An application of U/Th-series radiotracers to study groundwater transport processes in the surficial and Upper Floridan Aquifer System in central Florida, USA

Abstract

U-Th series radionuclides are effective, naturally occurring tracers for studying groundwater transport mechanisms. Dissolution and sorption/desorption processes involving Fe-Mn oxyhydroxides play a major role in the mobility of select trace elements and radionuclides. For example, as radium is strongly bound to manganese oxides in most natural waters, the behavior of Mn in groundwater can be expected to affect Ra adsorption–desorption rates. In this study, the redox state of the aquifer in central Florida was examined to investigate the groundwater mobility of Ra and other trace elements. From a suite of 13 groundwater samples and complementary soil core samples, U/Th parent–daughter disequilibria were utilized to obtain sorption–desorption rate constants for radium. The large observed variability in ²²²Rn and ²²⁴Ra activities can be attributed to changes in fine-scale, phosphorite-bearing lithologies. The range of ²²³Ra/²²⁶Ra activity ratios is quite large (0.003–0.156) relative to the theoretical ratio of aged host rock, 0.046, indicating faster replenishment of ²²³Ra compared to ²²⁶Ra. The adsorption rate ranged from 0.03 to 2.4 min⁻¹, corresponding to residence time of 0.4 to 33 min for Ra in groundwater. In contrast, the Ra desorption rate is slower, ranging from 0.5 to 21 × 10⁻⁴ min⁻¹, which corresponds to a desorption time scale of 0.3–14 days. The retardation factor varied between (0.12 ± 0.03 and 7.0 ± 2.7) × 10³. Within these samples, there was no significant correlation between the adsorption/desorption rate constants and the concentrations of redox-sensitive trace elements (i.e., Fe, Mn, or As), suggesting that redox processes alone do not control the adsorption–desorption constants. Furthermore, there is no apparent relationship between alkalinity and Ra adsorption-desorption rate constants, indicating that weathering processes alone do not control Ra sorption. The distribution coefficient varied between (0.16 and 9.3) × 10³ L kg⁻¹ (mean: 4.1 ± 4.0 × 10³). This study provides insight into the adsorption–desorption kinetics of Ra within an aquifer controlled by fine-scale lithogenic and redox processes.

1 Introduction

One promising area of groundwater transport research is studying constituent transport kinetics with isotope-based water mass dating and tracing techniques (e.g., Porcelli and Swarzenski, 2003; Kiro et al., 2015; Briganti et al., 2020; Garcia-Orellana et al., 2021). Naturally occurring U-Th series radionuclides have been developed and successfully utilized to enhance our understanding of groundwater transport processes and kinetics (Krishnaswami et al., 1982, 1991; Bourdon et al., 2003; Porcelli, 2008). Furthermore, they also serve as analogs for quantifying the distribution coefficient, retardation factor, and subsurface transport velocity of radioactive and stable nuclides, including chemical pollutants. The factors controlling the concentrations of U-Th series radionuclides in groundwater include variable weathering, adsorption, recoil, surface production, and decay rates derived from their intrinsic physical, chemical, and nuclear properties.

The study site is located within phosphorite-bearing deposits of Central Florida, where U/Th series radionuclides have been utilized to assess aquifer transport processes (Burnett and Veeh, 1977; Osmond and Cowart, 1982; Cowart and Burnett, 1994). Parent–daughter disequilibria of U-Th series radionuclides in groundwater systems are caused by transport and scavenging through several physicochemical processes, including adsorption–desorption, dissolution–precipitation, dispersion, ion-exchange, diffusion into blind pores, radioactive decay, and alpha recoil. Of the ²³⁸U-series radionuclides, the activities of ²³⁸U, ²³⁴Th, ²³⁴U, ²³⁰Th, ²²⁶Ra, and ²²²Rn in groundwater have been reported to vary over eight orders of magnitude, from ~10⁻² dpm L⁻¹ for ²³⁰Th to 10⁶ dpm L⁻¹ for ²²²Rn (Krishnaswami et al., 1982; Luo et al., 2000; Tricca et al., 2001; Porcelli and Swarzenski, 2003; Swarzenski et al., 2013; Vengosh et al., 2022). These large variations are attributed to differences in the affinity of the dissolved species to the aquifer matrix and their solubility and residence times in water. Pronounced disequilibria between parent–daughter pairs (i.e., ²³⁴U/²³⁸U activity ratios) can provide useful information for fingerprinting (i.e., source tracking) and age dating (e.g., Weinstein et al., 2021; Stirling et al., 2007).

The mechanisms that control retardation factors (R, the rate of transport of a chemical species decreased by a factor R relative to the groundwater flow rate due to interaction with aquifer host solid surfaces) and adsorption–desorption rate constants are still not fully understood; particularly, the dependence of these factors on physicochemical and hydrological aquifer characteristics. Previous studies have primarily focused on how the major ion concentrations control the adsorption/desorption rate constants and retardation factors of radium (Krishnaswami et al., 1982, 1991; Laul and Smith, 1988; Copenhaver et al., 1992, 1993; Ku et al., 1992; Hussain, 1995; Luo et al., 2000; Porcelli and Swarzenski, 2003; Swarzenski et al., 2013; Grozeva et al., 2022; Vengosh et al., 2022). However, little is known about the relationship between oxidation–reduction potential and dissolved oxygen concentration (i.e., hypoxic or anoxic conditions) on adsorption–desorption rate constants. These effects could prove to be important because the mobility of elements such as arsenic and other redox-sensitive species (Fe, Mn, NO²⁻, SO²⁻, etc.) depends on the oxidation–reduction state of an aquifer. The chemical form of Fe-Mn oxide coatings at mineral surfaces also depends on these oxidation–reduction conditions, which affect the removal of Ra when it is released into the groundwater by recoil mechanisms. The main objective of this investigation was to quantify the relationship between the concentrations of redox-sensitive species and adsorption–desorption rate constants and retardation factors obtained using ²²²Rn and Ra isotopes. For the given lithology of this study site, this study provides the rate of migration of Ra compared to that of groundwater and adds useful information for characterizing groundwater transport of trace metals and tracing groundwater flow.

