Experimental and Modeling Study of Core-Scale Three-Dimensional Rough Fracture Acidic Wastewater Reaction with Carbonate Rocks

Abstract

Phosphogypsum leachate significantly accelerates carbonate rock dissolution in karst regions. The dissolution mechanism of phosphogypsum leachate associated with carbonate rock interaction and the corresponding numerical simulation need further study. In this study, 3D digital core imaging was used to scan undisturbed carbonate rock specimens from phosphogypsum landfill sites, and corresponding 3D structural models were constructed. We carried out indoor dissolution experiments in which we used Scanning Electron Microscopy as well as Energy Dispersive Spectrometer to observe changes in the surface micromorphology and elemental content of the rock specimens under different dissolution conditions. A reactive numerical model was developed based on the 3D structural model obtained from 3D digital core imaging, and numerical simulation studies were conducted. The dissolution reaction between phosphogypsum leachate and carbonate rocks exhibited an initial rapid phase followed by gradual stabilization. The pH of the leachate showed an exponential negative correlation with the dissolution amount per unit area of the rock specimens, while a power-law negative correlation was observed between pH and chemical dissolution rates. The numerical model effectively reproduced the reactant concentration states observed in experiments, confirming its capability to simulate reaction processes within rock specimens. Simulation results demonstrated that preferential flow through fracture channels led to higher reactant concentrations near fractures due to incomplete reactions, whereas lower concentrations occurred in sub-fracture regions. As the fracture aperture increased, the concentration disparity between these regions became more pronounced, with higher concentration of reactants at the outlet.

1. Introduction

Phosphogypsum leachate significantly accelerates carbonate rock dissolution in karst regions [1,2,3]. Despite global reliance on landfill disposal for phosphogypsum waste management, frequent leakage incidents from storage sites have been documented to accelerate carbonate rock dissolution [4,5,6], thereby compromising the geological integrity of karst terrains [7]. This process fundamentally arises from the evolution of geotechnical structures and hydrochemical compositions [8,9], which alter water–rock interaction mechanisms by exacerbating heterogeneity in both hydrodynamic parameters (e.g., flow rate, velocity) and solute transport processes (chemical component distribution) [10,11,12]. To systematically investigate these phenomena, this study integrates experimental investigations with numerical simulations, which in recent years have proven effective in characterizing a range of geological dynamics [13].

The evolution of carbonate rock dissolution constitutes a complex, multi-process coupled system involving fluid percolation, solute transport and diffusion, and multiphase chemical reactions at mineral–fluid interfaces [14]. Extensive research has been conducted through static and dynamic dissolution experiments to investigate macro-/microstructural evolution and physico-mechanical property alterations in rocks under varying chemical and coupled field conditions [15,16]. In this field, researchers employ diverse methodologies: Scanning Electron Microscopy (SEM) [17,18], computed tomography with digital image processing (CT) [19,20,21], Raman spectroscopy [22,23], and nuclear magnetic resonance (NMR) techniques [24,25]. These investigations have yielded insights into acetic acid–carbonate reaction dynamics [26], fractal characteristics of karst morphologies [27], dissolution rate quantification [28], and kinetic model development [29]. Notably, most existing carbonate dissolution experiments [30,31,32] under reservoir conditions employ plug-flow [33] or rotating disk reactors [34]. These setups primarily replicate surface-mediated reactions. However, these surface-focused approaches fail to replicate the intrinsic petrogenetic processes in which acidic fluids migrate through pore networks characterized by hydrodynamically constrained pathways or conditions. Extensive research on factors influencing chemical dissolution processes has demonstrated that carbonate rock dissolution rates exhibit strong dependencies on solution pH, chemical composition [35,36], lithology (mineralogical constitution) [37], structural characteristics, CO₂ partial pressure [38], temperature, and hydrodynamic conditions. Experimental studies [39,40] demonstrate that pH critically controls carbonate dissolution rates. Kinetic analysis of dolomite dissolution [41] reveals limestone’s faster reaction kinetics compared to dolomite, necessitating strict mineralogical control in this study. Acetic acid-based dissolution experiments on four carbonate types show inverse temperature dependence and positive pressure correlation for dissolution efficiency, with temperature exerting greater influence than pressure [42]. Consequently, our experimental design incorporates pressure modulation while maintaining temperature constraints.

Building upon previous experimental findings, this study combines physical experimentation and numerical simulations to investigate the mechanism of interaction between phosphogypsum leachate and fractured carbonate rock. Unlike conventional surface reaction simulations, our approach incorporates critical factors influencing dissolution (e.g., fracture aperture variations) while systematically quantifying phosphogypsum–carbonate dissolution characteristics under different geochemical conditions. This methodology thereby provides more realistic representations of subsurface reactive transport processes compared to idealized surface reaction models.

This study consists of two main components: (1) physical experimentation and numerical modeling framework establishment, and (2) dissolution mechanism analysis. The first part focuses on static/dynamic dissolution experiment designs and numerical model setup (initial conditions, boundary constraints). The second part clarifies the reaction mechanisms between phosphogypsum leachate and carbonate rocks, with experimental data and simulations cross-validated to confirm results reliability.

