Modeling and mechanism of propagation of underground coal smoldering fires with thermal buoyancy driven
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摘要:
地下煤火蔓延模型与机制研究对我国煤炭资源绿色安全开采具有重要意义。目前地下煤火阴燃正向蔓延模型主要存在问题：简化的煤燃烧单步反应忽略了水分蒸发和热解吸热反应对蔓延的重要影响作用；缺乏实验数据验证模型的有效性。为此，构建了包含水分蒸发、煤热解和碳氧化三步反应体系的地下煤火阴燃正向蔓延数学模型；采用COMSOL Multiphysics有限元软件数值计算了该理论模型；开展了不同地裂缝渗透性条件下热浮力驱动地下煤火阴燃正向蔓延实验，进行对比实验和数值计算。结果表明：构建的模型揭示了地下煤火阴燃蔓延供氧控制机制，不仅能预测地下煤火阴燃正向蔓延高温区域的温度和蔓延速率，而且还能合理地预测阴燃多步反应速率以及氧气、煤、碳和灰分质量分数的时空演化。
Abstract:Modeling and understanding of underground coal fire is of significance for green-and-safe mining of coal resources in China. Two issues remain unsolved in forward-propagation models of underground coal smoldering fires: one-step coal oxidation has been too simple so that endothermic reactions such as water evaporation and pyrolysis that have important influence on smoldering propagation of underground coal fires have been not considered; and models have not been validated via experimental data. In this work, a three-step chemical reaction scheme including water evaporation, coal pyrolysis, and char oxidation was employed and mathematic model in terms of forward propagation of underground coal smoldering fires was established. The theoretical model was numerically calculated using COMSOL Multiphysics finite element software. The theoretical model was numerically calculated using COMSOL Multiphysics finite element software, and the forward smoldering spread experiment of underground coal fire driven by thermal buoyancy under different ground crack permeability conditions was carried out. Comparison experiment and numerical calculation were carried out. Results show that the proposed model not only owns good capability to predict the peak temperature and velocity of smoldering propagation of underground coal fire, but also can inversely plot multiple step chemical reactions as well as spatiotemporal evolutions of oxygen and solid species mass fractions. In addition, the controlling mechanism of smoldering propagation of underground coal fires was further revealed.
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煤储层含气量是煤层气资源勘探测试的关键参数[1-4]，也是表征煤储层开发潜力和确保矿井瓦斯安全的关键参数之一[4-11]；煤储层含气量测试可为煤层气资源量、储量估算和煤层气开发设计提供重要依据[4]。煤储层含气量测值的不准确性是导致煤层气资源计算出现差异的重要原因[12]。现阶段，我国煤炭资源勘探和煤层气资源勘探开发煤层含气量测试方法主要采用GB/T19559—2021《煤层气含量测定方法》提供的解吸法及其矫正计算方法[13-17]，其中损失气量计算采用最初10个地面实测解吸气量数据，由损失气时间与解吸时间和的平方根与累计解吸气量之间线性关系倒推零时间解吸气量得出。
