直接模拟非达西效应的页岩气藏免方程数值研究

微观尺度上Knudsen扩散、表面扩散以及吸脱附作用，导致页岩气的运移在气藏尺度上表现为非达西渗流。如何准确模拟气藏尺度的非达西渗流，是一个尚未得到有效解决的难题。针对这一难题，本项目提出了一种新的解决思路，该思路的核心是引入“免方程方法”，将岩心尺度非达西渗流的准确计算拓展到页岩气藏尺度。研究内容如下：提出基质非达西渗流免方程模型，在此基础上构建页岩气藏的“免方程-离散裂隙”数值方法。针对免方程模型中关键的“尺度提升”过程，基于POD（最佳正交分解）提出适用于复杂问题的Lift算子；针对免方程-离散裂隙方法中关键的基质（免方程区域）与裂隙（有方程区域）之间的耦合，基于“局部尺度提升”提出精度高、健壮性好的耦合过程。基于所发展的数值方法，实现直接考虑非达西效应的页岩气藏准确数值模拟，查明微观流动对页岩气藏宏观运移规律的影响，量化非达西效应对页岩气藏产能的影响，为页岩气商业开采提供技术支持。

Due to Knudsen diffusion, surface diffusion and adsorption/desorption in the microscale, seepage flow of shale gas in the reservoir scale shows non-Darcy feature. The capable method to accurately simulate the non-Darcy seepage flow in reservoir scale remains unrevealed. To overcome this problem, a new idea is proposed in this project and the main thought is that, by introducing Equation-free Method (EFM), the precise calculation of non-Darcy flow in rock core scale can be expanded to the whole reservoir. The main research is focus on the following contents: First, the EFM model for non-Darcy flow in the rock matrix is established and the “EFM-DFM (Discrete Fracture Modeling)” for reservoir simulation is proposed subsequently. Second, for the crucial scale-lifting process in EFM, an proper “Lift operator” for complex problem is developed based on the Proper Orthogonal Decomposition (POD). And, for the coupling between matrix (Equation-free region) and fracture (Darcy equation region) in EFM-DFM, an efficient and accurate coupling process is developed based on local scale-lifting. At last, based on the proposed numerical method above, accurate simulation of shale gas transport in reservoir can be performed with non-Darcy flow calculated directly. Thus, the influence of microscale flow on the shale gas seepage in reservoir scale can be clarified and the quantity of production capacity influenced by non-Darcy flow can be determined. With these efforts, it is expected to provide strong technical supports for shale gas development in the future.