2 Materials and methods

2.1 Study area

The study area encompasses the community of Fuller Heights and the immediate surrounding area in Polk County, central Florida, USA (Figure 1). Fuller Heights is a relatively small community (~3 km²), located ~2 km northwest of the town of Mulberry, which was established over half a century ago. The community is partially surrounded by heavy industrial activity. A large industrial park consisting of chemical industries adjoins the southeast and is serviced by a railroad. Additionally, there are two former phosphate-mine pits that were never filled in after mining operations to the south, as well as a regional wastewater treatment facility located adjacent to the community in the northeast. The broad geographic area, with land elevations ranging from ~30 to 40 m above sea level, is characterized by a network of surface drainage streams and ponds connecting wetlands, residential areas, and forests.

Figure 1

The geology across the Fuller Heights area is relatively uniform and includes clastic and carbonate lithologies representing Eocene through Pleistocene sedimentary deposits (Figures 2A, B). Starting at the surface, the first ~6 m below land surface (BLS) consists of unconsolidated Pleistocene and/or Pliocene-age medium-grained sands. The gradual transition to finer-grained material denotes the top of the Peace River Formation, a Miocene-age stratum composed of interbedded quartz sands, clays, and thin carbonates (Spechler and Kroening, 2007). Beneath the sandy clay, a gravel-sized phosphate-rich clay lithology representing the Bone Valley Member, which is highly prized by the phosphate mining industry, is sometimes encountered. The lower Peace River Formation contains a series of interbedded sands, sandy clays, and carbonates that extends down to ~18 m BLS. The top of the lower Miocene-age Arcadia Formation is likely represented by the transition from sand and clayey sand lithologies to substantial calcareous clay (Figures 2A, B). Fine-grained sand, phosphate, and interbedded partially dolomitized limestones are found within this clay unit. The Arcadia Formation transitions to interbedded limestones and calcareous clays that extend to depths below ~27 m BLS.

Figure 2

There are four aquifers present in the Fuller Heights area of central Florida (Spechler and Kroening, 2007). The surficial aquifer occurs in the unconsolidated clastic Pleistocene and/or Pliocene-age sands. An upper intermediate aquifer occurs within the relatively thin, discontinuous limestone beds and sands of the Peace River Formation. Most of the Peace River Formation is composed of poor-permeability clays, limiting the use of the upper intermediate aquifer to small-capacity domestic water supply. The potentiometric surface map indicates that the surficial and upper intermediate aquifers are inferred to be in communication.

A lower intermediate aquifer occurs within the Arcadia Formation limestones below the substantial calcareous clay zone and appears to be compartmentalized from the two shallower aquifers. The much deeper Floridan aquifer, which occurs in the lower Miocene through middle Eocene-aged calcareous sands, clays, and limestones, is the principal source of water regionally.

The Florida Department of Environmental Protection (FDEP) was requested in 2006 to determine the source(s) of high concentrations of arsenic and other redox-sensitive species in groundwater wells in Fuller Heights. For decades, this community has relied on private supply wells and septic tank systems for its water and sanitary sewer needs, respectively. Based on the varying depths and cased intervals of these potable wells, it is likely that groundwater is being withdrawn from the surficial and upper intermediate aquifers, with a few deeper wells penetrating the lower intermediate aquifer.

2.2 Field sampling

To geochemically fingerprint the source(s) of groundwater, sampling was conducted on a suite of groundwater wells (eight potable wells and six monitoring wells), four surface water sites, and a shallow vertical sedimentary core within a 3 km² area for this study (Figures 2A, B). The depths of private supply wells typically range from ~15–30 m BLS, with common open-hole intervals of ~6.1–9.1 m, but precise casing and perforation depth information is unavailable. The DEP-5 monitor well cluster (DEP-5S, DEP-5I, and DEP-5D) includes a set of three different well depths (shallow, intermediate, deep, respectively) at a single site.

Potable wells were sampled using the FDEP Standard Operating Procedure (SOP)—Field Sampling (FS) 2300 Guidelines for Drinking Water Sampling, while monitoring wells were sampled using SOP FS 2200 Guidelines for Groundwater Sampling. Sampling locations, aquifer descriptions, and standard water quality parameters (temperature, pH, dissolved oxygen, specific conductivity, salinity, and oxidation–reduction potential) were recorded and are presented in Table 1. Monitor wells were purged and sampled using either a Masterflex^® E/S portable peristaltic pump or a stainless steel and Teflon^® constructed Grundfos^® Redi-Flo2 submersible pump. The peristaltic pump was outfitted with L/S15 silicone tubing in the pump head and -inch (0.64 cm) i.d. polyethylene tubing placed down the well, while the submersible pump was connected to ” (1.27 cm) i.d. polyethylene tubing. The potable wells were prepared for sampling by purging the well and associated holding tanks and piping using the pump connected to the well. Groundwater samples were collected from the spigot located closest to the well itself. Wellbores were thoroughly flushed by pumping for at least 20 min to minimize the effects of aging (mainly for ²²³Ra, ²²⁴Ra, and ²²²Rn) and sorption losses during storage. All wells were purged until the stabilization criteria for pH, temperature, specific conductance, dissolved oxygen, and turbidity were met.

Measurements of temperature, pH, dissolved oxygen concentration, and specific conductivity were made using a calibrated YSI 600XL multi-parameter water quality sonde. The oxidation–reduction potential (ORP) was measured using the YSI 600XL (the quoted accuracy specification for the YSI ORP sensor is ±20 mV in natural water). Other ancillary parameters were determined by following established EPA protocols: EPA 300 for chloride and sulfate; EPA 310-1 for alkalinity; EPA 350.1 for ammonia; EPA 353.2 for nitrate and nitrite; EPA 365.4 for total phosphorus; EPA 376.2 for sulfide; EPA 6020 for elements including As, Fe, and Mn. Radon-222 activities were measured using a RAD7 detector routed through a single air–water exchanger (Burnett et al., 2001; Burnett and Dulaiova, 2003; Swarzenski et al., 2006). Radium-223 and ²²⁴Ra activities were assayed using a delayed-coincidence alpha counting technique (Moore and Arnold, 1996; Swarzenski et al., 2001, 2006). The ²²³Ra and ²²⁴Ra activities were recounted after ~20 days to correct for supported ²²⁴Ra activities (from ²²⁸Th decay) and were decay-corrected to the time of sampling. Propagated errors for the delayed coincidence counters are typically < 10%. After counting the short-lived Ra isotopes, the fiber was leached with a 6M HCl-H₂O₂-hydroxylamine hydrochloride mixture to quantitatively remove Ra from the fiber. The Ra was co-precipitated with Ba by adding a Ba(NO₃)₂–H₂SO₄ mixture (Moore, 1976). The BaSO₄ precipitate was counted after 20 days (allowing for the in-growth of ²²²Rn daughters) and analyzed in a high-purity Ge well detector coupled to an InSpector (CANBERRA Inc.). The ²²⁶Ra and ²²⁸Ra activities were quantified using gamma energies of 352 and 609 keV for ²²⁶Ra and 338 and 911 keV for ²²⁸Ra.

