In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d...In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.展开更多
为精确描述水力压裂后复杂裂缝系统的压力动态特征,提出一种基于扩散飞行时间(diffusive time of flight,DTOF)的快速数值试井分析方法.将嵌入式离散裂缝模型(embedded discrete fracture model,EDFM)与波前快速推进法(fast marching me...为精确描述水力压裂后复杂裂缝系统的压力动态特征,提出一种基于扩散飞行时间(diffusive time of flight,DTOF)的快速数值试井分析方法.将嵌入式离散裂缝模型(embedded discrete fracture model,EDFM)与波前快速推进法(fast marching method,FMM)相结合,建立以一维扩散飞行时间为空间坐标的渗流控制方程,并以此分析复杂裂缝系统试井曲线特征.研究表明,天然裂缝对非稳态渗流有较大影响,在天然裂缝和人工裂缝组合下,试井曲线表现出多种不同特征流动段的组合:仅考虑天然裂缝时,双对数曲线表现为井筒储集阶段、径向流阶段、过渡阶段和边界流阶段;考虑单一人工裂缝时,双对数曲线表现为井筒储集阶段、双线性流阶段、径向流阶段和边界流阶段;随着人工裂缝条数增加,储层的连通性得到较大改善,双对数曲线则表现为井筒储集阶段、线性流阶段和边界流阶段.本研究构建的数值模型在现场实例中得到了良好的应用,为复杂裂缝系统试井提供了新的方法.展开更多
基金the National Natural Science Fund(11661058,11761053)Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2017MS0107)+1 种基金Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07)National Undergraduate Innovative Training Project of Inner Mongolia University(201710126026).
文摘In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.
文摘为精确描述水力压裂后复杂裂缝系统的压力动态特征,提出一种基于扩散飞行时间(diffusive time of flight,DTOF)的快速数值试井分析方法.将嵌入式离散裂缝模型(embedded discrete fracture model,EDFM)与波前快速推进法(fast marching method,FMM)相结合,建立以一维扩散飞行时间为空间坐标的渗流控制方程,并以此分析复杂裂缝系统试井曲线特征.研究表明,天然裂缝对非稳态渗流有较大影响,在天然裂缝和人工裂缝组合下,试井曲线表现出多种不同特征流动段的组合:仅考虑天然裂缝时,双对数曲线表现为井筒储集阶段、径向流阶段、过渡阶段和边界流阶段;考虑单一人工裂缝时,双对数曲线表现为井筒储集阶段、双线性流阶段、径向流阶段和边界流阶段;随着人工裂缝条数增加,储层的连通性得到较大改善,双对数曲线则表现为井筒储集阶段、线性流阶段和边界流阶段.本研究构建的数值模型在现场实例中得到了良好的应用,为复杂裂缝系统试井提供了新的方法.
