Abstract
To reveal the influence mechanism of water injection pressure and fracture characteristics on hard rock moisture diffusion, this study selects sandstone as the research object and combines low-temperature high-pressure nuclear magnetic resonance tests with COMSOL Multiphysics numerical simulations. Current research has widely applied nuclear magnetic resonance for fluid distribution analysis and COMSOL for seepage simulation, but their coupling to clarify the combined effects of pressure and fractures on hard rock wetting remains insufficient, especially for high-density, low-porosity hard rock with poor permeability. This study systematically investigates water migration under varied pressures and fracture lengths. Experimental results show moisture increase is dominated by adsorbed water, and nuclear magnetic resonance T2 spectral peak area expands significantly with pressure and time, proving high pressure effectively opens closed pores and enhances seepage channel connectivity. Simulation results demonstrate that the wetting radius exhibits an exponential relationship with water injection pressure: it increases markedly when the pressure is below 11 MPa, stabilizes once exceeding this threshold, and reaches a maximum of approximately 2.25 m. Additionally, the wetting radius grows linearly with fracture length, indicating that longer fractures can effectively broaden the water diffusion range. These findings elucidate the dominant role of pressure and fractures, providing theoretical guidance and technical support for optimizing water injection parameters, improving wetting efficiency, and enhancing mining dust suppression.
1 Introduction
Coal, as an essential component of China’s primary energy structure, plays a critical role in the national economy (Chen H. et al., 2022). Ensuring the safe and efficient extraction of coal resources has long been a fundamental concern (Kang et al., 2023). During the processes of roadway excavation and coal extraction, a large amount of dust is inevitably generated during rock cutting, transportation of fragmented rock, and shotcrete support (Chen L. et al., 2022; Lu et al., 2022; Zhang et al., 2025). Such respirable dust not only deteriorates the working environment and endangers miners’ health but also reduces equipment visibility, affects operation accuracy, and may even trigger safety accidents, thus hindering safe and efficient mining production (Wang et al., 2019). Therefore, developing effective dust control technologies—particularly those that suppress dust at its source—is vital for ensuring mine safety and protecting workers’ health (Liu and Liu, 2020; Nie et al., 2025).
Among the various dust suppression techniques, water injection has been widely applied due to its direct source control, remarkable effectiveness, and relatively low cost (Zheng et al., 2026). The principle involves pre-injecting high-pressure water through boreholes into the rock mass, allowing water to penetrate and diffuse through the pore and fracture networks, thereby pre-wetting the rock and increasing its water content (Zhou et al., 2022; Wu et al., 2024). During subsequent mechanical fragmentation, the wetted rock particles adhere together, significantly reducing airborne dust formation (Xu et al., 2021; Shi et al., 2025; Wu et al., 2025a).
However, most existing studies on moisture enhancement focus on coal seams, which are comparatively soft. Hard rock, in contrast, is characterized by high density, low porosity, poor permeability, and irregular fracture development (Wu et al., 2025b). These properties lead to difficulties in water injection, limited wetting range, and unstable outcomes (Ge et al., 2023). Water often fails to infiltrate the micro-pores and fine fractures deep within the rock mass, resulting in a limited wetting radius and suboptimal dust suppression (Wu et al., 2025c). Moreover, the dynamic seepage mechanism of high-pressure water within complex hard rock structures and the governing factors influencing the expansion of the wetting front remain insufficiently understood (Liu et al., 2026).
Temperature is a critical factor affecting hard rock water injection especially in deep mining (Zhong et al., 2025). It alters rock pore-fracture structures through mineral thermal expansion or stress-induced fracture changes (Zhang et al., 2021; Wu et al., 2025a). It also modifies injected water properties by reducing viscosity and surface tension at higher levels to facilitate seepage or increasing viscosity at lower levels to hinder flow (Xu et al., 2023). Temperature gradients within rock masses cause uneven water diffusion and wetting (Zhong et al., 2025). Notably temperature interacts with water injection pressure and fracture characteristics creating a complex coupling effect that has not been fully clarified in current research.
Previous research provides valuable insight into the mechanisms of moisture enhancement (Huang et al., 2025). Jiang et al. employed internal and external water jets for dust suppression in cutting tests and reported over 90% and 65% reductions in dust concentration, respectively (Jiang et al., 2017). Zhao et al. studied the wetting influence range using bidirectional cross-drilled boreholes (Zhao et al., 2023). Wei et al. conducted wetting and triaxial seepage tests, analyzing the role of capillary effects during water injection and noting that higher pressures accelerated the stabilization of seepage flow (Wei et al., 2022; Wu et al., 2025a).
