Abstract At present, analyzing and predicting CBM production performance remains challenging, which can be attributed to the complex gas-water two phase flow and dynamic nature of petro-physical properties. For the sake of simplicity, the saturation distribution in coal seams is generally overlooked and characterized by average water saturation in previous literature, which one can easily handle analytically, semi-analytically, and numerically. However, average water saturation is inadequate to obtain the precise value of pseudo pressure for water/gas phase, which may generate large deviation compared with actual production behavior. To our best knowledge, the relationship between pressure and saturation in coal seams is still lacking in the petroleum industry. Thus, the main objective of this research is to gain a clear understanding of this issue. In this work, on the basis of rigorous derivation, a semi-analytical model for the relationship between pressure and saturation is developed, which comprehensively accounts for the presence of free gas at the early production stage, matrix shrinkage and gas desorption. Notably, the stress dependence effect is incorporated during the entire production process of CBM wells. Subsequently, employing the gas-water two phase relative permeability data, we present an iterative numerical algorithm to solve the model. Moreover, the proposed semi-analytical model is successfully verified against a numerical reservoir simulator. After that, we shed light on the influences of physical parameters upon the saturation distribution versus pressure and achieve a variety of new insights. This research, for the first time, presents a semi-analytical model to quantify the relationship between pressure and saturation, which fills the gap for the theory of gas-water two phase flow in CBM reservoirs. The proposed model is less data-intensive than performing a numerical simulation and turns out to be simple and powerful in the application. In addition, the new model can significantly contribute to the obtainment of precise pseudo pressure for water/gas phase, therefore lays the theoretical basis for the accurate production prediction for CBM wells.

中文翻译：

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煤层气储层压力与饱和度关系的半解析模型

摘要 目前，煤层气生产动态的分析和预测仍然具有挑战性，这可以归因于复杂的气水两相流和岩石物理性质的动态特性。为简单起见，煤层中的饱和度分布在以前的文献中通常被忽略，并以平均含水饱和度为特征，可以通过解析、半解析和数值方式轻松处理。然而，平均含水饱和度不足以获得精确的水/气相假压力值，与实际生产行为相比可能会产生较大的偏差。据我们所知，煤层压力与饱和度之间的关系在石油工业中仍然缺乏。因此，这项研究的主要目标是清楚地了解这个问题。本文在严格推导的基础上，建立了压力与饱和度关系的半解析模型，综合考虑了生产初期游离气的存在、基体收缩和气体解吸。值得注意的是，在煤层气井的整个生产过程中都包含了应力依赖效应。随后，利用气水两相相对渗透率数据，我们提出了一种迭代数值算法来求解模型。此外，所提出的半解析模型在数值油藏模拟器上得到了成功验证。之后，我们阐明了物理参数对饱和度分布与压力的影响，并获得了各种新见解。本研究首次提出了一种量化压力与饱和度关系的半解析模型，填补了煤层气水两相流理论的空白。与执行数值模拟相比，所提出的模型数据密集程度较低，并且在应用中简单而强大。此外，新模型对精确获取水/气相假压力具有重要意义，为煤层气井准确生产预测奠定了理论基础。填补了煤层气藏气水两相流理论的空白。与执行数值模拟相比，所提出的模型数据密集程度较低，并且在应用中简单而强大。此外，新模型对于获得精确的水/气相伪压力具有重要意义，为煤层气井的准确生产预测奠定了理论基础。填补了煤层气藏气水两相流理论的空白。与执行数值模拟相比，所提出的模型数据密集程度较低，并且在应用中简单而强大。此外，新模型对于获得精确的水/气相伪压力具有重要意义，为煤层气井的准确生产预测奠定了理论基础。