煤层气作为一种与煤伴生的非常规天然气矿产资源，高效开发与利用煤层气对减少矿井瓦斯事故、降低温室气体排放量、改善中国能源结构具有十分重要的意义。由于我国煤储层普遍具有低孔、低渗特征，通常采用煤层增透措施达到煤层气高效开采目的，其中以液氮为介质的无水化致裂增透技术因环保性、使用便捷性等优势受到了广泛关注。随着液氮致裂技术相关研究的不断深入，仅研究单一因素下煤体孔裂隙结构发育规律难以完整揭示液氮致裂煤体的作用机理，缺少液氮致裂过程表面现象和本质规律的必要联系，研究致裂过程多相多物理场耦合协同效应可完善液氮致裂煤体理论。

      本文推导了煤体水冰相变传热控制模型及液氮流动控制模型，采用FORTRAN语言开发了液氮冻结煤体二维仿真分析程序，对煤体结冰现象与温度场变化规律进行分析；在构建的液氮致裂煤体水冰相变数学模型基础上，建立液氮致裂含水煤体温度-应力-渗流多相耦合数学模型，运用COMSOL Multiphysics有限元分析软件对液氮致裂煤体多相能质传输与多物理场耦合过程进行数值模拟研究，讨论初始含水率、初始温度、液氮注入压力和三轴应力条件对液氮致裂煤体相含率和孔隙率、渗透率的影响，获得如下结论：

     （1）推导了液氮流动控制方程、液氮-煤体温度耦合控制方程与煤体水冰相变传热控制方程，建立了考虑液氮流动状态与能质传输特性、煤体水冰相变能质转化的液氮致裂煤体水冰相变数学模型。

     （2）利用FORTRAN语言开发典型算例，研究液氮冻结煤体温度场和水冰相含率的变化规律。研究表明，液氮对含水煤体的低温传热作用受入口效应和几何位置影响；模拟工况下，液氮冻结过程煤体水结冰与温度变化具有梯度变化特征，其中液氮对煤体的温度影响可划分为温度骤变区（4.5%）和恒温区，对水冰相变影响可划分为相变集中区（3.5%）和相变稳定区；沿煤体埋深方向上，煤体降温效果则可划分为集中变温区（2.5%）、平稳变化区（0.625%）和恒温区，水冰相变划分为剧烈相变区（3.125%）、平缓相变区（0.625%）和相变稳定区。

     （3）推导了液氮致裂含水煤体氮气渗流控制方程和考虑水冰冻胀应变的应力场控制方程，并将液氮致裂煤体简化为液氮汽化吸热、氮气渗流致裂两个过程，构建液氮致裂含水煤体温度-应力-渗流多相耦合数学模型，描述了液氮致裂煤体温度场、相变场、应力场、渗流场多相多物理场耦合协同作用机理。

     （4）开展多因素影响下液氮致裂煤体多相多物理场耦合数值模拟，获得了多因素（初始含水率、初始温度、液氮注入压力和三轴应力条件等）影响下含水煤体多相能质传输与转化和孔隙率的变化规律。研究表明：受致裂过程液氮低温、液氮汽化吸热、氮气渗流对流换热和未冻水结冰放热等共同影响，初始含水率与初始温度越高，煤体冻结区占比越小，煤体孔隙率、渗透率集中增大区占比减小，但煤体冻结区孔隙率、渗透率增大梯度与初始含水率呈正相关关系；不考虑煤体裂隙扩展与损伤作用时，增大初始含水率对氮气渗流阻塞作用增强，不利于煤体未冻结区孔隙演化；煤体孔隙率、渗透率与液氮注入压力、水平应力差呈正相关关系，与垂向应力呈负相关关系。

      本文构建了液氮致裂煤体水冰相变数学模型和液氮致裂含水煤体温度-应力-渗流多相耦合数学模型，通过数值模拟研究液氮致裂过程煤体水结冰现象与温度场变化规律及致裂过程多相多场耦合协同规律，研究结果对完善液氮致裂煤体理论，促进低温无水致裂等瓦斯抽采技术的推广应用，提高瓦斯灾害防治与煤层气资源开发水平具有重要价值。 

      As an unconventional natural gas resource associated with coal, the efficient development and utilization of coalbed methane is of great significance to reduce mine gas accidents, lower greenhouse gas emissions and improve China's energy structure. Since coal reservoirs in China are generally characterized by low porosity and low permeability, coal seam permeation enhancement measures are usually used to achieve efficient exploitation of coalbed methane, among which anhydrous fracturing technology using liquid nitrogen as the medium has received wide attention for its advantages of environmental friendliness and ease of use. As the research on liquid nitrogen fracturing technology continues, it is difficult to fully reveal the mechanism of liquid nitrogen fracturing coal by only studying the pore and fracture structure development law of coal under single factor, and the necessary connection between surface phenomenon and essential law of liquid nitrogen fracturing process is missing.

