Simulation Of Fractured Reservoirs Using Multiscale Mixed Finite Element Method

With the development of reservoir modeling and exploration technich,the highresolusion reservoir geological model is established.Understanding the high-resolusion reservoir numerical simulation is important for making predictions,assessing risk and developing strategies.Nearly all hydrocarbon reservoirs are affected in some way by natural factures,yet the effects of fractures often result in strong heterogeneity and multi-scale characteristics.The present reservoir simulators are mainly based on the dual-porosity model or equivalent continuum model.Although these two models are effective,they can't depict the multiscale flow characteristic at macro-scale.The discrete fracture model is suggested due to its high calculation precision and more realistic results.However,it is rarely possible to be used for real oil field problem because of its tremendous amount of computation by using present numerical method.Especially when we consider the influence of stress,it is computational costly.To this end,based on multiscale finite element method and homogenization theory,we compute the multiscale basis functions within the large scale blocks and construct the coarse scale system using these mulscale basis functions.The fine scale information is captured by constructing the multiscale basis functions.In this work,the multiscale formulation for Discrete Fracture Model(DFM)and Embedded Discrete Fracture Model are developed in the framework Multiscale Mixed Finite Element Method.The interaction between matrix and fractures is captured by multiscale velocity basis functions which are computed by solving DFM within coarse blocks.Then a hybrid multiscale formulation for numerical modeling of coupled flow and geomechanics is proposed.The displacement multiscale basis functions are constructed using multiscale finite element method while the multiscale mixed finite element method is applied to computer multiscale flow basis functions,including multiscale velocity basis functions and multiscale pressure basis functions.The fine scale information of stress field and flow field is integrated into these multiscale basis functions.Multiscale methods are type of dual-grid method includes a coarse grid system and a fine grid system.We take a further step and introduce a multigrid method.The solution space is decomposed into subspaces where DFM subsolutions can be computed by solving sparse and well-conditioned linear systems.By keeping only the coarse-scale part of the solution space,we furthermore obtain a reduced order model.The localized basis functions are constructed which can be used to obtain a near-linear complexity by performing truncation of the support of the gamblets.Finally,we consider the fast developing deep learning technique and proposed a multiscale deep learning model.The neural networks are trained on the coarse scale grid while the fine scale information is captured by constructing multiscale basis functions.The multiscale deep learning model will use less degree of freedom.At the end,an efficient multiscale numerical simulation theory and method is developed for numerical simulation of porous media.