Abstract
The interference of moisture in water-bearing coal seams on gas desorption is a key bottleneck restricting the accurate determination of in-situ pressure. In this study, we systematically elucidate the dual inhibition mechanisms of moisture on gas desorption through stepwise volume expansion experiments (moisture content gradient 0-5.11%) combined with multi-scale characterization techniques including low-field nuclear magnetic resonance, scanning electron microscopy, and mercury intrusion porosimetry. Two dominant mechanisms are identified: (1) Competitive adsorption, where moisture occupies mesopore surfaces (2–50 nm, dominant pore size 2.2–4.8 nm), leading to a 28.6% reduction in the Langmuir volume (a); (2) Pore throat blockage—capillary liquid bridges form within ink-bottle pores, hindering gas diffusion. Based on these mechanisms, a modified Langmuir model incorporating an adsorption attenuation coefficient (λ) is proposed, and a dual-mode pressure hierarchical/chained inversion algorithm is developed. The hierarchical method achieves a single-stage pressure inversion error < 1.65%, and the chained method shows a full-process inversion error of only 0.59% at a moisture content of 4.85%. The study indicates that the solidification effect of moisture on the pore system can enhance the predictability of pressure evolution. This method provides a theoretical framework for gas disaster prevention and control in water-bearing coal seams and contributes to improved accuracy in in-situ pressure determination.
Keywords: Pressure and gas- retaining coring, Hierarchical/chained inversion, Multi-stage expansion desorption, In-situ gas pressure
Subject terms: Energy science and technology, Engineering
Introduction
The accurate determination of in-situ gas pressure in coal seams directly affects the identification of coal and gas outburst risks and gas drainage in mines1, serving as the foundation for formulating mine safety production and disaster prevention measures. Currently2, direct pressure measurement methods are limited by sealing technology and hydrogeological interference, while indirect methods rely on extrapolating coal sample desorption curves. However, in water-bearing coal seams, moisture significantly alters desorption kinetics, leading to errors in these methods3–5. The in-situ pressure- and gas-preserved coring technology for deep coal seams, proposed by Academician Xie Heping’s team6,7, offers a novel approach to solving this problem by maintaining the coal core at its in-situ gas pressure condition. The core of this technology lies in the precise characterization of the volume-expansion and pressure rebalancing process within the coring device. During this process, the coal sample undergoes desorption through volume expansion (expansion desorption), exhibiting a gas desorption pattern fundamentally different from conventional atmospheric pressure desorption.
Research on atmospheric pressure desorption in water-bearing coal seams indicates that gas desorption under atmospheric conditions is influenced by multiple factors, including moisture content8,9, gas pressure10, particle size11, temperature12,13, and coal sample pore structure14. As the foundation of traditional methods, atmospheric pressure desorption (involving a single-step pressure release to atmospheric pressure) studies show that moisture in coal has an underlying influence on adsorption capacity and the desorption process15,16. Specifically, it manifests as: the adsorption capacity of coal for gas decreases with increasing moisture content17; the adsorbed gas quantity decreases with increasing moisture content18; and the desorption rate exhibits fluctuating attenuation as moisture content increases19. Traditional pressure-preserved coring technology relies on the principle of “adsorbed-free gas rebalancing.” However, in water-bearing coal seams, moisture induces non-equilibrium evolution of the adsorbed gas state, resulting in reduced applicability of the standard Langmuir equation20. Gao et al. discovered through multi-stage expansion experiments that when moisture content exceeds 5%, the gas pressure inversion error ranges from 2.22% (in dry samples) to 0.80% (in high-moisture samples), indicating that existing models require the incorporation of moisture correction parameters21.
Addressing issues such as the unquantified dynamic mechanism of moisture under stepwise pressure release, the lack of moisture adsorption models adapted to the expansion process, and the failure of pressure inversion algorithms to consider the ‘solidification effect’ of moisture on the pore system (the phenomenon of enhanced pressure response stability under high moisture content), this research establishes a framework for dual-path mechanism decoupling (competitive adsorption + pore blockage) - λ -modified model - hierarchical/chained dual-mode inversion. Through moisture gradient experiments (0%−5.11%) combined with multi-scale characterization methods (NMR/SEM/Mercury Intrusion Porosimetry), the influence mechanisms of moisture on mesoporous adsorption sites and ink-bottle pore throats are analyzed. Based on multi-stage expansion experiments (stepwise pressure release at 100 mL increments), novel hierarchical inversion and chained inversion calculation methods are proposed. The study develops a predictive theory for pressure rebalancing in water-bearing coal seams, suggests threshold design parameters for pressure-preserved coring devices, and provides technical guidance for mine safety.
Principle for in-situ gas pressure calculation in water-bearing coal samples
The Pressure and Gas-Retaining Coring Technology establishes a sealed pressure-preserved space within the coring device1. Based on the re-equilibration of free and adsorbed gas in the coal core, the theoretical calculation method for “coal seam in-situ gas pressure” is proposed by equating the in-situ gas mass of the coal seam with the equilibrated gas mass in the pressure-preserved space21. This calculation method adheres to the following core assumptions:
No gas loss occurs during the re-equilibration process of the coal sample from its in-situ state to the pressure-preserved space.
The adsorbed gas content follows the Langmuir equation; The free gas obeys the ideal gas law.
Derivation of the calculation principle
The total in-situ gas content m0(per unit mass of coal)21, comprising both adsorbed and free-state gas, is expressed as:
 |
1 |
where p1is the in-situ gas pressure of the coal seam (MPa); a, b is the adsorption constants of the coal sample (m³/t, MPa⁻¹); ϕ is the coal matrix porosity (%); ρc is the Apparent density of coal (kg/m³); Mg is the molecular mass of methane (g/mol); VM is the standard molar volume (L/mol); R is the universal gas constant (J/(mol·K)); T is the temperature (K).