In terms of nuclear magnetic resonance (NMR) technology, its non-invasive advantage in characterizing fluid distribution within rock masses has been widely acknowledged. This technology enables effective differentiation between adsorbed water and free water while reflecting the evolution of pore connectivity (Li et al., 2026). Existing research has fully validated its applicability in moisture migration tests of soft rocks such as coal seams, establishing its reliability in quantifying water content and pore structure changes under normal-temperature and low-pressure conditions (Qin et al., 2022; Wu et al., 2024). Despite these well-established merits, the technology still faces notable limitations in the context of hard rock water injection. Most studies have focused on conventional experimental conditions, lacking systematic exploration of high-pressure water injection scenarios that align with the requirements of actual hard rock mining engineering. Additionally, the dynamic coupling relationship between micro-pore compression, seepage channel expansion, and fluid migration in high-density, low-porosity hard rocks remains insufficiently clarified. A further gap lies in the ineffective integration of NMR-derived key parameters, such as the adsorbed/free water ratio, into engineering-scale simulation models, which results in a disconnect between laboratory test findings and practical engineering applications.
For COMSOL Multiphysics simulation, its inherent strength in integrating multi-physics processes including fluid-solid coupling and unsaturated seepage has solidified its position as a powerful tool for rock seepage analysis (Li and Li, 2025). Previous simulation studies have successfully predicted moisture diffusion in fractured rock masses, confirming the feasibility of numerical methods in revealing seepage laws (Shi et al., 2023; Yan et al., 2023). However, several limitations persist that hinder its optimal application in hard rock water injection research. Few simulation models quantitatively incorporate NMR-derived pore structure and fluid distribution parameters, leading to deviations between simulation assumptions and the actual physical properties of hard rocks. Moreover, the interactive effects of water injection pressure and fracture length on wetting radius expansion are often analyzed in isolation, and their synergistic mechanism in hard rock water injection has yet to be fully elucidated. Another critical issue is that simulation results lack sufficient validation from high-pressure experimental data, which impairs the reliability of the engineering guidance derived from these simulations.
Overall, current research on hard rock water injection confronts three core gaps. The scarcity of high-pressure NMR test data hinders the in-depth revelation of the dynamic transformation law of adsorbed water and free water during high-pressure water injection. The existing disconnection between laboratory-scale test results and engineering-scale simulation models leads to inaccurate prediction of wetting efficiency in actual mining operations. Furthermore, the synergistic effects of water injection pressure and fracture characteristics on hard rock wetting and diffusion are not fully understood, which limits the scientific optimization of water injection parameters in engineering practice.
To address these gaps, this study integrates low-temperature high-pressure NMR tests and COMSOL Multiphysics numerical simulation. Sandstone samples, selected as representative hard rock, are monitored in real time under different water injection pressures to capture the dynamic evolution of fluid distribution and the transformation between adsorbed and free water. A numerical simulation model calibrated by NMR-derived parameters is established to simulate water diffusion under varying water injection pressures and fracture lengths, thereby revealing the variation rules of wetting radius and determining optimal water injection parameters. This research bridges the gap between laboratory tests and engineering applications, providing valuable theoretical guidance and technical support for optimizing hard rock water injection parameters, improving wetting efficiency, and enhancing dust suppression in mining operations.
2 Test section
Injectability is closely related to the development and expansion of pores and fractures in hard rock. To investigate the evolution of fluid distribution under different pressure and surfactant conditions, this study employed NMR technology combined with a high-pressure water injection seepage device to analyze the dynamic variation of internal fluid distribution with changing water injection pressure and surfactant type.
2.1 Test principle
Nuclear Magnetic Resonance (NMR) is a non-invasive method for evaluating fluid distribution within rock cores by exploiting the magnetic resonance properties of atomic nuclei. Hydrogen nuclei (protons) resonate at specific frequencies under an external magnetic field B, producing detectable signals. When the sample is placed in the NMR instrument, radio-frequency (RF) pulses excite the nuclear spins away from equilibrium; as they return to equilibrium, they release RF energy. This relaxation process is characterized by two parameters: transverse relaxation time T2 and longitudinal relaxation time T1. T2 reflects how quickly spin interactions decay, while T1 describes recovery to equilibrium. The characteristics of these signals include oscillation frequency and decay time, which provide information about the internal fluid within the sample. Water molecules in rock usually exhibit shorter T2 values. The acquired NMR data are typically presented in the form of an intensity–time curve or a T2 spectrum.
The transverse relaxation time (T2) of pore fluids involves three independent relaxation mechanisms: surface relaxation, bulk relaxation, and diffusion relaxation, which can be expressed as follows:
In the formula: is the transverse bulk relaxation time of pore fluids; is the transverse surface relaxation time of pore fluids; is the transverse diffusion relaxation time of pore fluids.
Since the T2B value of water is extremely high (exceeding 3,000 m), 1/T2B can be neglected. Under a magnetic field with constant strength, the impact of diffusion relaxation on NMR signals is minimal, and the echo interval time is set to be very short, showing almost no characteristics of diffusion relaxation. Therefore, 1/T2Dcan also be ignored. Thus, it can be inferred that the transverse relaxation time of pore fluids is mainly affected by the surface relaxation mechanism, leading to the conclusion that the transverse relaxation time of fluids in pores is primarily determined by the surface relaxation mechanism. The formula is as follows:
In the formula: is the transverse relaxation rate, which is related to the physicochemical properties of the sample surface; is the surface area of the pores; is the volume of the pores.
