Effects of Permeability and Pyrite Distribution Heterogeneity on Pyrite Oxidation in Flooded Lignite Mine Dumps

Abstract

The role of sedimentary heterogeneity in reactive transport processes is becoming increasingly important as closed open-pit lignite mines are converted into post-mining lakes or pumped hydropower storage reservoirs. Flooding of the open pits introduces constant oxygen-rich inflows that reactivate pyrite oxidation within internal mine dumps. A reactive transport model coupling groundwater flow, advection–diffusion–dispersion, and geochemical reactions was applied to a 2D cross-section of a water-saturated mine dump to determine the processes governing pyrite oxidation. Spatially correlated fields representing permeability and pyrite distributions were generated via exponential covariance models reflecting the end-dumping depositional architecture, supported by a suite of scenarios with systematically varied correlation lengths and variances. Simulation results covering a time span of 100 years quantify the impact of heterogeneous permeability fields that result in preferential flow paths, which advance tracer breakthrough by ~15 % and increase the cumulative solute outflux up to 139 % relative to the homogeneous baseline. Low initial pyrite concentrations (0.05 wt %) allow for deeper oxygen penetration, extending oxidation fronts over the complete length of the modeling domain. Here, high initial pyrite concentrations (0.5 wt %) confine reactions close to the inlet. Kinetic oxidation allows for more precise simulation of redox dynamics, while equilibrium assumptions substantially reduce the computational time (>10×), but may oversimplify the redox system. We conclude that reliable risk assessments for post-mining redevelopment should not simplify numerical models by assuming average homogeneous porosity and mineral distributions, but have to incorporate site-specific spatial heterogeneity, as it critically controls acid generation, sulfate mobilization, and the timing of contaminant release.

1. Introduction

Abandoned open-pit coal mines in Europe are being repurposed as post-mining lakes for recreational uses, nature conservation, or fisheries [1,2,3,4,5,6,7]. With the ongoing energy transition towards renewable energy sources and a changing perspective on electrical energy generation, distribution, and storage, sustainable post-mining uses are evaluated [8], such as energy storage systems like pumped hydropower storage (PHS) [9,10,11,12,13]. Such projects can introduce new hydrological dynamics to these well-known systems, particularly when internal mine dumps, composed of heterogeneous, pyrite-bearing sediments, are subjected to sustained, oxygen-rich water inflow from the post-mining lake [14,15].

The governing stoichiometric chemical reaction for pyrite oxidation is

FeS₂ + 3.5O₂ + H₂O → Fe²⁺ + 2SO₄²⁻+ 2H⁺,

(1)

describing the release of acidity, sulfate, and iron (for partial and rate-determining reactions see [16,17]). The reaction is catalyzed by iron-oxidizing bacteria [17,18]. The disulfide oxidation is a common phenomenon observed in dump material of lignite mines at many locations [19,20]. Pyrite-rich sediments exposed to atmospheric oxygen during excavation and deposition undergo initial oxidation of the disulfide mineral [17,21]. Further, atmospheric oxygen may diffuse into the upper parts of exposed dump material and, together with convection, contribute to the long-term release of contaminants [22]. Precipitation that leaches through the respective sediments then transports these pyrite oxidation products into groundwater bodies present within the dump which may be connected to adjacent aquifers or other water bodies such as the post-mining lake [23,24,25]. Here, acidification and/or increased sulfate and metal concentrations pose risks to water quality and ecosystem health [26]. Flooding the respective sediments within the mine and parts of the mine dump limits the oxygen availability, and thus the extent of pyrite oxidation. Depending on local redox conditions and residence times, sulfate can be locally reduced and sulfides can precipitate [27].

Spatial heterogeneity—arising from varieties of lithological units with different grain sizes in combination with depositional processes such as end-dumping—controls flow pathways, solute residence times, and reaction fronts in porous media of mine dumps [28,29]. Heterogeneity manifests in layered grain size distributions, variable porosity, and uneven mineral distributions, all of which can promote preferential flow paths, localized reaction hotspots, and non-uniform contaminant plumes. Despite advances in reactive transport modeling of solutes in waste rock piles [29,30,31,32,33,34,35], often in simulations either homogeneity or simplified heterogeneity is assumed. In the context of lignite mine spoil piles, Gerke et al. (2001) [35] demonstrated with a coupled reactive transport model that chemical and physical heterogeneities influence acidification dynamics and solute leaching, particularly through their control of oxidation front propagation and buffering reactions. Their study highlights the importance of accounting for spatially variable hydraulic conductivity and sulfide distribution to accurately predict long-term acid mine drainage generation. Other studies investigated heterogeneity in saturated and unsaturated lignite mine soil with lysimeters [33], multi-step flow experiments with soil cores and simulations accompanying the experiments [36], or simulations verified by field data [37]. These field and laboratory investigations confirm that heterogeneity strongly modulates flow and solute transport in mine–soil systems.