The total gas mass mt0 in a pressure-preserved coal core of mass mc (kg) is given by:
 |
2 |
The total gas mass within the pressure-preserved space mt1 consists of three components:
 |
3 |
where Vcon is the total volume of the pressure-preserved space (m³); p2 is the equilibrium pressure in the pressure-preserved space (MPa).
The mass conservation equation is thus formulated as:
 |
4 |
Correction of the calculation principle
To improve calculation accuracy, two key corrections are introduced based on the aforementioned principles:
Real gas correction: the gas compressibility factor Z is incorporated to account for deviations from the ideal gas law21.
Moisture content correction: a modified Langmuir equation is adopted to characterize the adsorption behavior of water-bearing coal, where w denotes the moisture content and λ represents the adsorption attenuation coefficient.
The corrected model comprises the following equations
The corrected total in-situ gas mass mt0:
 |
5 |
where Z is the gas compressibility factor, w is the moisture content. λ is the Adsorption attenuation coefficient determined by fitting experimental data from isothermal adsorption tests.
The corrected total gas mass in the pressure-preserved space mt1:
 |
6 |
Model adjustment adapted to the experimental conditions
To align with the laboratory multi-stage pressure release experimental procedure, the model is adapted as follows:
The initial equilibrium state (simulating in-situ conditions) corresponds to coal samples under adsorption equilibrium within the sample chamber.
The post-expansion state (simulating the pressure-preserved space) represents the system after volumetric expansion of the sample chamber.
Accordingly, the model is specified as:
The total gas mass mt0 in the initial equilibrium state of the sample chamber:
 |
7 |
where: VFree is the free volume of the sample chamber (mL), calibrated via helium displacement.
The total gas mass mt1 in the equilibrium state after stepwise expansion:
 |
8 |
where VEx is the cumulative expansion chamber volume (mL).
The model is governed by the core mass conservation equation, Eq. (4).
Test methods and equipment
Gas adsorption and multi-stage expansion desorption equipment
The experiments employed a self-designed Reservoir Core Desorption Gas Pressure Testing and Analysis Simulation System22 (Fig. 1). This integrated apparatus comprises four key modules: (1) a vacuum degassing system for impurity removal; (2) a constant temperature control system maintaining 30 ± 0.1 °C; (3) an adsorption-expansion coupling system with adjustable expansion volume (0–105 mL); and (4) a multi-parameter acquisition system with 0.1-class accuracy pressure sensors and PT100 temperature probes.
Fig. 1.
System for testing and analyzing the pressure of desorption gas from reservoir rock cores.
Multi-scale pore analysis method and equipment for coal samples
The pore structure of coal samples was characterized through a multi-scale approach. At the macro- to mesoscale (50 nm–1 mm), mercury intrusion porosimetry (MIP) quantified macropore (> 50 nm) size distribution, while scanning electron microscopy (SEM) visualized pore topology, revealing characteristic ink-bottle pore throats (< 0.5 μm). In the meso-microscale range (2–50 nm), low-temperature N2 adsorption data were analyzed using combined density functional theory (DFT) and Barrett–Joyner–Halenda (BJH) models, with DFT resolving micropores (< 10 nm) and BJH covering mesopores (> 10 nm). At the molecular scale (< 2 nm), low-field nuclear magnetic resonance (NMR) provided T2 relaxation spectra for nanopore quantification, complemented by X-ray diffraction (XRD) and Fourier transform infrared (FTIR) spectroscopy for crystallographic and functional group analysis. As shown in Fig. 2, the multi-scale analytical framework is summarized.
Fig. 2.
Multiscale analytical approaches and associated investigation hierarchies in this work.
Standardized protocols ensured measurement consistency: SEM samples were prepared by ion sputtering; samples were degassed at 120 °C for 12 h before N2 adsorption; MIP used a pressure gradient of 0.5–60,000 psi; and NMR employed a CPMG sequence with 0.1 ms echo time. XRD analysis (Rigaku MiniFlex600, Cu target, 40 kV/15 mA, 2θ = 10–80°, step 0.01°) determined crystal parameters, while FTIR (KBr pellet method, 4000–400 cm− 1, 4 cm− 1 resolution, 32 scans) identified functional groups and chemical bonds, completing the multi-scale structural characterization.
Test method
Isothermal adsorption test
Isothermal adsorption tests were conducted to quantify the effect of moisture content (0%, 0.99%, 2.76%, 5.11%) on methane adsorption capacity. Experiments were performed at 30 °C using high-purity methane (99.99%), with gas pressure incrementally increased from 0.21 to 3.81 MPa in seven increments. Adsorption equilibrium was determined when pressure variation remained below 0.3%/h for two consecutive hours (according to the ASTM D1412 standard). Adsorbed gas content was calculated using the differential method by comparing the injected gas volumes (determined from reference chamber pressure changes) with the free gas content in the sample chamber.
Continuous expansion desorption test
The continuous expansion desorption test simulated the pressure release process during pressure-preserved coring. After achieving initial adsorption equilibrium at 3.33 MPa (corresponding to a burial depth of approximately 1,500 m), coal samples with varying moisture contents (0%, 1.06%, 2.66% and 4.85%) underwent five-stage expansion with cumulative volumes of 25, 45, 65, 85, and 100 mL. Pressure was continuously monitored, with equilibrium defined as a pressure variation below 0.5%/h for two consecutive hours after each expansion. The pressure response curves were analyzed to determine moisture effects on desorption kinetics and pressure inversion accuracy.
Test sample preparation
This study used typical anthracite coal samples from the Jincheng mining area in Shanxi Province. The raw coal was crushed and sieved into specific size fractions for different analyses: 1–3 mm particles for low-temperature N₂ adsorption, isothermal adsorption, and multi-stage expansion desorption tests; 3–6 mm particles for mercury intrusion porosimetry; and 25 × 50 mm cylindrical samples for NMR measurements. Proximate analysis showed fixed carbon content of 60.26%, volatile matter of 7.98%, and ash content of 30.15%, classifying it as medium-ash anthracite. Petrographic analysis indicated vitrinite reflectance Rmax = 4.33% and inertinite content of 53.32%, characteristic of coal with abundant micropores.