2. Materials and Methods

2.1. Experimental Material

2.1.1. Carbonate Rock

All rock specimens used in the experiment were Nanling Formation limestone, obtained from core specimens of the same stratum at a depth of 30–50 m in an industrial solid waste landfill. The specimens were selected for their relatively intact condition, with a height exceeding 30 mm and differing only in fracture aperture. The overall color of the rock specimens ranged from grayish-white to grayish-black, and they exhibited a microcrystalline structure. On the surface of the rocks, small areas of yellowish-brown weathering could be observed, likely caused by long-term natural erosion and oxidation, which altered the color of certain parts of the rock surface. Additionally, the rocks contained numerous calcite veins, with apertures ranging from 1–5 mm, which appeared as distinct linear patterns within the rock. Figure 1 illustrates some of the rock specimen: (a) shows the specimen with fracture apertures of 0.6 ~0.2 mm, (b) shows the specimen with fracture apertures of 0.2~0.05 mm, and (c) shows the specimen with fracture apertures of 0.05~0.01 mm.

The rock specimens were analyzed using an X-ray Diffractometer (XRD, DX-2700, Dandong Haoyuan Instrument Co., Ltd., Dandong, China). To minimize the impact of subjective factors on the analysis results of rock specimen mineral composition during XRD analysis, a Scanning Electron Microscopy (SEM, SU8010, Hitachi, Tokyo, Japan) equipped with an Energy Dispersive Spectrometer (EDS) was used to analyze the chemical composition of the rock specimens (see

Table 1. The EDS analysis results.

Element	C	O	Ca	Si	Al	Mg	K	S	Fe
Content	42.05%	40.99%	12.53%	1.43%	1.06%	0.80%	0.54%	0.38%	0.22%

). The mineral composition of the rocks was then determined by combining the EDS analysis results with the XRD analysis results, as shown in

Table 2. Mineral composition analysis table.

Mineral Name	Chemical Formula	Mineral Proportion
Calcite	CaCO3	65%
Alunite	KAl3(SO4)2(OH)6	8%
Anhydrite	CaSO4·2H2O	6%
Others	/	21%

. After measurement, it was found that the main component of all collected rock specimens is calcite, with the proportion of CaCO₃ ranging from 60% to 69%.

2.1.2. Phosphogypsum Leachate

The collected phosphogypsum leachate was placed in a refrigerator for low-temperature storage, and 300 mL of leachate was removed and sent to the testing center to determine the concentration of pH, Ca²⁺, Mg²⁺, total P, SO₄²⁻, F⁻, PO₄³⁻, and TDS. The test results are shown in

Table 3. Results of ion concentration tests in phosphogypsum leachate.

pH	Ca2+ [mg/L]	Mg2+ [mg/L]	Total P [mg/L]	SO42− [mg/L]	F− [mg/L]	PO43− [mg/L]	TDS [mg/L]
4.03	323	92	592	1789	10.54	337	5142

.

According to the results of ion concentration tests in phosphogypsum leachate, the phosphogypsum leachate obtained from the field is acidic. The concentrations of calcium ions, total P, and sulfate radicals in the solution are very high, and it also contains a certain amount of fluoride ions. Therefore, this paper focuses mainly on the concentrations of the above four substances.

2.2. Physical Experiment

2.2.1. Static Dissolution Experiments

Due to the limitations of natural conditions and indoor experimental conditions, the experiments were conducted in a closed indoor environment at 20 °C. Before the start of the experiment, rock specimens with different fracture widths were cut and polished, and a total of six specimens were prepared. Acid solutions with pH gradients of 2, 3, and 4 were prepared using 36% HCl dripped into the phosphogypsum leachate collected from the field. These solutions were then poured into six beakers, each with a capacity of 5000 mL. Among them, one beaker contained solution with pH 4, one beaker contained solution with pH 3, and four beakers contained solution with pH 2, making a total of six beakers. The duration of the static corrosion experiment was set to 30 days, and the experimental conditions are shown in

Table 4. Static dissolution experimental conditions.

Different pH Groups			Different Fracture Aperture Groups
Rock Specimen ID	Fracture Aperture [mm]	pH	Rock Specimen ID	Fracture Aperture [mm]	pH
HY01	0.5~0.3	4	HY04	0.6~0.1	2
HY02	0.6~0.4	3	HY05	0.3~0.1	2
HY03	0.7~0.3	2	HY06	0.05~0.01	2

. Notably, in static dissolution experiments, reactions between phosphogypsum leachate and carbonate rock stabilize within 30 days, enabling systematic analysis of dissolution characteristics. After 30 days of reaction, parameter variations diminish to marginal rates, rendering mechanistic trends statistically indistinguishable and insufficient for extrapolating dissolution dynamics. Therefore, the experimental duration was set to 30 days. A tiered monitoring strategy was adopted: high-frequency sampling and measuring during the preliminary stage (Days 0–2) captured critical value transitions, followed by reduced measurement frequency (Days 2–30) to track equilibrium trends as the system approached steady-state conditions.