应用上述方法，多年来我国在多个煤层气勘探开发区块获取了大量含气量数据。然而，目前煤层含气量计算仍有以下不足：吸附气欠饱和储层现场含气量测试的可靠性缺乏数值模拟验证，特别是损失气量估算的准确程度尚未有数值模型验证；另外，上述方法对含气饱和储层（吸附气、游离气均饱和，下同）含气量测试的准确性尚不清楚，饱和储层煤心含气量测试过程模拟尚未开展。基于此，选取新疆低煤化煤（本次为长焰煤）煤心为研究对象，构建了储层煤心含气量解吸-扩散数值模型，并通过模型计算分析了吸附气欠饱和与含气饱和储层煤心解吸动态，对比分析了数值模型与现场测试损失气量、解吸气量、残余气量构成的差异性，以期为我国低煤化储层煤层气勘探提供含气性分析新思路。
1. 测试方法
1.1 现场含气量相关测试
按照GB/T 19559—2021《煤层气含量测定方法》国家标准提供的方法，开展自然煤心采样，记录采样及装样时间，开展自然解吸气量连续测试和残余气测试；根据GB/T 19560—2008《煤的高压等温吸附试验方法》、GB/T 212—2008《煤的工业分析方法》等开展煤等温吸附实验和工业分析。现场煤心采样及上述相关工作开展于新疆某长焰煤储层煤层气开发先导试验区，煤心样品为长焰煤（属于低煤化度煤），且煤心对应的实测含气饱和度分别为54.77%、77.51%、99.79%。工业分析及煤岩组分分析成果见表1。
表 1 煤心工业分析及煤岩组分分析成果Table 1. Coal core industrial analysis and coal rock composition analysis results样品编号 直径/mm 长度/cm 宏观煤岩类型 平均镜质组最大反射率/% 水分/% 灰分/% 挥发分/% 镜质组组分/% 惰质组组分/% 壳质组组分/% BF-1 63.0 26.8 半亮煤 0.60 0.90 11.77 43.79 84.2 14.8 1.0 BF-2 60.1 30.0 半亮煤 0.61 0.86 22.08 40.45 79.6 19.4 1.0 BF-3 61.0 34.0 半亮煤 0.67 1.12 13.40 37.17 78.6 25.5 1.0 1.2 储层煤心含气量测试数值模拟流程
1.2.1 假设条件
煤是一种复杂的多孔介质，为了方便求解，通常对煤心样品做出以下假设：①煤屑由球形颗粒组成；②煤颗粒为均质、各向同性体；③CH4解吸-扩散遵从连续性原理；④扩散系数与浓度、时间和坐标无关；⑤煤屑瓦斯解吸为等温条件下的解吸过程；⑥煤心含气量测试过程中孔隙度不变。
1.2.2 控制方程
单位体积吸附气欠饱和储层煤心基质CH4质量可表述为（CH4全部吸附在煤基质表面，在储层压力条件下吸附解吸平衡，孔隙表面外不含游离CH4）：
$$ {m}_{\mathrm{m}\mathrm{u}}={\varphi }_{\mathrm{u}\mathrm{n}}(1-{\phi }_{\mathrm{m}})\left(\dfrac{100-{M}_{\mathrm{a}\mathrm{d}}-{A}_{\mathrm{a}\mathrm{d}}}{100}\right)\dfrac{{V}_{\mathrm{L}}{p}_{\mathrm{m}}}{{p}_{\mathrm{m}}+{p}_{\mathrm{L}}}{\rho }_{\mathrm{c}\mathrm{o}\mathrm{a}\mathrm{l}}{\rho }_{\mathrm{s}\mathrm{c}} $$ 式中：mmu为单位体积煤基质中赋存的瓦斯质量，g；φun为欠饱和储层含气饱和度，%；ϕm为基质孔隙度；Mad为空气干燥基水分含量，%；Aad为空气干燥基灰分产率，%；VL为朗缪尔体积，单分子层最大的吸附量，cm3/g；pm为基质孔隙中的CH4压力，MPa；pL为朗缪尔压力，吸附量为最大吸附量1/2时间的吸附平衡压力，MPa；ρcoal为煤视密度，kg/m3；ρsc为标准状态下的CH4密度，g/cm3。
煤心解吸至大气环境控制方程：
$$\begin{array}{c} \dfrac{\partial p}{\partial t}\left({\varphi }_{{\mathrm{un}}}\left(1-{\phi }_{{\mathrm{m}}}\right)\left(\dfrac{100-{{M}}_{\mathrm{a}\mathrm{d}}-{{A}}_{\mathrm{a}\mathrm{d}}}{100}\right)\dfrac{{V}_{{\mathrm{L}}}{p}_{{\mathrm{L}}}}{{\left(p+{p}_{{\mathrm{L}}}\right)}^{2}}{\rho }_{{\mathrm{coal}}}\dfrac{{M}_{{\mathrm{c}}}}{{V}_{{\mathrm{M}}}}\right)=\\ \nabla \left(\dfrac{{M}_{{\mathrm{c}}}}{RT}D\nabla p\right) \end{array} $$ 式中：t为时间，s；p为煤心孔隙气体压力，MPa；Mc为甲烷分子摩尔质量，kg/mol；VM为CH4分子摩尔体积，m3/mol；R为理想气体常数，J/（mol·K）；T为煤层温度，K；D为扩散系数，10−9 m2/s。
单位体积饱和储层煤心基质CH4质量可表述为（CH4在煤基质表面吸附饱和，且在储层压力条件下游离CH4充满孔隙）：
$$ \begin{array}{c} {m}_{{\mathrm{mo}}}=(1-{\phi }_{{\mathrm{m}}})\left(\dfrac{100-{{M}}_{\mathrm{a}\mathrm{d}}-{{A}}_{\mathrm{a}\mathrm{d}}}{100}\right)\dfrac{{V}_{{\mathrm{L}}}{p}_{{\mathrm{m}}}}{{p}_{{\mathrm{m}}}+{p}_{{\mathrm{L}}}}{\rho }_{{\mathrm{coal}}}{\rho }_{{\mathrm{sc}}}+\\ {\phi }_{{\mathrm{m}}}\dfrac{{M}_{{\mathrm{c}}}}{RT}{p}_{{\mathrm{m}}} \end{array} $$ 式中：mmo为初始条件下单位体积饱和储层煤心基质CH4质量，g。
