The analysis used actual gas and water production records from 11 vertical wells in the Shenfu Block. All had produced continuously for more than one year, had complete geological and production data and had original reservoir pressure of approximately 20 MPa. The principal target was the No. 8 + 9 coal seam, whose reported burial depth was 1,853.5–2,526.3 m and thickness was 3.2–22.9 m. The researchers classified wells according to their gas-production curves as decline type or stable type.

Average reservoir pressure and permeability were not measured directly during production. Instead, they were estimated with a coupled material-balance and permeability-prediction framework that incorporated adsorbed and free gas, gas-water production, pressure-dependent gas slippage, effective stress and coal-matrix shrinkage. The estimates for each well were generated by combining model parameters with its production history. The authors noted that the absence of independent measured reservoir-pressure data for direct calibration means that absolute pressure estimates and permeability-enhancement ratios may contain systematic errors.

The decline-type pattern was illustrated by well S2, which had an initial pressure-drawdown rate of 197.3 kPa/d. After 473 days of production, its average daily gas production was 3,318 m³/d and average daily water production was 4.05 m³/d. Its modeled average reservoir pressure declined from 21.92 MPa to 11.71 MPa, while modeled permeability increased by only 0.9%. Gas production rose rapidly at first but declined sharply after reaching a peak, and water production fell to almost zero in the later period.

Well S11 represented the stable-type pattern. Its initial drawdown rate was 131.14 kPa/d, and it had produced for 541 days at the data cutoff. Its average daily gas production was 8,073 m³/d and average daily water production was 2.39 m³/d. The model estimated that average reservoir pressure declined from 22.06 MPa to 3.7 MPa and that permeability increased by 5.4%. The researchers associated this broader modeled pressure reduction with a larger depressurized zone and progressively greater contributions from matrix shrinkage, allowing gas production to rise and then stabilize.

A comparison of geographically adjacent wells S7 and S3, which the authors said had similar geological conditions and fracturing parameters, highlighted the relationship between initial drawdown and later production. S7 had an initial drawdown rate of 245.733 kPa/d and reached peak gas production of 6,301 m³/d after about three months, but production subsequently declined. Its modeled average reservoir pressure fell from 21.7 MPa to 15.42 MPa, and modeled permeability increased by 0.8%. S3 had a slower initial drawdown rate of 117.433 kPa/d; its daily gas production increased and stabilized above 10,000 m³/d, while modeled average pressure declined from 20.6 MPa to 11.3 MPa.

The researchers proposed controlling the initial bottomhole flowing-pressure drawdown rate within 160 kPa/d. During the later part of the gas-production increase stage, they recommended increasing the rate by 50–100 kPa/d to promote gas desorption. During the later decline stage, they proposed reducing the drawdown rate to approximately 50 kPa/d. Simulations after 200 days of continuous drainage indicated that a moderate initial rate produced a larger modeled depressurized area and more sustained production trend than an excessively rapid rate.

The staged regime was applied to one Shenfu Block well. After implementation, the well reached peak gas production of 14,651 m³/d and then entered a high, stable-production period lasting more than 200 days, with daily gas production remaining above 9,000 m³/d. The authors described this field application as validation of the proposed regime and reported advantages in stable-production duration and productivity stability compared with previous wells in the block. Because only one application was described, the result does not by itself establish performance across the field.

The findings are bounded by the study’s small sample of 11 wells and its reliance on model-calculated rather than independently measured reservoir pressure and permeability. The analysis also did not account for inter-well interference or complex fracture networks, and the authors called for production-time pressure and permeability measurements, geomechanical simulations and multi-well interference models. They also cautioned that numerical thresholds should be adapted to other blocks according to local in-situ stress, reservoir pressure and permeability, rather than applied unchanged across all deep coalbed methane reservoirs.