In addition to the above two groups of experiments, a control group was also set up, also using carbonate rocks as specimens, with distilled water as solution.

2.2.2. Dynamic Dissolution Experiments

In a closed indoor space with the temperature controlled at 20 °C, dynamic dissolution experiments were conducted on six rock specimens with different fracture apertures using a homemade acrylic cylindrical mold reactor device. The experiments were divided into six groups.

Unlike the static dissolution experiment conditions mentioned above, the dynamic dissolution experiments introduced hydrodynamic conditions to the solution, with a pressure differential of 0.1 MPa between the inlet and outlet. The duration of the dynamic dissolution experiment was set to 15 days, and the experimental conditions are shown in

Table 5. Dynamic dissolution experimental conditions.

Different pH Groups			Different Fracture Aperture Groups
Rock Specimen ID	Fracture Aperture [mm]	pH	Rock Specimen ID	Fracture Aperture [mm]	pH
HY07	0.5~0.2	4	HY10	0.7~0.1	2
HY08	0.5~0.1	3	HY11	0.2~0.1	2
HY09	0.6~0.1	2	HY12	0.05~0.01	2

. It should be noted that in dynamic dissolution experiments, extending the reaction beyond 15 days causes fracturing of rock specimens, resulting in loss of cylindrical integrity. This structural degradation compromises systematic analysis of reactive transport mechanisms governing percolating fluids within fractures and pores. Consequently, the experimental duration was limited to 15 days. To ensure data reliability, a monitoring strategy combining high-frequency sampling and measuring during the preliminary stage (Days 0–2) with progressively reduced measurement intervals (Days 2–15) was implemented for periodic parameter quantification.

The equipment for this indoor dissolution experiment includes several 5000 mL beakers and an acrylic cylindrical mold reactor device. In the static dissolution experiment, phosphogypsum percolate and rock specimens were placed in beakers for reaction. In the dynamic dissolution experiment, phosphogypsum percolate and rock specimens were reacted in the acrylic cylindrical mold reactor device. The device (BT100-2J, Dichuang Technology Co., Ltd., Chengdu, China) is shown in Figure 2. It mainly consists of an adjustable peristaltic pump, a pressure gauge, a homemade acrylic cylindrical mold, and silicone tubes. The homemade acrylic cylindrical mold is made of acrylic sheet, also known as polymethyl methacrylate (PMMA), which has good light transmission, high plasticity, acid and alkali resistance, and strong ageing resistance. The acrylic cylindrical mold has an inner diameter of 8.5 cm, an outer diameter of 9.5 cm, and a wall thickness of 1 cm. The silicone tube has an inner diameter of 0.32 cm, an outer diameter of 0.64 cm, and a wall thickness of 0.16 cm. Both the inlet on the left side and the outlet on the right side of the acrylic cylindrical mold can be opened, allowing easy access to specimens with a diameter of approximately 85 mm.

2.3. Calculation Method of Dissolution Evaluation Parameters

To quantitatively reflect the dissolution process and characteristics, the following four parameters are involved: rock dissolution amount per unit area, dissolution rate, chemical dissolution rate, and the relative change rate of fracture aperture. The formulas are as follows:

(1) Dissolution amount per unit area

Dissolution amount per unit area refers to the mass or volume of rock lost due to dissolution per unit area. It is an important indicator that reflects the dissolution speed and intensity of rock specimens under experimental conditions [43], expressed as follows:

$$K={\displaystyle \frac{m_0-m_1}{S}}$$

(1)

where K is the dissolution amount per unit area [g/cm²], $m_0$ shows the mass of the rock specimen before dissolution [g], $m_1$ refers the mass of the rock specimen after dissolution [g], and S is the surface area of the rock specimen [cm²].

(2) Dissolution rate

The dissolution of rocks by acid is characterized by the amount of rock that can be dissolved by the acid solution, which is expressed as the dissolution rate. Under different pH conditions, the dissolution rates of different lithologies vary. Through this static and dynamic dissolution experiment, we can understand the size of the dissolution rate of phosphogypsum leachate on carbonate rock, as well as analyze the dissolution capacity of phosphogypsum leachate on carbonate rock. The dissolution rate is one of the methods to quantitatively evaluate the characteristics of this dissolution reaction:

$$R_c={\displaystyle \frac{W_1-W_2}{W_1}}\times 100\%$$

(2)

where W₁ shows the mass of the drying specimen before the experiment [g], and W₂ is the mass of the drying specimen after the experiment [g].

(3) The chemical dissolution rate

The chemical dissolution rate R serves as a quantitative indicator of the solubility strength of carbonate rocks [44], and is given by the following:

$$R={\displaystyle \frac{2.5X+3.5Y}{t}}$$

(3)

where R shows the chemical dissolution rate of the main minerals in carbonate rocks [mg/(s·L)], X gives the content of Ca²⁺ in the dissolution solution [mg/L], Y shows the content of Mg²⁺ in the dissolution solution [mg/L], t is the time of dissolution action [s]. For ease of subsequent calculations and plotting, this study converts the unit of R to mg/(d∙L) (where 1 d = 86,400 s).