Moisture content was regulated using the supersaturated salt solution method at 30 °C, with different saturated salt solutions (30%, 60% and 97% RH) producing moisture gradients of 0.99–5.11% (Table 1). Samples were first dried at 105 °C for 24 h, then equilibrated until the mass stabilized (< 0.1% change over 12 h).
Table 1.
Coal sample moisture content at various humidity levels.
| Test protocol | Dried | 30% RH | 60% RH | 97% RH |
|---|---|---|---|---|
| Isothermal adsorption experiment | 0 | 0.99 | 2.76 | 5.11 |
| Multi-stage diffusion desorption test | 0 | 1.06 | 2.66 | 4.85 |
Results
Multi-scale pore distribution characteristics of coal samples
Multiscale SEM Observations clearly reveal the evolutionary patterns of coal sample pore structures (Fig. 3). At 1 mm and 500 μm scales, the coal surface appears intact with only sporadic pores (5–10 μm diameter). At 200 μm scale, macroscopic fracture networks become visible (20–50 μm width) with “mountain-range” topography. The 100 μm scale identifies penetrating main fractures (≈ 35 μm width) surrounded by secondary pores from accumulated debris. The 30 μm scale highlights a micro-sized pore system (1–5 μm diameter) with significantly increased density. Characteristic ink-bottle pores (≈ 3 μm cavity diameter) are captured at 10 μm scale, while submicron pores (< 0.5 μm) are resolved at 5 μm scale. This hierarchical pore structure conforms to IUPAC classification standards (micropores < 2 nm, mesopores 2–50 nm, macropores ≥ 50 nm), where ink-bottle pore throats (< 0.5 μm width) directly cause gas diffusion blockage.
Fig. 3.
(a) Microscopic particle morphology of coal sample at 1 mm scale; (b) Surface morphology at 500 μm scale; (c) Surface morphology at 200 μm scale; (d) Surface morphology at 100 μm scale; (e) Morphology of interconnected fractures at 100 μm scale; (f) Distribution of micropores at 30 μm scale; (g) Ink-bottle pore blockage at 10 μm scale; (h) Typical morphology of ink-bottle pores at 10 μm scale; (i) Submicron pores at 5 μm scale.
Low-Temperature Nitrogen Adsorption data (Fig. 4a) corroborate SEM observations, showing maximum adsorption capacity of 3.429 cm³/g. The Type IV(a) + II composite isotherm exhibits characteristic features: a micropore-filling inflection at p/p0 = 0.01 confirms the presence of micropores, while the distinct hysteresis loop at p/p0 = 0.79 provides clear evidence of ink-bottle pore structures.
Fig. 4.
(a) Low-temperature nitrogen adsorption-desorption isotherms; (b) Pore structure characterization using DFT model; (c) Pore structure characterization using BJH model; (d) Pore structure characterization by nuclear magnetic resonance; (e) Relationship between mercury intrusion/extrusion volume and pore diameter.
Combined DFT/BJH analysis (Fig. 4b,c) reveals dominant pore sizes of 2.2–4.8 nm, with 1–4 nm micropores providing the primary surface area (BET 3.429 m²/g). These mesopores constitute the main adsorption spaces that are preferentially occupied by moisture. NMR T₂ spectra (Fig. 4d) show bimodal distribution - a mesopore peak (0.325–78.34 nm) and macropore peak (> 100 nm), confirming hierarchical porosity.
More importantly, the NMR data quantitatively verify that submicron throats (< 1 μm) account for 98.91% of pore structures, consistent with SEM findings. Mercury intrusion tests (Fig. 4e) provide critical evidence for pore throat characteristics: the intrusion curve shows abrupt surges at ≈ 190 nm, 35 nm, and beyond 18 nm, corresponding to different scales of pore throats observed in SEM images. The significant hysteresis between intrusion and extrusion curves clearly demonstrates the ink-bottle effect, where mercury becomes trapped in wider pore cavities connected through narrower throats. This phenomenon directly parallels the capillary liquid bridge formation by moisture in submicron throats (< 0.5 μm) that hinders gas diffusion. Mesopores (5–50 nm) dominate with 72.17% total mercury intrusion volume (Table 2).
Table 2.
Comprehensive characterization of coal sample pore parameters.
| Key parameter | Measurement method | Value | Structural correlation |
|---|---|---|---|
| Specific surface area (m²/g) | Multipoint BET | 3.429 | Micropore-dominated (corresponding to 30 nm SEM image) |
| Micropore surface area (m²/g) | t-plot method | 1.4435 | Contribution of micropores (< 2 nm) to surface area |
| Total pore volume (cm³/g) | DFT method | 0.003,390 | Mesopores as main constituents (10 nm SEM image) |
| Mesopore characteristic volume (cm³/g) | BJH desorption method | 0.002,239 | Specifically refers to pore volume within mesopore range |
| Average throat width (nm) | Mercury intrusion porosimetry (MIP) | 5.7683 | Ink-bottle pore throats (5 nm SEM image) |
Collectively, Fig. 4(a)-(e) establishes a comprehensive understanding of the pore system: while mesopores (2.2–4.8 nm) provide the dominant adsorption sites, the submicron throats (particularly < 0.5 μm ink-bottle pore throats) create critical bottlenecks for gas transport, which are preferentially blocked by moisture through capillary condensation.
Integrated characterization demonstrates mesopores as the primary structure, while micropores provide major adsorption sites (48% surface area contribution). However, ink-bottle throats (SEM-confirmed 40–50 nm width) combined with ultranarrow submicron throats (MIP/NMR-verified) collectively restrict gas diffusion. The tri-level structure (“macro fractures - mesopore cavities - micron-scale throats”) indicates that although mesopores provide main gas storage space, submicron throats (< 0.5 μm) create diffusion bottlenecks that critically constrain gas desorption kinetics in water-bearing coal seams, with moisture blockage effects predominantly targeting these narrow throats.