The aforementioned studies focused on (variable) unsaturated dump sediments. Since (partially) unsaturated mine dumps pose the major risk for pyrite oxidation and contaminant release, saturated, flow-through environments like internal mine dumps remain less understood, especially under the long-term, continuous oxidative conditions induced, e.g., by PHS operations using the post-mining lake as a storage reservoir [15]. Ref. [14] recently demonstrated that PHS cycling increases dissolved oxygen concentrations in post-mining lakes compared to natural systems, thereby enhancing the potential for subsurface pyrite oxidation. Similar conclusions have been drawn for subsurface coal mines and shafts that may be used for underground PHS (UPHS) [38,39]. However, the question remains open as to whether the findings for transport processes in the unsaturated zones of lignite mine dumps also apply to fully saturated media.

With this study we bridge that gap by developing a process-based reactive transport model to investigate how spatial heterogeneity affects pyrite oxidation and contaminant transport in a saturated internal lignite mine dump under sustained oxygen influx. Three research questions are specifically addressed:

• How do different aspects of permeability and pyrite distribution heterogeneities (e.g., correlation lengths, variances) affect the spatial and temporal patterns of solute transport?
• What role does heterogeneity play in controlling oxygen consumption, acid generation, and sulfate mobilization?
• Under which conditions can simplified modeling approaches (e.g., homogeneous domains or equilibrium assumptions to reduce computational times) adequately represent the integrated geochemical response of heterogeneous mine dumps?

We aim to provide insights into reactive transport in post-mining systems and make recommendations regarding the sustainable redevelopment of former lignite mines, by combining site-specific data from prior studies [14,15,40] with a geostatistical approach reflecting end-dumping depositional patterns (Figure 1). Our findings contribute to improved risk assessment, long-term water management, and regulatory planning for alternative end-uses of mine landscapes.

Figure 1. Conceptual model of the hydrogeological setting: a flooded lignite mine pit (right) supplies oxygen-rich water to an internal mine dump (center), which discharges into a receiving Quaternary aquifer (left).

2. Materials and Methods

2.1. Reactive Transport Model Formulation and Implementation

A comprehensive reactive transport model that couples groundwater flow, solute transport, and geochemical reactions was developed and employed to investigate spatial heterogeneity effects on solute transport within a lignite mine dump. The simulation environment TRANSPORTSE (Ver. 1.0.2) [41,42] describes saturated groundwater flow through the combination of mass conservation and Darcy’s law, while dissolved species transport follows the advection–diffusion–dispersion reaction equation. The mathematical formulation and detailed numerical implementation of this coupled modeling approach are comprehensively documented [41,42]. The Python-based simulation environment has been verified using multiple benchmark tests [41,42] and utilized in different studies regarding the evolution of leaching zones within potash seams [43,44] and gas hydrate formation [45,46,47], as well as temperature and salinity distributions in subsurface reservoirs [48,49].

The geochemical calculations are performed using the software PHREEQC (Ver. 3.7.3) [50], with the PhreeqPy-package (Ver. 0.5.1) [51], which solves the speciation and reaction equations based on a thermodynamic database (phreeqc.dat) [50] for aqueous speciation and mineral saturation, while considering kinetic rate laws for pyrite oxidation (Equations (1) and (2)). The geochemical system is determined by pyrite oxidation which represents the main source of acidity and sulfate in lignite mine dumps [20,22,52]. Acid buffer capacities in lignite mine dump sediments are often naturally or artificially provided by carbonates such as CaCO₃ [53,54]. In order to reduce the complexity of the chemical system and to highlight the impact of the heterogeneity of porosity and mineral distributions, pyrite was chosen to be initially available in the dump as the primary reactive mineral. However, minerals such as calcite, goethite, and gypsum could precipitate as secondary minerals based on the thermodynamic equilibrium conditions (Equations (3)–(5)). The other chemical components of the geochemical system originated from the post-mining lake water influx, which was derived from [15], and the groundwater composition [40] that was applied as the initial condition in the mine dump.

The governing reactions comprise pyrite oxidation (Equation (1)) with a kinetically controlled reaction following the rate law (Equation (2)) from [30,55]:

pyrite = A⋅(m/m0)^0.67⋅10^−8.19⋅[O₂]0.5⋅[H⁺]^−0.11⋅(1 − SR_pyrite),

(2)

where A is the reactive surface area (m²), m/m0 is the ratio of current to initial mineral mass (-), and SR is the saturation ratio of pyrite (-).