The Walker soil core was collected and sub-sampled at depths of 1.83, 5.18, 8.23, and 14.3 m to measure Th isotopes (²³²Th, ²³⁰Th, and ²²⁸Th) by alpha spectrometry (Trimble et al., 2004). Ra isotopes were also measured in the soil profile to evaluate the vertical variations in Ra concentrations. A suite of selected elemental analyses was conducted by ICP-MS for As, Fe, and Mn (Swarzenski et al., 2006).

The uncertainties reported in the activities of radionuclides are propagated errors arising from counting statistics, spike calibration (for alpha spectrometer determination), and calibration of the counting instruments. The activities of ²²⁴Ra, ²²³Ra, and ²²²Rn were decay corrected to the time of collection.

2.3 Modeling

The major sources of U-Th series radionuclides to groundwater systems include (a) congruent dissolution of aquifer solids; (b) in situ radioactive decay of dissolved parent nuclides; (c) direct recoil across the solid–liquid boundary resulting from radioactive decay in the solid; and (d) desorption from solid surfaces. The concentrations of U-Th series radionuclides in groundwater systems are thus governed by the rates of mineral dissolution–precipitation, adsorption/desorption rates of parent and daughter nuclides, the degree of retardation in nuclide mobility, the distribution of ²³⁸U, ²³⁵U, and ²³²Th in mineral grains, dispersive and diffusive transport of fluid, and other physicochemical properties of interest in the rock–water system (Krishnaswami et al., 1982; Ku et al., 1992, 1998; Porcelli and Swarzenski, 2003). The diffusion and dispersion of U-Th radionuclides were assumed to be small, and cases where their dissolution and precipitation are not significant were considered (Krishnaswami et al., 1982). Instead, the major source of short-lived radionuclides in solution is from recoil, both from aquifer solids (lattice-bound) and from the adsorbed parent isotopes. All four naturally occurring radium isotopes (²²⁶Ra, t_1/2 = 1,600 y from ²³⁰Th; ²²³Ra, t_1/2 = 11.4 d from ²²⁷Th; ²²⁴Ra, t_1/2 = 3.66 d from ²²⁸Th; and²²⁸Ra, t_1/2 = 5.77 y from ²³²Th) are directly derived from the alpha decay of an insoluble Th parent. These isotopes occur in subsurface fluids at concentration levels that are an order of magnitude higher than those of their immediate parent thorium isotopes due to a continuous supply via alpha decay.

In aquifers, radionuclides are operationally separated into three pools: dissolved, sorbed onto the solid matrix, and lattice-bound. The exchange of radionuclides (sorption–desorption) between the dissolved and sorbed phases occurs primarily through dissolution, precipitation, and/or recoil (Ku et al., 1992, 1998; Luo et al., 2000; Porcelli and Swarzenski, 2003).

It was demonstrated that the application of ²²⁴Ra–²²⁸Ra pair can be used to determine adsorption–desorption rate constants and retardation factors of Ra isotopes in both freshwater (Krishnaswami et al., 1982; Copenhaver et al., 1992) and saline water (Krishnaswami et al., 1991). Note that both ²²⁴Ra and ²²⁸Ra are produced by recoil from the host mineral; therefore, the production rates are expected to be equal, although ²²⁸Ra is the first decay product while ²²⁴Ra is the fourth decay product in the ²³²Th-series chain. Additionally, the concentration of ²²⁸Th is expected to be lower than that of ²³²Th due to recoil of ²²⁸Ra into the water. Thus, the estimated recoil rate of ²²⁴Ra is 70% that of ²²⁸Ra (Krishnaswami et al., 1982).

The fundamental assumptions include: (i) the major supply mechanism of short-lived Ra isotopes to groundwater is recoil rejection from the aquifer solids following their production via alpha decay of the parent Th; (ii) all radon-222 in groundwater is derived from recoil (with no removal of Rn by adsorption and no addition from desorption) and thus serves as a tool to quantify the recoil supply of alpha decay-produced U-Th nuclides to the groundwaters; and (iii) the decay and production of U-Th series radionuclides are in steady state. If P is the supply rate (dpm L⁻¹) of a nuclide to solution by dissolution, in situ production, and recoil (atoms s⁻¹ volume⁻¹), k₁ and k₂ are the first-order adsorption and desorption rate constants (time⁻¹), respectively, and N_d and Ns are the concentrations of the nuclide in water (atoms/volume of H₂O) and adsorbed on the aquifer matrix (expressed as equivalent concentration in water, atoms/volume of H₂O), then, from mass balance considerations (Krishnaswami et al., 1982), one can write the following equations (assuming radionuclide distributions are in steady state):

The ratio of the activity (Ω = λNd) of a nuclide to its production (P) in solution can be calculated from Equations 1, 2:

The adsorption and desorption rate constants are expected to be the same for two isotopes of the same element, assuming that isotopic fractionation is negligible. If “I” and “j” refer to two isotopes of an element, then using the mass balance equations for each of these nuclides can be combined and solved for k₁ and k₂ (Krishnaswami et al., 1982):

and

where i and j refer to two isotopes of the same element, specifically ²²⁴Ra and ²²⁸Ra in this study. From the measured activities of ²²²Rn, ²²⁴Ra, and ²²⁸Ra in the solution phase, and the specific activities of ²³⁰Th, ²²⁸Th, and ²³²Th in the solid phase, the values of k₁ and k₂ can be determined using Equations 4, 5.