Isothermal adsorption difference law of water-bearing coal samples
The isothermal adsorption experimental results reveal the dual inhibition mechanism of moisture on gas adsorption behavior in coal samples. Experimental data (Table 3) demonstrate a significant attenuation in gas adsorption capacity as moisture content increases from 0% to 5.11%: under high-pressure conditions (3.8 MPa), adsorption capacity decreased from 19.26 cm³/g to 10.11 cm³/g (attenuation rate 47.5%); while under low-pressure conditions (1.0 MPa), the attenuation was more pronounced, reaching only 33% of the dry sample’s adsorption capacity. This pressure-dependent attenuation characteristic shows close correlation with the multiscale pore structure of the coal samples.
Table 3.
Results of isothermal adsorption experiment.
| Moisture content (%) | Equilibrium gas pressure (MPa) | Adsorbed gas content (cm³/g) | Proportion of adsorbed gas (%) |
|---|---|---|---|
| 0.00% | 0.21 | 8.94 | 70.39 |
| 0.76 | 14.11 | 50.68 | |
| 1.14 | 16.28 | 44.01 | |
| 1.69 | 17.93 | 36.68 | |
| 2.60 | 18.72 | 27.94 | |
| 3.09 | 19.12 | 24.84 | |
| 3.81 | 19.26 | 21.08 | |
| 0.99 | 0.18 | 7.22 | 69.52 |
| 0.37 | 9.59 | 59.52 | |
| 0.81 | 12.28 | 46.07 | |
| 1.12 | 13.75 | 40.77 | |
| 1.68 | 15.16 | 33.42 | |
| 2.57 | 16.31 | 25.83 | |
| 3.15 | 17.55 | 23.26 | |
| 3.84 | 18.25 | 20.37 | |
| 2.76 | 0.33 | 5.63 | 49.21 |
| 0.79 | 8.25 | 37.10 | |
| 1.12 | 9.37 | 31.96 | |
| 1.65 | 10.61 | 26.39 | |
| 2.55 | 11.53 | 19.91 | |
| 3.06 | 12.64 | 18.13 | |
| 3.86 | 13.63 | 15.53 | |
| 5.11 | 0.43 | 2.99 | 29.69 |
| 0.79 | 4.44 | 25.37 | |
| 1.03 | 5.62 | 24.75 | |
| 1.52 | 6.79 | 21.09 | |
| 2.54 | 8.55 | 16.57 | |
| 3.02 | 9.45 | 15.48 | |
| 3.74 | 10.11 | 13.53 |
Table 4 presents the fundamental physical parameters of the experimental coal samples and the key parameters required for subsequent calculations. Based on the basic test results, the influence mechanism of moisture was quantitatively characterized by fitting the coal samples with the Langmuir model Eq. (9).
Table 4.
Values of basic physical parameters of coal sample.
| Basic parameters | Values | Basic parameters | Values |
|---|---|---|---|
| Adsorption constants a/(cm³/g) | 20.85 | Molar mass of methane/(g∙mol− 1) | 16 |
| Adsorption constants b/(MPa− 1) | 3.25 | geothermal temperature/(K) | 303.15 |
| Dry base moisture Mad/(%) | 0.85 | Molar volume of methane under standard conditions/(L∙mol− 1) | 22.4 |
| Ash content Aad/(%) | 30.41 | Ideal gas constant/(J∙mol− 1∙K− 1) | 8.314 |
| Volatile matter Vad/(%) | 8.81 | water content w1/(%) | 0.00% |
| Fixed carbon FCad/(%) | 59.93 | water content w2/(%) | 0.99% |
| Vitrinite/(%) | 45.7 | water content w3/(%) | 2.76% |
| Coal seam matrix porosity f/(%) | 6.5 | water content w4/(%) | 5.11% |
 |
9 |
where V is the gas adsorption capacity of coal sample, cm³/g; a is the adsorption constant, also known as Langmuir volume, cm³/g; b is the Adsorption constant, = 1/PL, where PL is Langmuir pressure, MPa⁻¹;P is the gas pressure at adsorption equilibrium, MPa.
Langmuir curve shapes show clear differentiation, as shown in Fig. 5. The curve for the dry coal sample (0.00% moisture content) is the steepest, gradually flattening as moisture content increases. The dry sample has the highest initial slope (corresponding to b = 3.25 MPa⁻¹), while at 5.11% moisture content it is the flattest (corresponding to b = 0.56 MPa⁻¹), indicating that higher moisture content requires higher pressure to achieve the same adsorption increment. This phenomenon is fully consistent with the linear attenuation of the adsorption constant b value (Table 5).
Fig. 5.
Langmuir fitting curve.
Table 5.
Calculation results of adsorption constants.
| Moisture content of coal sample | Adsorption constants | ||
|---|---|---|---|
| a/(cm3/g) | b/MPa− 1 | R 2 | |
| 0.00% | 20.85 | 3.25 | 0.994 |
| 0.99% | 19.71 | 2.21 | 0.994 |
| 2.76% | 15.20 | 1.53 | 0.992 |
| 5.11% | 14.89 | 0.56 | 0.999 |
As shown in Table 5, the Langmuir volume (a) decreases nonlinearly with increasing moisture content: from 20.85 cm³/g for the dry sample to 14.89 cm³/g at 5.11% moisture content. The attenuation is significant (27.1%) when moisture content is ≤ 2.76%, then tends to level off (2.0% change thereafter), indicating a saturation effect of moisture occupying adsorption sites. Simultaneously, the b value shows a linear attenuation trend with increasing moisture content, indicating that moisture significantly increases the adsorption energy barrier for methane.
This differential attenuation behavior is governed by the coal’s distinct pore structure. Mesopores (2.2–4.8 nm), constituting 72.17% of pore volume with high specific surface area (BET 3.429 m²/g), serve as the primary adsorption sites. Moisture preferentially occupies these mesopores (Fig. 3d), reducing effective adsorption space, as further evidenced by the Type IV(a) + II hysteresis in N2 adsorption isotherms (Fig. 4a) indicative of ink-bottle pore effects. Thus, moisture inhibits adsorption capacity mainly through mesopore blockage, while the linear attenuation of the b value reflects increased adsorption energy barriers due to moisture-gas interfacial interactions, independent of pore volume reduction.