(4) The relative change rate of fracture aperture

The relative change rate of fracture aperture can be used to express the relative change degree of rock specimen fracture aperture before and after the experiment, which is a dimensionless parameter:

$${\epsilon }_b={\displaystyle \frac{b_1-b_0}{b_0}}\times 100\%$$

(4)

where ${\epsilon }_b$ is relative change rate of fracture aperture; $b_0$ shows the initial average fracture aperture [mm], $b_1$ is the measured average aperture at the end of the reaction [mm].

2.4. Numerical Simulation

2.4.1. Control Equations

The governing equations for mass conservation and Darcy flux are expressed as follows:

$${\displaystyle \frac{\partial }{\partial t}}\left({ϵ}_p\rho \right)+\nabla ·\left(\rho u\right)=Q_m$$

(5)

$$u=-{\displaystyle \frac{k}{\mu }}\nabla p$$

(6)

where t is the time [s], ${ϵ}_p$ denotes the porosity, $\rho$ is the liquid density [kg/m³], $Q_m$ shows the reaction source [kg/(m³·s)], k gives the permeability [m²], $\mu$ represents the leachate kinetic viscosity [MPa·s], and $\nabla p$ is the pressure differential, which in this study is 0.1 MPa, u shows Darcy flux [m/s²]. k and ${ϵ}_p$ are from geotechnical tests and engineering reports.

The governing equation for diluted solute transport through porous media is expressed as follows:

$${\displaystyle \frac{\partial \left(\rho C\right)}{\partial t}}+\nabla ·\left(\rho Cv\right)=\nabla ·\left(D\nabla C\right)+R$$

(7)

where $\rho$ is the liquid density [kg/m³], C equals the concentration of the substance [mol/m³], t is time [s], v is the velocity vector of the leachate [m/s], D is diffusion coefficient [m²/s], R shows the reaction source [mol(m³·s)].

2.4.2. Initial and Boundary Conditions

This numerical simulation study focuses on the transport and transformation processes of selected reactive species (HF, H₂SO₄) in phosphogypsum leachate under dynamic dissolution conditions. The anisotropic flow behavior in fractured rock masses is primarily controlled by fracture network characteristics. Considering the substantial variations in fracture orientation, density, and connectivity among different rock specimens, we systematically selected specimens with nearly identical fracture attributes (including quantity, spatial distribution, and developmental direction) for dynamic dissolution experiments to ensure analytical consistency. This selection protocol justified the exclusive use of the HY10 specimen for subsequent numerical modeling. While pH variations influence reaction kinetics, they do not fundamentally modify solute transport mechanisms within the rock matrix. Consequently, the numerical simulations specifically addressed phosphogypsum leachate–carbonate rock dissolution interactions under pH = 2 conditions.

The HY10 rock specimen was imaged using a multi-scale high-resolution X-ray 3D digital core imaging system (X-CT, NanoVoxel4561, Sanying Precision Instruments Co., Ltd., Tianjin, China). The reconstructed 3D fracture model generated through Avizo’s image processing pipeline was subsequently exported in STL formats. These files were then imported into COMSOL Multiphysics (version 6.2) to establish a refined fracture mesh model. But the mesh model contained excessive mesh elements with incomplete curves and unclosed geometries, preventing direct conversion into a physical model. To address this, the fracture model was simplified. The rock specimen’s fracture parameters, including average fracture aperture (0.50 mm), dominant fracture orientation, and cumulative fracture length, were quantified using the Label Analysis module in Avizo software (version 2020.1). The original complex fracture network was replaced with five rectangular thin plates whose apertures matched the measured average value (0.50 mm), with identical spatial orientations and positions. A cylindrical host rock measuring 85 mm in diameter and 30 mm in height, consistent with the actual specimen dimensions, was then incorporated. By varying the plate thickness while maintaining aperture consistency, three models with fracture apertures of 0.20 mm, 0.50 mm, and 0.05 mm were established. Gravitational effects were excluded from all simulations. The cylindrical rock specimen model’s top surface was assigned as the inflow boundary (pressure inlet), and the bottom surface was designated as the outflow boundary (pressure outlet).

Fine hierarchy in COMSOL Multiphysics was selected based on a balanced consideration of average mesh quality and solver performance, prioritizing optimal trade-offs between numerical accuracy and computational efficiency. The meshing strategy employs a physics-controlled mesh generation approach, where the software automatically generates the computational grid based on predefined boundary conditions of the Darcy flow field and solute concentration field.

The model parameters were primarily derived from geotechnical experimental data, engineering reports, and empirical correlations. In COMSOL Multiphysics, the pH value and temperature were defined as global parameters, set to 2 and 293.15 K, respectively, under the Global Definitions node to establish consistent environmental conditions throughout the model. For the Darcy flow field configuration, the permeability (k), porosity (${ϵ}_p$), and specific storativity ($\mu S$) were adopted from

Table 6. Seepage calculation parameters table.

