Study Of Nonlinear Flow In Porous Media Based On Lattice Boltzmann Method

Nonlinear or non-Darcy flow is an important part of flow in porous media,it attainsan increasing attention and becomes a hot topic due to its wide applications in agriculture,energy,metallurgy,chemical engineering,material science,environment engineering,lifesciences,medicine etc.According to a large number literature published previously,it isfound that,owing to the complexity inherent in nonlinear flow in porous media,the physicsmechanics behind the nonlinear phenomena is not understood clearly,and there is no rea-sonable or accurate formula that can be used to describe this nonlinear effect.Up to now,there may be three methods that can be used to study nonlinear flow in porous media,one isexperimental method,which,as a traditional method,still plays an important role in inves-tigating flow in porous media,but there are also some constrains that limit its applicationsin practice,for example,the time and money spent on experiments are usually very large,and what is more,the practical experiments are usually affected by surrounding conditions.The second is analytical or approximate method,coupling with some assumptions or sim-plicities,it can be used to derive some analytical or approximate solution of nonlinear flowin porous media.The last one is numerical method,which becomes an important approachand attains increasing attention in solving many practical problems with the developmentof computer,compared with experimental method,it depends on mathematical model ofproblems,but it also has many merits,for instance,the expense of numerical method is less,and the surrounding effects can be reduced significantly,meanwhile,it also can be used tocircumvent some shortcomings inherent in analytical or approximate methods.Now,the numerical researches on nonlinear flow in porous media are to solve theNavier-Stokes equations at pore scale or REV scale with the traditional numerical methods(for example,finite difference method,finite volume method,finite element method andso on.).In the past several years,the numerical research,as an effective method to studynonlinear flow,attained great attention,and was applied in more and more fields.However,these numerical methods will face some problems when they are used to simulate flow inporous media:(1) The treatment on boundary condition is very complex,which leads to the fact thatthe stability of numerical method becomes much worse;(2) It is a hard work to discover the micro-scale effect for gas flow in porous media;(3) The computational expense is very large and the parallel efficiency is very low.Therefore,it is desirable to develop some advanced numerical methods,which can be used to investigate nonlinear flow in porous media,and further to built mathematic formula,this is also the theoretical premise to explain nonlinear physical mechanics.As a new mesoscopic method,Lattice Boltzmann method (LBM) originates from Lat-tice Gas Automata (LGA),but later it is shown that this method also can be derived fromcontinuum Boltzmann equation with proper discrete scheme.Unlike the traditional compu-tational fluid dynamics methods,LBM is derived from kinetic theory,which leads to LBMis not constrained by continuum hypothesis,it is just this reason that LBM can be used tosimulate pore scale flow with slippage effect in porous media,and successfully display slip-page effect.In addition,compared to traditional numerical methods (the methods to solveNavier-Stokes equations,for example,finite difference method,finite volume method,finiteelement method etc.),LBM has some distinguished characteristics,such as high efficiencyof computation,easy implementation for complex boundary conditions,fully parallelismand so on,what is more,the microscopic characteristic makes it be an effective approach tostudy flow with slippage effect in porous media.In this thesis,the theory of LBM is firstdeveloped,and then,some new and open problems of single phase nonlinear flow in porousmedia are studied with LBM.This thesis is composed of two parts:(1) In term of the theory related to LBM,a new boundary condition,i.e.,combinedboundary condition of bounce back and Maxwell diffusion,is first proposed,simultaneously,a detailed analysis on discrete effects of this boundary condition in single relaxation modeland multi-relaxation model is further presented,then,a novel model,which can be used tocircumvent shortcomings in previous models,is provided to solve the Poisson equation.Wewould like to point out that the development to LBM will provide a necessary premise forfollowing research on flow in porous media.(2) In term of the numerical research on nonlinear flow in porous media,the high-velocity nonlinear flow in porous media is first studied,in this subsection,we not onlypresent a more precise formula which can be used to describe high-velocity nonlinear flowin porous media,but also give a detailed analysis on physical mechanism for nonlinear phe-nomena which are usually observed at low Reynolds number,then,the slippage effect ofgas through porous media is also investigated,the physical mechanism of slippage effect isrevealed with the aid of the new theory developed in this thesis,finally,the electro-osmoticflow in porous media is also studied,a detailed analysis on effects of many factors on distri-bution of velocity is presented in this part,furthermore,the results derived in this part playan important role in solving problems in practice.In conclusion,we used LBM to investigate nonlinear flow in porous media at REVand pore scale,and made many valuable efforts to accelerate the applications of LBM inflow through porous media.Simultaneously,we propose a new lattice Boltzmann model to solve nonlinear Poisson-Boltzmann and a new combination boundary condition to complexporous media.In addition,a large number of numerical tests are conducted to verify thismethod in studying flow in porous media.This work can be viewed as a necessary basis forfuture studies.