The above equation can be further transformed into a relationship with pore radius:
In the formula: is the pore radius; is the geometric factor, with values of 3 and 2 for spherical and cylindrical pores, respectively.
It can be seen from this formula that when the transverse relaxation rate ρ2 is stable, the transverse relaxation time T2 of pore fluids in the test sample is proportional to the pore radius r. This indicates that the T2 values of water attached to the sample surface and water in small pores are smaller than those of water in large pores. Based on this principle, the T2 distribution curve obtained through inversion can be effectively used to determine the moisture distribution in different pore structures. Meanwhile, the area under the peak in the curve reflects the water content in the corresponding state within the specific T2 interval.
In this study, NMR is specifically applied to analyze the dynamic evolution of fluid distribution in hard rock during water injection, with a clear application process and parameter matching to address core research questions. The detailed application process is as follows. First, sandstone samples are processed into cylinders with diameter 50 mm and height 50 mm. Their sides and bottom are coated with waterproof glue to ensure one-dimensional unidirectional water absorption. Then, water injection tests are conducted using clean water and three types of wetting agents including 0.5‰ SAS solution, 0.5‰ BS-12 solution and 0.5‰ JFC solution under four pressure levels of 3 MPa, 6 MPa, 9 MPa and 12 MPa. Before testing, the NMR instrument is preheated for 24 h and calibrated with standard water samples to establish a linear correlation between T2 peak area and water content. During the test, the Carr-Purcell-Meiboom-Gill (CPMG) sequence is used for sampling, and NMR scanning is performed every 30 min to obtain T2 relaxation images. Finally, software inversion is used to calculate the peak area of different T2 intervals, distinguishing adsorbed water with T2 range of 0.1 ms–10 ms and free water with T2 range of 10 ms–100 ms, and analyzing the dynamic evolution of moisture distribution.
Key parameters of NMR application and their roles in solving research questions are elaborated as follows. First, equipment parameters: the instrument model is MacroMR12-150H-I, with a magnet strength of 0.3 ± 0.05 T, magnet temperature of 32 °C ± 0.01 °C, magnetic field homogeneity of 20 ppm, and frequency range of 10.64 MHz–14.90 MHz. These parameters ensure high precision and stability of scanning, avoiding signal distortion caused by environmental fluctuations, and laying a foundation for accurate identification of fluid states in hard rock with low porosity and poor permeability. Second, sampling parameters: the waiting time is 3 s which ensures full relaxation of protons to avoid signal overlap, the cumulative number of echoes is 4, the echo time is 0.084 ms which captures short T2 signals of adsorbed water in micro-pores without loss, and the number of echoes is 4,000. These parameters are tailored to the characteristics of hard rock, effectively capturing the relaxation signals of pore fluids, especially adsorbed water in micro-pores, which is crucial for revealing the dominant role of adsorbed water in the moisture increase of hard rock. Third, test parameters: the fixed sample size of diameter 50 mm and height 50 mm, combined with variable water injection pressures and wetting agent types, allows systematic investigation of how pressure and wetting agents affect fluid migration. The 30-min scanning interval dynamically tracks the temporal evolution of moisture content, helping to clarify the law of pore development and seepage channel connectivity under different pressures.
The quantitative calculation of water content based on NMR signals follows these steps: (1) Calibrate the NMR instrument using standard samples with known water content to establish a linear correlation between T2 peak area and water content; (2) For test samples, calculate the peak area of the T2 spectrum in specific intervals (0.1–10 ms for adsorbed water, 10–100 ms for free water) via inversion software; (3) Convert the peak area to actual water content using the pre-established calibration curve. This method ensures that the water content data directly correspond to the applied water injection pressure conditions, as each sample is tested under a constant pressure and scanned periodically to capture dynamic changes. By analyzing these data, information about the fluid at different positions inside the core sample, including content, distribution, and mobility, can be obtained, which helps to understand the rock pore structure and fluid distribution.
2.2 Test scheme and procedure
The low-temperature and high-pressure NMR device was manufactured by Suzhou Newmark NMR Technology Co., Ltd., with the model MacroMR12-150H-I. The magnet material is neodymium-iron-boron permanent magnet, the magnet temperature is 32 °C ± 0.01 °C, the magnetic field strength is (0.3 ± 0.05) T, the magnet stability is ≤300 Hz/Hour, the magnet frequency ranges from 10.64 to 14.90 MHz, the magnetic field homogeneity is 20 ppm, the length of the homogeneous region is 60 mm, and the magnet is arranged to facilitate horizontal testing of samples. The frequency source range is 1–30 MHz, the pulse control accuracy is 0.1 Hz, the maximum sampling bandwidth is 2000 kHz, and the pulse accuracy is 100 ns. The low-temperature and high-pressure NMR equipment is mainly used to analyze the T2 spectrum and porosity of sandstone samples for the study of core fluid distribution.
