Discrete Unified Gas Kinetic Scheme And Numerical Simulation Of Flows In Fractured Porous Media

The flow of fluids in fractured porous media is common in the fields of energy,environment,and chemical industry,such as the exploit of shale gas,petroleum engineering,and groundwater engineering.Due to the complex structure and strong heterogeneity of the fractured porous medium,it plays an increasingly important role to use numerical simulation methods to research.The mesoscopic method developed in recent years has great advantages in simulating the flow of such multi-scale problems due to its inherent full-scale characteristics and the convenience of processing complex boundaries and implementing in parallel.At present,scholars mainly use the lattice Boltzmann method(LBM)to study such problems.Although the classical LBM is simple and convenient,it cannot be implemented on unstructured grids,This disadvantage is more pronounced when characterizing complex structures in fracture system.Discrete Unified Gas Kinetics Scheme(DUGKS),which was proposed in 2013,is also a mesoscopic method.As a kind of finite volume method,it can be used on any unstructured grids with good stability and small numerical dissipation.It is very suitable for solving such multi-scale flow in fractured porous media with complex boundaries,but related researches have not been seen yet.In this paper,the DUGKS is developed for the incompressible flow in fractured porous media,and numerical simulations are carried out for several typical problems.Main work includes:(1)Based on OpenFOAM,a DUGKS solver specifically for isothermal incompressible flow problems is developed,which is much more efficient and easy to adopt any unstructured grid,which improves the flexibility of DUGKS for flow in porous media with complex geometry.(2)The seepage DUGKS method based on general seepage model is proposed and verified by Poiseuille flow,Couette flow and Cavity flow.The results show that the flow velocity can still be calculated accurately using DUGKS in conditions of large Da number and large Re number,and the accuracy is higher when using non-uniform grid;when the porosity approaches 1,DUGKS can accurately restores the standard Navier-Stokes equation.(3)DUGKS is applied to predict the permeability and simulate the flow field of homogeneous porous media at pore scale,and the validity is verified by the twodimensional and three-dimensional classical problems respectively,then the DUGKS is applied to the tube filled with a large number of random balls.The results of DUGKS are examined in macro and micro levels,which are consistent with other mainstream pore numerical method.(4)DUGKS method is used to simulate the flow in fractured porous media.The advantages of nonuniform grid are verified.A bedrock-fracture system constructed by two-dimensional rock slice is simulated by DUGKS,and the permeability of each part of the fracture system is calculated.The results show good consistency with the solution of literature at pore scale.The cubic law is reproduced,and the influence of the bedrock's permeability to fracture and whole fracture system is investigated,from the result of which we can determine the boundary of the cubic law.