Equilibrium-based secondary mineral formation, including calcite (CaCO₃; Equation (3)), goethite (FeOOH; Equation (4)), and gypsum (CaSO₄·2H₂O; Equation (5)):

CaCO₃ + H⁺ ⇌ Ca²⁺ + HCO₃⁻

(3)

Fe³⁺ + 2H₂O ⇌ FeOOH + 3H⁺

(4)

Ca²⁺ + SO₄²⁻ + 2H₂O ⇌ CaSO₄⋅2H₂O

(5)

For grid cells where mineral reactions occur (dissolution/precipitation), the changes in mineral volume fractions influence the porosity, which in turn affects the permeability (Equations (6)–(9)). The molar volume for each mineral is calculated from its molar mass and density:

V_m,i = M_i/ρ_m,i

(6)

where V_m,i is the molar volume of mineral i (cm³/mol), M_i the molar mass of mineral i (g/mol), and ρ_m,i is the density of mineral i (g/cm³).

The total volume change per unit volume of solution is then computed as:

ΔV= Σ[i = 1, 4] Δc_i × V_m,i,

(7)

where ΔV is the volume change (cm³/L), and Δc_i is the concentration change for mineral i (mol/L).

The porosity at time step n + 1 is updated based on the mineral volume changes:

ϕ_effⁿ⁺¹ = ϕ_effⁿ − ΔV/1000,

(8)

where ϕ_effⁿ and ϕ_effⁿ⁺¹ are the porosity at time steps n and n + 1, respectively (-).

The permeability–porosity relationship follows the empirical correlation proposed by Helmbold (1988, as cited in [56]):

K_xⁿ⁺¹ = K_zⁿ⁺¹ = (ϕ_effⁿ⁺¹/1.33)^4.545 × μ/(ρ_f × g),

(9)

where K_x and K_z are the permeability in the x and z directions (m²), μ is the dynamic viscosity (Pa·s), ρ_f is the fluid density (kg/m³), and g is the gravitational acceleration (m/s²).

The reactive transport model was verified with the numerical results and validated against the experimental data reported in a study by Battistel et al. (2019) [30], which presents laboratory flow-through tests and accompanying numerical models of pyrite oxidation in fully saturated 1D and 2D media. That study covered dissolved species transport, dissolved and undissolved gases transport, pyrite oxidation kinetics, and secondary mineral precipitation. Our simulations reproduced the study’s results with comparable accuracy for both the 1D and 2D configurations (see Figure A1). The chemical system of the present study is almost completely covered by these simulations, and the simulation environment TRANSPORTSE was previously successfully applied to large-scale problems (see Section 1); therefore we consider the validation and verification process sufficient for the present study, especially since no sufficient field data is available.

2.2. Geostatistical Field Generation and Heterogeneity Implementation

The investigated internal mine dump is constructed using the end-dumping technique, where unconsolidated sediments are deposited at the bench edge [31]. This construction method produces two characteristic features: (i) similar sediments deposit in loose layers oriented parallel to the slope angle, and (ii) grain sizes exhibit upward fining within these layers, also parallel to the slope [31].

Our geostatistical approach used exponential covariance models to generate spatially correlated random fields [57]. Effective porosity (ϕ_eff) served as the primary control on permeability and mineral distribution patterns. The random fields were generated using the GSTools (Ver.1.7.0) Python (Ver. 3.10.16) library [58] and projected onto a bench geometry that was taken from a cross-section of a prospective mine dump to represent the sedimentary layering described. The variance of ϕ_eff was constrained by given thresholds of 0.05–0.45 [22,59,60], while anisotropy was incorporated through estimated directional correlation lengths (λ_x and λ_z) oriented at 22° from horizontal to represent the depositional angle derived from the slope angle.

The exponential covariance model is defined as:

C(h) = σ² exp(−h/λ(θ))

(10)

where C(h) represents the covariance at separation distance h, σ2 denotes the variance (-), λ is the correlation length (m), and θ is the depositional angle (°). A constant random seed was kept throughout the different realizations to maintain comparability between the fields.

The generated random fields were transformed to achieve porosity distributions suitable for hydrogeological modeling (Figure 2). The transformation process involved a linear scaling of the standardized Gaussian fields followed by boundary constraints to ensure physical realism. The transformation applied a linear relationship between the random field and the target porosity statistics:

ϕ_eff = μ_eff + σ_eff × ξ

(11)

where ϕ_eff represents the transformed porosity field, μ_eff is the target mean effective porosity (-), σ_eff is the target standard deviation (-) derived from the input variance, and ξ is the standardized Gaussian random field. The transformed porosity values were subsequently constrained within the range of 0.05 to 0.45 through boundary clipping to prevent unrealistic porosity values that could lead to numerical instabilities in the transport calculations. Clipping did not affect the variance and mean of the porosity distributions as the number of clipped values remained low.