The key physical parameters of the selected rock samples are as follows: protodyakonov hardness coefficient = 3.6, internal friction angle = 37°40′, Poisson’s ratio = 0.26, average uniaxial compressive strength = 76.01 Mpa, saturated compressive strength = 63.49 Mpa, average softening coefficient = 0.58. Sandstone was chosen as the representative hard rock because it is widely distributed in mining engineering scenarios and exhibits typical hard rock characteristics (high density, low porosity, poor permeability) that are consistent with the research object of this study. Rock samples were cut using a rock cutting machine and finely processed with a double-sided grinding machine to prepare sandstone samples with a diameter of 50 mm and a height of 50 mm. The side and bottom surfaces of the core were coated with waterproof glue, and then the sample was placed in a pressure water injection device for water injection treatment to ensure one-dimensional unidirectional water absorption of the core. The samples are illustrated in Figure 1.
Water injection was performed with a high-pressure constant-flow injection system of model HPP-2000. The processed and sealed sample was fixed in the injection device’s pressure-bearing chamber, with its uncoated top surface hermetically connected to the system’s output port to prevent leakage. The injection system pipeline was pre-purged to remove residual air, ensuring continuous and stable supply of clean water. Four pressure levels were set as shown in Table 1. The specified pressure refers to the stable inlet pressure on the sample’s top surface, maintained by the system with a fluctuation range not exceeding ±0.05 MPa to drive water infiltration into the hard rock’s pore and fracture network. After pressure stabilization, NMR scanning was conducted every 30 min to record fluid distribution evolution.
The experimental workflow followed strict steps. Step 1: Pre-test preparation. The NMR equipment was preheated for 24 h and calibrated with standard water samples to establish a linear correlation between T2 peak area and water content. Step 2: Sample installation. Air-dried samples with waterproof glue coating were installed in the pressure-bearing chamber, and the connection was inspected for sealing. Step 3: Pressure application. The pipeline was purged, and the system was activated to gradually reach the target pressure, which was stably maintained without drop or leakage. Step 4: NMR scanning. Scans were performed at 0 min, 5 min, 10 min, 20 min, and 40 min after pressure stabilization to obtain T2 relaxation data. Step 5: Post-test processing. The system was depressurized, the sample was removed, and the chamber and scanning cavity were cleaned. The steps were repeated for samples under different pressures to ensure consistency and reliability.
The T2 spectrum distribution of the core was detected by NMR technology, and the Carr-Purcell-Meiboom-Gill (CPMG) sequence was used as the sampling method. The specific sampling parameters include: waiting time of 3 s, cumulative number of echoes of 4, echo time of 0.084 ms, and number of echoes of 4,000.
FIGURE 1
TABLE 1
| Sample number | Liquid | Pressure (MPa) |
|---|---|---|
| 1# | Clean water | 3 |
| 2# | Clean water | 6 |
| 3# | Clean water | 9 |
| 4# | Clean water | 12 |
Water injection test plan.
3 Test results
Transverse relaxation time in the range of 0.1–10 ms corresponds to adsorbed water; transverse relaxation time around 10–100 ms corresponds to free water (Yang et al., 2023; Zheng et al., 2023; Chen et al., 2024). Adsorbed water usually exists in the micro-pores and micro-fractures of rocks and is adsorbed on the solid surface by intermolecular forces. Free water usually exists in the larger pores or fractures of rocks and exists in a liquid state. The distribution of adsorbed water and free water in the sample and the changes in their occurrence states can provide information about the rock’s pore structure, permeability, and wettability characteristics, thereby reflecting the fluid distribution characteristics.
After inversion calculation by software, the test results of the T2 relaxation images are illustrated in Figure 2, and the peak areas of the samples are shown in Table 2:
FIGURE 2
TABLE 2
| Sample number | Water injection time (min) | Peak area (a. u.) | ||
|---|---|---|---|---|
| 0.1–10 m | 10–100 m | Total area (a. u.) | ||
| 1 # | 0 | 1,256.16 | 651.46 | 1907.62 |
| 5 | 3,123.91 | 963.50 | 4,087.41 | |
| 10 | 4,685.87 | 1,001.17 | 5,687.04 | |
| 20 | 8,330.43 | 1,190.51 | 9,520.93 | |
| 40 | 11627.89 | 1,211.67 | 12839.56 | |
| 2 # | 0 | 1,420.97 | 711.26 | 2,132.23 |
| 5 | 5,131.46 | 1,200.55 | 6,332.01 | |
| 10 | 8,894.53 | 1714.62 | 10609.15 | |
| 20 | 15394.38 | 1905.14 | 17299.52 | |
| 40 | 18815.35 | 2078.34 | 20893.69 | |
| 3 # | 0 | 1,456.82 | 708.56 | 2,165.38 |
| 5 | 8,532.11 | 1,234.57 | 9,766.68 | |
| 10 | 13423.98 | 1,530.82 | 14954.80 | |
| 20 | 21558.32 | 2,701.34 | 24259.65 | |
| 40 | 27035.26 | 3,025.22 | 30060.48 | |
| 4 # | 0 | 1,325.55 | 792.56 | 2,118.11 |
| 5 | 9,132.00 | 1,455.24 | 10587.24 | |
| 10 | 15511.22 | 1,684.33 | 17195.55 | |
| 20 | 23097.34 | 2,802.46 | 25899.80 | |
| 40 | 28156.32 | 3,199.35 | 31355.68 | |
Peak area statistics of sample 1 #∼4 #.
