Numerical Simulation Of Fluid Flow In Fractured-Vuggy Porous Media Based On Oil-Water Interface Tracking

Fractured-vuggy resevoir has complex structure due to the co-existene of multi-scale spaces like pores,fractures and vugs.And they connect with each other by many ways.Both free flow and porous media flow are present in this kind of reservoir.Moreover,the most basic characteristic for two phase fluid flow in the vugs is that there exists an obvious interphase boundary,whose shape changes with the mix systerm's movement.Therefore,how to model the fluid flow and track the moving interface exactly is a much more complicate and challenging work in the study on the mechanism of two phase flow in fractured-vuggy porous media.According to the characteristics of fractured-vuggy reservoir and based on the concept of discrete fractured-vuggy network model,coupling free-flow and porous media flow model is developed in this paper for the oil-water flow simulation.Firstly,starting from the micro-scale equation,Stokes-Darcy model,together with coupling interfacial boundary conditions,is derived on the basis of Volume Averaging method.Simplify this mathematical model under single phase fluid flow condition and then compare the analytical solution with experimental data to verify the vadility of the coupling interface conditions.2D numerical solution is obtained to make a comparison between Stokes-Darcy model(two-domain approach)and Brinkman model(single-domain).Then based on the Stokes-Darcy model,numerical simulation is conducted for oil-water systerm in the fractured-vuggy porous media.Two kinds of mathematical models,according to Phase Field method and Level Set method respectively,are developed.The two phase fluid flow in free-flow region is described by coupled Cahn-Hilliard equation(Phase Field)or Level Set equation(Level Set)and Navier-Stokes equation,likewise coupled Cahn-Hilliard equation(or Level Set equation)and Darcy equation is established in the porous media.Normal flux continuity,normal stress continuity and tangential stress jump(BJS)condition are satisfied on the interface between these two subregions.Connecting with other boundary and initial conditions,two different mathematical models,i.e.CHNSD and LSNSD,are finished.They nearly have the same results in 2D numerical simulation.But they can only describe the like-piston displacement due to the limitation of phase volume equation.Compared with Phase Field method,Level set method does not that fit for two phase coupling free-flow and porous media flow problem because it is time and memery consuming,and easily appears mass non-conversation.Especially,we use CHNSD model to simulate the vuggy porous media flow on a 2D vertical plane and get a similar result with the experiment.However,the tangential stresses computed by NS equation directly and BJS simulation do not match when interphase boundary and the interface between the two subdomains overlap.Therefore,according to the disadvantage of CHNSD model,we established another mathematical model to study the two phase coupling free-flow and porous media flow.Likewise,Phase Field method is still used in the free flow region,i.e.coupled Cahn-Hilliard-Navier-Stokes equations.But in the porous media,typical two phase Darcy theory is applied,including saturation equation and pressure equation.Normal flux continuity,normal stress continuity and tangential stress jump condition(extended BJS),which is modified by intruducing relative permeability are satisfied on the subdomain's interface.The numerical simulation has a similar result with experiment.The modeling result also shows velocity slip on the subdomain's interface.And there exists mass delivery between porous media region and free-flow region.What's more,the tangential stesses calculated by NS equation directly and extended BJS simulation match well with each other,which demonstrates again the vadility of the extended BJS in the mathematical model and numerical computation.Further,according to the above model,several flow simulations are conducted on simple 2D fractured-vuggy porous media and 3D vuggy porous media.The results show that in the fractured-vuggy porous media,fractures provide the main flow channel.The fluids flow along the big fractures first and gradually converge to a stable flow path.The time for water breakthrough in the production well is early and much residual oil cannot be exploited out.Vugs are the main reservoir spaces.If the isolate vugs can be connected by fractures,the oil is much more easily to be displaced out.The existence of vugs makes it later to produce water in the proction well.But after water breakthrough,the rate of water fraction rises quickly.In the 3D vuggy porous media,the displacement process is affected a lot by gravity.After the producted fluids come to the outlet,much oil remains at the top of the media.