碳酸盐岩基质酸化中蚓孔生长的三维扩散限制凝聚模型研究

The wormholes, being formed during matrix acidizing of carbonate reservoir, are vital to the capacity and permeability of near wellbole formation， consequently as well as acidizing efficiency. Previous experiments have been shown this type of wormholes grow extremely irregularly in the formation from axial, radial and circumferential directions of the wellbore. Up to now, mathematical models, which could not only discribe the irregular structure of the wormholes but also directly show the impact of practical engineering factors, are still not available. On the basis of the 2D diffusion limited aggregation (DLA) model eatablished by the applicant and the theories of fractal geometry , permeation fluid mechanics,chemical reaction kinetics and cellular automaton, this project will begin with the theoretical connection of the DLA simulation parameters to the practical factors, and then establish the 3D DLA model of wormhole propagation, in which the variation of the factors such as formation properties, acid fluid features,acid injection parameters and the well completion type could be taken into considered, by studying on the variation of the simulation parameters, such as seed particles，moving particles and the way how they move, aggregate and escape. Furthermore, core plug experiments will be applied to modify the 3D DLA model. Then finally, the modified DLA model will be used to simulate the process of wormholes' dynamical growth. As a result, the way how the wormholes' structures are changed, due to the impact of controllable factors(acid properties, acid injection condition and well completion type), which are quantitatively described by fractal dimension, multi-fractal spectrum and wormhole volume, can be understood. The progresses above will be very helpful and meaningful for improving the carbonate acidizing theory and enhancing carbonate reservoir exploitation.

碳酸盐岩基质酸化形成的酸蚀蚓孔对储层的储渗能力和酸化效果有重要的影响。实验发现，此类酸蚀蚓孔沿井筒的轴向、径向和周向呈三维不规则生长。现有数学模型中，尚缺少既能表征酸蚀蚓孔不规则生长又能体现工程因素影响的三维数学模型。本项目拟在已建立的二维酸蚀蚓孔扩散限制凝聚模型（DLA）的基础上，根据分形几何学、渗流力学、化学反应动力学和细胞自动机理论，分析DLA模拟规则与酸蚀蚓孔生长工程因素间的理论联系，从DLA的种子粒子、运动粒子及其运动、凝聚与逃逸规则等方面入手，构建能够直接体现地层性质、酸液性质、注酸条件、完井方式等因素影响的酸蚀蚓孔生长三维DLA模型；通过岩心实验修正模型，并采用修正模型模拟酸蚀蚓孔的动态生长行为，从而得到酸液性质、注酸条件和完井方式等可控因素影响下的酸蚀蚓孔特征参数（分形维数、多重分形谱及蚓孔体积）的变化规律，进而完善碳酸盐岩基质酸化理论体系，促进碳酸盐岩油气资源的高效开发。

碳酸盐岩基质酸化过程中形成的酸蚀蚓孔对酸化效果影响大。已有实验表明，酸液流动反应条件不同，酸蚀蚓孔生长形态各异。经过三年的研究，本项目成功将扩散限制凝聚模拟（DLA）方法引入到酸蚀蚓孔生长的研究中，建立了模拟规则与酸岩反应实际工程背景及其影响因素之间的理论联系，改进二维DLA酸蚀蚓孔模型，并建立了蚓孔地层渗透率计算方法及产能预测模型；在此基础上，构建了描述井筒尺度酸蚀蚓孔生长的三维DLA模型。鉴于蚓孔具有的自相似特点，采用分形维数和多重分形谱描述酸蚀蚓孔生长形态。经过模拟分析发现，凝聚团生长边界L、粒子扩散步长S以及粒子释放密度M对分形特征参数的影响最为显著，亦即，与蚓孔三维形态相关的三个关键因素为蚓孔的有效穿透距离、酸液的排量以及酸液的浓度。在此基础上，研制出大尺寸三维井筒酸蚀蚓孔物理模拟装置和方法，对酸蚀蚓孔三维DLA模型进行了物理实验验证。