酸压裂缝内酸液指进的计算机模拟与分形研究

Computer simulation and fractal study of the fingering of the acid in an acid-fracturing fracture

酸压裂缝内,低黏度酸液在高黏度前置液中发生指进现象.该现象对酸压施工效果有非常重要的影响.指进现象的内在随机性、复杂的酸岩反应以及酸液重力等因素的影响使得酸液指进形态非常复杂,采用传统方法不能进行准确研究.改进了扩散限制凝聚模型,建立了酸液指进扩散限制凝聚模型;根据正交设计,共进行了9次模拟,得到了不同模拟参数控制的酸液指进形态;采用数盒子方法求得所模拟的指进形态的分形维数平均值为1.67;通过极差分析发现,反映射孔孔眼间距的衬边中心距对指进形态的分形维数影响最大.

In the acid-fracturing fractures,the acid liquid of low viscosity occurs fingering phenomenon in the ahead liquid of high viscosity,which has very important influence on the result of the acid fracturing.The randomness of the fingering phenomenon,the chemical reaction between acid and rock in the fingering and the gravity of the acid liquid make the fingering morphology too complicated to be exactly studied through traditional methods.A diffusion-limited aggregation model for the fingering of acid liquid is presented by using modified Witten’s diffusion-limited aggregation model.Nine different fingering simulation patterns controlled by different simulation parameters are carried out based on the orthogonal design.The average fractal dimension of these fingering simulation patterns computed by the'box-counting'algorithm is 1.67.Furthermore,the results of extreme difference analysis show that the distance between the central distance of the liner edges which reflects the distance between the centers of two perforation holes has the greatest influence on the fractal dimension.