Subject of Research: Reservoir dynamics and drainage-rate optimization in 11 deep saturated coalbed methane wells in the Shenfu Block

Article Title: Reservoir dynamic evolution and drainage optimization in deep saturated coalbed methane of Shenfu Block

Article References: Wang, Y. J., Xu, H., Liu, Y. N., Liu, Y. C., Wu, H., Liu, D., Wu, X. Z., Dong, Y., Song, X. J., & Wang, J. W. (2026). Reservoir dynamic evolution and drainage optimization in deep saturated coalbed methane of Shenfu Block. PLOS One, 21(10), e0360289. https://doi.org/10.1371/journal.pone.0360289

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0360289

Keywords: coalbed methane, Shenfu Block, reservoir pressure, permeability, drainage optimization, production decline, pressure drawdown, gas desorption, Ordos Basin, reservoir modeling, Reservoir, dynamic

The motivation for the work stems from two of the most consequential applications of coal gas science. Gas diffusion behavior in coal particles underpins the development of coalbed methane, an increasingly important energy resource, and it also governs how quickly methane can desorb from freshly exposed coal during mining operations, which is central to predicting and preventing gas outbursts and explosions in underground mines. Because laboratory measurements of gas desorption are usually performed on crushed particles, the mathematical interpretation of those measurements depends directly on the assumed particle geometry. If that geometry is wrong, every diffusion coefficient extracted from the data inherits the error.

To confront the problem, the team began not with equations but with images. They obtained two-dimensional contours of real coal particles and extracted quantitative shape parameters, allowing them to characterize particle morphology across different scales in a statistically meaningful way. The results were unambiguous about the gap between idealization and reality. Coal particles exhibited median roundness values of 0.73 to 0.80, well below the value of 1.0 that a perfect circle would show, and median axial ratios ranging from 1.34 to 1.49, meaning the particles are substantially longer in one direction than another. Taken together, these measurements indicate that the actual particle shape is much closer to an ellipsoid than to a sphere.

That distinction might sound like a matter of academic pedantry, but the mathematics of diffusion is acutely sensitive to boundary geometry. In the standard spherical model, derived from the classical analytical framework established by Crank in 1975, gas molecules are assumed to diffuse radially inward from a spherical surface toward the center, with the surface-to-volume ratio determined entirely by the particle radius. An ellipsoid has a different distribution of distances between its surface and its interior, with shorter diffusion path lengths along the minor axis and longer ones along the major axis. As a result, the characteristic time for gas to escape from, or enter, an ellipsoidal particle differs from that of a sphere of equivalent volume, and the magnitude of that difference scales with how elongated the particle actually is.

The researchers coupled this geometric insight with a rigorous experimental and computational pipeline. They performed gas desorption experiments on coal particles and then used numerical forward modeling together with parameter optimization to infer the diffusion coefficients that best explained the observed desorption data. Crucially, they ran this inversion twice, once with a spherical model and once with an ellipsoidal model, so that the two geometric frameworks could be compared head to head against identical experimental evidence. This design isolates the effect of particle shape on the estimated diffusion coefficient, which is precisely the quantity that previous studies had left insufficiently quantified.

The evolution laws of the diffusion coefficients and gas pressures were then analyzed across varying particle sizes and adsorption pressures, revealing a consistent pattern. The spherical model generally overestimates gas diffusion coefficients and diffusion rates relative to the ellipsoidal model. More importantly, the deviation is not constant. It grows under lower adsorption pressures and for larger particle sizes, and in the most extreme case examined, the difference between the two models reached 8.94 × 10⁻¹³ m²/s. This means that engineers using spherical assumptions in low-pressure or coarse-particle conditions, which are common in field-relevant scenarios, would systematically misjudge how fast methane is released from the coal matrix.

Why does this systematic bias arise? Physically, the elongation of coal particles changes the effective diffusion path network within each grain. A sphere of equivalent volume concentrates its interior points at larger average distances from the surface than an ellipsoid does along its short axes, and the inversion of desorption data compensates for the mismatched geometry by inflating the fitted diffusion coefficient. In practical terms, a spherical model forces the data to fit a shape the particles do not have, so the estimated diffusivity absorbs the geometric error. The ellipsoidal model, by encoding the measured axial ratios, removes much of this compensating distortion and yields diffusion coefficients that better reflect the intrinsic transport properties of the coal matrix itself rather than artifacts of the assumed shape.

