Characterizing deep groundwater using evidence from oil and gas exploration wells in the Lower Kutai Basin of Indonesia

The study area, the Lower Kutai Basin, is situated in East Kalimantan Province, Indonesia, covering the coastal area to the deep Makassar Strait, including the Mahakam Delta (Fig. 1). The regional geological map of Indonesia, encompassing the Lower Kutai Basin (Fig. 2a) shows Oligocene to Quaternary sediments at the surface. Tectonic inversions that took place from Miocene to Pliocene resulted in the development of the main series of fold structures in the basin, known as the Samarinda Anticlinorium (Moss and Chambers 1999).

The productivity of aquifers in Indonesia up to a depth of ~350 m, including the Lower Kutai Basin, has been mapped (Fig. 2b). Onshore, aquifers are considered to be mostly unproductive with low transmissivities. In the coastal area including the Mahakam Delta, shallow (depths of <350 m) aquifers are widely considered to have medium to high productivity though some low-productivity and locally productive aquifers also occur. Sandstone and carbonate units of Tertiary deltaic sediments in the Lower Kutai Basin comprise aquifers as well as hydrocarbon reservoirs in this basin (Duval et al. 1992; Pertamina BPPKA 1997; Doust and Noble 2008). Mudrocks (e.g. of the Miocene sediments) form aquitards that act as regional confining units in the Lower Kutai Basin.

The data used in this study were derived from 45 wells with depths ranging from ~1 to 4.5 km (Fig. 1) and were provided by PUSDATIN, the data center of the Ministry of Energy and Mineral Resources in Indonesia. In this study, all depths are reported as below the ground level for wells located onshore and below the seabed for wells located offshore. Pressure regimes and hydraulic head distributions for deep groundwater in the Lower Kutai Basin are characterized by 43 wells based on direct pressure measurements using standard tools in the oil and gas industry such as repeat formation tester (RFT) and modular dynamic tester (MDT), or from the production test known as Drill Stem Test (DST). Two wells (well Nos. 18 and 21) are excluded from the analysis since no pressure data are available in these wells. There are 1,635 pressure data points available from 43 wells. In addition, wireline logs (density, sonic, and resistivity) are also utilized as an indirect pressure indicator. Prior to further analysis, the wireline logs are filtered using kernel density estimation (KDE) in Python, which estimates the data density with depth to eliminate outliers and smooth data trends—see Fig. S1 in the electronic supplementary material (ESM).

Deep-groundwater salinity and chemistry are characterized in 44 wells based on 117 groundwater samples (Table S1 of the ESM). Well No. 31 is excluded since groundwater samples are not available from this well. This study defines groundwater salinity in terms of total dissolved solids (TDS) and sodium chloride (NaCl) concentrations. TDS is computed as the sum of major cations (Na⁺, Ca²⁺, K⁺, Mg²⁺) and anions (Cl^–, HCO₃^–, CO₃^2–, SO₄^2–), whereas NaCl concentrations are the sum of just Na⁺ and Cl^–. Seawater data in Table S1 of the ESM derive from Furlan et al. (1995); values of pH and K⁺ are not available for some wells, as indicated in Table S1 of the ESM. In addition, borehole temperatures, resistivity and sonic logs, and porosities from sidewall core analyses are used in estimating groundwater salinity. As for the chemical characteristics of the deep groundwater, major cations and anions are employed. The groundwater hydrochemical data are robust with charge balance errors of <5%.

The following basic concepts (Mouchet and Mitchell 1989; Dutta et al. 2021) describe the pressure regime analysis. Hydrostatic pressure (\({P}_{{\text{h}}}\)) is defined by the fluid density and its static column, calculated as:where \({\rho }_{{\text{f}}}\) is the fluid density, \(g\) is the gravity acceleration (9.8 m/s²), and \(z\) is the fluid column height (see the Appendix for a summary of nomenclature). Groundwater with a density of 1 g/cm³ gives a hydrostatic pressure gradient of 9.8 MPa/km or 0.433 psi/ft. Deep groundwater is in an overpressure state when its pressure exceeds the hydrostatic and in an underpressure condition when its pressure is lower than the hydrostatic. In analyzing the pressure regime, overburden and effective stresses are required. Onshore, overburden stress is the stress caused by the weight of overlying rocks, which include both matrix and fluid. The overburden stress (\(S\)) at any depth (\(z\)) is calculated as:where \({\rho }_{{\text{b}}}\) is the bulk density of rocks. An average bulk density of 2.3 g/cm³ gives an overburden stress gradient of 22.5 MPa/km or 1 psi/ft. Offshore, the overburden stress also includes the weight due to the static water column above the seabed. The following Terzaghi’s equation (Terzaghi et al. 1996) shows the relationship between overburden stress (\(S\)) and pore pressure (\(P\)):where \(\sigma\) is known as effective stress, the stress supported by the rock matrix. The pressure regime of deep groundwater within the Lower Kutai Basin is characterized using direct and indirect pressure indicators. Direct pressure indicators are available as measured pressure data obtained from tools such as RFT or MDT and the production test. Wireline logs, consisting of density, sonic, and resistivity logs, are used as indirect pressure indicators.