To quantify this moisture effect, we introduce the adsorption attenuation coefficient λ into a modified Langmuir model. The model achieves excellent fit (R2 > 0.95) across moisture contents, yielding λ = 17.2 (Fig. 6), which provides a unified parameter for subsequent pressure inversion calculations.
 |
10 |
Fig. 6.
Modified Langmuir fitting curve.
The adsorption attenuation coefficient λ is a dimensionless parameter derived from fitting the experimental data in Table 5. The value λ = 17.2 characterizes the nonlinear relationship between adsorption capacity attenuation and moisture content (ω).
It is noteworthy that the inhibition of adsorption by moisture mainly manifests as a reduction in adsorption space due to mesopore blockage, while its effect on adsorption kinetics is reflected in the change of the b. This structure-function correspondence provides a new perspective for understanding gas occurrence patterns in water-bearing coal seams.
The difference law of multi-stage capacity expansion desorption of water-bearing coal samples
Based on the adsorption characteristic model for water-bearing coal samples established earlier, multi-stage expansion experiments further reveal the dynamic influence mechanism of moisture on gas desorption pressure evolution. The experiment simulates the pressure release process after pressure-preserved coring. After initial adsorption equilibrium (3.33 MPa), the pressure response characteristics of coal samples with different moisture contents were observed through stepwise volume expansion (cumulative 100 mL).
Experimental data (Table 6) show that the influence of moisture on the desorption process exhibits distinct stage characteristics:
Table 6.
Desorption equilibrium pressure and pressure drop in multi-stage expansion process.
| Expansion volume (mL) | Parameter | 0.00% (Dry) | 1.06% | 2.66% | 4.85% |
|---|---|---|---|---|---|
| 25 | Pressure (MPa) | 2.65 | 2.61 | 2.60 | 2.59 |
| Pressure drop (MPa) | 0.86 | 0.72 | 0.73 | 0.74 | |
| 45 | Pressure (MPa) | 2.25 | 2.21 | 2.19 | 2.17 |
| Pressure drop (MPa) | 0.40 | 0.40 | 0.41 | 0.42 | |
| 65 | Pressure (MPa) | 1.96 | 1.91 | 1.88 | 1.87 |
| Pressure drop (MPa) | 0.29 | 0.30 | 0.31 | 0.30 | |
| 85 | Pressure (MPa) | 1.74 | 1.68 | 1.65 | 1.64 |
| Pressure drop (MPa) | 0.22 | 0.23 | 0.23 | 0.23 | |
| 100 | Pressure (MPa) | 1.60 | 1.55 | 1.52 | 1.50 |
| Pressure drop (MPa) | 0.14 | 0.13 | 0.13 | 0.14 |
In the first expansion stage (25 mL), as moisture content increases from 0% to 4.85%, the pressure drop decreases from 0.86 MPa to 0.74 MPa (a reduction of 13.95%). This is directly related to the moisture blockage effect in ink-bottle pore throats (40–50 nm width, shown in previous SEM images). This capillary liquid bridge effect significantly reduces the effective diffusion channel area, leading to decreased desorption efficiency.
In subsequent expansion stages (20 mL×3), the pressure drop difference between samples with different moisture contents converges to 0.01–0.02 MPa, indicating that the moisture blockage effect reaches dynamic equilibrium after the first expansion. This phenomenon corroborates the observation in the adsorption experiment that the change in the a value slows down when moisture content > 2.76% (Table 5), jointly confirming the existence of a saturation threshold for moisture occupying adsorption sites.
These observations confirm the dual inhibition mechanism of moisture and support the establishment of a reliable inversion model. The 0.12 MPa pressure difference in the first expansion stage offers a critical early-time window for practical in-situ pressure estimation.
Experimental verification and mechanism analysis of multi-stage expansion pressure inverse calculation
Based on the adsorption-desorption characteristic model for water-bearing coal samples established earlier, this study innovatively proposes two gas pressure inversion calculation methods and systematically verifies their reliability through multi-stage expansion experiments (cumulative 100 mL). The experiment used the basic parameters listed in Table 5 (a = 20.85 m³/t, b = 3.25 MPa⁻¹, λ = 17.2 (fitted via Eq. (10)), with moisture content ω corresponding to 0.00%, 1.06%, 2.66%, 4.85%). Combined with the mass conservation equation, it accurately simulates the entire process of pressure-preserved coring.
Hierarchical Inversion is defined as a method that uses the equilibrium pressure at the current stage to inversely calculate the pressure at the previous stage (Table 7): uses the current post-expansion equilibrium pressure (p₂) to invert the pressure (p₁) after the previous expansion stage.
Chained Inversion is defined as a method that reconstructs the full-process pressure based on the cumulative expansion volume. (Table 8): uses the cumulative expansion volume as input to invert the initial equilibrium pressure (p₀ = 3.33 MPa).
Table 7.
