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.

Mimetic finite difference (MFD) method was applied to numerical simulation of non-Darcy flow in low permeability reservoirs. Principle of MFD method was described in details. And corresponding numerical formula of the non-Darcy flow model was developed. An IMPES scheme was used for solution of two-phase flow simulation. Several numerical examples are presented to demonstrate efficiency and applicability of the scheme.

A discrete fracture model is used to simulate water flooding in low permeability reservoirs considering nonlinear flow characteristic of matrix system.At first,we reduce dimension of fractures and propose a mathematical model.On this basis,unstructured grid and control volume finite difference method are applied to numerical computation considering complex geometry of fractures.Accuracy of simulator is validated through a simple example.At last,two water-injection tests are performed to analyze effect of different non-Darcy flow models.

A numerical method is developed to model nonlinear flow in heterogeneous and low-permeability reservoirs. In order to obtain pressure gradient of each gridcells precisely,we introduced two sets of physical quantities,cell face pressures and surface efflux for each gridcell. Principle of the method is elaborated based on single-phase fluid flow problem. Several numerical examples are presented to demonstrate efficiency and applicability of the scheme.

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.

Mathematical model with full tensorial permeability and mixed boundaries is presented to simulate single phase flow in heterogeneous reservoirs.A finite element method based on variational principle is proposed to solve the model.Fluid flows in homogeneous and heterogeneous reservoirs are simulated.It demonstrates that the finite element method is reliable and precise in determining flow behavior in heterogeneous reservoirs.It provides an important theoretical basis for detailed reservoir numerical simulation.