Abstract Although many breakthrough efforts have been made in recent years, it is still challenging to gain a clear knowledge of the variation regularities of effective gas/water phase permeability with the pressure depletion. The reasons behind this phenomenon can be attributed to the coexistence of multiple effects and the transition of the flow behavior at different production stages. To date, the fully-coupled model for effective gas/water phase permeability in coal-bed methane (CBM) reservoirs is still lacking and is significantly necessary to be developed. Firstly, the Palmer-Mansoori (PM) model is employed to represent the variation relationship between absolute permeability and pressure. Secondly, after rigorous derivation of the gas–water two phase partial differential equations in coal seams, the relationship between pressure and saturation in infinitesimal coal is obtained, which can be solved through an iterative algorithm. Subsequently, combined with the Corey relative permeability model, the relative gas/water phase permeability can be described as a function of pressure. Finally, coupling the absolute permeability model and relative permeability model, the effective gas/water phase permeability can also be quantified as a function of pressure or saturation. And the reliability and the accuracy of the proposed model is successfully verified through comparisons with experimental data and previous model collected from published literature. Furthermore, on the basis of the proposed semi-analytical model, the effects of critical desorption pressure, gas desorption capacity, stress dependence, and matrix shrinkage on effective permeability are identified. And many implications and direct insights are achieved through the sensitive analysis process. The semi-analytical model, for the first time, incorporates nearly all known mechanisms and can achieve more accurate characterization of effective permeability during the production process. Moreover, due to the concise form and precise feature, the proposed model will serve as a simple, practical and robust tool for the development of CBM reservoirs.

中文翻译：

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煤层气生产过程中有效气/水相渗透率的全耦合半解析模型

摘要 尽管近年来取得了许多突破性的努力，但要清楚地了解有效气/水相渗透率随压力枯竭的变化规律仍然具有挑战性。这种现象背后的原因可以归因于多种效应的并存以及不同生产阶段流动行为的转变。迄今为止，煤层气（CBM）储层有效气/水相渗透率的全耦合模型仍然缺乏，非常有必要开发。首先，采用Palmer-Mansoori (PM)模型来表示绝对渗透率与压力的变化关系。其次，经过严格推导煤层气水两相偏微分方程，得到了无穷小煤中压力与饱和度的关系，可以通过迭代算法求解。随后，结合 Corey 相对渗透率模型，可以将相对气/水相渗透率描述为压力的函数。最后，耦合绝对渗透率模型和相对渗透率模型，有效气/水相渗透率也可以量化为压力或饱和度的函数。通过与实验数据和从已发表的文献中收集的先前模型的比较，成功地验证了所提出模型的可靠性和准确性。此外，在提出的半解析模型的基础上，临界解吸压力、气体解吸能力、应力依赖性的影响，和基质收缩对有效渗透率的确定。通过敏感的分析过程获得了许多影响和直接的见解。半解析模型首次整合了几乎所有已知机制，可以更准确地表征生产过程中的有效渗透率。此外，由于形式简洁、特征精确，所提出的模型将成为煤层气储层开发的简单、实用和稳健的工具。