Figure 2. Spatially correlated effective porosity (ϕ_eff) fields generated using exponential covariance models with varying correlation lengths in z-direction.

The spatial permeability field (Figure 3) was estimated from effective porosity using the empirical relation from Equation (9). The transformation of the original field to the pyrite distribution was based on a field inversion, where the negative standardized random field was used as input to create an inverse correlation pattern. This inverted field was then subjected to a beta distribution transformation (Equations (12) and (13)). The beta distribution was chosen to maintain spatial correlation while ensuring positive values throughout the domain. As the geochemical model responds to relatively low pyrite concentrations, it requires a distribution that captures both maximum and very low concentrations that do not significantly influence oxygen transport within individual cells. Additionally, the beta distribution allows for precise control of the total mineral mass, ensuring a consistent pyrite inventory across all simulated scenarios through iterative optimization of the shape parameter. The standardized Gaussian field values were first converted to uniform probability ranks using the normal cumulative distribution function. These uniform ranks were subsequently transformed to beta distribution quantiles using the inverse beta cumulative distribution function with the shape parameters a and b, where b was fixed at 2.0, and a was optimized to maintain the pyrite mass balance. The beta transformation relationship is expressed as:

C_pyr = β⁻¹(r; a, b) × α_scale

(12)

where C_pyr represents the pyrite concentration (mol/m³), β⁻¹(r; a, b) denotes the inverse beta cumulative distribution function with shape parameters a and b applied to uniform ranks r, and α_scale is the scaling constant (-), which is calculated as follows:

α_scale = c_max × 1000/M_pyr

(13)

where c_max represents the maximum allowable pyrite concentration (5% of bulk density = 82.5 kg/m³, [19]), and M_pyr is the pyrite molecular weight (119.98 g/mol).

Figure 3. Example realization of heterogeneous fields for porosity, ϕ_eff, derived permeability, k, and pyrite concentration with variance = 0.005, λ_x = 15 m, and λ_z = 5 m.

The shape parameter a was optimized to achieve target average concentrations corresponding to 0.5% and 0.05% of total sediment mass [19,22,61], using a bulk density of 1650 kg/m³ [62]. The optimization employed bounded scalar minimization to match the target average concentration across the dump volume, ensuring consistent pyrite inventories across all realizations while maintaining the inverse spatial correlation with porosity (Figure 3).

2.3. Model Setup and Domain

The simulation domain represents a two-dimensional vertical cross-section through a section of the internal mine dump (Figure 1). The domain extends 503 m in the horizontal direction (x-axis) and 35 m in the vertical direction (z-axis). A nominal width of 1 m in the y-direction creates an effective 2.5D model.

The domain was discretized with the python library Geomodelator (Ver. 2.0) [63,64] using a regular grid with 1006 cells and 70 cells in the horizontal and vertical directions, respectively, resulting in uniform cell volumes of 0.25 m³ (Table 1). This discretization was selected following a grid sensitivity analysis to adequately distribute the effective porosity and mineral concentrations with the covariance model and to minimize numerical dispersion during the transport simulations, while maintaining feasible computational efforts per simulation scenario.

Table 1. Parametrization of the model maintained across all simulation scenarios.

Parameter	Value	Unit	Source
Domain length (x)	503	m	Internal project data
Domain length (z)	35
Grid cells (x × z × y)	1006 × 70 × 1	-
Cell volume	0.5 × 0.5 × 1	m3
Diffusion coefficient	2.0 × 10−9	m2/s	[59]
Hydraulic gradient	0.0036	-	[65]
Average hydraulic conductivity	1.5	m/d	[65]
Bulk density	1650	kg/m3	[62]
Temperature (constant)	9.1	°C	[66]
Simulation period	100	years
Maximum allowed time step size	2	days

The model domain represents a post-mining landscape comprising three hydrogeological zones (Figure 1): (i) a flooded post-mining lake serving as the water source (right boundary), (ii) a heterogeneous mine dump (central zone), and (iii) a receiving Quaternary aquifer (left boundary). Flow conditions were established using constant head boundaries at both lateral boundaries, creating a hydraulic gradient of approximately 0.0036 across the domain, consistent with equilibrated post-mining settings [65]. The internal mine dump was assigned an average hydraulic conductivity of 1.5 m/d [65], while the upper and lower domain boundaries were designated as no-flow conditions. We decided to limit the model domain to a single bench of the dump. It is assumed that the dominant flow direction in the bench is in the x-direction and compaction measures were carried out at the upper limits of each bench; thus limited vertical exchange between the different benches is expected.