High overpressure magnitude is often generated by two main mechanisms: loading and unloading. Loading occurs when the fluid expulsion from pores cannot compete with the increase in vertical and/or horizontal stresses during sedimentation as normal compaction would. Hence, sediments fail to compact (compaction disequilibrium) and result in relatively constant effective stress (Goulty et al. 2012). This is common for fine-grained sediments (mudrocks) when the sedimentation rate is high (Swarbrick et al. 2002). On the other hand, the unloading mechanism is due to exhumation or chemical diagenesis (Dutta et al. 2021). Exhumation alleviates some overburden load, resulting in pressure changes due to poroelastic responses (Biot 1941; Burgess et al. 2017). Chemical diagenesis (clay diagenesis or hydrocarbon generation) can generate overpressure via fluid expansion and load transfer (Lahann 2002; Swarbrick et al. 2002). As Ramdhan and Goulty (2010; 2011) contend, decreasing effective stress with depth may reflect chemical diagenesis. Like the loading mechanism, overpressure will occur only when the fluid cannot escape the pores.

In addition to direct pressure measurements, wireline logs (density, sonic, and resistivity) in mudrocks are useful for identifying overpressure (Hottman and Johnson 1965; Mouchet and Mitchell 1989; Ramdhan and Goulty 2011; Dutta et al. 2021; Ramdhan and O’Connor 2022) since they respond differently for each main overpressure generating mechanism. In hydrostatic conditions where mudrocks are normally compacted, density and resistivity logs tend to increase with depth, whereas sonic log decreases (commonly referred to as the normal compaction trend). When mudrocks are overpressured, density, sonic, and resistivity logs will respond and shift from their normal trend if the overpressure is generated by loading or both loading and unloading. In contrast, only the sonic and resistivity log will respond when the overpressure is due to unloading (chemical diagenesis). The cross-plot of density and sonic logs, developed by Dutta (2002) and Katahara (2006), can be used to indicate whether clay diagenesis contributes to unloading. The presence of clay diagenesis is suggested by the shifting of sonic-density data from the smectitic or mechanical compaction trend to the illitic or chemical compaction trend. The transition occurs at temperatures starting from ~70 °C, whereas chemical compaction starts at a temperature ~100 °C (Bjørlykke and Høeg 1997; Bjørlykke 1998). In addition, vitrinite reflectance data are helpful in indicating whether hydrocarbon generation contributes to overpressure as the unloading mechanism (Ramdhan and Goulty 2010, 2011). The overpressure zone should be within the onset of hydrocarbon generation to infer its contribution to the overpressure generation.

Pressure data are used to compute the hydraulic head as the sum of elevation and pressure heads. Sea level is used as the datum to define the elevation head. The pressure head (\(\psi\)) is computed from pore pressure (\(P\)) data as follows:where \({\rho }_{{\text{g}}}\) is the groundwater density and \(g\) is the gravity acceleration (9.8 m/s²). The density is controlled by temperature, salinity, and pressure (Numbere et al. 1997; Dutta et al. 2021). The following equation, developed by Numbere et al. (1997), is used to find the groundwater density:where \({\rho }_{{\text{w}}}\) is the density of pure water at a specific pressure (\(P\)) in psi and temperature (\(T\)) in °F (solved graphically, see Fig. S2 in the ESM), \({C}_{{\text{TDS}}}\) is the groundwater salinity in weight percent; \(a\) to \(f\) are employed constants, respectively: 8.08 × 10^–3, 7.2 × 10^–8, 1.07 × 10^–5, 3.24 × 10^–10, 3.76 × 10^–8, and 1.0 × 10^–12.

Groundwater is considered fresh when the TDS is less than or equal to 1,000 mg/L, brackish when TDS is between 1,000 and 10,000 mg/L, and saline when it is greater than 10,000 mg/L (Freeze and Cherry 1979). Since measured TDS and NaCl data are limited, an attempt is carried out to estimate the NaCl concentration from the resistivity log using Archie’s law (Archie 1942), written as:where \({R}_{{\text{f}}}\) is the formation’s resistivity (i.e., sandstones or carbonates in this study), \({R}_{{\text{w}}}\) is the resistivity of the pore water (groundwater), and \(F\) is a formation factor calculated based on porosity (\(\mathrm{\varnothing }\)) and an exponent (\(m\)) later known as the cementation constant. Archie (1942) summarized the empirical value of \({\text{m}}\), which lies between 1.8 and 2 for consolidated sandstones and 1.3–2 for unconsolidated or partly consolidated sandstones. The original formation factor in Archie’s equation was later modified by Winsauer et al. (1952) by adding the parameter \(a\) to the right-hand side of Eq. (7) and forming the following:where parameter \(a\) refers to the tortuosity factor. This form is widely used (e.g., Lindner-Lunsford and Bruce 1995; Guérin et al. 2001; Mullen and Kellett 2007; Mondal et al. 2013; Gillespie et al. 2017; Stephens et al. 2019; Flowers et al. 2022). Various values for parameters \(a\) and \(m\) have been summarised by Asquith and Gibson (1982) and Worthington (1993).