3 Results and discussion

3.1 Major ion geochemistry in surface and subsurface waters

The temperature, pH, alkalinity, oxidation–reduction potential (ORP), and concentrations of dissolved oxygen (DO) and major anions (chloride, nitrate and nitrite, sulfate, ammonia, and phosphorus) for the suite of groundwater samples are given in Table 1. The major ion geochemistry of the surface and groundwaters provides important information about their environmental conditions and serves as a basis for diagnosing whether surficial contamination via industrial activities has occurred.

The pH of groundwater samples varied between 5.3 and 7.7, indicating slightly acidic to relatively neutral conditions. Chloride concentrations ranged from 0.13 to 423 mmol L⁻¹ and generally correlated with specific conductance (SC) measurements (Table 1). Nitrate (+ nitrite) concentrations varied from 0.4 to 1,285 μmol N L⁻¹. Sulfate (+ sulfite) concentrations varied between 0.01 and 1.87 mmol L⁻¹, except for the three sites where subsurface waters from industrial effluents were collected. If sulfate reduction were occurring to a substantial extent, significantly elevated levels of H₂S would have been detected.

Dissolved oxygen concentrations, which are important for characterizing mineral species in the environment, ranged from 5.9 to 146 μmol L⁻¹ (Table 1). Based on DO concentrations, subsurface environments are classified as toxic (>30 μmol L⁻¹ with hematite, goethite, ferrihydrite, MnO₂-type phases with no organic matter), suboxic (< 30 μmol L⁻¹ O₂ ≥ 1 μmol L⁻¹, hematite, goethite, ferrihydrite, MnO₂-type phases, and minor organic matter), or anoxic (O₂ < 1 μmol L⁻¹) (Berner, 1981; Eby, 2004). Of the fourteen groundwater wells sampled, nine fall into the suboxic category and five are oxic. None of the groundwater samples were anoxic (< 1 μmol L⁻¹), implying the existence of relatively oxygenated conditions down to depths of at least 30 m. The oxidation–reduction potential (ORP), which measures the tendency of a water body to either gain (reduced) or lose (oxidized) electrons, varied from −82 to 226 mV. Water samples with a higher reduction potential tend to gain electrons, while water with a lower reduction potential tends to lose electrons.

Since casing depths were reasonably well-known for the private groundwater wells, depth profiles could be plotted with DEP-5 site wells whose casing depths were accurately recorded. The groundwater samples often lacked vertical trends for the measured geochemical parameters (Table 1). Temperature, DOC, specific conductance, chloride, nitrate (+ nitrite), sulfate (+ sulfite), and ammonia showed no systematic trends with depth (Table 1). Deeper wells (such as DEP-5D and Harrison well) had very low concentrations of both nitrate and sulfate, possibly suggesting that minor nitrate and sulfate reduction occurred at depth (Table 1). There were, however, distinct depth trends with pH, ORP, and phosphorus. The limited geochemical components also suggest partial compartmentalization between aquifer zones. The deeper aquifer samples appear to be characterized by neutral pH, elevated alkalinity, and low DO and ORP values compared with the shallow and upper intermediate aquifers (Table 1).

Surface water geochemistry exhibits high variability but appears to be affected by industrial activities compared to an uncontaminated nearby background (BKG) pond (Table 1). To geochemically fingerprint the source(s) of groundwater contamination, the waste stream from KC Industries (KCI—a fluoride manufacturer) was sampled. The waste stream was highly acidic (pH < 1) and contained the highest concentrations of phosphorus (3,551 mmol L⁻¹) and Cl⁻ concentrations (818 mmol L⁻¹), nearly three orders of magnitude higher than those in the potable groundwater wells (Table 1). Both the South and North ponds, historically utilized as wastewater holding pits, also have highly elevated phosphorus and Cl⁻ concentrations. However, none of the potable water wells, including the DEP-5S and DEP-5I wells, appear to have been affected by the high Cl⁻ concentrations found in the surface waters or the KCI waste stream. The primary source of Cl⁻ in the potable groundwater seems to be from the congruent dissolution of the aquifer matrix. Elevated phosphorus concentrations and low pH in the DEP-5S well may result from general surface activity contaminating the shallow aquifer while being partially compartmentalized from the deeper aquifers. The three industrial water monitor wells may indicate localized groundwater contamination, with the CW-16S clearly being affected by adjacent industrial activity.

