Partitioned time stepping schemes for the non-stationary dual-fracture-matrix fluid flow model |
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| Institution: | 1. School of Mathematical Sciences, East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, PR China;2. Department of Mathematics, Faculty of Science, Comilla University, Comilla 3506, Bangladesh;1. International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, China;2. Center of Excellence for Ocean Engineering, Center of Excellence for the Oceans, National Taiwan Ocean University, Keelung 202-24, Taiwan;1. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi''an 710072, China;2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi''an, 710072, China;3. School of Engineering, University of Liverpool, Liverpool L69 3GH, UK;4. Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi''an 710072, China;1. College of Civil Engineering, Hunan University, Changsha, China;2. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy;3. Key Laboratory for Damage Diagnosis of Engineering Structures of Hunan Province, Changsha, China |
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| Abstract: | This paper presents the coupled, and decoupled schemes for the naturally fractured reservoir consists of the triple-porosity medium. More specifically, the triple-porosity medium contains three contagious porous medium with more permeable macrofractures, less permeable microfractures, and matrix region which is often known as dual-fracture-matrix fluid flow model. Since the matrix has fluid communication with less permeable microfractures, and macrofratures are fed by the microfractures only, the global domain is divided into two subdomains by considering the traditional dual-porosity region and more permeable macrofractures region respectively. The flow and mass exchange between less permeable microfractures and more permeable macrofractures are modeled by two-fluid communication interface conditions while no-communication interface condition is imposed on between matrix and macrofractures region. The weak formulation and the well-posedness of the dual-fracture-matrix model are derived. Furthermore, coupled, implicit-explicit and data-passing partitioned schemes are proposed. The stability and the optimal convergence analysis are derived for both decoupled schemes. Five numerical examples are presented to illustrate the accuracy of the numerical methods and the applicability of the dual-fracture-matrix fluid flow model. Moreover, the parameter sensitivity analysis is performed in the fourth numerical example. |
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