The research team, led by He Shao and Jun Zhang of Taiyuan University of Technology together with Junhong Si of the North China Institute of Science and Technology, carried out an unusually comprehensive set of sorption experiments on four Chinese coals drawn from three coalbed methane-rich basins: the Qinshui Basin, the Eastern Ordos Basin and the Eastern Yunnan Basin. The samples spanned the full coalification spectrum. Two were high-rank anthracites, QS and YQ, with vitrinite reflectance values as high as 2.35 percent; one was a medium-rank bituminous coal, XCG; and one was a low-rank lignite, XLT. By grinding, sieving, cutting and polishing the coals, the researchers prepared both granular particles, ranging from less than 0.097 millimeters to 0.841 to 3.35 millimeters, and cylindrical cores of 13.5 by 13.5 millimeters, allowing them to test how geometry and particle size shape gas transport.

The core of the methodology is the particle method, a workhorse technique in coal science. Coal samples are placed in a sample cell connected to a reference cell inside a thermostatic water bath held to within 0.1 degrees Celsius. A dose of gas, carbon dioxide, methane or nitrogen, is released into the cell, and high-precision pressure transducers record the pressure decay every two seconds as molecules adsorb onto internal pore surfaces. The resulting sorption kinetic curves are then fitted with mathematical models to extract the apparent diffusion coefficient. In this study the team used two models: a modified unipore model, mUM, which assumes a single pore radius and whose boundary conditions match the manometric experiment, and the widely used bidisperse model, BM, which assumes a bimodal pore distribution with separate macro- and micropore diffusion coefficients. Notably, the mUM performed better for the anthracites, while the BM model fit the bituminous coal and lignite more successfully, confirming earlier suspicions that model choice matters, even if it does not overturn the qualitative trends.

What sets the new work apart is its breadth of controls. Beyond pressure, the researchers systematically varied nine potential influencing factors: calculation model, coal rank, sample geometry, particle size, sample mass, gas type, pressure application method, pressure step increment and experimental temperature, tested at 40 and 50 degrees Celsius. Pressure was applied in two distinct ways: incremental steps, in which the cell is evacuated only before the first step, and integral steps, in which the sample is vacuumed before every step. The magnitude of each pressure increment was also varied, with four-step large increments compared against six-step small increments. All samples were pretreated with supercritical carbon dioxide and vacuum dried at 110 degrees Celsius for 48 hours to remove moisture and residual gases, and helium leakage tests over 22,000 seconds confirmed the apparatus was gas-tight.

The results reproduced both of the previously reported behaviors, and then added a third that had rarely been seen. The medium-rank bituminous coal XCG and the low-rank lignite XLT showed apparent diffusion coefficients that decreased with rising pressure, consistent with one camp of earlier studies. The high-rank anthracites QS and YQ generally showed increasing coefficients with pressure, consistent with the other camp. But for the YQ anthracite with large particle sizes, granular YQ6 and the cylindrical core YQ4, tested under incremental pressure steps with small increments, the carbon dioxide diffusion coefficient did something unexpected: it first increased and then decreased. For YQ6, the value rose from 7.58 times ten to the minus eleventh square meters per second to 2.42 times ten to the minus tenth before falling back to 2.30 times ten to the minus tenth. For YQ4, the rise was even more dramatic, from 2.11 times ten to the minus ninth to 5.66 times ten to the minus ninth, followed by a steep drop to 3.63 times ten to the minus tenth. This non-monotonic pattern, rising then falling with stepwise pressure increases, had been essentially absent from the literature.

To explain it, the team borrowed a conceptual tool from chemical reaction kinetics: the distinction between overall reactions and their elementary steps. The particle method, they argue, is analogous to an overall reaction, yielding an apparent coefficient that lumps together every stage of gas migration. By deconstructing the measurement into its component sub-steps, external diffusion across the stagnant gas boundary layer, Fick diffusion in larger pores, Knudsen diffusion in smaller pores where molecules collide with walls more often than with each other, and configurational diffusion in pores barely wider than the molecules themselves, they could track how each mechanism evolves with pressure. Quantitatively, they calculated the Fick diffusion coefficient, which is inversely proportional to pressure, and the Knudsen diffusion coefficient, which depends on pore size and molecular velocity but is only indirectly tied to pressure through the mean free path of the gas molecules.