It can be seen from Table 2 that during the water injection process, the increase in moisture in the sample is mainly dominated by adsorbed water, while the growth of free water is limited. The peak area of free water only accounts for 8%–37% of the total peak area. This is because the proportion of large pores and fractures is relatively small, and they reach saturation in a short time during water injection, while medium and small pores make a major contribution to the increase in injection flow. Throughout the entire water injection process, the moisture content in the sample shows an increasing trend. As illustrated in Figure 2, when clean water is injected, the higher the water injection pressure, the faster the adsorbed water peak grows; at the same time, the adsorbed water peak value is higher, and the peak start time tends to shift to the left. This left shift of the adsorbed water peak start time is theoretically attributed to the compression of pore space and the enhancement of surface relaxation under high pressure: high water injection pressure compresses the micro-pores, reducing the pore radius (r), and according to the Equation 3, the transverse relaxation time (T2) of adsorbed water decreases, leading to the left shift of the peak start time in the T2 spectrum. This is because when the water injection pressure is increased, in the initial stage, various pores and fractures expand under the action of water pressure, the original pores expand and extend, some of them are connected to each other, and seepage channels are opened.
The statistical results of the adsorbed water peak area under different water injection pressures are illustrated in Figure 3. At the same time, the higher the water injection pressure, the larger the peak area; the peak area grows rapidly in the early stage of water injection, and the growth rate slows down in the later stage. This is because when the water injection pressure is increased, in the initial stage, various pores and fractures expand under the action of water pressure, the original pores expand and extend, some of them are connected to each other, and seepage channels are opened. With the further increase of water injection pressure, the rock enters the resistance stage; due to the simultaneous increase of confining pressure, the pore structure is difficult to develop, and when the water injection pressure is further increased, the effect of water pressure is no longer obvious.
FIGURE 3
4 Numerical simulation analysis
Through experimental research, the dynamic evolution law of fluid distribution in hard rock under different pressure conditions has been clarified. The core purpose of COMSOL simulation in this study is to establish a close mutual verification and complementary relationship with NMR experiments, forming a closed-loop research system that connects micro-scale fluid migration mechanisms and macro-scale wetting behavior. This relationship is reflected in bidirectional feedback between the two methods. On one hand, NMR experiments provide precise quantitative basis and validation standards for numerical simulation. The experiments accurately capture the dynamic transformation ratio between adsorbed water and free water, with free water accounting for only 8%–37% of the total moisture increase, along with the expansion characteristics of seepage channels under different water injection pressures and the evolution law of pore connectivity. These micro-scale data directly calibrate key parameters of the simulation model, including initial porosity, permeability evolution equation and fluid-solid coupling coefficient, ensuring the simulation truly reflects the intrinsic seepage mechanism of hard rock without relying on hypothetical parameters. On the other hand, numerical simulation effectively verifies and extends the conclusions of NMR experiments. The exponential growth trend of wetting radius with water injection pressure obtained by simulation is highly consistent with the growth law of T2 spectral peak area in NMR experiments. Both confirm that high pressure significantly promotes pore development and seepage connectivity, and the effect tends to stabilize when pressure exceeds 11 MPa, achieving cross-validation that ensures the reliability of research conclusions from multiple perspectives.
Furthermore, the mutual complementarity between the two methods breaks through the limitations of single research approaches. Constrained by sample size of diameter 50 mm and height 50 mm as well as experimental conditions, NMR experiments cannot simulate the wetting behavior of large-scale rock masses in actual mining engineering, nor can they accurately control and adjust fracture length to study its independent influence. COMSOL simulation makes up for these deficiencies by constructing an engineering-scale three-dimensional model with length 12 m, width 6.4 m and height 4.2 m, systematically exploring the influence of water injection pressure ranging from 3 MPa to 21 MPa and fracture length ranging from 0.3 m to 1.1 m on wetting radius in a wider parameter space. The linear relationship between wetting radius and fracture length revealed by simulation further supplements experimental findings, enriching the understanding of the comprehensive influence of pressure and fractures on hard rock wetting. Meanwhile, simulation results provide a macro-scale perspective for interpreting experimental phenomena: the rapid growth of adsorbed water peak area in NMR experiments corresponds to the expansion of seepage channels in simulation, and the slowing down of peak area growth in the later stage of experiments is consistent with the resistance stage of rock pore development in simulation. This mutual interpretation deepens the understanding of the intrinsic connection between micro-scale fluid behavior and macro-scale wetting effects.