3.2 Elemental abundances and activity ratios of ²³⁸U- and ²³²Th-series radionuclides in a soil core

The Walker soil core was subsampled at four depths (1.83, 5.18, 8.23, and 14.3 m) to obtain representative geochemical baseline data, but it only extends to about half the depth of the deepest groundwater well. The activities of ²³⁸U (as measured using ²³⁴Th) in the soil core varied between 3.5 and 43.7 dpm g⁻¹ (Table 2), with the highest activity found at 8.23 m (Table 2), which corresponded with the phosphorus peak (Figure 2B). The U-series radionuclides (²³⁴Th, ²³⁰Th, ²²⁶Ra, and ²¹⁰Pb) are about an order of magnitude higher at 5.18 and 8.23 m compared to 1.83 m depth, likely due to the reported phosphorite layers at these depths (Figure 2B). At 14.3 m, the U-series nuclide activities (²¹⁰Pb, ²³⁴Th, ²³⁰Th) are between those of the other three layers. The ²¹⁰Pb/²³⁸U activity ratios (AR), which varied between 0.91 and 1.59, had a mean value of 1.19 and showed no consistent trend with depth. The higher ²¹⁰Pb/²²⁶Ra activity ratios (AR) at 1.83 m (1.17 ± 0.11), 5.18 m (1.13 ± 0.03), and 14.3 m (1.14 ± 0.06) likely indicate the higher mobility of ²²⁶Ra [Kd = (4.1 ± 3.0) × 10³ to 7.4 ± 3.1 × 10³ (N = 75, IAEA, 2010)] compared to ²¹⁰Pb (9.01 × 10³ to 3.69 × 10⁵, IAEA, 2010; International Atomic Energy Agency, 2025). The higher mobility of Ra compared to Th preferentially leads to greater disequilibrium in subsurface environments (Hussain and Krishnaswami, 1980; Krishnaswami et al., 1982). There is also a significant disequilibrium between ²³⁰Th and its immediate daughter product ²²⁶Ra, with the ²²⁶Ra/²³⁰Th AR ranging between 0.37 ± 0.02 and 1.38 ± 0.06 (mean value of 0.89). The ²³²Th specific activity ranged from 0.66 ± 0.08 to 1.59 ± 0.04 dpm g⁻¹ (Table 2), which is significantly lower than the average upper crustal value of 2.52 dpm g⁻¹ (10.3 ppm ²³²Th, 1 ppm = 0.2448 dpm, calculated from values taken in Wedepohl, 1995). If ²³⁸U and ²³²Th are in secular equilibrium (in the host rock) with ²²⁶Ra and ²²⁸Ra, respectively, then the expected ²²⁶Ra/²²⁸Ra AR is 0.73 (²³⁸U upper crust average ²³⁸U concentration = 2.5 ppm or 1.85 dpm g⁻¹). The measured activity ratio varied between 9.4 ± 1.3 and 43.6 ± 6 (mean: 16.9), indicating gross disequilibrium in the aquifer host rock between the parent and daughter from ²³⁸U to ²²⁶Ra, as well as from ²³²Th to ²²⁸Ra. The mean ²¹⁰Pb/²³⁴Th activity ratio (AR) of >1.0 is indicative of dominant dissolution–weathering cycles, resulting in the sorption of daughter products on mineral surfaces, which can release higher amounts by recoil, as opposed to the expected loss of ²²²Rn, which would result in ²¹⁰Pb/²³⁴Th AR values < 1.0.

Higher concentrations of calcium, phosphorus, and aluminum in the sediment core likely track carbonate, phosphate, and lithologic changes, respectively. The abundances of Al and Sr varied by factors of 2.6 (1.44%−3.68%) and 3.7 (210–771 ppm), respectively (Table 2), indicating that the 1.83 m layer had the highest lithogenic sediment. The P and Ca concentrations varied by factors of 55 (1,060–58,800 ppm) and 138 (0.11%−15.2%), respectively, with the 8.23 m layer having the highest carbonate (Table 2). The Fe and Mn concentrations varied by factors of 7.2 (0.17%−1.23%) and 37 (9–333 ppm), respectively, with the highest concentrations at 14.3 m. The water chemistry at these different depths is also expected to differ due to these variations in lithology.

Long-term weathering and dissolution–precipitation cycles play a key role in controlling the activities of U-Th series nuclides in the groundwater system. Based on modeling calculations, Tricca et al. (2001) estimated that the surface coating of Th corresponds to about 10% of the total Th content of the rock and serves as the source of their daughter products, which are readily available to the water. The sorbed Th is proposed to be derived from an earlier stage of weathering in the formation of the aquifer, and its concentration in the surface coating is dependent on the solubility of ThO₂, which in turn depends on the chemical state of the aquifer (Reynolds et al., 2003).

3.3 Activities of ²²²Rn and Ra isotopes in groundwater

It has been shown that of all the U-Th daughter nuclides, ²²²Rn activity is the highest in groundwater systems due to the least reactive nature of radon and because it remains in groundwater without removal by precipitation or sorption. The activity of ²²²Rn varied between 6 and 51 × 10³ dpm L⁻¹, while ²²⁶Ra activities varied between 0.1 and 10.3 dpm L⁻¹ (Table 3). The activity of ²²²Rn is about 10³-10⁵ times higher than that of ²²⁶Ra or any other nuclide in the ²³⁸U decay series but is comparable to the amount derived from the congruent dissolution of solids with which the water is in contact. A plot of the activity ratio ²²²Rn/²²⁴Ra vs. ²²⁶Ra/²²⁸Ra does not show any systematic trend (Figure 3). Due to its short half-life, ²²²Rn reaches steady state relatively quickly, and hence the supply rate equals the decay rate. This assumes that the radionuclide activities in groundwater and on solid surfaces/host minerals are constant over time, at least on the timescale of the mean life of the radionuclide.

Figure 3

If one neglects advection and dispersion terms, the major sources of radium and radon in groundwater include congruent dissolution, recoil, and leaching of mineral surfaces due to changes in water chemistry. If most of ²²²Rn in the ground water is derived from the recoil of the daughter nuclide when ²²⁶Ra undergoes alpha decay, then other members of the U-Th series radionuclides must also originate from recoil input. From a comparison of the recoil and weathering terms in a one-dimensional advective transport equation that incorporates water–rock interactions, Porcelli and Swarzenski (2003) estimated the mean time for chemical weathering to be 10⁷ years; therefore, any nuclide with a half-life of < 10⁵ year would be supplied primarily by recoil. In a groundwater system, the differences in specific activities between ²³⁴Th-²³⁴U-²²⁶Ra-²²²Rn-²¹⁰Pb-²¹⁰Po of the ²³⁸U series are attributed to the differences in their residence times (or removal rates).