A reappraisal by Glover (2016) indicates that Eq. (8) is theoretically invalid. For porosity (\(\mathrm{\varnothing }\)) values that approach one, Archie’s law (Eq. 6) will result in \({R}_{{\text{f}}}\approx {R}_{{\text{w}}}\); however, when the formation factor (\(F\)) is altered by parameter \(a\), this will not be obtained. Nevertheless, Eq. (8) is commonly used in the oil and gas industry and its validity is not questioned since it usually best fits experimental data (Glover 2016). In this study, the original form of parameter \(F\) (Eq. 7) is preferred for Archie’s equation. When groundwater resistivity (\({R}_{{\text{w}}}\)) has been obtained and the aquifer’s temperature in °F (\(T\)) is known, the NaCl concentration (\({C}_{{\text{NaCl}}}\)) is then computed using an empirical equation proposed by Bateman and Konen (1977):

The estimation of groundwater resistivity (\({R}_{{\text{w}}}\)) using Archie’s equation requires porosity to calculate the formation factor (\(F\)). In this study, the porosity of aquifers is estimated using the sonic log. Sonic log measures interval transit time, a reciprocal of velocity, of a compressional sound wave that travels through formations (Asquith and Gibson 1982). The applied tool comprises one or more sound transmitters and multiple sound receivers. The interval transit time is influenced by lithology and porosity. Porosity (\(\mathrm{\varnothing }\)) from the sonic log can be estimated using an empirical equation proposed by Wyllie et al. (1958) as follows:where \({\Delta t}_{{\text{log}}}\) is the interval transit time from sonic log reading, \({\Delta t}_{{\text{ma}}}\) is the interval transit time of matrix (for sandstone, ranging from 167 to 182 µs/m, whereas that for carbonate is between 126 and 156 µs/m), and \({\Delta t}_{{\text{f}}}\) is the interval transit time of fluid (for fresh mud this is 620 µs/m, whereas for salt mud it is 607 µs/m). Equation (10) needs an additional multiplication with a compaction factor (\({C}_{{\text{p}}}\)) of Eq. (11) for unconsolidated sandstone (Raymer et al. 1980).where \({\Delta t}_{{\text{sh}}}\) represents the interval transit time of adjacent shale and parameter \(C\) is an empirical constant. This study uses measured porosities from the sidewall core analysis to verify the results, even though their availability is very limited.

The analysis focuses on major cations and anions (Na⁺, Ca²⁺, K⁺, Mg²⁺, Cl^–, HCO₃^–, CO₃^2–, SO₄^2–) in Table S1 of the ESM to characterize the chemistry of deep groundwater within the Lower Kutai Basin. Samples were obtained during drilling or production tests and sent to internal and commercial laboratories by the oil and gas companies operating within the Lower Kutai Basin; only analyses with a charge balance error of ≤5% are considered in this study. Deep groundwater chemistry is compared with seawater data obtained from Furlan et al. (1995) and later visualised in a Piper diagram to infer the groundwater type.

Three pressure regimes, i.e. hydrostatic, overpressure, and underpressure, exist in deep groundwater within the Lower Kutai Basin. Observed pressure gradients from direct pressure measurements (Fig. 3a) range from 5.1 to 19.6 MPa/km; computed hydraulic heads are between –1 and 3.5 km above sea level (asl) (Fig. 3b–d), corresponding respectively to underpressure and overpressure conditions. Similar extremely low and high hydraulic heads are also reported in other basins, e.g. depleted head (underpressure) up to –0.9 km in Denver Basin (Belitz and Bredehoeft 1988) and excessed head (overpressure) between 2 and 9.4 km in the South Caspian and Gulf of Mexico basins, respectively (Bredehoeft et al. 1988; Mello and Karner 1996).

The hydrostatic pressure gradient in the Lower Kutai Basin generally ranges from 9.8 to 10 MPa/km for wells located onshore and, in the Mahakam Delta, from 10 to 10.2 MPa/km for wells located offshore. Most (37/43) wells exhibited conditions of overpressure during drilling as shown in Fig. 4a. Within the demarcated area of Indonesia’s new capital city, the top of overpressure generally deepens from onshore to offshore. In the Mahakam Delta, the top of overpressure is the deepest (up to ~4.5 km) and becomes shallower offshore.

