EXPERIMENT OF ADSORPTION-DESORPTION HYSTERSIS OF GAS IN COAL SHALE BY USING NUCLEAR MAGNETIC RESONANCE SPECTRUMS
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摘要: 煤系页岩瓦斯主要以吸附态和游离态形式存在, 其解吸过程相对吸附过程具有普遍滞后现象, 因此从微细观角度定量研究其吸附−附解吸迟滞规律对页岩气井后期稳产增产具有重要意义. 在前人研究基础上结合核磁共振谱理论推导出能够准确表征煤系页岩瓦斯吸附−解吸迟滞效应微细观评价模型, 并采用核磁共振谱测试技术, 以双鸭山盆地东保卫煤矿三采区36# 煤层底板煤系页岩为研究对象, 进行煤系页岩瓦斯吸附−解吸迟滞效应核磁共振谱实验, 模拟不同储层原位应力状态煤系页岩瓦斯迟滞效应发生全过程, 进一步对吸附态瓦斯、游离态瓦斯以及微细观方法测定的宏观瓦斯迟滞规律进行定量化研究, 并对其发生机理以及其对深部煤系页岩瓦斯开采影响进行了初步探究. 结果表明: 应力状态下吸附态和游离瓦斯均有滞后效应; 瓦斯宏观迟滞系数与平均有效应力呈幂函数关系, 而瓦斯宏观迟滞效应中由吸附态或游离态瓦斯引起的迟滞系数与平均有效应力关系均可采用二次多项式拟合; 孔裂隙应力损伤和微孔隙瓦斯扩散受限耦合或许是煤系页岩瓦斯吸附−解吸迟滞效应产生根本原因之一.Abstract: Coal shale gas was mainly composed of adsorbed and porous medium-confined gas. The desorption of coal shale gas generally lagged behind the adsorption, therefore, it was significance to quantitatively study the adsorption and desorption hysteresis law from the micro perspective for stable production and stimulation of shale gas wells in the later stage. Based on a large number of fruitful previous studies and the theory of nuclear magnetic resonance spectrums, an improved micro evaluation model for the accurate characterization of the adsorption and desorption hysteresis effect of coal shale gas was deduced. In order to simulate the whole process of adsorption and desorption hysteresis of gas in coal shale, the nuclear magnetic resonance spectrum technique was applied for the experimental research on adsorption and desorption hysteresis of gas in coal shale from coal floor of No. 36 coal seam in No. 3 mining area of Dongbaowei Mine in Shuangyashan Basin. And on such bases, the micro quantitative research on adsorption and desorption hysteresis law of the adsorbed gas, porous medium-confined gas, macro gas measurement by micro method in coal shale was carried out, the mechanism of adsorption and desorption hysteresis and its influence on shale gas mining in deep coal measures were preliminarily explored. Results indicated that in the process of adsorption and desorption under stress state, both adsorbed and porous medium-confined gas had obvious hysteresis; the relationship between macroscopic hysteresis coefficient of gas and the average effective stress was power function; while the relationship between hysteresis coefficient and average effective stress caused by adsorbed gas could be fitted by quadratic polynomial, and it was the same with porous medium-confined gas. The coupling of stress damage and gas diffusion in the pore fracture structure of coal series shale might be one of the fundamental reasons for the gas adsorption and desorption hysteresis of coal shale.
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图 3 煤系页岩瓦斯吸附−解吸迟滞效应现场实验
Figure 3. Field experiment on hysteresis effect of gas adsorption-desorption in coal shale
图 4 煤系页岩瓦斯吸附−解吸迟滞效应实验装置连接示意图
Figure 4. Connection diagram of gas adsorption-desorption hysteresis effect experiment device for coal shale
图 9 游离态瓦斯迟滞效应评价模型
Figure 9. Evaluation model for hysteresis effect of porous medium-confined gas
图 10 瓦斯迟滞系数与平均有效应力关系
Figure 10. Relationship between hysteresis index of gas and average effective stress
表 1 迟滞效应宏观定量评价指标
Table 1. Macro quantitative evaluation index of hysteresis
Evaluation index Formula Parameter Reference Freundlich ${S_{{\rm{ad}}}} = {K_{{\rm{ad}}}}{C_{{\rm{ad}}}}^{1/{n_{{\rm{ad}}}}}$,
${S_{{\rm{de}}}} = {K_{{\rm{de}}}}{C_{{\rm{de}}}}^{1/{n_{{\rm{de}}}}}$,
$HI = \dfrac{{{n_{{\rm{de}}}}}}{{{n_{{\rm{ad}}}}}}$${S_{{\rm{ad}}}}$—equilibrium concentration of solid phase adsorption
${S_{{\rm{de}}}}$—equilibrium concentration of solid phase desorption
K—adsorption parameter
C—equilibrium concentration of adsorbent
${n_{{\rm{ad}}}}$—Freundlich adsorption index