Assuming that all the ²²²Rn is derived from recoil, the ²²²Rn concentration can be directly related to the recoil supply rate. The alpha recoil distance is ~200 Å and can vary by a factor of ~2 depending on the mineralogy of the host matrix (Kigoshi, 1971; Fleischer, 1980; Hashimoto et al., 1985; Sheng and Kuroda, 1986; summarized in Porcelli and Swarzenski, 2003). The recoil supply rates depend on several factors, including the distribution of ²³⁸U and ²³²Th in host rock minerals, recoil lengths (which depend on the recoil energy and matrix; details are provided in Porcelli and Swarzenski, 2003), the position of the nuclide in the decay chain, and differences in the chemical behavior of the nuclide (such as its amenability to leaching along recoil tracks). Note that the estimation of supply rates for longer-lived U and Th series nuclides requires data on the weathering rates of aquifer solids, and very limited data exist on this (Tricca et al., 2001). Additionally, the presence of accessory minerals hosting U and Th would result in uneven distributions of ²³⁸U and ²³²Th within the host rock, potentially leading to varying extents of recoil release of U-series and Th-series radionuclides. Very high activities of ²²²Rn in fluids compared to its immediate parent, ²²⁶Ra, have been attributed to several factors, including high concentrations of ²²⁶Ra in surface coatings on minerals and secondary phases, heterogeneous distributions of U and Th within the aquifer (which could result in preferential diffusion of Rn into the main groundwater flow), and the lack of chemical reactivity of Rn (Rama and Moore, 1984; Tricca et al., 2001; Reynolds et al., 2003). Furthermore, to explain the high emanation rates of ²²²Rn and ²²⁰Rn from a suite of minerals, but not any other nuclides in the U-Th series, Rama and Moore (1984) hypothesized that the presence of a network of nanopores within crystals, many of which intersect the grain surface, allows Rn to diffuse into the intergranular water, while other reactive nuclides such as Ra, Th, and Pb are adsorbed onto the walls of the nanopores. Through an irradiation experiment, Krishnaswami and Seidemann (1988) showed that Argon isotopes produced within a mineral grain did not leak out along with ²²²Rn, thus questioning the hypothesis proposed by Rama and Moore (1984). The ²²⁰Rn diffusion through mineral slabs was reported to be uneven and attributed to nanopore geometry (Rama and Moore, 1990). Tricca et al. (2001) estimated that the amount of Ra on the surface coatings relative to that in the water ranged from ~300 to 700 and proposed that the source of ²²²Rn is the precipitated Th (²³⁰Th and ²³²Th were hypothesized to be deposited on the grain surfaces during an earlier stage of high weathering rates in the formation of the aquifer) at saturation rather than at exchangeable sites in the surface coating. The concentrations of ²²²Rn in groundwater are typically a measure of how much ²²⁶Ra is present in the aquifer matrix and how much, and how easily, ²²²Rn escapes from the mineral grains that contain ²²⁶Ra.

In three monitoring wells at one vertical profile (DEP-5S, 5I, and 5D), the ²²⁶Ra activities varied by a factor of ~7 and the ²²²Rn activities varied by a factor ~6 (Table 3). The vertical variations of radium are attributed to differences in the lithology of the aquifer matrix (Figure 2B). Interestingly, the depth at which the highest ²²²Rn activity (DEP-5S) occurs does not correspond to the highest ²²⁶Ra activity (DEP-5D). The activity of dissolved ²²²Rn in the vertical profile (7.4–50.8 dpm g⁻¹ in the water, assuming groundwater density of 1.0 g cm⁻³) can be compared to the activity of ²²⁶Ra in the aquifer matrix in the vertical profile at the 4 depths (2.7–45.7 dpm g⁻¹, Table 2). From this comparison, it appears that most ²²⁶Ra in the host rock is within recoil distance of the surface [~200–300 Å (20–30 nm) in rocks and minerals]. The activities of ²²⁶Ra in the soil profile indicate that the concentration of U-enriched mineral phosphorite varies considerably (Figure 2B).

The diffusion coefficient (D) for Rn in air is ~0.1 cm² s⁻¹, which is about four orders magnitude higher than that in water, 10⁻⁵ cm² s⁻¹. The diffusion length (L) of ²²²Rn in air is ~ (D/λ)^1/2, where λ is the decay constant of ²²²Rn. The mean diffusion path length is estimated to be ~1.6 m in porous soil (Fleischer and Mogro-Campero, 1978). The corresponding diffusion length in water is ~16 cm, an order of magnitude lower than that in porous soil.

Using the assumption that other short-lived nuclides in the U-Th series are also introduced primarily by recoil into the groundwater system, Krishnaswami et al. (1982) obtained residence times of less than a few minutes for Ra and Th concerning sorption onto the aquifer solid matrix. Thus, a significant amount of Th (²³⁰Th for ²²⁶Ra, ²²⁸Th for ²²⁴Ra, ²²⁷Th for ²²³Ra) and Ra isotopes are likely to be sorbed on the aquifer solid matrix. The absorbed ²²⁶Ra is distributed in films and/or in the shallow surface layers (as deep as the recoil range) of the host minerals. Following alpha radioactive decay, it can release ²²²Rn directly into the aqueous phase. Radon from deeper regions of the crystals is unavailable without the development of large internal nanopore network structures. Furthermore, the assumption that radium isotopes are distributed uniformly or that the structural soundness of the host mineral has been frequently questioned (Tanner, 1978; Krishnaswami and Seidemann, 1988; Morawska and Phillips, 1993; Garver and Baskaran, 2004).

The ²²⁴Ra activity varied between 0.04 and 0.77 dpm L⁻¹, significantly lower than that of ²²⁶Ra (Table 3). Since the ²³²Th activities are considerably lower than ²³⁸U in the calcareous and phosphatic host rocks, this lower ²²⁴Ra activity is expected. Variations in the activities of ²²⁴Ra reflect differences in the amount of recoil from ²²⁸Th in the host rock as well as from sorbed ²²⁸Th. The activity of ²²⁸Ra in the groundwater varied between 0.04 and 0.30 dpm L⁻¹ (Table 3), most of which is directly derived from the recoil when ²³²Th undergoes radioactive decay; the amount of ²²⁸Ra derived from the sorbed ²³²Th is likely negligible. This adsorbed ²³²Th originates from congruent weathering, but the major cation/anion concentrations indicate that this type of weathering is minimal. Additionally, congruent weathering usually occurs over much longer time scales (Tricca et al., 2001).

3.4 ²²³Ra/²²⁶Ra activity ratios in groundwater

The ²²³Ra/²²⁶Ra AR ranged from 2.7 to 156 × 10⁻³ (Table 3). This can be compared to the ²³⁵U/²³⁸U activity ratio of 46 × 10⁻³ for the average upper Earth's crust. Both nuclides (²³⁵U and ²³⁸U) produce Ra after emitting three alphas in their decay chain. While the ²³⁵U-series includes ²²⁷Ac (T_1/2 = 21.8 years), the ²³⁸U series includes ²³⁴U, which has a much longer half-life than any other member in the ²³⁵U series. While the ²²³Ra/²²⁶Ra AR in aquifer solids within a closed system is expected to be 0.046, values as much as 25 times higher (from 0.18 to 1.21) have been reported in subsurface brines from western India (Krishnaswami et al., 1991). Such high ratios were attributed to the precipitation of both isotopes in barite within a groundwater system, but short-lived are radionuclides quickly replenished (Martin and Akber, 1999). Very low ratios of ²²³Ra/²²⁶Ra (0.002–0.025) have also been reported in geothermal brines, which is attributed either to recoil input (dependent on the isotopes' half-lives, as it is limited by the rate of diffusion through microfractures and nanopores) or to the weathering and leaching of Ra from solid phases (Hammond et al., 1988).