      In this paper, the water-ice phase change heat transfer control model and liquid nitrogen flow control model of coal are derived, and a two-dimensional simulation and analysis program of liquid nitrogen frozen coal is developed in FORTRAN language to analyze the freezing phenomenon and temperature field change law of coal; On the basis of the mathematical model of water-ice phase change in liquid nitrogen fractured coal, the temperature-stress-percolation multiphase coupling of liquid nitrogen fractured coal is established, and the COMSOL Multiphysics finite element analysis software was used to numerically simulate the multiphase flow energy-mass transport and multiphysics field coupling process of liquid nitrogen fractured coal, and the effects of initial water content, initial temperature, liquid nitrogen injection pressure and triaxial stress environment on the phase content, the porosity, and the permeability of liquid nitrogen fractured coal were discussed, and the main conclusions are as follows:

      (1) The liquid nitrogen flow control equation, liquid nitrogen-coal temperature coupling control equation and coal water-ice phase change heat transfer control equation are derived, and the mathematical model of water-ice phase change in liquid nitrogen fractured coal considering the liquid nitrogen flow state and energy-mass transfer characteristics and coal water-ice phase change energy-mass conversion is established.

      (2) A typical calculation case is developed using FORTRAN language to study the variation law of temperature field and water-ice phase content of liquid nitrogen frozen coal. The study shows that the low-temperature heat transfer effect of liquid nitrogen on water-bearing coal is influenced by the entrance effect and geometric position; Under the simulated working conditions, the water freezing and temperature change of coal during the freezing process of liquid nitrogen has the characteristics of gradient change, in which the temperature effect of liquid nitrogen on coal can be divided into the temperature abrupt change zone (4.5%) and the constant temperature zone, and the phase change effect on water-ice can be divided into the phase change concentration zone (3.5%) and the phase change stability zone. Along the direction of coal burial depth, the cooling effect of coal can be divided into the concentration temperature change zone (2.5%), the smooth change zone (0.625%) and the constant temperature zone, and the water-ice phase change is divided into the intense phase change zone (3.125%), the smooth phase change zone (0.625%) and the phase change stability zone.

      (3) The controlling equation of nitrogen seepage flow in liquid nitrogen fractured water-bearing coal and the controlling equation of stress field considering the strain of water-ice freezing and expansion are derived, the liquid nitrogen fractured coal is simplified into two processes of liquid nitrogen vaporization and heat absorption and nitrogen seepage flow fracturing, and a multiphase coupled mathematical model of temperature-stress-seepage flow in liquid nitrogen fractured water-bearing coal is constructed to describe the multiphase multi-physical field coupling synergistic mechanism of temperature, phase change, stress and seepage flow in liquid nitrogen fractured coal.

      (4) Numerical simulations of multiphase multiphysical fields coupled with liquid nitrogen fracturing coal under the influence of multiple factors were carried out to obtain the changes of multiphase energy-mass transport and transformation and porosity of water-bearing coal under the influence of multiple factors (initial water content, initial temperature, liquid nitrogen injection pressure and triaxial stress conditions, etc.). The study shows that under the joint influence of liquid nitrogen cryogenic, heat absorption by liquid nitrogen vaporization, convective heat exchange by nitrogen percolation and heat release by freezing of unfrozen water in the fracturing process,the higher the initial water content and initial temperature, the smaller the percentage of the frozen zone of coal, and the percentage of coal porosity and permeability concentration increase area decreases, but the gradient of increasing porosity and permeability in the frozen zone of the coal is positively correlated with the initial water content; When the fracture expansion and damage of the coal are not considered, increasing the initial water content has an enhanced blocking effect on nitrogen seepage, which is unfavorable to the pore evolution in the unfrozen zone of the coal; The porosity and permeability of coal are positively correlated with liquid nitrogen injection pressure and horizontal stress difference, and negatively correlated with vertical stress.

      This paper constructed a mathematical model of water-ice phase change in liquid nitrogen fractured coal and a temperature-stress-percolation coupled multiphase mathematical model of liquid nitrogen fractured coal, and investigated the water freezing phenomenon and temperature field change law of liquid nitrogen fractured coal and the multiphase multiphysical field coupling synergy law of fracturing process through numerical simulation. The results are of great value to improve the theory of liquid nitrogen fracturing, promote the application of low-temperature anhydrous fracturing and coalbed methane extraction technologies, and improve the level of gas disaster prevention and control and coalbed methane resources development.

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