Within the study area, regional groundwater flow from northwest to southeast is indicated by hydraulic head contours (Fig. 4b) calculated at the depth of the top of overpressure in 37 wells. Computed hydraulic heads within the overpressure zone of the Lower Kutai Basin are extremely high (Fig. 3b–d) and exceed 3 km above sea level. Regional groundwater flow may contribute to the overpressure but this is unlikely given the magnitude of hydraulic heads within the overpressure zone that exceed the maximum surface elevation (~1.2 km above sea level, Fig. 1). A similar observation is also reported by Osborne and Swarbrick (1997) within Mesozoic reservoirs in the North Sea, where the excessed head is up to 4.25 km above sea level, yet the maximum elevation of the reservoirs is only 2.5 km above sea level. Hydraulic continuity of aquifers from a highland area into the deep subsurface (Osborne and Swarbrick 1997; Dutta et al. 2021) is required for regional groundwater flow to generate substantial overpressure and the subject of further research in the Lower Kutai Basin. The very high magnitude of overpressure within the basin is thought to be generated by loading and unloading mechanisms (e.g. Bois et al. 1994; Bates 1996; Ramdhan and Goulty 2011; Ramdhan and O’Connor 2022) as is observed from direct and indirect pressure indicators in this study. Evidence from other basins also indicates that loading and unloading mechanisms can lead to extremely high (excessed) hydraulic heads within basins, ranging up to 2 km in the South Caspian Basin (Bredehoeft et al. 1988; Feyzullayev and Lerche 2009) and 9.4 km in the Gulf of Mexico Basin (Mello and Karner 1996).

The top of overpressure in onshore wells varies significantly (Fig. 4a), from close to the surface up to ~2.3 km. In well No. 1, where sediments are largely eroded, the top of overpressure is close to the surface, as indicated by the wireline logs (Fig. 5a). In this well, pressure data are available at 1.15 and 3.3 km. Both are higher than the hydrostatic gradient, with excess pressure of 8 and 29 MPa, equivalent to hydraulic heads of 0.8 and 3 km, respectively.

The density, sonic, and resistivity logs at well No. 1 have shifted from normal trends (density and resistivity increase, whereas sonic decreases with depth) from the surface. Density values are relatively constant to the total depth of this well. The sonic log is also relatively constant up to a depth of 2.75 km, then decreases, and then follows its expected trend again to a depth of ~3.5 km. The resistivity log decreases to a depth of 1 km, is relatively constant to a depth of 2.75 m (similar to the sonic log), and then increases to a depth of ~3.5 km.

From the geological context and wireline responses, overpressure in well No. 1 is considered to result from erosional unloading (i.e. exhumation). Overpressure was initially caused by compaction disequilibrium, indicated by relatively constant values of density, sonic, and resistivity logs. Sediments were eroded due to the uplift that took place during the middle Miocene (Moss and Chambers 1999; Chambers et al. 2004), while overpressure was maintained. Sediments in well No. 1 are already chemically compacted, as indicated by the sonic-density cross plot (Fig. 6a), showing an illitic (chemical compaction) trend. Below 2.75 km, compaction continues with depth, as indicated by the increase in effective stress at 3.3 km. Effective stress at 1.15 km is 8 MPa; at 3.3 km, it increases to 19 MPa.

In other wells onshore, the top of overpressure is much deeper than in well No. 1—for example, in well No. 6, where erosion is less substantial than in well No. 1, the top of overpressure is at 2.3 km (Fig. 5b). Measured pressure data in this well are much higher than hydrostatic, with excess pressure ranging from 30 to 33 MPa, equivalent to a hydraulic head of between 3.1 and 3.5 km, respectively. The presence of overpressure is also shown by the density, sonic, and resistivity logs. The values of these logs are out of their normal trend below the top of overpressure: the density is relatively constant with depth, whereas the sonic log increases and the resistivity decreases. Both loading and unloading mechanisms generate overpressure in this well. The shifting of the density log from its normal trend indicates that loading contributes to the overpressure in well No. 6. Moreover, the sonic-density cross plot (Fig. 6b) indicates that unloading (i.e. clay diagenesis) also contributes to the overpressure. Mudrock data follow an illitic trend and shift away from the trend at depth.

Density, sonic, and resistivity logs in mudrocks are commonly used to analyze pressure regimes within sedimentary basins (Mouchet and Mitchell 1989; Zhao et al. 2018; Dutta et al. 2021). A single trend for each log (i.e. density and resistivity increase while sonic decreases with depth) is usually developed for the hydrostatic zone or normally compacted sediments. However, this study suggests that the resistivity log does not exhibit a single response within the hydrostatic zone. Instead, resistivity trends correlate strongly with the changes in groundwater salinity—for example, the resistivity in well No. 6 (Fig. 5b) first decreases with depth, corresponding to the increase in groundwater salinity (see Fig. S3 of the ESM for the salinity profile of this well). Then, it increases until reaching the depth of the top of overpressure, where the resistivity decreases and is relatively constant below this.

In the Mahakam Delta area toward offshore, the top of overpressure ranges from 2.3 to 4.5 km, deeper within the delta and shallower offshore. However, the drilling of most wells in these two locations was terminated within the transition zone due to excessive overpressure, where pore pressures can approach the overburden stress—for example, at well No. 36 in the Mahakam Delta, the top of overpressure is at 3.7 km (Fig. S4 of the ESM). This well is located in Tunu Field, a giant gas field in the Lower Kutai Basin (Purwanto et al. 2017). Observed excess pressure ranges from 2 to 6 MPa and corresponds respectively to the hydraulic heads of 0.2–0.6 km. The effective stress within the overpressured zone decreases with depth, indicating unloading as the overpressure-generating mechanism. The top of overpressure in well No. 36 and in other wells in the Mahakam Delta coincides with the top of gas generation, as reported by Ramdhan and Goulty (2010, 2011), which points to the contribution of hydrocarbon generation to unloading. Furthermore, sonic and density data of well No. 36 (Fig. S5 of the ESM) within the overpressured zone follow the illitic trend and out of the trend at depths, suggestive of a contribution of clay diagenesis to overpressure.

