基于迎风差分格式的裂缝酸压数值模拟  

Numerical Simulation of Fracture-Type Acid Fracturing Based on Upwind Differential Scheme

作　　者：李义林[1] 李泰良 LI Yi-lin;LI Tai-liang(Guang’an Vocational and Technical College,Guang'an 638000,China;Xihua University,Chengdu 610039,China)

机构地区：[1]广安职业技术学院,四川广安638000 [2]西华大学经济学院,四川成都610039

出　　处：《数学的实践与认识》2020年第18期160-166,共7页Mathematics in Practice and Theory

摘　　要：低渗透致密碳酸盐岩储层现场施工时多采用酸化压裂的方式进行增产改造.酸压改造后的裂缝形态是评价施工效果的重要参数,酸压数值模拟能预测酸压后的裂缝形态,可以作为优化施工参数的工具,但裂缝酸压数值模拟计算中,由于数学模型复杂、计算量庞大等原因极易导致计算结果不收敛.针对此问题,本文以立方定律为基础,推导裂缝酸压数学模型,并构建了适用于本模型的迎风差分格式,随后采用迎风差分格式进行数值模拟计算.结果显示,迎风差分格式在计算粗糙裂缝的酸压数值模拟时收敛性好,数值模拟结果与理论相符.In the field construction of low-permeability and tight carbonate reservoirs,acid fracturing is often used to increase production.The fracture shape after acid fracturing is an important parameter to evaluate the construction effect.The numerical simulation of acid fracturing can predict the fracture shape after acid fracturing and can be used as a tool to optimize the construction parameters.The huge amount of calculation and other reasons can easily lead to non-convergence of calculation results.To solve this problem,based on the cubic law,the mathematical model of fracture-type acid fracturing is derived.The upwind difference scheme suitable for this model is constructed,and then the upwind difference scheme is used for numerical simulation calculation.The results show that the upwind differential scheme has good convergence when calculating the rough fracture numerical simulation,and the numerical simulation results are consistent with the theory.

关 键 词：迎风差分格式 酸化压裂 数值模拟 粗糙裂缝 

分 类 号：O242[理学—计算数学] TE357.2[理学—数学]