Evolution Mechanism of Shale Gas Reservoirs Permeability under Thermal-Fluid-Solid Coupling
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摘要: 为了研究热-流-固耦合作用下页岩渗透率的演化机制，考虑热解吸、有效应力和热膨胀对页岩渗透率的影响，提出了页岩的有效应力-渗透率模型，该模型能够分析吸附应变和热膨胀应变对页岩渗透率的影响机制。基于该模型和多孔介质弹性理论，建立了单轴应变条件下页岩气储层的热解吸渗透率模型，该模型能够探讨页岩渗透率随温度和孔隙压力的演化规律。利用室内实验观测的页岩岩样渗透率实验数据，验证了该模型的有效性和准确性。结果表明：(1)热解吸渗透率模型能较好地拟合恒压变温条件下的Marcellus页岩渗透率。(2) 探讨了恒温条件下页岩渗透率随孔压的演化机制，发现恒温条件下渗透率的演化规律呈“U形”，温度越高，渗透率随孔压下降的反弹现象越不明显。(3) 分析了恒压条件下页岩渗透率随温度的演化机制，发现恒压条件下渗透率随温度的演化规律呈“倒U形”，孔隙压力越大，温度对渗透率的影响越小。(4) 分别在恒温和恒压条件下对热解吸渗透率模型进行敏感性分析，发现泊松比越大，渗透率比值梯度越大，孔隙体积模量越大，渗透率比值梯度越小。恒压条件下，当线胀系数大于临界值或朗缪尔体应变小于临界值，渗透率的演化规律不呈现“倒U形”。恒温条件下，当朗缪尔体应变小于临界值时，渗透率的演化规律不呈现“U形”。Abstract: In order to study the evolution mechanism of shale permeability under thermal-fluid-solid coupling, the effective stress-permeability model of shale is developed considering the impact of thermal desorption and effective stress and thermal expansion on shale permeability. The proposed model is capable of revealing the influence mechanism of sorption strain and thermal expansion strain on shale permeability. Based on the model and the elastic theory of porous media, the thermal induced desorption permeability model of shale gas reservoirs under uniaxial strain condition was established. The model can discuss the evolution mechanism of shale permeability with temperature and pore pressure. The validity and accuracy of the model was verified against the laboratory measurements of shale core permeability. The following results were obtained: (1) The thermal induced desorption permeability model can fit the permeability of Marcellus shale under constant pressure and variable temperature. (2) The evolution mechanism of shale permeability with pore pressure under constant temperature is explored. The evolution law of permeability under constant temperature is U-shaped. The rebound of permeability with pore pressure decrease is less obvious with the increase of temperature. (3) The evolution mechanism of shale permeability with temperature under constant pressure condition is analyzed. The evolution law of permeability with temperature under constant pressure condition presents an inverted “U” shape. The influence of temperature on permeability is less with the increase of pore pressure. (4) The sensitivity analysis of thermal desorption permeability model under constant temperature and pressure was carried out. The larger the Poisson’s ratio is, the larger the permeability ratio gradient is. The larger the pore volume modulus, the smaller the permeability ratio gradient. At constant pore pressure, when the linear expansion coefficient is larger than the critical value or the Langmuir bulk strain is smaller than the critical value, the permeability evolution does not show an inverted “U” shape. At constant temperature, when Langmuir strain is less than critical value, permeability evolution does not show “U” shape.
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图 1 不同温度下热解吸模型解析解与裂隙页岩的实验数据对比
Figure 1. Comparison of analytical results of thermal-sorptive model and experimental data offractured shale under different temperatures
图 2 不同温度下热解吸模型解析解与完整页岩的实验数据对比
Figure 2. Comparison of analytical results of thermal-sorptive model and experimental data of intact shaleunder different temperatures
图 3 渗透率随温度和孔压的演化规律
Figure 3. Evolution of permeability withtemperature and pore pressure
图 4 不同孔压下渗透率随温度的演化规律
Figure 4. Evolution of permeability with temperatureunder different pore pressures
图 5 不同温度下渗透率随孔压的演化规律
Figure 5. Evolution of permeability with porepressure under different temperatures
图 6 恒压下泊松比对渗透率的影响
Figure 6. Effect of Poisson’s ratio on permeabilityunder constant pore pressure
图 7 恒压下孔隙体积模量对渗透率的影响
Figure 7. Effect of pore volume modulus onpermeability under constant pore pressure
图 8 恒压下线胀系数对渗透率的影响
Figure 8. Evolution of coefficient of linear expansionon permeability under constant pore pressure
图 9 恒压下Langmuir体应变对渗透率的影响
Figure 9. Evolution of Langmuir volume strain onpermeability under constant pore pressure
图 10 恒温下泊松比对渗透率的影响
Figure 10. Effect of Poisson’s ratio on permeabilityunder constant temperature
图 11 恒温下孔隙体积模量对渗透率的影响
Figure 11. Effect of pore volume modulus onpermeability under constant temperature
图 12 恒温下Langmuir体应变对渗透率的影响
Figure 12. Effect of Langmuir volume strain onpermeability under constant temperature
表 1 裂隙页岩的渗透率比
Table 1. Permeability ratio of fractured shale
Temperature/K k/k0 of fractured shale 295 1.000 303 1.044 313 1.113 323 1.211 
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表 2 完整页岩的渗透率比
Table 2. Permeability ratio of intact shale
Temperature/K k/k0 of intact shale Temperature/K k/k0 of intact shale 307.1 1.000 332.7 1.095 308.0 0.978 333.3 1.045 313.8 1.051 337.7 1.058 321.1 1.037 337.9 1.061 321.2 1.008 338.0 1.084 325.9 1.085
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