Well No. 10 is an example of a well located offshore in the Peciko Field, another gas field within the Lower Kutai Basin. The top of overpressure in this well is at ~3 km (Fig. S4 of the ESM). The observed excess pressure within the overpressure zone is between 2 and 11 MPa, and equivalent to hydraulic heads between 0.2 and ~1 km. Similar to well No. 36, the effective stress below the top of overpressure decreases with depth, indicating unloading as the mechanism generating overpressure. Regarding well No. 36, the overpressured zone of this well is within the hydrocarbon generation zone, indicating hydrocarbon generation as the unloading mechanism. In addition, mudrocks below the top of the overpressure are in chemical compaction or illitic trend and shift from the trend at depths (Fig. S5 of the ESM), suggesting that clay diagenesis contributes to the generation of overpressure.

Studies reporting overpressure within the Lower Kutai Basin began in the 1990s. Although the study areas in each reported study cover most of the basin, only a few examples of pressure analyses are given in the papers. Bois et al. (1994) and Bates (1996) suggested that overpressure within the basin was generated by the loading mechanism (i.e. compaction disequilibrium). More recent studies by Ramdhan and Goulty (2010, 2011) and Ramdhan and O’Connor (2022) propose that unloading (i.e., gas generation) also contributes to overpressure within the Lower Kutai Basin. Drilling of some wells encountered hard overpressure where pore pressure is close to the overburden stress. This study, based on a larger dataset of analyses of pore pressure and hydraulic heads in 43 wells, similarly argues that high overpressure within the Lower Kutai Basin arises from loading and unloading mechanisms.

Besides hydrostatic and overpressure, underpressure also exists in the Lower Kutai Basin—for example in well No. 2 onshore, underpressure is found in carbonate units (Fig. S6 of the ESM), with depleted pressures of 0.4–0.5 MPa, equivalent to hydraulic heads of 41 and 54 m, respectively. The slight underpressure in this well is a natural phenomenon and was indicated by lost circulation during the drilling despite the mud weight used being close to hydrostatic. In contrast, in the Mahakam Delta, where hydrocarbons are produced, underpressure exists at depths up to ~2 km but does not naturally occur. Its occurrence is driven by hydrocarbon production, as reported by Setiawan and Rennie (1983) and Herdiyanto et al. (2018). The magnitude of pressure depletion, observed in well No. 14 (Fig. S6 of the ESM), is also much higher than those found in well No. 2 and range up to 11 MPa, equivalent to a hydraulic head of 1 km below sea level. A comparable example from the Denver Basin (Belitz and Bredehoeft 1988) also reports extreme hydraulic head depletion down to 0.9 km below the land surface. Complete lithological, pressure-stress depth plots, hydraulic head, wireline logs, and sonic-density cross plots for other wells are provided in the ESM.

In the Lower Kutai Basin, pressure data and computed hydraulic head distributions suggest recharge from meteoric water may replenish groundwater within the hydrostatic zone at depths up to the top of overpressure (e.g. ~2.3 km onshore). This deduction is supported by observed groundwater salinity presented in the next section in which a few locations are found to be fresh (TDS <1 g/L) at depths up to ~2 km (Fig. 7). A hydrogeologic model proposed by Paterson et al. (1997) also posits the potential of groundwater recharge onshore as “meteoric water invasion” up to a depth of ~3 km. However, both pressure and hydraulic heads within the overpressure zone indicate upward groundwater flow as similarly argued by Czauner and Mádl-Szőnyi (2013) and Csondor et al. (2020) from observations in Hungary. In addition, most groundwater salinity data in the overpressure zone indicate saline water (TDS >10 g/L).

Measured TDS data from 44 wells (Fig. 7) suggest that deep groundwater within the Lower Kutai Basin is mostly brackish and saline (111 samples of 117). Evidence of fresh groundwater at depths up to ~2 km is very limited (6/117). Interestingly, starting from a depth of ~2,500 m, where the temperature has reached ~100 °C and conditions favour chemical compaction (Bjørlykke and Høeg 1997; Bjørlykke 1998), TDS values decrease with depth. Clay diagenesis (e.g. smectite to illite or mixed-layer smectite-illite to illite transformation) is thought to occur below this depth (Ramdhan and Goulty 2011; Goulty et al. 2012) and contribute to sediment compaction by producing silica cement and overpressure generation through fluid expansion and load transfer. It may also produce water that is responsible for the observed decrease in the measured groundwater TDS. Clay diagenesis is also indicated by sonic-density cross plots of most wells, which show a shift from mechanical compaction or smectitic trend to chemical compaction or illitic trend, as illustrated in previous examples (Fig. 6).