The NMR test results provide key input parameters for numerical simulation, while numerical simulation extends the laboratory-scale findings to engineering-scale scenarios, realizing the mutual verification and complementarity of experiments and simulations. Although these findings provide an important basis for understanding the moisture enhancement mechanism, the limitations of experimental conditions make it difficult to fully evaluate the details of the impact of water injection pressure and fracture length on the expansion of the wetting radius under actual engineering conditions. The interaction between these variables in hard rock is still complex. Therefore, this study combines laboratory tests with numerical simulation to systematically investigate this problem. To further study the complex interaction between these variables, this chapter will use COMSOL Multiphysics for numerical simulation research. Simulation research can not only explore the influence of the above factors in a wider parameter space but also help us understand the micro-mechanism in the moisture enhancement process without being restricted by physical test conditions.
Water injection wetting is a seepage change process from unsaturated to saturated state, which is affected by three mechanisms: pressure-driven seepage, capillary action, and diffusion. These three mechanisms have different effects on seepage. When the fractures are small, the capillary phenomenon slows down the moisture diffusion rate, and the movement is mainly lateral diffusion. The pressure applied by water injection plays a key role in the flow characteristics of water and the wetting degree of hard rock. Generally, water first passes through the large natural fractures in the rock; then, with the increase of water injection pressure, those closed or partially closed fractures will gradually open and connect with each other, and the seepage channels will continue to expand over time. This leads to the saturation of fractures and increases the wetting range of the rock mass. However, the water injection pressure inside the rock will decrease with the increase of distance, resulting in a significant reduction in the wetting degree inside the rock mass.
4.1 Hard rock water injection model
4.1.1 Model establishment
COMSOL Multiphysics is a comprehensive simulation software that supports modeling and analysis of physical processes in multiple fields such as structural mechanics, thermodynamics, fluid dynamics, and acoustics. The software can realize the simultaneous solution of multi-physics coupling problems, and complete high-precision numerical simulation by establishing and solving partial differential equations, so that users can deeply explore the complex multi-physics interaction mechanism. In this chapter, a hard rock water injection moisture enhancement model will be constructed based on COMSOL Multiphysics, focusing on analyzing the influence laws of water injection pressure and fracture length on the wetting radius.
This simulation adopts Darcy’s law and the solid mechanics field for fluid-solid coupling.
Mass Conservation Equation
In the formula:
is the fluid density;
is the fluid velocity vector;
is the time;
is the mass source term, and a positive value indicates inflow.
- 2.
Continuity Equation
During the water injection process, the compressibility of the liquid is not considered, and the mass conservation equation is satisfied in any region:
- 3.
Governing Equation
In the formula: is the density; is the damping coefficient; is the stress; is the body force.
In the mass conservation equation of the seepage field, the injected high-pressure water causes changes in the pore shape, which in turn affects the seepage field; at the same time, the pore water pressure distribution in the seepage field will affect the effective stress distribution in the stress field, further affecting the deformation behavior of the rock. Therefore, the relationship between porosity and volume strain is introduced:
In the formula:
is the porosity;
is the initial porosity;
is the volume strain. Among them,
is a built-in function of the software and does not need to be set separately.
- 4.
Darcy’s Equation
Darcy’s law describes the flow behavior of liquids through porous media. For the seepage flow of water in the pores of hard rock:
Using COMSOL Multiphysics software, a theoretical hard rock water injection model was constructed with a length of 12 m, a width of 6.4 m, and a height of 4.2 m. The borehole length is 10 m, and the borehole diameter is 0.075 m. A regular triangular mesh is used for division. Since the problem studied is fluid flow, the mesh division is relatively dense in narrow areas. For accurate solution, the algorithm in this section uses an adaptive mesh method to maintain mesh refinement in the interface area. The generated 3D geometric model includes 2,635 domain units, 436 boundary units, and 130 edge unit structures. The model diagram is illustrated in Figure 4.
FIGURE 4
4.1.2 Model boundary conditions and parameter settings
The model used in this simulation was optimized, and the specific settings are as follows:
The hard rock is regarded as an isotropic porous medium;
The water injected into the hard rock is assumed to be an incompressible liquid;
Considering the actual geological conditions of the auxiliary transport roadway, the bottom boundary is a fixed boundary, that is, the horizontal displacement and vertical displacement of the bottom boundary are zero; the horizontal displacement of the side boundaries is zero; the working face is a free boundary; the two sides of the model are pressure boundaries, and a load of 8 MPa is applied to simulate horizontal stress, and the water head is set to 0; a load of 8 MPa is applied to the top to simulate vertical stress; This 8 MPa stress setting is based on the in situ stress measurement data of the study area: the vertical and horizontal in situ stresses of the coal mine auxiliary transport roadway where the rock samples are collected are approximately 8 MPa, which is consistent with the actual engineering geological environment.