Model Component Names	k [m2]	${\mathit{ϵ}}_{\mathit{p}}$	$\mathit{\mu }\mathit{S}$ [1/Pa]
Matrix	4.6 × 10−14	0.05	1 × 10−5
Fracture	5.6 × 10−13	0.3	1 × 10−4

, while other hydrodynamic parameters utilized standard water properties from the COMSOL Multiphysics material library, neglecting the physicochemical discrepancies between phosphogypsum leachate and deionized water.

The reaction rates for chemical species must be configured within the Dilute Species Transport interface. Given that the pH of phosphogypsum leachate in our experiments varied within the range of 2–7, and considering only the first dissociation step of phosphoric acid, the dissolution interactions between phosphogypsum leachate and carbonate rock primarily involve three key chemical reactions,

CaCO₃ + H₂SO₄ ⇌ CaSO₄ + H₂O + CO₂↑

CaCO₃ + 2HF ⇌ CaF₂ + H₂O + CO2↑

CaCO₃ + 2H₃PO₄ ⇌ Ca(H₂PO₄)₂ + H₂O + CO₂↑

the quantification of reaction parameters was achieved through ion concentration measurements conducted prior to and at specific intervals during the dynamic dissolution experiments. The inflow concentration of Ca²⁺ was determined as 7.73 mol/m³, with the overall average dissolution rate of CaCO₃ in phosphogypsum leachate reaching 2.13 × 10⁻⁴ mol/(m³·s). Concurrently, the HF inflow concentration measured 0.6147 mol/m³, exhibiting an average reaction rate of 2.51 × 10⁻⁶ mol/(m³·s). For H₂SO₄, the inflow concentration was recorded at 18.62 mol/m³, with its average reaction rate calculated as 9.17 × 10⁻⁵ mol/(m³·s) using the empirical formula cited in references [45,46]. These derived values provide critical inputs for constraining the geochemical reaction kinetics in subsequent numerical simulations. The other initial and boundary conditions are organized in

Table 7. Initial and boundary conditions.

Upper Surface Pressure of the Model [MPa]	Lower Surface Pressure of the Model [MPa]	Side of the Model	Initial C(HF) [mol/m3]	Initial C(H2SO4) [mol/m3]
0.1	0	No-flow boundary	0.6147	18.62

.

3. Analysis and Discussion

3.1. Characteristics of Surface Micro-Morphological Changes

Figure 3 shows micro-morphological changes of rock specimens before and after reaction under different pH conditions. Macroscopic observations revealed distinct dissolution patterns: specimens from static dissolution experiments exhibited minimal surface alteration, primarily manifesting as slight color lightening, whereas dynamic dissolution specimens showed pronounced morphological changes, particularly in the HY10 specimen with the largest fracture aperture, where protruded particles, intensive etching pits, and dissolution striations developed along fracture margins.

Microscopic analysis further corroborated enhanced dissolution under hydrodynamic conditions. Pre-experiment specimens displayed intact mineral grains with well-defined polyhedral crystal boundaries and tightly packed micro-lamination structures. Post-static dissolution, the HY03 specimen exhibited the most severe micro-scale degradation among static groups, featuring fragmented crystal integrity and dense etching pits. In contrast, the dynamically treated HY09 specimen, despite only 15 days of reaction, demonstrated catastrophic surface erosion: complete obliteration of primary grain boundaries, extensive leaching of soluble components leaving insoluble skeletal frameworks, and pervasive micro-fracture networks.

EDS analysis (as summarized in

Table 8. Surface oxygen content of each specimen before and after the experiment.

	HY01	HY02	HY03	HY07	HY08	HY09
Surface oxygen content before experiment [%]	43.86	41.60	39.14	40.17	42.31	38.27
Surface oxygen content after experiment [%]	76.09	76.18	72.46	68.14	70.33	67.26

) revealed a systematic increase in surface oxygen content across all specimens, with static dissolution experiments demonstrating a more pronounced enhancement compared to dynamic dissolution counterparts.

3.2. Characteristics of Changes in Dissolution Amount per Unit Area and Dissolution Rate

As demonstrated in Figure 4, the dissolution amount per unit area and dissolution rate both exhibit a positive correlation with increasing acidity of phosphogypsum leachate, indicating enhanced carbonate rock dissolution under more acidic conditions. In static experiments, comparative analyses of specimens with varying fracture apertures at identical pH revealed a distinct inverse relationship between fracture aperture and dissolution intensity, following the order HY04 < HY05 < HY06. This phenomenon may be attributed to the preferential accumulation of flocculent reaction precipitates within narrow fractures and pores, which artificially inflates measured specimen mass through pore-clogging effects. Conversely, the dynamic experiments demonstrated that larger fracture apertures resulted in higher dissolution amounts per unit area and higher dissolution rates in the rock specimens.

Comparative analysis of dissolution amounts per unit area between static dissolution and dynamic dissolution experimental results (

Table 9. Dissolution amount per unit area for selected rock specimens.