3.5 ²²⁴Ra/²²⁸Ra activity ratios in groundwater

As both ²²⁴Ra and ²²⁸Ra are derived from the ²³²Th series, if all ²²⁴Ra and ²²⁸Ra in the fluid originate from congruent weathering or release from surface coatings on the mineral surfaces at the mineral–water interface, then production rates are expected to be equal. If the recoil of ²²⁸Ra allows it to enter the fluid phase, then the recoil rate of ²²⁴Ra in natural minerals is expected to be 1. The amount of sorbed ²³²Th is likely derived from the congruent dissolution of minerals. Thus, most of the ²²⁸Ra is directly derived from recoil when ²³²Th undergoes radioactive decay. ²²⁸Th is derived from this recoiled ²²⁸Ra and is removed quickly because of the short residence time of Th (Hussain and Krishnaswami, 1980). The ²²⁴Ra/²²⁸Ra in the present study varied between 0.79 and 4.17, with only one sample having a value of < 1.0 (out of 13; Table 3). In most groundwater studies, ²²⁴Ra/²²⁸Ra AR >1 has been reported (Krishnaswami et al., 1982; Davidson and Dickson, 1986; Krishnaswami et al., 1991; Luo et al., 2000; Tricca et al., 2001; Reynolds et al., 2003).

3.6 ²²⁶Ra/²²⁸Ra activity ratios in groundwater

The ²²⁶Ra/²²⁸Ra AR in groundwater ultimately depends on the ²³⁸U/²³²Th ratios in the host rocks. The ²²⁶Ra/²²⁸Ra AR in aquifer solids varied between 1.46 and 43 (Table 3), while in the three water samples where the core was collected, the ratio varied between 10.6 and 59 (3–119 across all the groundwater samples, Table 3). Radium-226 in the ²³⁸U series is the product of the third α decay, while ²²⁸Ra is the first α decay product in the ²³²Th series. Thus, ²²⁶Ra will have a more mobile pool of preceding radionuclides in the ²³⁸U decay chain compared to ²²⁸Ra, resulting in significantly higher ²²⁶Ra/²²⁸Ra AR in groundwater than in the host rock. When the desorption rate (Section 3.7) is fast (longer residence time on the mineral grain surfaces) compared to the mean life of ²²⁸Ra (8.3 years), the ²²⁶Ra/²²⁸Ra AR in the groundwater and that adsorbed on mineral surfaces are expected to be the same. Under such conditions, the measured ²²⁶Ra/²²⁸Ra AR in the groundwater should match that in the host rock. The differences in the activity ratios can be attributed to variations in the distribution of U and Th, leading to differing recoil rates from U and Th, variable losses of Th by sorption onto the host rocks, and changes in supply and/or sorption characteristics that result in a non-steady state for ²²⁶Ra along the groundwater flow line (Luo et al., 2000; Tricca et al., 2001; Porcelli and Swarzenski, 2003). Similar ²²⁶Ra/²²⁸Ra ARs in the host rocks and water have also been reported (Sturchio et al., 2001).

As the half-lives of ²²⁴Ra and ²²²Rn are both relatively short, they are expected to be in steady state in most groundwater systems. Consequently, the activities of these radionuclides in groundwater (dissolved + sorbed onto mineral grains for Ra) are expected to equal the recoil supply rate. In the four samples of the host rock, the ²²⁸Th/²³⁰Th AR varied between 0.02 and 0.47, likely due to variations in the ²³⁸U concentration, which is primarily controlled by phosphorite content. If Ra and Rn were to behave conservatively, the ²²⁴Ra/²²²Rn AR would be expected to be comparable to the ²²⁸Th/²³⁰Th AR values. However, the ²²⁴Ra/²²²Rn AR varied between 0.04 and 5.0 × 10⁻⁴ (with the lowest value reported in any freshwater aquifer) and is significantly lower than the ²²⁸Th/²³⁰Th AR values. In the ²³⁸U-decay chain, ²²²Rn is preceded by four α decays, while ²²⁴Ra in the ²³²Th-decay series is preceded by two, consequently, ²²²Rn production is suggested to be 50% higher due to precursors accumulated on surfaces (Porcelli and Swarzenski, 2003). The ²²⁴Ra/²²²Rn AR range can be compared to the values reported in other groundwater systems such as fresh water: (0.5–2.2) × 10⁻⁴ (Tricca et al., 2001), (0.8–1.0) × 10⁻⁴ (Luo et al., 2000), and (0.2–4.4) × 10⁻⁴ (Krishnaswami et al., 1982); sub-surface shallow brines: (500–9,600) × 10⁻⁴ (Krishnaswami et al., 1991). Since the residence time of Ra in saline water is long due to reduced sorption of Ra onto the host matrix, a large ²²⁴Ra/²²²Rn AR is expected. The similarity in the range of ²²⁴Ra/²²²Rn AR in freshwater systems suggests that the partitioning of Ra onto the aquifer matrix is similar, despite likely contrasting lithologies.

3.7 Adsorption–desorption rate constants and retardation factors

The production rates of Ra isotopes were calculated using ²²²Rn as the recoil flux monitor and were based on the relation (Krishnaswami et al., 1991):

where F_i and F_r are the recoil supply rates of Ra isotopes (²²⁴Ra or ²²⁸Ra) and ²²²Rn to the groundwater, respectively; Qi and Qr are the production rates of Ra isotopes and ²²²Rn in the aquifer solids, respectively; and ε is the rate of recoil supply of ²²⁴Ra or ²²⁸Ra relative to ²²²Rn. The value of ε can vary from a steady state value of ~1.5, if all the ²²⁶Ra recoiled into the groundwater remains in solution, to 0.86 if all the recoiled ²²⁶Ra is adsorbed onto the aquifer grain surfaces (Krishnaswami et al., 1982). We have assumed a value of 1.0 for ε.