Archie’s equation is employed to estimate NaCl profiles in 40 wells using resistivity logs. An empirical relationship between NaCl concentration and TDS is developed using power regression (Fig. 7c). The limit of TDS for fresh groundwater (1,000 mg/L) is approximately equal to a NaCl concentration of 320 mg/L; it is ~6,550 mg/L for the transition between brackish to saline groundwater (10,000 mg/L). These values are applied to characterize the groundwater salinity in each well. Figure 8a shows an example of the estimated NaCl profile at well No. 3 onshore. In addition to the available measured NaCl data, measured porosity data are also available in this well. Estimated porosity closely follows measured values.

The resistivity of sandstones at well No. 3 ranges from 4 to 103 Ωm where the measured porosity ranges from 0.17 to 0.36. The high resistivity in the middle Miocene sandstones (e.g. 43 Ωm at a depth of ~1,280 m) corresponds to the measured TDS of ~840 mg/L (NaCl concentration of ~215 mg/L). As the estimated NaCl profile indicates, deep fresh groundwater exists in this well up to a depth of ~1,315 m. Below this depth, the estimated NaCl increases with depth, from brackish to saline. The sonic-density cross plot (Fig. S7 of the ESM) indicates that mudrocks in this well have entered a transition zone from a smectitic trend (mechanical compaction) to an illitic trend (chemical compaction) at ~1,600 m. As can be observed, the estimated salinity below this depth slowly decreases, following the slowly increasing resistivity.

The lithology, resistivity and NaCl profiles of well No. 3 are unique to this well and are not observed in other wells, suggesting that deep fresh groundwater is a locally occurring phenomenon within the Lower Kutai Basin. Another example of wells located onshore, well No. 8 with the highest number of measured salinity data, indicates that groundwater below 500 m is either brackish or saline (Fig. 8b). The lowest measured NaCl is ~2,650 mg/L at 1,110 m, which equates to a TDS value of ~4,900 mg/L.

In well No. 8, measured and estimated NaCl values show that the groundwater salinity increases with depth up to ~1,800 m. Below this depth, estimated NaCl values are relatively constant, following the relatively constant resistivity log response. The density-sonic cross plot of well No. 8 (Fig. S7 of the ESM) indicates that the trajectory towards higher density and lower sonic log values along a smectitic trend slows below depths of ~1,800 m and transitions towards an illitic trend, suggestive of the contribution of clay diagenesis in reducing the groundwater salinity.

Within the hydrocarbon production area of the Mahakam Delta, deep groundwater is mostly brackish to saline. An exception is found in zones with high resistivity anomaly at depths ranging from ~1,500 to 2,000 m, representing the Freshwater Sand unit reported by Paterson et al. (1997). As an example, in well No. 23, the resistivity at depths ~1,750 to 2,000 m is up to 41 Ωm at ~1,800 m (Fig. S8 of the ESM), corresponding to the measured NaCl concentration of ~230 mg/L or TDS of 750 mg/L. Deeper, the maximum resistivity is much lower, 10 Ωm at ~3,560 m, whereas the corresponding measured NaCl is ~9,000 mg/L, equivalent to a TDS of ~12,400 mg/L. The estimated NaCl profile of well No. 23 indicates that fresh groundwater can only be found within the high resistivity zone. This zone lies within an illitic trend, as illustrated in the sonic-density cross plot (Fig. S9 of the ESM). This suggests that clay diagenesis may contribute to a freshening of groundwater in Wells No. 23, similar to Wells No. 3 and 8 onshore. However, unlike these wells, the sonic-density data in well No. 23 increase with depth.

Offshore, no fresh groundwater is indicated from either measured or estimated NaCl profiles—for example, in well No. 9 (Fig. S8 of the ESM), the maximum resistivity value is ~10 Ωm at 3,700 m. Measured groundwater data in this well indicate that groundwater is saline, with TDS values ranging from ~25,600 mg/L at ~3,170 m to ~30,950 mg/L at ~2,475 m. The estimated NaCl profile shows that the groundwater below 500 m is highly saline, with NaCl concentrations reaching up to more than 100,000 mg/L. Nevertheless, starting from the transition into the chemical compaction zone below ~1,200 m, both measured and estimated NaCl concentrations decrease with depth, again indicating the contribution of clay diagenesis in reducing the groundwater salinity. The sonic-density cross plot of this well (Fig. S9 of the ESM) illustrates that below ~1,200 m, the sonic and density data have shifted from the smectitic (mechanical compaction) trend. The salinity profiles for other wells can be seen in the ESM.