The borehole wall is set as a pressure boundary to simulate high-pressure water injection.
The setting of initial parameters for the numerical simulation is shown in Table 3.
TABLE 3
| Parameter | Parameter value and unit | Remark |
|---|---|---|
| 1,000 (kg·m-3) | Density of water | |
| 0.00114 (Pa·s) | Viscosity of water | |
| 0.074 (N/m) | Surface tension of water | |
| 2,580 (kg·m-3) | Density of hard rock | |
| 0.02 | Initial porosity | |
| 1 × 10−12 (m2) | Initial permeability | |
| 2 × 1010 (MPa) | Young’s modulus | |
| 9.82 (m·s-2) | Gravitational acceleration | |
| 0.26 | Poisson’s ratio |
Parameter table.
4.2 Analysis of numerical simulation results
4.2.1 Influence of water injection pressure on wetting radius
The wetting radius is affected by water injection pressure and fractures. First, the influence of water injection pressure on liquid diffusion in hard rock under fracture-free conditions was studied. In the numerical simulation, six water injection pressures were set: 3 MPa, 5 MPa, 7 MPa, 9 MPa, 11 MPa, and 13 MPa. To more intuitively study the influence of water injection pressure on the liquid diffusion law, other influencing factors were set under the same conditions, with the same boundary conditions and a water injection time of 2 h. The numerical simulation results are illustrated in Figure 5.
FIGURE 5
It can be seen from the figure that when the water injection pressure is 3–13 MPa, the pore water pressure decreases continuously from the borehole to the surrounding area. The pressure around the borehole wall is the highest, and as the distance from the borehole increases, the pore water pressure decreases gradually. The distribution of pore water pressure in the hard rock is circular or elliptical, and the radius increases with the increase of water injection pressure.
The YZ plane where the borehole is located was selected to draw the pore water pressure contour map. It can be observed from Figure 6 that the contour lines near the borehole are densely arranged, while as the distance from the borehole increases, the contour lines gradually become sparse. The reason for this phenomenon is that as the distance from the borehole increases, the pressure on the pore water decreases, so the influence of the pressure gradient weakens gradually.
FIGURE 6
The distribution curves of pore water pressure and flow velocity near the water injection borehole are illustrated in Figures 7, 8. It can be seen from Figure 7 that the image shows a single-peak symmetric distribution; the pore water pressure near the borehole is the largest, and around the center of the borehole, the pore water pressure in the surrounding area gradually decreases to zero. The greater the distance from the borehole, the smaller the pore water pressure, and the pore pressure and the distance from the borehole show a certain functional relationship, with a regular change process. It can be seen from Figure 8 that the distribution law of flow velocity in different regions of the hard rock is roughly the same as that of pore water pressure, both showing a single-peak symmetric distribution; the flow velocity at the borehole is the largest, and the flow velocity in the surrounding area centered on the borehole gradually decreases to zero. The overall trend is that the greater the distance from the borehole, the smaller the flow velocity. The difference is that the relationship curve between Darcy flow velocity and the distance from the borehole is not smooth and does not show a regular functional distribution.
FIGURE 7
FIGURE 8
Based on the relationship between water content and pore water pressure, 1.5 MPa was set as the wetting threshold. The range where the pore water pressure exceeds 1.5 MPa is regarded as the effective moisture enhancement region, while the range below this value is regarded as the non-moisture enhancement region. To more accurately analyze the influence of water injection pressure on the wetting radius, based on the previous simulation results, four additional different water injection pressures (15, 17, 19, 21 MPa) were added for the test. The fitting curve of the hard rock wetting radius under different water injection pressures measured in the test is illustrated in Figure 9. Using Origin analysis software to fit the curve, an exponential function equation was obtained (the fitting correlation coefficient reaches 0.9994):
FIGURE 9
In the formula: is the effective wetting radius of the rock mass, m; is the water injection pressure of the hard rock, MPa.
Figure 9 shows that the wetting radius and water injection pressure present an exponential relationship. Increasing the water injection pressure can effectively increase the wetting radius, thereby enhancing the water injection effect and expanding the wetting region. Within a specific range of water injection pressure, the maximum wetting radius of the hard rock will not exceed 2.25 m. When the water injection pressure exceeds 11 MPa, the increase rate of the wetting radius will decrease significantly, which is consistent with the previous analysis. At this time, further increasing the water injection pressure will put forward higher requirements on the water injection equipment, and the required economic cost will increase while the benefit is low. Therefore, considering cost-effectiveness, a water injection pressure of 11 MPa is a relatively ideal choice. During the on-site water injection process, the stress distribution of the hard rock is not uniform, and the seepage velocity also varies in different directions. Therefore, the result obtained by the software simulation is a macro average result, which is different from the actual situation. Nevertheless, this simulation still has important reference value for guiding the actual water injection operation.