Initial pressure conditions were established using hydrostatic equilibrium with atmospheric pressure (1.01325 × 10⁵ Pa) at the lake surface and increasing linearly with depth according to the following:

P(z) = P₀ + ρ_f × g × h,

(14)

where h represents the hydraulic head above the reference datum (m).

For solute transport, a constant concentration boundary was applied at the mine lake–dump interface. The inflowing water composition, derived from a previous modeling study [15], exhibited oxidizing conditions with pH 7.98 and dissolved oxygen at 11.34 mg/L (full saturation under atmospheric conditions). Additional constituents included sulfate (210.50 mg/L), calcium (101.07 mg/L), and trace concentrations of magnesium, sodium, potassium, iron, and chloride characteristic of mining-influenced waters (Table 2). Zero-gradient conditions for concentrations at the outflow boundary permitted unrestricted exit of solute.

Table 2. Water compositions used in the simulations [15]. IBE: Ion balance error.

Solution	pH	pe	Ca2+	Mg2+	Na+	K+	HCO3−	Fe	Cl−	SO42−	O(0)	IBE
	-		mg/L									%
Groundwater	7.38	−1.70	67.90	8.30	15.07	1.09	231.74	0.00	16.04	40.18	0.00	−3.38
Post-mining lake	7.99	14.07	101.07	8.93	13.32	1.11	99.98	0.00	14.12	210.50	11.34	−0.26

The domain was initialized with a hydrostatic pressure distribution and uniform temperature of 9.1 °C, representative of regional average annual temperature [66]. Local groundwater was equilibrated in each grid cell with its local mineral assemblage at initial pH 7.38 and mildly reducing conditions (pe = −1.7; Table 2) to establish physically consistent starting conditions.

A molecular diffusion coefficient in water of 2.0 × 10⁻⁹ m²/s was applied for all chemical species. Dispersivity values were set to zero to isolate mechanical dispersion arising from physical heterogeneity alone, as site-specific dispersivity data for mine dump sediments were not available and geological features could not be reliably assigned characteristic dispersivity values. For geochemical reactions, the pyrite oxidation rate was modeled using the rate law from [55] with a scaling factor of 2.8 [30]. Calcite, goethite, and gypsum precipitation were modeled as equilibrium-controlled reactions, as these processes typically occur rapidly relative to the simulation time scale.

The simulation period was set to 100 years to capture the long-term evolution of the system. This time frame allows for the establishment of a constant flow field, mineral dissolution, and precipitation, as well as the development of reactive fronts and species plumes within the heterogeneous domain.

2.4. Simulation Scenarios

By systematically varying two key heterogeneity parameters that describe the porosity and mineral distributions—the ratio of the correlation length in the x-direction (λ_x) to that in the z-direction (λ_z), and the variance (σ²)—a total of 94 distinct simulation scenarios were designed. Dedicated scenarios include homogeneous distributions of porosity and/or pyrite. Table 3 and Table A1 summarize all scenarios.

Table 3. Parameter variations that determine the simulation scenarios.

Parameter	Symbol	Value	Unit	Source
Correlation length x-direction	λx	15	m	Internal project data, derived from the cross-section
Correlation length z-direction	λz	2.5, 5, 10, 15	m
Depositional angle	θ	22	°
Variance, effective porosity	σ2eff	0.003, 0.005, 0.007	-	-
Total initial pyrite concentration		0.05, 0.5	wt%	[19,22,61]
Maximum pyrite concentration per cell	cmax	2.5, 5	wt%	[19]

3. Results

3.1. Solute Transport

The tracer reached 1% of its initial concentration after 20.5 years in the homogeneous scenario, compared to an average of 18.0 ± 1 years in heterogeneous cases (Figure 4). Over 100 years, heterogeneous scenarios released 105% of the total tracer mass relative to the homogeneous case, with individual scenarios ranging from 88% to 139%, depending on vertical correlation length (λ_z; Figure 5B). The highest outflux (139%) occurred at λ_z = 5 m, suggesting an optimal scale of layering that enhances channelized flow. The tracer reached 1% of its initial concentration after 16.5 years in the homogeneous scenario (Figure 4), which is approximately 4.0 years later than the average breakthrough time of the heterogeneous scenarios (12.5 years).

Figure 4. Tracer breakthrough curves at the outlet boundary, normalized to the final mass in the homogeneous scenario.