Rock Specimens ID	Fracture Aperture [mm]	Dissolution Amount Per Unit Area [g/cm2]
HY04	0.6~0.1	0.0252
HY05	0.3~0.1	0.0261
HY06	0.05~0.01	0.0289
HY10	0.7~0.1	0.3886
HY11	0.2~0.1	0.3392
HY12	0.05~0.01	0.2901

) revealed that under identical pH conditions and fracture apertures, rock specimens subjected to 15-day dynamic dissolution exhibited 10- to 15-fold higher areal dissolution values compared to those from 30-day static experiments. This significant disparity quantitatively demonstrates that hydrodynamic conditions substantially enhance carbonate rock dissolution intensity relative to stagnant systems, with advective solute transport mechanisms dominating the accelerated dissolution processes.

3.3. Characterization of Fracture Aperture Changes

The average fracture aperture of each specimen was quantified before and after experiments using X-CT, and the relative fracture aperture variation rates were calculated and plotted in Figure 5.

Both static and dynamic dissolution experiments exhibited similar trends in fracture aperture variation rates. Higher initial acidity of the phosphogypsum leachate correlated with greater relative aperture variation rates, while specimens with larger initial fracture apertures demonstrated higher post-reaction variation magnitudes. Notably, dynamic experiments yielded systematically higher aperture variation rates than static experiments, conclusively demonstrating that dissolution intensity under hydrodynamic conditions significantly exceeds that in stagnant systems.

3.4. Characterization of Changes in Phosphogypsum Leachate

3.4.1. Characterization of pH Changes

The experiments monitored pH variations in the leachate, generating characteristic pH evolution curves over time under different initial pH conditions (Figure 6). The time in the graph represents the time from the discovery of the lysate in the outlet section of the reactor. Specimens HY10, HY11, and HY12 required 2 h, 4 h, and 5 h, respectively, to reach leachate breakthrough, while other specimens exhibited comparable breakthrough times (2–3 h) (where 1 d = 24 h).

In static dissolution experiments, higher initial acidity of the phosphogypsum leachate correlated with extended effective reaction durations, prolonged equilibrium attainment times, and greater pH increases. This occurred due to progressive H⁺ ion consumption during acid–carbonate neutralization, which elevated pH over time. Notably, fracture aperture exerted negligible influence on dissolution rates in static systems.

Conversely, dynamic dissolution experiments demonstrated pH decreases throughout the reaction period, opposing the static trend. Leachates with higher initial acidity exhibited more pronounced pH declines. Additionally, smaller fracture apertures amplified pH variation magnitudes, extended stabilization periods, and resulted in higher stabilized pH values compared to wider apertures.

3.4.2. Characterization of TDS Changes

Figure 7 illustrates the variation of TDS over time. In static dissolution experiments employing phosphogypsum leachate at pH = 2, TDS exhibited an initial rapid decline followed by stabilization, a pattern attributed to accelerated H⁺-carbonate mineral reactions causing ionic depletion during the early stage, succeeded by reaction rate decay and ion-exchange equilibrium. Contrastingly, systems at pH = 3–4 demonstrated V-shaped TDS trajectories: an initial decrease succeeded by a gradual rebound. Notably, the inflection point marking the transition from TDS decline to recovery occurred earlier under pH = 4 conditions compared to pH = 3, indicating accelerated geochemical transformations in higher-pH environments. Higher initial acid concentrations in closed systems led to faster depletion of reactive acids and lower subsequent reaction rates [47]. This TDS reversal mechanism suggests early-stage H⁺ consumption and common-ion effects suppress Ca²⁺ dissolution, while later CO₂ dissolution promotes HCO₃⁻ accumulation.

Conversely, dynamic dissolution experiments showed opposing TDS evolution patterns characterized by an initial rapid increase followed by stabilization. Higher initial leachate pH enhanced TDS variation magnitudes, while smaller fracture apertures prolonged stabilization periods, reduced stabilized TDS values, and amplified cumulative TDS fluctuations compared to wider apertures.

3.4.3. Characteristics of Changes in Ca²⁺, SO₄²⁻, F⁻, and Total P Concentrations

Figure 8 delineates changes in the concentration of each ion. In static dissolution experiments, lower initial pH values of phosphogypsum leachate correlated with greater increases in Ca²⁺ concentrations and more pronounced decreases in F⁻ concentrations as the reaction progressed. Concurrently, SO₄²⁻ and total phosphorus concentrations stabilized but exhibited an overall declining trend, likely attributable to calcium sulfate precipitation (gypsum) from sulfuric acid–calcium carbonate reactions. The positively charged surfaces of calcium sulfate and calcium fluoride precipitates may electrostatically adsorb negatively charged ions, forming surface complexes characterized by P-O-Ca bonding. Additionally, partial incorporation of dihydrogen phosphate ions into the crystal lattice during gypsum growth could further contribute to phosphorus retention.

Conversely, dynamic dissolution experiments demonstrated inverted ion concentration trends relative to static conditions: Ca²⁺ concentrations decreased while F⁻ concentrations increased over time. Specimens with smaller fracture apertures required extended durations to reach concentration stabilization, and higher initial leachate acidity amplified concentration variations for both Ca²⁺ and F⁻. SO₄²⁻ and total P concentrations showed minimal fluctuations, gradually increasing throughout the experiments.