饱和储层煤心含气饱和度：
$$ {\varphi }_{{\mathrm{m}}}=\dfrac{{m}_{{\mathrm{mo}}}}{(1-{\phi }_{{\mathrm{m}}})\left(\dfrac{100-{{M}}_{\mathrm{a}\mathrm{d}}-{{A}}_{\mathrm{a}\mathrm{d}}}{100}\right)\dfrac{{V}_{{\mathrm{L}}}{p}_{0}}{{p}_{0}+{p}_{{\mathrm{L}}}}{\rho }_{{\mathrm{coal}}}{\rho }_{{\mathrm{sc}}}} $$ 煤心扩散、解吸控制方程：
$$ \begin{array}{c} \dfrac{\partial p}{\partial t}\left(\left(1 - {\phi }_{{\mathrm{m}}}\right)\left(\dfrac{100 - {{M}}_{\mathrm{a}\mathrm{d}} - {{A}}_{\mathrm{d}}}{100}\right)\dfrac{{V}_{{\mathrm{L}}}{p}_{{\mathrm{L}}}}{{\left(p + {p}_{{\mathrm{L}}}\right)}^{2}}{\rho }_{{\mathrm{coal}}}\dfrac{{M}_{{\mathrm{c}}}}{{V}_{{\mathrm{M}}}} + {\phi }_{{\mathrm{m}}}\dfrac{{M}_{{\mathrm{c}}}}{RT}\right) =\\ \nabla \left(\dfrac{{M}_{{\mathrm{c}}}}{RT}D\nabla p\right) \end{array} $$ 1.2.3 几何模型和边界条件
几何模型为实际圆柱体煤心物理模型，几何尺寸与现场测量一致；初始煤心各点孔隙压力为根据煤层气井试井储层压力推算得出，由于解吸时煤心已与大气接触，认为边界条件煤心柱面和断面表面压力为大气压力0.1 MPa。煤心几何模型如图1。
2. 结果与讨论
2.1 欠饱和储层煤心自然解吸测试与数值模拟
采用与煤心参数近似数据开展模拟并拟合解吸体积曲线，还原现场解吸参数和煤样特性参数。储层煤心参数实测值与拟合值对比见表2，煤心xy中心截面单位体积煤心含气性变化如图2。BF-1煤心累计解吸体积与解吸时间关系如图3。
表 2 储层煤心参数实测值与拟合值对比Table 2. Comparison between measured values and fitting values of coal core parameters of reservoir参数 实测值（BF1/BF2/BF3） 拟合值（BF1/BF2/BF3） 误差率/%
（BF1/BF2/BF3）储层压力/ MPa 9.88/9.25/8.96 9.88/9.25/8.96 0/0/0 兰氏压力/ MPa 1.92/2.05/1.65 1.92/2.05/1.65 0/0/0 兰氏体积/
（cm3·g−1）19.23/22.05/15.40 18.60/20.10/13.80 3.28/8.84/10.39 水分含量
（空干基）/%0.90/0.86/1.12 0.93/0.93/1.08 3.33/8.14/3.57 灰分产率
（干燥基）/%11.77/22.08/13.40 11.72/23.18/14.20 0.42/4.98/5.97 煤心密度/
（g· cm−3）1.36/1.44/1.44 1.36/1.44/1.44 0/0/0 孔隙度 0.10/0.09/0.08 0.10/0.08/0.072 0/11.1/10.0 扩散系数/
10−9（m2·s−1）4×10−9/—/— 3.70/1.00/0.80 7.50/—/— 含气
饱和度/%54.77/77.51/99.79 54.77/77.51/99.79 0/0/0 ![]()
图 2 煤心xy中心截面单位体积煤心含气性变化Figure 2. Change of gas content per unit volume of coal core at each position of xy central section of coal core由图2可知：解吸开始24 h，含气量快速下降，各时刻煤心中心位置含气量最高而边缘最低。
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图 3 煤心累计解吸体积与解吸时间关系Figure 3. Relationship between cumulative desorption volume and desorption time由图3可知：BF-1扣除损失气时间拟合累计解吸气量（6 427.66 cm3）与现场煤心累计解吸气量（6 346.73 cm3）接近，相差2.00%；未扣损失气时间模拟累计解吸量（7 361.4 cm3）大于上述二者，显示损失气的存在；同理，BF-2和BF-3也有类似结果。
吸附气饱和储层煤心现场解吸与数值模拟含气量构成对比见表3，BF-1、BF-2、BF-3煤心损失气时间（T）与解吸时间（t）和的平方根和解吸初期累计解吸气量回归关系如图4。