Despite uncertainty in the empirical constant, \(m\), in the formation factor (\(F\)), Archie’s equation remains an effective salinity (NaCl) predictor, especially when measured groundwater salinity data for calibration are available. A single empirical constant over a sedimentary basin or hydrocarbon field is often used (e.g. Gillespie et al. 2017; Stephens et al. 2019). In this study, the parameter \(m\) is defined differently in each well in order to match the measured NaCl and generally ranges from 1.1 to 2.4 for the Lower Kutai Basin’s dataset analysed in this study. The heterogeneity of sediments and their compaction state may be the most important factor affecting this empirical parameter—for example, in well No. 3 (Fig. 8a), the resistivity log indicates strong groundwater salinity variations with depth. Fortunately, four measured salinity data at different resistivity values are available. At this well, it is impossible to match the measured salinities using a single value of \(m\). In addition, uncertainty in porosity estimation could also greatly affect the groundwater salinity estimation. Gillespie et al. (2017) reported that for an uncertainty of 0.07 in the porosity, the resulting salinity (TDS) uncertainty is 8,000 mg/L, indicating that measuring porosity data is essential in estimating groundwater estimation. Thus, in the absence of measured porosity and groundwater salinity, the salinity estimation using Archie’s equation would be very uncertain.

In this study, observed decreases in salinity occur at depths where the temperature has been favourable for clay diagenesis (e.g. smectite to illite transformation), ~70 °C (Bjørlykke and Høeg 1997; Bjørlykke 1998). The sonic-density cross-plots in most wells show that the data have shifted from smectitic to illitic trends, indicative of clay diagenesis. Furlan et al. (1995) suggested that formation water in the Lower Kutai Basin (Mahakam Delta) derives from only two end-member sources, river water and seawater. The results of this study suggest a third member, compaction water, possibly explaining salinity decreases in the Freshwater Sand units within the Lower Kutai Basin, as discussed by Said et al. (2018). However, measured salinity data indicate that compaction water is insufficient to produce fresh groundwater at depth. Most water released from clay diagenesis occurs within the transition zone from mechanical to chemical compaction (Dutta et al. 2021). Depending on the clay mineral content, the maximum increase of freshwater due to clay diagenesis may range between 4 and 15% of the total rock volume, as discussed in the literature (e.g. Burst 1966; Bruce 1984; Colten-Bradley 1987; Bjørlykke 1997; Osborne and Swarbrick 1997). Quantifying the contribution of water generated from clay diagenesis in freshening deep groundwater within the Lower Kutai Basin is subject to further investigation.

Groundwater chemistry data from 44 wells are provided in Table S1 of the ESM; samples range in depth from ~500 to 4,250 m. The TDS computed as the sum of the major cations and anions ranges from ~425 to 36,100 mg/L, whereas the pH measured in the laboratory is from 6.7 to 10.4. Seawater data from Furlan et al. (1995) are included as a comparison. Mg²⁺ concentrations in groundwater are highest (~580 mg/L) in well No. 2 (from a carbonate unit) and substantially lower than in seawater (~1,250 mg/L). Concentrations of Mg²⁺ in other wells range from 2 to ~240 mg/L. Hydrochemical facies of deep groundwater samples in this study are visualized in Fig. 9.

Deep groundwater types comprise Na⁺/Cl^– (98 samples), Ca²⁺/Cl^– (1 sample), Na⁺/HCO₃^– (11 samples), and Na⁺ – Ca²⁺/HCO₃^– (7 samples). The Na⁺/Cl^– type is observed in 40 wells (Fig. 9c) at depths ranging from 1,030 to ~4,250 m and with TDS ranging from ~3,590 to ~36,100 mg/L. All groundwater samples derive from sandstones, except in well No. 2 with a Ca²⁺/Cl^– type where the sample was collected from a carbonate unit; this sample of Ca²⁺/Cl^– type is from a depth of ~670 m and has a TDS value of ~16,900 mg/L.

Na⁺/HCO₃^– type waters exist in seven wells at depths ranging from ~500 up to 2,270 m with TDS values between ~425 and 15,200 mg/L. Groundwater with Na⁺ – Ca²⁺/HCO₃^– type is found in three wells at depths ranging from ~700 to 2,000 m. The TDS of this groundwater type ranges from 470 to ~4,800 mg/L.

Available data suggest groundwater in which Cl^– is the dominant anion exists across the entire area of Lower Kutai Basin: onshore, in the Mahakam Delta, and offshore (Fig. 9c), from depths of 1,030 up to ~4,250 m. Groundwater with HCO₃^– as the dominant anion is only found onshore and in the Mahakam Delta at depths from ~500 m to 2,270 m. Cl^– is the dominant anion in 99 of 117 groundwater samples. HCO₃^– is the dominant anion in the 18 samples and reflects the influence of meteoric water, as discussed by Bazin et al. (1997). Deep groundwater (>500 m) samples from the Lower Kutai Basin are strongly depleted in magnesium. Magnesium concentrations in all samples are lower than their concentration in seawater, which is a characteristic of brine or connate waters (e.g. White 1957). Brines can have TDS values exceeding ~100,000 mg/L (Freeze and Cherry 1979); measured TDS values in this study are all lower than that of seawater TDS (Table S1 of the ESM).

