一种基于接触性理论的储层裂缝闭合新模型

New model of natural fracture closure based on microstructure

运用弹塑性理论,提出了一种更加合理的基于微观结构的新型裂缝闭合模型。在新模型中,首先,运用经典的接触力学理论,将裂缝表面微凸体受挤压状态分为完全弹性变形、弹塑性变形和完全塑性变形3个阶段,并且假设弹塑性变形阶段光滑且连续地衔接其他2种变形。为了更好地描述衔接过程,采用了样板函数,连接完全弹性变形和完全塑性变形状态方程,进而得出微凸体受挤压而压缩整个过程的数学模型。随后,引入当前关于概率分布的理论,合理优化出因为表面的微凸体受压缩而导致裂缝闭合的状态模型。最后,使用新模型模拟出裂缝闭合量随各项参数的变化,并与已有的完全弹性模型、完全塑性模型进行对比。结果表明,新模型中裂缝闭合量随各参数的变化介于完全弹性模型和完全塑性模型之间,裂缝受到有效应力而闭合的状态也更加符合预期,可以合理地体现裂缝逐渐闭合的状态。

Based on the elastic-plastic theory, a more reasonable fracture closure model is proposed. First, the classical theory of contact mechanics is applied, and the squeezed state of fracture surface asperities is classified into complete elastic deformation, elastic plastic deformation and full plastic deformation. In addition, it is assumed that the elastic-plastic deformation state is smooth and continuous with the other two kinds of deformation. In order to represent the joining process of complete elastic deformation and full plastic deformation properly, a template function is employed. Then the mathematical model of the whole process of the compression of the asperity is obtained. Subsequently, the theory of probability distribution is introduced to optimize the state model of fracture closure due to compression of the surface asperity. Finally, the new model is used to simulate the variation of fracture closure with various parameters, and compared with the results of existing complete elastic model and the fully plastic model. The results of the new model is in the mid of other two models, which is more in line with expectations and reasonably shows the state of the fracture closing process.