In-situ gas pressure calculation results based on multi-stage expansion test (Hierarchical inversion of previous stage pressure).
| Water content/% | In-situ gas pressure/MPa | Expansion volume/mL | Measured gas pressure/MPa | Calculated gas pressure/MPa | Error/% |
|---|---|---|---|---|---|
| 0.00 | 3.33 | 25 | 2.65 | 3.346 | 0.48 |
| 2.65 | 20 | 2.25 | 2.617 | 1.25 | |
| 2.25 | 20 | 1.96 | 2.231 | 0.84 | |
| 1.96 | 20 | 1.74 | 1.950 | 0.51 | |
| 1.74 | 15 | 1.60 | 1.728 | 0.69 | |
| 1.06 | 3.33 | 25 | 2.61 | 3.384 | 1.62 |
| 2.61 | 20 | 2.21 | 2.614 | 0.15 | |
| 2.21 | 20 | 1.91 | 2.205 | 0.23 | |
| 1.91 | 20 | 1.68 | 1.906 | 0.21 | |
| 1.68 | 15 | 1.55 | 1.687 | 0.42 | |
| 2.66 | 3.33 | 25 | 2.60 | 3.385 | 1.65 |
| 2.60 | 20 | 2.19 | 2.597 | 0.12 | |
| 2.19 | 20 | 1.88 | 2.175 | 0.68 | |
| 1.88 | 20 | 1.65 | 1.873 | 0.37 | |
| 1.65 | 15 | 1.52 | 1.656 | 0.36 | |
| 4.85 | 3.33 | 25 | 2.59 | 3.377 | 1.41 |
| 2.59 | 20 | 2.17 | 2.574 | 0.62 | |
| 2.17 | 20 | 1.87 | 2.164 | 0.28 | |
| 1.87 | 20 | 1.64 | 1.863 | 0.37 | |
| 1.64 | 15 | 1.50 | 1.635 | 0.30 |
Table 8.
Calculation results of graded gas pressure based on multi-stage expansion test (chained inversion of in-situ pressure, the initial gas pressure is 3.33 MPa).
| Water content/% | Expansion volume/mL | Sample volume ratio/% | Measured gas pressure/MPa | Calculated in-situ pressure/MPa | Error/% |
|---|---|---|---|---|---|
| 0.00 | 25 | 23.64 | 2.65 | 3.347 | 0.51 |
| 45 | 20.58 | 2.25 | 3.304 | 0.78 | |
| 65 | 18.22 | 1.96 | 3.276 | 1.62 | |
| 85 | 16.35 | 1.74 | 3.259 | 2.13 | |
| 100 | 15.18 | 1.60 | 3.235 | 2.85 | |
| 1.06 | 25 | 23.28 | 2.61 | 3.381 | 1.53 |
| 45 | 20.26 | 2.21 | 3.388 | 1.74 | |
| 65 | 17.94 | 1.91 | 3.381 | 1.53 | |
| 85 | 16.10 | 1.68 | 3.366 | 1.08 | |
| 100 | 14.94 | 1.55 | 3.386 | 1.68 | |
| 2.66 | 25 | 24.37 | 2.60 | 3.385 | 1.65 |
| 45 | 21.21 | 2.19 | 3.379 | 1.47 | |
| 65 | 18.79 | 1.88 | 3.353 | 0.69 | |
| 85 | 16.85 | 1.65 | 3.342 | 0.36 | |
| 100 | 15.65 | 1.52 | 3.354 | 0.72 | |
| 4.85 | 25 | 24.79 | 2.59 | 3.376 | 1.38 |
| 45 | 21.58 | 2.17 | 3.356 | 0.78 | |
| 65 | 19.11 | 1.87 | 3.347 | 0.51 | |
| 85 | 17.14 | 1.64 | 3.333 | 0.09 | |
| 100 | 15.91 | 1.50 | 3.323 | 0.21 |
The hierarchical inversion method for previous stage pressure is based on the mass conservation equation before and after expansion, using the measured equilibrium pressure (p₂) at the current expansion stage to inversely calculate the equilibrium pressure (p₁) after the previous expansion stage through iterative computation. Its core advantage lies in its universality across all moisture contents: relative error < 1.65% for all moisture content groups. For example: Dry sample (0.00%) average error 0.754% (e.g., inverting p₁=3.346 MPa from p₂=2.65 MPa, error − 0.016 MPa); High moisture content (4.85%) average error 0.596% (inverting p₁=3.377 MPa from p₂=2.59 MPa, error − 0.047 MPa). Dry coal samples show peak errors in the middle expansion stages, while high-moisture samples show uniform error distribution, indicating that the modified model with λ = 17.2 effectively unifies the moisture influence. However, the method exhibits a “dip” in error: maximum error occurs in intermediate expansion stages (cumulative 45–65 mL, 1.25% error for the second stage at 0.00% moisture), while errors at the first and last stages are lower. The non-uniform desorption in ink-bottle pore throats (Fig. 3) during stepwise pressure release causes pressure response fluctuations in the middle stages.
The chained inversion method for in-situ pressure uses the initial in-situ pressure (p₀=3.33 MPa) as the baseline and progressively models the pressure Attenuation through cumulative expansion volume, enabling full-process pressure reconstruction. the chained inversion method (Table 8) exhibits unique error suppression characteristics: as moisture content increases, the inversion error significantly decreases. At 4.85% moisture content, the inversion error decreases continuously with expansion to 0.21% (last stage), while the error for the dry sample accumulates to 2.85%. This phenomenon corresponds to the mechanism of mesopore blockage (72.17% proportion), indicating that moisture “solidifies” the pore system to some extent, enhancing the predictability of pressure evolution. As summarized in Table 9, the volume proportion (defined as the ratio of coal sample volume to total system volume, including both the sample chamber free volume and expansion chamber volume) demonstrates a critical control effect on inversion accuracy. the 16% threshold represents an empirical critical point - when volume proportion falls below this value, the dominance of free space gas leads to markedly reduced pressure response sensitivity, resulting in significantly increased inversion errors (e.g., dry sample error escalating from ≤ 0.78% to 2.85%). When using this method, attention must be paid to the volume threshold effect (Table 9).
Table 9.
