地球科学  2017, Vol. 42 Issue (8): 1356-1363. PDF     0

1. 中国地质大学构造与油气资源教育部重点实验室, 湖北武汉 430074;
2. 山西晋城无烟煤矿业集团有限责任公司煤与煤层气共采国家重点实验室, 山西晋城 048000;
3. 中国矿业大学地球科学与测绘工程学院, 北京 100083

Characteristics of Methane Diffusion in Coal Matrix and Its Effect on Gas Production
Li Guoqing1,2 , Meng Zhaoping2,3 , Liu Jinrong3
1. Key Laboratory of Tectonics and Petroleum Resources of the Ministry of Education, China University of Geosciences, Wuhan 430074, China;
2. State Key Laboratory of Coal and Coal-Bed Methane Simultaneous Extraction, Shanxi Jincheng Anthracite Mining Group Co. Ltd., Jincheng 048000, China;
3. College of Geoscience and Surveying Engineering, China University of Mining and Technology, Beijing 100083, China
Abstract: Diffusion is one of the key steps of methane transport in coal seam, yet our understanding of it is still insufficient. Taking the high rank coal bed methane (CBM) reservoir in the southern Qinshui basin, China as the study area, the patterns and quantitative characterization of methane diffusion in coal seam were analyzed based on microflows and nanoflows mechanics theory; the influence of diffusion property on gas production in coal seams of different coal textures was studied by using a numerical simulation software (Simed) in this study. Results show that the diffusion of methane in coal is driven by a chemical potential gradient and the diffusion modes include bulk diffusion, Knudsen diffusion and configurational diffusion. Various diffusion modes coexist and vary during the extraction of coalbed methane; the diffusion coefficient is influenced by temperature, gas pressure, gas type, moisture and pore structure of coal matrix, and the size of micropore varies due to the adsorption of methane and thereby the diffusion path will be transformed; the dynamic adsorption of methane on the coal matrix determines that methane diffusion in coal is a non-equillibrium process and that the diffusion coefficient is a function of adsorbed gas concentration; the results of numerical simulation based on quasi-steady diffusion show that the diffusion property has a slight influence on the long-term cumulative gas production while it exerts a significant effect on the short-term gas rate; if the diffusion coefficient is low, that is, the sorption time constant is relatively high, the peak gas rate will be relatively low while the gas rate will be relatively high in a period of time after reaching the peak gas rate; the gas production is more sensitive to sorption time constant for the low-permeability tectonically deformed coal seam than for the high-permeability one.
Key Words: coal bed methane    high rank coal seam    diffusion    gas rate    coal texture

0 引言

1 煤基质中甲烷扩散性能及表征参数 1.1 气体在多孔介质中的运移模式

 $Kn = \frac{\lambda }{d},$ (1)

 $\lambda = \frac{{{K_{\rm{B}}}T}}{{\sqrt 2 {\rm{\pi }}d_0^2p}},$ (2)

 ${k_{\rm{g}}} = {k_\infty }\left({1 + \frac{b}{{{p_{\rm{m}}}}}} \right),$ (3)
 ${p_{\rm{m}}} = \frac{{{p_{\rm{o}}} + {p_{\rm{i}}}}}{2},$ (4)
 $b = \frac{{4C\lambda {p_{\rm{m}}}}}{{{r_{\rm{H}}}}},$ (5)

 $\frac{{{k_{\rm{g}}}}}{{{k_\infty }}} = 1 + 4CKn,$ (6)

 Download: larger image 图 1 不同努森数的渗透率变化系数 Fig. 1 Variation coefficient of gas permeability at different Knudsen numbers
1.2 气体在多孔介质中的扩散模式

 Download: larger image 图 2 常温常压下孔隙大小对扩散系数的影响 Fig. 2 Influence of pore size on diffusion coefficient at normal temperature-pressure

 Download: larger image 图 3 甲烷分子运动平均自由程随温度的变化 Fig. 3 Variation of mean free path of methane over temperature
 Download: larger image 图 4 20 ℃下甲烷分子运动自由程随压力的变化 Fig. 4 Variation of mean free path of methane over pressure at 20 ℃

1.3 扩散性能的定量表征

 $D = \frac{{1.86 \times {{10}^{ - 3}}\varphi {T^{3/2}}{{\left({1/{M_1} + 1/{M_2}} \right)}^{1/2}}}}{{\xi p\sigma _{12}^2\mathit{\Omega }}},$ (7)

 $D = \frac{{2r}}{3}\sqrt {\frac{{8R}}{{{\rm{\pi }}M}}},$ (8)

 ${q_{\rm{m}}} = \frac{{{V_{\rm{m}}}\left[ {{C_{\rm{m}}} - C\left(p \right)} \right]}}{\tau },$ (9)
 $\tau = \frac{1}{{D\sigma }},$ (10)

 $\sigma = \frac{8}{{s_{\rm{f}}^2}},$ (11)

 $\tau = \frac{{s_{\rm{f}}^2}}{{8D}},$ (12)

2 高煤阶煤基质中甲烷扩散性能对煤层气井产能的影响

3 结果

 Download: larger image 图 5 不同吸附时间常数煤层产气速率 Fig. 5 Gas rate of a CBM well at different sorption time constants a.渗透率为0.2×10-15 m2；b.渗透率为5×10-15 m2

4 讨论 4.1 数值模拟假设条件的讨论

4.2 吸附浓度对扩散性能的影响

 $J = - L\frac{{\partial \mu }}{{\partial x}},$ (13)

 $\mu = {\mu ^0} + RT\ln \frac{p}{{{p_0}}},$ (14)

 ${D_{\rm{t}}} = RTL\frac{{{\rm{dln}}\frac{p}{{{p_0}}}}}{{{\rm{d}}C}}{D_0}\Gamma \left({p, c} \right),$ (15)

4.3 混合气体之间相互作用对扩散性能的影响

5 结论

(1) 煤基质微孔中甲烷的运移模式为构型扩散；在介孔和宏孔中，高压条件下甲烷的运移模式为体相扩散，低压条件下甲烷的运移模式为努森扩散或构型扩散模式；而在孔径超过1 μm的孔隙或裂隙中，扩散模式一般为体相扩散.在体相扩散中气体处于连续状态，而在努森扩散和构型扩散中，气体处于明显稀薄的状态；产气过程中多种扩散模式并存且呈动态变化.

(2) 基于拟稳态扩散的数值模拟研究表明，扩散性能强弱对于高煤阶煤层气井长期累计产气量几乎没有影响，而对短期产气速率具有较大的影响.扩散性能弱的气井，吸附时间常数较大，产气速率峰值较低，但峰值之后的一段时间内产气速率相对较高.与高渗煤层相比，低渗构造煤层的产气速率对吸附时间常数更敏感.

(3) 煤基质中气体扩散性能受基质孔隙度、孔径、迂曲度、温度、游离气体压力、气体分子类型以及气体分子与煤基质微孔表面之间的吸附作用影响，扩散系数是吸附量的函数.