考虑动边界的煤层不定常渗流研究

Study on the model of non-steady seepage flow in the process of coal-bed methane development, which could accurately and synthetically depict the gas transport mechanism and the seepage characteristics in low-permeable coal bed, can support solid theoretical foundation for the technologies of well testing and numerical simulation of coal-bed methane. In our presented model research, the effects of gas desorption of matrix, gas diffusion into cracks, formation permeability change due to the matrix shrinkage, sensitivity of formation pressure, gas slippage effect, and the threshold pressure gradient in low-permeable coal bed are considered comprehensively; furthermore, according to the production situation of coal-bed methane development, the coal-bed methane recovery mechanism and the dynamic characteristics of formation pressure, the whole drainage and production process of coal-bed methane is divided into three typical stages as the early stage, the medium stage and the later stage; and then the mathematical models of the non-steady seepage flow in coal bed are constructed under different stages respectively, including the model of single phase water seepage flow with moving boundaries, the model of two phase gas/water seepage flow with moving boundaries and the model of single phase gas seepage flow. Based on the spatial coordinate transformation method, stable finite difference method will be adopted to numerically solve these mathematical models of non-steady seepage flow in coal bed with moving boundaries; the correctness of the numerical solutions is verified by some exact analytical solutions by the similarity transformation method; and the validity of the constructed mathematical model is verified through the production data matching.

研究准确的能综合反映煤层气开发过程气体运移机理与低渗煤层渗流特征的不定常渗流模型，可以为煤层气的试井与数值模拟技术提供坚实的理论基础。本项目进行的模型研究拟综合考虑低渗煤层中的气体基质解吸、气体向裂隙扩散、基质收缩引起煤层渗透率变化、煤层压力敏感性、气体滑脱效应以及启动压力梯度的影响；并根据煤层气开采的产出状况、煤层气采出机理以及储层压力的动态特征，将整个煤层气排采过程详细划分为早期、中期和晚期三个典型的排采阶段，从而建立不同排采阶段下的煤层不定常渗流数学模型，这些模型包括考虑动边界的单相水渗流模型、考虑动边界的气/水两相渗流模型以及单相气渗流模型。拟采用基于空间坐标变换的稳定有限差分方法对考虑动边界的煤层不定常渗流模型进行数值求解；并利用相似变量变换方法所求精确解析解验证数值计算结果的正确性，依靠生产数据拟合验证所建数学模型的有效性。

首先，本项目研究了考虑启动压力梯度的低渗透多孔介质渗流动边界模型的精确解析与数值求解方法，并对数值算法计算程序的有效性进行了严格测试。在此基础上，进一步研究了对应煤层气开发的排采过程中三个不同排采特征阶段的低渗透煤层气的不定常渗流模型，包括煤层气排采早期阶段的单相水渗流动边界模型、排采中期阶段的气、水两相渗流动边界模型和排采末期阶段的单相气渗流模型。渗流模型综合考虑了煤层气排采过程中煤层压降区域内吸附气的解吸作用、煤层渗透率变化、低渗煤层中渗流存在启动压力梯度、气、水两相流、井筒储集、表皮效应等影响因素。这些渗流模型均采用了稳定的全隐式有限差分方法进行数值求解，进而获得了对应不同渗流模型下的井底压力与压力导数响应曲线以及地层压力分布曲线图版，并分析了各渗流参数的敏感性影响。这些研究结果为非常规气藏渗流规律在生产数据分析中的应用提供了理论基础。最后，还进一步研究了基于反褶积的单相煤层气渗流模型在生产数据分析的实际应用。