CAJ | 학술논문

基于全隐式法求解考虑低渗透油藏流动过程中启动压力梯度影响的二维油水两相流动数学模型；利用本征正交分解法从获取的快照中提取基函数，将原模型投影到基函数展成的低维子空间中构造相应的降阶模型；考虑到依据等时间间隔获取的快照的缺陷，利用CVT?Lloyd算法对快照进行聚类分析。实例计算表明：通过本征正交分解法构造降阶模型能很好地对原模型进行近似；通过基于聚类分析处理快照后，一方面减少数据冗余，生成空间分布更均匀的快照集合从而提高降阶模型的精度，另一方面过少的聚类数可能导致快照信息的缺失，影响最后模型的精度。
기우전은식법구해고필저삼투유장류동과정중계동압력제도영향적이유유수량상류동수학모형；이용본정정교분해법종획취적쾌조중제취기함수，장원모형투영도기함수전성적저유자공간중구조상응적강계모형；고필도의거등시간간격획취적쾌조적결함，이용CVT?Lloyd산법대쾌조진행취류분석。실례계산표명：통과본정정교분해법구조강계모형능흔호지대원모형진행근사；통과기우취류분석처리쾌조후，일방면감소수거용여，생성공간분포경균균적쾌조집합종이제고강계모형적정도，령일방면과소적취류수가능도치쾌조신식적결실，영향최후모형적정도。
A mathematical model for numerical simulation of 2D water?oil phase reservoir concerning start?up pressure gradient is solved with full implicit finite difference scheme. A reduced?order model is established by projecting original model in low dimension space formed by basis functions, which is produced from collected snapshots; CVT?Lloyd algorithm is employed in cluster analysis to tackle with flaws from collecting snapshots of same time interval. Computational results show that reduced?order model established based on POD is able to approximate the original model effectively. With cluster analysis, data reduction is eliminated, which could create uniform snapshots in space resulting in enhanced accuracy of reduce?order model. On the other hand, extremely limited clustering groups may lead to loss of information and thus impairing accuracy of reduced?order model.