranging from -5 to -2 ‰, gives mixture fraction values of 52 % for cluster I and 48 % for cluster II. Isotope results will be used to independently cross-check the validity of the mixing fractions derived from an inverse modeling involving chemical data (see Sect. 3.6).

Turonian evaporites are found to lie in between the CI deep aquifer and the Senonian and Miocene formations bearing the CT aquifer. CT waters can thus simply originate from ascending CI waters that dissolve Turonian evaporites, a process which does not involve any change in 18O content. Conversely, phreatic waters result, to a minor degree, from evaporation and mostly from dissolution of sabkha evaporites by 18O-enriched rainwater and mixing with CI/CT waters.

We assume that the relationship between 18O and Cl- data obtained in 1992 is stable with time, which is a logical assumption as times of transfer from CI to both CT and Phr are very long. Considering both 18O and Cl- data, CI, CT and Phr data populations can be categorized. The CI and CT do not show appreciable 18O variations and can be considered as a single population. The Phr samples consist, however, of different populations: cluster I, with δ18O values close to -8 and small Cl- concentrations, more specifically less than 35 mmol L-1; cluster II, with δ18O values larger than 3 and very large Cl- concentrations, more specifically larger than 4000 mmol L-1 (Table ); intermediate Phr samples resulting from mixing between clusters I and II (mixing line in Fig. , mixing curve in Fig. ) and from evaporation of cluster I (evaporation line in Fig. ). The mass-balance modeling has shown that relatively few phases are required to derive observed changes in water chemistry and to account for the hydrochemical evolution in Ouargla's region. The mineral phases' selection is based upon geological descriptions and analysis of rocks and sediments from the area .

The inverse model was constrained so that mineral phases from evaporites including gypsum, halite, mirabilite, glauberite, sylvite and bloedite were set to dissolve until they reach saturation, and calcite and dolomite were set to precipitate once they reached saturation. Cation exchange reactions of Ca2+, Mg2+, K+ and Na+ on exchange sites were included in the model to check which cations are adsorbed or desorbed during the process. Dissolution and desorption contribute as positive terms in the mass balance, as elements are released in solution. On the other hand, precipitation and adsorption contribute as negative terms, while elements are removed from the solution. CO2(g) dissolution is considered by PHREEQC as a dissolution of a mineral, whereas CO2(g) degassing is dealt with as if it were a mineral precipitation.

Inverse modeling leads to a quantitative assessment of the different solutes' acquisition processes and a mass balance for the salts that are dissolved or precipitated from CI, CT and Phr groundwaters (Fig. , Table ), as follows:

Transition from CI to CT involves gypsum, halite and sylvite dissolution, and some ion exchange, namely calcium and potassium fixation on exchange sites against magnesium release, with a very small and quite negligible amount of CO2(g) degassing. The maximum elemental concentration fractional error equals 1 %. The model consists of a minimum number of phases (i.e., six solid phases and CO2(g)); another model also implies dolomite precipitation with the same fractional error.

The main types of groundwaters occurring in the Ouargla basin are thus explained and could quantitatively be reconstructed. An exception is, however, sample P115, which is located exactly on the evaporation line of Phr cluster I. Despite numerous attempts, it could not be quantitatively rebuilt. Its 3H value (6.8) indicates that it is derived from a more or less recent water component with very small salt content, most possibly affected by rainwater and some preferential flow within the piezometer. As this is the only sample on this evaporation line, there remains doubt regarding its significance.

Globally, the summary of mass transfer reactions occurring in the studied system (Table ) shows that gypsum dissolution results in calcite precipitation and CO2(g) dissolution, thus acting as an inorganic carbon sink.