Figure 5. Total tracer mass leaving the domain during 100 simulated years, normalized to homogeneous case. (A) Averaged by scenario category with error bars representing the standard deviation of the individual scenarios within the category. (B) Per individual scenario with heterogeneous porosity and pyrite distributions, grouped by vertical correlation length (λ_z), with λ_x fixed at 15 m and error bars representing the standard deviation of the same scenarios with different variances in the transformed porosity distribution (Equation (11); see Figure A2 for more details).

Heterogeneous scenarios averaged 105% of the homogeneous scenarios total tracer outflux after 100 years (Figure 5A). Doubling the source term led to an average tracer total of 240% compared to the homogeneous scenario. Scenarios with homogeneous pyrite and heterogeneous porosity distribution reached 108% total tracer mass on average compared to the homogeneous case. Scenarios with λ_z = 15, 10, and 2.5 m achieved 98%, 96%, and 88%, respectively (Figure 5B). The λ_z = 5 m scenario exceeded all others at 139%. Applying different variances—0.003, 0.005, 0.007—to the porosity distributions during the field transformation (Equation (11)) results on average (for all correlation lengths) in 101%, 105%, and 109% total tracer mass compared to the homogeneous base case.

Scenarios with heterogeneous sediment but homogeneous pyrite distributions covered a similar data range as the completely homogeneous scenario. Scenarios with homogeneous sediment but heterogeneous pyrite distributions performed in a similar way to the completely heterogeneous scenarios.

3.2. Oxygen Consumption

Chemical reactions were concentrated in two spatial zones: the mixing and oxidation fronts. At the mixing front, where inflowing water mixed with resident groundwater, calcite became oversaturated and precipitated. In the heterogeneous scenarios, an average of 200 kg calcite precipitated and remained in the dump (SD: 174 kg); in the homogeneous scenario, only 0.4 kg remained (0.2%). The oxidation front initiated near the inlet in most scenarios and progressed only 4.5% of the horizontal modeling domain distance on average at 0.5 wt% initial pyrite concentration (Figure 6(A1–A4)). The homogeneous pyrite distributions confined oxidation to the first cells beyond the inlet (0.5–1 m). Lower initial pyrite concentrations (0.05 wt% vs. 0.5 wt%) resulted in broader oxidation zones with faster and further progression (Figure 6(B1–B4)).

Figure 6. Spatial distribution of pyrite depletion fraction after 100 years. Pyrite depletion fraction is the relative change in pyrite in the respective cell. Since all cells contained at least a very small amount of pyrite, the figure shows how far oxygen has traveled through the modeling domain. (A1–A4) Initial pyrite = 0.5 wt%. (B1–B4) Initial pyrite = 0.05 wt%. Decreasing λ_z from top to bottom.

Oxygen consumption averaged 97.8 and 66.8% (SD: 0.35% and 7.9%; Figure 7) for heterogeneous cases with 0.5 and 0.05 wt% of initial pyrite, respectively. Scenarios based on the thermodynamic equilibrium approach consumed 0.5% more oxygen than those with kinetically moderated reactions. For homogeneous porosity but heterogeneous pyrite distributions, oxygen consumption averaged 97.2 and 76.1% (SD: 1.4 and 11.6%), depending on the initial pyrite concentrations of wt% of 0.5 and 0.05%, respectively. Highest oxygen consumption was recorded with the homogeneous pyrite concentration distribution (98.9%).

Figure 7. Oxygen consumption percentages across different scenario categories. Boxplots show median (line), mean (cross), quartiles (whisker lines), and outliers (circles) for each category.

Figure 8 displays normalized oxygen concentration distributions after 100 years, depending on the porosity distribution and the amount of initial pyrite. Higher initial pyrite content (Figure 8(A1–A4)) resulted in complete oxygen depletion near the inlet. Lower pyrite content (Figure 8(B1–B4)) allowed deeper oxygen penetration, with heterogeneity creating spatially variable oxidation fronts.

Figure 8. Normalized oxygen concentration distributions after 100 years. (A1–A4) Initial pyrite = 0.5 wt%. (B1–B4) Initial pyrite = 0.05 wt%.

3.3. Mineral Balance

Total pyrite oxidation ranged from 1080 to 1710 kg for the heterogeneous scenarios. Relative to the initial mass, 0.2 to −1.4% of the pyrite oxidized over the simulation period with heterogeneous distributions based on the initial pyrite wt% (Figure 9). Lower initial pyrite concentrations showed higher relative oxidation rates. Doubling the influx resulted in a relative mass change of −0.3 and −2.7%, based on the initial pyrite mass.