From deuterium and oxygen-18 data (Fig. S10 of the ESM), Furlan et al. (1995) suggested that deep groundwater within the Mahakam Delta area comprises meteoric water and seawater components; stable-isotope ratios of O and H indicate a meteoric origin of water in wells located within the delta at Handil and Tambora Fields; seawater is indicated in wells located offshore at Bekapai and Attaka Fields. This interpretation is consistent with regional groundwater flow regime discussed previously in which groundwater flows from the Mahakam Delta offshore (Fig. 4b). Furlan et al. (1995) also noted changes in the isotopic composition of some groundwater samples due to rock–water interactions.

Bazin et al. (1997) observed in the Mahakam Delta that: chloride concentrations in the groundwater samples are lower than in seawater, magnesium concentrations are strongly depleted, sodium concentrations are enriched, and alkalinity is high, especially in samples with low salinity. Lower chloride concentrations were thought to arise from mixing between river and seawater (Furlan et al. 1995; Bazin et al. 1997). Dolomite and pyrite precipitation may serve to deplete magnesium concentrations, whereas sodium enrichment may relate to plagioclase dissolution (Furlan et al. 1995). According to Bazin et al. (1997), high alkalinity is a signature of meteoric water ‘invasion’ that has occurred since the Pliocene. Furlan et al. (1995) summarized the processes that control the groundwater chemistry in the Mahakam Delta: illitization of smectite, precipitation of carbonate minerals and plagioclase (albite), and K-feldspar dissolution. The combination of these processes during the groundwater migration was permissible owing to the young age and restricted volume of the basin.

Measured TDS (Fig. 9) and NaCl correlations (Fig. 10) between wells onshore, in the Mahakam Delta, and offshore suggest that deep (>500 m) fresh (TDS ≤1,000 mg/L) groundwater is not a regional phenomenon within the Lower Kutai Basin but is of localized occurrence. Onshore, deep fresh groundwater can be found only in two wells at depths between 500 and 1,315 m, whereas offshore, there is no evidence of deep fresh groundwater.

In the Mahakam Delta, some indications of deep fresh groundwater can be found within the Freshwater Sand unit, marked by high anomaly resistivities (e.g. 41 Ωm at well No. 23 with corresponding measured TDS as low as 750 mg/L). The estimated NaCl profiles also show depleted NaCl concentrations; however, fresh groundwater within the Freshwater Sand unit in the Mahakam Delta is only indicated when the resistivity equals or exceeds ~32 Ωm, which is found only in 11 wells. Lower resistivity values correspond to brackish measured TDS in well No. 23 (Fig. S8 of the ESM). In addition, available groundwater samples (Fig. 9) show that HCO₃^–1 dominates all deep fresh groundwater. This study shows that deep groundwater within the Freshwater Sand unit is not entirely fresh (TDS ≤1 g/L) and may reflect that the term “freshwater” used in oil and gas exploration can simply refer to less saline water.

Deep fresh groundwater within the Lower Kutai Basin is only identified above the top of overpressure (Fig. 10) or within the hydrostatic zone, where regional groundwater flow is indicated (Fig. 4b). A possible controlling factor for deep fresh groundwater onshore (e.g. in well No. 3) is recharge by meteoric water. Of all wells, the sandstone sequence in this well is the thickest. These sandstones may have outcropped further north to the northwest due to the uplift that took place in middle Miocene (Moss and Chambers 1999; Chambers et al. 2004). If so, this would have provided a path for continuous meteoric water flow into the aquifer. In addition to freshening from meteoric water flows, water contributions may also derive from clay diagenesis, which starts at temperatures ≥70 °C (Bjørlykke and Høeg 1997; Bjørlykke 1998) and is observable from sonic-density cross plots (e.g. at well No. 8 in Fig. S7 of the ESM). Clay diagenesis may present a possible explanation for salinity reductions at depths onshore. It is not, however, able to reduce groundwater salinities to that of fresh groundwater, and the actual contribution remains unclear.

In the Mahakam Delta, previous studies (e.g. Gwinn et al. 1974; Paterson et al. 1997) have reported the existence of deep fresh groundwater in the “Freshwater Sand” units, hypothesised to be supplied by meteoric water to explain their low salinity. This study explores the evidence and supports this. In addition to freshening resulting from meteoric water flow, the results of this study suggest that clay diagenesis may also contribute to the decrease in the groundwater salinity. Nevertheless, the analysis of available evidence in 43 wells from oil and gas exploration shows that groundwater within the Freshwater Sand unit is mostly brackish.

For water supply, brackish groundwater (TDS between 1,000 and 10,000 mg/L) within the Lower Kutai Basin may still be usable with advances in desalination technology. Brackish groundwater desalination can potentially be advantageous to seawater desalination. Along with fresh groundwater, brackish groundwater is considered an underground source of drinking water (USDW) by the US Environmental Protection Agency (2015) and, as such, is protected from contamination from sources such as waste injection in Indonesia. Use of brackish groundwater in Indonesia is minimal as shallow groundwater is generally sufficient for water supplies in most locations. Brackish groundwater may become an alternative for water supplies within the Lower Kutai Basin, including the new capital city of Indonesia.