The critical control effect of volume ratio.
| Volume proportion | Error (0.00% moisture) | Error (4.85% moisture) | Mechanism analysis |
|---|---|---|---|
| > 20% (Expansion ≤ 65 mL) | ≤ 0.78% | ≤ 0.78% | Sample dominates pressure response |
| < 16% (Expansion > 85 mL) | Sharply increases to 2.85% | Only 0.21% | Free space dilution effec |
The pressure inversion model verified through multi-stage expansion experiments forms a complete loop with the earlier findings: Ink-bottle pore throats (Fig. 3 shows throat width 40–50 nm) cause peak errors in the middle stages of Stepwise expansion (up to 1.25% in the second stage), while the moisture blockage effect in mesopores (2.2–4.8 nm, proportion 72.17%) reduces the error by 72% in the high-moisture group (4.85%) (from 2.85% for dry sample to 0.59%). the λ-modified model established earlier (λ = 17.2) successfully predicted the optimal inversion accuracy (0.21%) at 4.85% moisture content, fully consistent with the isothermal adsorption results. However, influenced by the free space Dilution effect, error spikes still occur when the coal sample volume proportion is < 16% (cumulative expansion > 85mL), reaching 2.85% for dry samples (Table 10).
Table 10.
Comparison of engineering significance of two kinds of inverse calculation methods.
| Inversion type | Advantages | Limitations | Applicable scenarios |
|---|---|---|---|
| Hierarchical inversion of previous stage pressure | Single-stage error < 1.65% | Requires step-by-step calculation, risk of cumulative error | Data recovery during equipment failure |
| Chained inversion of in-situ pressure | Cumulative error < 2.85% | Relies on initial pressure calibration | Full-process pressure reconstruction |
Based on this, engineering optimization schemes are proposed: ① Equipment design must control the coal sample volume proportion > 20% (cumulative expansion ≤ 65 mL), which can lock errors within 1.5%; ② Prioritize chained inversion for full-process pressure reconstruction, supplemented by hierarchical inversion to correct abnormal data points, thereby balancing system stability and calculation accuracy. These findings not only verify the conclusions regarding pore structure and moisture influence mechanisms (λ = 17.2) but also provide quantitative design standards for pressure-preserved coring technology.
Discussion
Microstructural and chemical basis for moisture influence mechanisms
Integrating multi-scale characterization (SEM, NMR, FTIR, XRD), this study elucidates the fundamental microstructural and chemical properties governing moisture’s impact on gas adsorption-desorption in coal.
SEM observations (Fig. 3) reveal a hierarchical pore structure featuring macroscopic fractures, interconnected micropores (1–5 μm), and critically, characteristic ink-bottle pores with submicron throats (< 0.5 μm). Complementary low-temperature N₂ adsorption (Fig. 4, Type IV(a) + II isotherm) and DFT/BJH analysis identify mesopores (2.2–4.8 nm) as dominant (72.17% of pore volume, Table 2). NMR T₂ spectra confirm bimodal pore size distribution. Crucially, the strong hydrophobicity of the coal, evidenced by FTIR (low oxygen-containing functional group proportion of 0.040, aliphatic/aromatic hydrocarbon ratio of 0.38, (Figs. 7, 8) and XRD (graphite-like interlayer spacing d₀₀₂ = 0.346 nm, large aromatic layer extension La = 1.2786 nm, stacking height Lc = 1.9151 nm, Table 11), dictates moisture behavior. This hydrophobicity prevents significant chemical adsorption of water onto coal molecules. Instead, moisture preferentially undergoes capillary condensation within ink-bottle pore throats (40–50 nm width, SEM Fig. 3g,h), forming liquid bridges, while hydrophobic effects hinder its entry into smaller micropores.
Fig. 7.
FTIR characterization.
Fig. 8.
Peak fitting results of infrared spectrum of coal samples. (a) 1000–1800 cm−1. (b) 700–900 cm−1. (c) 2800–3000 cm−1. (d) 3000–3600 cm−1.
Table 11.
XRD-derived structural parameters of coal samples.
| θ002/° | θ100/° | La/nm | Lc/nm | d002/nm | fa | N ave |
|---|---|---|---|---|---|---|
| 12.84 | 21.38 | 1.2786 | 1.9151 | 0.346 | 0.79 | 38.907 |
This specific moisture distribution drives the observed dual inhibition mechanisms:
Competitive adsorption: moisture occupies mesopore surfaces (2.2–4.8 nm), directly reducing available adsorption sites. Langmuir fitting confirms a nonlinear decrease in the a value from 20.85 to 14.89 cm3/g as moisture rises to 5.11%, with saturation above ~ 2.76% moisture—consistent with the dominant role of mesopores (72.17% by volume).
Pore throat blockage: capillary liquid bridges in ink-bottle throats (< 0.5 μm) hinder gas diffusion, reflected in the linear attenuation of the b from 3.25 to 0.56 MPa⁻¹, indicating increased energy barriers due to moisture-gas interfacial interactions.
Multi-stage expansion tests directly reflect these mechanisms: the first expansion (25 mL) shows the strongest moisture effect, with pressure drop decreasing from 0.86 MPa (dry) to 0.74 MPa (4.85% moisture). This stage-specific response aligns with liquid bridge blockage at critical throats during initial pressure release. As expansion continues, the effect diminishes, indicating dynamic rebalancing of liquid bridges, consistent with the a value saturation trend.
The inherent pore heterogeneity significantly impacts inversion precision. Hierarchical inversion shows peak errors in intermediate expansion stages (1.25% error at 45–65 mL for dry coal, Table 7), directly attributable to non-uniform desorption dynamics from ink-bottle throats during stepwise pressure release. Conversely, high-moisture samples (4.85%) exhibit lower and more stable inversion errors (average 0.596% for hierarchical, converging to 0.21% for chained inversion, Tables 7 and 8. This demonstrates that moisture blockage, by restricting major diffusion paths, effectively “homogenizes” or “solidifies” the pore system, dampening non-equilibrium desorption fluctuations and enhancing pressure predictability – a key factor enabling the high accuracy (0.59% full-process error) of the chained inversion method at 4.85% moisture.
Therefore, the coal’s specific pore architecture (abundant mesopores and ink-bottle throats) provides distinct physical domains for moisture, while its strong hydrophobic chemistry dictates moisture’s preferential capillary condensation within throats rather than molecular adsorption or micropore filling. This distribution drives the dual inhibition: competitive adsorption on mesopore surfaces reduces gas storage capacity (a value attenuation), while throat blockage impedes gas transport kinetics (b value attenuation and stage-dependent desorption suppression). Ultimately, this microstructural-chemical coupling governs both the fundamental gas behavior and the practical accuracy achievable in pressure inversion for water-bearing coal seams.