Figure 9. Relative pyrite mass change for varying initial pyrite concentrations. Boxplots show median (line), mean (cross), quartiles (whisker lines), and outliers (circles) for each category.

The amounts and location of goethite precipitation are equivalent to the dissolution of pyrite, since iron was not in a soluble state in most scenarios and immediately precipitated. Under heterogeneous sediment porosity and pyrite distributions, total goethite precipitation showed considerable variability. For the 0.5% initial pyrite concentration, precipitation ranged from 1257 to 1699 kg with a median of 1369 kg, while the 0.05% initial pyrite scenarios produced 1079 to 1306 kg with a median of 1255 kg. The double source term scenarios generated the highest goethite precipitation across both pyrite concentrations. The 0.5 wt% pyrite scenarios yielded a median precipitation of 2668 kg (range: 2510 to 3229 kg). And similarly, the 0.05 wt% pyrite scenarios showed a median of 2546 kg (range: 2040 to 2635 kg). When thermodynamic equilibrium was applied instead of kinetic reaction rates, median values were 1345 kg and 1228 kg for 0.5 wt% and 0.05 wt% pyrite concentrations, respectively, with ranges of 1234 to 1674 kg and 1067 to 1276 kg. Scenarios with homogeneous sediment properties produced median values of 1308 kg (0.5 wt% pyrite) and 1169 kg (0.05 wt% pyrite), with narrow interquartile ranges. The homogeneous pyrite distributions and completely homogeneous baseline case produced similar results with medians of 1469 kg (range from 1260 to 2041 kg) and 1400 kg for both the 0.5 and 0.05 wt% pyrite scenarios. Gypsum remained undersaturated throughout all simulations, and thus no gypsum precipitation was recorded.

3.4. Ion Concentration and Speciation

Maximum sulfate concentrations reached 768.5 mg/L in all scenarios. Sulfate breakthrough curves differed from tracer curves due to preexisting sulfate mobilization in the domain resulting from the initial equilibrium between groundwater and the mine dump sediments. Total sulfate mass flux varied between 627 and 992 kg for the heterogeneous scenarios despite similar average concentrations across the scenarios. The cumulative sulfate mass curves (Figure 10) show distinct groupings. Homogeneous and heterogeneous cases diverged after approximately 20 years, with heterogeneous scenarios showing more variable transport behavior.

Figure 10. Cumulative sulfate mass flow at the outlet, normalized to the homogeneous case.

Equilibrium-based pyrite oxidation scenarios demonstrated significantly enhanced computational efficiency, running 13 times faster than their kinetically controlled counterparts. The average simulation time was 52.4 h for kinetic models compared to 3.9 h for equilibrium-based approaches. The average sulfate concentrations and pH values differed by less than 1% between the two scenarios, but the oxidation fronts were noticeably sharper when the reactions were assumed to be at equilibrium. In contrast, incorporating kinetic controls caused a modest broadening or “smearing” of the front. Redox conditions shifted with average pe decrease from 8 to −2 due to complete oxygen consumption with the equilibrium approach. This shift influenced iron speciation, with Fe²⁺ concentrations reaching up to 0.145 mg/L compared to zero in kinetic scenarios.

Hydrogen carbonate in inflowing water and resident groundwater provided the only acid buffering capacity. Despite limited buffering, pH remained circumneutral (7.9–6.9) across all scenarios.

4. Discussion

4.1. Heterogeneity Accelerates Solute Transport and Alters Reaction Fronts

Heterogeneous systems exhibit earlier tracer breakthrough (by ~2 ± 1 years) and higher cumulative outflux (up to 139%) compared to their homogeneous equivalents. This acceleration stems from the presence of preferential flow paths due to spatially correlated porosity fields aligned with depositional layering. These channels bypass low-permeability zones, reducing effective residence times and increasing solute fluxes, even though average hydraulic conductivity is preserved. Similar phenomena have been found by simulating variable saturated flow in heterogeneous (lignite) mine spoils [33,37,67]. A definitive, systematic relationship between correlation length and breakthrough time could not be established in this work because the study was not designed to quantify this link; the chosen set of realizations serves to illustrate that correlation-length variations noticeably affect transport behavior. Additionally, retardation processes such as charge-dependent surface complexation [68,69], which correlate with permeability, may amplify the effect of sediment heterogeneity on the solute transport.