The production rates of ²²⁴Ra and ²²⁸Ra and the ratio of activity in solution to production (Ω₂₂₄ and Ω₂₂₈) are given in Table 4. Of the 12 groundwater samples, the Ω₂₂₄ and Ω₂₂₈ values ranged from 0.7 × 10⁻⁴ to 28 × 10⁻⁴ and from 1 × 10⁻⁴ to 61 × 10⁻⁴, respectively. If the activities of these nuclides are controlled by the amount of sorbed Fe and Mn, then, a likely relationship between (Ω₂₂₄ and Ω₂₂₈) and oxidation–reduction potential is expected. However, no relationship was found between Ω₂₂₄ or Ω₂₂₈ and ORP, or between adsorption or desorption rate constants and ORP (Figures 4A, C), indicating that redox cycling does not appear to play a role in the removal of Ra from solution onto solid particles or from solids into solution. The adsorption (k₁) rate constants calculated using Equation 4 varied between 0.03 and 2.4 min⁻¹, corresponding to a residence time of 0.4–33 min for Ra in the groundwater (Table 5). This range can be compared to values of 3–20 min previously reported for other groundwater systems (Krishnaswami et al., 1982; Copenhaver et al., 1992, 1993). However, these values are much lower than those reported for the subsurface brines from Kharagoda, India (Krishnaswami et al., 1991). The adsorption and desorption rate constants are plotted against ORP (Figure 4A) and alkalinity (Figure 4B), and no relationship is observed between rate constants when plotted against ORP and alkalinity. Additionally, Ω₂₂₈ appears to be constant for ORP values of −80 to 240 mV (Figure 4C).

Figure 4

The desorption rates are much slower, ranging from 0.5 × 10⁻⁴ to 21 × 10⁻⁴ min⁻¹, corresponding to desorption time scales of 0.3–14 days (Table 5). This range of values is comparable to those reported by others (Krishnaswami et al., 1982; Copenhaver et al., 1992, 1993). There is no positive correlation between the adsorption/desorption rate constants and the dissolved concentrations of As (Figure 5A), total Fe (Figure 5B), and Mn (Figure 6), suggesting that the redox processes do not affect the adsorption–desorption constants calculated using Ra (Figures 4A–C, 5A, B) in these samples. There is also no observed relationship between alkalinity and the calculated adsorption–desorption rate constants, likely indicating that congruent dissolution does not affect the rate constants (Figure 4B). There is a weak positive relationship between the concentrations of As and Fe (Figure 7). A recent study of hydrothermal groundwaters in Algeria showed a correlation between Ra activity and total dissolved solids, proposing that adsorption/desorption did not control the distribution of Ra in these waters (Zemour et al., 2023).

Figure 5

Figure 6

Figure 7

The retardation factor, R_f, defined as the ratio of a nuclide's production to its activity in solution (= 1/Ω, Equation 3), is expected to be the same for isotopes of the same element, even though the retardation factors depend on the different mean lives of the isotopes (Equation 3). The retardation factor (R_f) varied between 0.12 × 10³ and 7.0 × 10³ (Table 5). The R_f values are comparable to the k₁/k₂ ratios. The k₁/k₂ ratio, defined as the distribution coefficient (K), varied between 0.16 × 10³ and 9.3 × 10³ (Table 5). These values are comparable to those reported from other aquifers, such as groundwater from Connecticut (4.8 × 10³ to 123 × 10³, Krishnaswami et al., 1982), 0.6 × 10³ in the Long Island aquifer, and 50 × 10³ in Connecticut (Copenhaver et al., 1993), as well as 13 × 10³ in groundwater at the Nevada Test Site near Yucca Mountain (Copenhaver et al., 1992) and 5.21 ± 2.76 × 10³ (n = 48), summarized in International Atomic Energy Agency (2025). Since K >> 1, R_f ~ K, radium will migrate R_f times slower than the groundwater flow rate.

4 Conclusions

Based on the present study, the following conclusions are drawn:

• 1) The activities of ²²²Rn and ^{224, 223, 228, 226}Ra isotopes in 13 groundwater samples collected from an area of 3 km² varied over an order of magnitude horizontally and by a factor of ~6 vertically. This wide variation is attributed to differences in local lithology, with highly variable phosphorite content.

• 2) The activity ratio ²²⁶Ra/²²⁸Ra in a vertical profile of a soil core varied between 1.46 and 43.6 (mean: 16.9, n = 4), which is elevated relative to the variation in ²³²Th concentration by a factor of 2 (Table 2), while ²³⁴Th concentration varied by a factor of 12.5.

• 3) The activity ratios of ²²³Ra/²²⁶Ra in groundwater samples varied widely from 0.003 to 0.156. This contrasts with the value of 0.046 when ²²³Ra and ²²⁶Ra are in secular equilibrium with ²³⁵U and ²³⁸U, respectively. This broad range of values is attributed to the faster removal of both nuclides and slower desorption from the solid matrix, as well as differences in the regeneration rates of ²²³Ra and ²²⁶Ra.

• 4) The residence times of Ra with respect to removal by sorption ranged between 0.4 and 33 min while the corresponding residence time of Ra on the solid matrix with respect to desorption ranged between 0.3 and 14 days.

• 5) The distribution coefficient (K) values ranged between 0.16 × 10³ and 9.3 × 10³. This range of K values is similar to those reported in earlier published work. The retardation factor of Ra varied from (0.12 ± 0.03) to (7.0 ± 2.7) × 10³.

• 6) There is no relationship between ORP or alkalinity and adsorption and desorption rate constants, indicating that redox cycling does not appear to play a role in the removal of Ra.

• 7) There is no positive correlation between the adsorption–desorption rate constants and the concentrations of Fe, Mn, As, P, and alkalinity in groundwater, suggesting that the oxides of Fe and Mn do not control the removal behavior of Ra.

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