4.2.2 Influence of fractures on wetting radius
Using COMSOL Multiphysics numerical simulation software, numerical simulations were carried out on the effective wetting range of rock formation water injection under different fracture lengths (0.3 m, 0.6 m, 0.9 m, 1.1 m). The water injection pressure was 11 MPa, and the water injection time was set to 2 h. The numerical simulation results are illustrated in Figure 10.
FIGURE 10
Through the simulation and analysis of the pore water pressure field with different fracture lengths, it is found that in the entire region, the pore water pressure is the largest in the areas close to the borehole wall and fractures, and the pressure distribution is elliptical. Under a certain water injection pressure, the major axis of the ellipse increases with the increase of fracture length, and the minor axis also increases with the increase of fracture length, but the change is not obvious. As water seeps outward continuously, the water injection pressure on the rock formation decreases gradually; as the distance from the borehole and fractures increases, the pore water pressure decreases to zero gradually. Through numerical simulation calculation and using Origin analysis software to fit the curve, a linear equation was obtained:
In the formula: is the effective wetting radius of the rock mass, m; is the fracture length, m.
The relationship between the wetting radius and fracture length fitted by Origin analysis software is illustrated in Figure 11.
FIGURE 11
It can be seen from the figure that as the fracture length extends, the wetting radius increases accordingly, showing a linear relationship between the two. This means that water injection into hard rock in the presence of fractures can significantly expand the wetting region. Specifically, the longer the fracture, the larger the wetting radius. Therefore, water injection after hydraulic fracturing can enhance the wetting effect of hard rock.
5 Conclusion
In this study, a combination of experimental testing and numerical simulation was used to systematically investigate the influence of water injection pressure and fractures on the wetting and diffusion laws of hard rock. The main conclusions are as follows:
The NMR experimental results show that during the water injection process of hard rock, the increase in moisture is mainly dominated by adsorbed water, which is stored in the micro-pores of the rock, and the peak area of the T2 spectrum increases significantly with water injection time; while the growth of free water is very limited, and its peak area accounts for only 8%–37% of the total peak area. This reveals that the wetting process of hard rock is essentially a process in which water continuously overcomes capillary resistance, occupies and expands the micro-pore space under the drive of pressure. At the same time, the increase of water injection pressure can significantly accelerate the seepage rate of adsorbed water, which is manifested by the faster growth of the peak area of the T2 spectrum and higher peak value, proving that high pressure can effectively open and connect the original closed pores and broaden the seepage channels.
- 2.
The numerical simulation results show that the wetting radius and water injection pressure present an exponential function relationship, and the increase of water injection pressure will lead to the corresponding expansion of the wetting radius. However, the upper limit of the wetting radius of hard rock is within 2.25 m. When the water injection pressure exceeds 11 MPa, the increase rate of the wetting radius decreases significantly, and the growth amplitude slows down, indicating that beyond this pressure, further increasing the water injection pressure has a limited effect on expanding the wetting range.
- 3.
The fracture structure plays a guiding and expanding role in the wetting range. The simulation results show that the wetting radius increases linearly with the increase of fracture length. Water injection into hard rock under fractured conditions can effectively expand the wetting region, and the longer the fracture, the larger the wetting radius. The existence of fractures provides preferential seepage channels for water flow, making the wetting region expand preferentially along the direction of fractures, thus forming an elliptical wetting circle. This indicates that in engineering practice, water injection after hydraulic fracturing can enhance the wetting effect of hard rock.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
GW: Writing – original draft, Writing – review and editing. JJ: Writing – original draft, Writing – review and editing. HS: Writing – original draft, Writing – review and editing. XD: Writing – original draft, Writing – review and editing. YW: Writing – original draft, Writing – review and editing. KD: Data curation, Conceptualization, Software, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This work is supported by the Major Science and Technology Projects of China Coal, China (20231BY001).
Conflict of interest
Authors GW, JJ, HS, XD, YW, and KD were employed by China Coal No.5 Construction Co. Ltd. Authors GW, JJ, HS, XD, YW, and KD were employed by China Coal Construction Group Limited Corporation.
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Summary
Keywords
hard rock water injection, nuclear magnetic resonance, numerical simulation, rock fractures, water injection pressure, wetting and diffusion mechanism
Citation
Wang G, Jiang J, Sun H, Deng X, Wang Y and Di K (2026) Study on the mechanism of water injection pressure and fractures on wetting and diffusion of hard rock during water injection. Front. Earth Sci. 14:1760325. doi: 10.3389/feart.2026.1760325
Received
04 December 2025
Revised
17 January 2026
Accepted
26 January 2026
Published
18 February 2026
Volume
14 - 2026
Edited by
Hao Shi, Anhui University of Science and Technology, China
Reviewed by
Tao Zhang, Nantong University, China
Hongfeng Lu, Guangzhou Marine Geological Survey, China
Updates
Copyright
© 2026 Wang, Jiang, Sun, Deng, Wang and Di.
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*Correspondence: Guoyuan Wang, 24480733@qq.com
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.