3.5. Discussion

3.5.1. Relationship Between Conductivity, pH, and Chemical Dissolution Rate

The chemical dissolution rates of carbonate rocks are significantly influenced by external environmental conditions. In static dissolution experiments conducted with phosphogypsum leachate at an initial pH of 2, post-reaction analyses quantified Ca²⁺ and Mg²⁺ concentrations in the leachate and calculated chemical dissolution rates for each rock specimen (

Table 10. Electrical conductivity and chemical dissolution rate.

Rock Specimen ID	Conductivity [μS/cm]	Ca2+ [mg/L]	Mg2+ [mg/L]	Chemical Dissolution Rate [mg/(L·d)]
HY03	966	460.1	86.8	48.402
HY04	992	458.2	87.8	48.585
HY05	954	457.8	92.7	48.998
HY06	929	420.3	109.8	52.127

). Liu et al. [48] established a linear correlation between solution electrical conductivity (EC) and calcium ion content. Subsequent analysis of post-static dissolution leachates revealed a strong dependence of electrical conductivity on C(Ca²⁺), as evidenced by the positive correlation between these parameters in Figure 9. Conversely, an inverse relationship was observed between electrical conductivity and C(Mg²⁺).

Throughout the rock dissolution process, the continuous ionization of H⁺ from phosphogypsum leachate drives chemical reactions with carbonate minerals, consuming substantial H⁺ ions while releasing newly generated ions into the solution. These dynamic ionic exchanges critically modulate the leachate’s electrical conductivity, thereby regulating the dissolution kinetics between phosphogypsum leachate and carbonate rocks. Linear regression analysis of electrical conductivity versus chemical dissolution rates across four experimental groups revealed a positive correlation, with dissolution rates increasing proportionally to conductivity (slope = 0.08323). The linear fitting results are presented in Figure 10a.

3.5.2. Relationship Between pH and Chemical Dissolution Rate

Fitting analysis of dissolution per unit area for three rock specimens under static dissolution conditions across varying acidity levels of phosphogypsum leachate revealed an exponential relationship between leachate pH and areal dissolution rates. As illustrated by the fitted equations in Figure 10b, the dissolution per unit area decreased progressively with increasing leachate pH, exhibiting a diminishing rate of decrease that asymptotically approached stability at higher pH values.

To investigate whether an exponential relationship exists between pH and chemical dissolution rates, we conducted statistical analysis of pH variations and corresponding dissolution rates under leachate conditions with initial pH = 2. The results demonstrated a rapid initial decline in dissolution rates with increasing pH, followed by progressive stabilization. Comparative fitting of experimental data using both power function (Asym2Sig model) and exponential functions revealed superior correlation coefficients for the power function model (Figure 10c), indicating that the pH-dissolution rate relationship adheres more closely to the Asym2Sig power-law formulation. Further validation through analogous fitting analyses across multiple leachate pH groups (Figure 10d–f) consistently yielded high correlation coefficients, confirming the generalized applicability of the power function in describing these geochemical interactions.

3.5.3. Influence of the Presence or Absence of Hydrodynamic Conditions on Dissolution Effects

Significant disparities in dissolution efficacy were observed between static and dynamic experimental conditions. Comparative analysis of chemical dissolution rates at 24 h post-experiment initiation revealed that dynamic systems consistently exhibited 7.37–12.26 times higher rates than static systems across varying initial leachate pH levels (2~4), with the discrepancy amplifying under lower pH conditions, as demonstrated in Figure 11.

The pronounced disparity in chemical dissolution rates between static and dynamic experimental conditions arises from three interconnected mechanisms. Primarily, the transition to hydrodynamic conditions facilitates enhanced leachate penetration into rock pores and fractures, substantially expanding reactive interfacial areas between H⁺ ions and carbonate mineral surfaces, thereby accelerating dissolution kinetics. Additionally, the intensified dissociation of weak acids (e.g., hydrofluoric acid, phosphoric acid) under dynamic flow elevates leachate H⁺ concentrations, further amplifying proton-driven dissolution processes. Crucially, hydrodynamic forcing induces advective mass transport dominance, which dramatically enhances H⁺ delivery efficiency to reactive sites through accelerated convective transfer, synergistically elevating overall dissolution rates. This mechanistic cascade explains the order-of-magnitude enhancement in chemical dissolution rates observed under dynamic conditions compared to static systems.

3.6. Numerical Simulation Results

Post-simulation analyses yielded fracture-specific volumetric flow rates through cross-sectional integration: 3.15 × 10⁻⁶ m³/h for the 0.50 mm aperture model, 1.58 × 10⁻⁶ m³/h for the 0.20 mm model, and 1.26 × 10⁻⁶ m³/h for the 0.05 mm model.

