Mathematical Model of Coalbed Gas Flow with Klinkenberg Effects in Multi-Physical Fields and its Analytic Solution

Abstract

The deep-mining coal seam impacted by high in situ stress, where Klinkenberg effects for gas flow were very obvious due to low gas permeability, could be regarded as a porous and tight gas-bearing media. Moreover, the Klinkenberg effects had a significant effect on gas flow behavior of deep-mining coal seam. Based on the gas flow properties of deep-mining coal seams affected by in situ stress field, geothermal temperature field and geoelectric field, a new mathematical model of coalbed gas flow, which reflected the impact of Klinkenberg effects on coalbed gas flow properties in multi-physical fields, was developed by establishing the flow equation, state equation, and continuity equation and content equation of coalbed gas. The analytic solution was derived for the model of one-dimensional steady coalbed gas flow with Klinkenberg effects affected by in situ stress field and geothermal temperature field, and a sensitivity analysis of its physical parameters was carried out by comparing available analytic solutions and the measured values. The results show that the analytic solutions of this model of coalbed gas flow with Klinkenberg effects are closer to the measured values compared to those without Klinkenberg effects, and this model can reflect more accurately gas flow of deep-mining coal seams. Moreover, the analytic solution of this model is more sensitive to the change of Klinkenberg factor b and temperature grad G than depth h.Keywords Porous media · Klinkenberg effects · Multi-physical fields · Mathematical model of coalbed gas flow · Analytic solution Nomenclature A Ash of coal a Langmuir volume parameter, m 3 kg −1 123 408 G. Hu et al. b Klinkenberg factor, Pa c Langmuir pressure parameter, Pa −1 C 1 , C 2 Integral constant D 0 Gas diffusion coefficient when the pore pressure equals p 0 d Average coal micro-grain size of coal seam, m div Divergence of a vector E Electric intensity grad Gradient of a scalar h Depth, m K g Gas permeability of coal, m 2 K ∞ Absolute gas permeability under very high pressure, m 2 k σ 0 Value of K σ (0) when effective stress σ equals zero k T 0 Value of K T (0) when the temperature of coal theoretically equals zero L Oblique length of coal seam, L = h/ sin θ , m m Methane content reserved in the unit volume coal, m 3 m −3 m 0 Gas content in coal seam at initial time t 0 , m 3 m −3 m a Absorbed gas content in coal seam, m 3 m −3 m d Desorbable average gas content in coal seam, m 3 m −3 m f Free gas content, m 3 m −3

Coal and Coalbed Methane Co-Extraction Technology Based on the Ground Movement in the Yangquan Coalfield, China

“…In traditional coal mining, CBM is considered a type of hazardous gas, not only because of the danger of explosions and gas outbursts, but also because of serious threat to the safety of mine production [1][2][3][4][5][6]. In contrast, CH4, the main ingredient of CBM, is a greenhouse gas, whose greenhouse effect is ~21-23 times as strong as that of CO2 [7][8][9][10].…”

“…Among them, the coal seams in America and Australia are of little depth and high permeability, and surface well predrainage and underground directional long borehole drainage technologies are their major and minor strategies, respectively. Part of Germany and Poland are similar to the coal seam conditions in Chinese mining areas; however, their yields are low and the number of underground coal seams is relatively small; and the gas drainage is mainly dependent on the underground cross-measure boreholes gas drainage technology [1][2][3][4][5][6]15]. In contrast, the Chinese coal seams are of larger depth and high ground stress; therefore, underground drainage is the main approach to extract CBM.…”

The case for enhanced coalbed methane using hydraulic fracturing in the geostructural belt

“…The coal and gas outbursts have become the major natural disasters that challenge coal mine safety (Yuan, 2016). According to statistics, the secondary disasters caused by coal and gas outbursts account for more than 80% of the major coal mine accidents that have occurred (Hu et al, 2009a(Hu et al, , 2009b. Therefore, China has been one of the countries suffering from a serious coal and gas outburst problem (Hu et al, 2009a(Hu et al, , 2009b(Hu et al, , 2015.…”

“…According to statistics, the secondary disasters caused by coal and gas outbursts account for more than 80% of the major coal mine accidents that have occurred (Hu et al, 2009a(Hu et al, , 2009b. Therefore, China has been one of the countries suffering from a serious coal and gas outburst problem (Hu et al, 2009a(Hu et al, , 2009b(Hu et al, , 2015. Studies have shown that the actual outbursts area accounted for only 10 to 20% of the total areas of coal seam (He and Chen, 2009).…”

Sorption Rate of Carbon Dioxide on Coal

“…Thus, "desorption" means a number of processes resulting in the release of the sorbing gas from the sorbent. When speaking about the release of methane from a coal bed into an excavation, we typically mean the combination of the filtration (Crank 1975;Timofejew 1967;Pillalamarry et al 2011;Hu et al 2009;Wu et al 1998), diffusion, and sorption processes, which will further be referred to as "the sorption proper" (Harpalani and Chen 1997;Pillalamarry et al 2011;Day and Sakurovs 2008;Weniger et al 2010;CeglarskaStefańska and Zarębska 2005;Majewska et al 2009;Busch and Gensterblum 2011;Nagaoka and Imae 2003). Under laboratory conditions, in which case the investigations are carried out for small-sized grain samples, we can assume that the transportation of gas is influenced mainly by the diffusion processes.…”