A DUAL-POROSITY-STOKES MODEL AND FINITE ELEMENT METHOD FOR COUPLING DUAL-POROSITY FLOW AND FREE FLOW
A DUAL-POROSITY-STOKES MODEL AND FINITE ELEMENT METHOD FOR COUPLING DUAL-POROSITY FLOW AND FREE FLOW
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DOI：
10.1137/15m1044072
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发表时间：
2016-01-01
影响因子：
3.1
通讯作者：
Bai, Baojun
中科院分区：
文献类型：
--
作者：
Hou, Jiangyong;Qiu, Meilan;Bai, Baojun
本文提出了一种考虑双重孔隙介质中受限流动与嵌入大裂缝和管道中自由流动耦合的新模型，并对其进行了数值求解。例如，水力压裂致密/页岩油气储层中的流体流动就会出现这种情况。双孔隙度介质中既有基质又有微裂缝，用双孔隙度模型来描述流体流动。宏观裂缝和管道中的流动受Stokes方程控制。然后，通过双孔隙介质与宏观裂缝/管道界面上的4种物理有效界面条件对两种模型进行耦合，为实现物理真实的高精度模拟发挥了关键作用。这四种界面条件都是基于传统的双重孔隙模型和著名的Stokes-Darcy模型的基本性质构建的。推导了模型的弱表达式，并分析了模型的适定性。基于弱格式，提出了有限元空间半离散化方法，并采用了四种不同的格式进行完全离散化。分析了反向欧拉格式下全离散化的收敛性。通过4个数值实验验证了该模型的有效性，并验证了该模型和数值方法在数值解的最优收敛速度、宏观裂缝和管道周围的详细流动特征以及对实际问题的适用性等方面的特点。
In this paper, we propose and numerically solve a new model considering confined flow in dual-porosity media coupled with free flow in embedded macrofractures and conduits. Such situation arises, for example, for fluid flows in hydraulic fractured tight/shale oil/gas reservoirs. The flow in dual-porosity media, which consists of both matrix and microfractures, is described by a dual-porosity model. And the flow in the macrofractures and conduits is governed by the Stokes equation. Then the two models are coupled through four physically valid interface conditions on the interface between dual-porosity media and macrofractures/conduits, which play a key role in a physically faithful simulation with high accuracy. All the four interface conditions are constructed based on fundamental properties of the traditional dual-porosity model and the well-known Stokes-Darcy model. The weak formulation is derived for the proposed model, and the well-posedness of the model is analyzed. A finite element semidiscretization in space is presented based on the weak formulation, and four different schemes are then utilized for the full discretization. The convergence of the full discretization with the backward Euler scheme is analyzed. Four numerical experiments are presented to validate the proposed model and demonstrate the features of both the model and the numerical method, such as the optimal convergence rate of the numerical solution, the detail flow characteristics around macrofractures and conduits, and the applicability to the real world problems.