对比研究KGD、PKN与改进的P3D模型  

A Comparative Analysis of KGD, PKN, and a Modified P3D Model

作　　者：刘广涛 

机构地区：[1]数学地质四川省重点实验室,成都理工大学,四川 成都

出　　处：《应用数学进展》2023年第11期4570-4579,共10页Advances in Applied Mathematics

摘　　要：本文的目的是表征一个裂缝在特定时间的生长到其最终形状。对设计早期水力裂缝的二维模型KGD和模型PKN进行了分析、比较,并求解。并对P3D三维模型进行了修正,给出了真实的三维结果。通过假设裂缝的椭圆生长而不是圆形生长,产生了更真实的结果。特别要注意的是,由于断裂而形成的椭圆轨迹的参数在任何时刻都是变化的,这意味着在特定时间内的断裂轨迹,也不能用一个简单的数学方程来描述。使用MATLAB进行编程得出KGD、PKN和改进的P3D模型,并展示可视化后的结果。The paper is aiming to represent the growth of a fracture to its final shape at a specific time. 2D models i.e. KGD and PKN which most of the early hydraulic fractures were designed by applying one of these models were analyzed, compared and their equations solved. Moreover a P3D model is modified to give true 3D results. By assuming elliptical growth of the fracture and not the circular growth, a more realistic results generated. It is prudent to notice that the elliptic behavior which the fracture growing is representing has changing parameters at any moment, means the growth of a fracture in a specific period of time even in its simplest form does not obey a simple mathematical equation. Programming using MATLAB to derive KGD, PKN and improved P3D models and display visualized results.

关 键 词：PKN KGD 二维断裂模型 改进的P3D断裂模型 椭圆断裂 

分 类 号：G63[文化科学—教育学]