表 3 吸附气饱和储层煤心现场解吸与数值模拟含气量构成对比Table 3. Comparison of adsorbed gas saturated reservoirs between on-site desorption and numerical simulation of cores样品 含气饱和度/% 含气量构成 实测体积/cm3 占比/实测/% 拟合体积/cm3 占比（拟合）/% 实测-拟合误差/% BF-1 54.77 损失气 979.43 13.28 880.26 11.95 10.12 解吸气 6 346.73 86.06 6427.66 87.32 2.00 残余气 48.43 0.66 46.24 0.63 4.52 总含气量 7 374.59 100.00 7361.40 100.00 0.18 BF-2 77.51 损失气 823.04 7.80 755.37 7.03 8.22 解吸气 9680.43 91.78 9937.60 92.52 2.66 残余气 43.88 0.42 47.89 0.45 9.14 总含气量 10290.96 100.00 10740.86 100.00 1.83 BF-3 99.79 损失气 793.71 6.36 841.77 6.75 6.06 解吸气 11638.39 93.26 11575.20 92.84 0.54 残余气 47.56 0.38 50.32 0.40 5.80 总含气量 12479.66 100.00 12467.29 100.00 0.10 ![]()
图 4 煤心损失气时间与解吸时间和的平方根和解吸初期累计解吸气量回归关系Figure 4. Linear regression relationship between the square root of the sum of gas loss time and desorption time and cumulative amount of desorbed gas at initial stage of desorption对于BF-1煤心，现场测试BF-1煤心损失气量结果为979.43 cm3，与数值模拟结果前15 min解吸气量（880.26 cm3）（图4（a））接近。现场BF-1煤心解吸气量和残余气量与数值模型计算的解吸气量和残余气量也较接近。
BF-2和BF-3煤心现场测试煤心损失气量结果分别为823.04、793.71 cm3，略低于与数值模拟结果前15 min解吸气量（952.40、1015.80 cm3） （图4（b）、图4（c）），说明吸附气饱和度较高煤心解吸初期损失气量时间平方根法计算结果可能略偏小。这可能是吸附气饱和度较高，煤心内CH4浓度高，扩散作用更显著导致。用损失气时间与解吸时间和的平方根与解吸初期累计解吸气量的线性回归关系计算BF-2和BF-3煤心损失气量，发现基于数值模拟计算的损失气量结果（755.37、841.77 cm3）与基于现场实测的损失气量计算结果（832.04、793.71 cm3）较为接近。说明基于数值模拟数据利用时间平方根法计算的损失气量与实测时间平方根法估算的损失气量较为接近。
现场实测BF-1、BF-2和BF-3煤心解吸气量和残余气量与数值模型计算出的解吸气量和残余气量也较为接近，误差不超过10.12%（表3）。说明数值模型可以近似反映吸附气欠饱和储层煤心真实解吸过程和损失气量、解吸气量、残余气量特征。
2.2 饱和储层煤心含气量测试与数值模拟
以BF-1煤心为例，采用现场实测参数数据（表2），假设煤心处于饱和状态（即吸附气饱和、游离气在储层压力条件下充满孔隙也达到饱和状态），对现阶段现场含气量测试难度较大的含气饱和煤心解吸-扩散过程进行模拟。含气饱和煤心xy中心截面各位置单位体积煤心含气性变化如图5。
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图 5 含气饱和煤心xy中心截面各位置单位体积煤心含气性变化Figure 5. Change of gas content per unit volume of coal core at each position of xy center section of gas bearing saturated coal core由图5可知：解吸前24 h煤心含气量快速下降，各时刻煤心中心位置含气量最高而煤心边缘含气量最低。
损失气时间与解吸时间和的平方根和累计解吸气量的线性回归关系如图6。饱和储层煤心解吸-扩散数值模拟含气量构成预测见表4。
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图 6 损失气时间与解吸时间和的平方根和累计解吸气量的线性回归关系Figure 6. Linear regression relationship between the square root of the sum of gas loss time and desorption time and cumulative amount of desorbed gas表 4 饱和储层煤心解吸-扩散数值模拟含气量构成预测Table 4. Prediction of gas content composition of coal core desorption-diffusion numerical simulation in saturated core含气量构成 预测体积/cm3 占比/% 损失气 3 792.50 18.64 解吸气 16 460.70 80.90 残余气 93.51 0.46 总含气量 20 346.71 100.00 数值模拟显示，损失气时间内（15 min）假设的饱和煤心解吸-扩散气量达到4 441.3 cm3，相同损失气时间的情况下，约为相应吸附气欠饱和储层煤心此时间段解吸气量（即本例损失气量）的4倍。