The temporal evolution of bottom-surface Ca²⁺ concentrations is detailed in Figure 12. The 0.50 mm aperture model achieved concentration stabilization (9.98 mol/m³) at 27 h, consistent with dynamic dissolution experimental results. Similarly, the b = 0.20 mm and b = 0.05 mm models stabilized at 10.48 mol/m³ (60 h) and 10.6 mol/m³ (68 h), respectively, aligning with experimental observations. These results confirm the inverse correlation between fracture aperture and stabilization duration, where narrower apertures prolong equilibration periods while amplifying concentration variation magnitudes, mirroring patterns observed in experiments.

The spatial-temporal evolution of HF concentrations is presented in Figure 13, illustrating concentration distributions at three critical stages: initial conditions, leachate breakthrough at the reactor outlet, and steady-state equilibrium. Notably, specimens with varying fracture apertures exhibited distinct breakthrough times at the outlet, aligning temporally with observations from dynamic dissolution experiments. The HF concentration gradients demonstrate a consistent spatial attenuation from the inflow to outflow boundaries, with lower concentrations detected in the rock matrix beneath fractures. Following leachate breakthrough at the reactor outlet, preferential flow through fracture channels can be observed.

Further analysis reveals a positive correlation between fracture aperture and HF concentrations at the outlet, consistent with experimental measurements. Additionally, widening fracture apertures amplified concentration differentials between fracture zones and adjacent rock matrices, reflecting enhanced mass transport efficiency in larger flow pathways. The presence of preferential flow pathways fundamentally alters reactant transport dynamics in rock specimens. These findings quantitatively validate the critical role of fracture aperture in governing solute transport mechanisms during acid–rock interactions.

Numerical simulations predict the sulfuric acid (H₂SO₄) concentration evolution during reactive transport (Figure 14), revealing spatial attenuation patterns analogous to HF but differing significantly in concentration magnitudes and reaction kinetics. The H₂SO₄ concentration decreases progressively from inflow to outflow boundaries with notably lower concentrations observed in sub-fracture matrix regions. Similarly, preferential flow through fracture channels can be observed when the leachate breaks through to the reactor outlet. Based on the experimental framework, where only the first dissociation step of phosphoric acid was considered for reaction participation, it is hypothesized that sulfuric acid concentration dynamics mirror phosphate’s attenuation patterns under identical hydrodynamic and geochemical constraints.

4. Conclusions

This study employed an integrated approach combining physical experiments and numerical simulations to investigate the dissolution mechanisms of carbonate rocks with varying fracture apertures under phosphogypsum leachate exposure across different pH levels. Key findings are summarized as follows:

(1)

It is known from physical experiments that phosphogypsum leachate–carbonate rock interactions exhibit rapid initial dissolution followed by progressive stabilization. In this study, lower leachate pH correlated with accelerated dissolution rates, a phenomenon directly evidenced by microscale morphological alterations on carbonate rock surfaces. EDS analysis confirmed that dissolution-induced secondary minerals accumulate extensively on rock specimen surfaces. Fracture aperture minimally affects static dissolution patterns but critically influences dynamic systems—smaller apertures exhibit limited enlargement and delayed pH stabilization with higher final pH.

(2)

Comparative analysis of different physical experiments shows that the hydrodynamic conditions dramatically intensify dissolution. Dynamic systems exhibit 10–15 times greater dissolution amount per unit area than static conditions. Notably, the evolution trends of key geochemical parameters (pH, Ca²⁺, SO₄²⁻, F⁻, and total P concentrations) displayed opposing patterns between dynamic and static systems. Static dissolution experiments revealed a linear positive correlation between chemical dissolution rates of carbonate rocks and solution conductivity. Concurrently, phosphogypsum leachate pH demonstrated an exponential negative correlation with rock dissolution amount per unit area, while exhibiting a power-law negative correlation with chemical dissolution rates.

(3)

Numerical simulation results demonstrated that preferential flow through fracture channels led to higher reactant concentrations near fractures due to incomplete reactions, whereas lower concentrations occurred in sub-fracture regions. As the fracture aperture increased, the concentration disparity between these regions became more pronounced, with higher concentration of reactants at the outlet.

This study innovatively combines physical experimentation with numerical simulations to analyze and characterize the transport and transformation mechanisms of phosphogypsum leachate within rock fractures, employing more practical conditions for the reaction of phosphogypsum leachate with carbonate rock. This study provides novel insights into the geochemical interaction mechanisms of acidic fluids within geological matrices, providing a theoretical basis for the research of other acidic aqueous solutions. The findings offer critical guidelines for sustainable phosphogypsum management strategies and provide technical guidance for optimizing site selection and safety protocols in tailings disposal engineering, particularly in karst terrain with active dissolution processes.

This study acknowledges limitations in physical experimentation and numerical modeling:

(1)

The experimental analysis focused exclusively on limestone, excluding other carbonate variants (e.g., dolomite, magnesite). Future investigations should incorporate diverse carbonate lithologies with varying mineralogical compositions to comprehensively characterize dissolution mechanisms.

(2)

The numerical model simplified environmental variables, omitting temperature gradients, CO₂ partial pressure, and chemo-hydro-mechanical couplings. Enhanced simulations integrating these multi-physics interactions are required to improve predictive accuracy.