A multiscale deep learning model is proposed for fluid flow in porous media. The method is formulated on hierarchical grid system, that is, a coarse grid and a fine grid. Deep learning network is used to train data on the coarse gird. Source term and permeability field is treated as input parameter and coarse-scale solution is treated as output parameter. We construct multiscale basis functions by solving local flow problems within coarse gridcells. Heterogeneity and interactions between matrix and fracture are captured by basis functions. Oversampling technique is applied to get more accurate small-scale details. Numerical experiments show that the multiscale deep learning model is promising for flow simulation in heterogeneous and fractured porous media.

A locally conservative Galerkin (LCG) finite element method is proposed for two-phase flow simulations in heterogeneous porous media. The main idea of it is to use property of local conservation at steady state conditions to define a numerical flux at element boundaries. It provides a way to apply standard Ga/erkin finite element method in two-phase flow simulations in porous media. LCG method has all advantages of standard finite element method while explicitly conserving fluxes over each element. Several problems are solved to demonstrate accuracy of the method. All examples show that the formulation is accurate and robust, while CPU time is significantly less than mixed finite element method.

With equivalent concept of single fracture,a discrete-fracture model is developed,in which macroscopic fractures are described explicitly as(n-1) dimensional geometry elements.This simple step greatly improves efficiency of numerical simulation.The model can really reflect impact of fractures on fluid flow through fractured reservoirs simultaneously.A fully coupling discrete-fracture mathematical model is implemented using Galerkin finite element method.Validity and accuracy of the model and numerical algorithm are demonstrated through several examples.Effect of fractures on water flooding in fractured reservoirs is investigated.It demonstrates that the discrete-fracture model is valid for fractured reservoirs,especially for those reservoirs in which macroscopic fractures exist.