The implications ripple outward across the coal gas research community. Diffusion coefficients measured in the laboratory are routinely embedded into larger reservoir-scale simulations of coalbed methane recovery, into models of gas emission from mine working faces, and into indices used to assess the risk of coal and gas outbursts. If the input diffusivities are systematically inflated by spherical assumptions, reservoir productivity predictions may be overly optimistic, gas drainage designs may be misconfigured, and safety margins in mines may be thinner than intended. The authors argue that incorporating nonspherical morphology is essential for accurately characterizing gas diffusion in coal particles and that their ellipsoidal model offers improved theoretical rationality and engineering applicability compared with the entrenched spherical convention.

The study also fits into a broader movement toward geometric realism in porous media science. Related work has documented how grinding methods alter coal particle morphology, how three-dimensional X-ray computed tomography reveals the complex shapes of micron-sized coal grains, and how particle shape influences processes from flotation kinetics to sorption behavior. What sets this research apart is that it quantifies, with specific numbers, the price of ignoring shape in gas diffusion analysis, and then demonstrates a practical remedy. By first measuring roundness and axial ratios, then building forward and inverse numerical models on that measured geometry, the team provides a reproducible workflow that other laboratories can adopt without exotic instrumentation.

For an industry that depends on precise predictions of how methane behaves in coal, the message is straightforward. The sphere has been a useful fiction, but it is a fiction nonetheless. As coalbed methane development expands and gas disaster prevention remains a life-or-death concern in mining regions worldwide, models that respect the true, irregular, ellipsoid-like character of coal particles offer a path to more trustworthy science and, ultimately, safer and more efficient operations. The new results make clear that when it comes to gas moving through coal, shape is not a detail. It is part of the physics.

The findings also connect to a persistent puzzle in coal gas research: the observation that diffusion in coal powders behaves as a multi-rate process rather than a single, constant-coefficient phenomenon. Because coal contains pore systems spanning multiple scales, gas molecules encounter different transport regimes as they migrate through the matrix. Geometry adds another layer to this complexity, since the distribution of path lengths within an elongated particle naturally produces a spread of diffusion timescales. An ellipsoidal framework therefore aligns more naturally with the heterogeneous character of coal’s pore architecture than a sphere does.

The methodological approach deserves attention as well. Rather than deriving a closed-form analytical solution, the team relied on forward modeling paired with parameter optimization, an inverse-problem strategy in which model outputs are iteratively adjusted until they match measured desorption data. This approach has become increasingly common in coal permeability and diffusion studies, and it allows researchers to work with geometries that lack elegant analytical expressions. The trade-off is that results depend on the quality of the optimization, which makes the careful quantification of particle shape parameters a necessary foundation rather than an optional refinement.

Pressure dependence is another thread worth noting. Earlier experimental work has shown that gas diffusion coefficients in coal vary with adsorption pressure, and the present results indicate that the error introduced by spherical assumptions is itself pressure-dependent, growing as pressure falls. This coupling of geometric and pressure effects suggests that laboratory conditions must be matched carefully to field conditions when transferring measured diffusivities into reservoir or mine-safety models, since a coefficient calibrated at one pressure may mislead at another even before shape effects are considered.

Subject of Research: Effects of nonspherical coal particle morphology on gas diffusion behavior, quantified through desorption experiments and numerical modeling

Article Title: Effects of Nonspherical Morphology on Gas Diffusion in Coal Particles: Experiments and Numerical Modeling

Article References: Liu, Q., Li, Z., Wang, E., Sang, S., Mao, Z., Liu, X., Feng, X., Deng, S., Wang, D., & Zhang, X. (2026). Effects of Nonspherical Morphology on Gas Diffusion in Coal Particles: Experiments and Numerical Modeling. Natural Resources Research. https://doi.org/10.1007/s11053-026-10769-x

Image Credits: AI Generated

DOI: 10.1007/s11053-026-10769-x

Keywords: gas diffusion, coal particles, particle morphology, ellipsoidal model, diffusion coefficient, gas desorption, coalbed methane, numerical modeling, spherical model, adsorption pressure, particle size, mine safety