In-situ pressure inversion via hierarchical and chained methods
This study innovatively proposes and validates two pressure inversion algorithms: Hierarchical Inversion of Previous Stage Pressure and Chained Inversion of In-situ Pressure. Their core design principles and engineering significance are systematically explained below (Fig. 9).
Fig. 9.
Application workflow of two pressure back-calculation methods.
Hierarchical inversion of previous stage pressure: this method applies the mass conservation equation to iteratively calculate the equilibrium pressure of the previous stage (p1) using the measured pressure at the current expansion stage (p2). Key parameters include the adsorption constants (a = 20.85 m3/t, b = 3.25 MPa−1) and the adsorption attenuation coefficient (λ = 17.2).
Chained inversion of in-situ pressure: this approach establishes a pressure attenuation model based on cumulative expansion volume to reconstruct the full-process pressure, using the initial in-situ pressure (p0) as the baseline. The calculation incorporates volume proportion (coal sample volume to system total volume ratio) into the equation of state.
The foundation of both methods is a modified Langmuir model incorporating the adsorption attenuation coefficient λ (experimentally determined to be 17.2). This model effectively characterizes gas adsorption-desorption in moist coal by correcting for two key moisture effects: (1) competitive site occupation reducing the Langmuir volume (a); and (2) increased adsorption energy barrier linearly decreasing the adsorption constant (b) with moisture. This dual-correction mechanism contributes to the achieved accuracy (0.59% error at 4.85% moisture) across the moisture range (0–5.11%).
Hierarchical Inversion shows good performance in single-stage accuracy (< 1.65% error across all moisture levels), offering robustness against discontinuous data or equipment failure by enabling historical pressure reconstruction from partial records.
Chained Inversion shows self-correction under high moisture (error decreasing from 1.38% to 0.21% at 4.85% moisture during expansion), attributed to moisture’s “solidifying” effect stabilizing desorption. However, for dry coal, the error accumulates (up to 2.85% at > 85 mL expansion) when the coal volume proportion falls below ~ 16%, due to free space dilution reducing pressure sensitivity. Maintaining the coal volume proportion at > 20% (cumulative expansion ≤ 65 mL) helps control inversion error within 1.5%, providing an important design parameter.
For practical implementation, a hybrid strategy is recommended: prioritize Chained Inversion for systematic, full-process reconstruction, and supplement with Hierarchical Inversion for data recovery or cross-validation at critical points. Beyond technical innovation, this approach represents a notable paradigm shift: instead of treating moisture as interference to exclude, it quantifies its effect (λ) and integrates it into the core model (“active integration” versus “avoiding interference”). This provides improved performance in challenging water-bearing conditions and suggests that coal “defects” like moisture may contribute to precision enhancement when accurately modeled. Validated through multi-scale experiments, this method provides a reliable theoretical tool for gas pressure determination in water-bearing coal seams, with notable implications for gas disaster prevention and coalbed methane extraction. As pressure-preserved coring advances, this multi-stage expansion inversion approach shows promise as a standard method for such complex scenarios.
While the dual inhibition mechanisms are fundamentally generalizable, their quantitative manifestation is coal-specific. Key factors such as coal rank and mineralogy are expected to modulate the moisture effect, implying that the direct application of our λ-modified model to other coal types would necessitate further calibration and validation.
Summary and conclusions
Through multi-stage expansion experiments and multi-scale characterization, this work elucidates the dual inhibition mechanisms of moisture on gas desorption in water-bearing coal seams: moisture primarily occupies mesopore surfaces (2.2–4.8 nm, proportion for 72.17%) through competitive adsorption, causing a 28.6% attenuation of the Langmuir volume (a); and forming capillary liquid bridges within ink-bottle pore throats (throat width < 0.5 μm), blocking diffusion channels. The modified Langmuir model incorporating the adsorption attenuation coefficient (λ = 17.2) provides support for dual-mode hierarchical/chained inversion calculation methods: hierarchical inversion achieves a single-stage pressure reconstruction error of less than < 1.65% (e.g., inverting 3.33 MPa from 2.65 MPa with 0.48% error), which offers an approach to addressing local data anomalies; Chained inversion achieves a full-process error as low as 0.59% at 4.85% moisture content (e.g., inverting 3.323 MPa from 1.50 MPa in the last stage), which suggests improved accuracy compared to traditional indirect methods. The results indicate that the pore system solidification effect triggered by high moisture content (> 2.66%) enhances the predictability of pressure evolution, which is manifested as the error converging stepwise during chained inversion (decreasing from 1.38% to 0.21% at a moisture content of 4.85%). For engineering applications, maintaining the coal sample volume proportion in the pressure-preserved space at > 20% (cumulative expansion volume ≤ 65 mL) is recommended, as this condition limits the inversion error within 1.5%, thereby offering a reference for corer design.
Author contributions
Xiaoyu CHENG: Writing—original draft, Formal analysis, Investigation, Data curation. Zhipeng WANG: Writing—review & editing, Methodology, Supervision, Validation. Jie SONG: Resources, Software, Visualization. Cheng CHENG: Investigation, Validation. Bengao YANG: Conceptualization, Funding acquisition. Xingying MA: Project administration. Kunchen HE: Formal analysis. Mingzhong GAO: Conceptualization, Funding acquisition, Supervision (Lead).
Funding
This study gratefully acknowledges the National Key Research and Development Program of China (Grant No. 2023YFF0615404), the Project supported by the National Science Foundation for Distinguished Young Scholars of China (Grant No. 52225403), and the GuangDong Basic and Applied Basic Research Foundation (RCJC20210706091948015).
Data availability
The data used to support the findings of this study are available from the corresponding author upon request.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
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Data Availability Statement
The data used to support the findings of this study are available from the corresponding author upon request.