Scenarios with spatially heterogeneous permeability but homogeneous pyrite distributions showed transport behavior nearly identical to the fully heterogeneous cases, underscoring that flow architecture, not mineral distribution alone, governs early tracer breakthrough. In contrast, homogeneous porosity with heterogeneous pyrite distributions resulted in limited deviation from the baseline behavior with completely homogeneous sediments, suggesting that without preferential flow, mineral variability has a muted impact on bulk transport. This is especially true with the overall limitation of the dissolved oxygen concentration given in the studied scenarios, but may also be valid for similar scenarios in near-surface, partially saturated lignite mine spoils [33,34,35].

4.2. Widespread Oxidation Is Promoted by Pyrite Concentrations

Lower initial pyrite concentrations (0.05 wt%) led to oxidation fronts advancing up to 100% of the modeling domain length, compared to only ~4.5% in high-pyrite concentration (0.5 wt%) scenarios. This occurs because less pyrite is located along the flow paths, allowing for a deeper dissolved oxygen penetration through the dump and wider reactive zones [34]. While total pyrite mass oxidation is lower, its spatial extent and thus the sulfate release increase, potentially affecting larger volumes of groundwater and extending the footprint of contamination.

In practical terms, this suggests that areas with concentrated pyrite accumulations may pose a greater risk for the spatial extent of the oxidation front than similar or higher total pyrite amounts that are more evenly distributed, especially under continuous recharge. Homogeneous pyrite distributions, by contrast, confined oxidation to the near-inlet area, acting as an effective oxygen sink but limiting downstream impacts.

4.3. Equilibrium Assumptions Speed up Simulations but Distort Redox Speciation

Equilibrium-based pyrite oxidation reduced the computation time by 93% (52.4 to 3.9 h) while reproducing sulfate and pH within a relative error of 1% of the kinetic simulations. However, compared to the scenarios with kinetically moderated oxidation, the equilibrium approach led to very sharp oxidation fronts, complete oxygen depletion and a shift to reducing conditions (pe from 8 to −2), resulting in measurable Fe²⁺ concentrations (up to 0.14 mg/L), which were absent in the kinetic models. This reveals a critical trade-off of equilibrium models, which are efficient for screening or uncertainty analysis, whereas kinetic control can be essential for the quantitative prediction of redox zonation and metal mobility. For long-term forecasting in systems with fluctuating oxygen supply (e.g., PHS systems), kinetic formulations remain necessary to capture transient redox dynamics and the progression of the oxidation front in more detail.

4.4. Model Simplifications and Restrictions

The study is subject to several simplifications that may influence the quantitative transferability of the results to real-world mine dump systems: (i) the reactive transport simulations are confined to a 2D cross-section of a single bench, whereas actual dump bodies consist of three-dimensional benches with possible inter-bench hydraulic exchange, variable thicknesses, and lateral variations that can further modulate flow paths and reaction fronts [70]; (ii) the geochemical system is reduced to pyrite oxidation and calcite, goethite, and gypsum precipitation; additional mineral phases (e.g., silicates) or organic matter and microbial processes (e.g., sulfate-reducing bacteria [71]) are not represented, potentially underestimating natural attenuation processes such as sulfate reduction [27,72]; (iii) the stochastic generation of porosity and pyrite fields uses exponential covariance functions with a limited set of correlation lengths; other spatial structures (e.g., fractal heterogeneity, anisotropic channel networks) may produce different preferential flow patterns, but they are not captured here [73]; and (iv) model validation is restricted to laboratory benchmark tests; field-scale validation through tracer experiments, geophysical imaging, or long-term monitoring of a pilot dump would be required to confirm the applicability of the geostatistical approach, simulated breakthrough times, and acid-generation magnitudes.

4.5. Practical Implications for Mine Redevelopment and Management

The results of this study inform authorities, mining companies, and other stakeholders about several aspects of mine closure and post-mining land use:

• Sustained oxygen influx, e.g., by PHS operation will reactivate pyrite oxidation in internal mine dumps, especially in high-permeability zones. Monitoring should thus target flow paths, not just average pyrite content. Due to limited oxygen solubility and other oxygen-consuming processes, the extent of pyrite oxidation is low.
• Earlier contaminant breakthrough may occur in heterogeneous models than predicted by homogeneous ones.
• Low pyrite concentrations do not imply low environmental risk—dilute, widespread distributions may generate larger, longer-lasting plumes.
• Simplified geochemical models may suffice for estimating peak sulfate or pH, but lack simulating redox evolution and respective ion speciation.

Future work should investigate the impact of 3D heterogeneous settings on pyrite oxidation as well as lateral flow and channeling effects compared to the 2D ones applied in the present study. In this context, microbial sulfate reduction and electro-chemical surface charge effects have to be evaluated. Calibration by means of hydrologic field data will further support site-specific risk assessments and planning of pumped hydropower storage operations in former lignite mines.