${n_{{\rm{de}}}}$ —Freundlich desorption index[21-22] slope $HI = \dfrac{{{f_{{\rm{ad}}}}^\prime (C) - {f_{{\rm{de}}}}^\prime (C)}}{{{f_{{\rm{ad}}}}^\prime (C)}}$ ${f_{{\rm{ad}}}}^\prime (C)$, ${f_{{\rm{de}}}}^\prime (C)$—first derivative of characteristic equation [23] solid phase concentration $HI = \dfrac{{\max ({S_{{\rm{de}}}} - {S_{{\rm{ad}}}})}}{{{S_{{\rm{ad}}}}}}$,
$HI = {\left. {\dfrac{{\max ({S_{{\rm{de}}}} - {S_{{\rm{ad}}}})}}{{{S_{{\rm{ad}}}}}}} \right|_{T,C}}$${S_{{\rm{ad}}}}$—equilibrium concentration of solid phase adsorption
${S_{{\rm{de}}}}$—equilibrium concentration of solid phase desorption
C—equilibrium concentration of adsorbent
T—test temperature[24] area $HI = 100\left(\dfrac{{{A_{{\rm{de}}}} - {A_{{\rm{ad}}}}}}{{{A_{{\rm{ad}}}}}}\right)$ ${A_{{\rm{de}}}}$—area under desorption curve
${A_{{\rm{ad}}}}$—area under adsorption curve[25] 
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表 2 页岩特征参数
Table 2. Shale characteristic parameters
Name ρ/(g·cm−3) φ/% σbc/MPa E/GPa shale 2.43 1.6 ~ 5.0 3.0 ~ 18.7 13.5
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表 3 自由态瓦斯核磁共振谱特性实验方案
Table 3. Experiment of free gas by NMR spectrums
No. Confining
pressure
/MPaAxial
pressure
/MPaPore
pressure
/MPa1 1.79 2.13 1.35 2 3.09 3.54 2.46 3 4.03 4.93 3.52 4 4.99 5.71 4.43 5 6.02 6.46 5.44 6 7.01 7.56 6.50 7 8.89 9.41 8.29
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表 4 吸附过程核磁共振谱实验方案
Table 4. Experimental adsorption of gas by NMR spectrums
No. Confining
pressure
/MPaAxial
pressure
/MPaPore
pressure
/MPa1 1.78 2.24 1.31 2 2.97 3.61 2.24 3 4.04 4.47 3.37 4 5.02 5.43 4.39 5 6.02 6.44 5.65 6 7.01 7.45 6.33 7 8.79 9.34 7.89
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表 5 解吸过程核磁共振谱实验方案
Table 5. Experimental desorption of gas by NMR spectrums
No. Confining
pressure
/MPaAxial
pressure
/MPaPore
pressure
/MPa1 8.79 9.34 7.89 2 7.49 8.18 6.94 3 6.54 7.23 5.76 4 5.47 6.24 4.48 5 4.52 5.15 3.41 6 3.51 4.16 2.40 7 2.49 3.25 1.41 8 0.95 1.47 0.40
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表 6 常用吸附模型
Table 6. Common adsorption models
Model Model expression Adsorption R2 L $V = P{V_{\rm{L}}}/({P_{\rm{L}}} + P)$ 0.80002 F $V = {K_{\rm{b}}}{P^m}$ 0.93634 E-L $V = {K_{\rm{b}}}P{V_{\rm{L}}}/(1 + {K_{\rm{b}}}P + m\sqrt {{K_{\rm{b}}}P} )$ 0.99038 T $V = {K_{\rm{b}}}P{V_{\rm{L}}}/{[1 + {({K_{\rm{b}}}P)^m}]^{1/m}}$ 0.75002 B-BET $V = \dfrac{{{V_{\rm{m}}}CP}}{{({P^0} - P)[1 + (C - 1)(P/{P^0})]}}$ 0.76401 T-BET $V = \dfrac{{{V_{\rm{m}}}CP[1 - (n - 1)(P/{P^0}) + n{{(P/{P^0})}^{n + 1}}]}}{{({P^0} - P)[1 + (C - 1)(P/{P^0}) - C{{(P/{P^0})}^{n + 1}}]}}$ 0.93211 D-R $V = {V_0}\exp [ - D{\ln ^2}({P^0}/P)]$ 0.99475 D-A $V = {V_0}\exp [ - D{\ln ^m}({P^0}/P)]$ 0.56960 注: PL—Langmuir压力, MPa; VL—Langmuir体积, cm3/g; Vm—单层极限吸附量, cm3/g; P0—饱和蒸汽压力, MPa; C—吸附热常数; V0—最大吸附量, cm3/g; Kb—吸附经验常数; m—吸附剂非均质参数; n—模型参数; D—净吸附热常数.
Notes: PL—Langmuir pressure, MPa; VL—Langmuir volume, cm3/g; Vm—monolayer limit adsorption capacity, cm3/g; P0—saturated steam pressure, MPa; C—adsorption heat constant; V0—maximum adsorption capacity, cm3/g; Kb—adsorption empirical constant; m—adsorbent heterogeneity parameters; n—model parameter; D—final adsorption heat constant.
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表 7 常用解吸模型
Table 7. Common desorption models
Model Model expression Desorption R2 Weibull $V = {V_0}[1 - \exp ( - b{p^q})]$ 0.99660 desorption function $V = \dfrac{{abp}}{{1 + bp}} + c$ 0.97953 注: a—煤系页岩最大吸附量, cm3/g; b—吸附热、吸附速度与解吸速度综合函数, MPa−1; c—残余吸附量, cm3/g; V0—最大吸附量, cm3/g; b—吸附热常数; q—吸附质在孔隙表面的占位比.
Notes: a—maximum adsorption capacity of coal shale, cm3/g; b—comprehensive function of adsorption heat, adsorption rate and desorption rate, MPa−1; c—residual adsorption capacity, cm3/g; V0—maximum adsorption capacity, cm3/g; b—adsorption heat constant; q—occupation ratio of adsorbate on pore surface.
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