损失气时间与解吸时间和的平方根与解吸初期累计解吸气量的线性回归关系截距为正数（R2=0.9988），暗示采用解吸时间平方根与解吸初期累计解吸气量线性回归方法并不适用于饱和煤心损失气量的估算；采用解吸时间平方根与解吸初期累计解吸气量多项式回归方法，计算得煤心损失气量仅为433.11 cm3（R2=0.9988），甚至小于吸附气欠饱和储层煤心损失气量估算值，说明基于时间平方根与累计解吸气量的相关性分析方法可能无法准确估算损失气量。同时测试初期时间平方根与累计解吸气量的回归关系（图6蓝色标记）和损失气时间与累计气量的回归关系（图6红色标记，实测测不出部分）也存在较大差异，说明饱和煤心损失气时间解吸-扩散规律较为复杂，常规回归分析法可能难以实现对损失气量的准确估算。
由表4可知：饱和煤心损失气、解吸气、残余气占比分别为18.64%、80.90%、0.46%，其损失气占比高于吸附气欠饱和煤心损失气占比、解吸气占比低于吸附气欠饱和煤心解吸气占比。
数值模型可以近似反映吸附气欠饱和储层煤心真实解吸过程和损失气量、解吸气量、残余气量特征。目前，含气量现场测试手段很难达到对饱和煤心含气量的准确测试和估算，希望通过数值模拟为含气饱和煤心含气量分析提供思路。
3. 结 语
1）构建的吸附气欠饱和煤心解吸数值模型计算的损失气量、解吸气量和残余气量与现场测试相应结果接近（误差<10.12%），可近似反映吸附气欠饱和储层煤心含气量构成。
2）对于构建的含气饱和储层煤心数值模型，损失气时间与解吸时间和的平方根与解吸初期累计解吸气量的回归分析法预测损失气量误差较大。饱和煤心损失气时间解吸-扩散规律较为复杂，常规回归分析可能难以实现对损失气的准确估算。
3）相同损失气时间条件下，本例饱和煤心损失气总含气量占比（18.64%）高于吸附气欠饱和煤心损失气占比（11.95%），饱和煤心解吸气占比（80.90%）低于吸附气欠饱和煤心解吸气占比（87.32%），饱和煤心残余气占比（0.46%）低于吸附气欠饱和煤心残余气占比（0.63%）。
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图 1 热浮力驱动地裂缝气流作用下地下煤火阴燃实验示意图
Figure 1. Schematic diagram of underground coal smoldering fire experiment
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图 2 热浮力驱动作用下地下煤火阴燃正向蔓延模型验证
Figure 2. Validation of the proposed model against with experimental data
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图 3 不同泡沫孔隙率条件下供氧速率
Figure 3. Oxygen supply rate under different foam porosity conditions
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图 4 泡沫孔隙率为0.9522条件下t=6 h（第1列）、18 h（第2列）和30 h（第3列）的温度场及氧气体积分数、煤、碳、灰分质量分数分布
Figure 4. Cloud diagrams of temperature field, oxygen, coal, carbon and ash mass fraction distribution (from top to bottom) of t=6 h (the first column), 18 h (the second column) and 30 h (the third column) with condition of foam porosity of 0.952 2
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图 5 泡沫孔隙率为0.9522条件下中心轴线3个不同位置的反应速率
Figure 5. Chemical reaction rates of three different positions at the central axis with condition of foam porosity of 0.952 2
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图 6 不同泡沫孔隙率条件下中心轴线y=8 cm位置水分蒸发（rw）、煤热解（rp）和=碳氧化（ro）反应速率
Figure 6. Reaction rates of water evaporation(rw), coal pyrolysis(rp) and carbon oxidation(ro) at y=8 cm with different porosity of foam
表 1 煤阴燃反应动力学参数、化学计量系数和反应热
Table 1 Kinetic parameters, stoichiometric coefficients and reaction heat of coal smoldering reaction
反应 指前因子
（lgAj）活化能
（Ej）/(kJ·mol−1)反应级数
（ni）化学计量
系数
（vj）反应热
（ΔH）/(MJ·kg−1)水分蒸发 8.120 0 67.800 0 2.3702 0.200 2.260 00 煤热解 10.4136 194.6619 9.2711 0.731 0.335 00 碳氧化 8.0743 166.2853 2.1104 0.209 28.35132 
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