The key insight emerges from how pressure reshapes the boundary between these two diffusion regimes. As pressure rises, the mean molecular free path shrinks, which lowers the pore size threshold below which Knudsen diffusion dominates and reduces the number of pores available to it. But within a single pressure step, as gas adsorbs and pressure decays, the free path lengthens again, the upper pore size limit for Knudsen diffusion expands, and more pores switch into the Knudsen regime. Knudsen diffusion can therefore be temporarily enhanced during the later stage of a low-pressure step, an effect that fades away at higher pressures. Combining this quantitative tracking with pore structure data from five complementary techniques, mercury porosimetry, low-temperature nitrogen and carbon dioxide adsorption, scanning electron microscopy and transmission electron microscopy, the team showed that the anthracites are rich in micropores while the lower-rank coals contain more cleats, macropores and mesopores.

From this synthesis they proposed a qualitative conjecture they call pore-structure-regulated temporary enhancement of Knudsen diffusion. In micropore-rich anthracite, pressure-driven changes in the molecular mean free path temporarily boost the Knudsen diffusion coefficient and open up additional micropores and partial mesopores, between roughly 0.6 and 5.5 nanometers under these experimental conditions, as effective Knudsen pathways, lifting the apparent coefficient. As pressure continues to climb across multiple steps, the enhancement collapses and the coefficient falls. The conjecture also accounts for why the effect appears only under specific conditions: large particles preserve the long diffusion paths that let Knudsen contributions dominate, incremental pressure steps preserve pre-saturation patterns that favor the effect, and carbon dioxide’s small kinetic diameter of 0.330 nanometers, smaller than nitrogen at 0.364 or methane at 0.380 nanometers, grants it access to narrow micropores that the other gases cannot enter.

The study also delivered a methodological caution with wide relevance. The team found that the apparent diffusion coefficient alone can be misleading when comparing samples of different geometry or particle size. In one striking inversion, the YQ6 particles sorbed carbon dioxide faster than the YQ4 cylinders yet yielded a smaller diffusion coefficient, 7.58 times ten to the minus eleventh versus 2.03 times ten to the minus ninth square meters per second at the first pressure step. Normalizing by the square of the diffusion path length, giving the effective apparent diffusion coefficient D over r squared, restored consistency with the observed sorption rates. The researchers also found that gas type, temperature and sample mass had minimal impact on the overall pressure trends, while the choice of pressure application method did shift the trends for the anthracites, reinforcing that experimental protocol choices, long treated as细节, can determine which of the warring literature results a lab reproduces.

The implications reach beyond the laboratory. In carbon dioxide-enhanced coalbed methane operations, injected gas travels through the cleat system, diffuses into the matrix and displaces methane, which then flows to production wells; the diffusion coefficient governs how quickly that exchange proceeds, particularly during early injection stages and late-stage methane drainage when pressures are low, precisely the regime where the newly identified enhancement appears. For geological carbon sequestration, understanding how storage efficiency may vary with pressure helps assess long-term containment. The authors caution that their conjecture remains qualitative, that stress and coal swelling effects were not considered, and that only two models were tested, leaving room for further verification. But by simultaneously reproducing the increasing, decreasing and now non-monotonic pressure behaviors within a single controlled framework, and by supplying a physical mechanism that reconciles them, the study transforms a thirty-year-old contradiction into a coherent, testable picture of how gases truly navigate the labyrinth of coal.

Subject of Research: Pressure dependence of the apparent gas diffusion coefficient in the coal matrix under multiple experimental factors

Article Title: Experimental investigation on the pressure dependence of apparent gas diffusion coefficient in coal matrix under multiple potential factors

Article References: Experimental investigation on the pressure dependence of apparent gas diffusion coefficient in coal matrix under multiple potential factors. (n.d.). https://doi.org/10.1007/s44442-026-00121-6

Image Credits: AI Generated

DOI: 10.1007/s44442-026-00121-6

Keywords: coal matrix, apparent diffusion coefficient, gas pressure, Knudsen diffusion, Fick diffusion, carbon dioxide, coalbed methane, CO2 sequestration, coal rank, pore structure, particle method, anthracite